Sample records for splines mars approach

  1. Assessing the response of area burned to changing climate in western boreal North America using a Multivariate Adaptive Regression Splines (MARS) approach (United States)

    Michael S. Balshi; A. David McGuire; Paul Duffy; Mike Flannigan; John Walsh; Jerry Melillo


    We developed temporally and spatially explicit relationships between air temperature and fuel moisture codes derived from the Canadian Fire Weather Index System to estimate annual area burned at 2.5o (latitude x longitude) resolution using a Multivariate Adaptive Regression Spline (MARS) approach across Alaska and Canada. Burned area was...

  2. Assessing the response of area burned to changing climate in western boreal North America using a Multivariate Adaptive Regression Splines (MARS) approach (United States)

    Balshi, M. S.; McGuire, A.D.; Duffy, P.; Flannigan, M.; Walsh, J.; Melillo, J.


    Fire is a common disturbance in the North American boreal forest that influences ecosystem structure and function. The temporal and spatial dynamics of fire are likely to be altered as climate continues to change. In this study, we ask the question: how will area burned in boreal North America by wildfire respond to future changes in climate? To evaluate this question, we developed temporally and spatially explicit relationships between air temperature and fuel moisture codes derived from the Canadian Fire Weather Index System to estimate annual area burned at 2.5?? (latitude ?? longitude) resolution using a Multivariate Adaptive Regression Spline (MARS) approach across Alaska and Canada. Burned area was substantially more predictable in the western portion of boreal North America than in eastern Canada. Burned area was also not very predictable in areas of substantial topographic relief and in areas along the transition between boreal forest and tundra. At the scale of Alaska and western Canada, the empirical fire models explain on the order of 82% of the variation in annual area burned for the period 1960-2002. July temperature was the most frequently occurring predictor across all models, but the fuel moisture codes for the months June through August (as a group) entered the models as the most important predictors of annual area burned. To predict changes in the temporal and spatial dynamics of fire under future climate, the empirical fire models used output from the Canadian Climate Center CGCM2 global climate model to predict annual area burned through the year 2100 across Alaska and western Canada. Relative to 1991-2000, the results suggest that average area burned per decade will double by 2041-2050 and will increase on the order of 3.5-5.5 times by the last decade of the 21st century. To improve the ability to better predict wildfire across Alaska and Canada, future research should focus on incorporating additional effects of long-term and successional


    Directory of Open Access Journals (Sweden)

    I Nyoman Budiantara


    Full Text Available Regression analysis is constructed for capturing the influences of independent variables to dependent ones. It can be done by looking at the relationship between those variables. This task of approximating the mean function can be done essentially in two ways. The quiet often use parametric approach is to assume that the mean curve has some prespecified functional forms. Alternatively, nonparametric approach, .i.e., without reference to a specific form, is used when there is no information of the regression function form (Haerdle, 1990. Therefore nonparametric approach has more flexibilities than the parametric one. The aim of this research is to find the best fit model that captures relationship between admission test score to the GPA. This particular data was taken from the Department of Design Communication and Visual, Petra Christian University, Surabaya for year 1999. Those two approaches were used here. In the parametric approach, we use simple linear, quadric cubic regression, and in the nonparametric ones, we use B-Spline and Multivariate Adaptive Regression Splines (MARS. Overall, the best model was chosen based on the maximum determinant coefficient. However, for MARS, the best model was chosen based on the GCV, minimum MSE, maximum determinant coefficient. Abstract in Bahasa Indonesia : Analisa regresi digunakan untuk melihat pengaruh variabel independen terhadap variabel dependent dengan terlebih dulu melihat pola hubungan variabel tersebut. Hal ini dapat dilakukan dengan melalui dua pendekatan. Pendekatan yang paling umum dan seringkali digunakan adalah pendekatan parametrik. Pendekatan parametrik mengasumsikan bentuk model sudah ditentukan. Apabila tidak ada informasi apapun tentang bentuk dari fungsi regresi, maka pendekatan yang digunakan adalah pendekatan nonparametrik. (Haerdle, 1990. Karena pendekatan tidak tergantung pada asumsi bentuk kurva tertentu, sehingga memberikan fleksibelitas yang lebih besar. Tujuan penelitian ini

  4. Smoothing data series by means of cubic splines: quality of approximation and introduction of a repeating spline approach (United States)

    Wüst, Sabine; Wendt, Verena; Linz, Ricarda; Bittner, Michael


    Cubic splines with equidistant spline sampling points are a common method in atmospheric science, used for the approximation of background conditions by means of filtering superimposed fluctuations from a data series. What is defined as background or superimposed fluctuation depends on the specific research question. The latter also determines whether the spline or the residuals - the subtraction of the spline from the original time series - are further analysed.Based on test data sets, we show that the quality of approximation of the background state does not increase continuously with an increasing number of spline sampling points and/or decreasing distance between two spline sampling points. Splines can generate considerable artificial oscillations in the background and the residuals.We introduce a repeating spline approach which is able to significantly reduce this phenomenon. We apply it not only to the test data but also to TIMED-SABER temperature data and choose the distance between two spline sampling points in a way that is sensitive for a large spectrum of gravity waves.

  5. Smoothing data series by means of cubic splines: quality of approximation and introduction of a repeating spline approach

    Directory of Open Access Journals (Sweden)

    S. Wüst


    Full Text Available Cubic splines with equidistant spline sampling points are a common method in atmospheric science, used for the approximation of background conditions by means of filtering superimposed fluctuations from a data series. What is defined as background or superimposed fluctuation depends on the specific research question. The latter also determines whether the spline or the residuals – the subtraction of the spline from the original time series – are further analysed.Based on test data sets, we show that the quality of approximation of the background state does not increase continuously with an increasing number of spline sampling points and/or decreasing distance between two spline sampling points. Splines can generate considerable artificial oscillations in the background and the residuals.We introduce a repeating spline approach which is able to significantly reduce this phenomenon. We apply it not only to the test data but also to TIMED-SABER temperature data and choose the distance between two spline sampling points in a way that is sensitive for a large spectrum of gravity waves.

  6. Development of Technology Parameter Towards Shipbuilding Productivity Predictor Using Cubic Spline Approach

    Directory of Open Access Journals (Sweden)

    Bagiyo Suwasono


    Full Text Available Ability of production processes associated with state-of-the-art technology, which allows the shipbuilding, is customized with modern equipment. It will give impact to level of productivity and competitiveness. This study proposes a nonparametric regression cubic spline approach with 1 knot, 2 knots, and 3 knots. The application programs Tibco Spotfire S+ showed that a cubic spline with 2 knots (4.25 and 4.50 gave the best result with the value of GCV = 56.21556, and R2 = 94.03%.Estimation result of cubic spline with 2 knots for the PT. Batamec shipyard = 35.61 MH/CGT, PT. Dok & Perkapalan Surabaya = 27.49 MH/CGT, PT. Karimun Sembawang Shipyard = 27.49 MH/CGT, and PT. PAL Indonesia = 19.89 MH/CGT.

  7. Approach to Mars Field Geology (United States)

    Muehlberger, William; Rice, James W.; Parker, Timothy; Lipps, Jere H.; Hoffman, Paul; Burchfiel, Clark; Brasier, Martin


    The goals of field study on Mars are nothing less than to understand the processes and history of the planet at whatever level of detail is necessary. A manned mission gives us an unprecedented opportunity to use the immense power of the human mind to comprehend Mars in extraordinary detail. To take advantage of this opportunity, it is important to examine how we should approach the field study of Mars. In this effort, we are guided by over 200 years of field exploration experience on Earth as well as six manned missions exploring the Moon.

  8. A modified linear algebraic approach to electron scattering using cubic splines

    International Nuclear Information System (INIS)

    Kinney, R.A.


    A modified linear algebraic approach to the solution of the Schrodiner equation for low-energy electron scattering is presented. The method uses a piecewise cubic-spline approximation of the wavefunction. Results in the static-potential and the static-exchange approximations for e - +H s-wave scattering are compared with unmodified linear algebraic and variational linear algebraic methods. (author)

  9. SPLINE, Spline Interpolation Function

    International Nuclear Information System (INIS)

    Allouard, Y.


    1 - Nature of physical problem solved: The problem is to obtain an interpolated function, as smooth as possible, that passes through given points. The derivatives of these functions are continuous up to the (2Q-1) order. The program consists of the following two subprograms: ASPLERQ. Transport of relations method for the spline functions of interpolation. SPLQ. Spline interpolation. 2 - Method of solution: The methods are described in the reference under item 10

  10. A fourth order spline collocation approach for a business cycle model (United States)

    Sayfy, A.; Khoury, S.; Ibdah, H.


    A collocation approach, based on a fourth order cubic B-splines is presented for the numerical solution of a Kaleckian business cycle model formulated by a nonlinear delay differential equation. The equation is approximated and the nonlinearity is handled by employing an iterative scheme arising from Newton's method. It is shown that the model exhibits a conditionally dynamical stable cycle. The fourth-order rate of convergence of the scheme is verified numerically for different special cases.

  11. Multivariate Adaptative Regression Splines (MARS, una alternativa para el análisis de series de tiempo

    Directory of Open Access Journals (Sweden)

    Jairo Vanegas


    Full Text Available Multivariate Adaptative Regression Splines (MARS es un método de modelación no paramétrico que extiende el modelo lineal incorporando no linealidades e interacciones de variables. Es una herramienta flexible que automatiza la construcción de modelos de predicción, seleccionando variables relevantes, transformando las variables predictoras, tratando valores perdidos y previniendo sobreajustes mediante un autotest. También permite predecir tomando en cuenta factores estructurales que pudieran tener influencia sobre la variable respuesta, generando modelos hipotéticos. El resultado final serviría para identificar puntos de corte relevantes en series de datos. En el área de la salud es poco utilizado, por lo que se propone como una herramienta más para la evaluación de indicadores relevantes en salud pública. Para efectos demostrativos se utilizaron series de datos de mortalidad de menores de 5 años de Costa Rica en el periodo 1978-2008.

  12. A cubic B-spline Galerkin approach for the numerical simulation of the GEW equation

    Directory of Open Access Journals (Sweden)

    S. Battal Gazi Karakoç


    Full Text Available The generalized equal width (GEW wave equation is solved numerically by using lumped Galerkin approach with cubic B-spline functions. The proposed numerical scheme is tested by applying two test problems including single solitary wave and interaction of two solitary waves. In order to determine the performance of the algorithm, the error norms L2 and L∞ and the invariants I1, I2 and I3 are calculated. For the linear stability analysis of the numerical algorithm, von Neumann approach is used. As a result, the obtained findings show that the presented numerical scheme is preferable to some recent numerical methods.  

  13. Mars Global Surveyor Approach Image (United States)


    This image is the first view of Mars taken by the Mars Global Surveyor Orbiter Camera (MOC). It was acquired the afternoon of July 2, 1997 when the MGS spacecraft was 17.2 million kilometers (10.7 million miles) and 72 days from encounter. At this distance, the MOC's resolution is about 64 km per picture element, and the 6800 km (4200 mile) diameter planet is 105 pixels across. The observation was designed to show the Mars Pathfinder landing site at 19.4 N, 33.1 W approximately 48 hours prior to landing. The image shows the north polar cap of Mars at the top of the image, the dark feature Acidalia Planitia in the center with the brighter Chryse plain immediately beneath it, and the highland areas along the Martian equator including the canyons of the Valles Marineris (which are bright in this image owing to atmospheric dust). The dark features Terra Meridiani and Terra Sabaea can be seen at the 4 o`clock position, and the south polar hood (atmospheric fog and hazes) can be seen at the bottom of the image. Launched on November 7, 1996, Mars Global Surveyor will enter Mars orbit on Thursday, September 11 shortly after 6:00 PM PDT. After Mars Orbit Insertion, the spacecraft will use atmospheric drag to reduce the size of its orbit, achieving a circular orbit only 400 km (248 mi) above the surface in early March 1998, when mapping operations will begin.The Mars Global Surveyor is operated by the Mars Surveyor Operations Project managed for NASA by the Jet Propulsion Laboratory, Pasadena CA. The Mars Orbiter Camera is a duplicate of one of the six instruments originally developed for the Mars Observer mission. It was built and is operated under contract to JPL by an industry/university team led by Malin Space Science Systems, San Diego, CA.

  14. A numerical investigation of the GRLW equation using lumped Galerkin approach with cubic B-spline. (United States)

    Zeybek, Halil; Karakoç, S Battal Gazi


    In this work, we construct the lumped Galerkin approach based on cubic B-splines to obtain the numerical solution of the generalized regularized long wave equation. Applying the von Neumann approximation, it is shown that the linearized algorithm is unconditionally stable. The presented method is implemented to three test problems including single solitary wave, interaction of two solitary waves and development of an undular bore. To prove the performance of the numerical scheme, the error norms [Formula: see text] and [Formula: see text] and the conservative quantities [Formula: see text], [Formula: see text] and [Formula: see text] are computed and the computational data are compared with the earlier works. In addition, the motion of solitary waves is described at different time levels.

  15. Diffeomorphism Spline

    Directory of Open Access Journals (Sweden)

    Wei Zeng


    Full Text Available Conventional splines offer powerful means for modeling surfaces and volumes in three-dimensional Euclidean space. A one-dimensional quaternion spline has been applied for animation purpose, where the splines are defined to model a one-dimensional submanifold in the three-dimensional Lie group. Given two surfaces, all of the diffeomorphisms between them form an infinite dimensional manifold, the so-called diffeomorphism space. In this work, we propose a novel scheme to model finite dimensional submanifolds in the diffeomorphism space by generalizing conventional splines. According to quasiconformal geometry theorem, each diffeomorphism determines a Beltrami differential on the source surface. Inversely, the diffeomorphism is determined by its Beltrami differential with normalization conditions. Therefore, the diffeomorphism space has one-to-one correspondence to the space of a special differential form. The convex combination of Beltrami differentials is still a Beltrami differential. Therefore, the conventional spline scheme can be generalized to the Beltrami differential space and, consequently, to the diffeomorphism space. Our experiments demonstrate the efficiency and efficacy of diffeomorphism splines. The diffeomorphism spline has many potential applications, such as surface registration, tracking and animation.

  16. Theoretical complex Stark energies of lithium by a complex scaling plus the B-spline approach

    Energy Technology Data Exchange (ETDEWEB)

    Meng Huiyan [School of Applied Science of Taiyuan University of Science and Technology, Taiyuan 030024 (China); Zhang Yuexia; Kang Shuai; Shi Tingyn; Zhan Mingsheng [State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071 (China)], E-mail:, E-mail:, E-mail:


    The B-spline-based coordinate rotation method plus the model potential approach is applied to investigate the complex energies of low-lying resonances of the lithium atom in an electric field. Our results are compared with two recent calculations by a state-specific complex eigenvalue Schroedinger equation (CESE) (Themelis and Nicolaides 2001 J. Phys. B: At. Mol. Opt. Phys. 34 2905) and complex absorbing potential (CAP) (Sahoo and Ho 2000 J. Phys. B: At. Mol. Opt. Phys. 33 5151) methods, which are in controversy. The positions of resonances by the present calculation are found to be in agreement with theoretical data obtained by both the CESE and CAP methods. Our investigation clarifies that the contradiction about '4f{sub 0}' resonant position varies with the electric field. However, for the width of resonances, our results are only consistent with those by the CESE method for all strengths of the electric field under consideration. A detailed comparison on the m = 0 state among these three calculations shows that the unusual behaviour of width of resonances in the weak-field case by the CAP method is not a 'new' finding but a misguiding resulting from nonconvergent results. The systematic agreement between our model potential calculation and the ab initio calculation by the CESE for lithium indicates that the present proposed method is reliable and appropriate to simplify the calculation of the alkali metal atom in external fields.

  17. Preference learning with evolutionary Multivariate Adaptive Regression Spline model

    DEFF Research Database (Denmark)

    Abou-Zleikha, Mohamed; Shaker, Noor; Christensen, Mads Græsbøll


    This paper introduces a novel approach for pairwise preference learning through combining an evolutionary method with Multivariate Adaptive Regression Spline (MARS). Collecting users' feedback through pairwise preferences is recommended over other ranking approaches as this method is more appealing...... for function approximation as well as being relatively easy to interpret. MARS models are evolved based on their efficiency in learning pairwise data. The method is tested on two datasets that collectively provide pairwise preference data of five cognitive states expressed by users. The method is analysed...

  18. Mars for Earthlings: An Analog Approach to Mars in Undergraduate Education


    Chan, Marjorie; Kahmann-Robinson, Julia


    Mars for Earthlings (MFE) is a terrestrial Earth analog pedagogical approach to teaching undergraduate geology, planetary science, and astrobiology. MFE utilizes Earth analogs to teach Mars planetary concepts, with a foundational backbone in Earth science principles. The field of planetary science is rapidly changing with new technologies and higher-resolution data sets. Thus, it is increasingly important to understand geological concepts and processes for interpreting Mars data. MFE curricul...

  19. Mars

    CERN Document Server

    Payment, Simone


    This curriculum-based, fun, and approachable book offers everything young readers need to know to begin their study of the Red Planet. They will learn about the fundamental aspects of the Mars, including its size, mass, surface features, interior, orbit, and spin. Further, they will learn about the history of the missions to Mars, including the Viking spacecraft and the Curiosity and MAVEN rovers. Finally, readers will learn about why scientists think there's a chance that Mars is or was suitable for life. With stunning imagery from NASA itself, readers will have a front seat-view of the missi

  20. A New Predictive Model Based on the ABC Optimized Multivariate Adaptive Regression Splines Approach for Predicting the Remaining Useful Life in Aircraft Engines

    Directory of Open Access Journals (Sweden)

    Paulino José García Nieto


    Full Text Available Remaining useful life (RUL estimation is considered as one of the most central points in the prognostics and health management (PHM. The present paper describes a nonlinear hybrid ABC–MARS-based model for the prediction of the remaining useful life of aircraft engines. Indeed, it is well-known that an accurate RUL estimation allows failure prevention in a more controllable way so that the effective maintenance can be carried out in appropriate time to correct impending faults. The proposed hybrid model combines multivariate adaptive regression splines (MARS, which have been successfully adopted for regression problems, with the artificial bee colony (ABC technique. This optimization technique involves parameter setting in the MARS training procedure, which significantly influences the regression accuracy. However, its use in reliability applications has not yet been widely explored. Bearing this in mind, remaining useful life values have been predicted here by using the hybrid ABC–MARS-based model from the remaining measured parameters (input variables for aircraft engines with success. A correlation coefficient equal to 0.92 was obtained when this hybrid ABC–MARS-based model was applied to experimental data. The agreement of this model with experimental data confirmed its good performance. The main advantage of this predictive model is that it does not require information about the previous operation states of the aircraft engine.

  1. Mars for Earthlings: an analog approach to Mars in undergraduate education. (United States)

    Chan, Marjorie; Kahmann-Robinson, Julia


    Mars for Earthlings (MFE) is a terrestrial Earth analog pedagogical approach to teaching undergraduate geology, planetary science, and astrobiology. MFE utilizes Earth analogs to teach Mars planetary concepts, with a foundational backbone in Earth science principles. The field of planetary science is rapidly changing with new technologies and higher-resolution data sets. Thus, it is increasingly important to understand geological concepts and processes for interpreting Mars data. MFE curriculum is topically driven to facilitate easy integration of content into new or existing courses. The Earth-Mars systems approach explores planetary origins, Mars missions, rocks and minerals, active driving forces/tectonics, surface sculpting processes, astrobiology, future explorations, and hot topics in an inquiry-driven environment. Curriculum leverages heavily upon multimedia resources, software programs such as Google Mars and JMARS, as well as NASA mission data such as THEMIS, HiRISE, CRISM, and rover images. Two years of MFE class evaluation data suggest that science literacy and general interest in Mars geology and astrobiology topics increased after participation in the MFE curriculum. Students also used newly developed skills to create a Mars mission team presentation. The MFE curriculum, learning modules, and resources are available online at

  2. Spatial Variation of Seismic B-Values of the Empirical Law of the Magnitude-Frequency Distribution from a Bayesian Approach Based On Spline (B-Spline) Function in the North Anatolian Fault Zone, North of Turkey (United States)

    Türker, Tugba; Bayrak, Yusuf


    In this study, A Bayesian approach based on Spline (B-spline) function is used to estimate the spatial variations of the seismic b-values of the empirical law (G-R law) in the North Anatolian Fault Zone (NAFZ), North of Turkey. B-spline function method developed for estimation and interpolation of b-values. Spatial variations in b-values are known to reflect the stress field and can be used in earthquake hazard analysis. We proposed that b-values combined with seismicity and tectonic background. β=b*ln(10) function (the derivation of the G-R law) based on a Bayesian approach is used to estimate the b values and their standard deviations. A homogeneous instrumental catalog is used during the period 1900-2017. We divided into ten different seismic source regions based on epicenter distribution, tectonic, seismicity, faults in NAFZ. Three historical earthquakes (1343, MS = 7. 5, 1766, Ms=7.3, 1894, MS = 7. 0) are included in region 2 (Marmara Sea (Tekirdağ-Merkez-Kumburgaz-Çmarcik Basins)) where a large earthquake is expected in the near future because of a large earthquake hasn’t been observed for the instrumental period. The spatial variations in ten different seismogenic regions are estimated in NAFZ. In accordance with estimates, b-values are changed between 0.52±0.07 and 0.86±0.13. The high b values are estimated the Southern Branch of NAFZ (Edremit Fault Zones, Yenice-Gönen, Mustafa Kemal Paşa, Ulubat Faults) region, so it is related low stress. The low b values are estimated between Tokat-Erzincan region, so it is related high stress. The maps of 2D and 3D spatial variations (2D contour maps, classed post maps (a group the data into discrete classes), image maps (raster maps based on grid files), 3D wireframe (three-dimensional representations of grid files) and 3D surface) are plotted to the b-values. The spatial variations b-values can be used earthquake hazard analysis for NAFZ.

  3. Weighted cubic and biharmonic splines (United States)

    Kvasov, Boris; Kim, Tae-Wan


    In this paper we discuss the design of algorithms for interpolating discrete data by using weighted cubic and biharmonic splines in such a way that the monotonicity and convexity of the data are preserved. We formulate the problem as a differential multipoint boundary value problem and consider its finite-difference approximation. Two algorithms for automatic selection of shape control parameters (weights) are presented. For weighted biharmonic splines the resulting system of linear equations can be efficiently solved by combining Gaussian elimination with successive over-relaxation method or finite-difference schemes in fractional steps. We consider basic computational aspects and illustrate main features of this original approach.

  4. A Unified Energy Approach for B-Spline Snake In Medical Image Segmentation

    Directory of Open Access Journals (Sweden)

    Agung Alfiansyah


    Full Text Available The parametric snake is one of the preferred approaches in feature extraction from images because of their simplicity and efficiency. However the method has also limitations. In this paper an explicit snake that represented using BSpline applied for image segmentation is considered. In this paper, we identify some of these problems and propose efficient solutions to get around them. The proposed method is inspired by classical snake from Kass with some adaption for parametric curve. The paper also proposes new definitions of energy terms in the model to bring the snake performance more robust and efficient for image segmentation. This energy term unify the edge based and region based energy derived from the image data. The main objective of developed work is to develop an automatic method to segment the anatomical organs from medical images which is very hard and tedious to be performed manually. After this segmentation, the anatomical object can be further measured and analyzed to diagnose the anomaly in that organ. The results have shown that the proposed method has been proven qualitatively successful in segmenting different types of medical images.

  5. Advantages of a Modular Mars Surface Habitat Approach (United States)

    Rucker, Michelle A.; Hoffman, Stephan J.; Andrews, Alida; Watts, Kevin


    Early crewed Mars mission concepts developed by the National Aeronautics and Space Administration (NASA) assumed a single, large habitat would house six crew members for a 500-day Mars surface stay. At the end of the first mission, all surface equipment, including the habitat, -would be abandoned and the process would be repeated at a different Martian landing site. This work was documented in a series of NASA publications culminating with the Mars Design Reference Mission 5.0 (NASA-SP-2009-566). The Evolvable Mars Campaign (EMC) explored whether re-using surface equipment at a single landing site could be more affordable than the Apollo-style explore-abandon-repeat mission cadence. Initial EMC assumptions preserved the single, monolithic habitat, the only difference being a new requirement to reuse the surface habitat for multiple expedition crews. A trade study comparing a single large habitat versus smaller, modular habitats leaned towards the monolithic approach as more mass-efficient. More recent work has focused on the operational aspects of building up Mars surface infrastructure over multiple missions, and has identified compelling advantages of the modular approach that should be considered before making a final decision. This paper explores Mars surface mission operational concepts and integrated system analysis, and presents an argument for the modular habitat approach.

  6. Mars extant-life campaign using an approach based on Earth-analog habitats (United States)

    Palkovic, Lawrence A.; Wilson, Thomas J.


    The Mars Robotic Outpost group at JPL has identified sixteen potential momentous discoveries that if found on Mars would alter planning for the future Mars exploration program. This paper details one possible approach to the discovery of and response to the 'momentous discovery'' of extant life on Mars. The approach detailed in this paper, the Mars Extant-Life (MEL) campaign, is a comprehensive and flexible program to find living organisms on Mars by studying Earth-analog habitats of extremophile communities.

  7. Spline Variational Theory for Composite Bolted Joints

    National Research Council Canada - National Science Library

    Iarve, E


    .... Two approaches were implemented. A conventional mesh overlay method in the crack region to satisfy the crack face boundary conditions and a novel spline basis partitioning method were compared...

  8. Interpolating cubic splines

    CERN Document Server

    Knott, Gary D


    A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi­ cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi­ nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline func...


    Directory of Open Access Journals (Sweden)

    I Nyoman Budiantara


    Full Text Available We considered the nonparametric regression model : Zj = X(tj + ej, j = 1,2,…,n, where X(tj is the regression curve. The random error ej are independently distributed normal with a zero mean and a variance s2/bj, bj > 0. The estimation of X obtained by minimizing a Weighted Least Square. The solution of this optimation is a Weighted Spline Polynomial. Further, we give an application of weigted spline estimator in nonparametric regression. Abstract in Bahasa Indonesia : Diberikan model regresi nonparametrik : Zj = X(tj + ej, j = 1,2,…,n, dengan X (tj kurva regresi dan ej sesatan random yang diasumsikan berdistribusi normal dengan mean nol dan variansi s2/bj, bj > 0. Estimasi kurva regresi X yang meminimumkan suatu Penalized Least Square Terbobot, merupakan estimator Polinomial Spline Natural Terbobot. Selanjutnya diberikan suatu aplikasi estimator spline terbobot dalam regresi nonparametrik. Kata kunci: Spline terbobot, Regresi nonparametrik, Penalized Least Square.

  10. An efficient approach to numerical study of the coupled-BBM system with B-spline collocation method

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    khalid ali


    Full Text Available In the present paper, a numerical method is proposed for the numerical solution of a coupled-BBM system with appropriate initial and boundary conditions by using collocation method with cubic trigonometric B-spline on the uniform mesh points. The method is shown to be unconditionally stable using von-Neumann technique. To test accuracy the error norms2L, ?L are computed. Furthermore, interaction of two and three solitary waves are used to discuss the effect of the behavior of the solitary waves after the interaction. These results show that the technique introduced here is easy to apply. We make linearization for the nonlinear term.


    The purpose of this report is to provide a reference manual that could be used by investigators for making informed use of logistic regression using two methods (standard logistic regression and MARS). The details for analyses of relationships between a dependent binary response ...

  12. Straight-sided Spline Optimization

    DEFF Research Database (Denmark)

    Pedersen, Niels Leergaard


    Spline connection of shaft and hub is commonly applied when large torque capacity is needed together with the possibility of disassembly. The designs of these splines are generally controlled by different standards. In view of the common use of splines, it seems that few papers deal with splines ...

  13. A Hybrid PCA-CART-MARS-Based Prognostic Approach of the Remaining Useful Life for Aircraft Engines

    Directory of Open Access Journals (Sweden)

    Fernando Sánchez Lasheras


    Full Text Available Prognostics is an engineering discipline that predicts the future health of a system. In this research work, a data-driven approach for prognostics is proposed. Indeed, the present paper describes a data-driven hybrid model for the successful prediction of the remaining useful life of aircraft engines. The approach combines the multivariate adaptive regression splines (MARS technique with the principal component analysis (PCA, dendrograms and classification and regression trees (CARTs. Elements extracted from sensor signals are used to train this hybrid model, representing different levels of health for aircraft engines. In this way, this hybrid algorithm is used to predict the trends of these elements. Based on this fitting, one can determine the future health state of a system and estimate its remaining useful life (RUL with accuracy. To evaluate the proposed approach, a test was carried out using aircraft engine signals collected from physical sensors (temperature, pressure, speed, fuel flow, etc.. Simulation results show that the PCA-CART-MARS-based approach can forecast faults long before they occur and can predict the RUL. The proposed hybrid model presents as its main advantage the fact that it does not require information about the previous operation states of the input variables of the engine. The performance of this model was compared with those obtained by other benchmark models (multivariate linear regression and artificial neural networks also applied in recent years for the modeling of remaining useful life. Therefore, the PCA-CART-MARS-based approach is very promising in the field of prognostics of the RUL for aircraft engines.

  14. Designing interactively with elastic splines

    DEFF Research Database (Denmark)

    Brander, David; Bærentzen, Jakob Andreas; Fisker, Ann-Sofie


    We present an algorithm for designing interactively with C1 elastic splines. The idea is to design the elastic spline using a C1 cubic polynomial spline where each polynomial segment is so close to satisfying the Euler-Lagrange equation for elastic curves that the visual difference becomes neglig...... negligible. Using a database of cubic Bézier curves we are able to interactively modify the cubic spline such that it remains visually close to an elastic spline....

  15. P-Splines Using Derivative Information

    KAUST Repository

    Calderon, Christopher P.


    Time series associated with single-molecule experiments and/or simulations contain a wealth of multiscale information about complex biomolecular systems. We demonstrate how a collection of Penalized-splines (P-splines) can be useful in quantitatively summarizing such data. In this work, functions estimated using P-splines are associated with stochastic differential equations (SDEs). It is shown how quantities estimated in a single SDE summarize fast-scale phenomena, whereas variation between curves associated with different SDEs partially reflects noise induced by motion evolving on a slower time scale. P-splines assist in "semiparametrically" estimating nonlinear SDEs in situations where a time-dependent external force is applied to a single-molecule system. The P-splines introduced simultaneously use function and derivative scatterplot information to refine curve estimates. We refer to the approach as the PuDI (P-splines using Derivative Information) method. It is shown how generalized least squares ideas fit seamlessly into the PuDI method. Applications demonstrating how utilizing uncertainty information/approximations along with generalized least squares techniques improve PuDI fits are presented. Although the primary application here is in estimating nonlinear SDEs, the PuDI method is applicable to situations where both unbiased function and derivative estimates are available.

  16. Non polynomial B-splines (United States)

    Laksâ, Arne


    B-splines are the de facto industrial standard for surface modelling in Computer Aided design. It is comparable to bend flexible rods of wood or metal. A flexible rod minimize the energy when bending, a third degree polynomial spline curve minimize the second derivatives. B-spline is a nice way of representing polynomial splines, it connect polynomial splines to corner cutting techniques, which induces many nice and useful properties. However, the B-spline representation can be expanded to something we can call general B-splines, i.e. both polynomial and non-polynomial splines. We will show how this expansion can be done, and the properties it induces, and examples of non-polynomial B-spline.

  17. Mars

    CERN Document Server

    Day, Trevor


    Discusses the fundamental facts concerning this mysterious planet, including its mass, size, and atmosphere, as well as the various missions that helped planetary scientists document the geological history of Mars. This volume also describes Mars'' seasons with their surface effects on the planet and how they have changed over time.

  18. quadratic spline finite element method

    Directory of Open Access Journals (Sweden)

    A. R. Bahadir


    Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.

  19. Interpolation of natural cubic spline

    Directory of Open Access Journals (Sweden)

    Arun Kumar


    Full Text Available From the result in [1] it follows that there is a unique quadratic spline which bounds the same area as that of the function. The matching of the area for the cubic spline does not follow from the corresponding result proved in [2]. We obtain cubic splines which preserve the area of the function.

  20. Genetic and environmental smoothing of lactation curves with cubic splines. (United States)

    White, I M; Thompson, R; Brotherstone, S


    Most approaches to modeling lactation curves involve parametric curves with fixed or random coefficients. In either case, the resulting models require the specification on an underlying parametric curve. The fitting of splines represents a semiparametric approach to the problem. In the context of animal breeding, cubic smoothing splines are particularly convenient because they can be incorporated into a suitably constructed mixed model. The potential for the use of splines in modeling lactation curves is explored with a simple example, and the results are compared with those using a random regression model. The spline model provides greater flexibility at the cost of additional computation. Splines are shown to be capable of picking up features of the lactation curve that are missed by the random regression model.

  1. On Characterization of Quadratic Splines

    DEFF Research Database (Denmark)

    Chen, B. T.; Madsen, Kaj; Zhang, Shuzhong


    A quadratic spline is a differentiable piecewise quadratic function. Many problems in numerical analysis and optimization literature can be reformulated as unconstrained minimizations of quadratic splines. However, only special cases of quadratic splines are studied in the existing literature...... between the convexity of a quadratic spline function and the monotonicity of the corresponding LCP problem. It is shown that, although both conditions lead to easy solvability of the problem, they are different in general......., and algorithms are developed on a case by case basis. There lacks an analytical representation of a general or even a convex quadratic spline. The current paper fills this gap by providing an analytical representation of a general quadratic spline. Furthermore, for convex quadratic spline, it is shown...

  2. A computational intelligence approach to the Mars Precision Landing problem (United States)

    Birge, Brian Kent, III

    Various proposed Mars missions, such as the Mars Sample Return Mission (MRSR) and the Mars Smart Lander (MSL), require precise re-entry terminal position and velocity states. This is to achieve mission objectives including rendezvous with a previous landed mission, or reaching a particular geographic landmark. The current state of the art footprint is in the magnitude of kilometers. For this research a Mars Precision Landing is achieved with a landed footprint of no more than 100 meters, for a set of initial entry conditions representing worst guess dispersions. Obstacles to reducing the landed footprint include trajectory dispersions due to initial atmospheric entry conditions (entry angle, parachute deployment height, etc.), environment (wind, atmospheric density, etc.), parachute deployment dynamics, unavoidable injection error (propagated error from launch on), etc. Weather and atmospheric models have been developed. Three descent scenarios have been examined. First, terminal re-entry is achieved via a ballistic parachute with concurrent thrusting events while on the parachute, followed by a gravity turn. Second, terminal re-entry is achieved via a ballistic parachute followed by gravity turn to hover and then thrust vector to desired location. Third, a guided parafoil approach followed by vectored thrusting to reach terminal velocity is examined. The guided parafoil is determined to be the best architecture. The purpose of this study is to examine the feasibility of using a computational intelligence strategy to facilitate precision planetary re-entry, specifically to take an approach that is somewhat more intuitive and less rigid, and see where it leads. The test problems used for all research are variations on proposed Mars landing mission scenarios developed by NASA. A relatively recent method of evolutionary computation is Particle Swarm Optimization (PSO), which can be considered to be in the same general class as Genetic Algorithms. An improvement over

  3. Input point distribution for regular stem form spline modeling

    Directory of Open Access Journals (Sweden)

    Karel Kuželka


    Full Text Available Aim of study: To optimize an interpolation method and distribution of measured diameters to represent regular stem form of coniferous trees using a set of discrete points. Area of study: Central-Bohemian highlands, Czech Republic; a region that represents average stand conditions of production forests of Norway spruce (Picea abies [L.] Karst. in central Europe Material and methods: The accuracy of stem curves modeled using natural cubic splines from a set of measured diameters was evaluated for 85 closely measured stems of Norway spruce using five statistical indicators and compared to the accuracy of three additional models based on different spline types selected for their ability to represent stem curves. The optimal positions to measure diameters were identified using an aggregate objective function approach. Main results: The optimal positions of the input points vary depending on the properties of each spline type. If the optimal input points for each spline are used, then all spline types are able to give reasonable results with higher numbers of input points. The commonly used natural cubic spline was outperformed by other spline types. The lowest errors occur by interpolating the points using the Catmull-Rom spline, which gives accurate and unbiased volume estimates, even with only five input points. Research highlights: The study contributes to more accurate representation of stem form and therefore more accurate estimation of stem volume using data obtained from terrestrial imagery or other close-range remote sensing methods.

  4. Smoothing quadratic and cubic splines


    Oukropcová, Kateřina


    Title: Smoothing quadratic and cubic splines Author: Kateřina Oukropcová Department: Department of Numerical Mathematics Supervisor: RNDr. Václav Kučera, Ph.D., Department of Numerical Mathematics Abstract: The aim of this bachelor thesis is to study the topic of smoothing quadratic and cubic splines on uniform partitions. First, we define the basic con- cepts in the field of splines, next we introduce interpolating splines with a focus on their minimizing properties for odd degree and quadra...

  5. Hilbertian kernels and spline functions

    CERN Document Server

    Atteia, M


    In this monograph, which is an extensive study of Hilbertian approximation, the emphasis is placed on spline functions theory. The origin of the book was an effort to show that spline theory parallels Hilbertian Kernel theory, not only for splines derived from minimization of a quadratic functional but more generally for splines considered as piecewise functions type. Being as far as possible self-contained, the book may be used as a reference, with information about developments in linear approximation, convex optimization, mechanics and partial differential equations.

  6. Splines and variational methods

    CERN Document Server

    Prenter, P M


    One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text's first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimension

  7. The EH Interpolation Spline and Its Approximation

    Directory of Open Access Journals (Sweden)

    Jin Xie


    Full Text Available A new interpolation spline with two parameters, called EH interpolation spline, is presented in this paper, which is the extension of the standard cubic Hermite interpolation spline, and inherits the same properties of the standard cubic Hermite interpolation spline. Given the fixed interpolation conditions, the shape of the proposed splines can be adjusted by changing the values of the parameters. Also, the introduced spline could approximate to the interpolated function better than the standard cubic Hermite interpolation spline and the quartic Hermite interpolation splines with single parameter by a new algorithm.

  8. Forecasting the daily power output of a grid-connected photovoltaic system based on multivariate adaptive regression splines

    International Nuclear Information System (INIS)

    Li, Yanting; He, Yong; Su, Yan; Shu, Lianjie


    Highlights: • Suggests a nonparametric model based on MARS for output power prediction. • Compare the MARS model with a wide variety of prediction models. • Show that the MARS model is able to provide an overall good performance in both the training and testing stages. - Abstract: Both linear and nonlinear models have been proposed for forecasting the power output of photovoltaic systems. Linear models are simple to implement but less flexible. Due to the stochastic nature of the power output of PV systems, nonlinear models tend to provide better forecast than linear models. Motivated by this, this paper suggests a fairly simple nonlinear regression model known as multivariate adaptive regression splines (MARS), as an alternative to forecasting of solar power output. The MARS model is a data-driven modeling approach without any assumption about the relationship between the power output and predictors. It maintains simplicity of the classical multiple linear regression (MLR) model while possessing the capability of handling nonlinearity. It is simpler in format than other nonlinear models such as ANN, k-nearest neighbors (KNN), classification and regression tree (CART), and support vector machine (SVM). The MARS model was applied on the daily output of a grid-connected 2.1 kW PV system to provide the 1-day-ahead mean daily forecast of the power output. The comparisons with a wide variety of forecast models show that the MARS model is able to provide reliable forecast performance.

  9. Marginal longitudinal semiparametric regression via penalized splines

    KAUST Repository

    Al Kadiri, M.


    We study the marginal longitudinal nonparametric regression problem and some of its semiparametric extensions. We point out that, while several elaborate proposals for efficient estimation have been proposed, a relative simple and straightforward one, based on penalized splines, has not. After describing our approach, we then explain how Gibbs sampling and the BUGS software can be used to achieve quick and effective implementation. Illustrations are provided for nonparametric regression and additive models.

  10. Optimization of straight-sided spline design

    DEFF Research Database (Denmark)

    Pedersen, Niels Leergaard


    Spline connection of shaft and hub is commonly applied when large torque capacity is needed together with the possibility of disassembly. The designs of these splines are generally controlled by different standards. In view of the common use of splines, it seems that few papers deal with splines ...

  11. A Closed Mars Analog Simulation: The Approach of Crew 5 At the Mars Desert Research Station (United States)

    Clancey, William J.; Koga, Dennis (Technical Monitor)


    For twelve days in April 2002 we performed a closed simulation in the Mars Desert Research Station, isolated from other people, as on Mars, while performing systematic surface exploration and life support chores. Email provided our only means of contact; no phone or radio conversations were possible. All mission-related messages were mediated by a remote mission support team. This protocol enabled a systematic and controlled study of crew activities, scheduling, and use of space. The analysis presented here focuses on two questions: Where did the time go-why did people feel rushed and unable to complete their work? How can we measure and model productivity, to compare habitat designs, schedules, roles, and tools? Analysis suggests that a simple scheduling change-having lunch and dinner earlier, plus eliminating afternoon meetings-increased the available productive time by 41%.

  12. MOLA: The New Approach for Mars Global Cartography (United States)

    Duxbury, Thomas C.


    The MGS Orbiter is carrying the high-precision Mars Orbiter Laser Altimeter (MOLA) which, when combined with telemetered latitude data, provides a tie between inertial space and Mars-fixed coordinates to an accuracy of 100 m in latitude/longitude and 10 m in radius (1 sigma), orders of magnitude more accurate than previous global geodetic/ cartographic control data. Over the 2 year MGS mission lifetime, it is expected that over 30,000 MOLA Global Cartographic Control Points will be produced to form the basis for new and re-derived map and geodetic products, key to the analysis of existing and evolving MGS data as well as future Mars exploration.

  13. Lunar COTS: An Economical and Sustainable Approach to Reaching Mars (United States)

    Zuniga, Allison F.; Rasky, Daniel; Pittman, Robert B.; Zapata, Edgar; Lepsch, Roger


    The NASA COTS (Commercial Orbital Transportation Services) Program was a very successful program that developed and demonstrated cost-effective development and acquisition of commercial cargo transportation services to the International Space Station (ISS). The COTS acquisition strategy utilized a newer model than normally accepted in traditional procurement practices. This new model used Space Act Agreements where NASA entered into partnerships with industry to jointly share cost, development and operational risks to demonstrate new capabilities for mutual benefit. This model proved to be very beneficial to both NASA and its industry partners as NASA saved significantly in development and operational costs while industry partners successfully expanded their market share of the global launch transportation business. The authors, who contributed to the development of the COTS model, would like to extend this model to a lunar commercial services program that will push development of technologies and capabilities that will serve a Mars architecture and lead to an economical and sustainable pathway to transporting humans to Mars. Over the past few decades, several architectures for the Moon and Mars have been proposed and studied but ultimately halted or not even started due to the projected costs significantly exceeding NASA's budgets. Therefore a new strategy is needed that will fit within NASA's projected budgets and takes advantage of the US commercial industry along with its creative and entrepreneurial attributes. The authors propose a new COTS-like program to enter into partnerships with industry to demonstrate cost-effective, cis-lunar commercial services, such as lunar transportation, lunar ISRU operations, and cis-lunar propellant depots that can enable an economical and sustainable Mars architecture. Similar to the original COTS program, the goals of the proposed program, being notionally referred to as Lunar Commercial Orbital Transfer Services (LCOTS

  14. An Efficient Approach for Mars Sample Return Using Emerging Commercial Capabilities. (United States)

    Gonzales, Andrew A; Stoker, Carol R


    Mars Sample Return is the highest priority science mission for the next decade as recommended by the 2011 Decadal Survey of Planetary Science [1]. This article presents the results of a feasibility study for a Mars Sample Return mission that efficiently uses emerging commercial capabilities expected to be available in the near future. The motivation of our study was the recognition that emerging commercial capabilities might be used to perform Mars Sample Return with an Earth-direct architecture, and that this may offer a desirable simpler and lower cost approach. The objective of the study was to determine whether these capabilities can be used to optimize the number of mission systems and launches required to return the samples, with the goal of achieving the desired simplicity. All of the major element required for the Mars Sample Return mission are described. Mission system elements were analyzed with either direct techniques or by using parametric mass estimating relationships. The analysis shows the feasibility of a complete and closed Mars Sample Return mission design based on the following scenario: A SpaceX Falcon Heavy launch vehicle places a modified version of a SpaceX Dragon capsule, referred to as "Red Dragon", onto a Trans Mars Injection trajectory. The capsule carries all the hardware needed to return to Earth Orbit samples collected by a prior mission, such as the planned NASA Mars 2020 sample collection rover. The payload includes a fully fueled Mars Ascent Vehicle; a fueled Earth Return Vehicle, support equipment, and a mechanism to transfer samples from the sample cache system onboard the rover to the Earth Return Vehicle. The Red Dragon descends to land on the surface of Mars using Supersonic Retropropulsion. After collected samples are transferred to the Earth Return Vehicle, the single-stage Mars Ascent Vehicle launches the Earth Return Vehicle from the surface of Mars to a Mars phasing orbit. After a brief phasing period, the Earth Return

  15. An Efficient Approach for Mars Sample Return Using Emerging Commercial Capabilities (United States)

    Gonzales, Andrew A.; Stoker, Carol R.


    Mars Sample Return is the highest priority science mission for the next decade as recommended by the 2011 Decadal Survey of Planetary Science [1]. This article presents the results of a feasibility study for a Mars Sample Return mission that efficiently uses emerging commercial capabilities expected to be available in the near future. The motivation of our study was the recognition that emerging commercial capabilities might be used to perform Mars Sample Return with an Earth-direct architecture, and that this may offer a desirable simpler and lower cost approach. The objective of the study was to determine whether these capabilities can be used to optimize the number of mission systems and launches required to return the samples, with the goal of achieving the desired simplicity. All of the major element required for the Mars Sample Return mission are described. Mission system elements were analyzed with either direct techniques or by using parametric mass estimating relationships. The analysis shows the feasibility of a complete and closed Mars Sample Return mission design based on the following scenario: A SpaceX Falcon Heavy launch vehicle places a modified version of a SpaceX Dragon capsule, referred to as “Red Dragon”, onto a Trans Mars Injection trajectory. The capsule carries all the hardware needed to return to Earth Orbit samples collected by a prior mission, such as the planned NASA Mars 2020 sample collection rover. The payload includes a fully fueled Mars Ascent Vehicle; a fueled Earth Return Vehicle, support equipment, and a mechanism to transfer samples from the sample cache system onboard the rover to the Earth Return Vehicle. The Red Dragon descends to land on the surface of Mars using Supersonic Retropropulsion. After collected samples are transferred to the Earth Return Vehicle, the single-stage Mars Ascent Vehicle launches the Earth Return Vehicle from the surface of Mars to a Mars phasing orbit. After a brief phasing period, the Earth

  16. An efficient approach for Mars Sample Return using emerging commercial capabilities (United States)

    Gonzales, Andrew A.; Stoker, Carol R.


    Mars Sample Return is the highest priority science mission for the next decade as recommended by the 2011 Decadal Survey of Planetary Science (Squyres, 2011 [1]). This article presents the results of a feasibility study for a Mars Sample Return mission that efficiently uses emerging commercial capabilities expected to be available in the near future. The motivation of our study was the recognition that emerging commercial capabilities might be used to perform Mars Sample Return with an Earth-direct architecture, and that this may offer a desirable simpler and lower cost approach. The objective of the study was to determine whether these capabilities can be used to optimize the number of mission systems and launches required to return the samples, with the goal of achieving the desired simplicity. All of the major element required for the Mars Sample Return mission are described. Mission system elements were analyzed with either direct techniques or by using parametric mass estimating relationships. The analysis shows the feasibility of a complete and closed Mars Sample Return mission design based on the following scenario: A SpaceX Falcon Heavy launch vehicle places a modified version of a SpaceX Dragon capsule, referred to as ;Red Dragon;, onto a Trans Mars Injection trajectory. The capsule carries all the hardware needed to return to Earth Orbit samples collected by a prior mission, such as the planned NASA Mars 2020 sample collection rover. The payload includes a fully fueled Mars Ascent Vehicle; a fueled Earth Return Vehicle, support equipment, and a mechanism to transfer samples from the sample cache system onboard the rover to the Earth Return Vehicle. The Red Dragon descends to land on the surface of Mars using Supersonic Retropropulsion. After collected samples are transferred to the Earth Return Vehicle, the single-stage Mars Ascent Vehicle launches the Earth Return Vehicle from the surface of Mars to a Mars phasing orbit. After a brief phasing period, the


    Directory of Open Access Journals (Sweden)

    Otgon Cristian


    Full Text Available The paper aims to approach innovative financial instruments for the management of public resources. In the category of these innovative tools have been included polynomial spline functions used for budgetary sizing in the substantiating of fiscal and budgetary policies. In order to use polynomial spline functions there have been made a number of steps consisted in the establishment of nodes, the calculation of specific coefficients corresponding to the spline functions, development and determination of errors of approximation. Also in this paper was done extrapolation of series of property tax data using polynomial spline functions of order I. For spline impelementation were taken two series of data, one reffering to property tax as a resultative variable and the second one reffering to building tax, resulting a correlation indicator R=0,95. Moreover the calculation of spline functions are easy to solve and due to small errors of approximation have a great power of predictibility, much better than using ordinary least squares method. In order to realise the research there have been used as methods of research several steps, namely observation, series of data construction and processing the data with spline functions. The data construction is a daily series gathered from the budget account, reffering to building tax and property tax. The added value of this paper is given by the possibility of avoiding deficits by using spline functions as innovative instruments in the publlic finance, the original contribution is made by the average of splines resulted from the series of data. The research results lead to conclusion that the polynomial spline functions are recommended to form the elaboration of fiscal and budgetary policies, due to relatively small errors obtained in the extrapolation of economic processes and phenomena. Future research directions are taking in consideration to study the polynomial spline functions of second-order, third

  18. New approaches to the exploration: planet Mars and bacterial life


    Galletta, Giuseppe; Bertoloni, Giulio; D'Alessandro, Maurizio


    Planet Mars past environmental conditions were similar to the early Earth, but nowadays they are similar to those of a very cold desert, irradiated by intense solar UV light. However, some terrestrial lifeform showed the capability to adapt to very harsh environments, similar to the extreme condition of the Red Planet. In addition, recent discoveries of water in the Martian permafrost and of methane in the Martian atmosphere, have generated optimism regarding a potentially active subsurface M...

  19. Mars Relay Spacecraft: A Low-Cost Approach (United States)

    SvitekT, .; King, J.; Fulton, R.; McOmber, R.; Hastrup, R.; Miller, A.


    The next phase of Mars exploration will utilize numerous globally distributed small low-cost devices including landers penetrators microrovers and balloons. Direct-to-Earth communications links if required for these landers will drive the lander design for two reasons: a) mass and complexity needed for a steerable high-gain antenna and b) power requirements for a high-power amplifier (i.e. solar panel and battery mass). Total mass of the direct link hardware for several recent small-lander designs exceeded the mass of the scientific payload. Alternatively if communications are via a Mars-orbiting relay spacecraft resource requirements for the local UHF communication link are comparatively trivial: a simple whip antenna and less than 1 watt power. Clearly using a Mars relay spacecraft (MRS) is the preferred option if the MRS mission can be accomplished in an affordable and robust way. Our paper describes a point design for such a mission launched in the s001 or 2003 opportunity.

  20. Innovative Approaches for Seismic Studies of Mars (Invited) (United States)

    Banerdt, B.


    In addition to its intrinsic interest, Mars is particularly well-suited for studying the full range of processes and phenomena related to early terrestrial planet evolution, from initial differentiation to the start of plate tectonics. It is large and complex enough to have undergone most of the processes that affected early Earth but, unlike the Earth, has apparently not undergone extensive plate tectonics or other major reworking that erased the imprint of early events (as evidenced by the presence of cratered surfaces older than 4 Ga). The martian mantle should have Earth-like polymorphic phase transitions and may even support a perovskite layer near the core (depending on the actual core radius), a characteristic that would have major implications for core cooling and mantle convection. Thus even the most basic measurements of planetary structure, such as crustal thickness, core radius and state (solid/liquid), and gross mantle velocity structure would provide invaluable constraints on models of early planetary evolution. Despite this strong scientific motivation (and several failed attempts), Mars remains terra incognita from a seismic standpoint. This is due to an unfortunate convergence of circumstances, prominent among which are our uncertainty in the level of seismic activity and the relatively high cost of landing multiple long-lived spacecraft on Mars to comprise a seismic network for body-wave travel-time analysis; typically four to ten stations are considered necessary for this type of experiment. In this presentation I will address both of these issues. In order to overcome the concern about a possible lack of marsquakes with which to work, it is useful to identify alternative methods for using seismic techniques to probe the interior. Seismology without quakes can be accomplished in a number of ways. “Unconventional” sources of seismic energy include meteorites (which strike the surface of Mars at a relatively high rate), artificial projectiles

  1. Design Evaluation of Wind Turbine Spline Couplings Using an Analytical Model: Preprint

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Y.; Keller, J.; Wallen, R.; Errichello, R.; Halse, C.; Lambert, S.


    Articulated splines are commonly used in the planetary stage of wind turbine gearboxes for transmitting the driving torque and improving load sharing. Direct measurement of spline loads and performance is extremely challenging because of limited accessibility. This paper presents an analytical model for the analysis of articulated spline coupling designs. For a given torque and shaft misalignment, this analytical model quickly yields insights into relationships between the spline design parameters and resulting loads; bending, contact, and shear stresses; and safety factors considering various heat treatment methods. Comparisons of this analytical model against previously published computational approaches are also presented.

  2. A Blossoming Development of Splines

    CERN Document Server

    Mann, Stephen


    In this lecture, we study Bezier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles, as well as in modeling packages used by the computer animation industry. Bezier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface. The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geom

  3. Symmetric, discrete fractional splines and Gabor systems

    DEFF Research Database (Denmark)

    Søndergaard, Peter Lempel


    In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing the continu......In this paper we consider fractional splines as windows for Gabor frames. We introduce two new types of symmetric, fractional splines in addition to one found by Unser and Blu. For the finite, discrete case we present two families of splines: One is created by sampling and periodizing...... the continuous splines, and one is a truly finite, discrete construction. We discuss the properties of these splines and their usefulness as windows for Gabor frames and Wilson bases....

  4. Numerical Methods Using B-Splines (United States)

    Shariff, Karim; Merriam, Marshal (Technical Monitor)


    The seminar will discuss (1) The current range of applications for which B-spline schemes may be appropriate (2) The property of high-resolution and the relationship between B-spline and compact schemes (3) Comparison between finite-element, Hermite finite element and B-spline schemes (4) Mesh embedding using B-splines (5) A method for the incompressible Navier-Stokes equations in curvilinear coordinates using divergence-free expansions.

  5. Isogeometric analysis using T-splines

    KAUST Repository

    Bazilevs, Yuri


    We explore T-splines, a generalization of NURBS enabling local refinement, as a basis for isogeometric analysis. We review T-splines as a surface design methodology and then develop it for engineering analysis applications. We test T-splines on some elementary two-dimensional and three-dimensional fluid and structural analysis problems and attain good results in all cases. We summarize the current status of T-splines, their limitations, and future possibilities. © 2009 Elsevier B.V.

  6. Cubic spline functions for curve fitting (United States)

    Young, J. D.


    FORTRAN cubic spline routine mathematically fits curve through given ordered set of points so that fitted curve nearly approximates curve generated by passing infinite thin spline through set of points. Generalized formulation includes trigonometric, hyperbolic, and damped cubic spline fits of third order.

  7. Density Deconvolution With EPI Splines (United States)


    Comparison of Deconvolution Methods . . . . . . . . . . . . . . . 28 5 High-Fidelity and Low-Fidelity Simulation Output 31 5.1 Hydrofoil Concept...46 A.3 Hydrofoil Concept . . . . . . . . . . . . . . . . . . . . . . . . 47 A.4 Notes on Computation Time...Epi-Spline Estimates . . . . . . . . . . . 28 Figure 4.3 Deconvolution Method Comparison . . . . . . . . . . . . . . . . 29 Figure 5.1 Hydrofoil

  8. An Open Modelling Approach for Availability and Reliability of Systems - OpenMARS

    CERN Document Server

    Penttinen, Jussi-Pekka; Gutleber, Johannes


    This document introduces and gives specification for OpenMARS, which is an open modelling approach for availability and reliability of systems. It supports the most common risk assessment and operation modelling techniques. Uniquely OpenMARS allows combining and connecting models defined with different techniques. This ensures that a modeller has a high degree of freedom to accurately describe the modelled system without limitations imposed by an individual technique. Here the OpenMARS model definition is specified with a tool independent tabular format, which supports managing models developed in a collaborative fashion. Origin of our research is in Future Circular Collider (FCC) study, where we developed the unique features of our concept to model the availability and luminosity production of particle colliders. We were motivated to describe our approach in detail as we see potential further applications in performance and energy efficiency analyses of large scientific infrastructures or industrial processe...

  9. Stability of Spline-Type Systems in the Abelian Case

    Directory of Open Access Journals (Sweden)

    Darian Onchis


    Full Text Available In this paper, the stability of translation-invariant spaces of distributions over locally compact groups is stated as boundedness of synthesis and projection operators. At first, a characterization of the stability of spline-type spaces is given, in the standard sense of the stability for shift-invariant spaces, that is, linear independence characterizes lower boundedness of the synthesis operator in Banach spaces of distributions. The constructive nature of the proof for Theorem 2 enabled us to constructively realize the biorthogonal system of a given one. Then, inspired by the multiresolution analysis and the Lax equivalence for general discretization schemes, we approached the stability of a sequence of spline-type spaces as uniform boundedness of projection operators. Through Theorem 3, we characterize stable sequences of stable spline-type spaces.

  10. Stability of Spline-Type Systems in the Abelian Case. (United States)

    Onchis, Darian; Zappalà, Simone


    In this paper, the stability of translation-invariant spaces of distributions over locally compact groups is stated as boundedness of synthesis and projection operators. At first, a characterization of the stability of spline-type spaces is given, in the standard sense of the stability for shift-invariant spaces, that is, linear independence characterizes lower boundedness of the synthesis operator in Banach spaces of distributions. The constructive nature of the proof for Theorem 2 enabled us to constructively realize the biorthogonal system of a given one. Then, inspired by the multiresolution analysis and the Lax equivalence for general discretization schemes, we approached the stability of a sequence of spline-type spaces as uniform boundedness of projection operators. Through Theorem 3, we characterize stable sequences of stable spline-type spaces.

  11. A restricted cubic spline approach to assess the association between high fat fish intake and red blood cell EPA + DHA content. (United States)

    Sirot, V; Dumas, C; Desquilbet, L; Mariotti, F; Legrand, P; Catheline, D; Leblanc, J-C; Margaritis, I


    Fish, especially fatty fish, are the main contributor to eicosapentaenoic (EPA) and docosahexaenoic (DHA) intake. EPA and DHA concentrations in red blood cells (RBC) has been proposed as a cardiovascular risk factor, with 8% associated with the lowest and greatest protection, respectively. The relationship between high fat fish (HFF) intake and RBC EPA + DHA content has been little investigated on a wide range of fish intake, and may be non-linear. We aimed to study the shape of this relationship among high seafood consumers. Seafood consumption records and blood were collected from 384 French heavy seafood consumers and EPA and DHA were measured in RBC. A multivariate linear regression was performed using restricted cubic splines to consider potential non-linear associations. Thirty-six percent of subjects had an RBC EPA + DHA content lower than 4% and only 5% exceeded 8%. HFF consumption was significantly associated with RBC EPA + DHA content (P [overall association] = 0.021) adjusted for sex, tobacco status, study area, socioeconomic status, age, alcohol, other seafood, meat, and meat product intakes. This relationship was non-linear: for intakes higher than 200 g/wk, EPA + DHA content tended to stagnate. Tobacco status and fish contaminants were negatively associated with RBC EPA + DHA content. Because of the saturation for high intakes, and accounting for the concern with exposure to trace element contaminants, intake not exceeding 200 g should be considered. Copyright © 2010 Elsevier B.V. All rights reserved.

  12. Spline and spline wavelet methods with applications to signal and image processing

    CERN Document Server

    Averbuch, Amir Z; Zheludev, Valery A

    This volume provides universal methodologies accompanied by Matlab software to manipulate numerous signal and image processing applications. It is done with discrete and polynomial periodic splines. Various contributions of splines to signal and image processing from a unified perspective are presented. This presentation is based on Zak transform and on Spline Harmonic Analysis (SHA) methodology. SHA combines approximation capabilities of splines with the computational efficiency of the Fast Fourier transform. SHA reduces the design of different spline types such as splines, spline wavelets (SW), wavelet frames (SWF) and wavelet packets (SWP) and their manipulations by simple operations. Digital filters, produced by wavelets design process, give birth to subdivision schemes. Subdivision schemes enable to perform fast explicit computation of splines' values at dyadic and triadic rational points. This is used for signals and images upsampling. In addition to the design of a diverse library of splines, SW, SWP a...

  13. Autonomous optical navigation using nanosatellite-class instruments: a Mars approach case study (United States)

    Enright, John; Jovanovic, Ilija; Kazemi, Laila; Zhang, Harry; Dzamba, Tom


    This paper examines the effectiveness of small star trackers for orbital estimation. Autonomous optical navigation has been used for some time to provide local estimates of orbital parameters during close approach to celestial bodies. These techniques have been used extensively on spacecraft dating back to the Voyager missions, but often rely on long exposures and large instrument apertures. Using a hyperbolic Mars approach as a reference mission, we present an EKF-based navigation filter suitable for nanosatellite missions. Observations of Mars and its moons allow the estimator to correct initial errors in both position and velocity. Our results show that nanosatellite-class star trackers can produce good quality navigation solutions with low position (<300 {m}) and velocity (<0.15 {m/s}) errors as the spacecraft approaches periapse.

  14. Quadrotor system identification using the multivariate multiplex b-spline

    NARCIS (Netherlands)

    Visser, T.; De Visser, C.C.; Van Kampen, E.J.


    A novel method for aircraft system identification is presented that is based on a new multivariate spline type; the multivariate multiplex B-spline. The multivariate multiplex B-spline is a generalization of the recently introduced tensor-simplex B-spline. Multivariate multiplex splines obtain

  15. Characterizing vaccine-associated risks using cubic smoothing splines. (United States)

    Brookhart, M Alan; Walker, Alexander M; Lu, Yun; Polakowski, Laura; Li, Jie; Paeglow, Corrie; Puenpatom, Tosmai; Izurieta, Hector; Daniel, Gregory W


    Estimating risks associated with the use of childhood vaccines is challenging. The authors propose a new approach for studying short-term vaccine-related risks. The method uses a cubic smoothing spline to flexibly estimate the daily risk of an event after vaccination. The predicted incidence rates from the spline regression are then compared with the expected rates under a log-linear trend that excludes the days surrounding vaccination. The 2 models are then used to estimate the excess cumulative incidence attributable to the vaccination during the 42-day period after vaccination. Confidence intervals are obtained using a model-based bootstrap procedure. The method is applied to a study of known effects (positive controls) and expected noneffects (negative controls) of the measles, mumps, and rubella and measles, mumps, rubella, and varicella vaccines among children who are 1 year of age. The splines revealed well-resolved spikes in fever, rash, and adenopathy diagnoses, with the maximum incidence occurring between 9 and 11 days after vaccination. For the negative control outcomes, the spline model yielded a predicted incidence more consistent with the modeled day-specific risks, although there was evidence of increased risk of diagnoses of congenital malformations after vaccination, possibly because of a "provider visit effect." The proposed approach may be useful for vaccine safety surveillance.

  16. Construction of local integro quintic splines

    Directory of Open Access Journals (Sweden)

    T. Zhanlav


    Full Text Available In this paper, we show that the integro quintic splines can locally be constructed without solving any systems of equations. The new construction does not require any additional end conditions. By virtue of these advantages the proposed algorithm is easy to implement and effective. At the same time, the local integro quintic splines possess as good approximation properties as the integro quintic splines. In this paper, we have proved that our local integro quintic spline has superconvergence properties at the knots for the first and third derivatives. The orders of convergence at the knots are six (not five for the first derivative and four (not three for the third derivative.

  17. Spline methods for conversation equations

    International Nuclear Information System (INIS)

    Bottcher, C.; Strayer, M.R.


    The consider the numerical solution of physical theories, in particular hydrodynamics, which can be formulated as systems of conservation laws. To this end we briefly describe the Basis Spline and collocation methods, paying particular attention to representation theory, which provides discrete analogues of the continuum conservation and dispersion relations, and hence a rigorous understanding of errors and instabilities. On this foundation we propose an algorithm for hydrodynamic problems in which most linear and nonlinear instabilities are brought under control. Numerical examples are presented from one-dimensional relativistic hydrodynamics. 9 refs., 10 figs

  18. A chord error conforming tool path B-spline fitting method for NC machining based on energy minimization and LSPIA


    He, Shanshan; Ou, Daojiang; Yan, Changya; Lee, Chen-Han


    Piecewise linear (G01-based) tool paths generated by CAM systems lack G1 and G2 continuity. The discontinuity causes vibration and unnecessary hesitation during machining. To ensure efficient high-speed machining, a method to improve the continuity of the tool paths is required, such as B-spline fitting that approximates G01 paths with B-spline curves. Conventional B-spline fitting approaches cannot be directly used for tool path B-spline fitting, because they have shortages such as numerical...

  19. Comparative Analysis for Robust Penalized Spline Smoothing Methods

    Directory of Open Access Journals (Sweden)

    Bin Wang


    Full Text Available Smoothing noisy data is commonly encountered in engineering domain, and currently robust penalized regression spline models are perceived to be the most promising methods for coping with this issue, due to their flexibilities in capturing the nonlinear trends in the data and effectively alleviating the disturbance from the outliers. Against such a background, this paper conducts a thoroughly comparative analysis of two popular robust smoothing techniques, the M-type estimator and S-estimation for penalized regression splines, both of which are reelaborated starting from their origins, with their derivation process reformulated and the corresponding algorithms reorganized under a unified framework. Performances of these two estimators are thoroughly evaluated from the aspects of fitting accuracy, robustness, and execution time upon the MATLAB platform. Elaborately comparative experiments demonstrate that robust penalized spline smoothing methods possess the capability of resistance to the noise effect compared with the nonrobust penalized LS spline regression method. Furthermore, the M-estimator exerts stable performance only for the observations with moderate perturbation error, whereas the S-estimator behaves fairly well even for heavily contaminated observations, but consuming more execution time. These findings can be served as guidance to the selection of appropriate approach for smoothing the noisy data.

  20. Univariate Cubic L1 Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm

    Directory of Open Access Journals (Sweden)

    Shu-Cherng Fang


    Full Text Available We compare univariate L1 interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value and the antiderivative. Computational results indicate that second-derivative-based 5-point-window L1 splines preserve shape as well as or better than the other types of L1 splines. To calculate second-derivative-based 5-point-window L1 splines, we introduce an analysis-based, parallelizable algorithm. This algorithm is orders of magnitude faster than the previously widely used primal affine algorithm.

  1. Spline fitting for multi-set data

    International Nuclear Information System (INIS)

    Zhou Hongmo; Liu Renqiu; Liu Tingjin


    A spline fit method and program for multi-set data have been developed. Improvements have been made to have new functions: any order of spline as base, knot optimization and accurate calculation for error of fit value. The program has been used for practical evaluation of nuclear data

  2. Boosted regression trees, multivariate adaptive regression splines and their two-step combinations with multiple linear regression or partial least squares to predict blood-brain barrier passage: a case study. (United States)

    Deconinck, E; Zhang, M H; Petitet, F; Dubus, E; Ijjaali, I; Coomans, D; Vander Heyden, Y


    The use of some unconventional non-linear modeling techniques, i.e. classification and regression trees and multivariate adaptive regression splines-based methods, was explored to model the blood-brain barrier (BBB) passage of drugs and drug-like molecules. The data set contains BBB passage values for 299 structural and pharmacological diverse drugs, originating from a structured knowledge-based database. Models were built using boosted regression trees (BRT) and multivariate adaptive regression splines (MARS), as well as their respective combinations with stepwise multiple linear regression (MLR) and partial least squares (PLS) regression in two-step approaches. The best models were obtained using combinations of MARS with either stepwise MLR or PLS. It could be concluded that the use of combinations of a linear with a non-linear modeling technique results in some improved properties compared to the individual linear and non-linear models and that, when the use of such a combination is appropriate, combinations using MARS as non-linear technique should be preferred over those with BRT, due to some serious drawbacks of the BRT approaches.

  3. Positivity Preserving Interpolation Using Rational Bicubic Spline

    Directory of Open Access Journals (Sweden)

    Samsul Ariffin Abdul Karim


    Full Text Available This paper discusses the positivity preserving interpolation for positive surfaces data by extending the C1 rational cubic spline interpolant of Karim and Kong to the bivariate cases. The partially blended rational bicubic spline has 12 parameters in the descriptions where 8 of them are free parameters. The sufficient conditions for the positivity are derived on every four boundary curves network on the rectangular patch. Numerical comparison with existing schemes also has been done in detail. Based on Root Mean Square Error (RMSE, our partially blended rational bicubic spline is on a par with the established methods.

  4. Smoothing noisy spectroscopic data with many-knot spline method

    Energy Technology Data Exchange (ETDEWEB)

    Zhu, M.H. [Space Exploration Laboratory, Macau University of Science and Technology, Taipa, Macau (China)], E-mail:; Liu, L.G.; Qi, D.X.; You, Z.; Xu, A.A. [Space Exploration Laboratory, Macau University of Science and Technology, Taipa, Macau (China)


    In this paper, we present the development of a many-knot spline method derived to remove the statistical noise in the spectroscopic data. This method is an expansion of the B-spline method. Compared to the B-spline method, the many-knot spline method is significantly faster.

  5. Optimal Approximation of Biquartic Polynomials by Bicubic Splines

    Directory of Open Access Journals (Sweden)

    Kačala Viliam


    The goal of this paper is to resolve this problem. Unlike the spline curves, in the case of spline surfaces it is insufficient to suppose that the grid should be uniform and the spline derivatives computed from a biquartic polynomial. We show that the biquartic polynomial coefficients have to satisfy some additional constraints to achieve optimal approximation by bicubic splines.

  6. Spline interpolations besides wood model widely used in lactation (United States)

    Korkmaz, Mehmet


    In this study, for lactation curve, spline interpolations, alternative modeling passing through exactly all data points with respect to widely used Wood model applied to lactation data were be discussed. These models are linear spline, quadratic spline and cubic spline. The observed and estimated values according to spline interpolations and Wood model were given with their Error Sum of Squares and also the lactation curves of spline interpolations and widely used Wood model were shown on the same graph. Thus, the differences have been observed. The estimates for some intermediate values were done by using spline interpolations and Wood model. By using spline interpolations, the estimates of intermediate values could be made more precise. Furthermore, by using spline interpolations, the predicted values for missing or incorrect observation were very successful according to the values of Wood model. By using spline interpolations, new ideas and interpretations in addition to the information of the well-known classical analysis were shown to the investigators.

  7. Biomechanical Analysis with Cubic Spline Functions (United States)

    McLaughlin, Thomas M.; And Others


    Results of experimentation suggest that the cubic spline is a convenient and consistent method for providing an accurate description of displacement-time data and for obtaining the corresponding time derivatives. (MJB)

  8. On convexity and Schoenberg's variation diminishing splines

    International Nuclear Information System (INIS)

    Feng, Yuyu; Kozak, J.


    In the paper we characterize a convex function by the monotonicity of a particular variation diminishing spline sequence. The result extends the property known for the Bernstein polynomial sequence. (author). 4 refs

  9. Flexible regression models with cubic splines. (United States)

    Durrleman, S; Simon, R


    We describe the use of cubic splines in regression models to represent the relationship between the response variable and a vector of covariates. This simple method can help prevent the problems that result from inappropriate linearity assumptions. We compare restricted cubic spline regression to non-parametric procedures for characterizing the relationship between age and survival in the Stanford Heart Transplant data. We also provide an illustrative example in cancer therapeutics.

  10. An enhanced splined saddle method (United States)

    Ghasemi, S. Alireza; Goedecker, Stefan


    We present modifications for the method recently developed by Granot and Baer [J. Chem. Phys. 128, 184111 (2008)], 10.1063/1.2916716. These modifications significantly enhance the efficiency and reliability of the method. In addition, we discuss some specific features of this method. These features provide important flexibilities which are crucial for a double-ended saddle point search method in order to be applicable to complex reaction mechanisms. Furthermore, it is discussed under what circumstances this methods might fail to find the transition state and remedies to avoid such situations are provided. We demonstrate the performance of the enhanced splined saddle method on several examples with increasing complexity, isomerization of ammonia, ethane and cyclopropane molecules, tautomerization of cytosine, the ring opening of cyclobutene, the Stone-Wales transformation of the C60 fullerene, and finally rolling a small NaCl cube on NaCl(001) surface. All of these calculations are based on density functional theory. The efficiency of the method is remarkable in regard to the reduction of the total computational time.

  11. LD-Spline: Mapping SNPs on genotyping platforms to genomic regions using patterns of linkage disequilibrium

    Directory of Open Access Journals (Sweden)

    Bush William S


    Full Text Available Abstract Background Gene-centric analysis tools for genome-wide association study data are being developed both to annotate single locus statistics and to prioritize or group single nucleotide polymorphisms (SNPs prior to analysis. These approaches require knowledge about the relationships between SNPs on a genotyping platform and genes in the human genome. SNPs in the genome can represent broader genomic regions via linkage disequilibrium (LD, and population-specific patterns of LD can be exploited to generate a data-driven map of SNPs to genes. Methods In this study, we implemented LD-Spline, a database routine that defines the genomic boundaries a particular SNP represents using linkage disequilibrium statistics from the International HapMap Project. We compared the LD-Spline haplotype block partitioning approach to that of the four gamete rule and the Gabriel et al. approach using simulated data; in addition, we processed two commonly used genome-wide association study platforms. Results We illustrate that LD-Spline performs comparably to the four-gamete rule and the Gabriel et al. approach; however as a SNP-centric approach LD-Spline has the added benefit of systematically identifying a genomic boundary for each SNP, where the global block partitioning approaches may falter due to sampling variation in LD statistics. Conclusion LD-Spline is an integrated database routine that quickly and effectively defines the genomic region marked by a SNP using linkage disequilibrium, with a SNP-centric block definition algorithm.

  12. Exact sampling of the unobserved covariates in Bayesian spline models for measurement error problems. (United States)

    Bhadra, Anindya; Carroll, Raymond J


    In truncated polynomial spline or B-spline models where the covariates are measured with error, a fully Bayesian approach to model fitting requires the covariates and model parameters to be sampled at every Markov chain Monte Carlo iteration. Sampling the unobserved covariates poses a major computational problem and usually Gibbs sampling is not possible. This forces the practitioner to use a Metropolis-Hastings step which might suffer from unacceptable performance due to poor mixing and might require careful tuning. In this article we show for the cases of truncated polynomial spline or B-spline models of degree equal to one, the complete conditional distribution of the covariates measured with error is available explicitly as a mixture of double-truncated normals, thereby enabling a Gibbs sampling scheme. We demonstrate via a simulation study that our technique performs favorably in terms of computational efficiency and statistical performance. Our results indicate up to 62 and 54 % increase in mean integrated squared error efficiency when compared to existing alternatives while using truncated polynomial splines and B-splines respectively. Furthermore, there is evidence that the gain in efficiency increases with the measurement error variance, indicating the proposed method is a particularly valuable tool for challenging applications that present high measurement error. We conclude with a demonstration on a nutritional epidemiology data set from the NIH-AARP study and by pointing out some possible extensions of the current work.

  13. Placing Spline Knots in Neural Networks Using Splines as Activation Functions

    Czech Academy of Sciences Publication Activity Database

    Hlaváčková, Kateřina; Verleysen, M.


    Roč. 17, 3/4 (1997), s. 159-166 ISSN 0925-2312 R&D Projects: GA ČR GA201/93/0427; GA ČR GA201/96/0971 Keywords : cubic -spline function * approximation error * knots of spline function * feedforward neural network Impact factor: 0.422, year: 1997

  14. A Computational Intelligence (CI) Approach to the Precision Mars Lander Problem (United States)

    Birge, Brian; Walberg, Gerald


    A Mars precision landing requires a landed footprint of no more than 100 meters. Obstacles to reducing the landed footprint include trajectory dispersions due to initial atmospheric entry conditions such as entry angle, parachute deployment height, environment parameters such as wind, atmospheric density, parachute deployment dynamics, unavoidable injection error or propagated error from launch, etc. Computational Intelligence (CI) techniques such as Artificial Neural Nets and Particle Swarm Optimization have been shown to have great success with other control problems. The research period extended previous work on investigating applicability of the computational intelligent approaches. The focus of this investigation was on Particle Swarm Optimization and basic Neural Net architectures. The research investigating these issues was performed for the grant cycle from 5/15/01 to 5/15/02. Matlab 5.1 and 6.0 along with NASA's POST were the primary computational tools.

  15. A smoothing algorithm using cubic spline functions (United States)

    Smith, R. E., Jr.; Price, J. M.; Howser, L. M.


    Two algorithms are presented for smoothing arbitrary sets of data. They are the explicit variable algorithm and the parametric variable algorithm. The former would be used where large gradients are not encountered because of the smaller amount of calculation required. The latter would be used if the data being smoothed were double valued or experienced large gradients. Both algorithms use a least-squares technique to obtain a cubic spline fit to the data. The advantage of the spline fit is that the first and second derivatives are continuous. This method is best used in an interactive graphics environment so that the junction values for the spline curve can be manipulated to improve the fit.

  16. A geoethical approach to the geological and astrobiological exploration and research of the Moon and Mars (United States)

    Martinez-Frias, Jesus; Horneck, Gerda; de La Torre Noetzel, Rosa; Rull, Fernando

    Lunar and Mars exploration and research require not only scientific and technological inter-disciplinary cooperation, but also the consideration of budding ethical and scientific integrity issues. COSPAR's planetary protection policy (in coordination with the United Nations Com-mittee on the Peaceful Uses of Outer Space as well as various other bilateral and multilateral organizations) serves as the consensus standard for biological contamination prevention under the 1967 Outer Space Treaty1 . Space agencies Planetary Protection Policies are mostly consis-tent with the COSPAR policy. Geoethics was formerly promoted in 1991 as a new discipline, involving scientific and societal aspects2 , and its institutionalization was officially established in 2004 with the backing of the Association of Geoscientists for International Development, AGID3 (IUGS/ICSU). Recently, it has been proposed that the integration of geoethical issues in studies on planetary geology and astrobiology would enrich their methodological and con-ceptual character4-6 . The incorporation through geoethics of new questions and approaches associated to the "abiotic world" would involve: 1) extrapolating to space the recently defined and approved IUCN/UNESCO guidelines and recommendations on geodiversity7 as "planetary geodiversity", and 2) widening the classical concept of Planetary Protection, giving an addi-tional "abiotic" dimension to the exploration and research of the Moon and Mars. Given the geological characteristics and planetary evolution of the Moon and Mars, it is obvious that they require tailored geoethical approaches. Some fundamental aspects include, among others: the interrelation with bioethics and organics vs. inorganic contamination in Planetary Protection, the appropriate regulations of some necessary natural disturbances (e.g. on the Moon) dur-ing robotic and manned planetary missions, wilderness/planetary parks8,9 , the correct use of mineralogical and geochemical analytical

  17. Scripted Bodies and Spline Driven Animation

    DEFF Research Database (Denmark)

    Erleben, Kenny; Henriksen, Knud


    In this paper we will take a close look at the details and technicalities in applying spline driven animation to scripted bodies in the context of dynamic simulation. The main contributions presented in this paper are methods for computing velocities and accelerations in the time domain of the sp......In this paper we will take a close look at the details and technicalities in applying spline driven animation to scripted bodies in the context of dynamic simulation. The main contributions presented in this paper are methods for computing velocities and accelerations in the time domain...

  18. Schwarz and multilevel methods for quadratic spline collocation

    Energy Technology Data Exchange (ETDEWEB)

    Christara, C.C. [Univ. of Toronto, Ontario (Canada); Smith, B. [Univ. of California, Los Angeles, CA (United States)


    Smooth spline collocation methods offer an alternative to Galerkin finite element methods, as well as to Hermite spline collocation methods, for the solution of linear elliptic Partial Differential Equations (PDEs). Recently, optimal order of convergence spline collocation methods have been developed for certain degree splines. Convergence proofs for smooth spline collocation methods are generally more difficult than for Galerkin finite elements or Hermite spline collocation, and they require stronger assumptions and more restrictions. However, numerical tests indicate that spline collocation methods are applicable to a wider class of problems, than the analysis requires, and are very competitive to finite element methods, with respect to efficiency. The authors will discuss Schwarz and multilevel methods for the solution of elliptic PDEs using quadratic spline collocation, and compare these with domain decomposition methods using substructuring. Numerical tests on a variety of parallel machines will also be presented. In addition, preliminary convergence analysis using Schwarz and/or maximum principle techniques will be presented.

  19. Stabilized Discretization in Spline Element Method for Solution of Two-Dimensional Navier-Stokes Problems

    Directory of Open Access Journals (Sweden)

    Neng Wan


    Full Text Available In terms of the poor geometric adaptability of spline element method, a geometric precision spline method, which uses the rational Bezier patches to indicate the solution domain, is proposed for two-dimensional viscous uncompressed Navier-Stokes equation. Besides fewer pending unknowns, higher accuracy, and computation efficiency, it possesses such advantages as accurate representation of isogeometric analysis for object boundary and the unity of geometry and analysis modeling. Meanwhile, the selection of B-spline basis functions and the grid definition is studied and a stable discretization format satisfying inf-sup conditions is proposed. The degree of spline functions approaching the velocity field is one order higher than that approaching pressure field, and these functions are defined on one-time refined grid. The Dirichlet boundary conditions are imposed through the Nitsche variational principle in weak form due to the lack of interpolation properties of the B-splines functions. Finally, the validity of the proposed method is verified with some examples.

  20. Modeling positional effects of regulatory sequences with spline transformations increases prediction accuracy of deep neural networks. (United States)

    Avsec, Žiga; Barekatain, Mohammadamin; Cheng, Jun; Gagneur, Julien


    Regulatory sequences are not solely defined by their nucleic acid sequence but also by their relative distances to genomic landmarks such as transcription start site, exon boundaries, or polyadenylation site. Deep learning has become the approach of choice for modeling regulatory sequences because of its strength to learn complex sequence features. However, modeling relative distances to genomic landmarks in deep neural networks has not been addressed. Here we developed spline transformation, a neural network module based on splines to flexibly and robustly model distances. Modeling distances to various genomic landmarks with spline transformations significantly increased state-of-the-art prediction accuracy of in vivo RNA-binding protein binding sites for 120 out of 123 proteins. We also developed a deep neural network for human splice branchpoint based on spline transformations that outperformed the current best, already distance-based, machine learning model. Compared to piecewise linear transformation, as obtained by composition of rectified linear units, spline transformation yields higher prediction accuracy as well as faster and more robust training. As spline transformation can be applied to further quantities beyond distances, such as methylation or conservation, we foresee it as a versatile component in the genomics deep learning toolbox. Spline transformation is implemented as a Keras layer in the CONCISE python package: Analysis code is available at; Supplementary data are available at Bioinformatics online. © The Author(s) 2017. Published by Oxford University Press.

  1. Prospects of approach and characterization of Mar del Plata peri-urban, Argentina

    Directory of Open Access Journals (Sweden)

    Rosana Ferraro


    Full Text Available In Latin America in general, and in Argentina in particular, city growth without prior planning results in the formation of highly complex peri-urban areas. The urban-rural analysis based on the traditional model of country-city dichotomy is not enough to explain the processes that occur in these cities. On the basis of prior studies conducted in the peri- urban of Mar del Plata, Argentina, this paper aims to : a characterize the peri-urban by studying its functions throughout history, b propose a rereading for its further analysis through the complex systems theoretical-methodological approach, and c describe the main areas that account for its special heterogeneity and complexity. From an integral viewpoint, and taking the physical, sociocultural, productive, urban- residential and digester subsystems into account, the analysis of the peri-urban allowed to define areas with differential characteristics. Such areas admit higher disintegration in more detailed scales, making it easy to understand their operation and their problems. In conclusion, the complex systems approach results appropriate to promote the development of management strategies in areas as heterogeneous as the peri-urban.

  2. Limit Stress Spline Models for GRP Composites | Ihueze | Nigerian ...

    African Journals Online (AJOL)

    Spline functions were established on the assumption of three intervals and fitting of quadratic and cubic splines to critical stress-strain responses data. Quadratic ... of data points. Spline model is therefore recommended as it evaluates the function at subintervals, eliminating the error associated with wide range interpolation.

  3. The use of splines to analyze scanning tunneling microscopy data

    NARCIS (Netherlands)

    Wormeester, Herbert; Kip, Gerhardus A.M.; Sasse, A.G.B.M.; van Midden, H.J.P.


    Scanning tunneling microscopy (STM) requires a two‐dimensional (2D) image displaying technique for its interpretation. The flexibility and global approximation properties of splines, characteristic of a solid data reduction method as known from cubic spline interpolation, is called for. Splines were

  4. An Accelerated Development, Reduced Cost Approach to Lunar/Mars Exploration Using a Modular NTR-Based Space Transportation System (United States)

    Borowski, S.; Clark, J.; Sefcik, R.; Corban, R.; Alexander, S.


    ' NTR-based moon/Mars STS, examines performance sensitivities resulting from different 'mission mode' assumptions, and quantifies potential schedule and cost benefits resulting from this modular moon/Mars NTR vehicle approach.


    African Journals Online (AJOL)

    ES OBE

    Department of Mechanical Engineering, Anambra State. University of Science and Technology, Uli ... 12 were established. The optimization of quadratic and cubic models by gradient search optimization gave the critical strain as 0.024, .... 2.2.1 Derivation of Cubic Spline Equation. The basic assumptions to be used are: 1.

  6. Weighted thin-plate spline image denoising

    Czech Academy of Sciences Publication Activity Database

    Kašpar, Roman; Zitová, Barbara


    Roč. 36, č. 12 (2003), s. 3027-3030 ISSN 0031-3203 R&D Projects: GA ČR GP102/01/P065 Institutional research plan: CEZ:AV0Z1075907 Keywords : image denoising * thin-plate splines Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.611, year: 2003

  7. Evolvable Mars Campaign Long Duration Habitation Strategies: Architectural Approaches to Enable Human Exploration Missions (United States)

    Simon, Matthew A.; Toups, Larry; Howe, A. Scott; Wald, Samuel I.


    The Evolvable Mars Campaign (EMC) is the current NASA Mars mission planning effort which seeks to establish sustainable, realistic strategies to enable crewed Mars missions in the mid-2030s timeframe. The primary outcome of the Evolvable Mars Campaign is not to produce "The Plan" for sending humans to Mars, but instead its intent is to inform the Human Exploration and Operations Mission Directorate near-term key decisions and investment priorities to prepare for those types of missions. The FY'15 EMC effort focused upon analysis of integrated mission architectures to identify technically appealing transportation strategies, logistics build-up strategies, and vehicle designs for reaching and exploring Mars moons and Mars surface. As part of the development of this campaign, long duration habitats are required which are capable of supporting crew with limited resupply and crew abort during the Mars transit, Mars moons, and Mars surface segments of EMC missions. In particular, the EMC design team sought to design a single, affordable habitation system whose manufactured units could be outfitted uniquely for each of these missions and reused for multiple crewed missions. This habitat system must provide all of the functionality to safely support 4 crew for long durations while meeting mass and volume constraints for each of the mission segments set by the chosen transportation architecture and propulsion technologies. This paper describes several proposed long-duration habitation strategies to enable the Evolvable Mars Campaign through improvements in mass, cost, and reusability, and presents results of analysis to compare the options and identify promising solutions. The concepts investigated include several monolithic concepts: monolithic clean sheet designs, and concepts which leverage the co-manifested payload capability of NASA's Space Launch System (SLS) to deliver habitable elements within the Universal Payload Adaptor between the SLS upper stage and the Orion

  8. Gearbox Reliability Collaborative Analytic Formulation for the Evaluation of Spline Couplings

    Energy Technology Data Exchange (ETDEWEB)

    Guo, Yi [National Renewable Energy Lab. (NREL), Golden, CO (United States); Keller, Jonathan [National Renewable Energy Lab. (NREL), Golden, CO (United States); Errichello, Robert [GEARTECH, Houston, TX (United States); Halse, Chris [Romax Technology, Nottingham (United Kingdom)


    Gearboxes in wind turbines have not been achieving their expected design life; however, they commonly meet and exceed the design criteria specified in current standards in the gear, bearing, and wind turbine industry as well as third-party certification criteria. The cost of gearbox replacements and rebuilds, as well as the down time associated with these failures, has elevated the cost of wind energy. The National Renewable Energy Laboratory (NREL) Gearbox Reliability Collaborative (GRC) was established by the U.S. Department of Energy in 2006; its key goal is to understand the root causes of premature gearbox failures and improve their reliability using a combined approach of dynamometer testing, field testing, and modeling. As part of the GRC program, this paper investigates the design of the spline coupling often used in modern wind turbine gearboxes to connect the planetary and helical gear stages. Aside from transmitting the driving torque, another common function of the spline coupling is to allow the sun to float between the planets. The amount the sun can float is determined by the spline design and the sun shaft flexibility subject to the operational loads. Current standards address spline coupling design requirements in varying detail. This report provides additional insight beyond these current standards to quickly evaluate spline coupling designs.

  9. Review of NASA approach to space radiation risk assessments for Mars exploration. (United States)

    Cucinotta, Francis A


    Long duration space missions present unique radiation protection challenges due to the complexity of the space radiation environment, which includes high charge and energy particles and other highly ionizing radiation such as neutrons. Based on a recommendation by the National Council on Radiation Protection and Measurements, a 3% lifetime risk of exposure-induced death for cancer has been used as a basis for risk limitation by the National Aeronautics and Space Administration (NASA) for low-Earth orbit missions. NASA has developed a risk-based approach to radiation exposure limits that accounts for individual factors (age, gender, and smoking history) and assesses the uncertainties in risk estimates. New radiation quality factors with associated probability distribution functions to represent the quality factor's uncertainty have been developed based on track structure models and recent radiobiology data for high charge and energy particles. The current radiation dose limits are reviewed for spaceflight and the various qualitative and quantitative uncertainties that impact the risk of exposure-induced death estimates using the NASA Space Cancer Risk (NSCR) model. NSCR estimates of the number of "safe days" in deep space to be within exposure limits and risk estimates for a Mars exploration mission are described.

  10. Drilling on the Moon and Mars: Developing the Science Approach for Subsurface Exploration with Human Crews (United States)

    Stoker, C. R.; Zavaleta, J.; Bell, M.; Direto, S.; Foing, B.; Blake, D.; Kim, S.


    DOMEX (Drilling on the Moon and Mars in Human Exploration) is using analog missions to develop the approach for using human crews to perform science activities on the Moon and Mars involving exploration and sampling of the subsurface. Subsurface science is an important activity that may be uniquely enabled by human crews. DOMEX provides an opportunity to plan and execute planetary mission science activities without the expense and overhead of a planetary mission. Objectives: The objective of this first in a series of DOMEX missions were to 1) explore the regional area to understand the geologic context and determine stratigraphy and geologic history of various geologic units in the area. 2) Explore for and characterize sites for deploying a deep (10 m depth) drilling system in a subsequent field season. 3) Perform GPR on candidate drill sites. 4) Select sites that represent different geological units deposited in different epochs and collect soil cores using sterile procedures for mineralogical, organic and biological analysis. 5) Operate the MUM in 3 different sites representing different geological units and soil characteristics. 6) Collect rock and soil samples of sites visited and analyze them at the habitat. Results: At mission start the crew performed a regional survey to identify major geologic units that were correlated to recognized stratigraphy and regional geologic maps. Several candidate drill sites were identified. During the rest of the mission, successful GPR surveys were conducted in four locations. Soil cores were collected in 5 locations representing soils from 4 different geologic units, to depths up to 1m. Soil cores from two locations were analyzed with PCR in the laboratory. The remainder were reserved for subsequent analysis. XRD analysis was performed in the habitat and in the field on 39 samples, to assist with sample characterization, conservation, and archiving. MUM was deployed at 3 field locations and 1 test location (outside the

  11. B-spline design of digital FIR filter using evolutionary computation techniques (United States)

    Swain, Manorama; Panda, Rutuparna


    In the forth coming era, digital filters are becoming a true replacement for the analog filter designs. Here in this paper we examine a design method for FIR filter using global search optimization techniques known as Evolutionary computation via genetic algorithm and bacterial foraging, where the filter design considered as an optimization problem. In this paper, an effort is made to design the maximally flat filters using generalized B-spline window. The key to our success is the fact that the bandwidth of the filer response can be modified by changing tuning parameters incorporated well within the B-spline function. This is an optimization problem. Direct approach has been deployed to design B-spline window based FIR digital filters. Four parameters (order, width, length and tuning parameter) have been optimized by using GA and EBFS. It is observed that the desired response can be obtained with lower order FIR filters with optimal width and tuning parameters.

  12. Cubic B-spline calibration for 3D super-resolution measurements using astigmatic imaging. (United States)

    Proppert, Sven; Wolter, Steve; Holm, Thorge; Klein, Teresa; van de Linde, Sebastian; Sauer, Markus


    In recent years three-dimensional (3D) super-resolution fluorescence imaging by single-molecule localization (localization microscopy) has gained considerable interest because of its simple implementation and high optical resolution. Astigmatic and biplane imaging are experimentally simple methods to engineer a 3D-specific point spread function (PSF), but existing evaluation methods have proven problematic in practical application. Here we introduce the use of cubic B-splines to model the relationship of axial position and PSF width in the above mentioned approaches and compare the performance with existing methods. We show that cubic B-splines are the first method that can combine precision, accuracy and simplicity.

  13. Analyzing Single Molecule Localization Microscopy Data Using Cubic Splines. (United States)

    Babcock, Hazen P; Zhuang, Xiaowei


    The resolution of super-resolution microscopy based on single molecule localization is in part determined by the accuracy of the localization algorithm. In most published approaches to date this localization is done by fitting an analytical function that approximates the point spread function (PSF) of the microscope. However, particularly for localization in 3D, analytical functions such as a Gaussian, which are computationally inexpensive, may not accurately capture the PSF shape leading to reduced fitting accuracy. On the other hand, analytical functions that can accurately capture the PSF shape, such as those based on pupil functions, can be computationally expensive. Here we investigate the use of cubic splines as an alternative fitting approach. We demonstrate that cubic splines can capture the shape of any PSF with high accuracy and that they can be used for fitting the PSF with only a 2-3x increase in computation time as compared to Gaussian fitting. We provide an open-source software package that measures the PSF of any microscope and uses the measured PSF to perform 3D single molecule localization microscopy analysis with reasonable accuracy and speed.

  14. neoPASCAL: A Cubesat-based approach to validate Mars GCMs using a network of landed sensors (United States)

    Moores, John; Podmore, Hugh; Lee, Regina S. K.; Haberle, Robert


    Beginning in the 1990s, concepts for a network of 15-20 small (12.8 kg) landers to measure surface pressure across Mars were proposed (Merrihew et al., 1996). Such distributed measurements were seen as particularly valuable as they held the promise of validating Mars Global Circulation Models (GCMs), for which the diurnal and seasonal variations in surface pressure may be diagnostically related to atmospheric parameters (Haberle et al., 1996). MicroMET, later renamed PASCAL, was a Discovery contender, however, the total mass required for the 20 landers and a support orbiter presented a challenge compared to the delivered science.In the 20 years since this concept originated, miniaturization of spacecraft systems, sensors and components has made substantial progress. Several small planetary science spacecraft based on the CubeSat design approach will launch in the next few years. Yet, only one meteorological station (REMS) currently operates on the surface of Mars. Meanwhile, the output from atmospheric models have become ever more critical for understanding key Martian geological processes including volatile transport, identifying the extent and persistence of surface brines, understanding the sources and sinks of methane and investigating the past climate of Mars, to name only a few areas.As such, it is time to reconsider the PASCAL concept. We find that modern equipment opens up payload space in the original 12.8 kg entry-vehicles from 23 g to nearly 1 kg, sufficient for adding small imagers, spectrometers and other additional or alternate payloads to examine atmosphere and surface over a wide geographic range of settings. If, instead, we seek the minimum solution for spacecraft mass, we find that a pressure-sensing vehicle would mass < 250 g at entry making these spacecraft appealing secondary payloads for future Mars missions.

  15. Some splines produced by smooth interpolation

    Czech Academy of Sciences Publication Activity Database

    Segeth, Karel


    Roč. 319, 15 February (2018), s. 387-394 ISSN 0096-3003 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : smooth data approximation * smooth data interpolation * cubic spline Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.738, year: 2016 http://www. science science /article/pii/S0096300317302746?via%3Dihub

  16. Some splines produced by smooth interpolation

    Czech Academy of Sciences Publication Activity Database

    Segeth, Karel


    Roč. 319, 15 February (2018), s. 387-394 ISSN 0096-3003 R&D Projects: GA ČR GA14-02067S Institutional support: RVO:67985840 Keywords : smooth data approximation * smooth data interpolation * cubic spline Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 1.738, year: 2016

  17. Application of multivariate splines to discrete mathematics


    Xu, Zhiqiang


    Using methods developed in multivariate splines, we present an explicit formula for discrete truncated powers, which are defined as the number of non-negative integer solutions of linear Diophantine equations. We further use the formula to study some classical problems in discrete mathematics as follows. First, we extend the partition function of integers in number theory. Second, we exploit the relation between the relative volume of convex polytopes and multivariate truncated powers and giv...

  18. A unified metabolism for Mars: A new approach developed from research on extraterrestrial life detection by enzymatically induced exchange of O 18 (United States)


    A general graded life detection approach ranging from environmental and in situ observations to specific metabolic experiments on Mars is reported. A zero dead volume leak and computer mediated data acquisition system is also discussed. Soil analyses were also conducted.

  19. A Rigid Mid-Lift-to-Drag Ratio Approach to Human Mars Entry, Descent, and Landing (United States)

    Cerimele, Christopher J.; Robertson, Edward A.; Sostaric, Ronald R.; Campbell, Charles H.; Robinson, Phil; Matz, Daniel A.; Johnson, Breanna J.; Stachowiak, Susan J.; Garcia, Joseph A.; Bowles, Jeffrey V.; hide


    Current NASA Human Mars architectures require delivery of approximately 20 metric tons of cargo to the surface in a single landing. A proposed vehicle type for performing the entry, descent, and landing at Mars associated with this architecture is a rigid, enclosed, elongated lifting body shape that provides a higher lift-to-drag ratio (L/D) than a typical entry capsule, but lower than a typical winged entry vehicle (such as the Space Shuttle Orbiter). A rigid Mid-L/D shape has advantages for large mass Mars EDL, including loads management, range capability during entry, and human spaceflight heritage. Previous large mass Mars studies have focused more on symmetric and/or circular cross-section Mid-L/D shapes such as the ellipsled. More recent work has shown performance advantages for non-circular cross section shapes. This paper will describe efforts to design a rigid Mid-L/D entry vehicle for Mars which shows mass and performance improvements over previous Mid-L/D studies. The proposed concept, work to date and evolution, forward path, and suggested future strategy are described.

  20. PM10 modeling in the Oviedo urban area (Northern Spain) by using multivariate adaptive regression splines (United States)

    Nieto, Paulino José García; Antón, Juan Carlos Álvarez; Vilán, José Antonio Vilán; García-Gonzalo, Esperanza


    The aim of this research work is to build a regression model of the particulate matter up to 10 micrometers in size (PM10) by using the multivariate adaptive regression splines (MARS) technique in the Oviedo urban area (Northern Spain) at local scale. This research work explores the use of a nonparametric regression algorithm known as multivariate adaptive regression splines (MARS) which has the ability to approximate the relationship between the inputs and outputs, and express the relationship mathematically. In this sense, hazardous air pollutants or toxic air contaminants refer to any substance that may cause or contribute to an increase in mortality or serious illness, or that may pose a present or potential hazard to human health. To accomplish the objective of this study, the experimental dataset of nitrogen oxides (NOx), carbon monoxide (CO), sulfur dioxide (SO2), ozone (O3) and dust (PM10) were collected over 3 years (2006-2008) and they are used to create a highly nonlinear model of the PM10 in the Oviedo urban nucleus (Northern Spain) based on the MARS technique. One main objective of this model is to obtain a preliminary estimate of the dependence between PM10 pollutant in the Oviedo urban area at local scale. A second aim is to determine the factors with the greatest bearing on air quality with a view to proposing health and lifestyle improvements. The United States National Ambient Air Quality Standards (NAAQS) establishes the limit values of the main pollutants in the atmosphere in order to ensure the health of healthy people. Firstly, this MARS regression model captures the main perception of statistical learning theory in order to obtain a good prediction of the dependence among the main pollutants in the Oviedo urban area. Secondly, the main advantages of MARS are its capacity to produce simple, easy-to-interpret models, its ability to estimate the contributions of the input variables, and its computational efficiency. Finally, on the basis of

  1. Solving Buckmaster equation using cubic B-spline and cubic trigonometric B-spline collocation methods (United States)

    Chanthrasuwan, Maveeka; Asri, Nur Asreenawaty Mohd; Hamid, Nur Nadiah Abd; Majid, Ahmad Abd.; Azmi, Amirah


    The cubic B-spline and cubic trigonometric B-spline functions are used to set up the collocation in finding solutions for the Buckmaster equation. These splines are applied as interpolating functions in the spatial dimension while the finite difference method (FDM) is used to discretize the time derivative. The Buckmaster equation is linearized using Taylor's expansion and solved using two schemes, namely Crank-Nicolson and fully implicit. The von Neumann stability analysis is carried out on the two schemes and they are shown to be conditionally stable. In order to demonstrate the capability of the schemes, some problems are solved and compared with analytical and FDM solutions. The proposed methods are found to generate more accurate results than the FDM.

  2. PSPLINE: Princeton Spline and Hermite cubic interpolation routines (United States)

    McCune, Doug


    PSPLINE is a collection of Spline and Hermite interpolation tools for 1D, 2D, and 3D datasets on rectilinear grids. Spline routines give full control over boundary conditions, including periodic, 1st or 2nd derivative match, or divided difference-based boundary conditions on either end of each grid dimension. Hermite routines take the function value and derivatives at each grid point as input, giving back a representation of the function between grid points. Routines are provided for creating Hermite datasets, with appropriate boundary conditions applied. The 1D spline and Hermite routines are based on standard methods; the 2D and 3D spline or Hermite interpolation functions are constructed from 1D spline or Hermite interpolation functions in a straightforward manner. Spline and Hermite interpolation functions are often much faster to evaluate than other representations using e.g. Fourier series or otherwise involving transcendental functions.

  3. Intensity-based hierarchical elastic registration using approximating splines. (United States)

    Serifovic-Trbalic, Amira; Demirovic, Damir; Cattin, Philippe C


    We introduce a new hierarchical approach for elastic medical image registration using approximating splines. In order to obtain the dense deformation field, we employ Gaussian elastic body splines (GEBS) that incorporate anisotropic landmark errors and rotation information. Since the GEBS approach is based on a physical model in form of analytical solutions of the Navier equation, it can very well cope with the local as well as global deformations present in the images by varying the standard deviation of the Gaussian forces. The proposed GEBS approximating model is integrated into the elastic hierarchical image registration framework, which decomposes a nonrigid registration problem into numerous local rigid transformations. The approximating GEBS registration scheme incorporates anisotropic landmark errors as well as rotation information. The anisotropic landmark localization uncertainties can be estimated directly from the image data, and in this case, they represent the minimal stochastic localization error, i.e., the Cramér-Rao bound. The rotation information of each landmark obtained from the hierarchical procedure is transposed in an additional angular landmark, doubling the number of landmarks in the GEBS model. The modified hierarchical registration using the approximating GEBS model is applied to register 161 image pairs from a digital mammogram database. The obtained results are very encouraging, and the proposed approach significantly improved all registrations comparing the mean-square error in relation to approximating TPS with the rotation information. On artificially deformed breast images, the newly proposed method performed better than the state-of-the-art registration algorithm introduced by Rueckert et al. (IEEE Trans Med Imaging 18:712-721, 1999). The average error per breast tissue pixel was less than 2.23 pixels compared to 2.46 pixels for Rueckert's method. The proposed hierarchical elastic image registration approach incorporates the GEBS

  4. Higher-order numerical solutions using cubic splines (United States)

    Rubin, S. G.; Khosla, P. K.


    A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for several model problems.

  5. Image edges detection through B-Spline filters

    International Nuclear Information System (INIS)

    Mastropiero, D.G.


    B-Spline signal processing was used to detect the edges of a digital image. This technique is based upon processing the image in the Spline transform domain, instead of doing so in the space domain (classical processing). The transformation to the Spline transform domain means finding out the real coefficients that makes it possible to interpolate the grey levels of the original image, with a B-Spline polynomial. There exist basically two methods of carrying out this interpolation, which produces the existence of two different Spline transforms: an exact interpolation of the grey values (direct Spline transform), and an approximated interpolation (smoothing Spline transform). The latter results in a higher smoothness of the gray distribution function defined by the Spline transform coefficients, and is carried out with the aim of obtaining an edge detection algorithm which higher immunity to noise. Finally the transformed image was processed in order to detect the edges of the original image (the gradient method was used), and the results of the three methods (classical, direct Spline transform and smoothing Spline transform) were compared. The results were that, as expected, the smoothing Spline transform technique produced a detection algorithm more immune to external noise. On the other hand the direct Spline transform technique, emphasizes more the edges, even more than the classical method. As far as the consuming time is concerned, the classical method is clearly the fastest one, and may be applied whenever the presence of noise is not important, and whenever edges with high detail are not required in the final image. (author). 9 refs., 17 figs., 1 tab

  6. Mars Colony: Using Role-Play as a Pedagogical Approach to Teaching Science (United States)

    Dolenc, Nathan; Wood, Aja; Soldan, Katie; Tai, Robert H.


    In this article, the authors discuss role-play as a pedagogical strategy to engage kindergarten and first-grade students in science and engineering. They present a five-part Mars colony lesson that they developed for a blended class, during which students role-play a space-exploration story that enables them to gain a firsthand perspective of what…

  7. Optimal Approximation of Biquartic Polynomials by Bicubic Splines (United States)

    Kačala, Viliam; Török, Csaba


    Recently an unexpected approximation property between polynomials of degree three and four was revealed within the framework of two-part approximation models in 2-norm, Chebyshev norm and Holladay seminorm. Namely, it was proved that if a two-component cubic Hermite spline's first derivative at the shared knot is computed from the first derivative of a quartic polynomial, then the spline is a clamped spline of class C2 and also the best approximant to the polynomial. Although it was known that a 2 × 2 component uniform bicubic Hermite spline is a clamped spline of class C2 if the derivatives at the shared knots are given by the first derivatives of a biquartic polynomial, the optimality of such approximation remained an open question. The goal of this paper is to resolve this problem. Unlike the spline curves, in the case of spline surfaces it is insufficient to suppose that the grid should be uniform and the spline derivatives computed from a biquartic polynomial. We show that the biquartic polynomial coefficients have to satisfy some additional constraints to achieve optimal approximation by bicubic splines.

  8. Recursive B-spline approximation using the Kalman filter

    Directory of Open Access Journals (Sweden)

    Jens Jauch


    Full Text Available This paper proposes a novel recursive B-spline approximation (RBA algorithm which approximates an unbounded number of data points with a B-spline function and achieves lower computational effort compared with previous algorithms. Conventional recursive algorithms based on the Kalman filter (KF restrict the approximation to a bounded and predefined interval. Conversely RBA includes a novel shift operation that enables to shift estimated B-spline coefficients in the state vector of a KF. This allows to adapt the interval in which the B-spline function can approximate data points during run-time.

  9. Gaussian quadrature for splines via homotopy continuation: Rules for C2 cubic splines

    KAUST Repository

    Barton, Michael


    We introduce a new concept for generating optimal quadrature rules for splines. To generate an optimal quadrature rule in a given (target) spline space, we build an associated source space with known optimal quadrature and transfer the rule from the source space to the target one, while preserving the number of quadrature points and therefore optimality. The quadrature nodes and weights are, considered as a higher-dimensional point, a zero of a particular system of polynomial equations. As the space is continuously deformed by changing the source knot vector, the quadrature rule gets updated using polynomial homotopy continuation. For example, starting with C1C1 cubic splines with uniform knot sequences, we demonstrate the methodology by deriving the optimal rules for uniform C2C2 cubic spline spaces where the rule was only conjectured to date. We validate our algorithm by showing that the resulting quadrature rule is independent of the path chosen between the target and the source knot vectors as well as the source rule chosen.

  10. Survival estimation through the cumulative hazard function with monotone natural cubic splines. (United States)

    Bantis, Leonidas E; Tsimikas, John V; Georgiou, Stelios D


    In this paper we explore the estimation of survival probabilities via a smoothed version of the survival function, in the presence of censoring. We investigate the fit of a natural cubic spline on the cumulative hazard function under appropriate constraints. Under the proposed technique the problem reduces to a restricted least squares one, leading to convex optimization. The approach taken in this paper is evaluated and compared via simulations to other known methods such as the Kaplan Meier and the logspline estimator. Our approach is easily extended to address estimation of survival probabilities in the presence of covariates when the proportional hazards model assumption holds. In this case the method is compared to a restricted cubic spline approach that involves maximum likelihood. The proposed approach can be also adjusted to accommodate left censoring.

  11. Two Dimensional Complex Wavenumber Dispersion Analysis using B-Spline Finite Elements Method

    Directory of Open Access Journals (Sweden)

    Y. Mirbagheri


    Full Text Available  Grid dispersion is one of the criteria of validating the finite element method (FEM in simulating acoustic or elastic wave propagation. The difficulty usually arisen when using this method for simulation of wave propagation problems, roots in the discontinuous field which causes the magnitude and the direction of the wave speed vector, to vary from one element to the adjacent one. To solve this problem and improve the response accuracy, two approaches are usually suggested: changing the integration method and changing shape functions. The Finite Element iso-geometric analysis (IGA is used in this research. In the IGA, the B-spline or non-uniform rational B-spline (NURBS functions are used which improve the response accuracy, especially in one-dimensional structural dynamics problems. At the boundary of two adjacent elements, the degree of continuity of the shape functions used in IGA can be higher than zero. In this research, for the first time, a two dimensional grid dispersion analysis has been used for wave propagation in plane strain problems using B-spline FEM is presented. Results indicate that, for the same degree of freedom, the grid dispersion of B-spline FEM is about half of the grid dispersion of the classic FEM.

  12. Trajectory control of an articulated robot with a parallel drive arm based on splines under tension (United States)

    Yi, Seung-Jong

    Today's industrial robots controlled by mini/micro computers are basically simple positioning devices. The positioning accuracy depends on the mathematical description of the robot configuration to place the end-effector at the desired position and orientation within the workspace and on following the specified path which requires the trajectory planner. In addition, the consideration of joint velocity, acceleration, and jerk trajectories are essential for trajectory planning of industrial robots to obtain smooth operation. The newly designed 6 DOF articulated robot with a parallel drive arm mechanism which permits the joint actuators to be placed in the same horizontal line to reduce the arm inertia and to increase load capacity and stiffness is selected. First, the forward kinematic and inverse kinematic problems are examined. The forward kinematic equations are successfully derived based on Denavit-Hartenberg notation with independent joint angle constraints. The inverse kinematic problems are solved using the arm-wrist partitioned approach with independent joint angle constraints. Three types of curve fitting methods used in trajectory planning, i.e., certain degree polynomial functions, cubic spline functions, and cubic spline functions under tension, are compared to select the best possible method to satisfy both smooth joint trajectories and positioning accuracy for a robot trajectory planner. Cubic spline functions under tension is the method selected for the new trajectory planner. This method is implemented for a 6 DOF articulated robot with a parallel drive arm mechanism to improve the smoothness of the joint trajectories and the positioning accuracy of the manipulator. Also, this approach is compared with existing trajectory planners, 4-3-4 polynomials and cubic spline functions, via circular arc motion simulations. The new trajectory planner using cubic spline functions under tension is implemented into the microprocessor based robot controller and

  13. Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines. (United States)

    Grajeda, Laura M; Ivanescu, Andrada; Saito, Mayuko; Crainiceanu, Ciprian; Jaganath, Devan; Gilman, Robert H; Crabtree, Jean E; Kelleher, Dermott; Cabrera, Lilia; Cama, Vitaliano; Checkley, William


    Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p linear regression equation for both estimation and prediction of population- and individual-level growth in height. We show that cubic regression splines are superior to linear regression splines for the case of a small number of knots in both estimation and prediction with the full linear mixed effect model (AIC 19,352 vs. 19,598, respectively). While the regression parameters are more complex to interpret in the former, we argue that inference for any problem depends more on the estimated curve or differences in curves rather

  14. Piecewise linear regression splines with hyperbolic covariates

    International Nuclear Information System (INIS)

    Cologne, John B.; Sposto, Richard


    Consider the problem of fitting a curve to data that exhibit a multiphase linear response with smooth transitions between phases. We propose substituting hyperbolas as covariates in piecewise linear regression splines to obtain curves that are smoothly joined. The method provides an intuitive and easy way to extend the two-phase linear hyperbolic response model of Griffiths and Miller and Watts and Bacon to accommodate more than two linear segments. The resulting regression spline with hyperbolic covariates may be fit by nonlinear regression methods to estimate the degree of curvature between adjoining linear segments. The added complexity of fitting nonlinear, as opposed to linear, regression models is not great. The extra effort is particularly worthwhile when investigators are unwilling to assume that the slope of the response changes abruptly at the join points. We can also estimate the join points (the values of the abscissas where the linear segments would intersect if extrapolated) if their number and approximate locations may be presumed known. An example using data on changing age at menarche in a cohort of Japanese women illustrates the use of the method for exploratory data analysis. (author)

  15. BS Methods: A New Class of Spline Collocation BVMs (United States)

    Mazzia, Francesca; Sestini, Alessandra; Trigiante, Donato


    BS methods are a recently introduced class of Boundary Value Methods which is based on B-splines. They can also be interpreted as spline collocation methods. For uniform meshes, the coefficients defining the k-step BS method are just the values of the (k+1)-degree uniform B-spline and B-spline derivative at its integer active knots; for general nonuniform meshes they are computed by solving local linear systems whose dimension depends on k. An important specific feature of BS methods is the possibility to associate a spline of degree k+1 and smoothness Ck to the numerical solution produced by the k-step method of this class. Such spline collocates the differential equation at the knots, shares the convergence order with the numerical solution, and can be computed with negligible additional computational cost. Here a survey on such methods is given, presenting the general definition, the convergence and stability features, and introducing the strategy for the computation of the coefficients in the B-spline basis which define the associated spline. Finally, some related numerical results are also presented.

  16. Color management with a hammer: the B-spline fitter (United States)

    Bell, Ian E.; Liu, Bonny H. P.


    To paraphrase Abraham Maslow: If the only tool you have is a hammer, every problem looks like a nail. We have a B-spline fitter customized for 3D color data, and many problems in color management can be solved with this tool. Whereas color devices were once modeled with extensive measurement, look-up tables and trilinear interpolation, recent improvements in hardware have made B-spline models an affordable alternative. Such device characterizations require fewer color measurements than piecewise linear models, and have uses beyond simple interpolation. A B-spline fitter, for example, can act as a filter to remove noise from measurements, leaving a model with guaranteed smoothness. Inversion of the device model can then be carried out consistently and efficiently, as the spline model is well behaved and its derivatives easily computed. Spline-based algorithms also exist for gamut mapping, the composition of maps, and the extrapolation of a gamut. Trilinear interpolation---a degree-one spline---can still be used after nonlinear spline smoothing for high-speed evaluation with robust convergence. Using data from several color devices, this paper examines the use of B-splines as a generic tool for modeling devices and mapping one gamut to another, and concludes with applications to high-dimensional and spectral data.

  17. About some properties of bivariate splines with shape parameters (United States)

    Caliò, F.; Marchetti, E.


    The paper presents and proves geometrical properties of a particular bivariate function spline, built and algorithmically implemented in previous papers. The properties typical of this family of splines impact the field of computer graphics in particular that of the reverse engineering.

  18. Application of Semiparametric Spline Regression Model in Analyzing Factors that In uence Population Density in Central Java (United States)

    Sumantari, Y. D.; Slamet, I.; Sugiyanto


    Semiparametric regression is a statistical analysis method that consists of parametric and nonparametric regression. There are various approach techniques in nonparametric regression. One of the approach techniques is spline. Central Java is one of the most densely populated province in Indonesia. Population density in this province can be modeled by semiparametric regression because it consists of parametric and nonparametric component. Therefore, the purpose of this paper is to determine the factors that in uence population density in Central Java using the semiparametric spline regression model. The result shows that the factors which in uence population density in Central Java is Family Planning (FP) active participants and district minimum wage.

  19. Error bounds for two even degree tridiagonal splines

    Directory of Open Access Journals (Sweden)

    Gary W. Howell


    Full Text Available We study a C(1 parabolic and a C(2 quartic spline which are determined by solution of a tridiagonal matrix and which interpolate subinterval midpoints. In contrast to the cubic C(2 spline, both of these algorithms converge to any continuous function as the length of the largest subinterval goes to zero, regardless of “mesh ratios”. For parabolic splines, this convergence property was discovered by Marsden [1974]. The quartic spline introduced here achieves this convergence by choosing the second derivative zero at the breakpoints. Many of Marsden's bounds are substantially tightened here. We show that for functions of two or fewer coninuous derivatives the quartic spline is shown to give yet better bounds. Several of the bounds given here are optimal.

  20. A Risk-Constrained Multi-Stage Decision Making Approach to the Architectural Analysis of Mars Missions (United States)

    Kuwata, Yoshiaki; Pavone, Marco; Balaram, J. (Bob)


    This paper presents a novel risk-constrained multi-stage decision making approach to the architectural analysis of planetary rover missions. In particular, focusing on a 2018 Mars rover concept, which was considered as part of a potential Mars Sample Return campaign, we model the entry, descent, and landing (EDL) phase and the rover traverse phase as four sequential decision-making stages. The problem is to find a sequence of divert and driving maneuvers so that the rover drive is minimized and the probability of a mission failure (e.g., due to a failed landing) is below a user specified bound. By solving this problem for several different values of the model parameters (e.g., divert authority), this approach enables rigorous, accurate and systematic trade-offs for the EDL system vs. the mobility system, and, more in general, cross-domain trade-offs for the different phases of a space mission. The overall optimization problem can be seen as a chance-constrained dynamic programming problem, with the additional complexity that 1) in some stages the disturbances do not have any probabilistic characterization, and 2) the state space is extremely large (i.e, hundreds of millions of states for trade-offs with high-resolution Martian maps). To this purpose, we solve the problem by performing an unconventional combination of average and minimax cost analysis and by leveraging high efficient computation tools from the image processing community. Preliminary trade-off results are presented.


    Directory of Open Access Journals (Sweden)

    T. Dokken


    Full Text Available When viewed from distance, large parts of the topography of landmasses and the bathymetry of the sea and ocean floor can be regarded as a smooth background with local features. Consequently a digital elevation model combining a compact smooth representation of the background with locally added features has the potential of providing a compact and accurate representation for topography and bathymetry. The recent introduction of Locally Refined B-Splines (LR B-splines allows the granularity of spline representations to be locally adapted to the complexity of the smooth shape approximated. This allows few degrees of freedom to be used in areas with little variation, while adding extra degrees of freedom in areas in need of more modelling flexibility. In the EU fp7 Integrating Project IQmulus we exploit LR B-splines for approximating large point clouds representing bathymetry of the smooth sea and ocean floor. A drastic reduction is demonstrated in the bulk of the data representation compared to the size of input point clouds. The representation is very well suited for exploiting the power of GPUs for visualization as the spline format is transferred to the GPU and the triangulation needed for the visualization is generated on the GPU according to the viewing parameters. The LR B-splines are interoperable with other elevation model representations such as LIDAR data, raster representations and triangulated irregular networks as these can be used as input to the LR B-spline approximation algorithms. Output to these formats can be generated from the LR B-spline applications according to the resolution criteria required. The spline models are well suited for change detection as new sensor data can efficiently be compared to the compact LR B-spline representation.

  2. The Threat of Uncertainty: Why Using Traditional Approaches for Evaluating Spacecraft Reliability are Insufficient for Future Human Mars Missions (United States)

    Stromgren, Chel; Goodliff, Kandyce; Cirillo, William; Owens, Andrew


    Through the Evolvable Mars Campaign (EMC) study, the National Aeronautics and Space Administration (NASA) continues to evaluate potential approaches for sending humans beyond low Earth orbit (LEO). A key aspect of these missions is the strategy that is employed to maintain and repair the spacecraft systems, ensuring that they continue to function and support the crew. Long duration missions beyond LEO present unique and severe maintainability challenges due to a variety of factors, including: limited to no opportunities for resupply, the distance from Earth, mass and volume constraints of spacecraft, high sensitivity of transportation element designs to variation in mass, the lack of abort opportunities to Earth, limited hardware heritage information, and the operation of human-rated systems in a radiation environment with little to no experience. The current approach to maintainability, as implemented on ISS, which includes a large number of spares pre-positioned on ISS, a larger supply sitting on Earth waiting to be flown to ISS, and an on demand delivery of logistics from Earth, is not feasible for future deep space human missions. For missions beyond LEO, significant modifications to the maintainability approach will be required.Through the EMC evaluations, several key findings related to the reliability and safety of the Mars spacecraft have been made. The nature of random and induced failures presents significant issues for deep space missions. Because spare parts cannot be flown as needed for Mars missions, all required spares must be flown with the mission or pre-positioned. These spares must cover all anticipated failure modes and provide a level of overall reliability and safety that is satisfactory for human missions. This will require a large amount of mass and volume be dedicated to storage and transport of spares for the mission. Further, there is, and will continue to be, a significant amount of uncertainty regarding failure rates for spacecraft

  3. A low-cost approach to the exploration of Mars through a robotic technology demonstrator mission (United States)

    Ellery, Alex; Richter, Lutz; Parnell, John; Baker, Adam


    We present a proposed robotic mission to Mars—Vanguard—for the Aurora Arrow programme which combines an extensive technology demonstrator with a high scientific return. The novel aspect of this technology demonstrator is the demonstration of “water mining” capabilities for in situ resource utilisation (ISRU) in conjunction with high-value astrobiological investigation within a low-mass lander package of 70 kg. The basic architecture comprises a small lander, a micro-rover and a number of ground-penetrating moles. This basic architecture offers the possibility of testing a wide variety of generic technologies associated with space systems and planetary exploration. The architecture provides for the demonstration of specific technologies associated with planetary surface exploration, and with the Aurora programme specifically. Technology demonstration of ISRU will be a necessary precursor to any future human mission to Mars. Furthermore, its modest mass overhead allows the re-use of the already built Mars Express bus, making it a very low-cost option.

  4. Solving Dym equation using quartic B-spline and quartic trigonometric B-spline collocation methods (United States)

    Anuar, Hanis Safirah Saiful; Mafazi, Nur Hidayah; Hamid, Nur Nadiah Abd; Majid, Ahmad Abd.; Azmi, Amirah


    The nonlinear Dym equation is solved numerically using the quartic B-spline (QuBS) and quartic trigonometric B-spline (QuTBS) collocation methods. The QuBS and QuTBS are utilized as interpolating functions in the spatial dimension while the finite difference method (FDM) is applied to discretize the temporal space with the help of theta-weighted method. The nonlinear term in the Dym equation is linearized using Taylor's expansion. Two schemes are performed on both methods which are Crank-Nicolson and fully implicit. Applying the Von-Neumann stability analysis, these schemes are found to be conditionally stable. Several numerical examples of different forms are discussed and compared in term of errors with exact solutions and results from the FDM.

  5. Air quality modeling in the Oviedo urban area (NW Spain) by using multivariate adaptive regression splines. (United States)

    Nieto, P J García; Antón, J C Álvarez; Vilán, J A Vilán; García-Gonzalo, E


    The aim of this research work is to build a regression model of air quality by using the multivariate adaptive regression splines (MARS) technique in the Oviedo urban area (northern Spain) at a local scale. To accomplish the objective of this study, the experimental data set made up of nitrogen oxides (NO x ), carbon monoxide (CO), sulfur dioxide (SO2), ozone (O3), and dust (PM10) was collected over 3 years (2006-2008). The US National Ambient Air Quality Standards (NAAQS) establishes the limit values of the main pollutants in the atmosphere in order to ensure the health of healthy people. Firstly, this MARS regression model captures the main perception of statistical learning theory in order to obtain a good prediction of the dependence among the main pollutants in the Oviedo urban area. Secondly, the main advantages of MARS are its capacity to produce simple, easy-to-interpret models, its ability to estimate the contributions of the input variables, and its computational efficiency. Finally, on the basis of these numerical calculations, using the MARS technique, conclusions of this research work are exposed.

  6. A Novel Method for Gearbox Fault Detection Based on Biorthogonal B-spline Wavelet

    Directory of Open Access Journals (Sweden)

    Guangbin ZHANG


    Full Text Available Localized defects of gearbox tend to result in periodic impulses in the vibration signal, which contain important information for system dynamics analysis. So parameter identification of impulse provides an effective approach for gearbox fault diagnosis. Biorthogonal B-spline wavelet has the properties of compact support, high vanishing moment and symmetry, which are suitable to signal de-noising, fast calculation, and reconstruction. Thus, a novel time frequency distribution method is present for gear fault diagnosis by biorthogonal B-spline wavelet. Simulation study concerning singularity signal shows that this wavelet is effective in identifying the fault feature with coefficients map and coefficients line. Furthermore, an integrated approach consisting of wavelet decomposition, Hilbert transform and power spectrum density is used in applications. The results indicate that this method can extract the gearbox fault characteristics and diagnose the fault patterns effectively.

  7. A Generalized Approach to Model the Spectra and Radiation Dose Rate of Solar Particle Events on the Surface of Mars (United States)

    Guo, Jingnan; Zeitlin, Cary; Wimmer-Schweingruber, Robert F.; McDole, Thoren; Kühl, Patrick; Appel, Jan C.; Matthiä, Daniel; Krauss, Johannes; Köhler, Jan


    For future human missions to Mars, it is important to study the surface radiation environment during extreme and elevated conditions. In the long term, it is mainly galactic cosmic rays (GCRs) modulated by solar activity that contribute to the radiation on the surface of Mars, but intense solar energetic particle (SEP) events may induce acute health effects. Such events may enhance the radiation level significantly and should be detected as immediately as possible to prevent severe damage to humans and equipment. However, the energetic particle environment on the Martian surface is significantly different from that in deep space due to the influence of the Martian atmosphere. Depending on the intensity and shape of the original solar particle spectra, as well as particle types, the surface spectra may induce entirely different radiation effects. In order to give immediate and accurate alerts while avoiding unnecessary ones, it is important to model and well understand the atmospheric effect on the incoming SEPs, including both protons and helium ions. In this paper, we have developed a generalized approach to quickly model the surface response of any given incoming proton/helium ion spectra and have applied it to a set of historical large solar events, thus providing insights into the possible variety of surface radiation environments that may be induced during SEP events. Based on the statistical study of more than 30 significant solar events, we have obtained an empirical model for estimating the surface dose rate directly from the intensities of a power-law SEP spectra.

  8. Atmospheric Rotational Effects on Mars Based on the NASA Ames General Circulation Model: Angular Momentum Approach (United States)

    Sanchez, Braulio V.; Haberle, Robert M.; Schaeffer, James


    The objective of the investigation is to determine the motion of the rotational axis of Mars as a result of mass variations in the atmosphere and condensation and sublimation of CO2 ice on the polar caps. A planet experiences this type of motion if it has an atmosphere, which is changing its mass distribution with respect to the solid body of the planet and/or it is asymmetrically changing the amount of ice at the polar caps. The physical principle involved is the conservation of angular momentum, one can get a feeling for it by sitting on a well oiled swivel chair holding a rotating wheel on a horizontal direction and then changing the rotation axis of the wheel to a vertical direction. The person holding the wheel and the chair would begin to rotate in opposite direction to the rotation of the wheel. The motions of Mars atmosphere and the ice caps variations are obtained from a mathematical model developed at the NASA Ames Research Center. The model produces outputs for a time span of one Martian year, which is equivalent to 687 Earth days. The results indicate that Mars axis of rotation moves in a spiral with respect to a reference point on the surface of the planet. It can move as far away as 35.3 cm from the initial location as a result of both mass variations in the atmosphere and asymmetric ice variations at the polar caps. Furthermore the pole performs close to two revolutions around the reference point during a Martian year. This motion is a combination of two motions, one produced by the atmospheric mass variations and another due to the variations in the ice caps. The motion due to the atmospheric variations is a spiral performing about two and a half revolutions around the reference point during which the pole can move as far as 40.9 cm. The motion due to variations in the ice caps is a spiral performing almost three revolutions during which the pole can move as far as 32.8 cm.

  9. Efficient computation of smoothing splines via adaptive basis sampling

    KAUST Repository

    Ma, Ping


    © 2015 Biometrika Trust. Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. In this article, we develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. Except for the univariate case where the Reinsch algorithm is applicable, a smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is generally O(n3). We achieve a more scalable computation in the multivariate case by evaluating the smoothing spline using a smaller set of basis functions, obtained by an adaptive sampling scheme that uses values of the response variable. Our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as full basis smoothing splines. Using simulation studies and a large-scale deep earth core-mantle boundary imaging study, we show that the proposed method outperforms a sampling method that does not use the values of response variables.

  10. Shape Designing of Engineering Images Using Rational Spline Interpolation

    Directory of Open Access Journals (Sweden)

    Muhammad Sarfraz


    Full Text Available In modern days, engineers encounter a remarkable range of different engineering problems like study of structure, structure properties, and designing of different engineering images, for example, automotive images, aerospace industrial images, architectural designs, shipbuilding, and so forth. This paper purposes an interactive curve scheme for designing engineering images. The purposed scheme furnishes object designing not just in the area of engineering, but it is equally useful for other areas including image processing (IP, Computer Graphics (CG, Computer-Aided Engineering (CAE, Computer-Aided Manufacturing (CAM, and Computer-Aided Design (CAD. As a method, a piecewise rational cubic spline interpolant, with four shape parameters, has been purposed. The method provides effective results together with the effects of derivatives and shape parameters on the shape of the curves in a local and global manner. The spline method, due to its most generalized description, recovers various existing rational spline methods and serves as an alternative to various other methods including v-splines, gamma splines, weighted splines, and beta splines.

  11. Detrending of non-stationary noise data by spline techniques

    International Nuclear Information System (INIS)

    Behringer, K.


    An off-line method for detrending non-stationary noise data has been investigated. It uses a least squares spline approximation of the noise data with equally spaced breakpoints. Subtraction of the spline approximation from the noise signal at each data point gives a residual noise signal. The method acts as a high-pass filter with very sharp frequency cutoff. The cutoff frequency is determined by the breakpoint distance. The steepness of the cutoff is controlled by the spline order. (author) 12 figs., 1 tab., 5 refs

  12. Decomposition of LiDAR waveforms by B-spline-based modeling (United States)

    Shen, Xiang; Li, Qing-Quan; Wu, Guofeng; Zhu, Jiasong


    Waveform decomposition is a widely used technique for extracting echoes from full-waveform LiDAR data. Most previous studies recommended the Gaussian decomposition approach, which employs the Gaussian function in laser pulse modeling. As the Gaussian-shape assumption is not always satisfied for real LiDAR waveforms, some other probability distributions (e.g., the lognormal distribution, the generalized normal distribution, and the Burr distribution) have also been introduced by researchers to fit sharply-peaked and/or heavy-tailed pulses. However, these models cannot be universally used, because they are only suitable for processing the LiDAR waveforms in particular shapes. In this paper, we present a new waveform decomposition algorithm based on the B-spline modeling technique. LiDAR waveforms are not assumed to have a priori shapes but rather are modeled by B-splines, and the shape of a received waveform is treated as the mixture of finite transmitted pulses after translation and scaling transformation. The performance of the new model was tested using two full-waveform data sets acquired by a Riegl LMS-Q680i laser scanner and an Optech Aquarius laser bathymeter, comparing with three classical waveform decomposition approaches: the Gaussian, generalized normal, and lognormal distribution-based models. The experimental results show that the B-spline model performed the best in terms of waveform fitting accuracy, while the generalized normal model yielded the worst performance in the two test data sets. Riegl waveforms have nearly Gaussian pulse shapes and were well fitted by the Gaussian mixture model, while the B-spline-based modeling algorithm produced a slightly better result by further reducing 6.4% of fitting residuals, largely benefiting from alleviating the adverse impact of the ringing effect. The pulse shapes of Optech waveforms, on the other hand, are noticeably right-skewed. The Gaussian modeling results deviated significantly from original signals, and

  13. Nonlinear bias compensation of ZiYuan-3 satellite imagery with cubic splines (United States)

    Cao, Jinshan; Fu, Jianhong; Yuan, Xiuxiao; Gong, Jianya


    Like many high-resolution satellites such as the ALOS, MOMS-2P, QuickBird, and ZiYuan1-02C satellites, the ZiYuan-3 satellite suffers from different levels of attitude oscillations. As a result of such oscillations, the rational polynomial coefficients (RPCs) obtained using a terrain-independent scenario often have nonlinear biases. In the sensor orientation of ZiYuan-3 imagery based on a rational function model (RFM), these nonlinear biases cannot be effectively compensated by an affine transformation. The sensor orientation accuracy is thereby worse than expected. In order to eliminate the influence of attitude oscillations on the RFM-based sensor orientation, a feasible nonlinear bias compensation approach for ZiYuan-3 imagery with cubic splines is proposed. In this approach, no actual ground control points (GCPs) are required to determine the cubic splines. First, the RPCs are calculated using a three-dimensional virtual control grid generated based on a physical sensor model. Second, one cubic spline is used to model the residual errors of the virtual control points in the row direction and another cubic spline is used to model the residual errors in the column direction. Then, the estimated cubic splines are used to compensate the nonlinear biases in the RPCs. Finally, the affine transformation parameters are used to compensate the residual biases in the RPCs. Three ZiYuan-3 images were tested. The experimental results showed that before the nonlinear bias compensation, the residual errors of the independent check points were nonlinearly biased. Even if the number of GCPs used to determine the affine transformation parameters was increased from 4 to 16, these nonlinear biases could not be effectively compensated. After the nonlinear bias compensation with the estimated cubic splines, the influence of the attitude oscillations could be eliminated. The RFM-based sensor orientation accuracies of the three ZiYuan-3 images reached 0.981 pixels, 0.890 pixels, and 1

  14. Spline based iterative phase retrieval algorithm for X-ray differential phase contrast radiography. (United States)

    Nilchian, Masih; Wang, Zhentian; Thuering, Thomas; Unser, Michael; Stampanoni, Marco


    Differential phase contrast imaging using grating interferometer is a promising alternative to conventional X-ray radiographic methods. It provides the absorption, differential phase and scattering information of the underlying sample simultaneously. Phase retrieval from the differential phase signal is an essential problem for quantitative analysis in medical imaging. In this paper, we formalize the phase retrieval as a regularized inverse problem, and propose a novel discretization scheme for the derivative operator based on B-spline calculus. The inverse problem is then solved by a constrained regularized weighted-norm algorithm (CRWN) which adopts the properties of B-spline and ensures a fast implementation. The method is evaluated with a tomographic dataset and differential phase contrast mammography data. We demonstrate that the proposed method is able to produce phase image with enhanced and higher soft tissue contrast compared to conventional absorption-based approach, which can potentially provide useful information to mammographic investigations.

  15. Finite nucleus Dirac mean field theory and random phase approximation using finite B splines

    International Nuclear Information System (INIS)

    McNeil, J.A.; Furnstahl, R.J.; Rost, E.; Shepard, J.R.; Department of Physics, University of Maryland, College Park, Maryland 20742; Department of Physics, University of Colorado, Boulder, Colorado 80309)


    We calculate the finite nucleus Dirac mean field spectrum in a Galerkin approach using finite basis splines. We review the method and present results for the relativistic σ-ω model for the closed-shell nuclei 16 O and 40 Ca. We study the convergence of the method as a function of the size of the basis and the closure properties of the spectrum using an energy-weighted dipole sum rule. We apply the method to the Dirac random-phase-approximation response and present results for the isoscalar 1/sup -/ and 3/sup -/ longitudinal form factors of 16 O and 40 Ca. We also use a B-spline spectral representation of the positive-energy projector to evaluate partial energy-weighted sum rules and compare with nonrelativistic sum rule results

  16. Clustering Time-Series Gene Expression Data Using Smoothing Spline Derivatives

    Directory of Open Access Journals (Sweden)

    Martin PGP


    Full Text Available Microarray data acquired during time-course experiments allow the temporal variations in gene expression to be monitored. An original postprandial fasting experiment was conducted in the mouse and the expression of 200 genes was monitored with a dedicated macroarray at 11 time points between 0 and 72 hours of fasting. The aim of this study was to provide a relevant clustering of gene expression temporal profiles. This was achieved by focusing on the shapes of the curves rather than on the absolute level of expression. Actually, we combined spline smoothing and first derivative computation with hierarchical and partitioning clustering. A heuristic approach was proposed to tune the spline smoothing parameter using both statistical and biological considerations. Clusters are illustrated a posteriori through principal component analysis and heatmap visualization. Most results were found to be in agreement with the literature on the effects of fasting on the mouse liver and provide promising directions for future biological investigations.

  17. Clustering Time-Series Gene Expression Data Using Smoothing Spline Derivatives

    Directory of Open Access Journals (Sweden)

    S. Déjean


    Full Text Available Microarray data acquired during time-course experiments allow the temporal variations in gene expression to be monitored. An original postprandial fasting experiment was conducted in the mouse and the expression of 200 genes was monitored with a dedicated macroarray at 11 time points between 0 and 72 hours of fasting. The aim of this study was to provide a relevant clustering of gene expression temporal profiles. This was achieved by focusing on the shapes of the curves rather than on the absolute level of expression. Actually, we combined spline smoothing and first derivative computation with hierarchical and partitioning clustering. A heuristic approach was proposed to tune the spline smoothing parameter using both statistical and biological considerations. Clusters are illustrated a posteriori through principal component analysis and heatmap visualization. Most results were found to be in agreement with the literature on the effects of fasting on the mouse liver and provide promising directions for future biological investigations.

  18. Numerical solution of fractional differential equations using cubic B-spline wavelet collocation method (United States)

    Li, Xinxiu


    Physical processes with memory and hereditary properties can be best described by fractional differential equations due to the memory effect of fractional derivatives. For that reason reliable and efficient techniques for the solution of fractional differential equations are needed. Our aim is to generalize the wavelet collocation method to fractional differential equations using cubic B-spline wavelet. Analytical expressions of fractional derivatives in Caputo sense for cubic B-spline functions are presented. The main characteristic of the approach is that it converts such problems into a system of algebraic equations which is suitable for computer programming. It not only simplifies the problem but also speeds up the computation. Numerical results demonstrate the validity and applicability of the method to solve fractional differential equation.

  19. Identification of Hammerstein models with cubic spline nonlinearities. (United States)

    Dempsey, Erika J; Westwick, David T


    This paper considers the use of cubic splines, instead of polynomials, to represent the static nonlinearities in block structured models. It introduces a system identification algorithm for the Hammerstein structure, a static nonlinearity followed by a linear filter, where cubic splines represent the static nonlinearity and the linear dynamics are modeled using a finite impulse response filter. The algorithm uses a separable least squares Levenberg-Marquardt optimization to identify Hammerstein cascades whose nonlinearities are modeled by either cubic splines or polynomials. These algorithms are compared in simulation, where the effects of variations in the input spectrum and distribution, and those of the measurement noise are examined. The two algorithms are used to fit Hammerstein models to stretch reflex electromyogram (EMG) data recorded from a spinal cord injured patient. The model with the cubic spline nonlinearity provides more accurate predictions of the reflex EMG than the polynomial based model, even in novel data.

  20. Origin of the Medusae Fossae Formation, Mars: Insights from a synoptic approach (United States)

    Mandt, Kathleen E.; de Silva, Shanaka L.; Zimbelman, James R.; Crown, David A.


    The geologic origin of the Medusae Fossae Formation (MFF) has remained a mystery despite three decades of research. To better constrain its formation, an in-depth analysis of observations made in the literature was combined with a new survey of over 700 Mars Orbiter Camera narrow-angle images of the MFF to identify morphologic characteristics and material properties that define this formation as a whole. While previous work has identified clear agreement on some characteristics, our analysis identifies yardangs, collapse features, and layering as pervasive features of the MFF. Whereas collapse features and layering may implicate several different physical and chemical processes, yardangs provide vital information on material properties that inform about mechanical properties of the MFF lithology. Aspect ratios of megayardangs range from 3:1 to 50:1, and slope analyses reveal heights of up to 200 m with cliffs that are almost vertical. Other yardangs show lower aspect ratios and topographic profiles. These characteristics coupled to the presence of serrated margins, suggest that MFF lithology must be of weakly to heavily indurated material that lends itself to jointing. The characteristics and properties of the MFF are inconsistent with those of terrestrial pyroclastic fall deposits or loess, but are in common with large terrestrial ignimbrites, a hypothesis that explains all key observations with a single mechanism. Yardang fields developed in regionally extensive ignimbrite sheets in the central Andes display morphologic characteristics that correlate with degree of induration of the host lithology and suggest an origin by pyroclastic flow for the MFF.

  1. An Approach to Searching for Life on Mars, Europa, and Enceladus (United States)

    McKay, Christopher P.


    Near-term missions may be able to access samples of organic material from Mars, Europa, and Enceladus. The challenge for astrobiology will be to determine if this material is the remains of dead microorganisms or merely abiotic organic material. The remains of life that shares a common origin with life on Earth will be straightforward to detect using sophisticated methods such as DNA amplification. These methods are extremely sensitive but specific to Earth-like life. Detecting the remains of alien life—that does not have a genetic or biochemical commonality with Earth life—will be much more difficult. There is a general property of life that can be used to determine if organic material is of biological origin. This general property is the repeated use of a few specific organic molecules for the construction of biopolymers. For example, Earth-like life uses 20 amino acids to construct proteins, 5 nucleotide bases to construct DNA and RNA, and a few sugars to construct polysaccharides. This selectivity will result in a statistically anomalous distribution of organic molecules distinct from organic material of non-biological origin. Such a distinctive pattern, different from the pattern of Earth-like life, will be persuasive evidence for a second genesis of life.

  2. NASA Exploration Launch Projects Systems Engineering Approach for Astronaut Missions to the Moon, Mars, and Beyond (United States)

    Dumbacher, Daniel L.


    The U.S. Vision for Space Exploration directs NASA to design and develop a new generation of safe, reliable, and cost-effective transportation systems to hlfill the Nation s strategic goals and objectives. These launch vehicles will provide the capability for astronauts to conduct scientific exploration that yields new knowledge from the unique vantage point of space. American leadership in opening new fi-ontiers will improve the quality of life on Earth for generations to come. The Exploration Launch Projects office is responsible for delivering the Crew Launch Vehicle (CLV) that will loft the Crew Exploration Vehicle (CEV) into low-Earth orbit (LEO) early next decade, and for the heavy lift Cargo Launch Vehicle (CaLV) that will deliver the Lunar Surface Access Module (LSAM) to LEO for astronaut return trips to the Moon by 2020 in preparation for the eventual first human footprint on Mars. Crew travel to the International Space Station will be made available as soon possible after the Space Shuttle retires in 2010.

  3. Assessing time-by-covariate interactions in relative survival models using restrictive cubic spline functions. (United States)

    Bolard, P; Quantin, C; Abrahamowicz, M; Esteve, J; Giorgi, R; Chadha-Boreham, H; Binquet, C; Faivre, J


    The Cox model is widely used in the evaluation of prognostic factors in clinical research. However, in population-based studies, which assess long-term survival of unselected populations, relative-survival models are often considered more appropriate. In both approaches, the validity of proportional hazards hypothesis should be evaluated. We propose a new method in which restricted cubic spline functions are employed to model time-by-covariate interactions in relative survival analyses. The method allows investigation of the shape of possible dependence of the covariate effect on time without having to specify a particular functional form. Restricted cubic spline functions allow graphing of such time-by-covariate interactions, to test formally the proportional hazards assumption, and also to test the linearity of the time-by-covariate interaction. Application of our new method to assess mortality in colon cancer provides strong evidence against the proportional hazards hypothesis, which is rejected for all prognostic factors. The results corroborate previous analyses of similar data-sets, suggesting the importance of both modelling of non-proportional hazards and relative survival approach. We also demonstrate the advantages of using restricted cubic spline functions for modelling non-proportional hazards in relative-survival analysis. The results provide new insights in the estimated impact of older age and of period of diagnosis. Using restricted cubic splines in a relative survival model allows the representation of both simple and complex patterns of changes in relative risks over time, with a single parsimonious model without a priori assumptions about the functional form of these changes.

  4. Segmented Regression Based on B-Splines with Solved Examples

    Directory of Open Access Journals (Sweden)

    Miloš Kaňka


    Full Text Available The subject of the paper is segmented linear, quadratic, and cubic regression based on B-spline basis functions. In this article we expose the formulas for the computation of B-splines of order one, two, and three that is needed to construct linear, quadratic, and cubic regression. We list some interesting properties of these functions. For a clearer understanding we give the solutions of a couple of elementary exercises regarding these functions.

  5. Verifying single-station seismic approaches using Earth-based data: Preparation for data return from the InSight mission to Mars (United States)

    Panning, Mark P.; Beucler, Éric; Drilleau, Mélanie; Mocquet, Antoine; Lognonné, Philippe; Banerdt, W. Bruce


    The planned InSight mission will deliver a single seismic station containing 3-component broadband and short-period sensors to the surface of Mars in 2016. While much of the progress in understanding the Earth and Moon's interior has relied on the use of seismic networks for accurate location of sources, single station approaches can be applied to data returned from Mars in order to locate events and determine interior structure. In preparation for the data return from InSight, we use a terrestrial dataset recorded at the Global Seismic Network station BFO, located at the Black Forest Observatory in Germany, to verify an approach for event location and structure determination based on recordings of multiple orbit surface waves, which will be more favorable to record on Mars than Earth due to smaller planetary radius and potentially lower background noise. With this approach applied to events near the threshold of observability on Earth, we are able to determine epicentral distance within approximately 1° (corresponding to ∼60 km on Mars), and origin time within ∼30 s. With back azimuth determined from Rayleigh wave polarization, absolute locations are determined generally within an aperture of 10°, allowing for localization within large tectonic regions on Mars. With these locations, we are able to recover Earth mantle structure within ±5% (the InSight mission requirements for martian mantle structure) using 1D travel time inversions of P and S travel times for datasets of only 7 events. The location algorithm also allows for the measurement of great-circle averaged group velocity dispersion, which we measure between 40 and 200 s to scale the expected reliable frequency range of the InSight data from Earth to Mars data. Using the terrestrial data, we are able to resolve structure down to ∼200 km, but synthetic tests demonstrate we should be able to resolve martian structure to ∼400 km with the same frequency content given the smaller planetary size.

  6. Construction of Power Receiving Rectenna Using Mars- In-Situ Materials; A Low Energy Materials Processing Approach (United States)

    Curreri, Peter A.; Rose, M. Franklin (Technical Monitor)


    It is highly desirable to have a non-nuclear power rich option for the human exploration of Mars. Utilizing a Solar Electric Propulsion, SEP, / Power Beaming architecture for a non-nuclear power option for a human Mars base potentially avoids the weather and dust sensitivities of the surface photovoltaic option. Further from Mars areosynchronous orbit near year round power can be provided. Mission analysis, however, concludes that ultra high (245 GHz) frequencies or laser transmission technologies are required for Mars landed mass competitiveness with the surface photovoltaic option if the receiving rectifying antenna "rectenna" is transported from Earth. It is suggested in this paper that producing rectenna in situ on Mars surface might make a more conventional 5.8 GHz system competitive with surface PV. The premium of a competitive, robust, continuous base power might make the development of a 10 plus MWe class SEP for human Mars mission a more attractive non-nuclear option.

  7. Transport modeling and multivariate adaptive regression splines for evaluating performance of ASR systems in freshwater aquifers (United States)

    Forghani, Ali; Peralta, Richard C.


    The study presents a procedure using solute transport and statistical models to evaluate the performance of aquifer storage and recovery (ASR) systems designed to earn additional water rights in freshwater aquifers. The recovery effectiveness (REN) index quantifies the performance of these ASR systems. REN is the proportion of the injected water that the same ASR well can recapture during subsequent extraction periods. To estimate REN for individual ASR wells, the presented procedure uses finely discretized groundwater flow and contaminant transport modeling. Then, the procedure uses multivariate adaptive regression splines (MARS) analysis to identify the significant variables affecting REN, and to identify the most recovery-effective wells. Achieving REN values close to 100% is the desire of the studied 14-well ASR system operator. This recovery is feasible for most of the ASR wells by extracting three times the injectate volume during the same year as injection. Most of the wells would achieve RENs below 75% if extracting merely the same volume as they injected. In other words, recovering almost all the same water molecules that are injected requires having a pre-existing water right to extract groundwater annually. MARS shows that REN most significantly correlates with groundwater flow velocity, or hydraulic conductivity and hydraulic gradient. MARS results also demonstrate that maximizing REN requires utilizing the wells located in areas with background Darcian groundwater velocities less than 0.03 m/d. The study also highlights the superiority of MARS over regular multiple linear regressions to identify the wells that can provide the maximum REN. This is the first reported application of MARS for evaluating performance of an ASR system in fresh water aquifers.

  8. Comprehensive modeling of monthly mean soil temperature using multivariate adaptive regression splines and support vector machine (United States)

    Mehdizadeh, Saeid; Behmanesh, Javad; Khalili, Keivan


    Soil temperature (T s) and its thermal regime are the most important factors in plant growth, biological activities, and water movement in soil. Due to scarcity of the T s data, estimation of soil temperature is an important issue in different fields of sciences. The main objective of the present study is to investigate the accuracy of multivariate adaptive regression splines (MARS) and support vector machine (SVM) methods for estimating the T s. For this aim, the monthly mean data of the T s (at depths of 5, 10, 50, and 100 cm) and meteorological parameters of 30 synoptic stations in Iran were utilized. To develop the MARS and SVM models, various combinations of minimum, maximum, and mean air temperatures (T min, T max, T); actual and maximum possible sunshine duration; sunshine duration ratio (n, N, n/N); actual, net, and extraterrestrial solar radiation data (R s, R n, R a); precipitation (P); relative humidity (RH); wind speed at 2 m height (u 2); and water vapor pressure (Vp) were used as input variables. Three error statistics including root-mean-square-error (RMSE), mean absolute error (MAE), and determination coefficient (R 2) were used to check the performance of MARS and SVM models. The results indicated that the MARS was superior to the SVM at different depths. In the test and validation phases, the most accurate estimations for the MARS were obtained at the depth of 10 cm for T max, T min, T inputs (RMSE = 0.71 °C, MAE = 0.54 °C, and R 2 = 0.995) and for RH, V p, P, and u 2 inputs (RMSE = 0.80 °C, MAE = 0.61 °C, and R 2 = 0.996), respectively.

  9. A B-Spline Framework for Smooth Derivative Computation in Well Test Analysis Using Diagnostic Plots. (United States)

    Tago, Josué; Hernández-Espriú, Antonio


    In the oil and gas industry, well test analysis using derivative plots, has been the core technique in examining reservoir and well behavior over the last three decades. Recently, diagnostics plots have gained recognition in the field of hydrogeology; however, this tool is still underused by groundwater professionals. The foremost drawback is that the derivative function must be computed from noisy field measurements, usually based on finite-difference schemes, which complicates the analysis. We propose a B-spline framework for smooth derivative computation, referred to as Constrained Quartic B-Splines with Free Knots. The approach presents the following novelties in relation to methodological precedents: (1) the use of automatic equality derivative constraints, (2) a knot removal strategy and (3) the introduction of a Boolean shape parameter that defines the number of initial knots to choose. These can lead to evaluate both simple (manually recorded drawdown measurements) and complex (transducer measured records) datasets. Furthermore, we propose an additional shape preserving smoothing preprocess procedure, as a simple, fast and robust method to deal with extremely noisy signals. Our framework was tested in four pumping tests by comparing the spline derivative with regards to the Bourdet algorithm, and we found that the latter is rather noisy (even for large differentiation intervals) and the second derivative response is basically unreadable. In contrast, the spline first and second derivative led to smoother responses, which are more suitable for interpretation. We concluded that the proposed framework is a welcome contribution to evaluate reliable aquifer tests using derivative-diagnostic plots. © 2017, National Ground Water Association.

  10. Subpixel Snow Cover Mapping from MODIS Data by Nonparametric Regression Splines (United States)

    Akyurek, Z.; Kuter, S.; Weber, G. W.


    Spatial extent of snow cover is often considered as one of the key parameters in climatological, hydrological and ecological modeling due to its energy storage, high reflectance in the visible and NIR regions of the electromagnetic spectrum, significant heat capacity and insulating properties. A significant challenge in snow mapping by remote sensing (RS) is the trade-off between the temporal and spatial resolution of satellite imageries. In order to tackle this issue, machine learning-based subpixel snow mapping methods, like Artificial Neural Networks (ANNs), from low or moderate resolution images have been proposed. Multivariate Adaptive Regression Splines (MARS) is a nonparametric regression tool that can build flexible models for high dimensional and complex nonlinear data. Although MARS is not often employed in RS, it has various successful implementations such as estimation of vertical total electron content in ionosphere, atmospheric correction and classification of satellite images. This study is the first attempt in RS to evaluate the applicability of MARS for subpixel snow cover mapping from MODIS data. Total 16 MODIS-Landsat ETM+ image pairs taken over European Alps between March 2000 and April 2003 were used in the study. MODIS top-of-atmospheric reflectance, NDSI, NDVI and land cover classes were used as predictor variables. Cloud-covered, cloud shadow, water and bad-quality pixels were excluded from further analysis by a spatial mask. MARS models were trained and validated by using reference fractional snow cover (FSC) maps generated from higher spatial resolution Landsat ETM+ binary snow cover maps. A multilayer feed-forward ANN with one hidden layer trained with backpropagation was also developed. The mutual comparison of obtained MARS and ANN models was accomplished on independent test areas. The MARS model performed better than the ANN model with an average RMSE of 0.1288 over the independent test areas; whereas the average RMSE of the ANN model

  11. A North Sea approach for Mexico?; El marco Mar del Norte para Mexico?

    Energy Technology Data Exchange (ETDEWEB)

    Baker, George [, United States (United States)


    este se han dado en otras partes del globo terraqueo y es precisamente la intencion de este articulo mostrar como puede aplicarse en el caso de Mexico el arreglo acordado sobre el Mar del Norte. Las caracteristicas bilaterales de este arreglo conformado por incentivos y aperturas al mercado, requieren de la cooperacion de diferentes oficinas y sectores gubernamentales del gobierno federal para hacer posibles una serie de estipulaciones que regulen el trato y permitan a distintas empresas petroleras una interaccion sustanciosa que reditue para los duenos de ambas fronteras. En Mexico la responsabilidad de echar a andar proyectos de este tipo corresponde al poder legislativo en complicidad con las secretarias de asuntos externos y del trabajo. Los actuales modelos de accion y el monopolio Petroleos Mexicanos (PEMEX) en Mexico solo han logrado estancar el desarrollo del pais en este sector y mantener el desarrollo petrolifero en un nivel mediocre y deteriorado. Los beneficios de un tal arreglo se extenderian mas alla de lograr un desarrollo bilateral para los paises involucrados; sin embargo, recordemos que el gobierno de los Estados Unidos no esta al compas de los gobiernos pro-unificacion de fronteras. Para comenzar la unificacion de las regiones fronterizas Mexico debe documentar la ubicacion de los pozos fronterizos, sin embargo aun cuando se llegara a algun acuerdo deberan pasar anos antes que PEMEX desarrolle la tecnologia apropiada para explotar su parte de los yacimientos.

  12. Shape Preserving Interpolation Using C2 Rational Cubic Spline

    Directory of Open Access Journals (Sweden)

    Samsul Ariffin Abdul Karim


    Full Text Available This paper discusses the construction of new C2 rational cubic spline interpolant with cubic numerator and quadratic denominator. The idea has been extended to shape preserving interpolation for positive data using the constructed rational cubic spline interpolation. The rational cubic spline has three parameters αi, βi, and γi. The sufficient conditions for the positivity are derived on one parameter γi while the other two parameters αi and βi are free parameters that can be used to change the final shape of the resulting interpolating curves. This will enable the user to produce many varieties of the positive interpolating curves. Cubic spline interpolation with C2 continuity is not able to preserve the shape of the positive data. Notably our scheme is easy to use and does not require knots insertion and C2 continuity can be achieved by solving tridiagonal systems of linear equations for the unknown first derivatives di, i=1,…,n-1. Comparisons with existing schemes also have been done in detail. From all presented numerical results the new C2 rational cubic spline gives very smooth interpolating curves compared to some established rational cubic schemes. An error analysis when the function to be interpolated is ft∈C3t0,tn is also investigated in detail.

  13. Data assimilation using Bayesian filters and B-spline geological models

    KAUST Repository

    Duan, Lian


    This paper proposes a new approach to problems of data assimilation, also known as history matching, of oilfield production data by adjustment of the location and sharpness of patterns of geological facies. Traditionally, this problem has been addressed using gradient based approaches with a level set parameterization of the geology. Gradient-based methods are robust, but computationally demanding with real-world reservoir problems and insufficient for reservoir management uncertainty assessment. Recently, the ensemble filter approach has been used to tackle this problem because of its high efficiency from the standpoint of implementation, computational cost, and performance. Incorporation of level set parameterization in this approach could further deal with the lack of differentiability with respect to facies type, but its practical implementation is based on some assumptions that are not easily satisfied in real problems. In this work, we propose to describe the geometry of the permeability field using B-spline curves. This transforms history matching of the discrete facies type to the estimation of continuous B-spline control points. As filtering scheme, we use the ensemble square-root filter (EnSRF). The efficacy of the EnSRF with the B-spline parameterization is investigated through three numerical experiments, in which the reservoir contains a curved channel, a disconnected channel or a 2-dimensional closed feature. It is found that the application of the proposed method to the problem of adjusting facies edges to match production data is relatively straightforward and provides statistical estimates of the distribution of geological facies and of the state of the reservoir.

  14. A chord error conforming tool path B-spline fitting method for NC machining based on energy minimization and LSPIA

    Directory of Open Access Journals (Sweden)

    Shanshan He


    Full Text Available Piecewise linear (G01-based tool paths generated by CAM systems lack G1 and G2 continuity. The discontinuity causes vibration and unnecessary hesitation during machining. To ensure efficient high-speed machining, a method to improve the continuity of the tool paths is required, such as B-spline fitting that approximates G01 paths with B-spline curves. Conventional B-spline fitting approaches cannot be directly used for tool path B-spline fitting, because they have shortages such as numerical instability, lack of chord error constraint, and lack of assurance of a usable result. Progressive and Iterative Approximation for Least Squares (LSPIA is an efficient method for data fitting that solves the numerical instability problem. However, it does not consider chord errors and needs more work to ensure ironclad results for commercial applications. In this paper, we use LSPIA method incorporating Energy term (ELSPIA to avoid the numerical instability, and lower chord errors by using stretching energy term. We implement several algorithm improvements, including (1 an improved technique for initial control point determination over Dominant Point Method, (2 an algorithm that updates foot point parameters as needed, (3 analysis of the degrees of freedom of control points to insert new control points only when needed, (4 chord error refinement using a similar ELSPIA method with the above enhancements. The proposed approach can generate a shape-preserving B-spline curve. Experiments with data analysis and machining tests are presented for verification of quality and efficiency. Comparisons with other known solutions are included to evaluate the worthiness of the proposed solution.

  15. Modelling subject-specific childhood growth using linear mixed-effect models with cubic regression splines

    Directory of Open Access Journals (Sweden)

    Laura M. Grajeda


    Full Text Available Abstract Background Childhood growth is a cornerstone of pediatric research. Statistical models need to consider individual trajectories to adequately describe growth outcomes. Specifically, well-defined longitudinal models are essential to characterize both population and subject-specific growth. Linear mixed-effect models with cubic regression splines can account for the nonlinearity of growth curves and provide reasonable estimators of population and subject-specific growth, velocity and acceleration. Methods We provide a stepwise approach that builds from simple to complex models, and account for the intrinsic complexity of the data. We start with standard cubic splines regression models and build up to a model that includes subject-specific random intercepts and slopes and residual autocorrelation. We then compared cubic regression splines vis-à-vis linear piecewise splines, and with varying number of knots and positions. Statistical code is provided to ensure reproducibility and improve dissemination of methods. Models are applied to longitudinal height measurements in a cohort of 215 Peruvian children followed from birth until their fourth year of life. Results Unexplained variability, as measured by the variance of the regression model, was reduced from 7.34 when using ordinary least squares to 0.81 (p < 0.001 when using a linear mixed-effect models with random slopes and a first order continuous autoregressive error term. There was substantial heterogeneity in both the intercept (p < 0.001 and slopes (p < 0.001 of the individual growth trajectories. We also identified important serial correlation within the structure of the data (ρ = 0.66; 95 % CI 0.64 to 0.68; p < 0.001, which we modeled with a first order continuous autoregressive error term as evidenced by the variogram of the residuals and by a lack of association among residuals. The final model provides a parametric linear regression equation for both estimation and

  16. [Multimodal medical image registration using cubic spline interpolation method]. (United States)

    He, Yuanlie; Tian, Lianfang; Chen, Ping; Wang, Lifei; Ye, Guangchun; Mao, Zongyuan


    Based on the characteristic of the PET-CT multimodal image series, a novel image registration and fusion method is proposed, in which the cubic spline interpolation method is applied to realize the interpolation of PET-CT image series, then registration is carried out by using mutual information algorithm and finally the improved principal component analysis method is used for the fusion of PET-CT multimodal images to enhance the visual effect of PET image, thus satisfied registration and fusion results are obtained. The cubic spline interpolation method is used for reconstruction to restore the missed information between image slices, which can compensate for the shortage of previous registration methods, improve the accuracy of the registration, and make the fused multimodal images more similar to the real image. Finally, the cubic spline interpolation method has been successfully applied in developing 3D-CRT (3D Conformal Radiation Therapy) system.

  17. A cubic spline approximation for problems in fluid mechanics (United States)

    Rubin, S. G.; Graves, R. A., Jr.


    A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

  18. Viscous flow solutions with a cubic spline approximation (United States)

    Rubin, S. G.; Graves, R. A., Jr.


    A cubic spline approximation is used for the solution of several problems in fluid mechanics. This procedure provides a high degree of accuracy even with a nonuniform mesh, and leads to a more accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several typical integration schemes are presented. For two-dimensional flows a spline-alternating-direction-implicit (SADI) method is evaluated. The spline procedure is assessed and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

  19. Point based interactive image segmentation using multiquadrics splines (United States)

    Meena, Sachin; Duraisamy, Prakash; Palniappan, Kannappan; Seetharaman, Guna


    Multiquadrics (MQ) are radial basis spline function that can provide an efficient interpolation of data points located in a high dimensional space. MQ were developed by Hardy to approximate geographical surfaces and terrain modelling. In this paper we frame the task of interactive image segmentation as a semi-supervised interpolation where an interpolating function learned from the user provided seed points is used to predict the labels of unlabeled pixel and the spline function used in the semi-supervised interpolation is MQ. This semi-supervised interpolation framework has a nice closed form solution which along with the fact that MQ is a radial basis spline function lead to a very fast interactive image segmentation process. Quantitative and qualitative results on the standard datasets show that MQ outperforms other regression based methods, GEBS, Ridge Regression and Logistic Regression, and popular methods like Graph Cut,4 Random Walk and Random Forest.6

  20. A participatory approach for selecting cost-effective measures in the WFD context: the Mar Menor (SE Spain). (United States)

    Perni, Angel; Martínez-Paz, José M


    Achieving a good ecological status in water bodies by 2015 is one of the objectives established in the European Water Framework Directive. Cost-effective analysis (CEA) has been applied for selecting measures to achieve this goal, but this appraisal technique requires technical and economic information that is not always available. In addition, there are often local insights that can only be identified by engaging multiple stakeholders in a participatory process. This paper proposes to combine CEA with the active involvement of stakeholders for selecting cost-effective measures. This approach has been applied to the case study of one of the main coastal lagoons in the European Mediterranean Sea, the Mar Menor, which presents eutrophication problems. Firstly, face-to-face interviews were conducted to estimate relative effectiveness and relative impacts of a set of measures by means of the pairwise comparison technique. Secondly, relative effectiveness was used to estimate cost-effectiveness ratios. The most cost-effective measures were the restoration of watercourses that drain into the lagoon and the treatment of polluted groundwater. Although in general the stakeholders approved the former, most of them stated that the latter involved some uncertainties, which must be addressed before implementing it. Stakeholders pointed out that the PoM would have a positive impact not only on water quality, but also on fishing, agriculture and tourism in the area. This approach can be useful to evaluate other programmes, plans or projects related to other European environmental strategies. Copyright © 2013 Elsevier B.V. All rights reserved.

  1. Formation of Reflecting Surfaces Based on Spline Methods (United States)

    Zamyatin, A. V.; Zamyatina, E. A.


    The article deals with problem of reflecting barriers surfaces generation by spline methods. The cases of reflection when a geometric model is applied are considered. The surfaces of reflecting barriers are formed in such a way that they contain given points and the rays reflected at these points and hit at the defined points of specified surface. The reflecting barrier surface is formed by cubic splines. It enables a comparatively simple implementation of proposed algorithms in the form of software applications. The algorithms developed in the article can be applied in architecture and construction design for reflecting surface generation in optics and acoustics providing the geometrical model of reflex processes is used correctly.

  2. Interpolation in numerical optimization. [by cubic spline generation (United States)

    Hall, K. R.; Hull, D. G.


    The present work discusses the generation of the cubic-spline interpolator in numerical optimization methods which use a variable-step integrator with step size control based on local relative truncation error. An algorithm for generating the cubic spline with successive over-relaxation is presented which represents an improvement over that given by Ralston and Wilf (1967). Rewriting the code reduces the number of N-vectors from eight to one. The algorithm is formulated in such a way that the solution of the linear system set up yields the first derivatives at the nodal points. This method is as accurate as other schemes but requires the minimum amount of storage.

  3. Shape preserving rational cubic spline for positive and convex data

    Directory of Open Access Journals (Sweden)

    Malik Zawwar Hussain


    Full Text Available In this paper, the problem of shape preserving C2 rational cubic spline has been proposed. The shapes of the positive and convex data are under discussion of the proposed spline solutions. A C2 rational cubic function with two families of free parameters has been introduced to attain the C2 positive curves from positive data and C2 convex curves from convex data. Simple data dependent constraints are derived on free parameters in the description of rational cubic function to obtain the desired shape of the data. The rational cubic schemes have unique representations.

  4. Control theoretic splines optimal control, statistical, and path planning

    CERN Document Server

    Egerstedt, Magnus


    Splines, both interpolatory and smoothing, have a long and rich history that has largely been application driven. This book unifies these constructions in a comprehensive and accessible way, drawing from the latest methods and applications to show how they arise naturally in the theory of linear control systems. Magnus Egerstedt and Clyde Martin are leading innovators in the use of control theoretic splines to bring together many diverse applications within a common framework. In this book, they begin with a series of problems ranging from path planning to statistics to approximation.

  5. Solution of higher order boundary value problems by spline methods (United States)

    Chaurasia, Anju; Srivastava, P. C.; Gupta, Yogesh


    Spline solution of Boundary Value Problems has received much attention in recent years. It has proven to be a powerful tool due to the ease of use and quality of results. This paper concerns with the survey of methods that try to approximate the solution of higher order BVPs using various spline functions. The purpose of this article is to thrash out the problems as well as conclusions, reached by the numerous authors in the related field. We critically assess many important relevant papers, published in reputed journals during last six years.

  6. Steady-state solution of the PTC thermistor problem using a quadratic spline finite element method

    Directory of Open Access Journals (Sweden)

    Bahadir A. R.


    Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.

  7. Deficiencies in the Theory of Free-Knot and Variable-Knot Spline ...

    African Journals Online (AJOL)

    This paper revisits the theory and practical implementation of graduation of mortality rates using spline functions, and in particular, variable-knot cubic spline graduation. The paper contrasts the actuarial literature on free-knot splines with the mathematical literature. It finds that the practical difficulties of implementing ...

  8. Clinical Apply of Dual Energy CT (kVp switching) : A Novel Approach for MAR (Metal Artifact Reduction) Method

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Myeong Seong; Jeong, Jong Seong; Kim, Myeong Goo [National Cancer Center, Goyang (Korea, Republic of)


    The purpose of this article was to measure and compare the value of the metal artifact reduction (MAR) algorithm by Dual energy(kVp switching) CT (Computed Tomography) for non using MAR and we introduced new variable Dual energy CT applications through a clinical scan. The used equipment was GE Discovery 750HD with Dual-Energy system(kVp switching). CT scan was performed on the neck and abdomen area subject for patients. Studies were from Dec 20 2010 to Feb 10 2011 and included 25 subject patients with prosthesis. We were measured the HU (Hounsfield Unit) and noise value at metal artifact appear(focal loss of signal and white streak artifact area) according to the using MAR algorithm. Statistical analyses were performed using the paired sample t-test. In patient subject case, the statistical difference of showing HU was p=0.01 and p=0.04 respectively. At maximum black hole artifact area and white streak artifact area according to the using MAR algorithm. However noise was p=0.05 and p=0.04 respectively; and not the affected black hole and white streak artifact area. Dual Energy CT with the MAR algorithm technique is useful reduce metal artifacts and could improve the diagnostic value in the diagnostic image evaluation of metallic implants area.

  9. C2-rational cubic spline involving tension parameters

    Indian Academy of Sciences (India)

    preferred which preserves some of the characteristics of the function to be interpolated. In order to tackle such ... Shape preserving properties of the rational (cubic/quadratic) spline interpolant have been studied ... tension parameters which is used to interpolate the given monotonic data is described in. [6]. Shape preserving ...

  10. Differential constraints for bounded recursive identification with multivariate splines

    NARCIS (Netherlands)

    De Visser, C.C.; Chu, Q.P.; Mulder, J.A.


    The ability to perform online model identification for nonlinear systems with unknown dynamics is essential to any adaptive model-based control system. In this paper, a new differential equality constrained recursive least squares estimator for multivariate simplex splines is presented that is able

  11. Approximate Implicitization of Parametric Curves Using Cubic Algebraic Splines

    Directory of Open Access Journals (Sweden)

    Xiaolei Zhang


    Full Text Available This paper presents an algorithm to solve the approximate implicitization of planar parametric curves using cubic algebraic splines. It applies piecewise cubic algebraic curves to give a global G2 continuity approximation to planar parametric curves. Approximation error on approximate implicitization of rational curves is given. Several examples are provided to prove that the proposed method is flexible and efficient.

  12. Cubic spline approximation techniques for parameter estimation in distributed systems (United States)

    Banks, H. T.; Crowley, J. M.; Kunisch, K.


    Approximation schemes employing cubic splines in the context of a linear semigroup framework are developed for both parabolic and hyperbolic second-order partial differential equation parameter estimation problems. Convergence results are established for problems with linear and nonlinear systems, and a summary of numerical experiments with the techniques proposed is given.

  13. Connecting the Dots Parametrically: An Alternative to Cubic Splines. (United States)

    Hildebrand, Wilbur J.


    Discusses a method of cubic splines to determine a curve through a series of points and a second method for obtaining parametric equations for a smooth curve that passes through a sequence of points. Procedures for determining the curves and results of each of the methods are compared. (YP)

  14. C2-rational cubic spline involving tension parameters

    Indian Academy of Sciences (India)

    In the present paper, 1-piecewise rational cubic spline function involving tension parameters is considered which produces a monotonic interpolant to a given monotonic data set. It is observed that under certain conditions the interpolant preserves the convexity property of the data set. The existence and uniqueness of a ...

  15. Counterexamples to the B-spline Conjecture for Gabor Frames

    DEFF Research Database (Denmark)

    Lemvig, Jakob; Nielsen, Kamilla Haahr


    The frame set conjecture for B-splines Bn, n≥2, states that the frame set is the maximal set that avoids the known obstructions. We show that any hyperbola of the form ab=r, where r is a rational number smaller than one and a and b denote the sampling and modulation rates, respectively, has infin...

  16. Kriging and thin plate splines for mapping climate variables

    NARCIS (Netherlands)

    Boer, E.P.J.; Beurs, de K.M.; Hartkamp, A.D.


    Four forms of kriging and three forms of thin plate splines are discussed in this paper to predict monthly maximum temperature and monthly mean precipitation in Jalisco State of Mexico. Results show that techniques using elevation as additional information improve the prediction results

  17. Spline function fit for multi-sets of correlative data

    International Nuclear Information System (INIS)

    Liu Tingjin; Zhou Hongmo


    The Spline fit method for multi-sets of correlative data is developed. The properties of correlative data fit are investigated. The data of 23 Na(n, 2n) cross section are fitted in the cases with and without correlation

  18. Modelling Childhood Growth Using Fractional Polynomials and Linear Splines (United States)

    Tilling, Kate; Macdonald-Wallis, Corrie; Lawlor, Debbie A.; Hughes, Rachael A.; Howe, Laura D.


    Background There is increasing emphasis in medical research on modelling growth across the life course and identifying factors associated with growth. Here, we demonstrate multilevel models for childhood growth either as a smooth function (using fractional polynomials) or a set of connected linear phases (using linear splines). Methods We related parental social class to height from birth to 10 years of age in 5,588 girls from the Avon Longitudinal Study of Parents and Children (ALSPAC). Multilevel fractional polynomial modelling identified the best-fitting model as being of degree 2 with powers of the square root of age, and the square root of age multiplied by the log of age. The multilevel linear spline model identified knot points at 3, 12 and 36 months of age. Results Both the fractional polynomial and linear spline models show an initially fast rate of growth, which slowed over time. Both models also showed that there was a disparity in length between manual and non-manual social class infants at birth, which decreased in magnitude until approximately 1 year of age and then increased. Conclusions Multilevel fractional polynomials give a more realistic smooth function, and linear spline models are easily interpretable. Each can be used to summarise individual growth trajectories and their relationships with individual-level exposures. PMID:25413651

  19. Evaluation of Logistic Regression and Multivariate Adaptive Regression Spline Models for Groundwater Potential Mapping Using R and GIS

    Directory of Open Access Journals (Sweden)

    Soyoung Park


    Full Text Available This study mapped and analyzed groundwater potential using two different models, logistic regression (LR and multivariate adaptive regression splines (MARS, and compared the results. A spatial database was constructed for groundwater well data and groundwater influence factors. Groundwater well data with a high potential yield of ≥70 m3/d were extracted, and 859 locations (70% were used for model training, whereas the other 365 locations (30% were used for model validation. We analyzed 16 groundwater influence factors including altitude, slope degree, slope aspect, plan curvature, profile curvature, topographic wetness index, stream power index, sediment transport index, distance from drainage, drainage density, lithology, distance from fault, fault density, distance from lineament, lineament density, and land cover. Groundwater potential maps (GPMs were constructed using LR and MARS models and tested using a receiver operating characteristics curve. Based on this analysis, the area under the curve (AUC for the success rate curve of GPMs created using the MARS and LR models was 0.867 and 0.838, and the AUC for the prediction rate curve was 0.836 and 0.801, respectively. This implies that the MARS model is useful and effective for groundwater potential analysis in the study area.

  20. Mars bevares

    DEFF Research Database (Denmark)

    Hendricks, Vincent Fella; Hendricks, Elbert


    2009 er femåret for Mission Mars. I den anledning opridser de to kronikører, far og søn, hvorfor man bør lade planer om en bemandet tur til Mars forblive i skrivebordsskuffen......2009 er femåret for Mission Mars. I den anledning opridser de to kronikører, far og søn, hvorfor man bør lade planer om en bemandet tur til Mars forblive i skrivebordsskuffen...

  1. A spline-based regression parameter set for creating customized DARTEL MRI brain templates from infancy to old age

    Directory of Open Access Journals (Sweden)

    Marko Wilke


    Full Text Available This dataset contains the regression parameters derived by analyzing segmented brain MRI images (gray matter and white matter from a large population of healthy subjects, using a multivariate adaptive regression splines approach. A total of 1919 MRI datasets ranging in age from 1–75 years from four publicly available datasets (NIH, C-MIND, fCONN, and IXI were segmented using the CAT12 segmentation framework, writing out gray matter and white matter images normalized using an affine-only spatial normalization approach. These images were then subjected to a six-step DARTEL procedure, employing an iterative non-linear registration approach and yielding increasingly crisp intermediate images. The resulting six datasets per tissue class were then analyzed using multivariate adaptive regression splines, using the CerebroMatic toolbox. This approach allows for flexibly modelling smoothly varying trajectories while taking into account demographic (age, gender as well as technical (field strength, data quality predictors. The resulting regression parameters described here can be used to generate matched DARTEL or SHOOT templates for a given population under study, from infancy to old age. The dataset and the algorithm used to generate it are publicly available at Keywords: MRI template creation, Multivariate adaptive regression splines, DARTEL, Structural MRI

  2. Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods (United States)

    Ahmad, Azhar; Azmi, Amirah; Majid, Ahmad Abd.; Hamid, Nur Nadiah Abd


    In this paper, Nonlinear Schrödinger (NLS) equation with Neumann boundary conditions is solved using finite difference method (FDM) and cubic B-spline interpolation method (CuBSIM). First, the approach is based on the FDM applied on the time and space discretization with the help of theta-weighted method. However, our main interest is the second approach, whereby FDM is applied on the time discretization and cubic B-spline is utilized as an interpolation function in the space dimension with the same help of theta-weighted method. The CuBSIM is shown to be stable by using von Neumann stability analysis. The proposed method is tested on a test problem with single soliton motion of the NLS equation. The accuracy of the numerical results is measured by the Euclidean-norm and infinity-norm. CuBSIM is found to produce more accurate results than the FDM.

  3. Multivariate adaptive regression splines and neural network models for prediction of pile drivability

    Directory of Open Access Journals (Sweden)

    Wengang Zhang


    Full Text Available Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved. In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system's predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines (MARS, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network (BPNN and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses (MCS, Maximum tensile stresses (MTS, and Blow per foot (BPF. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.


    Directory of Open Access Journals (Sweden)

    M. Ahmadlou


    Full Text Available Land use change (LUC models used for modelling urban growth are different in structure and performance. Local models divide the data into separate subsets and fit distinct models on each of the subsets. Non-parametric models are data driven and usually do not have a fixed model structure or model structure is unknown before the modelling process. On the other hand, global models perform modelling using all the available data. In addition, parametric models have a fixed structure before the modelling process and they are model driven. Since few studies have compared local non-parametric models with global parametric models, this study compares a local non-parametric model called multivariate adaptive regression spline (MARS, and a global parametric model called artificial neural network (ANN to simulate urbanization in Mumbai, India. Both models determine the relationship between a dependent variable and multiple independent variables. We used receiver operating characteristic (ROC to compare the power of the both models for simulating urbanization. Landsat images of 1991 (TM and 2010 (ETM+ were used for modelling the urbanization process. The drivers considered for urbanization in this area were distance to urban areas, urban density, distance to roads, distance to water, distance to forest, distance to railway, distance to central business district, number of agricultural cells in a 7 by 7 neighbourhoods, and slope in 1991. The results showed that the area under the ROC curve for MARS and ANN was 94.77% and 95.36%, respectively. Thus, ANN performed slightly better than MARS to simulate urban areas in Mumbai, India.

  5. Using Multivariate Adaptive Regression Spline and Artificial Neural Network to Simulate Urbanization in Mumbai, India (United States)

    Ahmadlou, M.; Delavar, M. R.; Tayyebi, A.; Shafizadeh-Moghadam, H.


    Land use change (LUC) models used for modelling urban growth are different in structure and performance. Local models divide the data into separate subsets and fit distinct models on each of the subsets. Non-parametric models are data driven and usually do not have a fixed model structure or model structure is unknown before the modelling process. On the other hand, global models perform modelling using all the available data. In addition, parametric models have a fixed structure before the modelling process and they are model driven. Since few studies have compared local non-parametric models with global parametric models, this study compares a local non-parametric model called multivariate adaptive regression spline (MARS), and a global parametric model called artificial neural network (ANN) to simulate urbanization in Mumbai, India. Both models determine the relationship between a dependent variable and multiple independent variables. We used receiver operating characteristic (ROC) to compare the power of the both models for simulating urbanization. Landsat images of 1991 (TM) and 2010 (ETM+) were used for modelling the urbanization process. The drivers considered for urbanization in this area were distance to urban areas, urban density, distance to roads, distance to water, distance to forest, distance to railway, distance to central business district, number of agricultural cells in a 7 by 7 neighbourhoods, and slope in 1991. The results showed that the area under the ROC curve for MARS and ANN was 94.77% and 95.36%, respectively. Thus, ANN performed slightly better than MARS to simulate urban areas in Mumbai, India.

  6. Polynomial estimation of the smoothing splines for the new Finnish reference values for spirometry. (United States)

    Kainu, Annette; Timonen, Kirsi


    Background Discontinuity of spirometry reference values from childhood into adulthood has been a problem with traditional reference values, thus modern modelling approaches using smoothing spline functions to better depict the transition during growth and ageing have been recently introduced. Following the publication of the new international Global Lung Initiative (GLI2012) reference values also new national Finnish reference values have been calculated using similar GAMLSS-modelling, with spline estimates for mean (Mspline) and standard deviation (Sspline) provided in tables. The aim of this study was to produce polynomial estimates for these spline functions to use in lieu of lookup tables and to assess their validity in the reference population of healthy non-smokers. Methods Linear regression modelling was used to approximate the estimated values for Mspline and Sspline using similar polynomial functions as in the international GLI2012 reference values. Estimated values were compared to original calculations in absolute values, the derived predicted mean and individually calculated z-scores using both values. Results Polynomial functions were estimated for all 10 spirometry variables. The agreement between original lookup table-produced values and polynomial estimates was very good, with no significant differences found. The variation slightly increased in larger predicted volumes, but a range of -0.018 to +0.022 litres of FEV1 representing ± 0.4% of maximum difference in predicted mean. Conclusions Polynomial approximations were very close to the original lookup tables and are recommended for use in clinical practice to facilitate the use of new reference values.

  7. Iteratively re-weighted bi-cubic spline representation of corneal topography and its comparison to the standard methods. (United States)

    Zhu, Zhongxia; Janunts, Edgar; Eppig, Timo; Sauer, Tomas; Langenbucher, Achim


    The aim of this study is to represent the corneal anterior surface by utilizing radius and height data extracted from a TMS-2N topographic system with three different mathematical approaches and to simulate the visual performance. An iteratively re-weighted bi-cubic spline method is introduced for the local representation of the corneal surface. For comparison, two standard mathematical global representation approaches are used: the general quadratic function and the higher order Taylor polynomial approach. First, these methods were applied in simulations using three corneal models. Then, two real eye examples were investigated: one eye with regular astigmatism, and one eye which had undergone refractive surgery. A ray-tracing program was developed to evaluate the imaging performance of these examples with each surface representation strategy at the best focus plane. A 6 mm pupil size was chosen for the simulation. The fitting error (deviation) of the presented methods was compared. It was found that the accuracy of the topography representation was worst using the quadratic function and best with bicubic spline. The quadratic function cannot precisely describe the irregular corneal shape. In order to achieve a sub-micron fitting precision, the Taylor polynomial's order selection behaves adaptive to the corneal shape. The bi-cubic spline shows more stable performance. Considering the visual performance, the more precise the cornea representation is, the worse the visual performance is. The re-weighted bi-cubic spline method is a reasonable and stable method for representing the anterior corneal surface in measurements using a Placido-ring-pattern-based corneal topographer. Copyright © 2010. Published by Elsevier GmbH.

  8. Smooth ROC curves and surfaces for markers subject to a limit of detection using monotone natural cubic splines. (United States)

    Bantis, Leonidas E; Tsimikas, John V; Georgiou, Stelios D


    The use of ROC curves in evaluating a continuous or ordinal biomarker for the discrimination of two populations is commonplace. However, in many settings, marker measurements above or below a certain value cannot be obtained. In this paper, we study the construction of a smooth ROC curve (or surface in the case of three populations) when there is a lower or upper limit of detection. We propose the use of spline models that incorporate monotonicity constraints for the cumulative hazard function of the marker distribution. The proposed technique is computationally stable and simulation results showed a satisfactory performance. Other observed covariates can be also accommodated by this spline-based approach. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  9. Electrical power systems for Mars (United States)

    Giudici, Robert J.


    Electrical power system options for Mars Manned Modules and Mars Surface Bases were evaluated for both near-term and advanced performance potential. The power system options investigated for the Mission Modules include photovoltaics, solar thermal, nuclear reactor, and isotope power systems. Options discussed for Mars Bases include the above options with the addition of a brief discussion of open loop energy conversion of Mars resources, including utilization of wind, subsurface thermal gradients, and super oxides. Electrical power requirements for Mission Modules were estimated for three basic approaches: as a function of crew size; as a function of electric propulsion; and as a function of transmission of power from an orbiter to the surface of Mars via laser or radio frequency. Mars Base power requirements were assumed to be determined by production facilities that make resources available for follow-on missions leading to the establishment of a permanently manned Base. Requirements include the production of buffer gas and propellant production plants.

  10. Physics-based elastic image registration using splines and including landmark localization uncertainties. (United States)

    Wörz, Stefan; Rohr, Karl


    We introduce an elastic registration approach which is based on a physical deformation model and uses Gaussian elastic body splines (GEBS). We formulate an extended energy functional related to the Navier equation under Gaussian forces which also includes landmark localization uncertainties. These uncertainties are characterized by weight matrices representing anisotropic errors. Since the approach is based on a physical deformation model, cross-effects in elastic deformations can be taken into account. Moreover, we have a free parameter to control the locality of the transformation for improved registration of local geometric image differences. We demonstrate the applicability of our scheme based on 3D CT images from the Truth Cube experiment, 2D MR images of the brain, as well as 2D gel electrophoresis images. It turns out that the new scheme achieves more accurate results compared to previous approaches.

  11. Data reduction using cubic rational B-splines (United States)

    Chou, Jin J.; Piegl, Les A.


    A geometric method is proposed for fitting rational cubic B-spline curves to data that represent smooth curves including intersection or silhouette lines. The algorithm is based on the convex hull and the variation diminishing properties of Bezier/B-spline curves. The algorithm has the following structure: it tries to fit one Bezier segment to the entire data set and if it is impossible it subdivides the data set and reconsiders the subset. After accepting the subset the algorithm tries to find the longest run of points within a tolerance and then approximates this set with a Bezier cubic segment. The algorithm uses this procedure repeatedly to the rest of the data points until all points are fitted. It is concluded that the algorithm delivers fitting curves which approximate the data with high accuracy even in cases with large tolerances.

  12. Monotonicity preserving splines using rational cubic Timmer interpolation (United States)

    Zakaria, Wan Zafira Ezza Wan; Alimin, Nur Safiyah; Ali, Jamaludin Md


    In scientific application and Computer Aided Design (CAD), users usually need to generate a spline passing through a given set of data, which preserves certain shape properties of the data such as positivity, monotonicity or convexity. The required curve has to be a smooth shape-preserving interpolant. In this paper a rational cubic spline in Timmer representation is developed to generate interpolant that preserves monotonicity with visually pleasing curve. To control the shape of the interpolant three parameters are introduced. The shape parameters in the description of the rational cubic interpolant are subjected to monotonicity constrained. The necessary and sufficient conditions of the rational cubic interpolant are derived and visually the proposed rational cubic Timmer interpolant gives very pleasing results.

  13. Testing for cubic smoothing splines under dependent data. (United States)

    Nummi, Tapio; Pan, Jianxin; Siren, Tarja; Liu, Kun


    In most research on smoothing splines the focus has been on estimation, while inference, especially hypothesis testing, has received less attention. By defining design matrices for fixed and random effects and the structure of the covariance matrices of random errors in an appropriate way, the cubic smoothing spline admits a mixed model formulation, which places this nonparametric smoother firmly in a parametric setting. Thus nonlinear curves can be included with random effects and random coefficients. The smoothing parameter is the ratio of the random-coefficient and error variances and tests for linear regression reduce to tests for zero random-coefficient variances. We propose an exact F-test for the situation and investigate its performance in a real pine stem data set and by simulation experiments. Under certain conditions the suggested methods can also be applied when the data are dependent. © 2010, The International Biometric Society.

  14. High-order numerical solutions using cubic splines (United States)

    Rubin, S. G.; Khosla, P. K.


    The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.

  15. Data interpolation using rational cubic Ball spline with three parameters (United States)

    Karim, Samsul Ariffin Abdul


    Data interpolation is an important task for scientific visualization. This research introduces new rational cubic Ball spline scheme with three parameters. The rational cubic Ball will be used for data interpolation with or without true derivative values. Error estimation show that the proposed scheme works well and is a very good interpolant to approximate the function. All graphical examples are presented by using Mathematica software.

  16. Cubic Splines for Trachea and Bronchial Tubes Grid Generation

    Directory of Open Access Journals (Sweden)

    Eliandro Rodrigues Cirilo


    Full Text Available Grid generation plays an important role in the development of efficient numerical techniques for solving complex flows. Therefore, the present work develops a method for bidimensional blocks structured grid generation for geometries such as the trachea and bronchial tubes. A set of 55 blocks completes the geometry, whose contours are defined by cubic splines. Besides, this technique build on early ones because of its simplicity and efficiency in terms of very complex geometry grid generation.

  17. Uncertainty Quantification using Epi-Splines and Soft Information (United States)


    prediction of the behavior of constructed models of phenomena in physics, 1 biology, chemistry, ecology, engineered sytems , politics, etc. ... Results...spline framework being applied to one of the most common, yet most complex, systems known – the human body . Chapter 5 concludes the thesis by...complex a system known to man than that of the human body . The number of variables im- pacting the performance of one human over another in a given

  18. BSR: B-spline atomic R-matrix codes (United States)

    Zatsarinny, Oleg


    BSR is a general program to calculate atomic continuum processes using the B-spline R-matrix method, including electron-atom and electron-ion scattering, and radiative processes such as bound-bound transitions, photoionization and polarizabilities. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme by including terms of the Breit-Pauli Hamiltonian. New version program summaryTitle of program: BSR Catalogue identifier: ADWY Program summary URL: Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers on which the program has been tested: Microway Beowulf cluster; Compaq Beowulf cluster; DEC Alpha workstation; DELL PC Operating systems under which the new version has been tested: UNIX, Windows XP Programming language used: FORTRAN 95 Memory required to execute with typical data: Typically 256-512 Mwords. Since all the principal dimensions are allocatable, the available memory defines the maximum complexity of the problem No. of bits in a word: 8 No. of processors used: 1 Has the code been vectorized or parallelized?: no No. of lines in distributed program, including test data, etc.: 69 943 No. of bytes in distributed program, including test data, etc.: 746 450 Peripherals used: scratch disk store; permanent disk store Distribution format: tar.gz Nature of physical problem: This program uses the R-matrix method to calculate electron-atom and electron-ion collision processes, with options to calculate radiative data, photoionization, etc. The calculations can be performed in LS-coupling or in an intermediate-coupling scheme, with options to include Breit-Pauli terms in the Hamiltonian. Method of solution: The R-matrix method is used [P.G. Burke, K.A. Berrington, Atomic and Molecular Processes: An R-Matrix Approach, IOP Publishing, Bristol, 1993; P.G. Burke, W.D. Robb, Adv. At. Mol. Phys. 11 (1975) 143; K.A. Berrington, W.B. Eissner, P.H. Norrington, Comput

  19. Numerical simulation of Burgers' equation using cubic B-splines (United States)

    Lakshmi, C.; Awasthi, Ashish


    In this paper, a numerical θ scheme is proposed for solving nonlinear Burgers' equation. By employing Hopf-Cole transformation, the nonlinear Burgers' equation is linearized to the linear Heat equation. The resulting Heat equation is further solved by cubic B-splines. The time discretization of linear Heat equation is carried out using Crank-Nicolson scheme (θ = {1 \\over 2}) as well as backward Euler scheme (θ = 1). Accuracy in temporal direction is improved by using Richardson extrapolation. This method hence possesses fourth order accuracy both in space and time. The system of matrix which arises by using cubic splines is always diagonal. Therefore, working with splines has the advantage of reduced computational cost and easy implementation. Stability of the schemes have been discussed in detail and shown to be unconditionally stable. Three examples have been examined and the L2 and L∞ error norms have been calculated to establish the performance of the method. The numerical results obtained on applying this method have shown to give more accurate results than existing works of Kutluay et al. [1], Ozis et al. [2], Dag et al. [3], Salkuyeh et al. [4] and Korkmaz et al. [5].

  20. The estimation of time-varying risks in asset pricing modelling using B-Spline method (United States)

    Nurjannah; Solimun; Rinaldo, Adji


    Asset pricing modelling has been extensively studied in the past few decades to explore the risk-return relationship. The asset pricing literature typically assumed a static risk-return relationship. However, several studies found few anomalies in the asset pricing modelling which captured the presence of the risk instability. The dynamic model is proposed to offer a better model. The main problem highlighted in the dynamic model literature is that the set of conditioning information is unobservable and therefore some assumptions have to be made. Hence, the estimation requires additional assumptions about the dynamics of risk. To overcome this problem, the nonparametric estimators can also be used as an alternative for estimating risk. The flexibility of the nonparametric setting avoids the problem of misspecification derived from selecting a functional form. This paper investigates the estimation of time-varying asset pricing model using B-Spline, as one of nonparametric approach. The advantages of spline method is its computational speed and simplicity, as well as the clarity of controlling curvature directly. The three popular asset pricing models will be investigated namely CAPM (Capital Asset Pricing Model), Fama-French 3-factors model and Carhart 4-factors model. The results suggest that the estimated risks are time-varying and not stable overtime which confirms the risk instability anomaly. The results is more pronounced in Carhart’s 4-factors model.

  1. Fitting Cox Models with Doubly Censored Data Using Spline-Based Sieve Marginal Likelihood (United States)

    Li, Zhiguo; Owzar, Kouros


    In some applications, the failure time of interest is the time from an originating event to a failure event, while both event times are interval censored. We propose fitting Cox proportional hazards models to this type of data using a spline-based sieve maximum marginal likelihood, where the time to the originating event is integrated out in the empirical likelihood function of the failure time of interest. This greatly reduces the complexity of the objective function compared with the fully semiparametric likelihood. The dependence of the time of interest on time to the originating event is induced by including the latter as a covariate in the proportional hazards model for the failure time of interest. The use of splines results in a higher rate of convergence of the estimator of the baseline hazard function compared with the usual nonparametric estimator. The computation of the estimator is facilitated by a multiple imputation approach. Asymptotic theory is established and a simulation study is conducted to assess its finite sample performance. It is also applied to analyzing a real data set on AIDS incubation time. PMID:27239090

  2. CROSS DRIVE: A New Interactive and Immersive Approach for Exploring 3D Time-Dependent Mars Atmospheric Data in Distributed Teams (United States)

    Gerndt, Andreas M.; Engelke, Wito; Giuranna, Marco; Vandaele, Ann C.; Neary, Lori; Aoki, Shohei; Kasaba, Yasumasa; Garcia, Arturo; Fernando, Terrence; Roberts, David; CROSS DRIVE Team


    Atmospheric phenomena of Mars can be highly dynamic and have daily and seasonal variations. Planetary-scale wavelike disturbances, for example, are frequently observed in Mars' polar winter atmosphere. Possible sources of the wave activity were suggested to be dynamical instabilities and quasi-stationary planetary waves, i.e. waves that arise predominantly via zonally asymmetric surface properties. For a comprehensive understanding of these phenomena, single layers of altitude have to be analyzed carefully and relations between different atmospheric quantities and interaction with the surface of Mars have to be considered. The CROSS DRIVE project tries to address the presentation of those data with a global view by means of virtual reality techniques. Complex orbiter data from spectrometer and observation data from Earth are combined with global circulation models and high-resolution terrain data and images available from Mars Express or MRO instruments. Scientists can interactively extract features from those dataset and can change visualization parameters in real-time in order to emphasize findings. Stereoscopic views allow for perception of the actual 3D behavior of Mars's atmosphere. A very important feature of the visualization system is the possibility to connect distributed workspaces together. This enables discussions between distributed working groups. The workspace can scale from virtual reality systems to expert desktop applications to web-based project portals. If multiple virtual environments are connected, the 3D position of each individual user is captured and used to depict the scientist as an avatar in the virtual world. The appearance of the avatar can also scale from simple annotations to complex avatars using tele-presence technology to reconstruct the users in 3D. Any change of the feature set (annotations, cutplanes, volume rendering, etc.) within the VR is immediately exchanged between all connected users. This allows that everybody is always

  3. Mars Pathfinder (United States)

    Murdin, P.


    First of NASA's Discovery missions. Launched in December 1996 and arrived at Mars on 4 July 1997. Mainly intended as a technology demonstration mission. Used airbags to cushion the landing on Mars. The Carl Sagan Memorial station returned images of an ancient flood plain in Ares Vallis. The 10 kg Sojourner rover used an x-ray spectrometer to study the composition of rocks and travelled about 100 ...

  4. Quantitative structure-activity relationship study on BTK inhibitors by modified multivariate adaptive regression spline and CoMSIA methods. (United States)

    Xu, A; Zhang, Y; Ran, T; Liu, H; Lu, S; Xu, J; Xiong, X; Jiang, Y; Lu, T; Chen, Y


    Bruton's tyrosine kinase (BTK) plays a crucial role in B-cell activation and development, and has emerged as a new molecular target for the treatment of autoimmune diseases and B-cell malignancies. In this study, two- and three-dimensional quantitative structure-activity relationship (2D and 3D-QSAR) analyses were performed on a series of pyridine and pyrimidine-based BTK inhibitors by means of genetic algorithm optimized multivariate adaptive regression spline (GA-MARS) and comparative molecular similarity index analysis (CoMSIA) methods. Here, we propose a modified MARS algorithm to develop 2D-QSAR models. The top ranked models showed satisfactory statistical results (2D-QSAR: Q(2) = 0.884, r(2) = 0.929, r(2)pred = 0.878; 3D-QSAR: q(2) = 0.616, r(2) = 0.987, r(2)pred = 0.905). Key descriptors selected by 2D-QSAR were in good agreement with the conclusions of 3D-QSAR, and the 3D-CoMSIA contour maps facilitated interpretation of the structure-activity relationship. A new molecular database was generated by molecular fragment replacement (MFR) and further evaluated with GA-MARS and CoMSIA prediction. Twenty-five pyridine and pyrimidine derivatives as novel potential BTK inhibitors were finally selected for further study. These results also demonstrated that our method can be a very efficient tool for the discovery of novel potent BTK inhibitors.

  5. Solving nonlinear Benjamin-Bona-Mahony equation using cubic B-spline and cubic trigonometric B-spline collocation methods (United States)

    Rahan, Nur Nadiah Mohd; Ishak, Siti Noor Shahira; Hamid, Nur Nadiah Abd; Majid, Ahmad Abd.; Azmi, Amirah


    In this research, the nonlinear Benjamin-Bona-Mahony (BBM) equation is solved numerically using the cubic B-spline (CuBS) and cubic trigonometric B-spline (CuTBS) collocation methods. The CuBS and CuTBS are utilized as interpolating functions in the spatial dimension while the standard finite difference method (FDM) is applied to discretize the temporal space. In order to solve the nonlinear problem, the BBM equation is linearized using Taylor's expansion. Applying the von-Neumann stability analysis, the proposed techniques are shown to be unconditionally stable under the Crank-Nicolson scheme. Several numerical examples are discussed and compared with exact solutions and results from the FDM.

  6. Mission from Mars

    DEFF Research Database (Denmark)

    Dindler, Christian; Eriksson, Eva; Iversen, Ole Sejer


    In this paper a particular design method is propagated as a supplement to existing descriptive approaches to current practice studies especially suitable for gathering requirements for the design of children's technology. The Mission from Mars method was applied during the design of an electronic...

  7. Using Spline Regression in Semi-Parametric Stochastic Frontier Analysis: An Application to Polish Dairy Farms

    DEFF Research Database (Denmark)

    Czekaj, Tomasz Gerard; Henningsen, Arne

    -parametric regression based on kernel estimators. This approach combines the virtues of the DEA and the SFA, while avoiding their drawbacks: it avoids the specification of a functional form and at the same time accounts for statistical noise. More recently, this approach was used by Henderson and Simar (2005...... is criticised, because it cannot account for statistical noise such as random production shocks and measurement errors, which are inherent in more or less all production data sets. In contrast, the SFA is criticised, because it requires the specification of a functional form, which involves the risk......), Kumbhakar et al. (2007), and Henningsen and Kumbhakar (2009). The aim of this paper and its main contribution to the existing literature is the estimation semi-parametric stochastic frontier models using a different non-parametric estimation technique: spline regression (Ma et al. 2011). We apply...

  8. Predictors of anemia after bariatric surgery using multivariate adaptive regression splines. (United States)

    Lee, Yi-Chih; Lee, Tian-Shyug; Lee, Wei-Jei; Lin, Yang-Chu; Lee, Chia-Ko; Liew, Phui-Ly


    Anemia is the most common nutritional deficiency after bariatric surgery. The predictors of anemia have not been clearly identified. This issue is useful for selecting an appropriate surgery procedure for morbid obesity. From December 2000 to October 2007, a retrospective study of 442 obese patients after bariatric surgery with two years' follow-up data was conducted. Anemia was defined by hemoglobin (Hb) under 13mg/dL in male and 11.5mg/dL in female. We analyzed the clinical information and laboratory data during the initial evaluation of patients referred to bariatric surgery for predictors of anemia development after surgery. All data were analyzed by using multivariate adaptive regression splines (MARS) method. Of the patients, the mean age was 30.8±8.6 years; mean BMI was 40.7±7.8kg/m2 and preoperative mean hemoglobin (Hb) was 13.7±1.5g/ dL. The prevalence of anemia increased from preoperatively 5.4% to 38.0% two years after surgery. Mean Hb was significantly lower in patients receiving gastric bypass than in restrictive type surgery (11.9mg/dL vs. 13.1mg/dL, p=0.040) two years after surgery. Besides, the preoperative optimal value of hemoglobin to predict future anemia in MARS model is 15.6mg/dL. The prevalence of anemia increased to 38.0% two years after bariatric surgery. We obtained an optimal preoperative value of hemoglobin 15.6mg/dL to predict postoperative anemia, which was important in preoperative assessment for bariatric surgery. Patients undergone gastric bypass surgery developed more severe anemia than gastric banding or sleeve gastrectomy.

  9. Drought forecasting in eastern Australia using multivariate adaptive regression spline, least square support vector machine and M5Tree model (United States)

    Deo, Ravinesh C.; Kisi, Ozgur; Singh, Vijay P.


    Drought forecasting using standardized metrics of rainfall is a core task in hydrology and water resources management. Standardized Precipitation Index (SPI) is a rainfall-based metric that caters for different time-scales at which the drought occurs, and due to its standardization, is well-suited for forecasting drought at different periods in climatically diverse regions. This study advances drought modelling using multivariate adaptive regression splines (MARS), least square support vector machine (LSSVM), and M5Tree models by forecasting SPI in eastern Australia. MARS model incorporated rainfall as mandatory predictor with month (periodicity), Southern Oscillation Index, Pacific Decadal Oscillation Index and Indian Ocean Dipole, ENSO Modoki and Nino 3.0, 3.4 and 4.0 data added gradually. The performance was evaluated with root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (r2). Best MARS model required different input combinations, where rainfall, sea surface temperature and periodicity were used for all stations, but ENSO Modoki and Pacific Decadal Oscillation indices were not required for Bathurst, Collarenebri and Yamba, and the Southern Oscillation Index was not required for Collarenebri. Inclusion of periodicity increased the r2 value by 0.5-8.1% and reduced RMSE by 3.0-178.5%. Comparisons showed that MARS superseded the performance of the other counterparts for three out of five stations with lower MAE by 15.0-73.9% and 7.3-42.2%, respectively. For the other stations, M5Tree was better than MARS/LSSVM with lower MAE by 13.8-13.4% and 25.7-52.2%, respectively, and for Bathurst, LSSVM yielded more accurate result. For droughts identified by SPI ≤ - 0.5, accurate forecasts were attained by MARS/M5Tree for Bathurst, Yamba and Peak Hill, whereas for Collarenebri and Barraba, M5Tree was better than LSSVM/MARS. Seasonal analysis revealed disparate results where MARS/M5Tree was better than LSSVM. The results highlight the

  10. Is There Life on Mars? (United States)

    Allen, Bruce C.; Herreid, Clyde Freeman


    Presents a conflict scenario for a case study on whether there is evidence of past life on Mars. Includes details about the use of this case study in developing an interdisciplinary approach to scientific ethics. (DDR)

  11. SPLPKG WFCMPR WFAPPX, Wilson-Fowler Spline Generator for Computer Aided Design And Manufacturing (CAD/CAM) Systems

    International Nuclear Information System (INIS)

    Fletcher, S.K.


    1 - Description of program or function: The three programs SPLPKG, WFCMPR, and WFAPPX provide the capability for interactively generating, comparing and approximating Wilson-Fowler Splines. The Wilson-Fowler spline is widely used in Computer Aided Design and Manufacturing (CAD/CAM) systems. It is favored for many applications because it produces a smooth, low curvature fit to planar data points. Program SPLPKG generates a Wilson-Fowler spline passing through given nodes (with given end conditions) and also generates a piecewise linear approximation to that spline within a user-defined tolerance. The program may be used to generate a 'desired' spline against which to compare other Splines generated by CAD/CAM systems. It may also be used to generate an acceptable approximation to a desired spline in the event that an acceptable spline cannot be generated by the receiving CAD/CAM system. SPLPKG writes an IGES file of points evaluated on the spline and/or a file containing the spline description. Program WFCMPR computes the maximum difference between two Wilson-Fowler Splines and may be used to verify the spline recomputed by a receiving system. It compares two Wilson-Fowler Splines with common nodes and reports the maximum distance between curves (measured perpendicular to segments) and the maximum difference of their tangents (or normals), both computed along the entire length of the Splines. Program WFAPPX computes the maximum difference between a Wilson- Fowler spline and a piecewise linear curve. It may be used to accept or reject a proposed approximation to a desired Wilson-Fowler spline, even if the origin of the approximation is unknown. The maximum deviation between these two curves, and the parameter value on the spline where it occurs are reported. 2 - Restrictions on the complexity of the problem - Maxima of: 1600 evaluation points (SPLPKG), 1000 evaluation points (WFAPPX), 1000 linear curve breakpoints (WFAPPX), 100 spline Nodes

  12. Semisupervised feature selection via spline regression for video semantic recognition. (United States)

    Han, Yahong; Yang, Yi; Yan, Yan; Ma, Zhigang; Sebe, Nicu; Zhou, Xiaofang


    To improve both the efficiency and accuracy of video semantic recognition, we can perform feature selection on the extracted video features to select a subset of features from the high-dimensional feature set for a compact and accurate video data representation. Provided the number of labeled videos is small, supervised feature selection could fail to identify the relevant features that are discriminative to target classes. In many applications, abundant unlabeled videos are easily accessible. This motivates us to develop semisupervised feature selection algorithms to better identify the relevant video features, which are discriminative to target classes by effectively exploiting the information underlying the huge amount of unlabeled video data. In this paper, we propose a framework of video semantic recognition by semisupervised feature selection via spline regression (S(2)FS(2)R) . Two scatter matrices are combined to capture both the discriminative information and the local geometry structure of labeled and unlabeled training videos: A within-class scatter matrix encoding discriminative information of labeled training videos and a spline scatter output from a local spline regression encoding data distribution. An l2,1 -norm is imposed as a regularization term on the transformation matrix to ensure it is sparse in rows, making it particularly suitable for feature selection. To efficiently solve S(2)FS(2)R , we develop an iterative algorithm and prove its convergency. In the experiments, three typical tasks of video semantic recognition, such as video concept detection, video classification, and human action recognition, are used to demonstrate that the proposed S(2)FS(2)R achieves better performance compared with the state-of-the-art methods.

  13. Thin-plate spline analysis of mandibular growth. (United States)

    Franchi, L; Baccetti, T; McNamara, J A


    The analysis of mandibular growth changes around the pubertal spurt in humans has several important implications for the diagnosis and orthopedic correction of skeletal disharmonies. The purpose of this study was to evaluate mandibular shape and size growth changes around the pubertal spurt in a longitudinal sample of subjects with normal occlusion by means of an appropriate morphometric technique (thin-plate spline analysis). Ten mandibular landmarks were identified on lateral cephalograms of 29 subjects at 6 different developmental phases. The 6 phases corresponded to 6 different maturational stages in cervical vertebrae during accelerative and decelerative phases of the pubertal growth curve of the mandible. Differences in shape between average mandibular configurations at the 6 developmental stages were visualized by means of thin-plate spline analysis and subjected to permutation test. Centroid size was used as the measure of the geometric size of each mandibular specimen. Differences in size at the 6 developmental phases were tested statistically. The results of graphical analysis indicated a statistically significant change in mandibular shape only for the growth interval from stage 3 to stage 4 in cervical vertebral maturation. Significant increases in centroid size were found at all developmental phases, with evidence of a prepubertal minimum and of a pubertal maximum. The existence of a pubertal peak in human mandibular growth, therefore, is confirmed by thin-plate spline analysis. Significant morphological changes in the mandible during the growth interval from stage 3 to stage 4 in cervical vertebral maturation may be described as an upward-forward direction of condylar growth determining an overall "shrinkage" of the mandibular configuration along the measurement of total mandibular length. This biological mechanism is particularly efficient in compensating for major increments in mandibular size at the adolescent spurt.

  14. Achieving high data reduction with integral cubic B-splines (United States)

    Chou, Jin J.


    During geometry processing, tangent directions at the data points are frequently readily available from the computation process that generates the points. It is desirable to utilize this information to improve the accuracy of curve fitting and to improve data reduction. This paper presents a curve fitting method which utilizes both position and tangent direction data. This method produces G(exp 1) non-rational B-spline curves. From the examples, the method demonstrates very good data reduction rates while maintaining high accuracy in both position and tangent direction.

  15. Gravity Aided Navigation Precise Algorithm with Gauss Spline Interpolation

    Directory of Open Access Journals (Sweden)

    WEN Chaobin


    Full Text Available The gravity compensation of error equation thoroughly should be solved before the study on gravity aided navigation with high precision. A gravity aided navigation model construction algorithm based on research the algorithm to approximate local grid gravity anomaly filed with the 2D Gauss spline interpolation is proposed. Gravity disturbance vector, standard gravity value error and Eotvos effect are all compensated in this precision model. The experiment result shows that positioning accuracy is raised by 1 times, the attitude and velocity accuracy is raised by 1~2 times and the positional error is maintained from 100~200 m.

  16. C2-rational cubic spline involving tension parameters

    Indian Academy of Sciences (India)

    the impact of variation of parameters ri and ti on the shape of the interpolant. Some remarks are given in x 6. 2. The rational spline interpolant. Let P И fxign. iИ1 where a И x1 ` x2 ` ┴┴┴ ` xn И b, be a partition of the interval ЙaY bК, let fi, i И 1Y ... Y n be the function values at the data points. We set hi И xiЗ1 └ xiY ∆i И Е ...

  17. Optimal Design of Grooved Cam Profile Using Non-uniform Rational B-splines

    Directory of Open Access Journals (Sweden)

    Xuan Guantao


    Full Text Available In order to reduce the fatigue damage in grooved cam mechanisms, grooved cam profile was reconstructed with non-uniform rational B-splines (NURBS. Considering joint friction, dynamic model of grooved cam mechanisms was established and the contact stress between grooved cam and follower was calculated using Hertz contact theory. Taking the minimum contact stress and the minimum acceleration as optimal objectives, integrated design model for respective kinematic and dynamic design approaches was set up. The integrated design mode was optimized to search Pareto-optimal solution by an improved artificial fish swarm algorithm, and optimized NURBS profile for grooved cam was acquired. The results show NURBS profile has better kinematic and dynamic performances. The impacts on grooved cam mechanism are reduced and wear characteristics are improved.

  18. Using Spline Regression in Semi-Parametric Stochastic Frontier Analysis: An Application to Polish Dairy Farms

    DEFF Research Database (Denmark)

    Czekaj, Tomasz Gerard; Henningsen, Arne

    The estimation of the technical efficiency comprises a vast literature in the field of applied production economics. There are two predominant approaches: the non-parametric and non-stochastic Data Envelopment Analysis (DEA) and the parametric Stochastic Frontier Analysis (SFA). The DEA...... of specifying an unsuitable functional form and thus, model misspecification and biased parameter estimates. Given these problems of the DEA and the SFA, Fan, Li and Weersink (1996) proposed a semi-parametric stochastic frontier model that estimates the production function (frontier) by non-parametric......), Kumbhakar et al. (2007), and Henningsen and Kumbhakar (2009). The aim of this paper and its main contribution to the existing literature is the estimation semi-parametric stochastic frontier models using a different non-parametric estimation technique: spline regression (Ma et al. 2011). We apply...

  19. Numerical Evaluation of Arbitrary Singular Domain Integrals Using Third-Degree B-Spline Basis Functions

    Directory of Open Access Journals (Sweden)

    Jin-Xiu Hu


    Full Text Available A new approach is presented for the numerical evaluation of arbitrary singular domain integrals. In this method, singular domain integrals are transformed into a boundary integral and a radial integral which contains singularities by using the radial integration method. The analytical elimination of singularities condensed in the radial integral formulas can be accomplished by expressing the nonsingular part of the integration kernels as a series of cubic B-spline basis functions of the distance r and using the intrinsic features of the radial integral. In the proposed method, singularities involved in the domain integrals are explicitly transformed to the boundary integrals, so no singularities exist at internal points. A few numerical examples are provided to verify the correctness and robustness of the presented method.

  20. Numerical solution of the Black-Scholes equation using cubic spline wavelets (United States)

    Černá, Dana


    The Black-Scholes equation is used in financial mathematics for computation of market values of options at a given time. We use the θ-scheme for time discretization and an adaptive scheme based on wavelets for discretization on the given time level. Advantages of the proposed method are small number of degrees of freedom, high-order accuracy with respect to variables representing prices and relatively small number of iterations needed to resolve the problem with a desired accuracy. We use several cubic spline wavelet and multi-wavelet bases and discuss their advantages and disadvantages. We also compare an isotropic and anisotropic approach. Numerical experiments are presented for the two-dimensional Black-Scholes equation.

  1. Graph analysis of non-uniform rational B-spline-based metamodels (United States)

    Steuben, John C.; Turner, Cameron J.


    Over the past decade metamodels, also known as surrogate models, based on non-uniform rational B-splines (NURBs) have been developed. These metamodels exhibit unique properties that enable a wide range of computationally efficient analyses. Thus far, the analysis of these metamodels has been of a geometric nature, but in this article an approach based on graph theory is used. The properties of NURBs enable the interpretation of NURBs-based metamodels as graphs, and enable the demonstration of several analyses based on this structure. The general case of an analytically defined continuous-variable problem is given in the first example. A specific application in the field of robotic path planning constitutes the second example. Finally, an observation on the current state of this research, its merits and drawbacks, and an outline of future efforts that may increase its utility is provided.

  2. Moon and Mars gravity environment during parabolic flights: a new European approach to prepare for planetary exploration (United States)

    Pletser, Vladimir; Clervoy, Jean-Fran; Gharib, Thierry; Gai, Frederic; Mora, Christophe; Rosier, Patrice

    Aircraft parabolic flights provide repetitively up to 20 seconds of reduced gravity during ballis-tic flight manoeuvres. Parabolic flights are used to conduct short microgravity investigations in Physical and Life Sciences and in Technology, to test instrumentation prior to space flights and to train astronauts before a space mission. The European Space Agency (ESA) has organized since 1984 more than fifty parabolic flight campaigns for microgravity research experiments utilizing six different airplanes. More than 600 experiments were conducted spanning several fields in Physical Sciences and Life Sciences, namely Fluid Physics, Combustion Physics, Ma-terial Sciences, fundamental Physics and Technology tests, Human Physiology, cell and animal Biology, and technical tests of Life Sciences instrumentation. Since 1997, ESA uses the Airbus A300 'Zero G', the largest airplane in the world used for this type of experimental research flight and managed by the French company Novespace, a subsidiary of the French space agency CNES. From 2010 onwards, ESA and Novespace will offer the possibility of flying Martian and Moon parabolas during which reduced gravity levels equivalent to those on the Moon and Mars will be achieved repetitively for periods of more than 20 seconds. Scientists are invited to submit experiment proposals to be conducted at these partial gravity levels. This paper presents the technical capabilities of the Airbus A300 Zero-G aircraft used by ESA to support and conduct investigations at Moon-, Mars-and micro-gravity levels to prepare research and exploration during space flights and future planetary exploration missions. Some Physiology and Technology experiments performed during past ESA campaigns at 0, 1/6 an 1/3 g are presented to show the interest of this unique research tool for microgravity and partial gravity investigations.

  3. A wet-geology and cold-climate Mars model: Punctuation of a slow dynamic approach to equilibrium (United States)

    Kargel, J. S.


    It was suggested that Mars may have possessed a relatively warm humid climate and a vigorous hydrological cycle involving meteoric precipitation, oceans, and continental ice sheets. Baker hypothesized that these geologically active conditions may have been repeated several times; each of these dynamic epochs was followed by a collapse of the climate and hydrologic cycle of Mars into essentially current conditions, completing what is termed a 'Baker cycle'. The purpose is to present an endmember possibility that Martian glacial landscapes, including some that were previously considered to have formed under warm climatic conditions, might be explained by processes compatible with an extremely cold surface. Two aspects of hypothesized Martian glacial terrains were cited as favoring a warm climate during Baker cycles: (1) the formation of some landscapes, including possible eskers, tunnel channels, drumlins, and outwash plains, appears to have required liquid water, and (2) a liquid-surfaced ocean was probably necessary to feed the glaciers. The requirement for liquid water, if these features were correctly interpreted, is difficult to avoid; it is entirely possible that a comparatively warm climate was involved, but it is not clear that formation of landforms by wet-based glaciers actually requires a warm climate. Even less certain is the supposed requirement for liquid oceans. Formation of glaciers only requires a source of water or ice to supply an amount of precipitation that exceeds losses due to melting and sublimation. At Martian temperatures precipitation is very low, but so are melting and sublimation, so a large body of ice that is unstable with respect to sublimation may take the role of Earth's oceans in feeding the glaciers. Recent models suggest that even current Martian polar caps, long thought to be static bodies of ice and dust, might actually be slow-moving, cryogenic continental glaciers. Is it possible that subglacial processes beneath cryogenic

  4. Regional Densification of a Global VTEC Model Based on B-Spline Representations (United States)

    Erdogan, Eren; Schmidt, Michael; Dettmering, Denise; Goss, Andreas; Seitz, Florian; Börger, Klaus; Brandert, Sylvia; Görres, Barbara; Kersten, Wilhelm F.; Bothmer, Volker; Hinrichs, Johannes; Mrotzek, Niclas


    The project OPTIMAP is a joint initiative of the Bundeswehr GeoInformation Centre (BGIC), the German Space Situational Awareness Centre (GSSAC), the German Geodetic Research Institute of the Technical University Munich (DGFI-TUM) and the Institute for Astrophysics at the University of Göttingen (IAG). The main goal of the project is the development of an operational tool for ionospheric mapping and prediction (OPTIMAP). Two key features of the project are the combination of different satellite observation techniques (GNSS, satellite altimetry, radio occultations and DORIS) and the regional densification as a remedy against problems encountered with the inhomogeneous data distribution. Since the data from space-geoscientific mission which can be used for modeling ionospheric parameters, such as the Vertical Total Electron Content (VTEC) or the electron density, are distributed rather unevenly over the globe at different altitudes, appropriate modeling approaches have to be developed to handle this inhomogeneity. Our approach is based on a two-level strategy. To be more specific, in the first level we compute a global VTEC model with a moderate regional and spectral resolution which will be complemented in the second level by a regional model in a densification area. The latter is a region characterized by a dense data distribution to obtain a high spatial and spectral resolution VTEC product. Additionally, the global representation means a background model for the regional one to avoid edge effects at the boundaries of the densification area. The presented approach based on a global and a regional model part, i.e. the consideration of a regional densification is called the Two-Level VTEC Model (TLVM). The global VTEC model part is based on a series expansion in terms of polynomial B-Splines in latitude direction and trigonometric B-Splines in longitude direction. The additional regional model part is set up by a series expansion in terms of polynomial B-splines for

  5. Modeling and testing treated tumor growth using cubic smoothing splines. (United States)

    Kong, Maiying; Yan, Jun


    Human tumor xenograft models are often used in preclinical study to evaluate the therapeutic efficacy of a certain compound or a combination of certain compounds. In a typical human tumor xenograft model, human carcinoma cells are implanted to subjects such as severe combined immunodeficient (SCID) mice. Treatment with test compounds is initiated after tumor nodule has appeared, and continued for a certain time period. Tumor volumes are measured over the duration of the experiment. It is well known that untreated tumor growth may follow certain patterns, which can be described by certain mathematical models. However, the growth patterns of the treated tumors with multiple treatment episodes are quite complex, and the usage of parametric models is limited. We propose using cubic smoothing splines to describe tumor growth for each treatment group and for each subject, respectively. The proposed smoothing splines are quite flexible in modeling different growth patterns. In addition, using this procedure, we can obtain tumor growth and growth rate over time for each treatment group and for each subject, and examine whether tumor growth follows certain growth pattern. To examine the overall treatment effect and group differences, the scaled chi-squared test statistics based on the fitted group-level growth curves are proposed. A case study is provided to illustrate the application of this method, and simulations are carried out to examine the performances of the scaled chi-squared tests. Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

  6. Momentum analysis by using a quintic spline model for the track

    CERN Document Server

    Wind, H


    A method is described to determine the momentum of a particle when the (inhomogeneous) analysing magnetic field and the position of at least three points on the track are known. The model of the field is essentially a cubic spline and that of the track a quintic spline. (8 refs).

  7. A Multidimensional Spline Based Global Nonlinear Aerodynamic Model for the Cessna Citation II

    NARCIS (Netherlands)

    De Visser, C.C.; Mulder, J.A.


    A new method is proposed for the identification of global nonlinear models of aircraft non-dimensional force and moment coefficients. The method is based on a recent type of multivariate spline, the multivariate simplex spline, which can accurately approximate very large, scattered nonlinear

  8. B-spline solution of a singularly perturbed boundary value problem arising in biology

    International Nuclear Information System (INIS)

    Lin Bin; Li Kaitai; Cheng Zhengxing


    We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution.

  9. Item Response Theory with Estimation of the Latent Population Distribution Using Spline-Based Densities (United States)

    Woods, Carol M.; Thissen, David


    The purpose of this paper is to introduce a new method for fitting item response theory models with the latent population distribution estimated from the data using splines. A spline-based density estimation system provides a flexible alternative to existing procedures that use a normal distribution, or a different functional form, for the…

  10. B-LUT: Fast and low memory B-spline image interpolation. (United States)

    Sarrut, David; Vandemeulebroucke, Jef


    We propose a fast alternative to B-splines in image processing based on an approximate calculation using precomputed B-spline weights. During B-spline indirect transformation, these weights are efficiently retrieved in a nearest-neighbor fashion from a look-up table, greatly reducing overall computation time. Depending on the application, calculating a B-spline using a look-up table, called B-LUT, will result in an exact or approximate B-spline calculation. In case of the latter the obtained accuracy can be controlled by the user. The method is applicable to a wide range of B-spline applications and has very low memory requirements compared to other proposed accelerations. The performance of the proposed B-LUTs was compared to conventional B-splines as implemented in the popular ITK toolkit for the general case of image intensity interpolation. Experiments illustrated that highly accurate B-spline approximation can be obtained all while computation time is reduced with a factor of 5-6. The B-LUT source code, compatible with the ITK toolkit, has been made freely available to the community. 2009 Elsevier Ireland Ltd. All rights reserved.

  11. Comparison of fractional splines with polynomial splines; An Application on under-five year’s child mortality data in Pakistan (1960-2012

    Directory of Open Access Journals (Sweden)

    Saira Esar Esar


    Full Text Available Cubic splines are commonly used for capturing the changes in economic analysis. This is because of the fact that traditional regression including polynomial regression fail to capture the underlying changes in the corresponding response variables. Moreover, these variables do not change monotonically, i.e. there are discontinuities in the trend of these variables over a period of time. The objective of this research is to explain the movement of under-five child mortality in Pakistan over the past few decades through a combination of statistical techniques. While cubic splines explain the movement of under-five child mortality to a large extent, we cannot deny the possibility that splines with fractional powers might better explain the underlying movement. . Hence, we estimated the value of fractional power by nonlinear regression method and used it to develop the fractional splines. Although, the fractional spline model may have the potential to improve upon the cubic spline model, it does not demonstrate a real improvement in results of this case, but, perhaps, with a different data set.

  12. B-Spline potential function for maximum a-posteriori image reconstruction in fluorescence microscopy

    Directory of Open Access Journals (Sweden)

    Shilpa Dilipkumar


    Full Text Available An iterative image reconstruction technique employing B-Spline potential function in a Bayesian framework is proposed for fluorescence microscopy images. B-splines are piecewise polynomials with smooth transition, compact support and are the shortest polynomial splines. Incorporation of the B-spline potential function in the maximum-a-posteriori reconstruction technique resulted in improved contrast, enhanced resolution and substantial background reduction. The proposed technique is validated on simulated data as well as on the images acquired from fluorescence microscopes (widefield, confocal laser scanning fluorescence and super-resolution 4Pi microscopy. A comparative study of the proposed technique with the state-of-art maximum likelihood (ML and maximum-a-posteriori (MAP with quadratic potential function shows its superiority over the others. B-Spline MAP technique can find applications in several imaging modalities of fluorescence microscopy like selective plane illumination microscopy, localization microscopy and STED.

  13. Modelling daily dissolved oxygen concentration using least square support vector machine, multivariate adaptive regression splines and M5 model tree (United States)

    Heddam, Salim; Kisi, Ozgur


    In the present study, three types of artificial intelligence techniques, least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5T) are applied for modeling daily dissolved oxygen (DO) concentration using several water quality variables as inputs. The DO concentration and water quality variables data from three stations operated by the United States Geological Survey (USGS) were used for developing the three models. The water quality data selected consisted of daily measured of water temperature (TE, °C), pH (std. unit), specific conductance (SC, μS/cm) and discharge (DI cfs), are used as inputs to the LSSVM, MARS and M5T models. The three models were applied for each station separately and compared to each other. According to the results obtained, it was found that: (i) the DO concentration could be successfully estimated using the three models and (ii) the best model among all others differs from one station to another.

  14. Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows

    Directory of Open Access Journals (Sweden)

    Shu-Cherng Fang


    Full Text Available We analytically investigate univariate C1 continuous cubic L1 interpolating splines calculated by minimizing an L1 spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in the windows with linearity, convexity and oscillation properties of the resulting L1 spline. These analytical results provide the basis for a computationally efficient algorithm for calculation of L1 splines on 5-point windows.

  15. Research on None Uniform Rational B-spline Surface and Agent for Numerically Controlled Layout Design

    Directory of Open Access Journals (Sweden)

    Zhigang XU


    Full Text Available Research on the integrated NC conceptual layout design (I-NCC concerned with a broader area of interests. The key issues of I-NCC system are associated with NURBS and agent. Firstly, formulas for the derivatives and normal vectors of non-rational B-spline and NURBS are proved based on de BOOR’s recursive formula. Compared with the existing approaches targeting at the non-rational B- spline basis functions, these equations are directly targeted at the controlling points, so the algorithms and programs for NURBS curve and surface can also be applied to the derivatives and normals, the calculating performance is increased. A simplified equation is also proved in this paper. Secondly, the NC conceptual configuration design is transformed into a 3D cuboids layout problem by the introduction of three typical modules: translation module, rotation module and base module based on the analysis of the normal unit vector of work piece surface (in NURBS format. 3D cuboids layout problem is viewed as a generalization of the quadratic assignment problem and therefore belongs to the class of NP hard problems. Apart from the complexity and variety of 3D layout optimization algorithms, this paper introduces agent oriented cooperative design system. Agent models and the corresponding design management systems are put forward to deal with the creative NC layout design. Though the key theoretical issues are now applied to the NC system design, there should be more industrial applications because of the prevalent proliferation nature of NURBS and agent.

  16. CerebroMatic: A Versatile Toolbox for Spline-Based MRI Template Creation. (United States)

    Wilke, Marko; Altaye, Mekibib; Holland, Scott K


    Brain image spatial normalization and tissue segmentation rely on prior tissue probability maps. Appropriately selecting these tissue maps becomes particularly important when investigating "unusual" populations, such as young children or elderly subjects. When creating such priors, the disadvantage of applying more deformation must be weighed against the benefit of achieving a crisper image. We have previously suggested that statistically modeling demographic variables, instead of simply averaging images, is advantageous. Both aspects (more vs. less deformation and modeling vs. averaging) were explored here. We used imaging data from 1914 subjects, aged 13 months to 75 years, and employed multivariate adaptive regression splines to model the effects of age, field strength, gender, and data quality. Within the spm/cat12 framework, we compared an affine-only with a low- and a high-dimensional warping approach. As expected, more deformation on the individual level results in lower group dissimilarity. Consequently, effects of age in particular are less apparent in the resulting tissue maps when using a more extensive deformation scheme. Using statistically-described parameters, high-quality tissue probability maps could be generated for the whole age range; they are consistently closer to a gold standard than conventionally-generated priors based on 25, 50, or 100 subjects. Distinct effects of field strength, gender, and data quality were seen. We conclude that an extensive matching for generating tissue priors may model much of the variability inherent in the dataset which is then not contained in the resulting priors. Further, the statistical description of relevant parameters (using regression splines) allows for the generation of high-quality tissue probability maps while controlling for known confounds. The resulting CerebroMatic toolbox is available for download at

  17. Application of least square support vector machine and multivariate adaptive regression spline models in long term prediction of river water pollution (United States)

    Kisi, Ozgur; Parmar, Kulwinder Singh


    This study investigates the accuracy of least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5Tree) in modeling river water pollution. Various combinations of water quality parameters, Free Ammonia (AMM), Total Kjeldahl Nitrogen (TKN), Water Temperature (WT), Total Coliform (TC), Fecal Coliform (FC) and Potential of Hydrogen (pH) monitored at Nizamuddin, Delhi Yamuna River in India were used as inputs to the applied models. Results indicated that the LSSVM and MARS models had almost same accuracy and they performed better than the M5Tree model in modeling monthly chemical oxygen demand (COD). The average root mean square error (RMSE) of the LSSVM and M5Tree models was decreased by 1.47% and 19.1% using MARS model, respectively. Adding TC input to the models did not increase their accuracy in modeling COD while adding FC and pH inputs to the models generally decreased the accuracy. The overall results indicated that the MARS and LSSVM models could be successfully used in estimating monthly river water pollution level by using AMM, TKN and WT parameters as inputs.

  18. Perbaikan Metode Penghitungan Debit Sungai Menggunakan Cubic Spline Interpolation

    Directory of Open Access Journals (Sweden)

    Budi I. Setiawan


    Full Text Available Makalah ini menyajikan perbaikan metode pengukuran debit sungai menggunakan fungsi cubic spline interpolation. Fungi ini digunakan untuk menggambarkan profil sungai secara kontinyu yang terbentuk atas hasil pengukuran jarak dan kedalaman sungai. Dengan metoda baru ini, luas dan perimeter sungai lebih mudah, cepat dan tepat dihitung. Demikian pula, fungsi kebalikannnya (inverse function tersedia menggunakan metode. Newton-Raphson sehingga memudahkan dalam perhitungan luas dan perimeter bila tinggi air sungai diketahui. Metode baru ini dapat langsung menghitung debit sungaimenggunakan formula Manning, dan menghasilkan kurva debit (rating curve. Dalam makalah ini dikemukaan satu canton pengukuran debit sungai Rudeng Aceh. Sungai ini mempunyai lebar sekitar 120 m dan kedalaman 7 m, dan pada saat pengukuran mempunyai debit 41 .3 m3/s, serta kurva debitnya mengikuti formula: Q= 0.1649 x H 2.884 , dimana Q debit (m3/s dan H tinggi air dari dasar sungai (m.

  19. TPSLVM: a dimensionality reduction algorithm based on thin plate splines. (United States)

    Jiang, Xinwei; Gao, Junbin; Wang, Tianjiang; Shi, Daming


    Dimensionality reduction (DR) has been considered as one of the most significant tools for data analysis. One type of DR algorithms is based on latent variable models (LVM). LVM-based models can handle the preimage problem easily. In this paper we propose a new LVM-based DR model, named thin plate spline latent variable model (TPSLVM). Compared to the well-known Gaussian process latent variable model (GPLVM), our proposed TPSLVM is more powerful especially when the dimensionality of the latent space is low. Also, TPSLVM is robust to shift and rotation. This paper investigates two extensions of TPSLVM, i.e., the back-constrained TPSLVM (BC-TPSLVM) and TPSLVM with dynamics (TPSLVM-DM) as well as their combination BC-TPSLVM-DM. Experimental results show that TPSLVM and its extensions provide better data visualization and more efficient dimensionality reduction compared to PCA, GPLVM, ISOMAP, etc.

  20. Groundwater potential mapping using C5.0, random forest, and multivariate adaptive regression spline models in GIS. (United States)

    Golkarian, Ali; Naghibi, Seyed Amir; Kalantar, Bahareh; Pradhan, Biswajeet


    Ever increasing demand for water resources for different purposes makes it essential to have better understanding and knowledge about water resources. As known, groundwater resources are one of the main water resources especially in countries with arid climatic condition. Thus, this study seeks to provide groundwater potential maps (GPMs) employing new algorithms. Accordingly, this study aims to validate the performance of C5.0, random forest (RF), and multivariate adaptive regression splines (MARS) algorithms for generating GPMs in the eastern part of Mashhad Plain, Iran. For this purpose, a dataset was produced consisting of spring locations as indicator and groundwater-conditioning factors (GCFs) as input. In this research, 13 GCFs were selected including altitude, slope aspect, slope angle, plan curvature, profile curvature, topographic wetness index (TWI), slope length, distance from rivers and faults, rivers and faults density, land use, and lithology. The mentioned dataset was divided into two classes of training and validation with 70 and 30% of the springs, respectively. Then, C5.0, RF, and MARS algorithms were employed using R statistical software, and the final values were transformed into GPMs. Finally, two evaluation criteria including Kappa and area under receiver operating characteristics curve (AUC-ROC) were calculated. According to the findings of this research, MARS had the best performance with AUC-ROC of 84.2%, followed by RF and C5.0 algorithms with AUC-ROC values of 79.7 and 77.3%, respectively. The results indicated that AUC-ROC values for the employed models are more than 70% which shows their acceptable performance. As a conclusion, the produced methodology could be used in other geographical areas. GPMs could be used by water resource managers and related organizations to accelerate and facilitate water resource exploitation.

  1. Meshing Force of Misaligned Spline Coupling and the Influence on Rotor System

    Directory of Open Access Journals (Sweden)

    Guang Zhao


    Full Text Available Meshing force of misaligned spline coupling is derived, dynamic equation of rotor-spline coupling system is established based on finite element analysis, the influence of meshing force on rotor-spline coupling system is simulated by numerical integral method. According to the theoretical analysis, meshing force of spline coupling is related to coupling parameters, misalignment, transmitting torque, static misalignment, dynamic vibration displacement, and so on. The meshing force increases nonlinearly with increasing the spline thickness and static misalignment or decreasing alignment meshing distance (AMD. Stiffness of coupling relates to dynamic vibration displacement, and static misalignment is not a constant. Dynamic behaviors of rotor-spline coupling system reveal the following: 1X-rotating speed is the main response frequency of system when there is no misalignment; while 2X-rotating speed appears when misalignment is present. Moreover, when misalignment increases, vibration of the system gets intricate; shaft orbit departs from origin, and magnitudes of all frequencies increase. Research results can provide important criterions on both optimization design of spline coupling and trouble shooting of rotor systems.

  2. Mars Sample Return: Mars Ascent Vehicle Mission and Technology Requirements (United States)

    Bowles, Jeffrey V.; Huynh, Loc C.; Hawke, Veronica M.; Jiang, Xun J.


    A Mars Sample Return mission is the highest priority science mission for the next decade recommended by the recent Decadal Survey of Planetary Science, the key community input process that guides NASAs science missions. A feasibility study was conducted of a potentially simple and low cost approach to Mars Sample Return mission enabled by the use of developing commercial capabilities. Previous studies of MSR have shown that landing an all up sample return mission with a high mass capacity lander is a cost effective approach. The approach proposed is the use of an emerging commercially available capsule to land the launch vehicle system that would return samples to Earth. This paper describes the mission and technology requirements impact on the launch vehicle system design, referred to as the Mars Ascent Vehicle (MAV).

  3. NASA Mars Conference

    International Nuclear Information System (INIS)

    Reiber, D.B.


    Papers about Mars and Mars exploration are presented, covering topics such as Martian history, geology, volcanism, channels, moons, atmosphere, meteorology, water on the planet, and the possibility of life. The unmanned exploration of Mars is discussed, including the Phobos Mission, the Mars Observer, the Mars Aeronomy Observer, the seismic network, Mars sample return missions, and the Mars Ball, an inflatable-sectored-tire rover concept. Issues dealing with manned exploration of Mars are examined, such as the reasons for exploring Mars, mission scenarios, a transportation system for routine visits, technologies for Mars expeditions, the human factors for Mars missions, life support systems, living and working on Mars, and the report of the National Commission on Space

  4. Cubic spline function interpolation in atmosphere models for the software development laboratory: Formulation and data (United States)

    Kirkpatrick, J. C.


    A tabulation of selected altitude-correlated values of pressure, density, speed of sound, and coefficient of viscosity for each of six models of the atmosphere is presented in block data format. Interpolation for the desired atmospheric parameters is performed by using cubic spline functions. The recursive relations necessary to compute the cubic spline function coefficients are derived and implemented in subroutine form. Three companion subprograms, which form the preprocessor and processor, are also presented. These subprograms, together with the data element, compose the spline fit atmosphere package. Detailed FLOWGM flow charts and FORTRAN listings of the atmosphere package are presented in the appendix.

  5. Higher-order numerical solutions using cubic splines. [for partial differential equations (United States)

    Rubin, S. G.; Khosla, P. K.


    A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-

  6. Solving the nonlinear Schrödinger equation using cubic B-spline interpolation and finite difference methods on dual solitons (United States)

    Ahmad, Azhar; Azmi, Amirah; Majid, Ahmad Abd.; Hamid, Nur Nadiah Abd


    In this paper, Nonlinear Schrödinger (NLS) equation with Neumann boundary conditions is solved using cubic B-spline interpolation method (CuBSIM) and finite difference method (FDM). Firstly, FDM is applied on the time discretization and cubic B-spline is utilized as an interpolation function in the space dimension with the help of theta-weighted method. The second approach is based on the FDM applied on the time and space discretization with the help of theta-weighted method. The CuBSIM is shown to be stable by using von Neumann stability analysis. The proposed method is tested on the interaction of the dual solitons of the NLS equation. The accuracy of the numerical results is measured by the Euclidean-norm and infinity-norm. CuBSIM is found to produce more accurate results than the FDM.

  7. Numerical solution of system of boundary value problems using B-spline with free parameter (United States)

    Gupta, Yogesh


    This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

  8. Numerical treatment of Hunter Saxton equation using cubic trigonometric B-spline collocation method (United States)

    Hashmi, M. S.; Awais, Muhammad; Waheed, Ammarah; Ali, Qutab


    In this article, authors proposed a computational model based on cubic trigonometric B-spline collocation method to solve Hunter Saxton equation. The nonlinear second order partial differential equation arises in modeling of nematic liquid crystals and describes some aspects of orientation wave. The problem is decomposed into system of linear equations using cubic trigonometric B-spline collocation method with quasilinearization. To show the efficiency of the proposed method, two numerical examples have been tested for different values of t. The results are described using error tables and graphs and compared with the results existed in literature. It is evident that results are in good agreement with analytical solution and better than Arbabi, Nazari, and Davishi, Optik 127, 5255-5258 (2016). In current problem, it is also observed that the cubic trigonometric B-spline gives better results as compared to cubic B-spline.

  9. Cubic B-spline solution for two-point boundary value problem with AOR iterative method (United States)

    Suardi, M. N.; Radzuan, N. Z. F. M.; Sulaiman, J.


    In this study, the cubic B-spline approximation equation has been derived by using the cubic B-spline discretization scheme to solve two-point boundary value problems. In addition to that, system of cubic B-spline approximation equations is generated from this spline approximation equation in order to get the numerical solutions. To do this, the Accelerated Over Relaxation (AOR) iterative method has been used to solve the generated linear system. For the purpose of comparison, the GS iterative method is designated as a control method to compare between SOR and AOR iterative methods. There are two examples of proposed problems that have been considered to examine the efficiency of these proposed iterative methods via three parameters such as their number of iterations, computational time and maximum absolute error. The numerical results are obtained from these iterative methods, it can be concluded that the AOR iterative method is slightly efficient as compared with SOR iterative method.


    Directory of Open Access Journals (Sweden)

    Mikhail Lopatjuk


    Full Text Available The method and the algorithm of solving the problem of streamlining are presented. Neumann boundary problem is reduced to the solution of integral equations with given boundary conditions using the cubic spline-functions

  11. Vibration Analysis of Suspension Cable with Attached Masses by Non-linear Spline Function Method

    Directory of Open Access Journals (Sweden)

    Qin Jian


    Full Text Available The nonlinear strain and stress expressions of suspension cable are established from the basic condition of suspension structure on the Lagrange coordinates and the equilibrium equation of the suspension structure is obtained. The dynamics equations of motion of the suspended cable with attached masses are proposed according to the virtual work principle. Using the spline function as interpolation functions of displacement and spatial position, the spline function method of dynamics equation of suspension cable is formed in which the stiffness matrix is expressed by spline function, and the solution method of stiffness matrix, matrix assembly method based on spline integral, is put forwards which can save cost time efficiency. The vibration frequency of the suspension cable is calculated with different attached masses, which provides theoretical basis for valuing of safety coefficient of the bearing cable of the cableway.

  12. Acoustic Emission Signatures of Fatigue Damage in Idealized Bevel Gear Spline for Localized Sensing

    Directory of Open Access Journals (Sweden)

    Lu Zhang


    Full Text Available In many rotating machinery applications, such as helicopters, the splines of an externally-splined steel shaft that emerges from the gearbox engage with the reverse geometry of an internally splined driven shaft for the delivery of power. The splined section of the shaft is a critical and non-redundant element which is prone to cracking due to complex loading conditions. Thus, early detection of flaws is required to prevent catastrophic failures. The acoustic emission (AE method is a direct way of detecting such active flaws, but its application to detect flaws in a splined shaft in a gearbox is difficult due to the interference of background noise and uncertainty about the effects of the wave propagation path on the received AE signature. Here, to model how AE may detect fault propagation in a hollow cylindrical splined shaft, the splined section is essentially unrolled into a metal plate of the same thickness as the cylinder wall. Spline ridges are cut into this plate, a through-notch is cut perpendicular to the spline to model fatigue crack initiation, and tensile cyclic loading is applied parallel to the spline to propagate the crack. In this paper, the new piezoelectric sensor array is introduced with the purpose of placing them within the gearbox to minimize the wave propagation path. The fatigue crack growth of a notched and flattened gearbox spline component is monitored using a new piezoelectric sensor array and conventional sensors in a laboratory environment with the purpose of developing source models and testing the new sensor performance. The AE data is continuously collected together with strain gauges strategically positioned on the structure. A significant amount of continuous emission due to the plastic deformation accompanied with the crack growth is observed. The frequency spectra of continuous emissions and burst emissions are compared to understand the differences of plastic deformation and sudden crack jump. The

  13. Numerical Solutions for Convection-Diffusion Equation through Non-Polynomial Spline

    Directory of Open Access Journals (Sweden)

    Ravi Kanth A.S.V.


    Full Text Available In this paper, numerical solutions for convection-diffusion equation via non-polynomial splines are studied. We purpose an implicit method based on non-polynomial spline functions for solving the convection-diffusion equation. The method is proven to be unconditionally stable by using Von Neumann technique. Numerical results are illustrated to demonstrate the efficiency and stability of the purposed method.

  14. Human Mars Surface Mission Nuclear Power Considerations (United States)

    Rucker, Michelle A.


    A key decision facing Mars mission designers is how to power a crewed surface field station. Unlike the solar-powered Mars Exploration Rovers (MER) that could retreat to a very low power state during a Martian dust storm, human Mars surface missions are estimated to need at least 15 kilowatts of electrical (kWe) power simply to maintain critical life support and spacecraft functions. 'Hotel' loads alone for a pressurized crew rover approach two kWe; driving requires another five kWe-well beyond what the Curiosity rover’s Radioisotope Power System (RPS) was designed to deliver. Full operation of a four-crew Mars field station is estimated at about 40 kWe. Clearly, a crewed Mars field station will require a substantial and reliable power source, beyond the scale of robotic mission experience. This paper explores the applications for both fission and RPS nuclear options for Mars.

  15. Random regression analyses using B-splines to model growth of Australian Angus cattle

    Directory of Open Access Journals (Sweden)

    Meyer Karin


    Full Text Available Abstract Regression on the basis function of B-splines has been advocated as an alternative to orthogonal polynomials in random regression analyses. Basic theory of splines in mixed model analyses is reviewed, and estimates from analyses of weights of Australian Angus cattle from birth to 820 days of age are presented. Data comprised 84 533 records on 20 731 animals in 43 herds, with a high proportion of animals with 4 or more weights recorded. Changes in weights with age were modelled through B-splines of age at recording. A total of thirteen analyses, considering different combinations of linear, quadratic and cubic B-splines and up to six knots, were carried out. Results showed good agreement for all ages with many records, but fluctuated where data were sparse. On the whole, analyses using B-splines appeared more robust against "end-of-range" problems and yielded more consistent and accurate estimates of the first eigenfunctions than previous, polynomial analyses. A model fitting quadratic B-splines, with knots at 0, 200, 400, 600 and 821 days and a total of 91 covariance components, appeared to be a good compromise between detailedness of the model, number of parameters to be estimated, plausibility of results, and fit, measured as residual mean square error.

  16. Surface quality monitoring for process control by on-line vibration analysis using an adaptive spline wavelet algorithm (United States)

    Luo, G. Y.; Osypiw, D.; Irle, M.


    The dynamic behaviour of wood machining processes affects the surface finish quality of machined workpieces. In order to meet the requirements of increased production efficiency and improved product quality, surface quality information is needed for enhanced process control. However, current methods using high price devices or sophisticated designs, may not be suitable for industrial real-time application. This paper presents a novel approach of surface quality evaluation by on-line vibration analysis using an adaptive spline wavelet algorithm, which is based on the excellent time-frequency localization of B-spline wavelets. A series of experiments have been performed to extract the feature, which is the correlation between the relevant frequency band(s) of vibration with the change of the amplitude and the surface quality. The graphs of the experimental results demonstrate that the change of the amplitude in the selective frequency bands with variable resolution (linear and non-linear) reflects the quality of surface finish, and the root sum square of wavelet power spectrum is a good indication of surface quality. Thus, surface quality can be estimated and quantified at an average level in real time. The results can be used to regulate and optimize the machine's feed speed, maintaining a constant spindle motor speed during cutting. This will lead to higher level control and machining rates while keeping dimensional integrity and surface finish within specification.

  17. Dynamic metabolic flux analysis using B-splines to study the effects of temperature shift on CHO cell metabolism

    Directory of Open Access Journals (Sweden)

    Verónica S. Martínez


    Full Text Available Metabolic flux analysis (MFA is widely used to estimate intracellular fluxes. Conventional MFA, however, is limited to continuous cultures and the mid-exponential growth phase of batch cultures. Dynamic MFA (DMFA has emerged to characterize time-resolved metabolic fluxes for the entire culture period. Here, the linear DMFA approach was extended using B-spline fitting (B-DMFA to estimate mass balanced fluxes. Smoother fits were achieved using reduced number of knots and parameters. Additionally, computation time was greatly reduced using a new heuristic algorithm for knot placement. B-DMFA revealed that Chinese hamster ovary cells shifted from 37 °C to 32 °C maintained a constant IgG volume-specific productivity, whereas the productivity for the controls peaked during mid-exponential growth phase and declined afterward. The observed 42% increase in product titer at 32 °C was explained by a prolonged cell growth with high cell viability, a larger cell volume and a more stable volume-specific productivity. Keywords: Dynamic, Metabolism, Flux analysis, CHO cells, Temperature shift, B-spline curve fitting

  18. Micropolar Fluids Using B-spline Divergence Conforming Spaces

    KAUST Repository

    Sarmiento, Adel


    We discretized the two-dimensional linear momentum, microrotation, energy and mass conservation equations from micropolar fluids theory, with the finite element method, creating divergence conforming spaces based on B-spline basis functions to obtain pointwise divergence free solutions [8]. Weak boundary conditions were imposed using Nitsche\\'s method for tangential conditions, while normal conditions were imposed strongly. Once the exact mass conservation was provided by the divergence free formulation, we focused on evaluating the differences between micropolar fluids and conventional fluids, to show the advantages of using the micropolar fluid model to capture the features of complex fluids. A square and an arc heat driven cavities were solved as test cases. A variation of the parameters of the model, along with the variation of Rayleigh number were performed for a better understanding of the system. The divergence free formulation was used to guarantee an accurate solution of the flow. This formulation was implemented using the framework PetIGA as a basis, using its parallel stuctures to achieve high scalability. The results of the square heat driven cavity test case are in good agreement with those reported earlier.

  19. A Bézier-Spline-based Model for the Simulation of Hysteresis in Variably Saturated Soil (United States)

    Cremer, Clemens; Peche, Aaron; Thiele, Luisa-Bianca; Graf, Thomas; Neuweiler, Insa


    Most transient variably saturated flow models neglect hysteresis in the p_c-S-relationship (Beven, 2012). Such models tend to inadequately represent matrix potential and saturation distribution. Thereby, when simulating flow and transport processes, fluid and solute fluxes might be overestimated (Russo et al., 1989). In this study, we present a simple, computationally efficient and easily applicable model that enables to adequately describe hysteresis in the p_c-S-relationship for variably saturated flow. This model can be seen as an extension to the existing play-type model (Beliaev and Hassanizadeh, 2001), where scanning curves are simplified as vertical lines between main imbibition and main drainage curve. In our model, we use continuous linear and Bézier-Spline-based functions. We show the successful validation of the model by numerically reproducing a physical experiment by Gillham, Klute and Heermann (1976) describing primary drainage and imbibition in a vertical soil column. With a deviation of 3%, the simple Bézier-Spline-based model performs significantly better that the play-type approach, which deviates by 30% from the experimental results. Finally, we discuss the realization of physical experiments in order to extend the model to secondary scanning curves and in order to determine scanning curve steepness. {Literature} Beven, K.J. (2012). Rainfall-Runoff-Modelling: The Primer. John Wiley and Sons. Russo, D., Jury, W. A., & Butters, G. L. (1989). Numerical analysis of solute transport during transient irrigation: 1. The effect of hysteresis and profile heterogeneity. Water Resources Research, 25(10), 2109-2118. Beliaev, A.Y. & Hassanizadeh, S.M. (2001). A Theoretical Model of Hysteresis and Dynamic Effects in the Capillary Relation for Two-phase Flow in Porous Media. Transport in Porous Media 43: 487. doi:10.1023/A:1010736108256. Gillham, R., Klute, A., & Heermann, D. (1976). Hydraulic properties of a porous

  20. An algorithm based on a new DQM with modified extended cubic B-splines for numerical study of two dimensional hyperbolic telegraph equation

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    Brajesh Kumar Singh


    Full Text Available In this paper, a new approach “modified extended cubic B-Spline differential quadrature (mECDQ method” has been developed for the numerical computation of two dimensional hyperbolic telegraph equation. The mECDQ method is a DQM based on modified extended cubic B-spline functions as new base functions. The mECDQ method reduces the hyperbolic telegraph equation into an amenable system of ordinary differential equations (ODEs, in time. The resulting system of ODEs has been solved by adopting an optimal five stage fourth-order strong stability preserving Runge - Kutta (SSP-RK54 scheme. The stability of the method is also studied by computing the eigenvalues of the coefficient matrices. It is shown that the mECDQ method produces stable solution for the telegraph equation. The accuracy of the method is illustrated by computing the errors between analytical solutions and numerical solutions are measured in terms of L2 and L∞ and average error norms for each problem. A comparison of mECDQ solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes, which shows that the mECDQ solutions are converging very fast in comparison with the various existing schemes. Keywords: Differential quadrature method, Hyperbolic telegraph equation, Modified extended cubic B-splines, mECDQ method, Thomas algorithm

  1. Automatic lung lobe segmentation of COPD patients using iterative B-spline fitting (United States)

    Shamonin, D. P.; Staring, M.; Bakker, M. E.; Xiao, C.; Stolk, J.; Reiber, J. H. C.; Stoel, B. C.


    We present an automatic lung lobe segmentation algorithm for COPD patients. The method enhances fissures, removes unlikely fissure candidates, after which a B-spline is fitted iteratively through the remaining candidate objects. The iterative fitting approach circumvents the need to classify each object as being part of the fissure or being noise, and allows the fissure to be detected in multiple disconnected parts. This property is beneficial for good performance in patient data, containing incomplete and disease-affected fissures. The proposed algorithm is tested on 22 COPD patients, resulting in accurate lobe-based densitometry, and a median overlap of the fissure (defined 3 voxels wide) with an expert ground truth of 0.65, 0.54 and 0.44 for the three main fissures. This compares to complete lobe overlaps of 0.99, 0.98, 0.98, 0.97 and 0.87 for the five main lobes, showing promise for lobe segmentation on data of patients with moderate to severe COPD.

  2. Spline Truncated Multivariabel pada Permodelan Nilai Ujian Nasional di Kabupaten Lombok Barat

    Directory of Open Access Journals (Sweden)

    Nurul Fitriyani


    Full Text Available Regression model is used to analyze the relationship between dependent variable and independent variable. If the regression curve form is not known, then the regression curve estimation can be done by nonparametric regression approach. This study aimed to investigate the relationship between the value resulted by National Examination and the factors that influence it. The statistical analysis used was multivariable truncated spline, in order to analyze the relationship between variables. The research that has been done showed that the best model obtained by using three knot points. This model produced a minimum GCV value of 44.46 and the value of determination coefficient of 58.627%. The parameter test showed that all factors used were significantly influence the National Examination Score for Senior High School students in West Lombok Regency year 2017. The variables were as follows: National Examination Score of Junior High School; School or Madrasah Examination Score; the value of Student’s Report Card; Student’s House Distance to School; and Number of Student’s Siblings.

  3. Cubic smoothing splines background correction in on-line liquid chromatography-Fourier transform infrared spectrometry. (United States)

    Kuligowski, Julia; Carrión, David; Quintás, Guillermo; Garrigues, Salvador; de la Guardia, Miguel


    A background correction method for the on-line coupling of gradient liquid chromatography and Fourier transform infrared spectrometry (LC-FTIR) is proposed. The developed approach applies univariate background correction to each variable (i.e. each wave number) individually. Spectra measured in the region before and after each peak cluster are used as knots to model the variation of the eluent absorption intensity with time using cubic smoothing splines (CSS) functions. The new approach has been successfully tested on simulated as well as on real data sets obtained from injections of standard mixtures of polyethylene glycols with four different molecular weights in methanol:water, 2-propanol:water and ethanol:water gradients ranging from 30 to 90, 10 to 25 and from 10 to 40% (v/v) of organic modifier, respectively. Calibration lines showed high linearity with coefficients of determination higher than 0.98 and limits of detection between 0.4 and 1.4, 0.9 and 1.8, and 1.1 and 2.7 mgmL⁻¹ in methanol:water, 2-propanol:water and ethanol:water, respectively. Furthermore the method performance has been compared with a univariate background correction approach based on the use of a reference spectra matrix (UBC-RSM) to discuss the potential as well as pitfalls and drawbacks of the proposed approach. This method works without previous variable selection and provides minimal user-interaction, thus increasing drastically the feasibility of on-line coupling of gradient LC-FTIR. Copyright © 2010 Elsevier B.V. All rights reserved.

  4. Body Fat Percentage Prediction Using Intelligent Hybrid Approaches

    Directory of Open Access Journals (Sweden)

    Yuehjen E. Shao


    Full Text Available Excess of body fat often leads to obesity. Obesity is typically associated with serious medical diseases, such as cancer, heart disease, and diabetes. Accordingly, knowing the body fat is an extremely important issue since it affects everyone’s health. Although there are several ways to measure the body fat percentage (BFP, the accurate methods are often associated with hassle and/or high costs. Traditional single-stage approaches may use certain body measurements or explanatory variables to predict the BFP. Diverging from existing approaches, this study proposes new intelligent hybrid approaches to obtain fewer explanatory variables, and the proposed forecasting models are able to effectively predict the BFP. The proposed hybrid models consist of multiple regression (MR, artificial neural network (ANN, multivariate adaptive regression splines (MARS, and support vector regression (SVR techniques. The first stage of the modeling includes the use of MR and MARS to obtain fewer but more important sets of explanatory variables. In the second stage, the remaining important variables are served as inputs for the other forecasting methods. A real dataset was used to demonstrate the development of the proposed hybrid models. The prediction results revealed that the proposed hybrid schemes outperformed the typical, single-stage forecasting models.

  5. Evaluation of the spline reconstruction technique for PET

    Energy Technology Data Exchange (ETDEWEB)

    Kastis, George A., E-mail:; Kyriakopoulou, Dimitra [Research Center of Mathematics, Academy of Athens, Athens 11527 (Greece); Gaitanis, Anastasios [Biomedical Research Foundation of the Academy of Athens (BRFAA), Athens 11527 (Greece); Fernández, Yolanda [Centre d’Imatge Molecular Experimental (CIME), CETIR-ERESA, Barcelona 08950 (Spain); Hutton, Brian F. [Institute of Nuclear Medicine, University College London, London NW1 2BU (United Kingdom); Fokas, Athanasios S. [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB30WA (United Kingdom)


    Purpose: The spline reconstruction technique (SRT), based on the analytic formula for the inverse Radon transform, has been presented earlier in the literature. In this study, the authors present an improved formulation and numerical implementation of this algorithm and evaluate it in comparison to filtered backprojection (FBP). Methods: The SRT is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of “custom made” cubic splines. By restricting reconstruction only within object pixels and by utilizing certain mathematical symmetries, the authors achieve a reconstruction time comparable to that of FBP. The authors have implemented SRT in STIR and have evaluated this technique using simulated data from a clinical positron emission tomography (PET) system, as well as real data obtained from clinical and preclinical PET scanners. For the simulation studies, the authors have simulated sinograms of a point-source and three digital phantoms. Using these sinograms, the authors have created realizations of Poisson noise at five noise levels. In addition to visual comparisons of the reconstructed images, the authors have determined contrast and bias for different regions of the phantoms as a function of noise level. For the real-data studies, sinograms of an{sup 18}F-FDG injected mouse, a NEMA NU 4-2008 image quality phantom, and a Derenzo phantom have been acquired from a commercial PET system. The authors have determined: (a) coefficient of variations (COV) and contrast from the NEMA phantom, (b) contrast for the various sections of the Derenzo phantom, and (c) line profiles for the Derenzo phantom. Furthermore, the authors have acquired sinograms from a whole-body PET scan of an {sup 18}F-FDG injected cancer patient, using the GE Discovery ST PET/CT system. SRT and FBP reconstructions of the thorax have been visually evaluated. Results: The results indicate an improvement in FWHM and FWTM in both simulated and real

  6. An evaluation of prefiltered B-spline reconstruction for quasi-interpolation on the Body-Centered Cubic lattice. (United States)

    Csébfalvi, Balázs


    In this paper, we demonstrate that quasi-interpolation of orders two and four can be efficiently implemented on the Body-Centered Cubic (BCC) lattice by using tensor-product B-splines combined with appropriate discrete prefilters. Unlike the nonseparable box-spline reconstruction previously proposed for the BCC lattice, the prefiltered B-spline reconstruction can utilize the fast trilinear texture-fetching capability of the recent graphics cards. Therefore, it can be applied for rendering BCC-sampled volumetric data interactively. Furthermore, we show that a separable B-spline filter can suppress the postaliasing effect much more isotropically than a nonseparable box-spline filter of the same approximation power. Although prefilters that make the B-splines interpolating on the BCC lattice do not exist, we demonstrate that quasi-interpolating prefiltered linear and cubic B-spline reconstructions can still provide similar or higher image quality than the interpolating linear box-spline and prefiltered quintic box-spline reconstructions, respectively.

  7. MARS Validation Plan and Status

    International Nuclear Information System (INIS)

    Ahn, Seung-hoon; Cho, Yong-jin


    The KINS Reactor Thermal-hydraulic Analysis System (KINS-RETAS) under development is directed toward a realistic analysis approach of best-estimate (BE) codes and realistic assumptions. In this system, MARS is pivoted to provide the BE Thermal-Hydraulic (T-H) response in core and reactor coolant system to various operational transients and accidental conditions. As required for other BE codes, the qualification is essential to ensure reliable and reasonable accuracy for a targeted MARS application. Validation is a key element of the code qualification, and determines the capability of a computer code in predicting the major phenomena expected to occur. The MARS validation was made by its developer KAERI, on basic premise that its backbone code RELAP5/MOD3.2 is well qualified against analytical solutions, test or operational data. A screening was made to select the test data for MARS validation; some models transplanted from RELAP5, if already validated and found to be acceptable, were screened out from assessment. It seems to be reasonable, but does not demonstrate whether code adequacy complies with the software QA guidelines. Especially there may be much difficulty in validating the life-cycle products such as code updates or modifications. This paper presents the plan for MARS validation, and the current implementation status

  8. Practical box splines for reconstruction on the body centered cubic lattice. (United States)

    Entezari, Alireza; Van De Ville, Dimitri; Möeller, Torsten


    We introduce a family of box splines for efficient, accurate and smooth reconstruction of volumetric data sampled on the Body Centered Cubic (BCC) lattice, which is the favorable volumetric sampling pattern due to its optimal spectral sphere packing property. First, we construct a box spline based on the four principal directions of the BCC lattice that allows for a linear C(0) reconstruction. Then, the design is extended for higher degrees of continuity. We derive the explicit piecewise polynomial representation of the C(0) and C(2) box splines that are useful for practical reconstruction applications. We further demonstrate that approximation in the shift-invariant space---generated by BCC-lattice shifts of these box splines---is {twice} as efficient as using the tensor-product B-spline solutions on the Cartesian lattice (with comparable smoothness and approximation order, and with the same sampling density). Practical evidence is provided demonstrating that not only the BCC lattice is generally a more accurate sampling pattern, but also allows for extremely efficient reconstructions that outperform tensor-product Cartesian reconstructions.

  9. Reconstruction of 4-D dynamic SPECT images from inconsistent projections using a Spline initialized FADS algorithm (SIFADS). (United States)

    Abdalah, Mahmoud; Boutchko, Rostyslav; Mitra, Debasis; Gullberg, Grant T


    In this paper, we propose and validate an algorithm of extracting voxel-by-voxel time activity curves directly from inconsistent projections applied in dynamic cardiac SPECT. The algorithm was derived based on factor analysis of dynamic structures (FADS) approach and imposes prior information by applying several regularization functions with adaptively changing relative weighting. The anatomical information of the imaged subject was used to apply the proposed regularization functions adaptively in the spatial domain. The algorithm performance is validated by reconstructing dynamic datasets simulated using the NCAT phantom with a range of different input tissue time-activity curves. The results are compared to the spline-based and FADS methods. The validated algorithm is then applied to reconstruct pre-clinical cardiac SPECT data from canine and murine subjects. Images, generated from both simulated and experimentally acquired data confirm the ability of the new algorithm to solve the inverse problem of dynamic SPECT with slow gantry rotation.

  10. A finite strain Eulerian formulation for compressible and nearly incompressible hyperelasticity using high-order B-spline finite elements

    KAUST Repository

    Duddu, Ravindra


    We present a numerical formulation aimed at modeling the nonlinear response of elastic materials using large deformation continuum mechanics in three dimensions. This finite element formulation is based on the Eulerian description of motion and the transport of the deformation gradient. When modeling a nearly incompressible solid, the transport of the deformation gradient is decomposed into its isochoric part and the Jacobian determinant as independent fields. A homogeneous isotropic hyperelastic solid is assumed and B-splines-based finite elements are used for the spatial discretization. A variational multiscale residual-based approach is employed to stabilize the transport equations. The performance of the scheme is explored for both compressible and nearly incompressible applications. The numerical results are in good agreement with theory illustrating the viability of the computational scheme. © 2011 John Wiley & Sons, Ltd.

  11. The 'Mission to Mars' Case Study, Galbraith's Star Model and other Relevant Organization Theory, Critically Evaluate the Reorganization of the Mars Programme that Resulted from the Introduction of the 'Faster, Better, Cheaper' Approach at NASA

    Directory of Open Access Journals (Sweden)

    Felisa Córdova G.


    Full Text Available In the 1990s, NASA implemented a programme named "Faster, Better, Cheaper," (FBC which involved essential changes to the way in which the organization used to be established. It was a huge organizational and transformational effort that required delivering dramatic advances in robustness, flexibility, and efficiency. Nevertheless in 1999, the failures of two consecutive Mars Climate Orbiter and Polar Lander missions brought to a stop of the FBC programme. We critically analyze and evaluate NASA's reorganization across of two models of organization theory such as the Diamond and Star, which show that FBC style needed a super-high-tech, a high level of complexity and novelty, and a time-critical pace. In addition, the majority of the missions' failures were also because of the short schedule, limited budget, and a deficient coordination of the processes management particularly in learning.

  12. Mars - Water Ice Clouds (United States)


    The Jet Propulsion Laboratory's Mars Surveyor Operations Project operates the Mars Global Surveyor spacecraft with its industrial partner, Lockheed Martin Astronautics, from facilities in Pasadena, CA and Denver, CO.

  13. Geology of Mars

    International Nuclear Information System (INIS)

    Soderblom, L.A.


    The geology of Mars and the results of the Mariner 4, 6/7, and 9 missions and the Viking mission are reviewed. The Mars chronology and geologic modification are examined, including chronological models for the inactive planet, the active planet, and crater flux. The importance of surface materials is discussed and a multispectral map of Mars is presented. Suggestions are given for further studies of the geology of Mars using the Viking data. 5 references

  14. T-Spline Based Unifying Registration Procedure for Free-Form Surface Workpieces in Intelligent CMM

    Directory of Open Access Journals (Sweden)

    Zhenhua Han


    Full Text Available With the development of the modern manufacturing industry, the free-form surface is widely used in various fields, and the automatic detection of a free-form surface is an important function of future intelligent three-coordinate measuring machines (CMMs. To improve the intelligence of CMMs, a new visual system is designed based on the characteristics of CMMs. A unified model of the free-form surface is proposed based on T-splines. A discretization method of the T-spline surface formula model is proposed. Under this discretization, the position and orientation of the workpiece would be recognized by point cloud registration. A high accuracy evaluation method is proposed between the measured point cloud and the T-spline surface formula. The experimental results demonstrate that the proposed method has the potential to realize the automatic detection of different free-form surfaces and improve the intelligence of CMMs.

  15. Smoothing two-dimensional Malaysian mortality data using P-splines indexed by age and year (United States)

    Kamaruddin, Halim Shukri; Ismail, Noriszura


    Nonparametric regression implements data to derive the best coefficient of a model from a large class of flexible functions. Eilers and Marx (1996) introduced P-splines as a method of smoothing in generalized linear models, GLMs, in which the ordinary B-splines with a difference roughness penalty on coefficients is being used in a single dimensional mortality data. Modeling and forecasting mortality rate is a problem of fundamental importance in insurance company calculation in which accuracy of models and forecasts are the main concern of the industry. The original idea of P-splines is extended to two dimensional mortality data. The data indexed by age of death and year of death, in which the large set of data will be supplied by Department of Statistics Malaysia. The extension of this idea constructs the best fitted surface and provides sensible prediction of the underlying mortality rate in Malaysia mortality case.

  16. Modeling Seismic Wave Propagation Using Time-Dependent Cauchy-Navier Splines (United States)

    Kammann, P.


    Our intention is the modeling of seismic wave propagation from displacement measurements by seismographs at the Earth's surface. The elastic behaviour of the Earth is usually described by the Cauchy-Navier equation. A system of fundamental solutions for the Fourier transformed Cauchy-Navier equation are the Hansen vectors L, M and N. We apply an inverse Fourier transform to obtain an orthonormal function system depending on time and space. By means of this system we construct certain splines, which are then used for interpolating the given data. Compared to polynomial interpolation, splines have the advantage that they minimize some curvature measure and are, therefore, smoother. First, we test this method on a synthetic wave function. Afterwards, we apply it to realistic earthquake data. (P. Kammann, Modelling Seismic Wave Propagation Using Time-Dependent Cauchy-Navier Splines, Diploma Thesis, Geomathematics Group, Department of Mathematics, University of Kaiserslautern, 2005)

  17. Cubic spline interpolation of functions with high gradients in boundary layers (United States)

    Blatov, I. A.; Zadorin, A. I.; Kitaeva, E. V.


    The cubic spline interpolation of grid functions with high-gradient regions is considered. Uniform meshes are proved to be inefficient for this purpose. In the case of widely applied piecewise uniform Shishkin meshes, asymptotically sharp two-sided error estimates are obtained in the class of functions with an exponential boundary layer. It is proved that the error estimates of traditional spline interpolation are not uniform with respect to a small parameter, and the error can increase indefinitely as the small parameter tends to zero, while the number of nodes N is fixed. A modified cubic interpolation spline is proposed, for which O((ln N/N)4) error estimates that are uniform with respect to the small parameter are obtained.

  18. Error Estimates Derived from the Data for Least-Squares Spline Fitting

    Energy Technology Data Exchange (ETDEWEB)

    Jerome Blair


    The use of least-squares fitting by cubic splines for the purpose of noise reduction in measured data is studied. Splines with variable mesh size are considered. The error, the difference between the input signal and its estimate, is divided into two sources: the R-error, which depends only on the noise and increases with decreasing mesh size, and the Ferror, which depends only on the signal and decreases with decreasing mesh size. The estimation of both errors as a function of time is demonstrated. The R-error estimation requires knowledge of the statistics of the noise and uses well-known methods. The primary contribution of the paper is a method for estimating the F-error that requires no prior knowledge of the signal except that it has four derivatives. It is calculated from the difference between two different spline fits to the data and is illustrated with Monte Carlo simulations and with an example.

  19. Adaptive spline autoregression threshold method in forecasting Mitsubishi car sales volume at PT Srikandi Diamond Motors (United States)

    Susanti, D.; Hartini, E.; Permana, A.


    Sale and purchase of the growing competition between companies in Indonesian, make every company should have a proper planning in order to win the competition with other companies. One of the things that can be done to design the plan is to make car sales forecast for the next few periods, it’s required that the amount of inventory of cars that will be sold in proportion to the number of cars needed. While to get the correct forecasting, on of the methods that can be used is the method of Adaptive Spline Threshold Autoregression (ASTAR). Therefore, this time the discussion will focus on the use of Adaptive Spline Threshold Autoregression (ASTAR) method in forecasting the volume of car sales in PT.Srikandi Diamond Motors using time series data.In the discussion of this research, forecasting using the method of forecasting value Adaptive Spline Threshold Autoregression (ASTAR) produce approximately correct.

  20. Europe is going to Mars (United States)


    for future exploration. ESA is now able to afford Mars Express because it will be built more quickly and cheaply than any other comparable mission. It will be the first of the Agency's new flexible missions, based on maximum reuse of technology off-the-shelf and from other missions (the Rosetta cometary mission in this case). Mars Express will explore the extent to which innovative working practices, now made possible by the maturity of Europe's space industry, can cut mission costs and the time from concept to launch : a new kind of relationship with industrial partners is starting. "We are adopting a new approach to management by delegating to Matra Marconi Space (the prime contractor) responsibility for the whole project. This means we can reduce the ESA's management costs" says Bonnet. Despite the knock-down price, however, the future of Mars Express has hung in the balance because of the steady erosion of ESA's space science budget since 1995. Last November, the SPC said the mission could go ahead only if it could be afforded without affecting missions already approved, especially the FIRST infra-red observatory and the Planck mission to measure the cosmic microwave background. On 19/20 May, the SPC, which has the ultimate decision over the Agency's science missions, agreed that the level of resources allowed was just sufficient to allow Mars Express to go ahead. "To do such an ambitious mission for so little money is a challenge and we have decided to meet", says Balsiger.

  1. Mars: The Viking Discoveries. (United States)

    French, Bevan M.

    This booklet describes the results of NASA's Viking spacecraft on Mars. It is intended to be useful for the teacher of basic courses in earth science, space science, astronomy, physics, or geology, but is also of interest to the well-informed layman. Topics include why we should study Mars, how the Viking spacecraft works, the winds of Mars, the…

  2. Preconditioning cubic spline collocation method by FEM and FDM for elliptic equations

    Energy Technology Data Exchange (ETDEWEB)

    Kim, Sang Dong [KyungPook National Univ., Taegu (Korea, Republic of)


    In this talk we discuss the finite element and finite difference technique for the cubic spline collocation method. For this purpose, we consider the uniformly elliptic operator A defined by Au := -{Delta}u + a{sub 1}u{sub x} + a{sub 2}u{sub y} + a{sub 0}u in {Omega} (the unit square) with Dirichlet or Neumann boundary conditions and its discretization based on Hermite cubic spline spaces and collocation at the Gauss points. Using an interpolatory basis with support on the Gauss points one obtains the matrix A{sub N} (h = 1/N).

  3. Natural spline interpolation and exponential parameterization for length estimation of curves (United States)

    Kozera, R.; Wilkołazka, M.


    This paper tackles the problem of estimating a length of a regular parameterized curve γ from an ordered sample of interpolation points in arbitrary Euclidean space by a natural spline. The corresponding tabular parameters are not given and are approximated by the so-called exponential parameterization (depending on λ ∈ [0, 1]). The respective convergence orders α(λ) for estimating length of γ are established for curves sampled more-or-less uniformly. The numerical experiments confirm a slow convergence orders α(λ) = 2 for all λ ∈ [0, 1) and a cubic order α(1) = 3 once natural spline is used.

  4. About a family of C2 splines with one free generating function

    Directory of Open Access Journals (Sweden)

    Igor Verlan


    Full Text Available The problem of interpolation of discrete set of data on the interval [a, b] representing the function f is investigated. A family of C*C splines with one free generating function is introduced in order to solve this problem. Cubic C*C splines belong to this family. The required conditions which must satisfy the generating function in order to obtain explicit interpolants are presented and examples of generating functions are given. Mathematics Subject Classification: 2000: 65D05, 65D07, 41A05, 41A15.

  5. GA Based Rational cubic B-Spline Representation for Still Image Interpolation

    Directory of Open Access Journals (Sweden)

    Samreen Abbas


    Full Text Available In this paper, an image interpolation scheme is designed for 2D natural images. A local support rational cubic spline with control parameters, as interpolatory function, is being optimized using Genetic Algorithm (GA. GA is applied to determine the appropriate values of control parameter used in the description of rational cubic spline. Three state-of-the-art Image Quality Assessment (IQA models with traditional one are hired for comparison with existing image interpolation schemes and perceptual quality check of resulting images. The results show that the proposed scheme is better than the existing ones in comparison.

  6. Evaluation of Two New Smoothing Methods in Equating: The Cubic B-Spline Presmoothing Method and the Direct Presmoothing Method (United States)

    Cui, Zhongmin; Kolen, Michael J.


    This article considers two new smoothing methods in equipercentile equating, the cubic B-spline presmoothing method and the direct presmoothing method. Using a simulation study, these two methods are compared with established methods, the beta-4 method, the polynomial loglinear method, and the cubic spline postsmoothing method, under three sample…

  7. Analysis of crustal structure of Venus utilizing residual Line-of-Sight (LOS) gravity acceleration and surface topography data. A trial of global modeling of Venus gravity field using harmonic spline method (United States)

    Fang, Ming; Bowin, Carl


    To construct Venus' gravity disturbance field (or gravity anomaly) with the spacecraft-observer line of site (LOS) acceleration perturbation data, both a global and a local approach can be used. The global approach, e.g., spherical harmonic coefficients, and the local approach, e.g., the integral operator method, based on geodetic techniques are generally not the same, so that they must be used separately for mapping long wavelength features and short wavelength features. Harmonic spline, as an interpolation and extrapolation technique, is intrinsically flexible to both global and local mapping of a potential field. Theoretically, it preserves the information of the potential field up to the bound by sampling theorem regardless of whether it is global or local mapping, and is never bothered with truncation errors. The improvement of harmonic spline methodology for global mapping is reported. New basis functions, a singular value decomposition (SVD) based modification to Parker & Shure's numerical procedure, and preliminary results are presented.

  8. APROXIMACIÓN TAFONÓMICA EN LOS DEPÓSITOS HUMANOS DEL SITIO ARQUEOLÓGICO CANÍMAR ABAJO, MATANZAS, CUBA (Taphonomic approach on the human deposits of the Canímar Abajo archaeological site, Matanzas, Cuba

    Directory of Open Access Journals (Sweden)

    Stephen Díaz-Franco


    Full Text Available Se destaca la importancia de la interpretación tafonómica en el sitio Canímar Abajo, Matanzas, Cuba; mediante el análisis de las causas de la preservación diferencial de los depósitos humanos exhumados durante las campañas realizadas entre los años 2004 al 2007. Se identifican tres grandes momentos de utilización del sitio, observables en la estratigrafía, de los cuales dos son etapas sepulcrales y la otra de procesamiento de alimentos. Atendiendo al efecto macroscópico de los procesos diagenéticos pre y posenterramiento, durante la etapa bioestratinómica y fosildiagenética, se identifican los principales mecanismos de alteración tafonómica en las entidades y elementos registrados en dichos momentos como son: la biodegradación, relleno sedimentario, bioerosión, disolución, distorsión tafonómica, cremación, desarticulación y dispersión. Se explica en qué consiste cada uno mostrando la acción de los factores intrínsecos y extrínsecos (naturales y/o antrópicos sobre los enterramientos.We offer information about the importance of the taphonomic analysis in the "Canímar Abajo" site, Matanzas, Cuba; by analyzing the causes of differential preservation of human deposits exhumed during the campaigns from 2004 to 2007. Three main moments of use of the site were identified, observable in the stratigraphy, two of wich are stages of burial and other food processing. The diagenetic post and pre-burial processes were identified through the macroscopic effects on the entities and elements recovered. The main taphonomic alteration mechanisms were identified like biodegradation, sediment filling, bioerosion, sedimentary refilling, taphonomic distortion, cremation, disarticulation and dispersal. It explains what each showing the action of intrinsic and extrinsic factors (natural and/or human on the burials.

  9. Lectures on constructive approximation Fourier, spline, and wavelet methods on the real line, the sphere, and the ball

    CERN Document Server

    Michel, Volker


    Lectures on Constructive Approximation: Fourier, Spline, and Wavelet Methods on the Real Line, the Sphere, and the Ball focuses on spherical problems as they occur in the geosciences and medical imaging. It comprises the author’s lectures on classical approximation methods based on orthogonal polynomials and selected modern tools such as splines and wavelets. Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include: * the advantages and disadvantages of Fourier, spline, and wavelet methods * theory and numerics of orthogonal polynomials on intervals, spheres, and balls * cubic splines and splines based on reproducing kernels * multiresolution analysis using wavelet...

  10. Emirates Mars Mission Planetary Protection Plan (United States)

    Awadhi, Mohsen Al


    . 2.The spacecraft is deployed from the launch vehicle and powers on. 3.Within the first month, the spacecraft executes a trajectory correction maneuver to remove the launch bias. The target of this maneuver may still have a small bias to further reduce the probability of inadvertently impacting Mars. 4.Four additional trajectory correction maneuvers are scheduled and planned in the interplanetary cruise in order to target the precise arrival conditions at Mars. The targeted arrival conditions are specified by an altitude above the surface of Mars and an inclination relative to Mars' equator. The closest approach to Mars during the Mars Orbit Insertion (MOI) is over 600 km and the periapsis altitude of the first orbit about Mars is nominally 500 km. The inclination of the first orbit about Mars is nominally around 18 degrees. 5.The Mars Orbit Insertion is performed as a pitch-over burn, approaching no closer than approximately 600 km, and targeting a capture orbit period of 35-40 hours. 6.The spacecraft Capture Orbit has a nominal periapse altitude of 500 km, a nominal apoapse altitude of approximately 45,000 km, and a nominal period of approximately 35 hours. The mission expects that this orbit will be somewhat different after executing the real MOI due to maneuver execution errors. The full range of expected Capture Orbit sizes is acceptable from a planetary protection perspective. 7.The spacecraft remains in the Capture Orbit for two months. 8.The spacecraft then executes three maneuvers in the Transition to Science phase, raising the orbital periapse, raising the orbit inclination, adjusting the apoapse, and placing the argument of periapse near a value of 177 deg. The three maneuvers are nominally one week apart. The first maneuver is large and will raise the periapse significantly, thereafter significantly reducing the probability of Amal impacting Mars in the future.

  11. A cubic B-spline-based hybrid registration of lung CT images for a dynamic airway geometric model with large deformation. (United States)

    Yin, Youbing; Hoffman, Eric A; Ding, Kai; Reinhardt, Joseph M; Lin, Ching-Long


    The goal of this study is to develop a matching algorithm that can handle large geometric changes in x-ray computed tomography (CT)-derived lung geometry occurring during deep breath maneuvers. These geometric relationships are further utilized to build a dynamic lung airway model for computational fluid dynamics (CFD) studies of pulmonary air flow. The proposed algorithm is based on a cubic B-spline-based hybrid registration framework that incorporates anatomic landmark information with intensity patterns. A sequence of invertible B-splines is composed in a multiresolution framework to ensure local invertibility of the large deformation transformation and a physiologically meaningful similarity measure is adopted to compensate for changes in voxel intensity due to inflation. Registrations are performed using the proposed approach to match six pairs of 3D CT human lung datasets. Results show that the proposed approach has the ability to match the intensity pattern and the anatomical landmarks, and ensure local invertibility for large deformation transformations. Statistical results also show that the proposed hybrid approach yields significantly improved results as compared with approaches using either landmarks or intensity alone.

  12. Testing of Space Suit Materials for Mars (United States)

    Larson, Kristine


    Human missions to Mars may require radical changes in our approach to EVA suit design. A major challenge is the balance of building a suit robust enough to complete 50 EVAs in the dirt under intense UV exposure without losing mechanical strength or compromising its mobility. We conducted ground testing on both current and new space suit materials to determine performance degradation after exposure to 2500 hours of Mars mission equivalent UV. This testing will help mature the material technologies and provide performance data that can be used by not only the space suit development teams but for all Mars inflatable and soft goods derived structures from airlocks to habitats.

  13. A B-spline image registration based CAD scheme to evaluate drug treatment response of ovarian cancer patients (United States)

    Tan, Maxine; Li, Zheng; Moore, Kathleen; Thai, Theresa; Ding, Kai; Liu, Hong; Zheng, Bin


    Ovarian cancer is the second most common cancer amongst gynecologic malignancies, and has the highest death rate. Since the majority of ovarian cancer patients (>75%) are diagnosed in the advanced stage with tumor metastasis, chemotherapy is often required after surgery to remove the primary ovarian tumors. In order to quickly assess patient response to the chemotherapy in the clinical trials, two sets of CT examinations are taken pre- and post-therapy (e.g., after 6 weeks). Treatment efficacy is then evaluated based on Response Evaluation Criteria in Solid Tumors (RECIST) guideline, whereby tumor size is measured by the longest diameter on one CT image slice and only a subset of selected tumors are tracked. However, this criterion cannot fully represent the volumetric changes of the tumors and might miss potentially problematic unmarked tumors. Thus, we developed a new CAD approach to measure and analyze volumetric tumor growth/shrinkage using a cubic B-spline deformable image registration method. In this initial study, on 14 sets of pre- and post-treatment CT scans, we registered the two consecutive scans using cubic B-spline registration in a multiresolution (from coarse to fine) framework. We used Mattes mutual information metric as the similarity criterion and the L-BFGS-B optimizer. The results show that our method can quantify volumetric changes in the tumors more accurately than RECIST, and also detect (highlight) potentially problematic regions that were not originally targeted by radiologists. Despite the encouraging results of this preliminary study, further validation of scheme performance is required using large and diverse datasets in future.

  14. Spatial and temporal interpolation of satellite-based aerosol optical depth measurements over North America using B-splines (United States)

    Pfister, Nicolas; O'Neill, Norman T.; Aube, Martin; Nguyen, Minh-Nghia; Bechamp-Laganiere, Xavier; Besnier, Albert; Corriveau, Louis; Gasse, Geremie; Levert, Etienne; Plante, Danick


    Satellite-based measurements of aerosol optical depth (AOD) over land are obtained from an inversion procedure applied to dense dark vegetation pixels of remotely sensed images. The limited number of pixels over which the inversion procedure can be applied leaves many areas with little or no AOD data. Moreover, satellite coverage by sensors such as MODIS yields only daily images of a given region with four sequential overpasses required to straddle mid-latitude North America. Ground based AOD data from AERONET sun photometers are available on a more continuous basis but only at approximately fifty locations throughout North America. The object of this work is to produce a complete and coherent mapping of AOD over North America with a spatial resolution of 0.1 degree and a frequency of three hours by interpolating MODIS satellite-based data together with available AERONET ground based measurements. Before being interpolated, the MODIS AOD data extracted from different passes are synchronized to the mapping time using analyzed wind fields from the Global Multiscale Model (Meteorological Service of Canada). This approach amounts to a trajectory type of simplified atmospheric dynamics correction method. The spatial interpolation is performed using a weighted least squares method applied to bicubic B-spline functions defined on a rectangular grid. The least squares method enables one to weight the data accordingly to the measurement errors while the B-splines properties of local support and C2 continuity offer a good approximation of AOD behaviour viewed as a function of time and space.

  15. Approximation and geomatric modeling with simplex B-splines associates with irregular triangular

    NARCIS (Netherlands)

    Auerbach, S.; Gmelig Meyling, R.H.J.; Neamtu, M.; Neamtu, M.; Schaeben, H.


    Bivariate quadratic simplical B-splines defined by their corresponding set of knots derived from a (suboptimal) constrained Delaunay triangulation of the domain are employed to obtain a C1-smooth surface. The generation of triangle vertices is adjusted to the areal distribution of the data in the

  16. Physically Based Modeling and Simulation with Dynamic Spherical Volumetric Simplex Splines (United States)

    Tan, Yunhao; Hua, Jing; Qin, Hong


    In this paper, we present a novel computational modeling and simulation framework based on dynamic spherical volumetric simplex splines. The framework can handle the modeling and simulation of genus-zero objects with real physical properties. In this framework, we first develop an accurate and efficient algorithm to reconstruct the high-fidelity digital model of a real-world object with spherical volumetric simplex splines which can represent with accuracy geometric, material, and other properties of the object simultaneously. With the tight coupling of Lagrangian mechanics, the dynamic volumetric simplex splines representing the object can accurately simulate its physical behavior because it can unify the geometric and material properties in the simulation. The visualization can be directly computed from the object’s geometric or physical representation based on the dynamic spherical volumetric simplex splines during simulation without interpolation or resampling. We have applied the framework for biomechanic simulation of brain deformations, such as brain shifting during the surgery and brain injury under blunt impact. We have compared our simulation results with the ground truth obtained through intra-operative magnetic resonance imaging and the real biomechanic experiments. The evaluations demonstrate the excellent performance of our new technique. PMID:20161636

  17. Quadratic vs cubic spline-wavelets for image representations and compression

    NARCIS (Netherlands)

    P.C. Marais; E.H. Blake; A.A.M. Kuijk (Fons)


    textabstractThe Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary transform data. The use of semi-orthogonal quadratic spline wavelets

  18. Quadratic vs cubic spline-wavelets for image representation and compression

    NARCIS (Netherlands)

    P.C. Marais; E.H. Blake; A.A.M. Kuijk (Fons)


    htmlabstractThe Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary ransform data. The use of semi-orthogonal quadratic spline wavelets

  19. Spline Trajectory Algorithm Development: Bezier Curve Control Point Generation for UAVs (United States)

    Howell, Lauren R.; Allen, B. Danette


    A greater need for sophisticated autonomous piloting systems has risen in direct correlation with the ubiquity of Unmanned Aerial Vehicle (UAV) technology. Whether surveying unknown or unexplored areas of the world, collecting scientific data from regions in which humans are typically incapable of entering, locating lost or wanted persons, or delivering emergency supplies, an unmanned vehicle moving in close proximity to people and other vehicles, should fly smoothly and predictably. The mathematical application of spline interpolation can play an important role in autopilots' on-board trajectory planning. Spline interpolation allows for the connection of Three-Dimensional Euclidean Space coordinates through a continuous set of smooth curves. This paper explores the motivation, application, and methodology used to compute the spline control points, which shape the curves in such a way that the autopilot trajectory is able to meet vehicle-dynamics limitations. The spline algorithms developed used to generate these curves supply autopilots with the information necessary to compute vehicle paths through a set of coordinate waypoints.

  20. Fractional and complex pseudo-splines and the construction of Parseval frames

    DEFF Research Database (Denmark)

    Massopust, Peter; Forster, Brigitte; Christensen, Ole


    in complex transform techniques for signal and image analyses. We also show that in analogue to the integer case, the generalized pseudo-splines lead to constructions of Parseval wavelet frames via the unitary extension principle. The regularity and approximation order of this new class of generalized...

  1. Kinetic energy classification and smoothing for compact B-spline basis sets in quantum Monte Carlo (United States)

    Krogel, Jaron T.; Reboredo, Fernando A.


    Quantum Monte Carlo calculations of defect properties of transition metal oxides have become feasible in recent years due to increases in computing power. As the system size has grown, availability of on-node memory has become a limiting factor. Saving memory while minimizing computational cost is now a priority. The main growth in memory demand stems from the B-spline representation of the single particle orbitals, especially for heavier elements such as transition metals where semi-core states are present. Despite the associated memory costs, splines are computationally efficient. In this work, we explore alternatives to reduce the memory usage of splined orbitals without significantly affecting numerical fidelity or computational efficiency. We make use of the kinetic energy operator to both classify and smooth the occupied set of orbitals prior to splining. By using a partitioning scheme based on the per-orbital kinetic energy distributions, we show that memory savings of about 50% is possible for select transition metal oxide systems. For production supercells of practical interest, our scheme incurs a performance penalty of less than 5%.

  2. Groundwater head responses due to random stream stage fluctuations using basis splines (United States)

    Knight, J. H.; Rassam, D. W.


    Stream-aquifer interactions are becoming increasingly important processes in water resources and riparian management. The linearized Boussinesq equation describes the transient movement of a groundwater free surface in unconfined flow. Some standard solutions are those corresponding to an input, which is a delta function impulse, or to its integral, a unit step function in the time domain. For more complicated inputs, the response can be expressed as a convolution integral, which must be evaluated numerically. When the input is a time series of measured data, a spline function or piecewise polynomial can easily be fitted to the data. Any such spline function can be expressed in terms of a finite series of basis splines with numerical coefficients. The analytical groundwater response functions corresponding to these basis splines are presented, thus giving a direct and accurate way to calculate the groundwater response for a random time series input representing the stream stage. We use the technique to estimate responses due to a random stream stage time series and show that the predicted heads compare favorably to those obtained from numerical simulations using the Modular Three-Dimensional Finite-Difference Ground-Water Flow Model (MODFLOW) simulations; we then demonstrate how to calculate residence times used for estimating riparian denitrification during bank storage.

  3. B-Spline Approximations of the Gaussian, their Gabor Frame Properties, and Approximately Dual Frames

    DEFF Research Database (Denmark)

    Christensen, Ole; Kim, Hong Oh; Kim, Rae Young


    of a very simple form, leading to “almost perfect reconstruction� within any desired error tolerance whenever the product ab is sufficiently small. In contrast, the known (exact) dual windows have a very complicated form. A similar analysis is sketched with the scaled B-splines replaced by certain...

  4. Integration by cell algorithm for Slater integrals in a spline basis

    International Nuclear Information System (INIS)

    Qiu, Y.; Fischer, C.F.


    An algorithm for evaluating Slater integrals in a B-spline basis is introduced. Based on the piecewise property of the B-splines, the algorithm divides the two-dimensional (r 1 , r 2 ) region into a number of rectangular cells according to the chosen grid and implements the two-dimensional integration over each individual cell using Gaussian quadrature. Over the off-diagonal cells, the integrands are separable so that each two-dimensional cell-integral is reduced to a product of two one-dimensional integrals. Furthermore, the scaling invariance of the B-splines in the logarithmic region of the chosen grid is fully exploited such that only some of the cell integrations need to be implemented. The values of given Slater integrals are obtained by assembling the cell integrals. This algorithm significantly improves the efficiency and accuracy of the traditional method that relies on the solution of differential equations and renders the B-spline method more effective when applied to multi-electron atomic systems

  5. Validating the Multidimensional Spline Based Global Aerodynamic Model for the Cessna Citation II

    NARCIS (Netherlands)

    De Visser, C.C.; Mulder, J.A.


    The validation of aerodynamic models created using flight test data is a time consuming and often costly process. In this paper a new method for the validation of global nonlinear aerodynamic models based on multivariate simplex splines is presented. This new method uses the unique properties of the

  6. Application of Cubic Box Spline Wavelets in the Analysis of Signal Singularities

    Directory of Open Access Journals (Sweden)

    Rakowski Waldemar


    Full Text Available In the subject literature, wavelets such as the Mexican hat (the second derivative of a Gaussian or the quadratic box spline are commonly used for the task of singularity detection. The disadvantage of the Mexican hat, however, is its unlimited support; the disadvantage of the quadratic box spline is a phase shift introduced by the wavelet, making it difficult to locate singular points. The paper deals with the construction and properties of wavelets in the form of cubic box splines which have compact and short support and which do not introduce a phase shift. The digital filters associated with cubic box wavelets that are applied in implementing the discrete dyadic wavelet transform are defined. The filters and the algorithme à trous of the discrete dyadic wavelet transform are used in detecting signal singularities and in calculating the measures of signal singularities in the form of a Lipschitz exponent. The article presents examples illustrating the use of cubic box spline wavelets in the analysis of signal singularities.

  7. Detection and correction of laser induced breakdown spectroscopy spectral background based on spline interpolation method (United States)

    Tan, Bing; Huang, Min; Zhu, Qibing; Guo, Ya; Qin, Jianwei


    Laser-induced breakdown spectroscopy (LIBS) is an analytical technique that has gained increasing attention because of many applications. The production of continuous background in LIBS is inevitable because of factors associated with laser energy, gate width, time delay, and experimental environment. The continuous background significantly influences the analysis of the spectrum. Researchers have proposed several background correction methods, such as polynomial fitting, Lorenz fitting and model-free methods. However, less of them apply these methods in the field of LIBS Technology, particularly in qualitative and quantitative analyses. This study proposes a method based on spline interpolation for detecting and estimating the continuous background spectrum according to its smooth property characteristic. Experiment on the background correction simulation indicated that, the spline interpolation method acquired the largest signal-to-background ratio (SBR) over polynomial fitting, Lorenz fitting and model-free method after background correction. These background correction methods all acquire larger SBR values than that acquired before background correction (The SBR value before background correction is 10.0992, whereas the SBR values after background correction by spline interpolation, polynomial fitting, Lorentz fitting, and model-free methods are 26.9576, 24.6828, 18.9770, and 25.6273 respectively). After adding random noise with different kinds of signal-to-noise ratio to the spectrum, spline interpolation method acquires large SBR value, whereas polynomial fitting and model-free method obtain low SBR values. All of the background correction methods exhibit improved quantitative results of Cu than those acquired before background correction (The linear correlation coefficient value before background correction is 0.9776. Moreover, the linear correlation coefficient values after background correction using spline interpolation, polynomial fitting, Lorentz

  8. Mass Spectrometry on Future Mars Landers (United States)

    Brinckerhoff, W. B.; Mahaffy, P. R.


    Mass spectrometry investigations on the 2011 Mars Science Laboratory (MSL) and the 2018 ExoMars missions will address core science objectives related to the potential habitability of their landing site environments and more generally the near-surface organic inventory of Mars. The analysis of complex solid samples by mass spectrometry is a well-known approach that can provide a broad and sensitive survey of organic and inorganic compounds as well as supportive data for mineralogical analysis. The science value of such compositional information is maximized when one appreciates the particular opportunities and limitations of in situ analysis with resource-constrained instrumentation in the context of a complete science payload and applied to materials found in a particular environment. The Sample Analysis at Mars (SAM) investigation on MSL and the Mars Organic Molecule Analyzer (MOMA) investigation on ExoMars will thus benefit from and inform broad-based analog field site work linked to the Mars environments where such analysis will occur.

  9. Cars on Mars (United States)

    Landis, Geoffrey A.


    Mars is one of the most fascinating planets in the solar system, featuring an atmosphere, water, and enormous volcanoes and canyons. The Mars Pathfinder, Global Surveyor, and Odyssey missions mark the first wave of the Planet Earth's coming invasion of the red planet, changing our views of the past and future of the planet and the possibilities of life. Scientist and science-fiction writer Geoffrey A. Landis will present experiences on the Pathfinder mission, the challenges of using solar power on the surface of Mars, and present future missions to Mars such as the upcoming Mars Twin Rovers, which will launch two highly-capable vehicles in 2003 to explore the surface of Mars.

  10. Quick trips to Mars

    International Nuclear Information System (INIS)

    Hornung, R.


    The design of a Mars Mission Vehicle that would have to be launched by two very heavy lift launch vehicles is described along with plans for a mission to Mars. The vehicle has three nuclear engine for rocket vehicle application (NERVA) boosters with a fourth in the center that acts as a dual mode system. The fourth generates electrical power while in route, but it also helps lift the vehicle out of earth orbit. A Mars Ascent Vehicle (MAV), a Mars transfer vehicle stage, and a Mars Excursion Vehicle (MEV) are located on the front end of this vehicle. Other aspects of this research including aerobraking, heat shielding, nuclear thermal rocket engines, a mars mission summary, closed Brayton cycle with and without regeneration, liquid hydrogen propellant storage, etc. are addressed

  11. Liturgical calendar for Mars

    Directory of Open Access Journals (Sweden)

    Piotr Karocki


    Full Text Available This article presents problems related to creating liturgical calendar for Mars colonists, assumed to land on Mars (accordingly to Mars One Project in year 2024. It consist of five parts: why to colonize space; brief history of Earth calendar; deep correlation of liturgical calendar (e.g. fests with astronomical events; last two parts present idea of civil Martian calendar and list difficulties related to extraterrestrial liturgical calendar.

  12. Mars at Opposition (United States)

    Riddle, Bob


    On January 29, Mars will reach opposition, a point along its orbit around the Sun where Mars will be directly opposite from the Sun in a two-planet and Sun line-up with the Earth in between. At this opposition, the Earth and Mars will be separated by nearly 100 million km. An opposition is similar to a full Moon in that the planet at opposition…

  13. Digital cartography of Mars (United States)

    Batson, R. M.


    A medium-resolution Digital Image Model (DIM) of Mars is being compiled. A DIM is a mosaic of radiometrically corrected, photometrically modelled spacecraft images displaying accurate reflectance properties at uniform resolution, and geometrically tied to the best available control. The Mars medium-resolution DIM contains approximately 4700 Viking Orbiter image frames that were used to compile the recently completed 1:2,000,000-scale controlled photomosaic series of Mars. This DIM provides a planimetric control base to which all other Mars maps will be registered. A similar control base of topographic elevations (Digital Terrain Model, or DTM) is also being compiled. These products are scheduled for completion in 1989.

  14. Radiation chemistry in exploration of Mars

    International Nuclear Information System (INIS)

    Zagorski, Z.P.


    Problems of exploration of Mars are seldom connected with radiation research. Improvements in such approach, more and more visible, are reported in this paper, written by the present author working on prebiotic chemistry and origins of life on Earth. Objects on Mars subjected to radiation are very different from those on Earth. Density of the Martian atmosphere is by two orders smaller than over Earth and does not protect the surface of Mars from ionizing radiations, contrary to the case of Earth, shielded by the equivalent of ca. 3 meters of concrete. High energy protons from the Sun are diverted magnetically around Earth, and Mars is deprived of that protection. The radiolysis of martian '' air '' (95.3% of carbon dioxide) starts with the formation of CO 2 + , whereas the primary product over Earth is N 2 + ion radical. The lack of water vapor over Mars prevents the formation of many secondary products. The important feature of Martian regolith is the possibility of the presence of hydrated minerals, which could have been formed milliards years ago, when (probably) water was present on Mars. The interface of the atmosphere and the regolith can be the site of many chemical reactions, induced also by intensive UV, which includes part of the vacuum UV. Minerals like sodalite, discovered on Mars can contribute as reagents in many reactions. Conclusions are dedicated to questions of the live organisms connected with exploration of Mars; from microorganisms, comparatively resistant to ionizing radiation, to human beings, considered not to be fit to manned flight, survival on Mars and return to Earth. Pharmaceuticals proposed as radiobiological protection cannot improve the situation. Exploration over the distance of millions of kilometers performed successfully without presence of man, withstands more easily the presence of ionizing radiation. (author)

  15. An Adaptive B-Spline Method for Low-order Image Reconstruction Problems - Final Report - 09/24/1997 - 09/24/2000

    Energy Technology Data Exchange (ETDEWEB)

    Li, Xin; Miller, Eric L.; Rappaport, Carey; Silevich, Michael


    A common problem in signal processing is to estimate the structure of an object from noisy measurements linearly related to the desired image. These problems are broadly known as inverse problems. A key feature which complicates the solution to such problems is their ill-posedness. That is, small perturbations in the data arising e.g. from noise can and do lead to severe, non-physical artifacts in the recovered image. The process of stabilizing these problems is known as regularization of which Tikhonov regularization is one of the most common. While this approach leads to a simple linear least squares problem to solve for generating the reconstruction, it has the unfortunate side effect of producing smooth images thereby obscuring important features such as edges. Therefore, over the past decade there has been much work in the development of edge-preserving regularizers. This technique leads to image estimates in which the important features are retained, but computationally the y require the solution of a nonlinear least squares problem, a daunting task in many practical multi-dimensional applications. In this thesis we explore low-order models for reducing the complexity of the re-construction process. Specifically, B-Splines are used to approximate the object. If a ''proper'' collection B-Splines are chosen that the object can be efficiently represented using a few basis functions, the dimensionality of the underlying problem will be significantly decreased. Consequently, an optimum distribution of splines needs to be determined. Here, an adaptive refining and pruning algorithm is developed to solve the problem. The refining part is based on curvature information, in which the intuition is that a relatively dense set of fine scale basis elements should cluster near regions of high curvature while a spares collection of basis vectors are required to adequately represent the object over spatially smooth areas. The pruning part is a greedy

  16. IJslandse inzichten op Mars

    NARCIS (Netherlands)

    de Vet, S.


    Vulkaanuitbarstingen onder gletsjers, zoals de vliegverkeer-verlammende uitbarsting van de vulkaan Eyjafjallajökull in IJsland in 2010, lijken in veel opzichten op vulkaanuitbarstingen die ooit op Mars voorkwamen. Dankzij de landschappelijke gelijkenissen tussen onze aarde en Mars is het mogelijk om

  17. Microscope on Mars (United States)


    This image taken at Meridiani Planum, Mars by the panoramic camera on the Mars Exploration Rover Opportunity shows the rover's microscopic imager (circular device in center), located on its instrument deployment device, or 'arm.' The image was acquired on the ninth martian day or sol of the rover's mission.

  18. The overprotection of Mars (United States)

    Fairén, Alberto G.; Schulze-Makuch, Dirk


    Planetary protection policies aim to guard Solar System bodies from biological contamination from spacecraft. Costly efforts to sterilize Mars spacecraft need to be re-evaluated, as they are unnecessarily inhibiting a more ambitious agenda to search for extant life on Mars.

  19. High Accuracy Spline Explicit Group (SEG Approximation for Two Dimensional Elliptic Boundary Value Problems.

    Directory of Open Access Journals (Sweden)

    Joan Goh

    Full Text Available Over the last few decades, cubic splines have been widely used to approximate differential equations due to their ability to produce highly accurate solutions. In this paper, the numerical solution of a two-dimensional elliptic partial differential equation is treated by a specific cubic spline approximation in the x-direction and finite difference in the y-direction. A four point explicit group (EG iterative scheme with an acceleration tool is then applied to the obtained system. The formulation and implementation of the method for solving physical problems are presented in detail. The complexity of computational is also discussed and the comparative results are tabulated to illustrate the efficiency of the proposed method.

  20. Selected Aspects of Wear Affecting Keyed Joints and Spline Connections During Operation of Aircrafts

    Directory of Open Access Journals (Sweden)

    Gębura Andrzej


    Full Text Available The paper deals with selected deficiencies of spline connections, such as angular or parallel misalignment (eccentricity and excessive play. It is emphasized how important these deficiencies are for smooth operation of the entire driving units. The aim of the study is to provide a kind of a reference list with such deficiencies with visual symptoms of wear, specification of mechanical measurements for mating surfaces, mathematical description of waveforms for dynamic variability of motion in such connections and visualizations of the connection behaviour acquired with the use of the FAM-C and FDM-A. Attention is paid to hazards to flight safety when excessively worn spline connections are operated for long periods of time

  1. Modeling of type-2 fuzzy cubic B-spline surface for flood data problem in Malaysia (United States)

    Bidin, Mohd Syafiq; Wahab, Abd. Fatah


    Malaysia possesses a low and sloping land areas which may cause flood. The flood phenomenon can be analyzed if the surface data of the study area can be modeled by geometric modeling. Type-2 fuzzy data for the flood data is defined using type-2 fuzzy set theory in order to solve the uncertainty of complex data. Then, cubic B-spline surface function is used to produce a smooth surface. Three main processes are carried out to find a solution to crisp type-2 fuzzy data which is fuzzification (α-cut operation), type-reduction and defuzzification. Upon conducting these processes, Type-2 Fuzzy Cubic B-Spline Surface Model is applied to visualize the surface data of the flood areas that are complex uncertainty.

  2. Inverting travel times with a triplication. [spline fitting technique applied to lunar seismic data reduction (United States)

    Jarosch, H. S.


    A method based on the use of constrained spline fits is used to overcome the difficulties arising when body-wave data in the form of T-delta are reduced to the tau-p form in the presence of cusps. In comparison with unconstrained spline fits, the method proposed here tends to produce much smoother models which lie approximately in the middle of the bounds produced by the extremal method. The method is noniterative and, therefore, computationally efficient. The method is applied to the lunar seismic data, where at least one triplication is presumed to occur in the P-wave travel-time curve. It is shown, however, that because of an insufficient number of data points for events close to the antipode of the center of the lunar network, the present analysis is not accurate enough to resolve the problem of a possible lunar core.

  3. Investigation of confined hydrogen atom in spherical cavity, using B-splines basis set

    Directory of Open Access Journals (Sweden)

    M Barezi


    Full Text Available Studying confined quantum systems (CQS is very important in nano technology. One of the basic CQS is a hydrogen atom confined in spherical cavity. In this article, eigenenergies and eigenfunctions of hydrogen atom in spherical cavity are calculated, using linear variational method. B-splines are used as basis functions, which can easily construct the trial wave functions with appropriate boundary conditions. The main characteristics of B-spline are its high localization and its flexibility. Besides, these functions have numerical stability and are able to spend high volume of calculation with good accuracy. The energy levels as function of cavity radius are analyzed. To check the validity and efficiency of the proposed method, extensive convergence test of eigenenergies in different cavity sizes has been carried out.

  4. Numerical simulation of reaction-diffusion systems by modified cubic B-spline differential quadrature method

    International Nuclear Information System (INIS)

    Mittal, R.C.; Rohila, Rajni


    In this paper, we have applied modified cubic B-spline based differential quadrature method to get numerical solutions of one dimensional reaction-diffusion systems such as linear reaction-diffusion system, Brusselator system, Isothermal system and Gray-Scott system. The models represented by these systems have important applications in different areas of science and engineering. The most striking and interesting part of the work is the solution patterns obtained for Gray Scott model, reminiscent of which are often seen in nature. We have used cubic B-spline functions for space discretization to get a system of ordinary differential equations. This system of ODE’s is solved by highly stable SSP-RK43 method to get solution at the knots. The computed results are very accurate and shown to be better than those available in the literature. Method is easy and simple to apply and gives solutions with less computational efforts.

  5. Spline- and wavelet-based models of neural activity in response to natural visual stimulation. (United States)

    Gerhard, Felipe; Szegletes, Luca


    We present a comparative study of the performance of different basis functions for the nonparametric modeling of neural activity in response to natural stimuli. Based on naturalistic video sequences, a generative model of neural activity was created using a stochastic linear-nonlinear-spiking cascade. The temporal dynamics of the spiking response is well captured with cubic splines with equidistant knot spacings. Whereas a sym4-wavelet decomposition performs competitively or only slightly worse than the spline basis, Haar wavelets (or histogram-based models) seem unsuitable for faithfully describing the temporal dynamics of the sensory neurons. This tendency was confirmed with an application to a real data set of spike trains recorded from visual cortex of the awake monkey.

  6. Isotopic reconstruction of the weaning process in the archaeological population of Canímar Abajo, Cuba: A Bayesian probability mixing model approach.

    Directory of Open Access Journals (Sweden)

    Yadira Chinique de Armas

    Full Text Available The general lack of well-preserved juvenile skeletal remains from Caribbean archaeological sites has, in the past, prevented evaluations of juvenile dietary changes. Canímar Abajo (Cuba, with a large number of well-preserved juvenile and adult skeletal remains, provided a unique opportunity to fully assess juvenile paleodiets from an ancient Caribbean population. Ages for the start and the end of weaning and possible food sources used for weaning were inferred by combining the results of two Bayesian probability models that help to reduce some of the uncertainties inherent to bone collagen isotope based paleodiet reconstructions. Bone collagen (31 juveniles, 18 adult females was used for carbon and nitrogen isotope analyses. The isotope results were assessed using two Bayesian probability models: Weaning Ages Reconstruction with Nitrogen isotopes and Stable Isotope Analyses in R. Breast milk seems to have been the most important protein source until two years of age with some supplementary food such as tropical fruits and root cultigens likely introduced earlier. After two, juvenile diets were likely continuously supplemented by starch rich foods such as root cultigens and legumes. By the age of three, the model results suggest that the weaning process was completed. Additional indications suggest that animal marine/riverine protein and maize, while part of the Canímar Abajo female diets, were likely not used to supplement juvenile diets. The combined use of both models here provided a more complete assessment of the weaning process for an ancient Caribbean population, indicating not only the start and end ages of weaning but also the relative importance of different food sources for different age juveniles.

  7. Correlation studies for B-spline modeled F2 Chapman parameters obtained from FORMOSAT-3/COSMIC data

    Directory of Open Access Journals (Sweden)

    M. Limberger


    Full Text Available The determination of ionospheric key quantities such as the maximum electron density of the F2 layer NmF2, the corresponding F2 peak height hmF2 and the F2 scale height HF2 are of high relevance in 4-D ionosphere modeling to provide information on the vertical structure of the electron density (Ne. The Ne distribution with respect to height can, for instance, be modeled by the commonly accepted F2 Chapman layer. An adequate and observation driven description of the vertical Ne variation can be obtained from electron density profiles (EDPs derived by ionospheric radio occultation measurements between GPS and low Earth orbiter (LEO satellites. For these purposes, the six FORMOSAT-3/COSMIC (F3/C satellites provide an excellent opportunity to collect EDPs that cover most of the ionospheric region, in particular the F2 layer. For the contents of this paper, F3/C EDPs have been exploited to determine NmF2, hmF2 and HF2 within a regional modeling approach. As mathematical base functions, endpoint-interpolating polynomial B-splines are considered to model the key parameters with respect to longitude, latitude and time. The description of deterministic processes and the verification of this modeling approach have been published previously in Limberger et al. (2013, whereas this paper should be considered as an extension dealing with related correlation studies, a topic to which less attention has been paid in the literature. Relations between the B-spline series coefficients regarding specific key parameters as well as dependencies between the three F2 Chapman key parameters are in the main focus. Dependencies are interpreted from the post-derived correlation matrices as a result of (1 a simulated scenario without data gaps by taking dense, homogenously distributed profiles into account and (2 two real data scenarios on 1 July 2008 and 1 July 2012 including sparsely, inhomogeneously distributed F3/C EDPs. Moderate correlations between hmF2 and HF2 as

  8. An adaptive multi-spline refinement algorithm in simulation based sailboat trajectory optimization using onboard multi-core computer systems

    Directory of Open Access Journals (Sweden)

    Dębski Roman


    Full Text Available A new dynamic programming based parallel algorithm adapted to on-board heterogeneous computers for simulation based trajectory optimization is studied in the context of “high-performance sailing”. The algorithm uses a new discrete space of continuously differentiable functions called the multi-splines as its search space representation. A basic version of the algorithm is presented in detail (pseudo-code, time and space complexity, search space auto-adaptation properties. Possible extensions of the basic algorithm are also described. The presented experimental results show that contemporary heterogeneous on-board computers can be effectively used for solving simulation based trajectory optimization problems. These computers can be considered micro high performance computing (HPC platforms-they offer high performance while remaining energy and cost efficient. The simulation based approach can potentially give highly accurate results since the mathematical model that the simulator is built upon may be as complex as required. The approach described is applicable to many trajectory optimization problems due to its black-box represented performance measure and use of OpenCL.

  9. A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements


    Soliman, A. A.


    Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.

  10. A Galerkin Solution for Burgers' Equation Using Cubic B-Spline Finite Elements

    Directory of Open Access Journals (Sweden)

    A. A. Soliman


    Full Text Available Numerical solutions for Burgers’ equation based on the Galerkins’ method using cubic B-splines as both weight and interpolation functions are set up. It is shown that this method is capable of solving Burgers’ equation accurately for values of viscosity ranging from very small to large. Three standard problems are used to validate the proposed algorithm. A linear stability analysis shows that a numerical scheme based on a Cranck-Nicolson approximation in time is unconditionally stable.

  11. Cubic spline reflectance estimates using the Viking lander camera multispectral data (United States)

    Park, S. K.; Huck, F. O.


    A technique was formulated for constructing spectral reflectance estimates from multispectral data obtained with the Viking lander cameras. The output of each channel was expressed as a linear function of the unknown spectral reflectance producing a set of linear equations which were used to determine the coefficients in a representation of the spectral reflectance estimate as a natural cubic spline. The technique was used to produce spectral reflectance estimates for a variety of actual and hypothetical spectral reflectances.

  12. Free vibration of symmetric angle ply truncated conical shells under different boundary conditions using spline method

    Energy Technology Data Exchange (ETDEWEB)

    Viswanathan, K. K.; Aziz, Z. A.; Javed, Saira; Yaacob, Y. [Universiti Teknologi Malaysia, Johor Bahru (Malaysia); Pullepu, Babuji [S R M University, Chennai (India)


    Free vibration of symmetric angle-ply laminated truncated conical shell is analyzed to determine the effects of frequency parameter and angular frequencies under different boundary condition, ply angles, different material properties and other parameters. The governing equations of motion for truncated conical shell are obtained in terms of displacement functions. The displacement functions are approximated by cubic and quintic splines resulting into a generalized eigenvalue problem. The parametric studies have been made and discussed.

  13. Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation (United States)

    Bialecki, Bernard


    Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N2log2N) andO(N2log2log2N) arithmetic operations, respectively.

  14. Explicit Gaussian quadrature rules for C^1 cubic splines with symmetrically stretched knot sequence

    KAUST Repository

    Ait-Haddou, Rachid


    We provide explicit expressions for quadrature rules on the space of C^1 cubic splines with non-uniform, symmetrically stretched knot sequences. The quadrature nodes and weights are derived via an explicit recursion that avoids an intervention of any numerical solver and the rule is optimal, that is, it requires minimal number of nodes. Numerical experiments validating the theoretical results and the error estimates of the quadrature rules are also presented.

  15. Optimal Knot Selection for Least-squares Fitting of Noisy Data with Spline Functions

    Energy Technology Data Exchange (ETDEWEB)

    Jerome Blair


    An automatic data-smoothing algorithm for data from digital oscilloscopes is described. The algorithm adjusts the bandwidth of the filtering as a function of time to provide minimum mean squared error at each time. It produces an estimate of the root-mean-square error as a function of time and does so without any statistical assumptions about the unknown signal. The algorithm is based on least-squares fitting to the data of cubic spline functions.

  16. Direct Numerical Simulation of Incompressible Pipe Flow Using a B-Spline Spectral Method (United States)

    Loulou, Patrick; Moser, Robert D.; Mansour, Nagi N.; Cantwell, Brian J.


    A numerical method based on b-spline polynomials was developed to study incompressible flows in cylindrical geometries. A b-spline method has the advantages of possessing spectral accuracy and the flexibility of standard finite element methods. Using this method it was possible to ensure regularity of the solution near the origin, i.e. smoothness and boundedness. Because b-splines have compact support, it is also possible to remove b-splines near the center to alleviate the constraint placed on the time step by an overly fine grid. Using the natural periodicity in the azimuthal direction and approximating the streamwise direction as periodic, so-called time evolving flow, greatly reduced the cost and complexity of the computations. A direct numerical simulation of pipe flow was carried out using the method described above at a Reynolds number of 5600 based on diameter and bulk velocity. General knowledge of pipe flow and the availability of experimental measurements make pipe flow the ideal test case with which to validate the numerical method. Results indicated that high flatness levels of the radial component of velocity in the near wall region are physical; regions of high radial velocity were detected and appear to be related to high speed streaks in the boundary layer. Budgets of Reynolds stress transport equations showed close similarity with those of channel flow. However contrary to channel flow, the log layer of pipe flow is not homogeneous for the present Reynolds number. A topological method based on a classification of the invariants of the velocity gradient tensor was used. Plotting iso-surfaces of the discriminant of the invariants proved to be a good method for identifying vortical eddies in the flow field.

  17. Discrete quintic spline for boundary value problem in plate deflation theory (United States)

    Wong, Patricia J. Y.


    We propose a numerical scheme for a fourth-order boundary value problem arising from plate deflation theory. The scheme involves a discrete quintic spline, and it is of order 4 if a parameter takes a specific value, else it is of order 2. We also present a well known numerical example to illustrate the efficiency of our method as well as to compare with other numerical methods proposed in the literature.

  18. Nonlinear Multivariate Spline-Based Control Allocation for High-Performance Aircraft


    Tol, H.J.; De Visser, C.C.; Van Kampen, E.; Chu, Q.P.


    High performance flight control systems based on the nonlinear dynamic inversion (NDI) principle require highly accurate models of aircraft aerodynamics. In general, the accuracy of the internal model determines to what degree the system nonlinearities can be canceled; the more accurate the model, the better the cancellation, and with that, the higher the performance of the controller. In this paper a new control system is presented that combines NDI with multivariate simplex spline based con...

  19. A splitting algorithm for the wavelet transform of cubic splines on a nonuniform grid (United States)

    Sulaimanov, Z. M.; Shumilov, B. M.


    For cubic splines with nonuniform nodes, splitting with respect to the even and odd nodes is used to obtain a wavelet expansion algorithm in the form of the solution to a three-diagonal system of linear algebraic equations for the coefficients. Computations by hand are used to investigate the application of this algorithm for numerical differentiation. The results are illustrated by solving a prediction problem.

  20. SGTR assessment using MARS

    International Nuclear Information System (INIS)

    Raines, J.C.; Dawson, S.M.; Deitke, B.; Henry, R.E.


    During the course of a plant accident, a consistent understanding of the plant response is vital to support an accident manager's decision making process. One tool that can provide assistance to the plant staff in assessing conditions in the plant during accident conditions is the MAAP Accident Response System (MARS) software. During an accident, MARS utilizes the on-line data from the plant instrumentation to initialize the Modular Accident Analysis Program (MAAP) code. Once initialized, MARS tracks and characterizes the plant behavior through the use of integrated logic modules. These logic modules provide the user with important information about the status of systems and the possible cause of the accident. The MARS logic modules evaluate relevant available plant instrumentation and the observations of the operating staff using fuzzy logic. The fuzzy logic is applied to provide a transition between areas where one is absolutely sure that a situation has not occurred to a condition where one is absolutely certain that a situation has occurred. One example of the use of logic modules in MARS is illustrated by that used to assess if a steam generator tube rupture (SGTR) event has occurred. Each piece of relevant plant data is evaluated to determine if it is consistent with the symptoms of a SGTR. Each of the evaluations for the individual plant instruments and the operating staff observations are assembled to determine an overall confidence which characterizes the likelihood that a SGTR is occurring. Additional MARS logic modules are used to determine confidence levels for other types of accident events. The conclusions arrived at by each individual logic module are expressed as confidence levels. The logic module confidence levels can be graphically displayed using the MARS Graphical Users Interface (GUI), to indicate the confidence level MARS has assessed for each accident type. The GUI shows the identification of the possible accident types, but is not limited

  1. B-spline algebraic diagrammatic construction: Application to photoionization cross-sections and high-order harmonic generation

    Energy Technology Data Exchange (ETDEWEB)

    Ruberti, M.; Averbukh, V. [Department of Physics, Imperial College London, Prince Consort Road, London SW7 2AZ (United Kingdom); Decleva, P. [Dipartimento di Scienze Chimiche, Universita’ di Trieste, Via Giorgieri 1, I-34127 Trieste (Italy)


    We present the first implementation of the ab initio many-body Green's function method, algebraic diagrammatic construction (ADC), in the B-spline single-electron basis. B-spline versions of the first order [ADC(1)] and second order [ADC(2)] schemes for the polarization propagator are developed and applied to the ab initio calculation of static (photoionization cross-sections) and dynamic (high-order harmonic generation spectra) quantities. We show that the cross-section features that pose a challenge for the Gaussian basis calculations, such as Cooper minima and high-energy tails, are found to be reproduced by the B-spline ADC in a very good agreement with the experiment. We also present the first dynamic B-spline ADC results, showing that the effect of the Cooper minimum on the high-order harmonic generation spectrum of Ar is correctly predicted by the time-dependent ADC calculation in the B-spline basis. The present development paves the way for the application of the B-spline ADC to both energy- and time-resolved theoretical studies of many-electron phenomena in atoms, molecules, and clusters.

  2. Nonlinear registration using B-spline feature approximation and image similarity (United States)

    Kim, June-Sic; Kim, Jae Seok; Kim, In Young; Kim, Sun Il


    The warping methods are broadly classified into the image-matching method based on similar pixel intensity distribution and the feature-matching method using distinct anatomical feature. Feature based methods may fail to match local variation of two images. However, the method globally matches features well. False matches corresponding to local minima of the underlying energy functions can be obtained through the similarity based methods. To avoid local minima problem, we proposes non-linear deformable registration method utilizing global information of feature matching and the local information of image matching. To define the feature, gray matter and white matter of brain tissue are segmented by Fuzzy C-Mean (FCM) algorithm. B-spline approximation technique is used for feature matching. We use a multi-resolution B-spline approximation method which modifies multilevel B-spline interpolation method. It locally changes the resolution of the control lattice in proportion to the distance between features of two images. Mutual information is used for similarity measure. The deformation fields are locally refined until maximize the similarity. In two 3D T1 weighted MRI test, this method maintained the accuracy by conventional image matching methods without the local minimum problem.

  3. On developing B-spline registration algorithms for multi-core processors. (United States)

    Shackleford, J A; Kandasamy, N; Sharp, G C


    Spline-based deformable registration methods are quite popular within the medical-imaging community due to their flexibility and robustness. However, they require a large amount of computing time to obtain adequate results. This paper makes two contributions towards accelerating B-spline-based registration. First, we propose a grid-alignment scheme and associated data structures that greatly reduce the complexity of the registration algorithm. Based on this grid-alignment scheme, we then develop highly data parallel designs for B-spline registration within the stream-processing model, suitable for implementation on multi-core processors such as graphics processing units (GPUs). Particular attention is focused on an optimal method for performing analytic gradient computations in a data parallel fashion. CPU and GPU versions are validated for execution time and registration quality. Performance results on large images show that our GPU algorithm achieves a speedup of 15 times over the single-threaded CPU implementation whereas our multi-core CPU algorithm achieves a speedup of 8 times over the single-threaded implementation. The CPU and GPU versions achieve near-identical registration quality in terms of RMS differences between the generated vector fields.

  4. On developing B-spline registration algorithms for multi-core processors

    International Nuclear Information System (INIS)

    Shackleford, J A; Kandasamy, N; Sharp, G C


    Spline-based deformable registration methods are quite popular within the medical-imaging community due to their flexibility and robustness. However, they require a large amount of computing time to obtain adequate results. This paper makes two contributions towards accelerating B-spline-based registration. First, we propose a grid-alignment scheme and associated data structures that greatly reduce the complexity of the registration algorithm. Based on this grid-alignment scheme, we then develop highly data parallel designs for B-spline registration within the stream-processing model, suitable for implementation on multi-core processors such as graphics processing units (GPUs). Particular attention is focused on an optimal method for performing analytic gradient computations in a data parallel fashion. CPU and GPU versions are validated for execution time and registration quality. Performance results on large images show that our GPU algorithm achieves a speedup of 15 times over the single-threaded CPU implementation whereas our multi-core CPU algorithm achieves a speedup of 8 times over the single-threaded implementation. The CPU and GPU versions achieve near-identical registration quality in terms of RMS differences between the generated vector fields.

  5. Probing Mars’ atmosphere with ExoMars Mars Climate Sounder


    Irwin, Patrick G. J.; Calcutt, S. B.; Read, P. L.; Bowles, N. E.; Lewis, S.


    The 2016 Mars Trace Gas Mission will carry with it the ExoMars Mars Climate Sounder instrument, a development of the very successful Mars Climate Sounder instrument already in orbit about Mars on NASA's Mars Reconnaissance Orbiter spacecraft. EMCS will continue the monitoring of Mars global temperature/pressure/aerosol field, and will also be able to measure the vertical profile of water vapour across the planet from 0 – 50 km. Key components of EMCS will be provided by Oxford, Reading and Ca...

  6. EMMI-Electric solar wind sail facilitated Manned Mars Initiative (United States)

    Janhunen, Pekka; Merikallio, Sini; Paton, Mark


    The novel propellantless electric solar wind sail concept promises efficient low thrust transportation in the Solar System outside Earth's magnetosphere. Combined with asteroid mining to provide water and synthetic cryogenic rocket fuel in orbits of Earth and Mars, possibilities for affordable continuous manned presence on Mars open up. Orbital fuel and water enable reusable bidirectional Earth-Mars vehicles for continuous manned presence on Mars and allow smaller fuel fraction of spacecraft than what is achievable by traditional means. Water can also be used as radiation shielding of the manned compartment, thus reducing the launch mass further. In addition, the presence of fuel in the orbit of Mars provides the option for an all-propulsive landing, thus potentially eliminating issues of heavy heat shields and augmenting the capability of pinpoint landing. With this E-sail enabled scheme, the recurrent cost of continuous bidirectional traffic between Earth and Mars might ultimately approach the recurrent cost of running the International Space Station, ISS.

  7. Non-Equilibrium Thermodynamic Chemistry and the Composition of the Atmosphere of Mars (United States)

    Levine, J. S.; Summers, M. E.


    A high priority objective of the Mars Exploration Program is to Determine if life exists today (MEPAG Goal I, Objective A). The measurement of gases of biogenic origin may be an approach to detect the presence of microbial life on the surface or subsurface of Mars. Chemical thermodynamic calculations indicate that on both Earth and Mars, certain gases should exist in extremely low concentrations, if at all. Microbial metabolic activity is an important non-equilibrium chemistry process on Earth, and if microbial life exists on Mars, may be an important nonequilibrium chemistry process on Mars. The non-equilibrium chemistry of the atmosphere of Mars is discussed in this paper.

  8. Mars Observer's costly solitude (United States)

    Travis, John


    An evaluation is presented of the ramifications of the loss of contact with the Mars Observer spacecraft in August, 1993; the Observer constituted the first NASA mission to Mars in 17 years. It is noted that most, if not all of the scientists involved with the mission will have to find alternative employment within 6 months. The loss of the Observer will leave major questions concerning the geologic history of Mars, and its turbulent atmospheric circulation, unanswered. A detailed account of the discovery of the loss of communications, the unsuccessful steps taken to rectify the problem, and the financial losses incurred through the failure of the mission, are also given.

  9. Transportation-Driven Mars Surface Operations Supporting an Evolvable Mars Campaign (United States)

    Toups, Larry; Brown, Kendall; Hoffman, Stephen J.


    This paper describes the results of a study evaluating options for supporting a series of human missions to a single Mars surface destination. In this scenario the infrastructure emplaced during previous visits to this site is leveraged in following missions. The goal of this single site approach to Mars surface infrastructure is to enable "Steady State" operations by at least 4 crew for up to 500 sols at this site. These characteristics, along with the transportation system used to deliver crew and equipment to and from Mars, are collectively known as the Evolvable Mars Campaign (EMC). Information in this paper is presented in the sequence in which it was accomplished. First, a logical buildup sequence of surface infrastructure was developed to achieve the desired "Steady State" operations on the Mars surface. This was based on a concept of operations that met objectives of the EMC. Second, infrastructure capabilities were identified to carry out this concept of operations. Third, systems (in the form of conceptual elements) were identified to provide these capabilities. This included top-level mass, power and volume estimates for these elements. Fourth, the results were then used in analyses to evaluate three options (18t, 27t, and 40t landed mass) of Mars Lander delivery capability to the surface. Finally, Mars arrival mass estimates were generated based upon the entry, descent, and landing requirements for inclusion in separate assessments of in-space transportation capabilities for the EMC.

  10. Mars Global Surveyor Images (United States)


    High resolution images that help scientists fine tune the landing site for NASA's Mars Surveyor lander mission are shown. These images reveal a smooth surface in the southern cratered highlands near the Nepenthes Mensae.

  11. Mars Electric Reusable Flyer (United States)

    National Aeronautics and Space Administration — One of the main issues with a Mars flight vehicle concept that can be reused and cover long distances for maximum surface data gathering is its ability to take off,...

  12. Mars' Inner Core (United States)


    This figure shows a cross-section of the planet Mars revealing an inner, high density core buried deep within the interior. Dipole magnetic field lines are drawn in blue, showing the global scale magnetic field that one associates with dynamo generation in the core. Mars must have one day had such a field, but today it is not evident. Perhaps the energy source that powered the early dynamo has shut down. The differentiation of the planet interior - heavy elements like iron sinking towards the center of the planet - can provide energy as can the formation of a solid core from the liquid.The Jet Propulsion Laboratory's Mars Surveyor Operations Project operates the Mars Global Surveyor spacecraft with its industrial partner, Lockheed Martin Astronautics, from facilities in Pasadena, CA and Denver, CO. JPL is an operating division of California Institute of Technology (Caltech).

  13. Mars Technology Project (United States)

    National Aeronautics and Space Administration — NASA’s Mars Exploration Program (MEP) calls for a series of highly ambitious missions over the next decade and beyond. The overall goals of the MEP must be...

  14. Mars' core and magnetism. (United States)

    Stevenson, D J


    The detection of strongly magnetized ancient crust on Mars is one of the most surprising outcomes of recent Mars exploration, and provides important insight about the history and nature of the martian core. The iron-rich core probably formed during the hot accretion of Mars approximately 4.5 billion years ago and subsequently cooled at a rate dictated by the overlying mantle. A core dynamo operated much like Earth's current dynamo, but was probably limited in duration to several hundred million years. The early demise of the dynamo could have arisen through a change in the cooling rate of the mantle, or even a switch in convective style that led to mantle heating. Presently, Mars probably has a liquid, conductive outer core and might have a solid inner core like Earth.


    National Aeronautics and Space Administration — The Mars Pathfinder (MPF) Radio Science (RS) data archive contains both raw radio tracking data collected during the surface lifetime of the MPF Lander and results...

  16. Mars Rover Photos API (United States)

    National Aeronautics and Space Administration — This API is designed to collect image data gathered by NASA's Curiosity, Opportunity, and Spirit rovers on Mars and make it more easily available to other...

  17. Mars Environment Sensor Materials (United States)

    National Aeronautics and Space Administration — The project vision is to enable sensors and other components to be durable to the unique low Mars orbital environment so that science and pathfinder data can be...

  18. Status of MARS Code

    Energy Technology Data Exchange (ETDEWEB)

    N.V. Mokhov


    Status and recent developments of the MARS 14 Monte Carlo code system for simulation of hadronic and electromagnetic cascades in shielding, accelerator and detector components in the energy range from a fraction of an electronvolt up to 100 TeV are described. these include physics models both in strong and electromagnetic interaction sectors, variance reduction techniques, residual dose, geometry, tracking, histograming. MAD-MARS Beam Line Build and Graphical-User Interface.

  19. Discovery concepts for Mars (United States)

    Luhmann, J. G.; Russell, C. T.; Brace, L. H.; Nagy, A. F.; Jakosky, B. M.; Barth, C. A.; Waite, J. H.


    Two focused Mars missions that would fit within the guidelines for the proposed Discovery line are discussed. The first mission would deal with the issue of the escape of the atmosphere (Mars') to space. A complete understanding of this topic is crucial to deciphering the evolution of the atmosphere, climate change, and volatile inventories. The second mission concerns the investigation of remanent magnetization of the crust and its relationship to the ionosphere and the atmosphere.

  20. Natural Cubic Spline Regression Modeling Followed by Dynamic Network Reconstruction for the Identification of Radiation-Sensitivity Gene Association Networks from Time-Course Transcriptome Data. (United States)

    Michna, Agata; Braselmann, Herbert; Selmansberger, Martin; Dietz, Anne; Hess, Julia; Gomolka, Maria; Hornhardt, Sabine; Blüthgen, Nils; Zitzelsberger, Horst; Unger, Kristian


    Gene expression time-course experiments allow to study the dynamics of transcriptomic changes in cells exposed to different stimuli. However, most approaches for the reconstruction of gene association networks (GANs) do not propose prior-selection approaches tailored to time-course transcriptome data. Here, we present a workflow for the identification of GANs from time-course data using prior selection of genes differentially expressed over time identified by natural cubic spline regression modeling (NCSRM). The workflow comprises three major steps: 1) the identification of differentially expressed genes from time-course expression data by employing NCSRM, 2) the use of regularized dynamic partial correlation as implemented in GeneNet to infer GANs from differentially expressed genes and 3) the identification and functional characterization of the key nodes in the reconstructed networks. The approach was applied on a time-resolved transcriptome data set of radiation-perturbed cell culture models of non-tumor cells with normal and increased radiation sensitivity. NCSRM detected significantly more genes than another commonly used method for time-course transcriptome analysis (BETR). While most genes detected with BETR were also detected with NCSRM the false-detection rate of NCSRM was low (3%). The GANs reconstructed from genes detected with NCSRM showed a better overlap with the interactome network Reactome compared to GANs derived from BETR detected genes. After exposure to 1 Gy the normal sensitive cells showed only sparse response compared to cells with increased sensitivity, which exhibited a strong response mainly of genes related to the senescence pathway. After exposure to 10 Gy the response of the normal sensitive cells was mainly associated with senescence and that of cells with increased sensitivity with apoptosis. We discuss these results in a clinical context and underline the impact of senescence-associated pathways in acute radiation response of normal

  1. Estimated breeding values and association mapping for persistency and total milk yield using natural cubic smoothing splines. (United States)

    Verbyla, Klara L; Verbyla, Arunas P


    For dairy producers, a reliable description of lactation curves is a valuable tool for management and selection. From a breeding and production viewpoint, milk yield persistency and total milk yield are important traits. Understanding the genetic drivers for the phenotypic variation of both these traits could provide a means for improving these traits in commercial production. It has been shown that Natural Cubic Smoothing Splines (NCSS) can model the features of lactation curves with greater flexibility than the traditional parametric methods. NCSS were used to model the sire effect on the lactation curves of cows. The sire solutions for persistency and total milk yield were derived using NCSS and a whole-genome approach based on a hierarchical model was developed for a large association study using single nucleotide polymorphisms (SNP). Estimated sire breeding values (EBV) for persistency and milk yield were calculated using NCSS. Persistency EBV were correlated with peak yield but not with total milk yield. Several SNP were found to be associated with both traits and these were used to identify candidate genes for further investigation. NCSS can be used to estimate EBV for lactation persistency and total milk yield, which in turn can be used in whole-genome association studies.

  2. On the equivalence of spherical splines with least-squares collocation and Stokes's formula for regional geoid computation (United States)

    Ophaug, Vegard; Gerlach, Christian


    This work is an investigation of three methods for regional geoid computation: Stokes's formula, least-squares collocation (LSC), and spherical radial base functions (RBFs) using the spline kernel (SK). It is a first attempt to compare the three methods theoretically and numerically in a unified framework. While Stokes integration and LSC may be regarded as classic methods for regional geoid computation, RBFs may still be regarded as a modern approach. All methods are theoretically equal when applied globally, and we therefore expect them to give comparable results in regional applications. However, it has been shown by de Min (Bull Géod 69:223-232, 1995. doi: 10.1007/BF00806734) that the equivalence of Stokes's formula and LSC does not hold in regional applications without modifying the cross-covariance function. In order to make all methods comparable in regional applications, the corresponding modification has been introduced also in the SK. Ultimately, we present numerical examples comparing Stokes's formula, LSC, and SKs in a closed-loop environment using synthetic noise-free data, to verify their equivalence. All agree on the millimeter level.

  3. Terrestrial Analogs to Mars (United States)

    Farr, T. G.; Arcone, S.; Arvidson, R. W.; Baker, V.; Barlow, N. G.; Beaty, D.; Bell, M. S.; Blankenship, D. D.; Bridges, N.; Briggs, G.; Bulmer, M.; Carsey, F.; Clifford, S. M.; Craddock, R. A.; Dickerson, P. W.; Duxbury, N.; Galford, G. L.; Garvin, J.; Grant, J.; Green, J. R.; Gregg, T. K. P.; Guinness, E.; Hansen, V. L.; Hecht, M. H.; Holt, J.; Howard, A.; Keszthelyi, L. P.; Lee, P.; Lanagan, P. D.; Lentz, R. C. F.; Leverington, D. W.; Marinangeli, L.; Moersch, J. E.; Morris-Smith, P. A.; Mouginis-Mark, P.; Olhoeft, G. R.; Ori, G. G.; Paillou, P.; Reilly, J. F., II; Rice, J. W., Jr.; Robinson, C. A.; Sheridan, M.; Snook, K.; Thomson, B. J.; Watson, K.; Williams, K.; Yoshikawa, K.


    It is well recognized that interpretations of Mars must begin with the Earth as a reference. The most successful comparisons have focused on understanding geologic processes on the Earth well enough to extrapolate to Mars' environment. Several facets of terrestrial analog studies have been pursued and are continuing. These studies include field workshops, characterization of terrestrial analog sites, instrument tests, laboratory measurements (including analysis of Martian meteorites), and computer and laboratory modeling. The combination of all these activities allows scientists to constrain the processes operating in specific terrestrial environments and extrapolate how similar processes could affect Mars. The Terrestrial Analogs for Mars Community Panel has considered the following two key questions: (1) How do terrestrial analog studies tie in to the Mars Exploration Payload Assessment Group science questions about life, past climate, and geologic evolution of Mars, and (2) How can future instrumentation be used to address these questions. The panel has considered the issues of data collection, value of field workshops, data archiving, laboratory measurements and modeling, human exploration issues, association with other areas of solar system exploration, and education and public outreach activities.

  4. Life on Mars (United States)

    McKay, Christopher P.; Cuzzi, Jeffrey (Technical Monitor)


    Although the Viking results may indicate that Mars has no life today, the possibility exists that Mars may hold the best record of the events that led to the origin of life. There is direct geomorphological evidence that in the past Mars had large amounts of liquid water on its surface. Atmospheric models would suggest that this early period of hydrological activity was due to the presence of a thick atmosphere and the resulting warmer temperatures. From a biological perspective the existence of liquid water, by itself motivates the question of the origin of life on Mars. From studies of the Earth's earliest biosphere we know that by 3.5 Gyr. ago, life had originated on Earth and reached a fair degree of biological sophistication. Surface activity and erosion on Earth make it difficult to trace the history of life before the 3.5 Gyr timeframe. If Mars did maintain a clement environment for longer than it took for life to originate on Earth, then the question of the origin of life on Mars follows naturally.

  5. The MARS2013 Mars analog mission. (United States)

    Groemer, Gernot; Soucek, Alexander; Frischauf, Norbert; Stumptner, Willibald; Ragonig, Christoph; Sams, Sebastian; Bartenstein, Thomas; Häuplik-Meusburger, Sandra; Petrova, Polina; Evetts, Simon; Sivenesan, Chan; Bothe, Claudia; Boyd, Andrea; Dinkelaker, Aline; Dissertori, Markus; Fasching, David; Fischer, Monika; Föger, Daniel; Foresta, Luca; Fritsch, Lukas; Fuchs, Harald; Gautsch, Christoph; Gerard, Stephan; Goetzloff, Linda; Gołebiowska, Izabella; Gorur, Paavan; Groemer, Gerhard; Groll, Petra; Haider, Christian; Haider, Olivia; Hauth, Eva; Hauth, Stefan; Hettrich, Sebastian; Jais, Wolfgang; Jones, Natalie; Taj-Eddine, Kamal; Karl, Alexander; Kauerhoff, Tilo; Khan, Muhammad Shadab; Kjeldsen, Andreas; Klauck, Jan; Losiak, Anna; Luger, Markus; Luger, Thomas; Luger, Ulrich; McArthur, Jane; Moser, Linda; Neuner, Julia; Orgel, Csilla; Ori, Gian Gabriele; Paternesi, Roberta; Peschier, Jarno; Pfeil, Isabella; Prock, Silvia; Radinger, Josef; Ramirez, Barbara; Ramo, Wissam; Rampey, Mike; Sams, Arnold; Sams, Elisabeth; Sandu, Oana; Sans, Alejandra; Sansone, Petra; Scheer, Daniela; Schildhammer, Daniel; Scornet, Quentin; Sejkora, Nina; Stadler, Andrea; Stummer, Florian; Taraba, Michael; Tlustos, Reinhard; Toferer, Ernst; Turetschek, Thomas; Winter, Egon; Zanella-Kux, Katja


    We report on the MARS2013 mission, a 4-week Mars analog field test in the northern Sahara. Nineteen experiments were conducted by a field crew in Morocco under simulated martian surface exploration conditions, supervised by a Mission Support Center in Innsbruck, Austria. A Remote Science Support team analyzed field data in near real time, providing planning input for the management of a complex system of field assets; two advanced space suit simulators, four robotic vehicles, an emergency shelter, and a stationary sensor platform in a realistic work flow were coordinated by a Flight Control Team. A dedicated flight planning group, external control centers for rover tele-operations, and a biomedical monitoring team supported the field operations. A 10 min satellite communication delay and other limitations pertinent to human planetary surface activities were introduced. The fields of research for the experiments were geology, human factors, astrobiology, robotics, tele-science, exploration, and operations research. This paper provides an overview of the geological context and environmental conditions of the test site and the mission architecture, in particular the communication infrastructure emulating the signal travel time between Earth and Mars. We report on the operational work flows and the experiments conducted, including a deployable shelter prototype for multiple-day extravehicular activities and contingency situations.

  6. The analysis of internet addiction scale using multivariate adaptive regression splines. (United States)

    Kayri, M


    Determining real effects on internet dependency is too crucial with unbiased and robust statistical method. MARS is a new non-parametric method in use in the literature for parameter estimations of cause and effect based research. MARS can both obtain legible model curves and make unbiased parametric predictions. In order to examine the performance of MARS, MARS findings will be compared to Classification and Regression Tree (C&RT) findings, which are considered in the literature to be efficient in revealing correlations between variables. The data set for the study is taken from "The Internet Addiction Scale" (IAS), which attempts to reveal addiction levels of individuals. The population of the study consists of 754 secondary school students (301 female, 443 male students with 10 missing data). MARS 2.0 trial version is used for analysis by MARS method and C&RT analysis was done by SPSS. MARS obtained six base functions of the model. As a common result of these six functions, regression equation of the model was found. Over the predicted variable, MARS showed that the predictors of daily Internet-use time on average, the purpose of Internet-use, grade of students and occupations of mothers had a significant effect (Pdependency level prediction. The fact that MARS revealed extent to which the variable, which was considered significant, changes the character of the model was observed in this study.

  7. Landslide susceptibility modeling in a landslide prone area in Mazandarn Province, north of Iran: a comparison between GLM, GAM, MARS, and M-AHP methods (United States)

    Pourghasemi, Hamid Reza; Rossi, Mauro


    Landslides are identified as one of the most important natural hazards in many areas throughout the world. The essential purpose of this study is to compare general linear model (GLM), general additive model (GAM), multivariate adaptive regression spline (MARS), and modified analytical hierarchy process (M-AHP) models and assessment of their performances for landslide susceptibility modeling in the west of Mazandaran Province, Iran. First, landslides were identified by interpreting aerial photographs, and extensive field works. In total, 153 landslides were identified in the study area. Among these, 105 landslides were randomly selected as training data (i.e. used in the models training) and the remaining 48 (30 %) cases were used for the validation (i.e. used in the models validation). Afterward, based on a deep literature review on 220 scientific papers (period between 2005 and 2012), eleven conditioning factors including lithology, land use, distance from rivers, distance from roads, distance from faults, slope angle, slope aspect, altitude, topographic wetness index (TWI), plan curvature, and profile curvature were selected. The Certainty Factor (CF) model was used for managing uncertainty in rule-based systems and evaluation of the correlation between the dependent (landslides) and independent variables. Finally, the landslide susceptibility zonation was produced using GLM, GAM, MARS, and M-AHP models. For evaluation of the models, the area under the curve (AUC) method was used and both success and prediction rate curves were calculated. The evaluation of models for GLM, GAM, and MARS showed 90.50, 88.90, and 82.10 % for training data and 77.52, 70.49, and 78.17 % for validation data, respectively. Furthermore, The AUC value of the produced landslide susceptibility map using M-AHP showed a training value of 77.82 % and validation value of 82.77 % accuracy. Based on the overall assessments, the proposed approaches showed reasonable results for landslide

  8. Mars at Ls 357o (United States)


    31 January 2006 This picture is a composite of Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) daily global images acquired at Ls 357o during a previous Mars year. This month, Mars looks similar, as Ls 357o occurred in mid-January 2006. The picture shows the south polar region of Mars. Over the course of the month, additional faces of Mars as it appears at this time of year are being posted for MOC Picture of the Day. Ls, solar longitude, is a measure of the time of year on Mars. Mars travels 360o around the Sun in 1 Mars year. The year begins at Ls 0o, the start of northern spring and southern autumn. Season: Northern Winter/Southern Summer

  9. Mars at Ls 324o (United States)


    29 November 2005 This picture is a composite of Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) daily global images acquired at Ls 324o during a previous Mars year. This month, Mars looks similar, as Ls 324o occurred in mid-November 2005. The picture shows the south polar region of Mars. Over the course of the month, additional faces of Mars as it appears at this time of year are being posted for MOC Picture of the Day. Ls, solar longitude, is a measure of the time of year on Mars. Mars travels 360o around the Sun in 1 Mars year. The year begins at Ls 0o, the start of northern spring and southern autumn. Season: Northern Winter/Southern Summer

  10. Numerical discretization-based estimation methods for ordinary differential equation models via penalized spline smoothing with applications in biomedical research. (United States)

    Wu, Hulin; Xue, Hongqi; Kumar, Arun


    Differential equations are extensively used for modeling dynamics of physical processes in many scientific fields such as engineering, physics, and biomedical sciences. Parameter estimation of differential equation models is a challenging problem because of high computational cost and high-dimensional parameter space. In this article, we propose a novel class of methods for estimating parameters in ordinary differential equation (ODE) models, which is motivated by HIV dynamics modeling. The new methods exploit the form of numerical discretization algorithms for an ODE solver to formulate estimating equations. First, a penalized-spline approach is employed to estimate the state variables and the estimated state variables are then plugged in a discretization formula of an ODE solver to obtain the ODE parameter estimates via a regression approach. We consider three different order of discretization methods, Euler's method, trapezoidal rule, and Runge-Kutta method. A higher-order numerical algorithm reduces numerical error in the approximation of the derivative, which produces a more accurate estimate, but its computational cost is higher. To balance the computational cost and estimation accuracy, we demonstrate, via simulation studies, that the trapezoidal discretization-based estimate is the best and is recommended for practical use. The asymptotic properties for the proposed numerical discretization-based estimators are established. Comparisons between the proposed methods and existing methods show a clear benefit of the proposed methods in regards to the trade-off between computational cost and estimation accuracy. We apply the proposed methods t an HIV study to further illustrate the usefulness of the proposed approaches. © 2012, The International Biometric Society.

  11. Approaching Borderlands. Literary Representation of the Border in the Novel Their dogs came with them by Helena María Viramontes

    Directory of Open Access Journals (Sweden)

    Markéta Riebová


    Full Text Available Using three mutually interwoven theoretical approaches, the article analyses the complexity of the borderlands space in the literary representation of Los Angeles in the novel Their dogs came with them by Helena Maria Viramontes.

  12. Revision Total Hip Arthroplasty With a Monoblock Splined Tapered Grit-Blasted Titanium Stem. (United States)

    Hellman, Michael D; Kearns, Sean M; Bohl, Daniel D; Haughom, Bryan D; Levine, Brett R


    In revision total hip arthroplasty (THA), proximal femoral bone loss creates a challenge of achieving adequate stem fixation. The purpose of this study was to examine the outcomes of a monoblock, splined, tapered femoral stem in revision THA. Outcomes of revision THA using a nonmodular, splined, tapered femoral stem from a single surgeon were reviewed. With a minimum of 2-year follow-up, there were 68 cases (67 patients). Paprosky classification was 3A or greater in 85% of the cases. Preoperative and postoperative Harris Hip Scores (HHS), radiographic subsidence and osseointegration, limb length discrepancy, complications, and reoperations were analyzed. The Harris Hip Score improved from 37.4 ± SD 19.4 preoperatively to 64.6 ± SD 21.8 at final follow-up (P revision procedures-8 for septic indications and 8 for aseptic indications. Subsidence occurred at a rate of 3.0% and dislocation at 7.4%. Limb length discrepancy of more than 1 cm after revision was noted in 13.6% of patients. Bone ingrowth was observed in all but 4 patients (94.1%). At 4-year follow-up, Kaplan-Meier estimated survival was 72.9% (95% confidence interval [CI] 57.0-83.8) for all causes of revision, 86.6% (95% CI 72.0-93.9) for all aseptic revision, and 95.5% (95% CI 86.8-98.5) for aseptic femoral revision. Although complications were significant, revision for femoral aseptic loosening occurred in only 3 patients. Given the ability of this monoblock splined tapered stem to adequately provide fixation during complex revision THA, it remains a viable option in the setting of substantial femoral bone defects. Copyright © 2017 Elsevier Inc. All rights reserved.

  13. Interpolating Spline Curve-Based Perceptual Encryption for 3D Printing Models

    Directory of Open Access Journals (Sweden)

    Giao N. Pham


    Full Text Available With the development of 3D printing technology, 3D printing has recently been applied to many areas of life including healthcare and the automotive industry. Due to the benefit of 3D printing, 3D printing models are often attacked by hackers and distributed without agreement from the original providers. Furthermore, certain special models and anti-weapon models in 3D printing must be protected against unauthorized users. Therefore, in order to prevent attacks and illegal copying and to ensure that all access is authorized, 3D printing models should be encrypted before being transmitted and stored. A novel perceptual encryption algorithm for 3D printing models for secure storage and transmission is presented in this paper. A facet of 3D printing model is extracted to interpolate a spline curve of degree 2 in three-dimensional space that is determined by three control points, the curvature coefficients of degree 2, and an interpolating vector. Three control points, the curvature coefficients, and interpolating vector of the spline curve of degree 2 are encrypted by a secret key. The encrypted features of the spline curve are then used to obtain the encrypted 3D printing model by inverse interpolation and geometric distortion. The results of experiments and evaluations prove that the entire 3D triangle model is altered and deformed after the perceptual encryption process. The proposed algorithm is responsive to the various formats of 3D printing models. The results of the perceptual encryption process is superior to those of previous methods. The proposed algorithm also provides a better method and more security than previous methods.

  14. Guidelines for 2008 MARS exercise

    CERN Multimedia

    HR Department


    Full details of the Merit Appraisal and Recognition Scheme (MARS) are available via the HR Department’s homepage or directly on the Department’s MARS web page: You will find on these pages: MARS procedures including the MARS timetable for proposals and decisions; Regulations with links to the scheme’s statutory basis; Frequently Asked Questions; Useful documents with links to relevant documentation; e.g. mandate of the Senior Staff Advisory Committee (SSAC); Related links and contacts. HR Department Tel. 73566

  15. Bivariate spline solution of time dependent nonlinear PDE for a population density over irregular domains. (United States)

    Gutierrez, Juan B; Lai, Ming-Jun; Slavov, George


    We study a time dependent partial differential equation (PDE) which arises from classic models in ecology involving logistic growth with Allee effect by introducing a discrete weak solution. Existence, uniqueness and stability of the discrete weak solutions are discussed. We use bivariate splines to approximate the discrete weak solution of the nonlinear PDE. A computational algorithm is designed to solve this PDE. A convergence analysis of the algorithm is presented. We present some simulations of population development over some irregular domains. Finally, we discuss applications in epidemiology and other ecological problems. Copyright © 2015 Elsevier Inc. All rights reserved.

  16. Numerical solution of the controlled Duffing oscillator by semi-orthogonal spline wavelets

    International Nuclear Information System (INIS)

    Lakestani, M; Razzaghi, M; Dehghan, M


    This paper presents a numerical method for solving the controlled Duffing oscillator. The method can be extended to nonlinear calculus of variations and optimal control problems. The method is based upon compactly supported linear semi-orthogonal B-spline wavelets. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique

  17. Complex wavenumber Fourier analysis of the B-spline based finite element method

    Czech Academy of Sciences Publication Activity Database

    Kolman, Radek; Plešek, Jiří; Okrouhlík, Miloslav


    Roč. 51, č. 2 (2014), s. 348-359 ISSN 0165-2125 R&D Projects: GA ČR(CZ) GAP101/11/0288; GA ČR(CZ) GAP101/12/2315; GA ČR GPP101/10/P376; GA ČR GA101/09/1630 Institutional support: RVO:61388998 Keywords : elastic wave propagation * dispersion errors * B-spline * finite element method * isogeometric analysis Subject RIV: JR - Other Machinery Impact factor: 1.513, year: 2014

  18. Gaussian quadrature rules for C 1 quintic splines with uniform knot vectors

    KAUST Repository

    Bartoň, Michael


    We provide explicit quadrature rules for spaces of C1C1 quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. Each rule is optimal, that is, requires the minimal number of nodes, for a given function space. For each of nn subintervals, generically, only two nodes are required which reduces the evaluation cost by 2/32/3 when compared to the classical Gaussian quadrature for polynomials over each knot span. Numerical experiments show fast convergence, as nn grows, to the “two-third” quadrature rule of Hughes et al. (2010) for infinite domains.

  19. Solid T-spline Construction from Boundary Triangulations with Arbitrary Genus Topology (United States)


    sculpture model has genus two and (a) (b) (c) Fig. 11. The solid T-spline construction result for the “Eight” model. (a) The constructed solid T...1,536) 5,735 (16, 16) 200 1,440 (0.10, 1.00) 8.5 Sculpture 2 (8,635, 17,276) 10,549 (16, 16) 252 7,072 (0.09, 1.00) 41.5 (a) (b) (c) (d) (e) (f) (g) (h...isogeometric analysis result. 10 (a) (b) (c) (d) (e) (f) (g) (h) Fig. 14. Sculpture model with genus two. (a) The input boundary triangle mesh; (b) the

  20. A quadratic spline maximum entropy method for the computation of invariant densities

    Directory of Open Access Journals (Sweden)

    DING Jiu


    Full Text Available The numerical recovery of an invariant density of the Frobenius-Perron operator corresponding to a nonsingular transformation is depicted by using quadratic spline functions. We implement a maximum entropy method to approximate the invariant density. The proposed method removes the ill-conditioning in the maximum entropy method, which arises by the use of polynomials. Due to the smoothness of the functions and a good convergence rate, the accuracy in the numerical calculation increases rapidly as the number of moment functions increases. The numerical results from the proposed method are supported by the theoretical analysis.

  1. Pseudo-cubic thin-plate type Spline method for analyzing experimental data

    International Nuclear Information System (INIS)

    Crecy, F. de.


    A mathematical tool, using pseudo-cubic thin-plate type Spline, has been developed for analysis of experimental data points. The main purpose is to obtain, without any a priori given model, a mathematical predictor with related uncertainties, usable at any point in the multidimensional parameter space. The smoothing parameter is determined by a generalized cross validation method. The residual standard deviation obtained is significantly smaller than that of a least square regression. An example of use is given with critical heat flux data, showing a significant decrease of the conception criterion (minimum allowable value of the DNB ratio). (author) 4 figs., 1 tab., 7 refs

  2. The Mars Plasma Environment

    CERN Document Server

    Russell, C. T


    Mars sits very exposed to the solar wind and, because it is a small planet, has but a weak hold on its atmosphere. The solar wind therefore plays an important role in the evolution of the martian atmosphere. Over the last four decades a series of European missions, first from the Soviet Union and more recently from the European Space Agency, together with a single investigation from the U.S., the Mars Global Surveyor spacecraft, have added immeasurably to our understanding of the interplay between the solar wind and Mars atmosphere. Most recently the measurements of the plasma and fast neutral populations, conducted on the Mars Express spacecraft by the ASPERA-3 instrument have been acquired and analyzed. Their presentation to the public, most notably at the workshop "The Solar Wind Interaction and Atmosphere Evolution of Mars" held in Kiruna in early 2006, was the inspiration for this series of articles. However participation in the Kiruna conference was not a selection criterion for this volume. The papers ...

  3. Magnetic storms on Mars

    DEFF Research Database (Denmark)

    Vennerstrøm, Susanne


    Based on data from the Mars Global Surveyor magnetometer we examine periods of significantly enhanced magnetic disturbances in the martian space environment. Using almost seven years of observations during the maximum and early declining phase of the previous solar cycle the occurrence pattern...... and typical time profile of such periods is investigated and compared to solar wind measurements at Earth. Typical durations of the events are 20–40h, and there is a tendency for large events to last longer, but a large spread in duration and intensity are found. The large and medium intensity events at Mars...... field disturbance at Mars is solar wind dynamic pressure variations associated with the eccentricity of the martian orbit around the Sun....

  4. Remanent magnetism at Mars (United States)

    Curtis, S. A.; Ness, N. F.


    It is shown that a strong case can be made for an intrinsic magnetic field of dynamo origin for Mars earlier in its history. The typical equatorial magnetic field intensity would have been equal to about 0.01-0.1 gauss. The earlier dynamo activity is no longer extant, but a significant remanent magnetic field may exist. A highly non-dipole magnetic field could result from the remanent magnetization of the surface. Remanent magnetization may thus play an important role in the Mars solar wind interactions, in contrast to Venus with its surface temperatures above the Curie point. The anomalous characteristics of Mars'solar wind interaction compared to that of Venus may be explicable on this basis.

  5. Analysis of ambulatory blood pressure monitor data using a hierarchical model incorporating restricted cubic splines and heterogeneous within-subject variances. (United States)

    Lambert, P C; Abrams, K R; Jones, D R; Halligan, A W; Shennan, A


    Hypertensive disorders of pregnancy are associated with significant maternal and foetal morbidity. Measurement of blood pressure remains the standard way of identifying individuals at risk. There is growing interest in the use of ambulatory blood pressure monitors (ABPM), which can record an individual's blood pressure many times over a 24-hour period. From a clinical perspective interest lies in the shape of the blood pressure profile over a 24-hour period and any differences in the profile between groups. We propose a two-level hierarchical linear model incorporating all ABPM data into a single model. We contrast a classical approach with a Bayesian approach using the results of a study of 206 pregnant women who were asked to wear an ABPM for 24 hours after referral to an obstetric day unit with high blood pressure. As the main interest lies in the shape of the profile, we use restricted cubic splines to model the mean profiles. The use of restricted cubic splines provides a flexible way to model the mean profiles and to make comparisons between groups. From examining the data and the fit of the model it is apparent that there were heterogeneous within-subject variances in that some women tend to have more variable blood pressure than others. Within the Bayesian framework it is relatively easy to incorporate a random effect to model the between-subject variation in the within-subject variances. Although there is substantial heterogeneity in the within-subject variances, allowing for this in the model has surprisingly little impact on the estimates of the mean profiles or their confidence/credible intervals. We thus demonstrate a powerful method for analysis of ABPM data and also demonstrate how heterogeneous within-subject variances can be modelled from a Bayesian perspective. Copyright 2001 John Wiley & Sons, Ltd.


    Jiang, Fei; Ma, Yanyuan; Wang, Yuanjia

    We propose a generalized partially linear functional single index risk score model for repeatedly measured outcomes where the index itself is a function of time. We fuse the nonparametric kernel method and regression spline method, and modify the generalized estimating equation to facilitate estimation and inference. We use local smoothing kernel to estimate the unspecified coefficient functions of time, and use B-splines to estimate the unspecified function of the single index component. The covariance structure is taken into account via a working model, which provides valid estimation and inference procedure whether or not it captures the true covariance. The estimation method is applicable to both continuous and discrete outcomes. We derive large sample properties of the estimation procedure and show different convergence rate of each component of the model. The asymptotic properties when the kernel and regression spline methods are combined in a nested fashion has not been studied prior to this work even in the independent data case.

  7. Meteorites on Mars (United States)

    Flynn, G. J.; Mckay, D. S.


    Four types of meteoritic material should be found on Mars: (1) micrometeorites, many of which will survive atmospheric entry unmelted, which should fall relatively uniformly over the planet's surface, (2) ablation products from larger meteorites which ablate, break up and burn up in the Mars atmosphere, (3) debris from large, crater forming objects, which, by analogy to terrestrial and lunar impact events, will be concentrated in the crater ejecta blankets (except for rare, large events, such as the proposed C-T event on earth, which can distribute debris on a planetary scale), and (4) debris from the early, intense bombardment, which, in many areas of the planet, may now be incorporated into rocks by geologic processes subsequent to the intense bombardment era. To estimate the extent of meteoritic addition to indigenous Martian material, the meteoritic flux on Mars must be known. It is estimated that the overall flux is twice that for the Moon and 1.33 that for Earth. For small particles, whose orbital evolution is dominated by Poynting Robertson drag, the flux at Mars can be estimated from the Earth flux. The smaller Martian gravitational enhancement as well as the decrease in the spatial density of interplanetary dust with increasing heliocentric distance should reduce the flux of small particles at Mars to about 0.33 times the flux at Earth. Because of the smaller planetary cross-section the total infalling mass at Mars is then estimated to be 0.09 time the infalling mass in the micrometeorite size range at Earth.

  8. The geology of Mars (United States)

    Mutch, T. A.; Arvidson, R. E.; Head, J. W., III; Jones, K. L.; Saunders, R. S.


    The book constitutes a topographic/geologic atlas of Mars compiled on the basis of data from the various Mariner missions. A large number of maps has been included which systematically describe the character and distribution of the principal landforms: craters, channels, volcanoes, and faults; also related properties such as albedo, elevation, and wind streaks. Pictures of all the important topographic features have been included. The discussion of the material is carried out with a minimum of technical detail, and Mars is examined within a context of interplanetary comparisons.

  9. Lakes on Mars

    CERN Document Server

    Cabrol, Nathalie A


    On Earth, lakes provide favorable environments for the development of life and its preservation as fossils. They are extremely sensitive to climate fluctuations and to conditions within their watersheds. As such, lakes are unique markers of the impact of environmental changes. Past and current missions have now demonstrated that water once flowed at the surface of Mars early in its history. Evidence of ancient ponding has been uncovered at scales ranging from a few kilometers to possibly that of the Arctic ocean. Whether life existed on Mars is still unknown; upcoming missions may find critic

  10. Mars Obliquity Cycle Illustration (United States)


    The tilt of Mars' spin axis (obliquity) varies cyclically over hundreds of thousands of years, and affects the sunlight falling on the poles. Because the landing site of NASA's Phoenix Mars Lander is so near the north pole, higher sun and warmer temperatures during high obliquity lead to warmer, more humid surface environments, and perhaps thicker, more liquid-like films of water in soil. The Phoenix Mission is led by the University of Arizona, Tucson, on behalf of NASA. Project management of the mission is by NASA's Jet Propulsion Laboratory, Pasadena, Calif. Spacecraft development is by Lockheed Martin Space Systems, Denver.

  11. Mars Gashopper Airplane, Phase I (United States)

    National Aeronautics and Space Administration — The Mars Gas Hopper Airplane, or "gashopper" is a novel concept for propulsion of a robust Mars flight and surface exploration vehicle that utilizes indigenous CO2...

  12. Non-stationary hydrologic frequency analysis using B-spline quantile regression (United States)

    Nasri, B.; Bouezmarni, T.; St-Hilaire, A.; Ouarda, T. B. M. J.


    Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic and water resources systems under the assumption of stationarity. However, with increasing evidence of climate change, it is possible that the assumption of stationarity, which is prerequisite for traditional frequency analysis and hence, the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extremes based on B-Spline quantile regression which allows to model data in the presence of non-stationarity and/or dependence on covariates with linear and non-linear dependence. A Markov Chain Monte Carlo (MCMC) algorithm was used to estimate quantiles and their posterior distributions. A coefficient of determination and Bayesian information criterion (BIC) for quantile regression are used in order to select the best model, i.e. for each quantile, we choose the degree and number of knots of the adequate B-spline quantile regression model. The method is applied to annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in the variable of interest and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for an annual maximum and minimum discharge with high annual non-exceedance probabilities.

  13. A spectral/B-spline method for the Navier-Stokes equations in unbounded domains

    International Nuclear Information System (INIS)

    Dufresne, L.; Dumas, G.


    The numerical method presented in this paper aims at solving the incompressible Navier-Stokes equations in unbounded domains. The problem is formulated in cylindrical coordinates and the method is based on a Galerkin approximation scheme that makes use of vector expansions that exactly satisfy the continuity constraint. More specifically, the divergence-free basis vector functions are constructed with Fourier expansions in the θ and z directions while mapped B-splines are used in the semi-infinite radial direction. Special care has been taken to account for the particular analytical behaviors at both end points r=0 and r→∞. A modal reduction algorithm has also been implemented in the azimuthal direction, allowing for a relaxation of the CFL constraint on the timestep size and a possibly significant reduction of the number of DOF. The time marching is carried out using a mixed quasi-third order scheme. Besides the advantages of a divergence-free formulation and a quasi-spectral convergence, the local character of the B-splines allows for a great flexibility in node positioning while keeping narrow bandwidth matrices. Numerical tests show that the present method compares advantageously with other similar methodologies using purely global expansions

  14. Fuzzy topological digital space and digital fuzzy spline of electroencephalography during epileptic seizures (United States)

    Shah, Mazlina Muzafar; Wahab, Abdul Fatah


    Epilepsy disease occurs because of there is a temporary electrical disturbance in a group of brain cells (nurons). The recording of electrical signals come from the human brain which can be collected from the scalp of the head is called Electroencephalography (EEG). EEG then considered in digital format and in fuzzy form makes it a fuzzy digital space data form. The purpose of research is to identify the area (curve and surface) in fuzzy digital space affected by inside epilepsy seizure in epileptic patient's brain. The main focus for this research is to generalize fuzzy topological digital space, definition and basic operation also the properties by using digital fuzzy set and the operations. By using fuzzy digital space, the theory of digital fuzzy spline can be introduced to replace grid data that has been use previously to get better result. As a result, the flat of EEG can be fuzzy topological digital space and this type of data can be use to interpolate the digital fuzzy spline.


    Directory of Open Access Journals (Sweden)

    Joel Domínguez Viveros


    Full Text Available The objectives were to estimate variance components, and direct (h2 and maternal (m2 heritability in the growth of Tropicarne cattle based on a random regression model using B-Splines for random effects modeling. Information from 12 890 monthly weightings of 1787 calves, from birth to 24 months old, was analyzed. The pedigree included 2504 animals. The random effects model included genetic and permanent environmental (direct and maternal of cubic order, and residuals. The fixed effects included contemporaneous groups (year – season of weighed, sex and the covariate age of the cow (linear and quadratic. The B-Splines were defined in four knots through the growth period analyzed. Analyses were performed with the software Wombat. The variances (phenotypic and residual presented a similar behavior; of 7 to 12 months of age had a negative trend; from birth to 6 months and 13 to 18 months had positive trend; after 19 months were maintained constant. The m2 were low and near to zero, with an average of 0.06 in an interval of 0.04 to 0.11; the h2 also were close to zero, with an average of 0.10 in an interval of 0.03 to 0.23.

  16. A function using cubic splines for the analysis of alpha-particle spectra from silicon detectors

    CERN Document Server

    Lozano, J C; Fernández, F


    A function based on the characteristics of the alpha-particle lines obtained with silicon semiconductor detectors and modified by using cubic splines is proposed to parametrize the shape of the peaks. A reduction in the number of parameters initially considered in other proposals was carried out in order to improve the stability of the optimization process. It was imposed by the boundary conditions for the cubic splines term. This function was then able to describe peaks with highly anomalous shapes with respect to those expected from this type of detector. Some criteria were implemented to correctly determine the area of the peaks and their errors. Comparisons with other well-established functions revealed excellent agreement in the final values obtained from both fits. Detailed studies on reliability of the fitting results were carried out and the application of the function is proposed. Although the aim was to correct anomalies in peak shapes, the peaks showing the expected shapes were also well fitted. Ac...

  17. Segmentation of ultrasound images of the carotid using RANSAC and cubic splines. (United States)

    Rocha, Rui; Campilho, Aurélio; Silva, Jorge; Azevedo, Elsa; Santos, Rosa


    A new algorithm is proposed for the semi-automatic segmentation of the near-end and the far-end adventitia boundary of the common carotid artery in ultrasound images. It uses the random sample consensus method to estimate the most significant cubic splines fitting the edge map of a longitudinal section. The consensus of the geometric model (a spline) is evaluated through a new gain function, which integrates the responses to different discriminating features of the carotid boundary: the proximity of the geometric model to any edge or to valley shaped edges; the consistency between the orientation of the normal to the geometric model and the intensity gradient; and the distance to a rough estimate of the lumen boundary. A set of 50 longitudinal B-mode images of the common carotid and their manual segmentations performed by two medical experts were used to assess the performance of the method. The image set was taken from 25 different subjects, most of them having plaques of different classes (class II to class IV), sizes and shapes. The quantitative evaluation showed promising results, having detection errors similar to the ones observed in manual segmentations for 95% of the far-end boundaries and 73% of the near-end boundaries. 2011 Elsevier Ireland Ltd. All rights reserved.


    Directory of Open Access Journals (Sweden)

    Nanik Suciati


    Full Text Available Penelitian ini menyusun representasi multiresolusi untuk kurva B-spline kubik yang menginterpolasi titik-titik ujung dengan basis wavelets. Representasi multiresolusi ini digunakan untuk mendukung beberapa tipe pengeditan kurva, yaitu penghalusan kurva dengan tingkat resolusi kontinyu untuk menghilangkan detail-detail kurva yang tidak diinginkan, pengeditan bentuk keseluruhan kurva dengan tetap mempertahankan detaildetailnya, perubahan detail-detail kurva tanpa mempengaruhi bentuk keseluruhannya, dan pengeditan satubagian tertentu dari kurva melalui manipulasi secara langsung terhadap titik-titik kontrolnya. Untuk menguji kemampuan representasi multiresolusi dalam mendukung empat tipe manipulasi kurva tersebut, disusun program pengeditan kurva dengan menggunakan bahasa pemrograman Visual C++ pada komputer Pentium 133 MHz, memori 16 Mbyte, sistem operasi Windows 95, lingkungan pengembangan Microsoft DevelopmentStudio 97 dan pustaka Microsoft Foundation Class. Dari hasil uji coba program diketahui bahwa representasi multiresolusi memberikan dukungan yang sangat baik terhadap tipe-tipe pengeditan seperti yang disebutkan di atas. Representasi multiresolusi tidak membutuhkan memori penyimpan ekstra selain dari yang digunakan untuk menyimpan titik kontrol. Dari hasil uji coba program menggunakan ratusan titik kontrol, algoritma berjalan cukup cepat dan memadai berkaitan dengan tuntutan komunikasi interaktif antara user dan program.Kata kunci: B-Spline, Wavelet, Multiresolusi

  19. Microscopic Model of Automobile Lane-changing Virtual Desire Trajectory by Spline Curves

    Directory of Open Access Journals (Sweden)

    Yulong Pei


    Full Text Available With the development of microscopic traffic simulation models, they have increasingly become an important tool for transport system analysis and management, which assist the traffic engineer to investigate and evaluate the performance of transport network systems. Lane-changing model is a vital component in any traffic simulation model, which could improve road capacity and reduce vehicles delay so as to reduce the likelihood of congestion occurrence. Therefore, this paper addresses the virtual desire trajectory, a vital part to investigate the behaviour divided into four phases. Based on the boundary conditions, β-spline curves and the corresponding reverse algorithm are introduced firstly. Thus, the relation between the velocity and length of lane-changing is constructed, restricted by the curvature, steering velocity and driving behaviour. Then the virtual desire trajectory curves are presented by Matlab and the error analysis results prove that this proposed description model has higher precision in automobile lane-changing process reconstruction, compared with the surveyed result. KEY WORDS: traffic simulation, lane-changing model, virtual desire trajectory, β-spline curves, driving behaviour

  20. Transforming wealth: using the inverse hyperbolic sine (IHS) and splines to predict youth's math achievement. (United States)

    Friedline, Terri; Masa, Rainier D; Chowa, Gina A N


    The natural log and categorical transformations commonly applied to wealth for meeting the statistical assumptions of research may not always be appropriate for adjusting for skewness given wealth's unique properties. Finding and applying appropriate transformations is becoming increasingly important as researchers consider wealth as a predictor of well-being. We present an alternative transformation-the inverse hyperbolic sine (IHS)-for simultaneously dealing with skewness and accounting for wealth's unique properties. Using the relationship between household wealth and youth's math achievement as an example, we apply the IHS transformation to wealth data from US and Ghanaian households. We also explore non-linearity and accumulation thresholds by combining IHS transformed wealth with splines. IHS transformed wealth relates to youth's math achievement similarly when compared to categorical and natural log transformations, indicating that it is a viable alternative to other transformations commonly used in research. Non-linear relationships and accumulation thresholds emerge that predict youth's math achievement when splines are incorporated. In US households, accumulating debt relates to decreases in math achievement whereas accumulating assets relates to increases in math achievement. In Ghanaian households, accumulating assets between the 25th and 50th percentiles relates to increases in youth's math achievement. Copyright © 2014 Elsevier Inc. All rights reserved.

  1. Non-Stationary Hydrologic Frequency Analysis using B-Splines Quantile Regression (United States)

    Nasri, B.; St-Hilaire, A.; Bouezmarni, T.; Ouarda, T.


    Hydrologic frequency analysis is commonly used by engineers and hydrologists to provide the basic information on planning, design and management of hydraulic structures and water resources system under the assumption of stationarity. However, with increasing evidence of changing climate, it is possible that the assumption of stationarity would no longer be valid and the results of conventional analysis would become questionable. In this study, we consider a framework for frequency analysis of extreme flows based on B-Splines quantile regression, which allows to model non-stationary data that have a dependence on covariates. Such covariates may have linear or nonlinear dependence. A Markov Chain Monte Carlo (MCMC) algorithm is used to estimate quantiles and their posterior distributions. A coefficient of determination for quantiles regression is proposed to evaluate the estimation of the proposed model for each quantile level. The method is applied on annual maximum and minimum streamflow records in Ontario, Canada. Climate indices are considered to describe the non-stationarity in these variables and to estimate the quantiles in this case. The results show large differences between the non-stationary quantiles and their stationary equivalents for annual maximum and minimum discharge with high annual non-exceedance probabilities. Keywords: Quantile regression, B-Splines functions, MCMC, Streamflow, Climate indices, non-stationarity.

  2. Fuzzy B-spline optimization for urban slum three-dimensional reconstruction using ENVISAT satellite data (United States)

    Marghany, Maged


    A critical challenges in urban aeras is slums. In fact, they are considered a source of crime and disease due to poor-quality housing, unsanitary conditions, poor infrastructures and occupancy security. The poor in the dense urban slums are the most vulnerable to infection due to (i) inadequate and restricted access to safety, drinking water and sufficient quantities of water for personal hygiene; (ii) the lack of removal and treatment of excreta; and (iii) the lack of removal of solid waste. This study aims to investigate the capability of ENVISAT ASAR satellite and Google Earth data for three-dimensional (3-D) slum urban reconstruction in developed countries such as Egypt. The main objective of this work is to utilize some 3-D automatic detection algorithm for urban slum in ENVISAT ASAR and Google Erath images were acquired in Cairo, Egypt using Fuzzy B-spline algorithm. The results show that the fuzzy algorithm is the best indicator for chaotic urban slum as it can discriminate between them from its surrounding environment. The combination of Fuzzy and B-spline then used to reconstruct 3-D of urban slum. The results show that urban slums, road network, and infrastructures are perfectly discriminated. It can therefore be concluded that the fuzzy algorithm is an appropriate algorithm for chaotic urban slum automatic detection in ENVSIAT ASAR and Google Earth data.

  3. B-spline solver for one-electron Schrödinger equation (United States)

    Romanowski, Zbigniew


    A numerical algorithm for solving the one-electron Schrödinger equation is presented. The algorithm is based on the Finite Element method, and the basis functions are tensor products of univariate B-splines. The application of cubic or higher order B-splines guarantees that the searched solution belongs to a continuous and one time differentiable function space, which is a desirable property in the Kohn-Sham equation context from the Density Functional Theory with pseudopotential approximation. The theoretical background of the numerical algorithm is presented, and additionally, the implementation on parallel computers with distributed memory is described. The current implementation of the algorithm uses the MPI, HYPRE and ParMETIS libraries to distribute matrices on processing units. Additionally, the POBPC algorithm from HYPRE library is used to solve the algebraic generalized eigenvalue problem. The proposed algorithm works for any smooth interaction potential, where the domain of the problem is a finite subspace of the ℝ3 space. The accuracy of the algorithm is demonstrated for a selected interaction potential. In the current stage, the algorithm can be applied to solve the linearized Kohn-Sham equation for molecular systems.

  4. Fuzzy B-spline optimization for urban slum three-dimensional reconstruction using ENVISAT satellite data

    International Nuclear Information System (INIS)

    Marghany, Maged


    A critical challenges in urban aeras is slums. In fact, they are considered a source of crime and disease due to poor-quality housing, unsanitary conditions, poor infrastructures and occupancy security. The poor in the dense urban slums are the most vulnerable to infection due to (i) inadequate and restricted access to safety, drinking water and sufficient quantities of water for personal hygiene; (ii) the lack of removal and treatment of excreta; and (iii) the lack of removal of solid waste. This study aims to investigate the capability of ENVISAT ASAR satellite and Google Earth data for three-dimensional (3-D) slum urban reconstruction in developed countries such as Egypt. The main objective of this work is to utilize some 3-D automatic detection algorithm for urban slum in ENVISAT ASAR and Google Erath images were acquired in Cairo, Egypt using Fuzzy B-spline algorithm. The results show that the fuzzy algorithm is the best indicator for chaotic urban slum as it can discriminate between them from its surrounding environment. The combination of Fuzzy and B-spline then used to reconstruct 3-D of urban slum. The results show that urban slums, road network, and infrastructures are perfectly discriminated. It can therefore be concluded that the fuzzy algorithm is an appropriate algorithm for chaotic urban slum automatic detection in ENVSIAT ASAR and Google Earth data

  5. Hybrid B-Spline Collocation Method for Solving the Generalized Burgers-Fisher and Burgers-Huxley Equations

    Directory of Open Access Journals (Sweden)

    Imtiaz Wasim


    Full Text Available In this study, we introduce a new numerical technique for solving nonlinear generalized Burgers-Fisher and Burgers-Huxley equations using hybrid B-spline collocation method. This technique is based on usual finite difference scheme and Crank-Nicolson method which are used to discretize the time derivative and spatial derivatives, respectively. Furthermore, hybrid B-spline function is utilized as interpolating functions in spatial dimension. The scheme is verified unconditionally stable using the Von Neumann (Fourier method. Several test problems are considered to check the accuracy of the proposed scheme. The numerical results are in good agreement with known exact solutions and the existing schemes in literature.

  6. The Asymptotic Behavior of Particle Size Distribution Undergoing Brownian Coagulation Based on the Spline-Based Method and TEMOM Model

    Directory of Open Access Journals (Sweden)

    Qing He


    Full Text Available In this paper, the particle size distribution is reconstructed using finite moments based on a converted spline-based method, in which the number of linear system of equations to be solved reduced from 4m × 4m to (m + 3 × (m + 3 for (m + 1 nodes by using cubic spline compared to the original method. The results are verified by comparing with the reference firstly. Then coupling with the Taylor-series expansion moment method, the evolution of particle size distribution undergoing Brownian coagulation and its asymptotic behavior are investigated.

  7. Numerical solution of Riccati equation using the cubic B-spline scaling functions and Chebyshev cardinal functions (United States)

    Lakestani, Mehrdad; Dehghan, Mehdi


    Two numerical techniques are presented for solving the solution of Riccati differential equation. These methods use the cubic B-spline scaling functions and Chebyshev cardinal functions. The methods consist of expanding the required approximate solution as the elements of cubic B-spline scaling function or Chebyshev cardinal functions. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the new techniques. The methods are easy to implement and produce very accurate results.

  8. Vulkanisme en water op Mars?

    NARCIS (Netherlands)

    Van Loef, J.; Schmets, A.J.M.


    In januari 2004 werd Mars bezocht door de tweeling robotverkenners Spirit en Opportunity. Zij werden erop uitgestuurd om eindelijk het definitieve antwoord te geven op de vraag of er leven op Mars is geweest. Alles wijst er inmiddels op dat er op Mars ooit vloeibaar water stroomde. Of daarmee een

  9. Methane on Mars: Thermodynamic Equilibrium and Photochemical Calculations (United States)

    Levine, J. S.; Summers, M. E.; Ewell, M.


    The detection of methane (CH4) in the atmosphere of Mars by Mars Express and Earth-based spectroscopy is very surprising, very puzzling, and very intriguing. On Earth, about 90% of atmospheric ozone is produced by living systems. A major question concerning methane on Mars is its origin - biological or geological. Thermodynamic equilibrium calculations indicated that methane cannot be produced by atmospheric chemical/photochemical reactions. Thermodynamic equilibrium calculations for three gases, methane, ammonia (NH3) and nitrous oxide (N2O) in the Earth s atmosphere are summarized in Table 1. The calculations indicate that these three gases should not exist in the Earth s atmosphere. Yet they do, with methane, ammonia and nitrous oxide enhanced 139, 50 and 12 orders of magnitude above their calculated thermodynamic equilibrium concentration due to the impact of life! Thermodynamic equilibrium calculations have been performed for the same three gases in the atmosphere of Mars based on the assumed composition of the Mars atmosphere shown in Table 2. The calculated thermodynamic equilibrium concentrations of the same three gases in the atmosphere of Mars is shown in Table 3. Clearly, based on thermodynamic equilibrium calculations, methane should not be present in the atmosphere of Mars, but it is in concentrations approaching 30 ppbv from three distinct regions on Mars.

  10. Mars at war (United States)


    Whether the climate of early Mars was warm and wet or cold and dry remains unclear, but the debate is overheated. With a growing toolbox and increasing data to tackle the open questions, progress is possible if there is openness to bridging the divide.

  11. Mars Mission Specialist (United States)

    Burton, Bill; Ogden, Kate; Walker, Becky; Bledsoe, Leslie; Hardage, Lauren


    For the last several years, the authors have implemented an integrated Mars Colony project for their third-grade classes. Students explored several considerations related to colonizing and inhabiting a new world, including food sources, types of citizens, transportation, and housing design. Nearly everything about the project was open-ended, full…

  12. Watersporen op Mars

    NARCIS (Netherlands)

    Seijmonsbergen, A.C.; Cammeraat, L.H.; Jansen, B.


    SAMENVATTING De discussie over het voorkomen van water op Mars, in vaste of vloeibare vorm, nu en in het verleden, is nog steeds in volle gang. Dat geldt ook voor het effect van mogelijk aanwezig water op de landschapsontwikkeling van de Rode Planeet. Met het vrijkomen van steeds meer nieuwe

  13. Ancient aliens on mars

    CERN Document Server

    Bara, Mike


    Best-selling author and Secret Space Program researcher Bara brings us this lavishly illustrated volume on alien structures on Mars. Was there once a vast, technologically advanced civilization on Mars, and did it leave evidence of its existence behind for humans to find eons later? Did these advanced extraterrestrial visitors vanish in a solar system wide cataclysm of their own making, only to make their way to Earth and start anew? Was Mars once as lush and green as the Earth, and teeming with life? Did Mars once orbit a missing member of the solar system, a "Super Earth” that vanished in a disaster that devastated life on Earth and Venus and left us only the asteroid belt as evidence of its once grand existence? Did the survivors of this catastrophe leave monuments and temples behind, arranged in a mathematical precision designed to teach us the Secret of a new physics that could lift us back to the stars? Does the planet have an automated defense shield that swallows up robotic probes if they wander int...

  14. Hurry along please, for the Mars Express (United States)


    at sharply defined wavelengths. PFS will also monitor temperature changes on the surface, and investigate the seasonal frost on Mars. To provide minerological information about the surface of Mars is the job of the mapping spectrometer OMEGA, supervised by the Institut d'Astrophysique Spatiale at Orsay near Paris. It will observe the gases and dust in the atmosphere too, but the main aim of OMEGA is to use visible and infrared signatures to distinguish materials on the surface -- silicates, hydrated minerals, oxides and carbonates, organic frosts and ices. Confirming Europe's chance to make a distinctive and original contribution to the study of Mars is a unique German instrument, the High Resolution Stereo Camera. It will provide unprecedented images in stereo and colour, showing details of the surface down to 12-15 metres, across huge areas. Its images will enable scientists to re-evaluate the the history of Mars and its volcanic and water-eroded features, as well as giving clearer impressions of dust storms, frost and other weather-related events. The principal investigator for the stereo camera is at the Institut für Planetenerkundung in Berlin. A valuable addition to the science of Mars Express requires no special onboard equipment. The Radio Science Experiment, masterminded at the University of Cologne, will use the radio communications link between the spacecraft and the Earth to probe the martian atmosphere. Effects of the martian surface on radio signals reflected from it will give fresh clues to the surface composition, and the radio science observations will help to refine the measurements of heights and effects of gravity, made with the stereo camera. Family resemblances between the experiments on Mars Express and those selected for the Rosetta mission to Comet Wirtanen show a coherence in ESA's approach to the science of the Solar System. Rosetta is due to fly a few months before Mars Express. The lander option In addition to the seven excellent

  15. The Small Mars System (United States)

    Fantino, E.; Grassi, M.; Pasolini, P.; Causa, F.; Molfese, C.; Aurigemma, R.; Cimminiello, N.; de la Torre, D.; Dell'Aversana, P.; Esposito, F.; Gramiccia, L.; Paudice, F.; Punzo, F.; Roma, I.; Savino, R.; Zuppardi, G.


    The Small Mars System is a proposed mission to Mars. Funded by the European Space Agency, the project has successfully completed Phase 0. The contractor is ALI S.c.a.r.l., and the study team includes the University of Naples ;Federico II;, the Astronomical Observatory of Capodimonte and the Space Studies Institute of Catalonia. The objectives of the mission are both technological and scientific, and will be achieved by delivering a small Mars lander carrying a dust particle analyser and an aerial drone. The former shall perform in situ measurements of the size distribution and abundance of dust particles suspended in the Martian atmosphere, whereas the latter shall demonstrate low-altitude flight in the rarefied planetary environment. The mission-enabling technology is an innovative umbrella-like heat shield, known as IRENE, developed and patented by ALI. The mission is also a technological demonstration of the shield in the upper atmosphere of Mars. The core characteristics of SMS are the low cost (120 M€) and the small size (320 kg of wet mass at launch, 110 kg at landing), features which stand out with respect to previous Mars landers. To comply with them is extremely challenging at all levels, and sets strict requirements on the choice of the materials, the sizing of payloads and subsystems, their arrangement inside the spacecraft and the launcher's selection. In this contribution, the mission and system concept and design are illustrated and discussed. Special emphasis is given to the innovative features and to the challenges faced in the development of the work.

  16. Mars Surface Environmental Issues (United States)

    Charles, John


    Planetary exploration by astronauts will require extended periods of habitation on a planet's surface, under the influence of environmental factors that are different from those of Earth and the spacecraft that delivered the crew to the planet. Human exploration of Mars, a possible near-term planetary objective, can be considered a challenging scenario. Mission scenarios currently under consideration call for surface habitation periods of from 1 to 18 months on even the earliest expeditions. Methods: Environmental issues associated with Mars exploration have been investigated by NASA and the National Space Biomedical Research Institute (NSBRI) as part of the Bioastronautics Critical Path Roadmap Project (see http :// Results: Arrival on Mars will immediately expose the crew to gravity only 38% of that at Earth's surface in possibly the first prolonged exposure to gravity other than the 1G of Earth's surface and the zero G of weightless space flight, with yet unknown effects on crew physiology. The radiation at Mars' surface is not well documented, although the planet's bulk and even its thin atmosphere may moderate the influx of galactic cosmic radiation and energetic protons from solar flares. Secondary radiation from activated components of the soil must also be considered. Ultrafine and larger respirable and nonrespirable particles in Martian dust introduced into the habitat after surface excursions may induce pulmonary inflammation exacerbated by the additive reactive and oxidizing nature of the dust. Stringent decontamination cannot eliminate mechanical and corrosive effects of the dust on pressure suits and exposed machinery. The biohazard potential of putative indigenous Martian microorganisms may be assessed by comparison with analog environments on Earth. Even in their absence, human microorganisms, if not properly controlled, can be a threat to the crew's health. Conclusions: Mars' surface offers a substantial challenge to the

  17. [MaRS Project (United States)

    Aruljothi, Arunvenkatesh


    The Space Exploration Division of the Safety and Mission Assurances Directorate is responsible for reducing the risk to Human Space Flight Programs by providing system safety, reliability, and risk analysis. The Risk & Reliability Analysis branch plays a part in this by utilizing Probabilistic Risk Assessment (PRA) and Reliability and Maintainability (R&M) tools to identify possible types of failure and effective solutions. A continuous effort of this branch is MaRS, or Mass and Reliability System, a tool that was the focus of this internship. Future long duration space missions will have to find a balance between the mass and reliability of their spare parts. They will be unable take spares of everything and will have to determine what is most likely to require maintenance and spares. Currently there is no database that combines mass and reliability data of low level space-grade components. MaRS aims to be the first database to do this. The data in MaRS will be based on the hardware flown on the International Space Stations (ISS). The components on the ISS have a long history and are well documented, making them the perfect source. Currently, MaRS is a functioning excel workbook database; the backend is complete and only requires optimization. MaRS has been populated with all the assemblies and their components that are used on the ISS; the failures of these components are updated regularly. This project was a continuation on the efforts of previous intern groups. Once complete, R&M engineers working on future space flight missions will be able to quickly access failure and mass data on assemblies and components, allowing them to make important decisions and tradeoffs.

  18. The Mars Pathfinder mission (United States)

    Golombek, Matthew P.


    Mars Pathfinder, one of the first Discovery-class missions (quick, low-cost projects with focused science objectives), will land a single spacecraft with a microrover and several instruments on the surface of Mars in 1997. Pathfinder will be the first mission to use a rover, carrying a chemical analysis instrument, to characterize the rocks and soils in a landing area over hundreds of square meters on Mars, which will provide a calibration point or ``ground truth'' for orbital remote sensing observations. In addition to the rover, which also performs a number of technology experiments, Pathfinder carries three science instruments: a stereoscopic imager with spectral filters on an extendable mast, an alpha proton X ray spectrometer, and an atmospheric structure instrument/metereology package. The instruments, the rover technology experiments, and the telemetry system will allow investigations of the surface morphology and geology at submeter to a hundred meters scale, the petrology and geochemistry of rocks and soils, the magnetic properties of dust, soil mechanics and properties, a variety of atmospheric investigations, and the rotational and orbital dynamics of Mars. Landing downstream from the mouth of a giant catastrophic outflow channel, Ares Vallis at 19.5°N, 32.8°W, offers the potential of identifying and analyzing a wide variety of crustal materials, from the ancient heavily cratered terrain, intermediate-aged ridged plains, and reworked channel deposits, thus allowing first-order scientific investigations of the early differentiation and evolution of the crust, the development of weathering products, and the early environments and conditions on Mars.

  19. Geometric modelling of channel present in reservoir petroleum using Bezier splines; Modelagem da geometria de paleocanais presentes em reservatorios petroliferos usando splines de Bezier

    Energy Technology Data Exchange (ETDEWEB)

    Araujo, Carlos Eduardo S. [Universidade Federal de Campina Grande, PB (Brazil). Programa de Recursos Humanos 25 da ANP]. E-mail:; Silva, Rosana M. da [Universidade Federal de Campina Grande, PB (Brazil). Dept. de Matematica e Estatistica]. E-mail:


    This work presents an implementation of a synthetic model of a channel found in oil reservoir. The generation these models is one of the steps to the characterization and simulation of the equal probable three-dimensional geological scenery. O implemented model was obtained from fitting techniques of geometric modeling of curves and surfaces to the geological parameters (width, thickness, sinuosity and preferential direction) that defines the form to be modeled. The parameter sinuosity is related with the parameter wave length and the local amplitude of the channel, the parameter preferential direction indicates the way of the flow and the declivity of the channel. The modeling technique used to represent the surface of the channel is the sweeping technique, the consist in effectuate a translation operation from a curve along a guide curve. The guide curve, in our implementation, was generated by the interpolation of points obtained form sampled values or simulated of the parameter sinuosity, using the cubic splines of Bezier technique. A semi-ellipse, determinate by the parameter width and thickness, representing a transversal section of the channel, is the transferred curve through the guide curve, generating the channel surface. (author)

  20. NeuroMap: A spline-based interactive open-source software for spatiotemporal mapping of 2D and 3D MEA data

    Directory of Open Access Journals (Sweden)

    Oussama eAbdoun


    Full Text Available A major characteristic of neural networks is the complexity of their organization at various spatial scales, from microscopic local circuits to macroscopic brain-scale areas. Understanding how neural information is processed thus entails the ability to study them at multiple scales simultaneously. This is made possible using microelectrodes array (MEA technology. Indeed, high-density MEAs provide large-scale covering (several mm² of whole neural structures combined with microscopic resolution (about 50µm of unit activity. Yet, current options for spatiotemporal representation of MEA-collected data remain limited. Here we present NeuroMap, a new interactive Matlab-based software for spatiotemporal mapping of MEA data. NeuroMap uses thin plate spline interpolation, which provides several assets with respect to conventional mapping methods used currently. First, any MEA design can be considered, including 2D or 3D, regular or irregular, arrangements of electrodes. Second, spline interpolation allows the estimation of activity across the tissue with local extrema not necessarily at recording sites. Finally, this interpolation approach provides a straightforward analytical estimation of the spatial Laplacian for better current sources localization. In this software, coregistration of 2D MEA data on the anatomy of the neural tissue is made possible by fine matching of anatomical data with electrode positions using rigid deformation based correction of anatomical pictures. Overall, NeuroMap provides substantial material for detailed spatiotemporal analysis of MEA data. The package is distributed under GNU General Public License (GPL and available at

  1. Trajectory Design for the Phobos and Deimos & Mars Environment Spacecraft (United States)

    Genova, Anthony L.; Korsmeyer, David J.; Loucks, Michel E.; Yang, Fan Yang; Lee, Pascal


    The presented trajectory design and analysis was performed for the Phobos and Deimos & Mars Environment (PADME) mission concept as part of a NASA proposal submission managed by NASA Ames Research Center in the 2014-2015 timeframe. The PADME spacecraft would be a derivative of the successfully flown Lunar Atmosphere & Dust Environment Explorer (LADEE) spacecraft. While LADEE was designed to enter low-lunar orbit, the PADME spacecraft would instead enter an elliptical Mars orbit of 2-week period. This Mars orbit would pass by Phobos near periapsis on successive orbits and then raise periapsis to yield close approaches of Deimos every orbit thereafter.

  2. Mars Ascent Vehicle-Propellant Aging (United States)

    Dankanich, John; Rousseau, Jeremy; Williams, Jacob


    This project is to develop and test a new propellant formulation specifically for the Mars Ascent Vehicle (MAV) for the robotic Mars Sample Return mission. The project was initiated under the Planetary Sciences Division In-Space Propulsion Technology (ISPT) program and is continuing under the Mars Exploration Program. The two-stage, solid motor-based MAV has been the leading MAV solution for more than a decade. Additional studies show promise for alternative technologies including hybrid and bipropellant options, but the solid motor design has significant propellant density advantages well suited for physical constraints imposed while using the SkyCrane descent stage. The solid motor concept has lower specific impulse (Isp) than alternatives, but if the first stage and payload remain sufficiently small, the two-stage solid MAV represents a potential low risk approach to meet the mission needs. As the need date for the MAV slips, opportunities exist to advance technology with high on-ramp potential. The baseline propellant for the MAV is currently the carboxyl terminated polybutadiene (CTPB) based formulation TP-H-3062 due to its advantageous low temperature mechanical properties and flight heritage. However, the flight heritage is limited and outside the environments, the MAV must endure. The ISPT program competed a propellant formulation project with industry and selected ATK to develop a new propellant formulation specifically for the MAV application. Working with ATK, a large number of propellant formulations were assessed to either increase performance of a CTPB propellant or improve the low temperature mechanical properties of a hydroxyl terminated polybutadiene (HTPB) propellant. Both propellants demonstrated potential to increase performance over heritage options, but an HTPB propellant formulation, TP-H-3544, was selected for production and testing. The test plan includes propellant aging first at high vacuum conditions, representative of the Mars transit

  3. The Norwegian Healthier Goats program--modeling lactation curves using a multilevel cubic spline regression model. (United States)

    Nagel-Alne, G E; Krontveit, R; Bohlin, J; Valle, P S; Skjerve, E; Sølverød, L S


    In 2001, the Norwegian Goat Health Service initiated the Healthier Goats program (HG), with the aim of eradicating caprine arthritis encephalitis, caseous lymphadenitis, and Johne's disease (caprine paratuberculosis) in Norwegian goat herds. The aim of the present study was to explore how control and eradication of the above-mentioned diseases by enrolling in HG affected milk yield by comparison with herds not enrolled in HG. Lactation curves were modeled using a multilevel cubic spline regression model where farm, goat, and lactation were included as random effect parameters. The data material contained 135,446 registrations of daily milk yield from 28,829 lactations in 43 herds. The multilevel cubic spline regression model was applied to 4 categories of data: enrolled early, control early, enrolled late, and control late. For enrolled herds, the early and late notations refer to the situation before and after enrolling in HG; for nonenrolled herds (controls), they refer to development over time, independent of HG. Total milk yield increased in the enrolled herds after eradication: the total milk yields in the fourth lactation were 634.2 and 873.3 kg in enrolled early and enrolled late herds, respectively, and 613.2 and 701.4 kg in the control early and control late herds, respectively. Day of peak yield differed between enrolled and control herds. The day of peak yield came on d 6 of lactation for the control early category for parities 2, 3, and 4, indicating an inability of the goats to further increase their milk yield from the initial level. For enrolled herds, on the other hand, peak yield came between d 49 and 56, indicating a gradual increase in milk yield after kidding. Our results indicate that enrollment in the HG disease eradication program improved the milk yield of dairy goats considerably, and that the multilevel cubic spline regression was a suitable model for exploring effects of disease control and eradication on milk yield. Copyright © 2014

  4. Improvement of the Cubic Spline Function Sets for a Synthesis of the Axial Power Distribution of a Core Protection System

    International Nuclear Information System (INIS)

    Koo, Bon-Seung; Lee, Chung-Chan; Zee, Sung-Quun


    Online digital core protection system(SCOPS) for a system-integrated modular reactor is being developed as a part of a plant protection system at KAERI. SCOPS calculates the minimum CHFR and maximum LPD based on several online measured system parameters including 3-level ex-core detector signals. In conventional ABB-CE digital power plants, cubic spline synthesis technique has been used in online calculations of the core axial power distributions using ex-core detector signals once every 1 second in CPC. In CPC, pre-determined cubic spline function sets are used depending on the characteristics of the ex-core detector responses. But this method shows an unnegligible power distribution error for the extremely skewed axial shapes by using restrictive function sets. Therefore, this paper describes the cubic spline method for the synthesis of an axial power distribution and it generates several new cubic spline function sets for the application of the core protection system, especially for the severely distorted power shapes needed reactor type

  5. A Dual Source Ion Trap Mass Spectrometer for the Mars Organic Molecule Analyzer of ExoMars 2018 (United States)

    Brickerhoff, William B.; vanAmerom, F. H. W.; Danell, R. M.; Arevalo, R.; Atanassova, M.; Hovmand, L.; Mahaffy, P. R.; Cotter, R. J.


    We present details on the objectives, requirements, design and operational approach of the core mass spectrometer of the Mars Organic Molecule Analyzer (MOMA) investigation on the 2018 ExoMars mission. The MOMA mass spectrometer enables the investigation to fulfill its objective of analyzing the chemical composition of organic compounds in solid samples obtained from the near surface of Mars. Two methods of ionization are realized, associated with different modes of MOMA operation, in a single compact ion trap mass spectrometer. The stringent mass and power constraints of the mission have led to features such as low voltage and low frequency RF operation [1] and pulse counting detection.

  6. Mars by Way of Storytellers and Patrons (United States)

    Polk, C.

    A business model is presented in which space-themed entertainment and educational media are harnessed to the goal of designing and financing the establishment of a self-sustaining Mars outpost. The model draws from two precedents: (i) The National Geographic Society's use of media sales to fund research and (ii) the historical role of patrons in the process of creativity. These precedents are combined in an international non-governmental organization (INGO) that is governed by the individuals who participate in the media businesses branded by the INGO - these individuals constitute a patron base of several tens of millions. Requiring only modest penetration into global media markets, expenditures of USD 5 billion per year (in 2008 dollars) can commence in 2025 and continue at an accelerating rate until the Mars outpost is established. The financing approach utilized, combined with a decision authority that is free to consider a broad range of solutions, will advance the technical state-of-the-art and result in an Earth-Mars infrastructure capable of expanding the initial Mars outpost into humanity's first second home.

  7. 2016 Mars Insight Mission Design and Navigation (United States)

    Abilleira, Fernando; Frauenholz, Ray; Fujii, Ken; Wallace, Mark; You, Tung-Han


    Scheduled for a launch in the 2016 Earth to Mars opportunity, the Interior Exploration using Seismic Investigations, Geodesy, and Heat Transport (InSight) Mission will arrive to Mars in late September 2016 with the primary objective of placing a science lander on the surface of the Red Planet followed by the deployment of two science instruments to investigate the fundamental processes of terrestrial planet formation and evolution. In order to achieve a successful landing, the InSight Project has selected a launch/arrival strategy that satisfies the following key and driving requirements: (1) Deliver a total launch mass of 727 kg, (2) target a nominal landing site with a cumulative Delta V99 less than 30 m/s, and (3) approach EDL with a V-infinity upper limit of 3.941 km/s and (4) an entry flight-path angle (EFPA) of -12.5 +/- 0.26 deg, 3-sigma; the InSight trajectories have been designed such that they (5) provide UHF-band communications via Direct-To-Earth and MRO from Entry through landing plus 60 s, (6) with injection aimpoints biased away from Mars such that the probability of the launch vehicle upper stage impacting Mars is less than 1.0 X 10(exp 4) for fifty years after launch, and (7) non-nominal impact probabilities due to failure during the Cruise phase less than 1.0 X 10(exp 2).

  8. A Note on Penalized Regression Spline Estimation in the Secondary Analysis of Case-Control Data

    KAUST Repository

    Gazioglu, Suzan


    Primary analysis of case-control studies focuses on the relationship between disease (D) and a set of covariates of interest (Y, X). A secondary application of the case-control study, often invoked in modern genetic epidemiologic association studies, is to investigate the interrelationship between the covariates themselves. The task is complicated due to the case-control sampling, and to avoid the biased sampling that arises from the design, it is typical to use the control data only. In this paper, we develop penalized regression spline methodology that uses all the data, and improves precision of estimation compared to using only the controls. A simulation study and an empirical example are used to illustrate the methodology.

  9. Full-turn symplectic map from a generator in a Fourier-spline basis

    International Nuclear Information System (INIS)

    Berg, J.S.; Warnock, R.L.; Ruth, R.D.; Forest, E.


    Given an arbitrary symplectic tracking code, one can construct a full-turn symplectic map that approximates the result of the code to high accuracy. The map is defined implicitly by a mixed-variable generating function. The implicit definition is no great drawback in practice, thanks to an efficient use of Newton's method to solve for the explicit map at each iteration. The generator is represented by a Fourier series in angle variables, with coefficients given as B-spline functions of action variables. It is constructed by using results of single-turn tracking from many initial conditions. The method has been appliedto a realistic model of the SSC in three degrees of freedom. Orbits can be mapped symplectically for 10 7 turns on an IBM RS6000 model 320 workstation, in a run of about one day

  10. A Mathematical Spline-Based Model of Cardiac Left Ventricle Anatomy and Morphology

    Directory of Open Access Journals (Sweden)

    Sergei Pravdin


    Full Text Available Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibers. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualization, such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously-made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilize finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.

  11. A Spline-Based Lack-Of-Fit Test for Independent Variable Effect in Poisson Regression. (United States)

    Li, Chin-Shang; Tu, Wanzhu


    In regression analysis of count data, independent variables are often modeled by their linear effects under the assumption of log-linearity. In reality, the validity of such an assumption is rarely tested, and its use is at times unjustifiable. A lack-of-fit test is proposed for the adequacy of a postulated functional form of an independent variable within the framework of semiparametric Poisson regression models based on penalized splines. It offers added flexibility in accommodating the potentially non-loglinear effect of the independent variable. A likelihood ratio test is constructed for the adequacy of the postulated parametric form, for example log-linearity, of the independent variable effect. Simulations indicate that the proposed model performs well, and misspecified parametric model has much reduced power. An example is given.

  12. COLLINARUS: collection of image-derived non-linear attributes for registration using splines (United States)

    Chappelow, Jonathan; Bloch, B. Nicolas; Rofsky, Neil; Genega, Elizabeth; Lenkinski, Robert; DeWolf, William; Viswanath, Satish; Madabhushi, Anant


    We present a new method for fully automatic non-rigid registration of multimodal imagery, including structural and functional data, that utilizes multiple texutral feature images to drive an automated spline based non-linear image registration procedure. Multimodal image registration is significantly more complicated than registration of images from the same modality or protocol on account of difficulty in quantifying similarity between different structural and functional information, and also due to possible physical deformations resulting from the data acquisition process. The COFEMI technique for feature ensemble selection and combination has been previously demonstrated to improve rigid registration performance over intensity-based MI for images of dissimilar modalities with visible intensity artifacts. Hence, we present here the natural extension of feature ensembles for driving automated non-rigid image registration in our new technique termed Collection of Image-derived Non-linear Attributes for Registration Using Splines (COLLINARUS). Qualitative and quantitative evaluation of the COLLINARUS scheme is performed on several sets of real multimodal prostate images and synthetic multiprotocol brain images. Multimodal (histology and MRI) prostate image registration is performed for 6 clinical data sets comprising a total of 21 groups of in vivo structural (T2-w) MRI, functional dynamic contrast enhanced (DCE) MRI, and ex vivo WMH images with cancer present. Our method determines a non-linear transformation to align WMH with the high resolution in vivo T2-w MRI, followed by mapping of the histopathologic cancer extent onto the T2-w MRI. The cancer extent is then mapped from T2-w MRI onto DCE-MRI using the combined non-rigid and affine transformations determined by the registration. Evaluation of prostate registration is performed by comparison with the 3 time point (3TP) representation of functional DCE data, which provides an independent estimate of cancer

  13. Determination of transients and compensation capacities of breath-by-breath analysis by cubic splines. (United States)

    von Golitschek, M; Schardt, F W


    The development of breath-by-breath analysis during an ergospirometry improved the precision of the measurement. However, the abundance of data yields oscillating curves which make it very difficult to detect exactly the breakpoints, maxima and minima. By using cubic splines one is able to smooth the curve of the primary data without falsifying or distorting it. A breakpoint marks the beginning of a hyperventilation with an nonlinear increase of VE or the beginning of an excess value of CO2. Furthermore, the amount of CO2 required to compensate for the acid-base balance as well as the oxygen debt in the recovery phase can be calculated by the area under the curve.

  14. Local Convexity-Preserving C 2 Rational Cubic Spline for Convex Data (United States)

    Abd Majid, Ahmad; Ali, Jamaludin Md.


    We present the smooth and visually pleasant display of 2D data when it is convex, which is contribution towards the improvements over existing methods. This improvement can be used to get the more accurate results. An attempt has been made in order to develop the local convexity-preserving interpolant for convex data using C 2 rational cubic spline. It involves three families of shape parameters in its representation. Data dependent sufficient constraints are imposed on single shape parameter to conserve the inherited shape feature of data. Remaining two of these shape parameters are used for the modification of convex curve to get a visually pleasing curve according to industrial demand. The scheme is tested through several numerical examples, showing that the scheme is local, computationally economical, and visually pleasing. PMID:24757421

  15. A numerical solution of the linear Boltzmann equation using cubic B-splines. (United States)

    Khurana, Saheba; Thachuk, Mark


    A numerical method using cubic B-splines is presented for solving the linear Boltzmann equation. The collision kernel for the system is chosen as the Wigner-Wilkins kernel. A total of three different representations for the distribution function are presented. Eigenvalues and eigenfunctions of the collision matrix are obtained for various mass ratios and compared with known values. Distribution functions, along with first and second moments, are evaluated for different mass and temperature ratios. Overall it is shown that the method is accurate and well behaved. In particular, moments can be predicted with very few points if the representation is chosen well. This method produces sparse matrices, can be easily generalized to higher dimensions, and can be cast into efficient parallel algorithms. © 2012 American Institute of Physics

  16. A Novel Structure and Design Optimization of Compact Spline-Parameterized UWB Slot Antenna

    Directory of Open Access Journals (Sweden)

    Koziel Slawomir


    Full Text Available In this paper, a novel structure of a compact UWB slot antenna and its design optimization procedure has been presented. In order to achieve a sufficient number of degrees of freedom necessary to obtain a considerable size reduction rate, the slot is parameterized using spline curves. All antenna dimensions are simultaneously adjusted using numerical optimization procedures. The fundamental bottleneck here is a high cost of the electromagnetic (EM simulation model of the structure that includes (for reliability an SMA connector. Another problem is a large number of geometry parameters (nineteen. For the sake of computational efficiency, the optimization process is therefore performed using variable-fidelity EM simulations and surrogate-assisted algorithms. The optimization process is oriented towards explicit reduction of the antenna size and leads to a compact footprint of 199 mm2 as well as acceptable matching within the entire UWB band. The simulation results are validated using physical measurements of the fabricated antenna prototype.

  17. B-spline based finite element method in one-dimensional discontinuous elastic wave propagation

    Czech Academy of Sciences Publication Activity Database

    Kolman, Radek; Okrouhlík, Miloslav; Berezovski, A.; Gabriel, Dušan; Kopačka, Ján; Plešek, Jiří


    Roč. 46, June (2017), s. 382-395 ISSN 0307-904X R&D Projects: GA ČR(CZ) GAP101/12/2315; GA MŠk(CZ) EF15_003/0000493 Grant - others:AV ČR(CZ) DAAD-16-12; AV ČR(CZ) ETA-15-03 Program:Bilaterální spolupráce; Bilaterální spolupráce Institutional support: RVO:61388998 Keywords : discontinuous elastic wave propagation * B-spline finite element method * isogeometric analysis * implicit and explicit time integration * dispersion * spurious oscillations Subject RIV: BI - Acoustics OBOR OECD: Acoustics Impact factor: 2.350, year: 2016

  18. Mars, earth, and ice

    International Nuclear Information System (INIS)

    Cordell, B.M.


    Possible mechanisms to explain the global ice covering of Mars, and previous ice ages on the earth, are considered. Evidence for the Milankovitch effect is found in the close correspondence of earth's past climate with its orbital variations, as recorded principally in ocean sediments, and the role of CO 2 is discussed. Mars' range of obliquity, 10 times that of the earth, and orbital eccentricity, fluctuating over a range 2 1/2 times that of the earth, could produce an important climate-driving cycle. Mathematical models of the Martian surface and atmosphere based on Viking data suggest that escaped CO 2 could create a surface pressure of 1-3 bars. Other factors such as the effect of continental drift, the increased brightness of the sun, and planetary reversals of magnetic field polarity are discussed, and the questions of where Martian water and CO 2 have gone are considered

  19. EquiMar

    DEFF Research Database (Denmark)

    Johnstone, C. M.; McCombes, T.; Bahaj, A. S.


    At the present time there are no approved standards or recognised best practices being implemented for the performance appraisal and benchmarking of wave and tidal energy converters. As such, this develops considerable misunderstanding between device developers, testing centres, investors....../ financiers etc when attempting to quantify the performance of a device since it makes it very difficult to reference and benchmark the performance of a marine energy converter. The EC Framework Programme VII EquiMar project has set out to develop a suite of Best Practices to be adopted when undertaking...... the performance evaluation of such systems in order to address this deficiency. This paper reports the development of a set of ‘Best Practices’ within the ECFPVII EquiMar project to be adopted for the performance quantification of wave and tidal energy converters as they evolve from an engineering concept...

  20. Fossil life on Mars (United States)

    Walter, M. R.


    Three major problems beset paleontologists searching for morphological evidence of life on early Earth: selecting a prospective site; finding biogenic structures; and distinguishing biogenic from abiogenic structures. The same problems arise on Mars. Terrestrial experience suggests that, with the techniques that can be employed remotely, ancient springs, including hot springs, are more prospective than lake deposits. If, on the other hand, the search is for chemical evidence, the strategy can be very different, and lake deposits are attractive targets. Lakes and springs frequenly occur in close proximity, and therefore a strategy that combines the two would seem to maximize the chance of success. The strategy for a search for stromatolite on Mars is discussed.

  1. Polygonal terrains on Mars

    Directory of Open Access Journals (Sweden)

    Pedro Pina


    Full Text Available The presence of water ice on Mars is well established. Some featureson the planet point to the occurrence of processes similar to those that take place in periglacial areas of Earth. One of the clues for this is the existence of small-scale polygonal terrains. In this paper, we present a methodology that aims at the automated identification of polygonal patterns on high-spatial resolution images of the surface of Mars. In the context of the research project TERPOLI, this step will be complemented with a full characterization, in both geometric and topological terms, of thenetworks detected. In this manner, we hope to collect data that will lead to a better understanding of the conditions of formation of the polygons, and of their temporal evolution; namely, we intend to identify different groups of polygons and to compare them with terrestrial examples.

  2. The politics of Mars (United States)

    Schmitt, Harrison H.


    A discussion is presented comparing past and present major accomplishments of the U.S. and the Soviet Union in space. It concludes that the Soviets are presently well ahead of the U.S. in several specific aspects of space accomplishment and speculates that the Soviet strategy is directed towards sending a man to the vicinity of Mars by the end of this century. A major successful multinational space endeavor, INTELSAT, is reviewed and it is suggested that the manned exploration of Mars offers a unique opportunity for another such major international cooperative effort. The current attitude of U.S. leadership and the general public is assessed as uniformed or ambivalent about the perceived threat of Soviet dominance in space.

  3. Seismology on Mars (United States)

    Anderson, D. L.; Miller, W. F.; Latham, G. V.; Nakamura, Y.; Toksoz, M. N.; Dainty, A. M.; Duennebier, F. K.; Lazarewicz, A. R.; Kovach, R. L.; Knight, T. C. D.


    High-quality data (uncontaminated by lander or wind noise) obtained with a three-axis short-period seismometer operating on Mars in the Utopia Planitia region are analyzed. No large events have been detected during the first five months of operation covered in the present paper. This indicates that Mars is less seismically active than the earth. Winds, and therefore a seismic background, began to intrude into the nighttime hours, starting with sol 119 (sol is a Martian day). The seismic background correlates well with wind velocity, and is proportional to the square of the wind velocity, as is appropriate for turbulent flow. A local seismic event of a magnitude of 3 and a distance of 110 km was detected on sol 80. It is interpreted as a natural seismic event.

  4. Geophysics of Mars (United States)

    Wells, R. A.


    A physical model of Mars is presented on the basis of light-scattering observations of the Martian atmosphere and surface and interior data obtained from observations of the geopotential field. A general description of the atmosphere is presented, with attention given to the circulation and the various cloud types, and data and questions on the blue haze-clearing effect and the seasonal darkening wave are summarized and the Mie scattering model developed to explain these observations is presented. The appearance of the planet from earth and spacecraft through Mariner 9 is considered, and attention is given to the preparation of topographical contour maps, the canal problem and large-scale lineaments observed from Mariner 9, the gravity field and shape of the planet and the application of Runcorn's geoid/convection theory to Mars. Finally, a summary of Viking results is presented and their application to the understanding of Martian geophysics is discussed.

  5. Artificial structures on Mars (United States)

    Van Flandern, T.


    Approximately 70,000 images of the surface of Mars at a resolution of up to 1.4 meters per pixel, taken by the Mars Global Surveyor spacecraft, are now in public archives. Approximately 1% of those images show features that can be broadly described as `special shapes', `tracks, trails, and possible vegetation', `spots, stripes, and tubes', `artistic imagery', and `patterns and symbols'. Rather than optical illusions and tricks of light and shadow, most of these have the character that, if photographed on Earth, no one would doubt that they were the products of large biology and intelligence. In a few cases, relationships, context, and fulfillment of a priori predictions provide objective evidence of artificiality that is exempt from the influence of experimenter biases. Only controlled test results can be trusted because biases are strong and operate both for and against artificiality.

  6. Mining the Mars Atmosphere (United States)

    Finn, John E.; Sridhar, K. R.


    A series of concepts have been developed to mine the atmosphere of Mars and process it to extract or generate compressed carbon dioxide, compressed buffer gas mixtures of nitrogen and argon, water, oxygen, carbon monoxide, and/or carbon. Such products can be of use to science instruments, robotic, and human missions. The products can be for utility purposes, life support, propulsion (both interplanetary and on the planet's surface), and power generation.

  7. Magnetotelluric (MT) data smoothing based on B-Spline algorithm and qualitative spectral analysis (United States)

    Handyarso, Accep; Grandis, Hendra


    Data processing is one of the essential steps to obtain optimum response function of the Earth's subsurface. The MT Data processing is based on the Fast Fourier Transform (FFT) algorithm which converts the time series data into its frequency domain counterpart. The FFT combined with statistical algorithm constitute the Robust Processing algorithm which is widely implemented in MT data processing software. The Robust Processing has three variants, i.e. No Weight (NW), Rho Variance (RV), and Ordinary Coherency (OC). The RV and OC options allow for denoising the data but in many cases the Robust Processing still results in not so smooth sounding curve due to strong noise presence during measurement, such that the Crosspower (XPR) analysis must be conducted in the data processing. The XPR analysis is very time consuming step within the data processing. The collaboration of B-Spline algorithm and Qualitative Spectral Analysis in the frequency domain could be of advantages as an alternative for these steps. The technique is started by using the best coherency from the Robust Processing results. In the Qualitative Spectral Analysis one can determine which part of the data based on frequency that is more or less reliable, then the next process invokes B-Spline algorithm for data smoothing. This algorithm would select the best fit of the data trend in the frequency domain. The smooth apparent resistivity and phase sounding curves can be considered as more appropriate to represent the subsurface. This algorithm has been applied to the real MT data from several survey and give satisfactory results.

  8. A Quadratic Spline based Interface (QUASI) reconstruction algorithm for accurate tracking of two-phase flows (United States)

    Diwakar, S. V.; Das, Sarit K.; Sundararajan, T.


    A new Quadratic Spline based Interface (QUASI) reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature. The fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous PLIC approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves. The conversion is achieved by a sequence of predictor-corrector operations enforcing function ( C0) and derivative ( C1) continuity at the cell boundaries using simple analytical expressions for the continuity requirements. The efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations. These benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature. Quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes; only in situations where the interface geometry is primarily flat, the rate of convergence becomes linear with the mesh size. The flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location. As a consequence, it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface. This has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium. Finally, the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water.

  9. Creating high-resolution digital elevation model using thin plate spline interpolation and Monte Carlo simulation

    International Nuclear Information System (INIS)

    Pohjola, J.; Turunen, J.; Lipping, T.


    In this report creation of the digital elevation model of Olkiluoto area incorporating a large area of seabed is described. The modeled area covers 960 square kilometers and the apparent resolution of the created elevation model was specified to be 2.5 x 2.5 meters. Various elevation data like contour lines and irregular elevation measurements were used as source data in the process. The precision and reliability of the available source data varied largely. Digital elevation model (DEM) comprises a representation of the elevation of the surface of the earth in particular area in digital format. DEM is an essential component of geographic information systems designed for the analysis and visualization of the location-related data. DEM is most often represented either in raster or Triangulated Irregular Network (TIN) format. After testing several methods the thin plate spline interpolation was found to be best suited for the creation of the elevation model. The thin plate spline method gave the smallest error in the test where certain amount of points was removed from the data and the resulting model looked most natural. In addition to the elevation data the confidence interval at each point of the new model was required. The Monte Carlo simulation method was selected for this purpose. The source data points were assigned probability distributions according to what was known about their measurement procedure and from these distributions 1 000 (20 000 in the first version) values were drawn for each data point. Each point of the newly created DEM had thus as many realizations. The resulting high resolution DEM will be used in modeling the effects of land uplift and evolution of the landscape in the time range of 10 000 years from the present. This time range comes from the requirements set for the spent nuclear fuel repository site. (orig.)

  10. Mars Observer camera (United States)

    Malin, M. C.; Danielson, G. E.; Ingersoll, A. P.; Masursky, H.; Veverka, J.; Ravine, M. A.; Soulanille, T. A.


    The Mars Observer camera (MOC) is a three-component system (one narrow-angle and two wide-angle cameras) designed to take high spatial resolution pictures of the surface of Mars and to obtain lower spatial resolution, synoptic coverage of the planet's surface and atmosphere. The cameras are based on the 'push broom' technique; that is, they do not take 'frames' but rather build pictures, one line at a time, as the spacecraft moves around the planet in its orbit. MOC is primarily a telescope for taking extremely high resolution pictures of selected locations on Mars. Using the narrow-angle camera, areas ranging from 2.8 km x 2.8 km to 2.8 km x 25.2 km (depending on available internal digital buffer memory) can be photographed at about 1.4 m/pixel. Additionally, lower-resolution pictures (to a lowest resolution of about 11 m/pixel) can be acquired by pixel averaging; these images can be much longer, ranging up to 2.8 x 500 km at 11 m/pixel. High-resolution data will be used to study sediments and sedimentary processes, polar processes and deposits, volcanism, and other geologic/geomorphic processes.

  11. Chemical composition of Mars

    International Nuclear Information System (INIS)

    Morgan, J.W.; Anders, E.


    The composition of Mars has been calculated from a cosmochemical model which assumes that planets and chondrites underwent the same 4 fractionation processes in the solar nebula. Because elements of similar volatility stay together in these processes, only 4 index elements are needed to calculate the abundances of all 83 elements in the planet. The values chosen are U = 28 ppb, K = 62 ppm, Fe = 26.72% and Tl = 0.14 ppb. The mantle of Mars is an iron-rich garnet wehrlite. It is nearly identical to the previously reported bulk Moon composition. The core makes up 0.19 of the planet and contains 3.5% S - much less than estimated by other models. Volatiles have nearly Moon-like abundances, being depleted relative to the Earth. The water abundance corresponds to a 9 m layer, but could be higher by as much as a factor of 11. Comparison of model compositions for 5 differentiated planets (Earth, Venus, Mars, Moon, and eucrite parent body) suggests that volatile depletion correlates mainly with size rather than with radial distance from the Sun. However, the relatively high volatile content of shergottites and some chondrites shows that the correlation is not simple; other factors must also be involved. (author)

  12. Sustainable Mars Sample Return (United States)

    Alston, Christie; Hancock, Sean; Laub, Joshua; Perry, Christopher; Ash, Robert


    The proposed Mars sample return mission will be completed using natural Martian resources for the majority of its operations. The system uses the following technologies: In-Situ Propellant Production (ISPP), a methane-oxygen propelled Mars Ascent Vehicle (MAV), a carbon dioxide powered hopper, and a hydrogen fueled balloon system (large balloons and small weather balloons). The ISPP system will produce the hydrogen, methane, and oxygen using a Sabatier reactor. a water electrolysis cell, water extracted from the Martian surface, and carbon dioxide extracted from the Martian atmosphere. Indigenous hydrogen will fuel the balloon systems and locally-derived methane and oxygen will fuel the MAV for the return of a 50 kg sample to Earth. The ISPP system will have a production cycle of 800 days and the estimated overall mission length is 1355 days from Earth departure to return to low Earth orbit. Combining these advanced technologies will enable the proposed sample return mission to be executed with reduced initial launch mass and thus be more cost efficient. The successful completion of this mission will serve as the next step in the advancement of Mars exploration technology.

  13. Mars Aqueous Processing System (United States)

    Berggren, Mark; Wilson, Cherie; Carrera, Stacy; Rose, Heather; Muscatello, Anthony; Kilgore, James; Zubrin, Robert


    The goal of the Mars Aqueous Processing System (MAPS) is to establish a flexible process that generates multiple products that are useful for human habitation. Selectively extracting useful components into an aqueous solution, and then sequentially recovering individual constituents, can obtain a suite of refined or semi-refined products. Similarities in the bulk composition (although not necessarily of the mineralogy) of Martian and Lunar soils potentially make MAPS widely applicable. Similar process steps can be conducted on both Mars and Lunar soils while tailoring the reaction extents and recoveries to the specifics of each location. The MAPS closed-loop process selectively extracts, and then recovers, constituents from soils using acids and bases. The emphasis on Mars involves the production of useful materials such as iron, silica, alumina, magnesia, and concrete with recovery of oxygen as a byproduct. On the Moon, similar chemistry is applied with emphasis on oxygen production. This innovation has been demonstrated to produce high-grade materials, such as metallic iron, aluminum oxide, magnesium oxide, and calcium oxide, from lunar and Martian soil simulants. Most of the target products exhibited purities of 80 to 90 percent or more, allowing direct use for many potential applications. Up to one-fourth of the feed soil mass was converted to metal, metal oxide, and oxygen products. The soil residue contained elevated silica content, allowing for potential additional refining and extraction for recovery of materials needed for photovoltaic, semiconductor, and glass applications. A high-grade iron oxide concentrate derived from lunar soil simulant was used to produce a metallic iron component using a novel, combined hydrogen reduction/metal sintering technique. The part was subsequently machined and found to be structurally sound. The behavior of the lunar-simulant-derived iron product was very similar to that produced using the same methods on a Michigan iron

  14. International cooperation for Mars exploration and sample return (United States)

    Levy, Eugene H.; Boynton, William V.; Cameron, A. G. W.; Carr, Michael H.; Kitchell, Jennifer H.; Mazur, Peter; Pace, Norman R.; Prinn, Ronald G.; Solomon, Sean C.; Wasserburg, Gerald J.


    The National Research Council's Space Studies Board has previously recommended that the next major phase of Mars exploration for the United States involve detailed in situ investigations of the surface of Mars and the return to earth for laboratory analysis of selected Martian surface samples. More recently, the European space science community has expressed general interest in the concept of cooperative Mars exploration and sample return. The USSR has now announced plans for a program of Mars exploration incorporating international cooperation. If the opportunity becomes available to participate in Mars exploration, interest is likely to emerge on the part of a number of other countries, such as Japan and Canada. The Space Studies Board's Committee on Cooperative Mars Exploration and Sample Return was asked by the National Aeronautics and Space Administration (NASA) to examine and report on the question of how Mars sample return missions might best be structured for effective implementation by NASA along with international partners. The committee examined alternatives ranging from scientific missions in which the United States would take a substantial lead, with international participation playing only an ancillary role, to missions in which international cooperation would be a basic part of the approach, with the international partners taking on comparably large mission responsibilities. On the basis of scientific strategies developed earlier by the Space Studies Board, the committee considered the scientific and technical basis of such collaboration and the most mutually beneficial arrangements for constructing successful cooperative missions, particularly with the USSR.

  15. First MARS Outpost: Development Considerations and Concepts (United States)

    Bell, L.


    The Sasakawa International Center for Space Architecture (SICSA) is undertaking a multi-year research and design study that is exploring near and long-term commercial space development opportunities. The central goal of this activity is to conceptualize a scenario of sequential, integrated private enterprise initiatives that can carry humankind forward to Mars. This presentation highlights planning considerations and design concepts for establishing a first settlement on Mars. The outpost would support surface missions lasting up to about 500 days and would serve as the initial stage of a larger and continuously operational development which would utilize Mars resources to be less reliant on materials from Earth. Key elements of this first stage mission development sequence include a new heavy-lift Earth-to-orbit launch vehicle; a plasma- drive Mars transit vehicle; habitat modules for crews in transit to and from Mars; "hard" and "inflatable" surface habitats and laboratories; a mobile power unit; a spacecraft to assist orbital assembly; and vehicles to lift crews off the Mars surface and land them safely back on Earth from LEO. SICSA's space development approach differs in fundamental ways from conventional NASA-sponsored initiatives. First, virtually all baseline planning assumptions are influenced by the private sector-driven nature of an approach that aims to avoid all possible reliance upon government financing, agendas and schedules. In this regard, any involvements with NASA or the space agencies of other countries would be premised upon mutual public-corporate partnership benefits rather than upon federal contract awards, management and control. Another potential difference relates to program philosophy. Unlike Apollo Program "sprint" missions which culminated with footprints and flagpoles on the Moon, the aim is to realize sustainable and continuing planetary exploration and development progress. This goal can be advanced through approaches that

  16. Guidelines for 2007 MARS exercise

    CERN Multimedia

    HR Department


    Following the introduction of the new Merit Appraisal and Recognition Scheme (MARS), full details of the scheme are now available via the HR Department's homepage or directly on the Department's MARS web page: in English: or French: You will find on this page: 'Introduction to MARS' with detailed information presented in Frequently Asked Questions; these include the MARS timetable for proposals and decisions; 'Regulations' with links to the scheme's statutory documents; 'Procedures and Forms' and 'Useful Information' with links to all the relevant documentation; these include the mandates of the Senior Staff Advisory Committee (SSAC) and the Technical Engineers and Administrative Careers Committee (TEACC). HR Department Tel. 73566

  17. The Topography of Mars: Understanding the Surface of Mars Through the Mars Orbiter Laser Altimeter (United States)

    Derby, C. A.; Neumann, G. A.; Sakimoto, S. E.


    The Mars Orbiter Laser Altimeter has been orbiting Mars since 1997 and has measured the topography of Mars with a meter of vertical accuracy. This new information has improved our understanding of both the surface and the interior of Mars. The topographic globe and the labeled topographic map of Mars illustrate these new data in a format that can be used in a classroom setting. The map is color shaded to show differences in elevation on Mars, presenting Mars with a different perspective than traditional geological and geographic maps. Through the differences in color, students can see Mars as a three-dimensional surface and will be able to recognize features that are invisible in imagery. The accompanying lesson plans are designed for middle school science students and can be used both to teach information about Mars as a planet and Mars in comparison to Earth, fitting both the solar system unit and the Earth science unit in a middle school curriculum. The lessons are referenced to the National Benchmark standards for students in grades 6-8 and cover topics such as Mars exploration, the Mars Orbiter Laser Altimeter, resolution and powers of 10, gravity, craters, seismic waves and the interior structure of a planet, isostasy, and volcanoes. Each lesson is written in the 5 E format and includes a student content activity and an extension showing current applications of Mars and MOLA data. These activities can be found at Funding for this project was provided by the Maryland Space Grant Consortium and the MOLA Science Team, Goddard Space Flight Center.

  18. Mars subsurface investigation by MARSIS and SHARAD (United States)

    Picardi, Giovanni; Loukas, Alessandro; Masdea, Arturo; Mastrogiuseppe, Marco; Restano, Marco; Seu, Roberto


    This paper is addressed to MARSIS (Mars Advanced Radar for Subsurface and Ionosphere Sounding in Mars Express ESA mission) data inversion. The data inversion gives an estimation of the materials composing the different detected interfaces, including the impurity (inclusion) of the first layer, if any, and its percentage, by the evaluation of the values of the permittivity that would generate the observed radio echoes. The methodology utilized for the data inversion is applied in different areas of the Mars South Pole and the results are reported for each area. The scattering behavior of the surface and subsurface (flat or rough), according with the geometrical structure, is estimated by the shape of the radar echoes and is utilized for the correction of their power; in such a way the contributions due to the surface and subsurface shape are estimated and the corrected echoes contain only the surface and subsurface material features. In this paper, in order to define the main topics of the data inversion, are only considered areas where flat surfaces are present and clutter echoes are negligible; the clutter cancellation can be applied according with the well known techniques. The scattering (volume scattering) due to the inclusion in the host material has been considered. Several frames, from SHARAD (SHAllow RADar in Mars Reconnaissance Orbiter US mission), in the same Mars area, have been analyzed and they confirmed the layer attenuation obtained by MARSIS data. Within the MARSIS papers this one presents a quantitative and scientific parametric data inversion, based on a physical approach and gives numerical results on the dielectric constant of the detected interface.

  19. NASAs Evolvable Mars Campaign: Mars Moons Robotic Precursor (United States)

    Gernhardt, Michael L.; Abercromby, Andrew F. J.; Abell, Paul A.; Love, Stanley G.; Lee, David E.; Chappell, Steven P.; Howe, A. Scott; Friedensen, Victoria


    Human exploration missions to the moons of Mars are being considered within NASA's Evolvable Mars Campaign (EMC) as an intermediate step for eventual human exploration and pioneering of the surface of Mars. A range of mission architectures is being evaluated in which human crews would explore one or both moons for as little as 14 days or for as long as 500 days with a variety of orbital and surface habitation and mobility options being considered. Relatively little is known about the orbital, surface, or subsurface characteristics of either moon. This makes them interesting but challenging destinations for human exploration missions during which crewmembers must be able to effectively conduct scientific exploration without being exposed to undue risks due to radiation, dust, micrometeoroids, or other hazards. A robotic precursor mission to one or both moons will be required to provide data necessary for the design and operation of subsequent human systems and for the identification and prioritization of scientific exploration objectives. This paper identifies and discusses considerations for the design of such a precursor mission based on current human mission architectures. Objectives of a Mars' moon precursor in support of human missions are expected to include: 1) identifying hazards on the surface and the orbital environment at up to 50-km distant retrograde orbits; 2) collecting data on physical characteristics for planning of detailed human proximity and surface operations; 3) performing remote sensing and in situ science investigations to refine and focus future human scientific activities; and 4) prospecting for in situ resource utilization. These precursor objectives can be met through a combination or remote sensing (orbital) and in-situ (surface) measurements. Analysis of spacecraft downlink signals using radio science techniques would measure the moon's mass, mass distribution, and gravity field, which will be necessary to enable trajectory planning

  20. Prediction of Frequency for Simulation of Asphalt Mix Fatigue Tests Using MARS and ANN

    Directory of Open Access Journals (Sweden)

    Ali Reza Ghanizadeh


    Full Text Available Fatigue life of asphalt mixes in laboratory tests is commonly determined by applying a sinusoidal or haversine waveform with specific frequency. The pavement structure and loading conditions affect the shape and the frequency of tensile response pulses at the bottom of asphalt layer. This paper introduces two methods for predicting the loading frequency in laboratory asphalt fatigue tests for better simulation of field conditions. Five thousand (5000 four-layered pavement sections were analyzed and stress and strain response pulses in both longitudinal and transverse directions was determined. After fitting the haversine function to the response pulses by the concept of equal-energy pulse, the effective length of the response pulses were determined. Two methods including Multivariate Adaptive Regression Splines (MARS and Artificial Neural Network (ANN methods were then employed to predict the effective length (i.e., frequency of tensile stress and strain pulses in longitudinal and transverse directions based on haversine waveform. It is indicated that, under controlled stress and strain modes, both methods (MARS and ANN are capable of predicting the frequency of loading in HMA fatigue tests with very good accuracy. The accuracy of ANN method is, however, more than MARS method. It is furthermore shown that the results of the present study can be generalized to sinusoidal waveform by a simple equation.

  1. Prediction of frequency for simulation of asphalt mix fatigue tests using MARS and ANN. (United States)

    Ghanizadeh, Ali Reza; Fakhri, Mansour


    Fatigue life of asphalt mixes in laboratory tests is commonly determined by applying a sinusoidal or haversine waveform with specific frequency. The pavement structure and loading conditions affect the shape and the frequency of tensile response pulses at the bottom of asphalt layer. This paper introduces two methods for predicting the loading frequency in laboratory asphalt fatigue tests for better simulation of field conditions. Five thousand (5000) four-layered pavement sections were analyzed and stress and strain response pulses in both longitudinal and transverse directions was determined. After fitting the haversine function to the response pulses by the concept of equal-energy pulse, the effective length of the response pulses were determined. Two methods including Multivariate Adaptive Regression Splines (MARS) and Artificial Neural Network (ANN) methods were then employed to predict the effective length (i.e., frequency) of tensile stress and strain pulses in longitudinal and transverse directions based on haversine waveform. It is indicated that, under controlled stress and strain modes, both methods (MARS and ANN) are capable of predicting the frequency of loading in HMA fatigue tests with very good accuracy. The accuracy of ANN method is, however, more than MARS method. It is furthermore shown that the results of the present study can be generalized to sinusoidal waveform by a simple equation.

  2. Revisiting Nuclear Thermal Propulsion for Human Mars Exploration (United States)

    Percy, Thomas K.; Rodriguez, Mitchell


    Nuclear Thermal Propulsion (NTP) has long been considered as a viable in-space transportation alternative for delivering crew and cargo to the Martian system. While technology development work in nuclear propulsion has continued over the year, general interest in NTP propulsion applications has historically been tied directly to the ebb and flow of interest in sending humans to explore Mars. As far back as the 1960’s, plans for NTP-based human Mars exploration have been proposed and periodically revisited having most recently been considered as part of NASA Design Reference Architecture (DRA) 5.0. NASA has been investigating human Mars exploration strategies tied to its current Journey to Mars for the past few years however, NTP has only recently been added into the set of alternatives under consideration for in-space propulsion under the Mars Study Capability (MSC) team, formerly the Evolvable Mars Campaign (EMC) team. The original charter of the EMC was to find viable human Mars exploration approaches that relied heavily on technology investment work already underway, specifically related to the development of large Solar Electric Propulsion (SEP) systems. The EMC team baselined several departures from traditional Mars exploration ground rules to enable these types of architectures. These ground rule changes included lower energy conjunction class trajectories with corresponding longer flight times, aggregation of mission elements in cis-Lunar space rather than Low Earth Orbit (LEO) and, in some cases, the pre-deployment of Earth return propulsion systems to Mars. As the MSC team continues to refine the in-space transportation trades, an NTP-based architecture that takes advantage of some of these ground rule departures is being introduced.

  3. Frontier In-Situ Resource Utilization for Enabling Sustained Human Presence on Mars (United States)

    Moses, Robert W.; Bushnell, Dennis M.


    The currently known resources on Mars are massive, including extensive quantities of water and carbon dioxide and therefore carbon, hydrogen and oxygen for life support, fuels and plastics and much else. The regolith is replete with all manner of minerals. In Situ Resource Utilization (ISRU) applicable frontier technologies include robotics, machine intelligence, nanotechnology, synthetic biology, 3-D printing/additive manufacturing and autonomy. These technologies combined with the vast natural resources should enable serious, pre- and post-human arrival ISRU to greatly increase reliability and safety and reduce cost for human colonization of Mars. Various system-level transportation concepts employing Mars produced fuel would enable Mars resources to evolve into a primary center of trade for the inner solar system for eventually nearly everything required for space faring and colonization. Mars resources and their exploitation via extensive ISRU are the key to a viable, safe and affordable, human presence beyond Earth. The purpose of this paper is four-fold: 1) to highlight the latest discoveries of water, minerals, and other materials on Mars that reshape our thinking about the value and capabilities of Mars ISRU; 2) to summarize the previous literature on Mars ISRU processes, equipment, and approaches; 3) to point to frontier ISRU technologies and approaches that can lead to safe and affordable human missions to Mars; and 4) to suggest an implementation strategy whereby the ISRU elements are phased into the mission campaign over time to enable a sustainable and increasing human presence on Mars.

  4. Chemical composition of Mars (United States)

    Morgan, J.W.; Anders, E.


    The composition of Mars has been calculated from the cosmochemical model of Ganapathy and Anders (1974) which assumes that planets and chondrites underwent the same 4 fractionation processes in the solar nebula. Because elements of similar volatility stay together in these processes, only 4 index elements (U, Fe, K and Tl or Ar36) are needed to calculate the abundances of all 83 elements in the planet. The values chosen are U = 28 ppb, K = 62 ppm (based on K U = 2200 from orbital ??-spectrometry and on thermal history calculations by Tokso??z and Hsui (1978) Fe = 26.72% (from geophysical data), and Tl = 0.14 ppb (from the Ar36 and Ar40 abundances measured by Viking). The mantle of Mars is an iron-rich [Mg/(Mg + Fe) = 0.77] garnet wehrlite (?? = 3.52-3.54 g/cm3), similar to McGetchin and Smyth's (1978) estimate but containing more Ca and Al. It is nearly identical to the bulk Moon composition of Morgan et al. (1978b). The core makes up 0.19 of the planet and contains 3.5% S-much less than estimated by other models. Volatiles have nearly Moon-like abundances, being depleted relative to the Earth by factors of 0.36 (K-group, Tcond = 600-1300 K) or 0.029 (Tl group, Tcond planets (Earth, Venus, Mars, Moon, and eucrite parent body) suggests that volatile depletion correlates mainly with size rather than with radial distance from the Sun. However, the relatively high volatile content of shergottites and some chondrites shows that the correlation is not simple; other factors must also be involved. ?? 1979.

  5. MarsSedEx I and II: Experimental investigation of gravity effects on sedimentation on Mars (United States)

    Kuhn, N. J.; Kuhn, B.; Gartmann, A.


    Sorting of sedimentary rocks is a proxy for the environmental conditions at the time of deposition, in particular the runoff that moved and deposited the material forming the rocks. Settling of sediment is strongly influenced by the gravity of a planetary body. As a consequence, sorting of a sedimentary rock varies with gravity for a given depth and velocity of surface runoff. Theoretical considerations for spheres indicate that sorting is less uniform on Mars than on Earth for runoff of identical depth. The effects of gravity on flow hydraulics limit the use of common, semi-empirical models developed to simulate particle settling in terrestrial environments, on Mars. Assessing sedimentation patterns on Mars, aimed at identifying strata potentially hosting traces of life, is potentially affected by such uncertainties. Using first-principle approaches, e.g. through Computational Fluid Dynamics, for calculating settling velocities on other planetary bodies requires a large effort and is limited by the values of boundary conditions, e.g. the shape of the particle. The degree of uncertainty resulting from the differences in gravity on Earth and Mars was therefore tested during three reduced-gravity flights, the MarsSedEx I and II missions, conducted in November 2012 and 2013. Nine types of sediment, ranging in size, shape and density were tested in custom-designed settling tubes during parabolas of Martian gravity lasting 20 to 25 seconds. Based on the observed settling velocities, the uncertainties of empirical relationships developed on Earth to assess particle settling on Mars are discussed. In addition, the potential effects of reduced gravity on patterns of erosion, transport and sorting of sediment, including the implications for identifying strata bearing traces of past life on are examined.

  6. Mars Thermal Inertia (United States)


    This image shows the global thermal inertia of the Martian surface as measured by the Thermal Emission Spectrometer (TES) instrument on the Mars Global Surveyor. The data were acquired during the first 5000 orbits of the MGS mapping mission. The pattern of inertia variations observed by TES agrees well with the thermal inertia maps made by the Viking Infrared Thermal Mapper experiment, but the TES data shown here are at significantly higher spatial resolution (15 km versus 60 km).The TES instrument was built by Santa Barbara Remote Sensing and is operated by Philip R. Christensen, of Arizona State University, Tempe, AZ.

  7. Moon-Mars Initiative (United States)


    On 27 May, the AGU Council unanimously adopted a position statement on NASA's strategic plan released in February 2005:: "A New Age of Exploration: NASA's Direction for 2005 and Beyond". This strategy incorporates U.S. President Bush's vision for manned space flight to Moon and Mars as described in "A Renewed Spirit of Discovery: The President's Vision for U.S. Space Exploration" announced in January 2004. The statement was drafted by a panel chaired by Eric Barron of Penn State University. AGU calls for the U.S. Administration, Congress, and NASA to continue their commitment to innovative Earth and space science programs. This commitment has placed the U.S. in an international leadership position. It enables environmental stewardship, promotes economic vitality, engages the next generation of scientists and engineers, protects life and property, and fosters exploration. It is, however, threatened by new financial demands placed on NASA by the return to human space flight using the space shuttle, finishing the space station, and launching the Moon-Mars initiative.

  8. Safety during MARS exercise

    CERN Multimedia


    It is MARS(1) time again! All employed members of the CERN personnel are currently undergoing the annual MARS evaluations.   This is also a good occasion for supervisors and their supervisees to fill in or update the OHS-0-0-3 form(2) “Identification of occupational hazards”. Filling in the OHS-0-0-3 form is an opportunity to assess any safety issues related to the supervisee's activities.  Each of us should, together with our supervisor, regularly identify and assess the hazards we may be exposed to in the course of our professional activities and reflect on how to control and mitigate them. When filling in the OHS form for the first time, it is important to determine any potential hazards as well as the corresponding preventive measures, in particular training and protective equipment. When updating the form, please review the available information to ensure that it still corresponds to the current activities. The form should be updated w...

  9. [Cryptobiosphere of Mars]. (United States)

    Gal'chenko, V F


    The US Viking missions (1975-1976) failed to discover any biological activity on the surface of Mars. Yet, life may exist in the planet lithosphere which was found to contain a substantial amount of water. Martian interior can also provide microbial cryptolife with sources of carbon (CO, CO2, CH4) and energy (reduced elements and compounds, e.g. H2, CO, H2S, NH4+, CH4, Fe3+). Microorganisms identical to the Earth's anaerobic methanogens, sulfate reducers, acetogens, denitrifiers etc. are the most probable Martian aborigines. Well-balanced continuous functioning of the Martian cryptobiosphere implies closure of biochemical carbon, sulfur and nitrogen cycles which cannot be reached but with participation of organotrophic and anaerobic hydrolytic and zymotic organisms, ammonifiers and denitrifiers. Considering the low intensity of biological and chemical processes in the absence of surface hydrosphere, low-power atmosphere and cryptobiosphere closure on Mars, and slow global energy matter cycles, evolution of the presumable Martian cryptolife should also go at a slack pace and directions and forms of the evolution of living substance can have little in common with those on Earth. Comprehensive investigations of the Martian biota will employ a great variety of geochemical, radi- and stable isotope, microbiological, enzymatic and molecular biology methods.

  10. Life on Mars

    International Nuclear Information System (INIS)

    Venkatavaradan, V.S.


    The miniature biological laboratory of the Viking-1 lander had three experiments to determine, whether the micro-organisms of the Martian soil has: (1) photo-synthetic activity (2) metabolic process activity (utilisation of nutrients) and (3) respiration. The Martian soil was warmed in an incubator and exposed to carbon dioxide (containing C 14 ) in presence of xenon arc lamp to simulate the Sun. If the Martian organisms of the expected type are present in the soil, the gas released during the heating would be radio-active which can be detected by a radiation counter. The three experiments had given positive signals denoting the presence of micro-organisms on the surface of Mars. The presence of superoxide in the soil would be poisonous to life but it is likely that organisms may survive deeper below the soil, where the chemicals would not be formed. The Viking-2 results also offered similar results. However, the basic question whether there is life on Mars still remains unanswered. (K.M.)

  11. Tectonic evolution of Mars

    International Nuclear Information System (INIS)

    Wise, D.U.; Golombek, M.P.; McGill, G.E.


    Any model for the tectonic evolution of Mars must account for two major crustal elements: the Tharsis bulge and the topographically low and lightly crated northern third of the planet. Ages determined by crater density indicate that both of these elements came into existence very early in Martian history, a conclusion that holds no matter which of the current crater density versus age curves is used. The size of these two major crustal elements and their sequential development suggest that both may be related to a global-scale internal process. It is proposed that the resurfacing of the northern third of Mars is related to subcrustal erosion and isostatic foundering during the life of a first-order convection cell. With the demise of the cell, denser segregations of metallic materials began to coalesce as a gravitatively unstable layer which finally overturned to form the core. In the overturn, lighter crustal materials was shifted laterally and underplated beneath Tharsis to cause rapid and permanent isostatic rise. This was followed by a long-lived thermal phase produced by the hot underplate and by the gravitative energy of core formation slowly making its way to the surface to produce the Tharsis volcanics

  12. Mars oxygen production system design (United States)

    Cotton, Charles E.; Pillow, Linda K.; Perkinson, Robert C.; Brownlie, R. P.; Chwalowski, P.; Carmona, M. F.; Coopersmith, J. P.; Goff, J. C.; Harvey, L. L.; Kovacs, L. A.


    The design and construction phase is summarized of the Mars oxygen demonstration project. The basic hardware required to produce oxygen from simulated Mars atmosphere was assembled and tested. Some design problems still remain with the sample collection and storage system. In addition, design and development of computer compatible data acquisition and control instrumentation is ongoing.

  13. Water and Life on Mars (United States)

    McKay, Christopher P.; DeVincenzi, Donald (Technical Monitor)


    Mars appears to be cold dry and dead world. However there is good evidence that early in its history it had liquid water, more active volcanism, and a thicker atmosphere. Mars had this earth-like environment over three and a half billion years ago, during the same time that life appeared on Earth. The main question in the exploration of Mars then is the search for a independent origin of life on that planet. Ecosystems in cold, dry locations on Earth - such as the Antarctic - provide examples of how life on Mars might have survived and where to look for fossils. Although the Viking results may indicate that Mars has no life today, there is direct geomorphological evidence that, in the past, Mars had large amounts of liquid water on its surface - possibly due to a thicker atmosphere. From a biological perspective the existence of liquid water, by itself motivates the question of the origin of life on Mars. One of the martian meteorites dates back to this early period and may contain evidence consistent with life. From studies of the Earth's earliest biosphere we know that by 3.5 Gyr. ago, life had originated on Earth and reached a fair degree of biological sophistication. Surface activity and erosion on Earth make it difficult to trace the history of life before the 3.5 Gyr timeframe. Ecosystems in cold, dry locations on Earth - such as the Antarctic - provide examples of how life on Mars might have survived and where to look for fossils.

  14. Atmospheric Models for Mars Aerocapture (United States)

    Justus, C. G.; Duvall, Aleta; Keller, Vernon W.


    level Mars atmospheric model. Applications include systems design, performance analysis, and operations planning for aerobraking, entry descent and landing, and aerocapture. Typical Mars aerocapture periapsis altitudes (for systems with rigid- aeroshell heat shields) are about 50 km. This altitude is above the 0-40 km height range covered by Mars Global Surveyor Thermal Emission Spectrometer (TES) nadir observations. Recently, TES limb sounding data have been made available, spanning more than two Mars years (more than 200,000 data profiles) with altitude coverage up to about 60 km, well within the height range of interest for aerocapture. Results are presented comparing Mars-GRAM atmospheric density with densities from TES nadir and limb sounding observations. A new Mars-GRAM feature is described which allows individual TES nadir or limb profiles to be extracted from the large TES databases, and to be used as an optional replacement for standard Mars-GRAM background (climatology) conditions. For Monte-Carlo applications such as aerocapture guidance and control studies, Mars-GRAM perturbations are available using these TES profile background conditions.

  15. 'Endurance' Courtesy of Mars Express (United States)


    NASA's Mars Exploration Rover Opportunity used its panoramic camera to capture this false-color image of the interior of 'Endurance Crater' on the rover's 188th martian day (Aug. 4, 2004). The image data were relayed to Earth by the European Space Agency's Mars Express orbiter. The image was generated from separate frames using the cameras 750-, 530- and 480-nanometer filters.

  16. Numerical simulation of two dimensional sine-Gordon solitons using modified cubic B-spline differential quadrature method

    Directory of Open Access Journals (Sweden)

    H. S. Shukla


    Full Text Available In this paper, a modified cubic B-spline differential quadrature method (MCB-DQM is employed for the numerical simulation of two-space dimensional nonlinear sine-Gordon equation with appropriate initial and boundary conditions. The modified cubic B-spline works as a basis function in the differential quadrature method to compute the weighting coefficients. Accordingly, two dimensional sine-Gordon equation is transformed into a system of second order ordinary differential equations (ODEs. The resultant system of ODEs is solved by employing an optimal five stage and fourth-order strong stability preserving Runge–Kutta scheme (SSP-RK54. Numerical simulation is discussed for both damped and undamped cases. Computational results are found to be in good agreement with the exact solution and other numerical results available in the literature.

  17. A meshless scheme for partial differential equations based on multiquadric trigonometric B-spline quasi-interpolation

    International Nuclear Information System (INIS)

    Gao Wen-Wu; Wang Zhi-Gang


    Based on the multiquadric trigonometric B-spline quasi-interpolant, this paper proposes a meshless scheme for some partial differential equations whose solutions are periodic with respect to the spatial variable. This scheme takes into account the periodicity of the analytic solution by using derivatives of a periodic quasi-interpolant (multiquadric trigonometric B-spline quasi-interpolant) to approximate the spatial derivatives of the equations. Thus, it overcomes the difficulties of the previous schemes based on quasi-interpolation (requiring some additional boundary conditions and yielding unwanted high-order discontinuous points at the boundaries in the spatial domain). Moreover, the scheme also overcomes the difficulty of the meshless collocation methods (i.e., yielding a notorious ill-conditioned linear system of equations for large collocation points). The numerical examples that are presented at the end of the paper show that the scheme provides excellent approximations to the analytic solutions. (general)

  18. La obtención y proyección de tablas de mortalidad empleando curvas. Spline

    Directory of Open Access Journals (Sweden)

    Alejandro MINA-VALDÉS


    Full Text Available Una de las herramientas del análisis numérico es el uso de polinomios de n-ésimo orden para interpolar entre n + 1 puntos, teniéndose casos en donde estas funciones polinómicas pueden llevar a resultados erróneos. Una alternativa es la de aplicar polinomios de orden inferior a subconjuntos de datos. Estos polinomios conectados se llaman funciones de interpolación segmentaria (spline functions. En este artículo se presenta la herramienta que el análisis numérico proporciona como instrumento técnico necesario para llevar a cabo todos los procedimientos matemáticos existentes con base a algoritmos que permitan su simulación o cálculo, en especial, las funciones splines definidas a trozos (por tramos, con interpolación mediante ellas, dando lugar a el ajuste de curvas spline con base en la serie de sobrevivientes lx de una tabla abreviada de mortalidad mexicana, con el fin de desagregarla por edad desplegada, respetando las concavidades que por el efecto de la mortalidad en las primeras edades y en las siguientes se tienen en la experiencia mexicana. También empleando las curvas splines se presentan las simulaciones que permiten obtener escenarios futuros de las series de sobrevivientes lx, que dan lugar a las proyecciones de la mortalidad mexicana para los años 2010-2050, las que generan las tablas completas de mortalidad para hombres y mujeres de dicho periodo, resaltando las diferencias entre sexos y edades de sus probabilidades de supervivencia y las ganancias en las esperanzas de vida.

  19. Contour propagation using non-uniform cubic B-splines for lung tumor delineation in 4D-CT. (United States)

    Liu, Yongchuan; Jin, Renchao; Chen, Mi; Song, Enmin; Xu, Xiangyang; Zhang, Sheng; Hung, Chih-Cheng


    Accurate target delineation is a critical step in radiotherapy. In this study, a robust contour propagation method is proposed to help physicians delineate lung tumors in four-dimensional computer tomography (4D-CT) images efficiently and accurately. The proposed method starts with manually delineated contours on the reference phase. Each contour is fitted by a non-uniform cubic B-spline curve, and its deformation on the target phase is achieved by moving its control vertexes such that the intensity similarity between the two contours is maximized. Since contour is usually the boundary of lesion or tissue which may deform quite differently from the tissues outside the boundary, the proposed method treats each contour as a deformable entity, a non-uniform cubic B-spline curve, and focuses on the registration of contour entity instead of the entire image to avoid the deformation of contour to be smoothed by its surrounding tissues, meanwhile to greatly reduce the time consumption while keeping the accuracy of the contour propagation. Eighteen 4D-CT cases with 444 gross tumor volume (GTV) contours manually delineated slice by slice on the maximal inhale and exhale phases are used to verify the proposed method. The Jaccard similarity coefficient (JSC) between the propagated GTV and the manually delineated GTV is 0.885 ± 0.026, and the Hausdorff distance (HD) is [Formula: see text] mm. In addition, the time for propagating GTV to all the phases is 3.67 ± 3.41 minutes. The results are better than fast adaptive stochastic gradient descent (FASGD) B-spline method, 3D+t B-spline method and diffeomorphic Demons method. The proposed method is useful to help physicians delineate target volumes efficiently and accurately.

  20. Investigation of electron and hydrogenic-donor states confined in a permeable spherical box using B-splines

    Directory of Open Access Journals (Sweden)

    T Nikbakht


    Full Text Available   Effects of quantum size and potential shape on the spectra of an electron and a hydrogenic-donor at the center of a permeable spherical cavity have been calculated, using linear variational method. B-splines have been used as basis functions. By extensive convergence tests and comparing with other results given in the literature, the validity and efficiency of the method were confirmed.