Linear Methods for Image Interpolation
Pascal Getreuer
2011-01-01
We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.
Linear Methods for Image Interpolation
Directory of Open Access Journals (Sweden)
Pascal Getreuer
2011-09-01
Full Text Available We discuss linear methods for interpolation, including nearest neighbor, bilinear, bicubic, splines, and sinc interpolation. We focus on separable interpolation, so most of what is said applies to one-dimensional interpolation as well as N-dimensional separable interpolation.
Comparing interpolation schemes in dynamic receive ultrasound beamforming
DEFF Research Database (Denmark)
Kortbek, Jacob; Andresen, Henrik; Nikolov, Svetoslav
2005-01-01
In medical ultrasound interpolation schemes are of- ten applied in receive focusing for reconstruction of image points. This paper investigates the performance of various interpolation scheme by means of ultrasound simulations of point scatterers in Field II. The investigation includes conventional...... B-mode imaging and synthetic aperture (SA) imaging using a 192-element, 7 MHz linear array transducer with λ pitch as simulation model. The evaluation consists primarily of calculations of the side lobe to main lobe ratio, SLMLR, and the noise power of the interpolation error. When using...... conventional B-mode imaging and linear interpolation, the difference in mean SLMLR is 6.2 dB. With polynomial interpolation the ratio is in the range 6.2 dB to 0.3 dB using 2nd to 5th order polynomials, and with FIR interpolation the ratio is in the range 5.8 dB to 0.1 dB depending on the filter design...
Quadratic Interpolation and Linear Lifting Design
Directory of Open Access Journals (Sweden)
Joel Solé
2007-03-01
Full Text Available A quadratic image interpolation method is stated. The formulation is connected to the optimization of lifting steps. This relation triggers the exploration of several interpolation possibilities within the same context, which uses the theory of convex optimization to minimize quadratic functions with linear constraints. The methods consider possible knowledge available from a given application. A set of linear equality constraints that relate wavelet bases and coefficients with the underlying signal is introduced in the formulation. As a consequence, the formulation turns out to be adequate for the design of lifting steps. The resulting steps are related to the prediction minimizing the detail signal energy and to the update minimizing the l2-norm of the approximation signal gradient. Results are reported for the interpolation methods in terms of PSNR and also, coding results are given for the new update lifting steps.
Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI
Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.
2015-01-01
Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085
Spatial interpolation schemes of daily precipitation for hydrologic modeling
Hwang, Y.; Clark, M.R.; Rajagopalan, B.; Leavesley, G.
2012-01-01
Distributed hydrologic models typically require spatial estimates of precipitation interpolated from sparsely located observational points to the specific grid points. We compare and contrast the performance of regression-based statistical methods for the spatial estimation of precipitation in two hydrologically different basins and confirmed that widely used regression-based estimation schemes fail to describe the realistic spatial variability of daily precipitation field. The methods assessed are: (1) inverse distance weighted average; (2) multiple linear regression (MLR); (3) climatological MLR; and (4) locally weighted polynomial regression (LWP). In order to improve the performance of the interpolations, the authors propose a two-step regression technique for effective daily precipitation estimation. In this simple two-step estimation process, precipitation occurrence is first generated via a logistic regression model before estimate the amount of precipitation separately on wet days. This process generated the precipitation occurrence, amount, and spatial correlation effectively. A distributed hydrologic model (PRMS) was used for the impact analysis in daily time step simulation. Multiple simulations suggested noticeable differences between the input alternatives generated by three different interpolation schemes. Differences are shown in overall simulation error against the observations, degree of explained variability, and seasonal volumes. Simulated streamflows also showed different characteristics in mean, maximum, minimum, and peak flows. Given the same parameter optimization technique, LWP input showed least streamflow error in Alapaha basin and CMLR input showed least error (still very close to LWP) in Animas basin. All of the two-step interpolation inputs resulted in lower streamflow error compared to the directly interpolated inputs. ?? 2011 Springer-Verlag.
Image Interpolation Scheme based on SVM and Improved PSO
Jia, X. F.; Zhao, B. T.; Liu, X. X.; Song, H. P.
2018-01-01
In order to obtain visually pleasing images, a support vector machines (SVM) based interpolation scheme is proposed, in which the improved particle swarm optimization is applied to support vector machine parameters optimization. Training samples are constructed by the pixels around the pixel to be interpolated. Then the support vector machine with optimal parameters is trained using training samples. After the training, we can get the interpolation model, which can be employed to estimate the unknown pixel. Experimental result show that the interpolated images get improvement PNSR compared with traditional interpolation methods, which is agrees with the subjective quality.
Peters, Andre; Nehls, Thomas; Wessolek, Gerd
2016-06-01
Weighing lysimeters with appropriate data filtering yield the most precise and unbiased information for precipitation (P) and evapotranspiration (ET). A recently introduced filter scheme for such data is the AWAT (Adaptive Window and Adaptive Threshold) filter (Peters et al., 2014). The filter applies an adaptive threshold to separate significant from insignificant mass changes, guaranteeing that P and ET are not overestimated, and uses a step interpolation between the significant mass changes. In this contribution we show that the step interpolation scheme, which reflects the resolution of the measuring system, can lead to unrealistic prediction of P and ET, especially if they are required in high temporal resolution. We introduce linear and spline interpolation schemes to overcome these problems. To guarantee that medium to strong precipitation events abruptly following low or zero fluxes are not smoothed in an unfavourable way, a simple heuristic selection criterion is used, which attributes such precipitations to the step interpolation. The three interpolation schemes (step, linear and spline) are tested and compared using a data set from a grass-reference lysimeter with 1 min resolution, ranging from 1 January to 5 August 2014. The selected output resolutions for P and ET prediction are 1 day, 1 h and 10 min. As expected, the step scheme yielded reasonable flux rates only for a resolution of 1 day, whereas the other two schemes are well able to yield reasonable results for any resolution. The spline scheme returned slightly better results than the linear scheme concerning the differences between filtered values and raw data. Moreover, this scheme allows continuous differentiability of filtered data so that any output resolution for the fluxes is sound. Since computational burden is not problematic for any of the interpolation schemes, we suggest always using the spline scheme.
Interpolation-free scanning and sampling scheme for tomographic reconstructions
International Nuclear Information System (INIS)
Donohue, K.D.; Saniie, J.
1987-01-01
In this paper a sampling scheme is developed for computer tomography (CT) systems that eliminates the need for interpolation. A set of projection angles along with their corresponding sampling rates are derived from the geometry of the Cartesian grid such that no interpolation is required to calculate the final image points for the display grid. A discussion is presented on the choice of an optimal set of projection angles that will maintain a resolution comparable to a sampling scheme of regular measurement geometry, while minimizing the computational load. The interpolation-free scanning and sampling (IFSS) scheme developed here is compared to a typical sampling scheme of regular measurement geometry through a computer simulation
Huang, Ai-Mei; Nguyen, Truong
2009-04-01
In this paper, we address the problems of unreliable motion vectors that cause visual artifacts but cannot be detected by high residual energy or bidirectional prediction difference in motion-compensated frame interpolation. A correlation-based motion vector processing method is proposed to detect and correct those unreliable motion vectors by explicitly considering motion vector correlation in the motion vector reliability classification, motion vector correction, and frame interpolation stages. Since our method gradually corrects unreliable motion vectors based on their reliability, we can effectively discover the areas where no motion is reliable to be used, such as occlusions and deformed structures. We also propose an adaptive frame interpolation scheme for the occlusion areas based on the analysis of their surrounding motion distribution. As a result, the interpolated frames using the proposed scheme have clearer structure edges and ghost artifacts are also greatly reduced. Experimental results show that our interpolated results have better visual quality than other methods. In addition, the proposed scheme is robust even for those video sequences that contain multiple and fast motions.
International Nuclear Information System (INIS)
Gao Wen-Wu; Wang Zhi-Gang
2014-01-01
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)
Directory of Open Access Journals (Sweden)
Tao Chen
2017-05-01
Full Text Available The spatial distribution of precipitation is an important aspect of water-related research. The use of different interpolation schemes in the same catchment may cause large differences and deviations from the actual spatial distribution of rainfall. Our study analyzes different methods of spatial rainfall interpolation at annual, daily, and hourly time scales to provide a comprehensive evaluation. An improved regression-based scheme is proposed using principal component regression with residual correction (PCRR and is compared with inverse distance weighting (IDW and multiple linear regression (MLR interpolation methods. In this study, the meso-scale catchment of the Fuhe River in southeastern China was selected as a typical region. Furthermore, a hydrological model HEC-HMS was used to calculate streamflow and to evaluate the impact of rainfall interpolation methods on the results of the hydrological model. Results show that the PCRR method performed better than the other methods tested in the study and can effectively eliminate the interpolation anomalies caused by terrain differences between observation points and surrounding areas. Simulated streamflow showed different characteristics based on the mean, maximum, minimum, and peak flows. The results simulated by PCRR exhibited the lowest streamflow error and highest correlation with measured values at the daily time scale. The application of the PCRR method is found to be promising because it considers multicollinearity among variables.
Plasma simulation with the Differential Algebraic Cubic Interpolated Propagation scheme
Energy Technology Data Exchange (ETDEWEB)
Utsumi, Takayuki [Japan Atomic Energy Research Inst., Tokai, Ibaraki (Japan). Tokai Research Establishment
1998-03-01
A computer code based on the Differential Algebraic Cubic Interpolated Propagation scheme has been developed for the numerical solution of the Boltzmann equation for a one-dimensional plasma with immobile ions. The scheme advects the distribution function and its first derivatives in the phase space for one time step by using a numerical integration method for ordinary differential equations, and reconstructs the profile in phase space by using a cubic polynomial within a grid cell. The method gives stable and accurate results, and is efficient. It is successfully applied to a number of equations; the Vlasov equation, the Boltzmann equation with the Fokker-Planck or the Bhatnagar-Gross-Krook (BGK) collision term and the relativistic Vlasov equation. The method can be generalized in a straightforward way to treat cases such as problems with nonperiodic boundary conditions and higher dimensional problems. (author)
A fast and accurate dihedral interpolation loop subdivision scheme
Shi, Zhuo; An, Yalei; Wang, Zhongshuai; Yu, Ke; Zhong, Si; Lan, Rushi; Luo, Xiaonan
2018-04-01
In this paper, we propose a fast and accurate dihedral interpolation Loop subdivision scheme for subdivision surfaces based on triangular meshes. In order to solve the problem of surface shrinkage, we keep the limit condition unchanged, which is important. Extraordinary vertices are handled using modified Butterfly rules. Subdivision schemes are computationally costly as the number of faces grows exponentially at higher levels of subdivision. To address this problem, our approach is to use local surface information to adaptively refine the model. This is achieved simply by changing the threshold value of the dihedral angle parameter, i.e., the angle between the normals of a triangular face and its adjacent faces. We then demonstrate the effectiveness of the proposed method for various 3D graphic triangular meshes, and extensive experimental results show that it can match or exceed the expected results at lower computational cost.
Optimal Interpolation scheme to generate reference crop evapotranspiration
Tomas-Burguera, Miquel; Beguería, Santiago; Vicente-Serrano, Sergio; Maneta, Marco
2018-05-01
We used an Optimal Interpolation (OI) scheme to generate a reference crop evapotranspiration (ETo) grid, forcing meteorological variables, and their respective error variance in the Iberian Peninsula for the period 1989-2011. To perform the OI we used observational data from the Spanish Meteorological Agency (AEMET) and outputs from a physically-based climate model. To compute ETo we used five OI schemes to generate grids for the five observed climate variables necessary to compute ETo using the FAO-recommended form of the Penman-Monteith equation (FAO-PM). The granularity of the resulting grids are less sensitive to variations in the density and distribution of the observational network than those generated by other interpolation methods. This is because our implementation of the OI method uses a physically-based climate model as prior background information about the spatial distribution of the climatic variables, which is critical for under-observed regions. This provides temporal consistency in the spatial variability of the climatic fields. We also show that increases in the density and improvements in the distribution of the observational network reduces substantially the uncertainty of the climatic and ETo estimates. Finally, a sensitivity analysis of observational uncertainties and network densification suggests the existence of a trade-off between quantity and quality of observations.
LINEAR2007, Linear-Linear Interpolation of ENDF Format Cross-Sections
International Nuclear Information System (INIS)
2007-01-01
1 - Description of program or function: LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form. Codes used subsequently need thus to consider only linear-linear data. IAEA1311/15: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. Modifications from previous versions: - Linear VERS. 2007-1 (JAN. 2007): checked against all ENDF/B-VII; increased page size from 60,000 to 600,000 points 2 - Method of solution: Each section of data is considered separately. Each section of File 3, 23, and 27 data consists of a table of cross section versus energy with any of five interpolation laws. LINEAR will replace each section with a new table of energy versus cross section data in which the interpolation law is always linear in energy and cross section. The histogram (constant cross section between two energies) interpolation law is converted to linear-linear by substituting two points for each initial point. The linear-linear is not altered. For the log-linear, linear-log and log- log laws, the cross section data are converted to linear by an interval halving algorithm. Each interval is divided in half until the value at the middle of the interval can be approximated by linear-linear interpolation to within a given accuracy. The LINEAR program uses a multipoint fractional error thinning algorithm to minimize the size of each cross section table
Hybrid vehicle optimal control : Linear interpolation and singular control
Delprat, S.; Hofman, T.
2015-01-01
Hybrid vehicle energy management can be formulated as an optimal control problem. Considering that the fuel consumption is often computed using linear interpolation over lookup table data, a rigorous analysis of the necessary conditions provided by the Pontryagin Minimum Principle is conducted. For
Implementing fuzzy polynomial interpolation (FPI and fuzzy linear regression (LFR
Directory of Open Access Journals (Sweden)
Maria Cristina Floreno
1996-05-01
Full Text Available This paper presents some preliminary results arising within a general framework concerning the development of software tools for fuzzy arithmetic. The program is in a preliminary stage. What has been already implemented consists of a set of routines for elementary operations, optimized functions evaluation, interpolation and regression. Some of these have been applied to real problems.This paper describes a prototype of a library in C++ for polynomial interpolation of fuzzifying functions, a set of routines in FORTRAN for fuzzy linear regression and a program with graphical user interface allowing the use of such routines.
LINTAB, Linear Interpolable Tables from any Continuous Variable Function
International Nuclear Information System (INIS)
1988-01-01
1 - Description of program or function: LINTAB is designed to construct linearly interpolable tables from any function. The program will start from any function of a single continuous variable... FUNKY(X). By user input the function can be defined, (1) Over 1 to 100 X ranges. (2) Within each X range the function is defined by 0 to 50 constants. (3) At boundaries between X ranges the function may be continuous or discontinuous (depending on the constants used to define the function within each X range). 2 - Method of solution: LINTAB will construct a table of X and Y values where the tabulated (X,Y) pairs will be exactly equal to the function (Y=FUNKY(X)) and linear interpolation between the tabulated pairs will be within any user specified fractional uncertainty of the function for all values of X within the requested X range
An adaptive interpolation scheme for molecular potential energy surfaces
Kowalewski, Markus; Larsson, Elisabeth; Heryudono, Alfa
2016-08-01
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task—especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm based on polyharmonic splines combined with a partition of unity approach. The adaptive node refinement allows to greatly reduce the number of sample points by employing a local error estimate. The algorithm and its scaling behavior are evaluated for a model function in 2, 3, and 4 dimensions. The developed algorithm allows for a more rapid and reliable interpolation of a potential energy surface within a given accuracy compared to the non-adaptive version.
A New Interpolation Approach for Linearly Constrained Convex Optimization
Espinoza, Francisco
2012-08-01
In this thesis we propose a new class of Linearly Constrained Convex Optimization methods based on the use of a generalization of Shepard\\'s interpolation formula. We prove the properties of the surface such as the interpolation property at the boundary of the feasible region and the convergence of the gradient to the null space of the constraints at the boundary. We explore several descent techniques such as steepest descent, two quasi-Newton methods and the Newton\\'s method. Moreover, we implement in the Matlab language several versions of the method, particularly for the case of Quadratic Programming with bounded variables. Finally, we carry out performance tests against Matab Optimization Toolbox methods for convex optimization and implementations of the standard log-barrier and active-set methods. We conclude that the steepest descent technique seems to be the best choice so far for our method and that it is competitive with other standard methods both in performance and empirical growth order.
Novel Threshold Changeable Secret Sharing Schemes Based on Polynomial Interpolation.
Yuan, Lifeng; Li, Mingchu; Guo, Cheng; Choo, Kim-Kwang Raymond; Ren, Yizhi
2016-01-01
After any distribution of secret sharing shadows in a threshold changeable secret sharing scheme, the threshold may need to be adjusted to deal with changes in the security policy and adversary structure. For example, when employees leave the organization, it is not realistic to expect departing employees to ensure the security of their secret shadows. Therefore, in 2012, Zhang et al. proposed (t → t', n) and ({t1, t2,⋯, tN}, n) threshold changeable secret sharing schemes. However, their schemes suffer from a number of limitations such as strict limit on the threshold values, large storage space requirement for secret shadows, and significant computation for constructing and recovering polynomials. To address these limitations, we propose two improved dealer-free threshold changeable secret sharing schemes. In our schemes, we construct polynomials to update secret shadows, and use two-variable one-way function to resist collusion attacks and secure the information stored by the combiner. We then demonstrate our schemes can adjust the threshold safely.
Accurate B-spline-based 3-D interpolation scheme for digital volume correlation
Ren, Maodong; Liang, Jin; Wei, Bin
2016-12-01
An accurate and efficient 3-D interpolation scheme, based on sampling theorem and Fourier transform technique, is proposed to reduce the sub-voxel matching error caused by intensity interpolation bias in digital volume correlation. First, the influence factors of the interpolation bias are investigated theoretically using the transfer function of an interpolation filter (henceforth filter) in the Fourier domain. A law that the positional error of a filter can be expressed as a function of fractional position and wave number is found. Then, considering the above factors, an optimized B-spline-based recursive filter, combining B-spline transforms and least squares optimization method, is designed to virtually eliminate the interpolation bias in the process of sub-voxel matching. Besides, given each volumetric image containing different wave number ranges, a Gaussian weighting function is constructed to emphasize or suppress certain of wave number ranges based on the Fourier spectrum analysis. Finally, a novel software is developed and series of validation experiments were carried out to verify the proposed scheme. Experimental results show that the proposed scheme can reduce the interpolation bias to an acceptable level.
Interpolation from Grid Lines: Linear, Transfinite and Weighted Method
DEFF Research Database (Denmark)
Lindberg, Anne-Sofie Wessel; Jørgensen, Thomas Martini; Dahl, Vedrana Andersen
2017-01-01
When two sets of line scans are acquired orthogonal to each other, intensity values are known along the lines of a grid. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid l...
Linear, Transﬁnite and Weighted Method for Interpolation from Grid Lines Applied to OCT Images
DEFF Research Database (Denmark)
Lindberg, Anne-Sofie Wessel; Jørgensen, Thomas Martini; Dahl, Vedrana Andersen
2018-01-01
of a square grid, but are unknown inside each square. To view these values as an image, intensities need to be interpolated at regularly spaced pixel positions. In this paper we evaluate three methods for interpolation from grid lines: linear, transfinite and weighted. The linear method does not preserve...... and the stability of the linear method further away. An important parameter influencing the performance of the interpolation methods is the upsampling rate. We perform an extensive evaluation of the three interpolation methods across a range of upsampling rates. Our statistical analysis shows significant difference...... in the performance of the three methods. We find that the transfinite interpolation works well for small upsampling rates and the proposed weighted interpolation method performs very well for all upsampling rates typically used in practice. On the basis of these findings we propose an approach for combining two OCT...
International Nuclear Information System (INIS)
Sulbhewar, Litesh N; Raveendranath, P
2014-01-01
An efficient piezoelectric smart beam finite element based on Reddy’s third-order displacement field and layerwise linear potential is presented here. The present formulation is based on the coupled polynomial field interpolation of variables, unlike conventional piezoelectric beam formulations that use independent polynomials. Governing equations derived using a variational formulation are used to establish the relationship between field variables. The resulting expressions are used to formulate coupled shape functions. Starting with an assumed cubic polynomial for transverse displacement (w) and a linear polynomial for electric potential (φ), coupled polynomials for axial displacement (u) and section rotation (θ) are found. This leads to a coupled quadratic polynomial representation for axial displacement (u) and section rotation (θ). The formulation allows accommodation of extension–bending, shear–bending and electromechanical couplings at the interpolation level itself, in a variationally consistent manner. The proposed interpolation scheme is shown to eliminate the locking effects exhibited by conventional independent polynomial field interpolations and improve the convergence characteristics of HSDT based piezoelectric beam elements. Also, the present coupled formulation uses only three mechanical degrees of freedom per node, one less than the conventional formulations. Results from numerical test problems prove the accuracy and efficiency of the present formulation. (paper)
A comparison of linear interpolation models for iterative CT reconstruction.
Hahn, Katharina; Schöndube, Harald; Stierstorfer, Karl; Hornegger, Joachim; Noo, Frédéric
2016-12-01
Recent reports indicate that model-based iterative reconstruction methods may improve image quality in computed tomography (CT). One difficulty with these methods is the number of options available to implement them, including the selection of the forward projection model and the penalty term. Currently, the literature is fairly scarce in terms of guidance regarding this selection step, whereas these options impact image quality. Here, the authors investigate the merits of three forward projection models that rely on linear interpolation: the distance-driven method, Joseph's method, and the bilinear method. The authors' selection is motivated by three factors: (1) in CT, linear interpolation is often seen as a suitable trade-off between discretization errors and computational cost, (2) the first two methods are popular with manufacturers, and (3) the third method enables assessing the importance of a key assumption in the other methods. One approach to evaluate forward projection models is to inspect their effect on discretized images, as well as the effect of their transpose on data sets, but significance of such studies is unclear since the matrix and its transpose are always jointly used in iterative reconstruction. Another approach is to investigate the models in the context they are used, i.e., together with statistical weights and a penalty term. Unfortunately, this approach requires the selection of a preferred objective function and does not provide clear information on features that are intrinsic to the model. The authors adopted the following two-stage methodology. First, the authors analyze images that progressively include components of the singular value decomposition of the model in a reconstructed image without statistical weights and penalty term. Next, the authors examine the impact of weights and penalty on observed differences. Image quality metrics were investigated for 16 different fan-beam imaging scenarios that enabled probing various aspects
Interpolation of polytopic control Lyapunov functions for discrete–time linear systems
Nguyen, T.T.; Lazar, M.; Spinu, V.; Boje, E.; Xia, X.
2014-01-01
This paper proposes a method for interpolating two (or more) polytopic control Lyapunov functions (CLFs) for discrete--time linear systems subject to polytopic constraints, thereby combining different control objectives. The corresponding interpolated CLF is used for synthesis of a stabilizing
Energy band structure of Cr by the Slater-Koster interpolation scheme
International Nuclear Information System (INIS)
Seifu, D.; Mikusik, P.
1986-04-01
The matrix elements of the Hamiltonian between nine localized wave-functions in tight-binding formalism are derived. The symmetry adapted wave-functions and the secular equations are formed by the group theory method for high symmetry points in the Brillouin zone. A set of interaction integrals is chosen on physical ground and fitted via the Slater-Koster interpolation scheme to the abinito band structure of chromium calculated by the Green function method. Then the energy band structure of chromium is interpolated and extrapolated in the Brillouin zone. (author)
SIGMA1-2007, Doppler Broadening ENDF Format Linear-Linear. Interpolated Point Cross Section
International Nuclear Information System (INIS)
2007-01-01
1 - Description of problem or function: SIGMA-1 Doppler broadens evaluated Cross sections given in the linear-linear interpolation form of the ENDF/B Format to one final temperature. The data is Doppler broadened, thinned, and output in the ENDF/B Format. IAEA0854/15: This version include the updates up to January 30, 2007. Changes in ENDF/B-VII Format and procedures, as well as the evaluations themselves, make it impossible for versions of the ENDF/B pre-processing codes earlier than PREPRO 2007 (2007 Version) to accurately process current ENDF/B-VII evaluations. The present code can handle all existing ENDF/B-VI evaluations through release 8, which will be the last release of ENDF/B-VI. 2 - Modifications from previous versions: Sigma-1 VERS. 2007-1 (Jan. 2007): checked against all ENDF/B-VII; increased page size from 60,000 to 360,000 energy points 3 - Method of solution: The energy grid is selected to ensure that the broadened data is linear-linear interpolable. SIGMA-1 starts from the free-atom Doppler broadening equations and adds the assumptions of linear data within the table and constant data outside the range of the table. If the Original data is not at zero Kelvin, the data is broadened by the effective temperature difference to the final temperature. If the data is already at a temperature higher than the final temperature, Doppler broadening is not performed. 4 - Restrictions on the complexity of the problem: The input to SIGMA-1 must be data which vary linearly in energy and cross section between tabulated points. The LINEAR program provides such data. LINEAR uses only the ENDF/B BCD Format tape and copies all sections except File 3 as read. Since File 3 data are in identical Format for ENDF/B Versions I through VI, the program can be used with all these versions. - The present version Doppler broadens only to one final temperature
Linear and Quadratic Interpolators Using Truncated-Matrix Multipliers and Squarers
Directory of Open Access Journals (Sweden)
E. George Walters III
2015-11-01
Full Text Available This paper presents a technique for designing linear and quadratic interpolators for function approximation using truncated multipliers and squarers. Initial coefficient values are found using a Chebyshev-series approximation and then adjusted through exhaustive simulation to minimize the maximum absolute error of the interpolator output. This technique is suitable for any function and any precision up to 24 bits (IEEE single precision. Designs for linear and quadratic interpolators that implement the 1/x, 1/ √ x, log2(1+2x, log2(x and 2x functions are presented and analyzed as examples. Results show that a proposed 24-bit interpolator computing 1/x with a design specification of ±1 unit in the last place of the product (ulp error uses 16.4% less area and 15.3% less power than a comparable standard interpolator with the same error specification. Sixteen-bit linear interpolators for other functions are shown to use up to 17.3% less area and 12.1% less power, and 16-bit quadratic interpolators are shown to use up to 25.8% less area and 24.7% less power.
An efficient coupled polynomial interpolation scheme for shear mode sandwich beam finite element
Directory of Open Access Journals (Sweden)
Litesh N. Sulbhewar
Full Text Available An efficient piezoelectric sandwich beam finite element is presented here. It employs the coupled polynomial field interpolation scheme for field variables which incorporates electromechanical coupling at interpolation level itself; unlike conventional sandwich beam theory (SBT based formulations available in the literature. A variational formulation is used to derive the governing equations, which are used to establish the relationships between field variables. These relations lead to the coupled polynomial field descriptions of variables, unlike conventional SBT formulations which use assumed independent polynomials. The relative axial displacement is expressed only by coupled terms containing contributions from other mechanical and electrical variables, thus eliminating use of the transverse displacement derivative as a degree of freedom. A set of coupled shape function based on these polynomials has shown the improvement in the convergence characteristics of the SBT based formulation. This improvement in the performance is achieved with one nodal degree of freedom lesser than the conventional SBT formulations.
Zhao, Huawei; Chen, Chi; Hu, Jiankun; Qin, Jing
2015-01-01
We present two approaches that exploit biometric data to address security problems in the body sensor networks: a new key negotiation scheme based on the fuzzy extractor technology and an improved linear interpolation encryption method. The first approach designs two attack games to give the formal definition of fuzzy negotiation that forms a new key negotiation scheme based on fuzzy extractor technology. According to the definition, we further define a concrete structure of fuzzy negotiation...
KTOE, KEDAK to ENDF/B Format Conversion with Linear Linear Interpolation
International Nuclear Information System (INIS)
Panini, Gian Carlo
1985-01-01
1 - Nature of physical problem solved: This code performs a fully automated translation from KEDAK into ENDF-4 or -5 format. Output is on tape in card image format. 2 - Method of solution: Before translation the reactions are sorted in the ENDF format order. Linear-linear interpolation rule is preserved. The resonance parameters for both resolved and unresolved, could also be translated and a background cross section is formed as the difference of the calculated contribution from the parameters and the point-wise data given in the original file. Elastic angular distributions originally given in tabulated form are converted into Legendre polynomial coefficients. Energy distributions are calculated using a simple evaporation model with the temperature expressed as a function of the incident mass. 3 - Restrictions on the complexity of the problem: The existing restrictions both on KEDAK and ENDF have been applied to the array sizes used in the code, except for the number of points in a section which in the ENDF format are limited to 5000 points. The code only translates one material at a time
International Nuclear Information System (INIS)
Bensiali, Bouchra; Bodi, Kowsik; Ciraolo, Guido; Ghendrih, Philippe; Liandrat, Jacques
2013-01-01
In this work, we compare different interpolation operators in the context of particle tracking with an emphasis on situations involving velocity field with steep gradients. Since, in this case, most classical methods give rise to the Gibbs phenomenon (generation of oscillations near discontinuities), we present new methods for particle tracking based on subdivision schemes and especially on the Piecewise Parabolic Harmonic (PPH) scheme which has shown its advantage in image processing in presence of strong contrasts. First an analytic univariate case with a discontinuous velocity field is considered in order to highlight the effect of the Gibbs phenomenon on trajectory calculation. Theoretical results are provided. Then, we show, regardless of the interpolation method, the need to use a conservative approach when integrating a conservative problem with a velocity field deriving from a potential. Finally, the PPH scheme is applied in a more realistic case of a time-dependent potential encountered in the edge turbulence of magnetically confined plasmas, to compare the propagation of density structures (turbulence bursts) with the dynamics of test particles. This study highlights the difference between particle transport and density transport in turbulent fields
Interpolation problem for the solutions of linear elasticity equations based on monogenic functions
Grigor'ev, Yuri; Gürlebeck, Klaus; Legatiuk, Dmitrii
2017-11-01
Interpolation is an important tool for many practical applications, and very often it is beneficial to interpolate not only with a simple basis system, but rather with solutions of a certain differential equation, e.g. elasticity equation. A typical example for such type of interpolation are collocation methods widely used in practice. It is known, that interpolation theory is fully developed in the framework of the classical complex analysis. However, in quaternionic analysis, which shows a lot of analogies to complex analysis, the situation is more complicated due to the non-commutative multiplication. Thus, a fundamental theorem of algebra is not available, and standard tools from linear algebra cannot be applied in the usual way. To overcome these problems, a special system of monogenic polynomials the so-called Pseudo Complex Polynomials, sharing some properties of complex powers, is used. In this paper, we present an approach to deal with the interpolation problem, where solutions of elasticity equations in three dimensions are used as an interpolation basis.
Interpolation between multi-dimensional histograms using a new non-linear moment morphing method
Baak, M.; Gadatsch, S.; Harrington, R.; Verkerke, W.
2015-01-01
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model׳s parameters and transformed according to a specific
Directory of Open Access Journals (Sweden)
Litesh N. Sulbhewar
Full Text Available The convergence characteristic of the conventional two-noded Euler-Bernoulli piezoelectric beam finite element depends on the configuration of the beam cross-section. The element shows slower convergence for the asymmetric material distribution in the beam cross-section due to 'material-locking' caused by extension-bending coupling. Hence, the use of conventional Euler-Bernoulli beam finite element to analyze piezoelectric beams which are generally made of the host layer with asymmetrically surface bonded piezoelectric layers/patches, leads to increased computational effort to yield converged results. Here, an efficient coupled polynomial interpolation scheme is proposed to improve the convergence of the Euler-Bernoulli piezoelectric beam finite elements, by eliminating ill-effects of material-locking. The equilibrium equations, derived using a variational formulation, are used to establish relationships between field variables. These relations are used to find a coupled quadratic polynomial for axial displacement, having contributions from an assumed cubic polynomial for transverse displacement and assumed linear polynomials for layerwise electric potentials. A set of coupled shape functions derived using these polynomials efficiently handles extension-bending and electromechanical couplings at the field interpolation level itself in a variationally consistent manner, without increasing the number of nodal degrees of freedom. The comparison of results obtained from numerical simulation of test problems shows that the convergence characteristic of the proposed element is insensitive to the material configuration of the beam cross-section.
Turning Avatar into Realistic Human Expression Using Linear and Bilinear Interpolations
Hazim Alkawaz, Mohammed; Mohamad, Dzulkifli; Rehman, Amjad; Basori, Ahmad Hoirul
2014-06-01
The facial animation in term of 3D facial data has accurate research support of the laser scan and advance 3D tools for complex facial model production. However, the approach still lacks facial expression based on emotional condition. Though, facial skin colour is required to offers an effect of facial expression improvement, closely related to the human emotion. This paper presents innovative techniques for facial animation transformation using the facial skin colour based on linear interpolation and bilinear interpolation. The generated expressions are almost same to the genuine human expression and also enhance the facial expression of the virtual human.
The analysis of decimation and interpolation in the linear canonical transform domain.
Xu, Shuiqing; Chai, Yi; Hu, Youqiang; Huang, Lei; Feng, Li
2016-01-01
Decimation and interpolation are the two basic building blocks in the multirate digital signal processing systems. As the linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing, it is worthwhile and interesting to analyze the decimation and interpolation in the LCT domain. In this paper, the definition of equivalent filter in the LCT domain have been given at first. Then, by applying the definition, the direct implementation structure and polyphase networks for decimator and interpolator in the LCT domain have been proposed. Finally, the perfect reconstruction expressions for differential filters in the LCT domain have been presented as an application. The proposed theorems in this study are the bases for generalizations of the multirate signal processing in the LCT domain, which can advance the filter banks theorems in the LCT domain.
Directory of Open Access Journals (Sweden)
Maheswari Subramanian
2018-01-01
Full Text Available Information hiding techniques have a significant role in recent application areas. Steganography is the embedding of information within an innocent cover work in a way which cannot be detected by any person without accessing the steganographic key. The proposed work uses a steganographic scheme for useful information with the help of human skin tone regions as cover image. The proposed algorithm has undergone Lagrange interpolation encryption for enhancement of the security of the hidden information. First, the skin tone regions are identified by using YCbCr color space which can be used as a cover image. Image pixels which belong to the skin regions are used to carry more secret bits, and the secret information is hidden in both horizontal and vertical sequences of the skin areas of the cover image. The secret information will hide behind the human skin regions rather than other objects in the same image because the skin pixels have high intensity value. The performance of embedding is done and is quite invisible by the vector discrete wavelet transformation (VDWT technique. A new Lagrange interpolation-based encryption method is introduced to achieve high security of the hidden information with higher payload and better visual quality.
Linearly interpolated sub-symbol optical phase noise suppression in CO-OFDM system.
Hong, Xuezhi; Hong, Xiaojian; He, Sailing
2015-02-23
An optical phase noise suppression algorithm, LI-SCPEC, based on phase linear interpolation and sub-symbol processing is proposed for CO-OFDM system. By increasing the temporal resolution of carrier phase tracking through dividing one symbol into several sub-blocks, i.e., sub-symbols, inter-carrier-interference (ICI) mitigation is achieved in the proposed algorithm. Linear interpolation is employed to obtain a reliable temporal reference for sub-symbol phase estimation. The new algorithm, with only a few number of sub-symbols (N(B) = 4), can provide a considerably larger laser linewidth tolerance than several other ICI mitigation algorithms as demonstrated by Monte-Carlo simulations. Numerical analysis verifies that the best performance is achieved with an optimal and moderate number of sub-symbols. Complexity analysis shows that the required number of complex-valued multiplications is independent of the number of sub-symbols used in the proposed algorithm.
Saini, Harsh; Raicar, Gaurav; Dehzangi, Abdollah; Lal, Sunil; Sharma, Alok
2015-12-07
Protein subcellular localization is an important topic in proteomics since it is related to a protein׳s overall function, helps in the understanding of metabolic pathways, and in drug design and discovery. In this paper, a basic approximation technique from natural language processing called the linear interpolation smoothing model is applied for predicting protein subcellular localizations. The proposed approach extracts features from syntactical information in protein sequences to build probabilistic profiles using dependency models, which are used in linear interpolation to determine how likely is a sequence to belong to a particular subcellular location. This technique builds a statistical model based on maximum likelihood. It is able to deal effectively with high dimensionality that hinders other traditional classifiers such as Support Vector Machines or k-Nearest Neighbours without sacrificing performance. This approach has been evaluated by predicting subcellular localizations of Gram positive and Gram negative bacterial proteins. Copyright © 2015 Elsevier Ltd. All rights reserved.
An Online Method for Interpolating Linear Parametric Reduced-Order Models
Amsallem, David; Farhat, Charbel
2011-01-01
A two-step online method is proposed for interpolating projection-based linear parametric reduced-order models (ROMs) in order to construct a new ROM for a new set of parameter values. The first step of this method transforms each precomputed ROM into a consistent set of generalized coordinates. The second step interpolates the associated linear operators on their appropriate matrix manifold. Real-time performance is achieved by precomputing inner products between the reduced-order bases underlying the precomputed ROMs. The proposed method is illustrated by applications in mechanical and aeronautical engineering. In particular, its robustness is demonstrated by its ability to handle the case where the sampled parameter set values exhibit a mode veering phenomenon. © 2011 Society for Industrial and Applied Mathematics.
Restoring the missing features of the corrupted speech using linear interpolation methods
Rassem, Taha H.; Makbol, Nasrin M.; Hasan, Ali Muttaleb; Zaki, Siti Syazni Mohd; Girija, P. N.
2017-10-01
One of the main challenges in the Automatic Speech Recognition (ASR) is the noise. The performance of the ASR system reduces significantly if the speech is corrupted by noise. In spectrogram representation of a speech signal, after deleting low Signal to Noise Ratio (SNR) elements, the incomplete spectrogram is obtained. In this case, the speech recognizer should make modifications to the spectrogram in order to restore the missing elements, which is one direction. In another direction, speech recognizer should be able to restore the missing elements due to deleting low SNR elements before performing the recognition. This is can be done using different spectrogram reconstruction methods. In this paper, the geometrical spectrogram reconstruction methods suggested by some researchers are implemented as a toolbox. In these geometrical reconstruction methods, the linear interpolation along time or frequency methods are used to predict the missing elements between adjacent observed elements in the spectrogram. Moreover, a new linear interpolation method using time and frequency together is presented. The CMU Sphinx III software is used in the experiments to test the performance of the linear interpolation reconstruction method. The experiments are done under different conditions such as different lengths of the window and different lengths of utterances. Speech corpus consists of 20 males and 20 females; each one has two different utterances are used in the experiments. As a result, 80% recognition accuracy is achieved with 25% SNR ratio.
Interpolation between multi-dimensional histograms using a new non-linear moment morphing method
Energy Technology Data Exchange (ETDEWEB)
Baak, M., E-mail: max.baak@cern.ch [CERN, CH-1211 Geneva 23 (Switzerland); Gadatsch, S., E-mail: stefan.gadatsch@nikhef.nl [Nikhef, PO Box 41882, 1009 DB Amsterdam (Netherlands); Harrington, R. [School of Physics and Astronomy, University of Edinburgh, Mayfield Road, Edinburgh, EH9 3JZ, Scotland (United Kingdom); Verkerke, W. [Nikhef, PO Box 41882, 1009 DB Amsterdam (Netherlands)
2015-01-21
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates are often required to model the impact of systematic uncertainties.
Interpolation between multi-dimensional histograms using a new non-linear moment morphing method
International Nuclear Information System (INIS)
Baak, M.; Gadatsch, S.; Harrington, R.; Verkerke, W.
2015-01-01
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates are often required to model the impact of systematic uncertainties
Interpolation between multi-dimensional histograms using a new non-linear moment morphing method
Baak, Max; Harrington, Robert; Verkerke, Wouter
2014-01-01
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates is often required to model the impact of systematic uncertainties.
Interpolation between multi-dimensional histograms using a new non-linear moment morphing method
Baak, Max; Harrington, Robert; Verkerke, Wouter
2015-01-01
A prescription is presented for the interpolation between multi-dimensional distribution templates based on one or multiple model parameters. The technique uses a linear combination of templates, each created using fixed values of the model's parameters and transformed according to a specific procedure, to model a non-linear dependency on model parameters and the dependency between them. By construction the technique scales well with the number of input templates used, which is a useful feature in modern day particle physics, where a large number of templates is often required to model the impact of systematic uncertainties.
Genetic design of interpolated non-linear controllers for linear plants
International Nuclear Information System (INIS)
Ajlouni, N.
2000-01-01
The techniques of genetic algorithms are proposed as a means of designing non-linear PID control systems. It is shown that the use of genetic algorithms for this purpose results in highly effective non-linear PID control systems. These results are illustrated by using genetic algorithms to design a non-linear PID control system and contrasting the results with an optimally tuned linear PID controller. (author)
The Canadian Precipitation Analysis (CaPA): Evaluation of the statistical interpolation scheme
Evans, Andrea; Rasmussen, Peter; Fortin, Vincent
2013-04-01
CaPA (Canadian Precipitation Analysis) is a data assimilation system which employs statistical interpolation to combine observed precipitation with gridded precipitation fields produced by Environment Canada's Global Environmental Multiscale (GEM) climate model into a final gridded precipitation analysis. Precipitation is important in many fields and applications, including agricultural water management projects, flood control programs, and hydroelectric power generation planning. Precipitation is a key input to hydrological models, and there is a desire to have access to the best available information about precipitation in time and space. The principal goal of CaPA is to produce this type of information. In order to perform the necessary statistical interpolation, CaPA requires the estimation of a semi-variogram. This semi-variogram is used to describe the spatial correlations between precipitation innovations, defined as the observed precipitation amounts minus the GEM forecasted amounts predicted at the observation locations. Currently, CaPA uses a single isotropic variogram across the entire analysis domain. The present project investigates the implications of this choice by first conducting a basic variographic analysis of precipitation innovation data across the Canadian prairies, with specific interest in identifying and quantifying potential anisotropy within the domain. This focus is further expanded by identifying the effect of storm type on the variogram. The ultimate goal of the variographic analysis is to develop improved semi-variograms for CaPA that better capture the spatial complexities of precipitation over the Canadian prairies. CaPA presently applies a Box-Cox data transformation to both the observations and the GEM data, prior to the calculation of the innovations. The data transformation is necessary to satisfy the normal distribution assumption, but introduces a significant bias. The second part of the investigation aims at devising a bias
Tracking sharp interface of two fluids by the CIP (cubic-interpolated propagation) scheme
International Nuclear Information System (INIS)
Yabe, T.; Xiao, F.
1993-01-01
A method to treat a sharp discontinuity by the density function is proposed. The surface of the density function is described by one grid throughout the calculation even when the surface is largely distorted. This description is made possible by the CIP method combined with variable transformation. This scheme is applied to the linear wave propagation in one- and two-dimensions. In the nonlinear case, the injection of heavier fluid into lighter fluid his calculated and the winding of mushroom structure is successfully treated by the density function. (author)
Directory of Open Access Journals (Sweden)
Pakhnutov I.A.
2017-04-01
Full Text Available the paper deals with iterative interpolation methods in forms of similar recursive procedures defined by a sort of simple functions (interpolation basis not necessarily real valued. These basic functions are kind of arbitrary type being defined just by wish and considerations of user. The studied interpolant construction shows virtue of versatility: it may be used in a wide range of vector spaces endowed with scalar product, no dimension restrictions, both in Euclidean and Hilbert spaces. The choice of basic interpolation functions is as wide as possible since it is subdued nonessential restrictions. The interpolation method considered in particular coincides with traditional polynomial interpolation (mimic of Lagrange method in real unidimensional case or rational, exponential etc. in other cases. The interpolation as iterative process, in fact, is fairly flexible and allows one procedure to change the type of interpolation, depending on the node number in a given set. Linear interpolation basis options (perhaps some nonlinear ones allow to interpolate in noncommutative spaces, such as spaces of nondegenerate matrices, interpolated data can also be relevant elements of vector spaces over arbitrary numeric field. By way of illustration, the author gives the examples of interpolation on the real plane, in the separable Hilbert space and the space of square matrices with vektorvalued source data.
ZZ POINT-2004, Linearly Interpolable ENDF/B-VI.8 Data for 13 Temperatures
International Nuclear Information System (INIS)
Cullen, Dermott E.
2004-01-01
A - Description or function: The ENDF/B data library, ENDF/B-VI, Release 8 was processed into the form of temperature dependent cross sections. The original evaluated data include cross sections represented in the form of a combination of resonance parameters and/or tabulated energy dependent cross sections, nominally at 0 Kelvin temperature. For use in applications, these ENDF/B-VI, Release 8 data were processed into the form of temperature dependent cross sections at eight temperatures between 0 and 2100 Kelvin, in steps of 300 Kelvin. It has also been processed to five astrophysics like temperatures, 1, 10, 100 eV, 1 and 10 keV. At each temperature the cross sections are tabulated and linearly interpolable in energy with a tolerance of 0.1 %. POINT2004 contains all of the evaluations in the ENDF/B-VI general purpose library, which contains evaluations for 328 materials (isotopes or naturally occurring elemental mixtures of isotopes). No special purpose ENDF/B-VI libraries, such as fission products, thermal scattering, photon interaction data are included. The majority of these evaluations are complete, in the sense that they include all cross sections over the energy range 10 e-5 eV to at least 20 MeV. B - Methods: The PREPRO2002 code system was used to process the ENDF/B data. Listed below are the steps, including the PREPRO2002 codes, which were used to process the data in the order in which the codes were run. 1) Linearly interpolable, tabulated cross sections (LINEAR); 2) Including the resonance contribution (RECENT); 3) Doppler broaden all cross sections to temperature (SIGMA1); 4) Check data, define redundant cross sections by summation (FIXUP)
Directory of Open Access Journals (Sweden)
Mateusz Szcześniak
2015-02-01
Full Text Available Ground-based precipitation data are still the dominant input type for hydrological models. Spatial variability in precipitation can be represented by spatially interpolating gauge data using various techniques. In this study, the effect of daily precipitation interpolation methods on discharge simulations using the semi-distributed SWAT (Soil and Water Assessment Tool model over a 30-year period is examined. The study was carried out in 11 meso-scale (119–3935 km2 sub-catchments lying in the Sulejów reservoir catchment in central Poland. Four methods were tested: the default SWAT method (Def based on the Nearest Neighbour technique, Thiessen Polygons (TP, Inverse Distance Weighted (IDW and Ordinary Kriging (OK. =The evaluation of methods was performed using a semi-automated calibration program SUFI-2 (Sequential Uncertainty Fitting Procedure Version 2 with two objective functions: Nash-Sutcliffe Efficiency (NSE and the adjusted R2 coefficient (bR2. The results show that: (1 the most complex OK method outperformed other methods in terms of NSE; and (2 OK, IDW, and TP outperformed Def in terms of bR2. The median difference in daily/monthly NSE between OK and Def/TP/IDW calculated across all catchments ranged between 0.05 and 0.15, while the median difference between TP/IDW/OK and Def ranged between 0.05 and 0.07. The differences between pairs of interpolation methods were, however, spatially variable and a part of this variability was attributed to catchment properties: catchments characterised by low station density and low coefficient of variation of daily flows experienced more pronounced improvement resulting from using interpolation methods. Methods providing higher precipitation estimates often resulted in a better model performance. The implication from this study is that appropriate consideration of spatial precipitation variability (often neglected by model users that can be achieved using relatively simple interpolation methods can
International Nuclear Information System (INIS)
Kemp, R.C.
1988-01-01
The use of the triple points of deuterium and xenon is investigated in some interpolation schemes for platinum resistance thermometers between 13.8 K and 273 K. The use of these triple points together is shown to lead to a large sensitivity to errors in the realization of the boiling point of water or the triple point of gallium and of the triple point of xenon for interpolated temperatures below 25 K. The behaviour of these interpolation schemes is presented as evidence that the large non-uniqueness observed in temperature scales between 84 K and 273 K is due in part to measurement errors at the boiling point of water. The use of the triple point of xenon and in interpolation scheme between 25 K and 273 K is shown to lead to a large sensitivity to calibration errors in the triple points of xenon and gallium between 25 K and 54 K. (orig.)
ZZ POINT-2007, linearly interpolable ENDF/B-VII.0 data for 14 temperatures
International Nuclear Information System (INIS)
Cullen, Dermott E.
2007-01-01
A - Description or function: The ENDF/B data library, ENDF/B-VII.0 was processed into the form of temperature dependent cross sections. The original evaluated data include cross sections represented in the form of a combination of resonance parameters and/or tabulated energy dependent cross sections, nominally at 0 Kelvin temperature. For use in applications, these ENDF/B-VII.0 data were processed into the form of temperature dependent cross sections at eight temperatures: 0, 300, 600, 900, 1200, 1500, 1800 and 2100 Kelvin. It has also been processed to six astrophysics like temperatures: 0.1, 1, 10, 100 eV, 1 and 10 keV. At each temperature the cross sections are tabulated and linearly interpolable in energy with a tolerance of 0.1 %. POINT 2007 contains all of the evaluations in the ENDF/B-VII general purpose library, which contains 78 new evaluations + 315 old ones: total 393 nuclides. It also includes 16 new elemental evaluations replaced by isotopic evaluations + 19 old ones. No special purpose ENDF/B-VII libraries, such as fission products, thermal scattering, photon interaction data are included. These evaluations include all cross sections over the energy range 10 e-5 eV to at least 20 MeV. The list of nuclides is indicated. B - Methods: The PREPRO 2007 code system was used to process the ENDF/B data. Listed below are the steps, including the PREPRO2007 codes, which were used to process the data in the order in which the codes were run. 1) Linearly interpolable, tabulated cross sections (LINEAR) 2) Including the resonance contribution (RECENT) 3) Doppler broaden all cross sections to temperature (SIGMA1) 4) Check data, define redundant cross sections by summation (FIXUP) 5) Update evaluation dictionary in MF/MT=1/451 (DICTIN) C - Restrictions: Due to recent changes in ENDF-6 Formats and Procedures only the latest version of the ENDF/B Pre-processing codes, namely PREPRO 2007, can be used to accurately process all current ENDF/B-VII evaluations. The use of
International Nuclear Information System (INIS)
Ducru, Pablo; Josey, Colin; Dibert, Karia; Sobes, Vladimir; Forget, Benoit; Smith, Kord
2017-01-01
This paper establishes a new family of methods to perform temperature interpolation of nuclear interactions cross sections, reaction rates, or cross sections times the energy. One of these quantities at temperature T is approximated as a linear combination of quantities at reference temperatures (T_j). The problem is formalized in a cross section independent fashion by considering the kernels of the different operators that convert cross section related quantities from a temperature T_0 to a higher temperature T — namely the Doppler broadening operation. Doppler broadening interpolation of nuclear cross sections is thus here performed by reconstructing the kernel of the operation at a given temperature T by means of linear combination of kernels at reference temperatures (T_j). The choice of the L_2 metric yields optimal linear interpolation coefficients in the form of the solutions of a linear algebraic system inversion. The optimization of the choice of reference temperatures (T_j) is then undertaken so as to best reconstruct, in the L∞ sense, the kernels over a given temperature range [T_m_i_n,T_m_a_x]. The performance of these kernel reconstruction methods is then assessed in light of previous temperature interpolation methods by testing them upon isotope "2"3"8U. Temperature-optimized free Doppler kernel reconstruction significantly outperforms all previous interpolation-based methods, achieving 0.1% relative error on temperature interpolation of "2"3"8U total cross section over the temperature range [300 K,3000 K] with only 9 reference temperatures.
A fast iterative scheme for the linearized Boltzmann equation
Wu, Lei; Zhang, Jun; Liu, Haihu; Zhang, Yonghao; Reese, Jason M.
2017-06-01
Iterative schemes to find steady-state solutions to the Boltzmann equation are efficient for highly rarefied gas flows, but can be very slow to converge in the near-continuum flow regime. In this paper, a synthetic iterative scheme is developed to speed up the solution of the linearized Boltzmann equation by penalizing the collision operator L into the form L = (L + Nδh) - Nδh, where δ is the gas rarefaction parameter, h is the velocity distribution function, and N is a tuning parameter controlling the convergence rate. The velocity distribution function is first solved by the conventional iterative scheme, then it is corrected such that the macroscopic flow velocity is governed by a diffusion-type equation that is asymptotic-preserving into the Navier-Stokes limit. The efficiency of this new scheme is assessed by calculating the eigenvalue of the iteration, as well as solving for Poiseuille and thermal transpiration flows. We find that the fastest convergence of our synthetic scheme for the linearized Boltzmann equation is achieved when Nδ is close to the average collision frequency. The synthetic iterative scheme is significantly faster than the conventional iterative scheme in both the transition and the near-continuum gas flow regimes. Moreover, due to its asymptotic-preserving properties, the synthetic iterative scheme does not need high spatial resolution in the near-continuum flow regime, which makes it even faster than the conventional iterative scheme. Using this synthetic scheme, with the fast spectral approximation of the linearized Boltzmann collision operator, Poiseuille and thermal transpiration flows between two parallel plates, through channels of circular/rectangular cross sections and various porous media are calculated over the whole range of gas rarefaction. Finally, the flow of a Ne-Ar gas mixture is solved based on the linearized Boltzmann equation with the Lennard-Jones intermolecular potential for the first time, and the difference
Comparison of BiLinearly Interpolated Subpixel Sensitivity Mapping and Pixel-Level Decorrelation
Challener, Ryan C.; Harrington, Joseph; Cubillos, Patricio; Foster, Andrew S.; Deming, Drake; WASP Consortium
2016-10-01
Exoplanet eclipse signals are weaker than the systematics present in the Spitzer Space Telescope's Infrared Array Camera (IRAC), and thus the correction method can significantly impact a measurement. BiLinearly Interpolated Subpixel Sensitivity (BLISS) mapping calculates the sensitivity of the detector on a subpixel grid and corrects the photometry for any sensitivity variations. Pixel-Level Decorrelation (PLD) removes the sensitivity variations by considering the relative intensities of the pixels around the source. We applied both methods to WASP-29b, a Saturn-sized planet with a mass of 0.24 ± 0.02 Jupiter masses and a radius of 0.84 ± 0.06 Jupiter radii, which we observed during eclipse twice with the 3.6 µm and once with the 4.5 µm channels of IRAC aboard Spitzer in 2010 and 2011 (programs 60003 and 70084, respectively). We compared the results of BLISS and PLD, and comment on each method's ability to remove time-correlated noise. WASP-29b exhibits a strong detection at 3.6 µm and no detection at 4.5 µm. Spitzer is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G.
Security of Linear Secret-Sharing Schemes Against Mass Surveillance
DEFF Research Database (Denmark)
Giacomelli, Irene; Olimid, Ruxandra; Ranellucci, Samuel
2015-01-01
by a proprietary code that the provider (“big brother”) could manipulate to covertly violate the privacy of the users (by implementing Algorithm-Substitution Attacks or ASAs). First, we formalize the security notion that expresses the goal of big brother and prove that for any linear secret-sharing scheme...... there exists an undetectable subversion of it that efficiently allows surveillance. Second, we formalize the security notion that assures that a sharing scheme is secure against ASAs and construct the first sharing scheme that meets this notion....
Pixel-Level Decorrelation and BiLinearly Interpolated Subpixel Sensitivity applied to WASP-29b
Challener, Ryan; Harrington, Joseph; Cubillos, Patricio; Blecic, Jasmina; Deming, Drake
2017-10-01
Measured exoplanet transit and eclipse depths can vary significantly depending on the methodology used, especially at the low S/N levels in Spitzer eclipses. BiLinearly Interpolated Subpixel Sensitivity (BLISS) models a physical, spatial effect, which is independent of any astrophysical effects. Pixel-Level Decorrelation (PLD) uses the relative variations in pixels near the target to correct for flux variations due to telescope motion. PLD is being widely applied to all Spitzer data without a thorough understanding of its behavior. It is a mathematical method derived from a Taylor expansion, and many of its parameters do not have a physical basis. PLD also relies heavily on binning the data to remove short time-scale variations, which can artifically smooth the data. We applied both methods to 4 eclipse observations of WASP-29b, a Saturn-sized planet, which was observed twice with the 3.6 µm and twice with the 4.5 µm channels of Spitzer's IRAC in 2010, 2011 and 2014 (programs 60003, 70084, and 10054, respectively). We compare the resulting eclipse depths and midpoints from each model, assess each method's ability to remove correlated noise, and discuss how to choose or combine the best data analysis methods. We also refined the orbit from eclipse timings, detecting a significant nonzero eccentricity, and we used our Bayesian Atmospheric Radiative Transfer (BART) code to retrieve the planet's atmosphere, which is consistent with a blackbody. Spitzer is operated by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. This work was supported by NASA Planetary Atmospheres grant NNX12AI69G and NASA Astrophysics Data Analysis Program grant NNX13AF38G.
Linear source approximation scheme for method of characteristics
International Nuclear Information System (INIS)
Tang Chuntao
2011-01-01
Method of characteristics (MOC) for solving neutron transport equation based on unstructured mesh has already become one of the fundamental methods for lattice calculation of nuclear design code system. However, most of MOC codes are developed with flat source approximation called step characteristics (SC) scheme, which is another basic assumption for MOC. A linear source (LS) characteristics scheme and its corresponding modification for negative source distribution were proposed. The OECD/NEA C5G7-MOX 2D benchmark and a self-defined BWR mini-core problem were employed to validate the new LS module of PEACH code. Numerical results indicate that the proposed LS scheme employs less memory and computational time compared with SC scheme at the same accuracy. (authors)
A revised ground-motion and intensity interpolation scheme for shakemap
Worden, C.B.; Wald, D.J.; Allen, T.I.; Lin, K.; Garcia, D.; Cua, G.
2010-01-01
We describe a weighted-average approach for incorporating various types of data (observed peak ground motions and intensities and estimates from groundmotion prediction equations) into the ShakeMap ground motion and intensity mapping framework. This approach represents a fundamental revision of our existing ShakeMap methodology. In addition, the increased availability of near-real-time macroseismic intensity data, the development of newrelationships between intensity and peak ground motions, and new relationships to directly predict intensity from earthquake source information have facilitated the inclusion of intensity measurements directly into ShakeMap computations. Our approach allows for the combination of (1) direct observations (ground-motion measurements or reported intensities), (2) observations converted from intensity to ground motion (or vice versa), and (3) estimated ground motions and intensities from prediction equations or numerical models. Critically, each of the aforementioned data types must include an estimate of its uncertainties, including those caused by scaling the influence of observations to surrounding grid points and those associated with estimates given an unknown fault geometry. The ShakeMap ground-motion and intensity estimates are an uncertainty-weighted combination of these various data and estimates. A natural by-product of this interpolation process is an estimate of total uncertainty at each point on the map, which can be vital for comprehensive inventory loss calculations. We perform a number of tests to validate this new methodology and find that it produces a substantial improvement in the accuracy of ground-motion predictions over empirical prediction equations alone.
An active interferometer-stabilization scheme with linear phase control
DEFF Research Database (Denmark)
Andresen, Esben Ravn; Krishnamachari, v v; Potma, E O
2006-01-01
We report a simple and robust computer-based active interferometer stabilization scheme which does not require modulation of the interfering beams and relies on an error signal which is linearly related to the optical path difference. In this setup, a non-collinearly propagating reference laser...... beam stabilizes the interference output of the laser light propagating collinearly through the interferometer. This stabilization scheme enables adjustable phase control with 20 ms switching times in the range from 0.02π radians to 6π radians at 632.8 nm....
Alconis, Jenalyn; Eco, Rodrigo; Mahar Francisco Lagmay, Alfredo; Lester Saddi, Ivan; Mongaya, Candeze; Figueroa, Kathleen Gay
2014-05-01
In response to the slew of disasters that devastates the Philippines on a regular basis, the national government put in place a program to address this problem. The Nationwide Operational Assessment of Hazards, or Project NOAH, consolidates the diverse scientific research being done and pushes the knowledge gained to the forefront of disaster risk reduction and management. Current activities of the project include installing rain gauges and water level sensors, conducting LIDAR surveys of critical river basins, geo-hazard mapping, and running information education campaigns. Approximately 700 automated weather stations and rain gauges installed in strategic locations in the Philippines hold the groundwork for the rainfall visualization system in the Project NOAH web portal at http://noah.dost.gov.ph. The system uses near real-time data from these stations installed in critical river basins. The sensors record the amount of rainfall in a particular area as point data updated every 10 to 15 minutes. The sensor sends the data to a central server either via GSM network or satellite data transfer for redundancy. The web portal displays the sensors as a placemarks layer on a map. When a placemark is clicked, it displays a graph of the rainfall data for the past 24 hours. The rainfall data is harvested by batch determined by a one-hour time frame. The program uses linear interpolation as the methodology implemented to visually represent a near real-time rainfall map. The algorithm allows very fast processing which is essential in near real-time systems. As more sensors are installed, precision is improved. This visualized dataset enables users to quickly discern where heavy rainfall is concentrated. It has proven invaluable on numerous occasions, such as last August 2013 when intense to torrential rains brought about by the enhanced Southwest Monsoon caused massive flooding in Metro Manila. Coupled with observations from Doppler imagery and water level sensors along the
International Nuclear Information System (INIS)
Chen, H.-H.; Chen, C.-S.; Lee, C.-I
2009-01-01
This paper investigates the synchronization of unidirectional and bidirectional coupled unified chaotic systems. A balanced coupling coefficient control method is presented for global asymptotic synchronization using the Lyapunov stability theorem and a minimum scheme with no constraints/constraints. By using the result of the above analysis, the balanced coupling coefficients are then designed to achieve the chaos synchronization of linearly coupled unified chaotic systems. The feasibility and effectiveness of the proposed chaos synchronization scheme are verified via numerical simulations.
Schulte, Friederike A; Lambers, Floor M; Mueller, Thomas L; Stauber, Martin; Müller, Ralph
2014-04-01
Time-lapsed in vivo micro-computed tomography is a powerful tool to analyse longitudinal changes in the bone micro-architecture. Registration can overcome problems associated with spatial misalignment between scans; however, it requires image interpolation which might affect the outcome of a subsequent bone morphometric analysis. The impact of the interpolation error itself, though, has not been quantified to date. Therefore, the purpose of this ex vivo study was to elaborate the effect of different interpolator schemes [nearest neighbour, tri-linear and B-spline (BSP)] on bone morphometric indices. None of the interpolator schemes led to significant differences between interpolated and non-interpolated images, with the lowest interpolation error found for BSPs (1.4%). Furthermore, depending on the interpolator, the processing order of registration, Gaussian filtration and binarisation played a role. Independent from the interpolator, the present findings suggest that the evaluation of bone morphometry should be done with images registered using greyscale information.
Improvements and validation of the linear surface characteristics scheme
International Nuclear Information System (INIS)
Santandrea, S.; Jaboulay, J.C.; Bellier, P.; Fevotte, F.; Golfier, H.
2009-01-01
In this paper we present the last improvements of the recently proposed linear surface (LS) characteristics scheme for unstructured meshes. First we introduce a new numerical tracking technique, specifically adapted to the LS method, which tailors transverse integration weights to take into account the geometrical discontinuities that appear along the pipe affected to every trajectory in classical characteristics schemes. Another development allows using the volumetric flux variation of the LS method to re-compute step-wise constant fluxes to be used in other parts of a computational scheme. This permits to take greater advantage of the higher precision of the LS method without necessarily conceiving specialized theories for all the modular functionalities of a spectral code such as APOLLO2. Moreover we present a multi-level domain decomposition method for solving the synthetic acceleration operator that is used to accelerate the free iterations for the LS method. We discuss all these new developments by illustrating some benchmarks results obtained with the LS method. This is done by detailed comparisons with Monte-Carlo calculations. In particular we show that the new method can be used not only as a reference tool, but also inside a suitable industrial calculation scheme
Design of a Control System for a Maglev Planar Motor Based on Two-Dimension Linear Interpolation
Directory of Open Access Journals (Sweden)
Feng Xing
2017-08-01
Full Text Available In order to realize the high speed and high-precision control of a maglev planar motor, a high-precision electromagnetic model is needed in the first place, which can also contribute to meeting the real-time running requirements. Traditionally, the electromagnetic model is based on analytical calculations. However, this neglects the model simplification and the manufacturing errors, which may bring certain errors to the model. Aiming to handle this inaccuracy, this paper proposes a novel design method for a maglev planar motor control system based on two-dimensional linear interpolation. First, the magnetic field is divided into several regions according to the symmetry of the Halbach magnetic array, and the uniform grid method is adopted to partition one of these regions. Second, targeting this region, it is possible to sample the electromagnetic forces and torques on each node of the grid and obtain the complete electromagnetic model in this region through the two-dimensional linear interpolation method. Third, the whole electromagnetic model of the maglev planar motor can be derived according to the symmetry of the magnetic field. Finally, the decoupling method and controller are designed according to this electromagnetic model, and thereafter, the control model can be established. The designed control system is demonstrated through simulations and experiments to feature better accuracy and meet the requirements of real-time control.
Novel method of interpolation and extrapolation of functions by a linear initial value problem
CSIR Research Space (South Africa)
Shatalov, M
2008-09-01
Full Text Available A novel method of function approximation using an initial value, linear, ordinary differential equation (ODE) is presented. The main advantage of this method is to obtain the approximation expressions in a closed form. This technique can be taught...
Optimal interpolation schemes to constrain pmPM2.5 in regional modeling over the United States
Sousan, Sinan Dhia Jameel
This thesis presents the use of data assimilation with optimal interpolation (OI) to develop atmospheric aerosol concentration estimates for the United States at high spatial and temporal resolutions. Concentration estimates are highly desirable for a wide range of applications, including visibility, climate, and human health. OI is a viable data assimilation method that can be used to improve Community Multiscale Air Quality (CMAQ) model fine particulate matter (PM2.5) estimates. PM2.5 is the mass of solid and liquid particles with diameters less than or equal to 2.5 µm suspended in the gas phase. OI was employed by combining model estimates with satellite and surface measurements. The satellite data assimilation combined 36 x 36 km aerosol concentrations from CMAQ with aerosol optical depth (AOD) measured by MODIS and AERONET over the continental United States for 2002. Posterior model concentrations generated by the OI algorithm were compared with surface PM2.5 measurements to evaluate a number of possible data assimilation parameters, including model error, observation error, and temporal averaging assumptions. Evaluation was conducted separately for six geographic U.S. regions in 2002. Variability in model error and MODIS biases limited the effectiveness of a single data assimilation system for the entire continental domain. The best combinations of four settings and three averaging schemes led to a domain-averaged improvement in fractional error from 1.2 to 0.97 and from 0.99 to 0.89 at respective IMPROVE and STN monitoring sites. For 38% of OI results, MODIS OI degraded the forward model skill due to biases and outliers in MODIS AOD. Surface data assimilation combined 36 × 36 km aerosol concentrations from the CMAQ model with surface PM2.5 measurements over the continental United States for 2002. The model error covariance matrix was constructed by using the observational method. The observation error covariance matrix included site representation that
Shape Preserving Interpolation Using C2 Rational Cubic Spline
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Samsul Ariffin Abdul Karim
2016-01-01
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.
A linear construction of perfect secret sharing schemes
Dijk, van M.; Santis, De A.
1995-01-01
In this paper, we generalize the vector space construction due to Brickell [5]. This generalization, introduced by Bertilsson [1], leads to perfect secret sharing schemes with rational information rates in which the secret can be computed efficiently by each qualified group. A one to one
A Note on Cubic Convolution Interpolation
Meijering, E.; Unser, M.
2003-01-01
We establish a link between classical osculatory interpolation and modern convolution-based interpolation and use it to show that two well-known cubic convolution schemes are formally equivalent to two osculatory interpolation schemes proposed in the actuarial literature about a century ago. We also discuss computational differences and give examples of other cubic interpolation schemes not previously studied in signal and image processing.
A Meshfree Quasi-Interpolation Method for Solving Burgers’ Equation
Directory of Open Access Journals (Sweden)
Mingzhu Li
2014-01-01
Full Text Available The main aim of this work is to consider a meshfree algorithm for solving Burgers’ equation with the quartic B-spline quasi-interpolation. Quasi-interpolation is very useful in the study of approximation theory and its applications, since it can yield solutions directly without the need to solve any linear system of equations and overcome the ill-conditioning problem resulting from using the B-spline as a global interpolant. The numerical scheme is presented, by using the derivative of the quasi-interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable. Compared to other numerical methods, the main advantages of our scheme are higher accuracy and lower computational complexity. Meanwhile, the algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.
Investigation on the MOC with a linear source approximation scheme in three-dimensional assembly
International Nuclear Information System (INIS)
Zhu, Chenglin; Cao, Xinrong
2014-01-01
Method of characteristics (MOC) for solving neutron transport equation has already become one of the fundamental methods for lattice calculation of nuclear design code system. At present, MOC has three schemes to deal with the neutron source of the transport equation: the flat source approximation of the step characteristics (SC) scheme, the diamond difference (DD) scheme and the linear source (LS) characteristics scheme. The MOC for SC scheme and DD scheme need large storage space and long computing time when they are used to calculate large-scale three-dimensional neutron transport problems. In this paper, a LS scheme and its correction for negative source distribution were developed and added to DRAGON code. This new scheme was compared with the SC scheme and DD scheme which had been applied in this code. As an open source code, DRAGON could solve three-dimensional assembly with MOC method. Detailed calculation is conducted on two-dimensional VVER-1000 assembly under three schemes of MOC. The numerical results indicate that coarse mesh could be used in the LS scheme with the same accuracy. And the LS scheme applied in DRAGON is effective and expected results are achieved. Then three-dimensional cell problem and VVER-1000 assembly are calculated with LS scheme and SC scheme. The results show that less memory and shorter computational time are employed in LS scheme compared with SC scheme. It is concluded that by using LS scheme, DRAGON is able to calculate large-scale three-dimensional problems with less storage space and shorter computing time
Muhamadiev, È rgash; Nazarov, Murtazo
2015-01-01
© 2014 Elsevier Inc. In this paper the interpolation inequality of Szepessy [12, Lemma 4.2] is revisited. The lower bound in the above reference is proven to be proportional to p^{-2}, where p is a polynomial degree, that goes fast to zero
Monotone piecewise bicubic interpolation
International Nuclear Information System (INIS)
Carlson, R.E.; Fritsch, F.N.
1985-01-01
In a 1980 paper the authors developed a univariate piecewise cubic interpolation algorithm which produces a monotone interpolant to monotone data. This paper is an extension of those results to monotone script C 1 piecewise bicubic interpolation to data on a rectangular mesh. Such an interpolant is determined by the first partial derivatives and first mixed partial (twist) at the mesh points. Necessary and sufficient conditions on these derivatives are derived such that the resulting bicubic polynomial is monotone on a single rectangular element. These conditions are then simplified to a set of sufficient conditions for monotonicity. The latter are translated to a system of linear inequalities, which form the basis for a monotone piecewise bicubic interpolation algorithm. 4 references, 6 figures, 2 tables
Optimized Quasi-Interpolators for Image Reconstruction.
Sacht, Leonardo; Nehab, Diego
2015-12-01
We propose new quasi-interpolators for the continuous reconstruction of sampled images, combining a narrowly supported piecewise-polynomial kernel and an efficient digital filter. In other words, our quasi-interpolators fit within the generalized sampling framework and are straightforward to use. We go against standard practice and optimize for approximation quality over the entire Nyquist range, rather than focusing exclusively on the asymptotic behavior as the sample spacing goes to zero. In contrast to previous work, we jointly optimize with respect to all degrees of freedom available in both the kernel and the digital filter. We consider linear, quadratic, and cubic schemes, offering different tradeoffs between quality and computational cost. Experiments with compounded rotations and translations over a range of input images confirm that, due to the additional degrees of freedom and the more realistic objective function, our new quasi-interpolators perform better than the state of the art, at a similar computational cost.
A High-Accuracy Linear Conservative Difference Scheme for Rosenau-RLW Equation
Directory of Open Access Journals (Sweden)
Jinsong Hu
2013-01-01
Full Text Available We study the initial-boundary value problem for Rosenau-RLW equation. We propose a three-level linear finite difference scheme, which has the theoretical accuracy of Oτ2+h4. The scheme simulates two conservative properties of original problem well. The existence, uniqueness of difference solution, and a priori estimates in infinite norm are obtained. Furthermore, we analyze the convergence and stability of the scheme by energy method. At last, numerical experiments demonstrate the theoretical results.
An implicit iterative scheme for solving large systems of linear equations
International Nuclear Information System (INIS)
Barry, J.M.; Pollard, J.P.
1986-12-01
An implicit iterative scheme for the solution of large systems of linear equations arising from neutron diffusion studies is presented. The method is applied to three-dimensional reactor studies and its performance is compared with alternative iterative approaches
Kent, James; Holdaway, Daniel
2015-01-01
A number of geophysical applications require the use of the linearized version of the full model. One such example is in numerical weather prediction, where the tangent linear and adjoint versions of the atmospheric model are required for the 4DVAR inverse problem. The part of the model that represents the resolved scale processes of the atmosphere is known as the dynamical core. Advection, or transport, is performed by the dynamical core. It is a central process in many geophysical applications and is a process that often has a quasi-linear underlying behavior. However, over the decades since the advent of numerical modelling, significant effort has gone into developing many flavors of high-order, shape preserving, nonoscillatory, positive definite advection schemes. These schemes are excellent in terms of transporting the quantities of interest in the dynamical core, but they introduce nonlinearity through the use of nonlinear limiters. The linearity of the transport schemes used in Goddard Earth Observing System version 5 (GEOS-5), as well as a number of other schemes, is analyzed using a simple 1D setup. The linearized version of GEOS-5 is then tested using a linear third order scheme in the tangent linear version.
Muhamadiev, Èrgash
2015-03-01
© 2014 Elsevier Inc. In this paper the interpolation inequality of Szepessy [12, Lemma 4.2] is revisited. The lower bound in the above reference is proven to be proportional to p^{-2}, where p is a polynomial degree, that goes fast to zero as p increases. We prove that the lower bound is proportional to ln^{2} p which is an increasing function. Moreover, we prove that this estimate is sharp.
Directory of Open Access Journals (Sweden)
Peng Jiang
2013-01-01
Full Text Available The authors attempt to construct the exact finite-difference schemes for linear stochastic differential equations with constant coefficients. The explicit solutions to Itô and Stratonovich linear stochastic differential equations with constant coefficients are adopted with the view of providing exact finite-difference schemes to solve them. In particular, the authors utilize the exact finite-difference schemes of Stratonovich type linear stochastic differential equations to solve the Kubo oscillator that is widely used in physics. Further, the authors prove that the exact finite-difference schemes can preserve the symplectic structure and first integral of the Kubo oscillator. The authors also use numerical examples to prove the validity of the numerical methods proposed in this paper.
Stein, A.
1991-01-01
The theory and practical application of techniques of statistical interpolation are studied in this thesis, and new developments in multivariate spatial interpolation and the design of sampling plans are discussed. Several applications to studies in soil science are
Analysis of ECT Synchronization Performance Based on Different Interpolation Methods
Directory of Open Access Journals (Sweden)
Yang Zhixin
2014-01-01
Full Text Available There are two synchronization methods of electronic transformer in IEC60044-8 standard: impulsive synchronization and interpolation. When the impulsive synchronization method is inapplicability, the data synchronization of electronic transformer can be realized by using the interpolation method. The typical interpolation methods are piecewise linear interpolation, quadratic interpolation, cubic spline interpolation and so on. In this paper, the influences of piecewise linear interpolation, quadratic interpolation and cubic spline interpolation for the data synchronization of electronic transformer are computed, then the computational complexity, the synchronization precision, the reliability, the application range of different interpolation methods are analyzed and compared, which can serve as guide studies for practical applications.
Acceleration of step and linear discontinuous schemes for the method of characteristics in DRAGON5
Directory of Open Access Journals (Sweden)
Alain Hébert
2017-09-01
Full Text Available The applicability of the algebraic collapsing acceleration (ACA technique to the method of characteristics (MOC in cases with scattering anisotropy and/or linear sources was investigated. Previously, the ACA was proven successful in cases with isotropic scattering and uniform (step sources. A presentation is first made of the MOC implementation, available in the DRAGON5 code. Two categories of schemes are available for integrating the propagation equations: (1 the first category is based on exact integration and leads to the classical step characteristics (SC and linear discontinuous characteristics (LDC schemes and (2 the second category leads to diamond differencing schemes of various orders in space. The acceleration of these MOC schemes using a combination of the generalized minimal residual [GMRES(m] method preconditioned with the ACA technique was focused on. Numerical results are provided for a two-dimensional (2D eight-symmetry pressurized water reactor (PWR assembly mockup in the context of the DRAGON5 code.
Interpolation in Spaces of Functions
Directory of Open Access Journals (Sweden)
K. Mosaleheh
2006-03-01
Full Text Available In this paper we consider the interpolation by certain functions such as trigonometric and rational functions for finite dimensional linear space X. Then we extend this to infinite dimensional linear spaces
Linear and nonlinear schemes applied to pitch control of wind turbines.
Geng, Hua; Yang, Geng
2014-01-01
Linear controllers have been employed in industrial applications for many years, but sometimes they are noneffective on the system with nonlinear characteristics. This paper discusses the structure, performance, implementation cost, advantages, and disadvantages of different linear and nonlinear schemes applied to the pitch control of the wind energy conversion systems (WECSs). The linear controller has the simplest structure and is easily understood by the engineers and thus is widely accepted by the industry. In contrast, nonlinear schemes are more complicated, but they can provide better performance. Although nonlinear algorithms can be implemented in a powerful digital processor nowadays, they need time to be accepted by the industry and their reliability needs to be verified in the commercial products. More information about the system nonlinear feature is helpful to simplify the controller design. However, nonlinear schemes independent of the system model are more robust to the uncertainties or deviations of the system parameters.
An online re-linearization scheme suited for Model Predictive and Linear Quadratic Control
DEFF Research Database (Denmark)
Henriksen, Lars Christian; Poulsen, Niels Kjølstad
This technical note documents the equations for primal-dual interior-point quadratic programming problem solver used for MPC. The algorithm exploits the special structure of the MPC problem and is able to reduce the computational burden such that the computational burden scales with prediction...... horizon length in a linear way rather than cubic, which would be the case if the structure was not exploited. It is also shown how models used for design of model-based controllers, e.g. linear quadratic and model predictive, can be linearized both at equilibrium and non-equilibrium points, making...
International Nuclear Information System (INIS)
Silva, Filipe da; Pinto, Martin Campos; Després, Bruno; Heuraux, Stéphane
2015-01-01
This work analyzes the stability of the Yee scheme for non-stationary Maxwell's equations coupled with a linear current model with density fluctuations. We show that the usual procedure may yield unstable scheme for physical situations that correspond to strongly magnetized plasmas in X-mode (TE) polarization. We propose to use first order clustered discretization of the vectorial product that gives back a stable coupling. We validate the schemes on some test cases representative of direct numerical simulations of X-mode in a magnetic fusion plasma including turbulence
Image Interpolation with Contour Stencils
Pascal Getreuer
2011-01-01
Image interpolation is the problem of increasing the resolution of an image. Linear methods must compromise between artifacts like jagged edges, blurring, and overshoot (halo) artifacts. More recent works consider nonlinear methods to improve interpolation of edges and textures. In this paper we apply contour stencils for estimating the image contours based on total variation along curves and then use this estimation to construct a fast edge-adaptive interpolation.
Lorenzi, Juan M.; Stecher, Thomas; Reuter, Karsten; Matera, Sebastian
2017-10-01
Many problems in computational materials science and chemistry require the evaluation of expensive functions with locally rapid changes, such as the turn-over frequency of first principles kinetic Monte Carlo models for heterogeneous catalysis. Because of the high computational cost, it is often desirable to replace the original with a surrogate model, e.g., for use in coupled multiscale simulations. The construction of surrogates becomes particularly challenging in high-dimensions. Here, we present a novel version of the modified Shepard interpolation method which can overcome the curse of dimensionality for such functions to give faithful reconstructions even from very modest numbers of function evaluations. The introduction of local metrics allows us to take advantage of the fact that, on a local scale, rapid variation often occurs only across a small number of directions. Furthermore, we use local error estimates to weigh different local approximations, which helps avoid artificial oscillations. Finally, we test our approach on a number of challenging analytic functions as well as a realistic kinetic Monte Carlo model. Our method not only outperforms existing isotropic metric Shepard methods but also state-of-the-art Gaussian process regression.
Multiscale empirical interpolation for solving nonlinear PDEs
Calo, Victor M.
2014-12-01
In this paper, we propose a multiscale empirical interpolation method for solving nonlinear multiscale partial differential equations. The proposed method combines empirical interpolation techniques and local multiscale methods, such as the Generalized Multiscale Finite Element Method (GMsFEM). To solve nonlinear equations, the GMsFEM is used to represent the solution on a coarse grid with multiscale basis functions computed offline. Computing the GMsFEM solution involves calculating the system residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully-resolved fine scale one. The empirical interpolation method uses basis functions which are built by sampling the nonlinear function we want to approximate a limited number of times. The coefficients needed for this approximation are computed in the offline stage by inverting an inexpensive linear system. The proposed multiscale empirical interpolation techniques: (1) divide computing the nonlinear function into coarse regions; (2) evaluate contributions of nonlinear functions in each coarse region taking advantage of a reduced-order representation of the solution; and (3) introduce multiscale proper-orthogonal-decomposition techniques to find appropriate interpolation vectors. We demonstrate the effectiveness of the proposed methods on several nonlinear multiscale PDEs that are solved with Newton\\'s methods and fully-implicit time marching schemes. Our numerical results show that the proposed methods provide a robust framework for solving nonlinear multiscale PDEs on a coarse grid with bounded error and significant computational cost reduction.
Transfinite C2 interpolant over triangles
International Nuclear Information System (INIS)
Alfeld, P.; Barnhill, R.E.
1984-01-01
A transfinite C 2 interpolant on a general triangle is created. The required data are essentially C 2 , no compatibility conditions arise, and the precision set includes all polynomials of degree less than or equal to eight. The symbol manipulation language REDUCE is used to derive the scheme. The scheme is discretized to two different finite dimensional C 2 interpolants in an appendix
Lunardi, Alessandra
2018-01-01
This book is the third edition of the 1999 lecture notes of the courses on interpolation theory that the author delivered at the Scuola Normale in 1998 and 1999. In the mathematical literature there are many good books on the subject, but none of them is very elementary, and in many cases the basic principles are hidden below great generality. In this book the principles of interpolation theory are illustrated aiming at simplification rather than at generality. The abstract theory is reduced as far as possible, and many examples and applications are given, especially to operator theory and to regularity in partial differential equations. Moreover the treatment is self-contained, the only prerequisite being the knowledge of basic functional analysis.
Holdaway, Daniel; Kent, James
2015-01-01
The linearity of a selection of common advection schemes is tested and examined with a view to their use in the tangent linear and adjoint versions of an atmospheric general circulation model. The schemes are tested within a simple offline one-dimensional periodic domain as well as using a simplified and complete configuration of the linearised version of NASA's Goddard Earth Observing System version 5 (GEOS-5). All schemes which prevent the development of negative values and preserve the shape of the solution are confirmed to have nonlinear behaviour. The piecewise parabolic method (PPM) with certain flux limiters, including that used by default in GEOS-5, is found to support linear growth near the shocks. This property can cause the rapid development of unrealistically large perturbations within the tangent linear and adjoint models. It is shown that these schemes with flux limiters should not be used within the linearised version of a transport scheme. The results from tests using GEOS-5 show that the current default scheme (a version of PPM) is not suitable for the tangent linear and adjoint model, and that using a linear third-order scheme for the linearised model produces better behaviour. Using the third-order scheme for the linearised model improves the correlations between the linear and non-linear perturbation trajectories for cloud liquid water and cloud liquid ice in GEOS-5.
A positron beam for the linear collider scheme of a B-meson factory
International Nuclear Information System (INIS)
Chehab, R.
1988-02-01
An approach for a conventional positron source intended to a BantiB linear collider scheme is here given. Optical matching devices between the source and the accelerator are considered and some comparisons are made regarding the maximum acceptance and the positron beam qualities. Focusing in the preaccelerator and in the main linac are also considered. Heating and radiation problems which may introduce severe limitations are only partly examined
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios
2013-07-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
An implicit meshless scheme for the solution of transient non-linear Poisson-type equations
Bourantas, Georgios; Burganos, Vasilis N.
2013-01-01
A meshfree point collocation method is used for the numerical simulation of both transient and steady state non-linear Poisson-type partial differential equations. Particular emphasis is placed on the application of the linearization method with special attention to the lagging of coefficients method and the Newton linearization method. The localized form of the Moving Least Squares (MLS) approximation is employed for the construction of the shape functions, in conjunction with the general framework of the point collocation method. Computations are performed for regular nodal distributions, stressing the positivity conditions that make the resulting system stable and convergent. The accuracy and the stability of the proposed scheme are demonstrated through representative and well-established benchmark problems. © 2013 Elsevier Ltd.
Belazi, Akram; Abd El-Latif, Ahmed A.; Diaconu, Adrian-Viorel; Rhouma, Rhouma; Belghith, Safya
2017-01-01
In this paper, a new chaos-based partial image encryption scheme based on Substitution-boxes (S-box) constructed by chaotic system and Linear Fractional Transform (LFT) is proposed. It encrypts only the requisite parts of the sensitive information in Lifting-Wavelet Transform (LWT) frequency domain based on hybrid of chaotic maps and a new S-box. In the proposed encryption scheme, the characteristics of confusion and diffusion are accomplished in three phases: block permutation, substitution, and diffusion. Then, we used dynamic keys instead of fixed keys used in other approaches, to control the encryption process and make any attack impossible. The new S-box was constructed by mixing of chaotic map and LFT to insure the high confidentiality in the inner encryption of the proposed approach. In addition, the hybrid compound of S-box and chaotic systems strengthened the whole encryption performance and enlarged the key space required to resist the brute force attacks. Extensive experiments were conducted to evaluate the security and efficiency of the proposed approach. In comparison with previous schemes, the proposed cryptosystem scheme showed high performances and great potential for prominent prevalence in cryptographic applications.
Edge-detect interpolation for direct digital periapical images
International Nuclear Information System (INIS)
Song, Nam Kyu; Koh, Kwang Joon
1998-01-01
The purpose of this study was to aid in the use of the digital images by edge-detect interpolation for direct digital periapical images using edge-deted interpolation. This study was performed by image processing of 20 digital periapical images; pixel replication, linear non-interpolation, linear interpolation, and edge-sensitive interpolation. The obtained results were as follows ; 1. Pixel replication showed blocking artifact and serious image distortion. 2. Linear interpolation showed smoothing effect on the edge. 3. Edge-sensitive interpolation overcame the smoothing effect on the edge and showed better image.
Energy Technology Data Exchange (ETDEWEB)
C. Tennant, S.V. Benson, D. Douglas, P. Evtushenko, R.A. Legg
2011-09-01
We describe an electron bunch compression scheme suitable for use in a light source driven by a superconducting radio frequency (SRF) linac. The key feature is the use of a recirculating linac to perform the initial bunch compression. Phasing of the second pass beam through the linac is chosen to de-chirp the electron bunch prior to acceleration to the final energy in an SRF linac ('afterburner'). The final bunch compression is then done at maximum energy. This scheme has the potential to circumvent some of the most technically challenging aspects of current longitudinal matches; namely transporting a fully compressed, high peak current electron bunch through an extended SRF environment, the need for a RF harmonic linearizer and the need for a laser heater. Additional benefits include a substantial savings in capital and operational costs by efficiently using the available SRF gradient.
International Nuclear Information System (INIS)
Clarisse, J.M.
2007-01-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
Linear triangular optimization technique and pricing scheme in residential energy management systems
Anees, Amir; Hussain, Iqtadar; AlKhaldi, Ali Hussain; Aslam, Muhammad
2018-06-01
This paper presents a new linear optimization algorithm for power scheduling of electric appliances. The proposed system is applied in a smart home community, in which community controller acts as a virtual distribution company for the end consumers. We also present a pricing scheme between community controller and its residential users based on real-time pricing and likely block rates. The results of the proposed optimization algorithm demonstrate that by applying the anticipated technique, not only end users can minimise the consumption cost, but it can also reduce the power peak to an average ratio which will be beneficial for the utilities as well.
Interpolation for de-Dopplerisation
Graham, W. R.
2018-05-01
'De-Dopplerisation' is one aspect of a problem frequently encountered in experimental acoustics: deducing an emitted source signal from received data. It is necessary when source and receiver are in relative motion, and requires interpolation of the measured signal. This introduces error. In acoustics, typical current practice is to employ linear interpolation and reduce error by over-sampling. In other applications, more advanced approaches with better performance have been developed. Associated with this work is a large body of theoretical analysis, much of which is highly specialised. Nonetheless, a simple and compact performance metric is available: the Fourier transform of the 'kernel' function underlying the interpolation method. Furthermore, in the acoustics context, it is a more appropriate indicator than other, more abstract, candidates. On this basis, interpolators from three families previously identified as promising - - piecewise-polynomial, windowed-sinc, and B-spline-based - - are compared. The results show that significant improvements over linear interpolation can straightforwardly be obtained. The recommended approach is B-spline-based interpolation, which performs best irrespective of accuracy specification. Its only drawback is a pre-filtering requirement, which represents an additional implementation cost compared to other methods. If this cost is unacceptable, and aliasing errors (on re-sampling) up to approximately 1% can be tolerated, a family of piecewise-cubic interpolators provides the best alternative.
International Nuclear Information System (INIS)
VanMeter, N. M.; Lougovski, P.; Dowling, Jonathan P.; Uskov, D. B.; Kieling, K.; Eisert, J.
2007-01-01
We introduce schemes for linear-optical quantum state generation. A quantum state generator is a device that prepares a desired quantum state using product inputs from photon sources, linear-optical networks, and postselection using photon counters. We show that this device can be concisely described in terms of polynomial equations and unitary constraints. We illustrate the power of this language by applying the Groebner-basis technique along with the notion of vacuum extensions to solve the problem of how to construct a quantum state generator analytically for any desired state, and use methods of convex optimization to identify bounds to success probabilities. In particular, we disprove a conjecture concerning the preparation of the maximally path-entangled |n,0>+|0,n> (NOON) state by providing a counterexample using these methods, and we derive a new upper bound on the resources required for NOON-state generation
Spatiotemporal Interpolation Methods for Solar Event Trajectories
Filali Boubrahimi, Soukaina; Aydin, Berkay; Schuh, Michael A.; Kempton, Dustin; Angryk, Rafal A.; Ma, Ruizhe
2018-05-01
This paper introduces four spatiotemporal interpolation methods that enrich complex, evolving region trajectories that are reported from a variety of ground-based and space-based solar observatories every day. Our interpolation module takes an existing solar event trajectory as its input and generates an enriched trajectory with any number of additional time–geometry pairs created by the most appropriate method. To this end, we designed four different interpolation techniques: MBR-Interpolation (Minimum Bounding Rectangle Interpolation), CP-Interpolation (Complex Polygon Interpolation), FI-Interpolation (Filament Polygon Interpolation), and Areal-Interpolation, which are presented here in detail. These techniques leverage k-means clustering, centroid shape signature representation, dynamic time warping, linear interpolation, and shape buffering to generate the additional polygons of an enriched trajectory. Using ground-truth objects, interpolation effectiveness is evaluated through a variety of measures based on several important characteristics that include spatial distance, area overlap, and shape (boundary) similarity. To our knowledge, this is the first research effort of this kind that attempts to address the broad problem of spatiotemporal interpolation of solar event trajectories. We conclude with a brief outline of future research directions and opportunities for related work in this area.
International Nuclear Information System (INIS)
Franzè, Giuseppe; Lucia, Walter; Tedesco, Francesco
2014-01-01
This paper proposes a Model Predictive Control (MPC) strategy to address regulation problems for constrained polytopic Linear Parameter Varying (LPV) systems subject to input and state constraints in which both plant measurements and command signals in the loop are sent through communication channels subject to time-varying delays (Networked Control System (NCS)). The results here proposed represent a significant extension to the LPV framework of a recent Receding Horizon Control (RHC) scheme developed for the so-called robust case. By exploiting the parameter availability, the pre-computed sequences of one- step controllable sets inner approximations are less conservative than the robust counterpart. The resulting framework guarantees asymptotic stability and constraints fulfilment regardless of plant uncertainties and time-delay occurrences. Finally, experimental results on a laboratory two-tank test-bed show the effectiveness of the proposed approach
Adaptive Digital Predistortion Schemes to Linearize RF Power Amplifiers with Memory Effects
Institute of Scientific and Technical Information of China (English)
ZHANG Peng; WU Si-liang; ZHANG Qin
2008-01-01
To compensate for nonlinear distortion introduced by RF power amplifiers (PAs) with memory effects, two correlated models, namely an extended memory polynomial (EMP) model and a memory lookup table (LUT) model, are proposed for predistorter design. Two adaptive digital predistortion (ADPD) schemes with indirect learning architecture are presented. One adopts the EMP model and the recursive least square (RLS) algorithm, and the other utilizes the memory LUT model and the least mean square (LMS) algorithm. Simulation results demonstrate that the EMP-based ADPD yields the best linearization performance in terms of suppressing spectral regrowth. It is also shown that the ADPD based on memory LUT makes optimum tradeoff between performance and computational complexity.
An algebraic approach to linear-optical schemes for deterministic quantum computing
International Nuclear Information System (INIS)
Aniello, Paolo; Cagli, Ruben Coen
2005-01-01
Linear-optical passive (LOP) devices and photon counters are sufficient to implement universal quantum computation with single photons, and particular schemes have already been proposed. In this paper we discuss the link between the algebraic structure of LOP transformations and quantum computing. We first show how to decompose the Fock space of N optical modes in finite-dimensional subspaces that are suitable for encoding strings of qubits and invariant under LOP transformations (these subspaces are related to the spaces of irreducible unitary representations of U (N). Next we show how to design in algorithmic fashion LOP circuits which implement any quantum circuit deterministically. We also present some simple examples, such as the circuits implementing a cNOT gate and a Bell state generator/analyser
Interpolation functors and interpolation spaces
Brudnyi, Yu A
1991-01-01
The theory of interpolation spaces has its origin in the classical work of Riesz and Marcinkiewicz but had its first flowering in the years around 1960 with the pioneering work of Aronszajn, Calderón, Gagliardo, Krein, Lions and a few others. It is interesting to note that what originally triggered off this avalanche were concrete problems in the theory of elliptic boundary value problems related to the scale of Sobolev spaces. Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. Further development in the 1970s and 1980s included the solution by the authors of this book of one of the outstanding questions in the theory of the real method, the K-divisibility problem. In a way, this book harvests the r...
Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation
Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua
2018-06-01
Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.
Smooth Phase Interpolated Keying
Borah, Deva K.
2007-01-01
Smooth phase interpolated keying (SPIK) is an improved method of computing smooth phase-modulation waveforms for radio communication systems that convey digital information. SPIK is applicable to a variety of phase-shift-keying (PSK) modulation schemes, including quaternary PSK (QPSK), octonary PSK (8PSK), and 16PSK. In comparison with a related prior method, SPIK offers advantages of better performance and less complexity of implementation. In a PSK scheme, the underlying information waveform that one seeks to convey consists of discrete rectangular steps, but the spectral width of such a waveform is excessive for practical radio communication. Therefore, the problem is to smooth the step phase waveform in such a manner as to maintain power and bandwidth efficiency without incurring an unacceptably large error rate and without introducing undesired variations in the amplitude of the affected radio signal. Although the ideal constellation of PSK phasor points does not cause amplitude variations, filtering of the modulation waveform (in which, typically, a rectangular pulse is converted to a square-root raised cosine pulse) causes amplitude fluctuations. If a power-efficient nonlinear amplifier is used in the radio communication system, the fluctuating-amplitude signal can undergo significant spectral regrowth, thus compromising the bandwidth efficiency of the system. In the related prior method, one seeks to solve the problem in a procedure that comprises two major steps: phase-value generation and phase interpolation. SPIK follows the two-step approach of the related prior method, but the details of the steps are different. In the phase-value-generation step, the phase values of symbols in the PSK constellation are determined by a phase function that is said to be maximally smooth and that is chosen to minimize the spectral spread of the modulated signal. In this step, the constellation is divided into two groups by assigning, to information symbols, phase values
Directory of Open Access Journals (Sweden)
Huaiqing Zhang
2014-01-01
Full Text Available The spectral leakage has a harmful effect on the accuracy of harmonic analysis for asynchronous sampling. This paper proposed a time quasi-synchronous sampling algorithm which is based on radial basis function (RBF interpolation. Firstly, a fundamental period is evaluated by a zero-crossing technique with fourth-order Newton’s interpolation, and then, the sampling sequence is reproduced by the RBF interpolation. Finally, the harmonic parameters can be calculated by FFT on the synchronization of sampling data. Simulation results showed that the proposed algorithm has high accuracy in measuring distorted and noisy signals. Compared to the local approximation schemes as linear, quadric, and fourth-order Newton interpolations, the RBF is a global approximation method which can acquire more accurate results while the time-consuming is about the same as Newton’s.
Relevance of sampling schemes in light of Ruelle's linear response theory
International Nuclear Information System (INIS)
Lucarini, Valerio; Wouters, Jeroen; Faranda, Davide; Kuna, Tobias
2012-01-01
We reconsider the theory of the linear response of non-equilibrium steady states to perturbations. We first show that using a general functional decomposition for space–time dependent forcings, we can define elementary susceptibilities that allow us to construct the linear response of the system to general perturbations. Starting from the definition of SRB measure, we then study the consequence of taking different sampling schemes for analysing the response of the system. We show that only a specific choice of the time horizon for evaluating the response of the system to a general time-dependent perturbation allows us to obtain the formula first presented by Ruelle. We also discuss the special case of periodic perturbations, showing that when they are taken into consideration the sampling can be fine-tuned to make the definition of the correct time horizon immaterial. Finally, we discuss the implications of our results in terms of strategies for analysing the outputs of numerical experiments by providing a critical review of a formula proposed by Reick
National Research Council Canada - National Science Library
Ingel, R
1999-01-01
... (which require derivative information) interpolation functions as well as standard Lagrangian functions, which can be linear, quadratic or cubic, have been used to construct the interpolation windows...
Directory of Open Access Journals (Sweden)
Shahid Hasnain
2017-07-01
Full Text Available This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman
2017-07-01
This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.
Woźniak, M.
2016-06-02
We study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme with a linearized right-hand side operator. It was applied in solving the Cahn-Hilliard parabolic equation with a nonlinear, fourth-order elliptic part. The second order of the approximation along the time variable was proven. Moreover, the good scalability of the software based on this scheme was confirmed during simulations. We verify the proposed time integration scheme by monitoring the Ginzburg-Landau free energy. The numerical simulations are performed by using a parallel multi-frontal direct solver executed over STAMPEDE Linux cluster. Its scalability was compared to the results of the three direct solvers, including MUMPS, SuperLU and PaSTiX.
Midgley, S M
2004-01-21
A novel parameterization of x-ray interaction cross-sections is developed, and employed to describe the x-ray linear attenuation coefficient and mass energy absorption coefficient for both elements and mixtures. The new parameterization scheme addresses the Z-dependence of elemental cross-sections (per electron) using a simple function of atomic number, Z. This obviates the need for a complicated mathematical formalism. Energy dependent coefficients describe the Z-direction curvature of the cross-sections. The composition dependent quantities are the electron density and statistical moments describing the elemental distribution. We show that it is possible to describe elemental cross-sections for the entire periodic table and at energies above the K-edge (from 6 keV to 125 MeV), with an accuracy of better than 2% using a parameterization containing not more than five coefficients. For the biologically important elements 1 coefficients. At higher energies, the parameterization uses fewer coefficients with only two coefficients needed at megavoltage energies.
Stereo matching and view interpolation based on image domain triangulation.
Fickel, Guilherme Pinto; Jung, Claudio R; Malzbender, Tom; Samadani, Ramin; Culbertson, Bruce
2013-09-01
This paper presents a new approach for stereo matching and view interpolation problems based on triangular tessellations suitable for a linear array of rectified cameras. The domain of the reference image is initially partitioned into triangular regions using edge and scale information, aiming to place vertices along image edges and increase the number of triangles in textured regions. A region-based matching algorithm is then used to find an initial disparity for each triangle, and a refinement stage is applied to change the disparity at the vertices of the triangles, generating a piecewise linear disparity map. A simple post-processing procedure is applied to connect triangles with similar disparities generating a full 3D mesh related to each camera (view), which are used to generate new synthesized views along the linear camera array. With the proposed framework, view interpolation reduces to the trivial task of rendering polygonal meshes, which can be done very fast, particularly when GPUs are employed. Furthermore, the generated views are hole-free, unlike most point-based view interpolation schemes that require some kind of post-processing procedures to fill holes.
B. Koren (Barry); M.R. Lewis; E.H. van Brummelen (Harald); B. van Leer
2001-01-01
textabstractA finite-volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities. The novel ingredient in the method is a two-fluid linearized Godunov scheme, allowing for flux computations in case of different fluids (e.g., water and
International Nuclear Information System (INIS)
Mieussens, Luc
2013-01-01
The unified gas kinetic scheme (UGKS) of K. Xu et al. (2010) [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme
I. Kuba; J. Zavacky; J. Mihalik
1995-01-01
This paper presents the use of B spline functions in various digital signal processing applications. The theory of one-dimensional B spline interpolation is briefly reviewed, followed by its extending to two dimensions. After presenting of one and two dimensional spline interpolation, the algorithms of image interpolation and resolution increasing were proposed. Finally, experimental results of computer simulations are presented.
Probabilistic teleportation scheme of two-mode entangled photon states by using linear optic element
Institute of Scientific and Technical Information of China (English)
XIANG Shao-hua
2003-01-01
A scheme for teleporting two-mode entangled photon states with the successful probability 33.3% is proposed. In the scheme, the teleporte d qubit is two-mode photon entangled states, and two pairs of EPR pair are used as quantum channel between a sender and a receiver. This procedure is achieved by using two 50/50 symmetric beam splitters and four photon number detectors wit h the help of classical information.
Directory of Open Access Journals (Sweden)
Huapeng Yu
2015-02-01
Full Text Available The Kalman filter (KF has always been used to improve north-finding performance under practical conditions. By analyzing the characteristics of the azimuth rotational inertial measurement unit (ARIMU on a stationary base, a linear state equality constraint for the conventional KF used in the fine north-finding filtering phase is derived. Then, a constrained KF using the state equality constraint is proposed and studied in depth. Estimation behaviors of the concerned navigation errors when implementing the conventional KF scheme and the constrained KF scheme during stationary north-finding are investigated analytically by the stochastic observability approach, which can provide explicit formulations of the navigation errors with influencing variables. Finally, multiple practical experimental tests at a fixed position are done on a postulate system to compare the stationary north-finding performance of the two filtering schemes. In conclusion, this study has successfully extended the utilization of the stochastic observability approach for analytic descriptions of estimation behaviors of the concerned navigation errors, and the constrained KF scheme has demonstrated its superiority over the conventional KF scheme for ARIMU stationary north-finding both theoretically and practically.
SPLINE, Spline Interpolation Function
International Nuclear Information System (INIS)
Allouard, Y.
1977-01-01
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
Flexible aluminum tubes and a least square multi-objective non-linear optimization scheme
International Nuclear Information System (INIS)
Endelt, Benny; Nielsen, Karl Brian; Olsen, Soeren
2004-01-01
The automotive industry currently uses rubber hoses as the media carrier between e.g. the radiator and the engine, and the basic idea is to replace the rubber hoses with flexible aluminum tubes.A good quality is defined through several quality measurements, i.e. in the current case the key objective is to produce a flexible convolution through optimization of the tool geometry, but the process should also be stable, and the process stability is evaluated through Forming Limit Diagrams. Typically the defined objectives are conflicting, i.e. the optimized configuration represents therefore a trade-off between the individual objectives, in this case flexibility versus process stability.The optimization problem is solved through iteratively minimizing the object function. A second-order least square scheme is used for the approximation of the quadratic model, and the change in the design parameters is evaluated through the trust region scheme and box constraints are introduced within the trust region framework. Furthermore, the object function is minimized by applying the non-monotone scheme, and the trust region subproblem is solved by applying the Cholesky factorization scheme.An optimal bell shaped geometry is identified and the design is verified experimentally
Directory of Open Access Journals (Sweden)
Carlos A Bustamante Chaverra
2013-03-01
Full Text Available Un método sin malla es desarrollado para solucionar una versión genérica de la ecuación no lineal de convección-difusión-reacción en dominios bidimensionales. El método de Interpolación Local Hermítica (LHI es empleado para la discretización espacial, y diferentes estrategias son implementadas para solucionar el sistema de ecuaciones no lineales resultante, entre estas iteración de Picard, método de Newton-Raphson y el Método de Homotopía truncado (HAM. En el método LHI las Funciones de Base Radial (RBFs son empleadas para construir una función de interpolación. A diferencia del Método de Kansa, el LHI es aplicado localmente y los operadores diferenciales de las condiciones de frontera y la ecuación gobernante son utilizados para construir la función de interpolación, obteniéndose una matriz de colocación simétrica. El método de Newton-Rapshon se implementa con matriz Jacobiana analítica y numérica, y las derivadas de la ecuación gobernante con respecto al paramétro de homotopía son obtenidas analíticamente. El esquema numérico es veriﬁcado mediante la comparación de resultados con las soluciones analíticas de las ecuaciones de Burgers en una dimensión y Richards en dos dimensiones. Similares resultados son obtenidos para todos los solucionadores que se probaron, pero mejores ratas de convergencia son logradas con el método de Newton-Raphson en doble iteración.A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diﬀusion-reaction equation in two-dim-ensional domains. The Local Hermitian Interpolation (LHI method is employed for the spatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM. The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs
Revisiting Veerman’s interpolation method
DEFF Research Database (Denmark)
Christiansen, Peter; Bay, Niels Oluf
2016-01-01
and (c) FEsimulations. A comparison of the determined forming limits yields insignificant differences in the limit strain obtainedwith Veerman’s method or exact Lagrangian interpolation for the two sheet metal forming processes investigated. Theagreement with the FE-simulations is reasonable.......This article describes an investigation of Veerman’s interpolation method and its applicability for determining sheet metalformability. The theoretical foundation is established and its mathematical assumptions are clarified. An exact Lagrangianinterpolation scheme is also established...... for comparison. Bulge testing and tensile testing of aluminium sheets containingelectro-chemically etched circle grids are performed to experimentally determine the forming limit of the sheet material.The forming limit is determined using (a) Veerman’s interpolation method, (b) exact Lagrangian interpolation...
Generalized interpolative quantum statistics
International Nuclear Information System (INIS)
Ramanathan, R.
1992-01-01
A generalized interpolative quantum statistics is presented by conjecturing a certain reordering of phase space due to the presence of possible exotic objects other than bosons and fermions. Such an interpolation achieved through a Bose-counting strategy predicts the existence of an infinite quantum Boltzmann-Gibbs statistics akin to the one discovered by Greenberg recently
CMB anisotropies interpolation
Zinger, S.; Delabrouille, Jacques; Roux, Michel; Maitre, Henri
2010-01-01
We consider the problem of the interpolation of irregularly spaced spatial data, applied to observation of Cosmic Microwave Background (CMB) anisotropies. The well-known interpolation methods and kriging are compared to the binning method which serves as a reference approach. We analyse kriging
Zhang, X.; Van Wee, G.P.
2011-01-01
In this paper, we introduce a new duration dependent parking fee regime based on the travel cost for an entire day, rather than a single commute trip. Commuters are assumed to reside at one end of a linear city and work in a business center at the other end. A two-stage differential method is used
Feature displacement interpolation
DEFF Research Database (Denmark)
Nielsen, Mads; Andresen, Per Rønsholt
1998-01-01
Given a sparse set of feature matches, we want to compute an interpolated dense displacement map. The application may be stereo disparity computation, flow computation, or non-rigid medical registration. Also estimation of missing image data, may be phrased in this framework. Since the features...... often are very sparse, the interpolation model becomes crucial. We show that a maximum likelihood estimation based on the covariance properties (Kriging) show properties more expedient than methods such as Gaussian interpolation or Tikhonov regularizations, also including scale......-selection. The computational complexities are identical. We apply the maximum likelihood interpolation to growth analysis of the mandibular bone. Here, the features used are the crest-lines of the object surface....
Extension Of Lagrange Interpolation
Directory of Open Access Journals (Sweden)
Mousa Makey Krady
2015-01-01
Full Text Available Abstract In this paper is to present generalization of Lagrange interpolation polynomials in higher dimensions by using Gramers formula .The aim of this paper is to construct a polynomials in space with error tends to zero.
Keene, Scott T.; Melianas, Armantas; Fuller, Elliot J.; van de Burgt, Yoeri; Talin, A. Alec; Salleo, Alberto
2018-06-01
Neuromorphic devices are becoming increasingly appealing as efficient emulators of neural networks used to model real world problems. However, no hardware to date has demonstrated the necessary high accuracy and energy efficiency gain over CMOS in both (1) training via backpropagation and (2) in read via vector matrix multiplication. Such shortcomings are due to device non-idealities, particularly asymmetric conductance tuning in response to uniform voltage pulse inputs. Here, by formulating a general circuit model for capacitive ion-exchange neuromorphic devices, we show that asymmetric nonlinearity in organic electrochemical neuromorphic devices (ENODes) can be suppressed by an appropriately chosen write scheme. Simulations based upon our model suggest that a nonlinear write-selector could reduce the switching voltage and energy, enabling analog tuning via a continuous set of resistance states (100 states) with extremely low switching energy (~170 fJ · µm‑2). This work clarifies the pathway to neural algorithm accelerators capable of parallelism during both read and write operations.
Positivity Preserving Interpolation Using Rational Bicubic Spline
Directory of Open Access Journals (Sweden)
Samsul Ariffin Abdul Karim
2015-01-01
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.
A FAST MORPHING-BASED INTERPOLATION FOR MEDICAL IMAGES: APPLICATION TO CONFORMAL RADIOTHERAPY
Directory of Open Access Journals (Sweden)
Hussein Atoui
2011-05-01
Full Text Available A method is presented for fast interpolation between medical images. The method is intended for both slice and projective interpolation. It allows offline interpolation between neighboring slices in tomographic data. Spatial correspondence between adjacent images is established using a block matching algorithm. Interpolation of image intensities is then carried out by morphing between the images. The morphing-based method is compared to standard linear interpolation, block-matching-based interpolation and registrationbased interpolation in 3D tomographic data sets. Results show that the proposed method scored similar performance in comparison to registration-based interpolation, and significantly outperforms both linear and block-matching-based interpolation. This method is applied in the context of conformal radiotherapy for online projective interpolation between Digitally Reconstructed Radiographs (DRRs.
Fractional Delayer Utilizing Hermite Interpolation with Caratheodory Representation
Directory of Open Access Journals (Sweden)
Qiang DU
2018-04-01
Full Text Available Fractional delay is indispensable for many sorts of circuits and signal processing applications. Fractional delay filter (FDF utilizing Hermite interpolation with an analog differentiator is a straightforward way to delay discrete signals. This method has a low time-domain error, but a complicated sampling module than the Shannon sampling scheme. A simplified scheme, which is based on Shannon sampling and utilizing Hermite interpolation with a digital differentiator, will lead a much higher time-domain error when the signal frequency approaches the Nyquist rate. In this letter, we propose a novel fractional delayer utilizing Hermite interpolation with Caratheodory representation. The samples of differential signal are obtained by Caratheodory representation from the samples of the original signal only. So, only one sampler is needed and the sampling module is simple. Simulation results for four types of signals demonstrate that the proposed method has significantly higher interpolation accuracy than Hermite interpolation with digital differentiator.
Energy Technology Data Exchange (ETDEWEB)
Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp [Earth and Planetary Sciences, Tokyo Institute of Technology, Tokyo 152-8551 (Japan)
2016-03-15
Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme, we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.
Data-adapted moving least squares method for 3-D image interpolation
International Nuclear Information System (INIS)
Jang, Sumi; Lee, Yeon Ju; Jeong, Byeongseon; Nam, Haewon; Lee, Rena; Yoon, Jungho
2013-01-01
In this paper, we present a nonlinear three-dimensional interpolation scheme for gray-level medical images. The scheme is based on the moving least squares method but introduces a fundamental modification. For a given evaluation point, the proposed method finds the local best approximation by reproducing polynomials of a certain degree. In particular, in order to obtain a better match to the local structures of the given image, we employ locally data-adapted least squares methods that can improve the classical one. Some numerical experiments are presented to demonstrate the performance of the proposed method. Five types of data sets are used: MR brain, MR foot, MR abdomen, CT head, and CT foot. From each of the five types, we choose five volumes. The scheme is compared with some well-known linear methods and other recently developed nonlinear methods. For quantitative comparison, we follow the paradigm proposed by Grevera and Udupa (1998). (Each slice is first assumed to be unknown then interpolated by each method. The performance of each interpolation method is assessed statistically.) The PSNR results for the estimated volumes are also provided. We observe that the new method generates better results in both quantitative and visual quality comparisons. (paper)
International Nuclear Information System (INIS)
Schuller, S.; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1990-01-01
This report presents a description of the design of a digital time meter. This time meter should be able to measure, by means of interpolation, times of 100 ns with an accuracy of 50 ps. In order to determine the best principle for interpolation, three methods were simulated at the computer with a Pascal code. On the basis of this the best method was chosen and used in the design. In order to test the principal operation of the circuit a part of the circuit was constructed with which the interpolation could be tested. The remainder of the circuit was simulated with a computer. So there are no data available about the operation of the complete circuit in practice. The interpolation part however is the most critical part, the remainder of the circuit is more or less simple logic. Besides this report also gives a description of the principle of interpolation and the design of the circuit. The measurement results at the prototype are presented finally. (author). 3 refs.; 37 figs.; 2 tabs
Multivariate Birkhoff interpolation
Lorentz, Rudolph A
1992-01-01
The subject of this book is Lagrange, Hermite and Birkhoff (lacunary Hermite) interpolation by multivariate algebraic polynomials. It unifies and extends a new algorithmic approach to this subject which was introduced and developed by G.G. Lorentz and the author. One particularly interesting feature of this algorithmic approach is that it obviates the necessity of finding a formula for the Vandermonde determinant of a multivariate interpolation in order to determine its regularity (which formulas are practically unknown anyways) by determining the regularity through simple geometric manipulations in the Euclidean space. Although interpolation is a classical problem, it is surprising how little is known about its basic properties in the multivariate case. The book therefore starts by exploring its fundamental properties and its limitations. The main part of the book is devoted to a complete and detailed elaboration of the new technique. A chapter with an extensive selection of finite elements follows as well a...
Wavelet-Smoothed Interpolation of Masked Scientific Data for JPEG 2000 Compression
Energy Technology Data Exchange (ETDEWEB)
Brislawn, Christopher M. [Los Alamos National Laboratory
2012-08-13
How should we manage scientific data with 'holes'? Some applications, like JPEG 2000, expect logically rectangular data, but some sources, like the Parallel Ocean Program (POP), generate data that isn't defined on certain subsets. We refer to grid points that lack well-defined, scientifically meaningful sample values as 'masked' samples. Wavelet-smoothing is a highly scalable interpolation scheme for regions with complex boundaries on logically rectangular grids. Computation is based on forward/inverse discrete wavelet transforms, so runtime complexity and memory scale linearly with respect to sample count. Efficient state-of-the-art minimal realizations yield small constants (O(10)) for arithmetic complexity scaling, and in-situ implementation techniques make optimal use of memory. Implementation in two dimensions using tensor product filter banks is straighsorward and should generalize routinely to higher dimensions. No hand-tuning required when the interpolation mask changes, making the method aeractive for problems with time-varying masks. Well-suited for interpolating undefined samples prior to JPEG 2000 encoding. The method outperforms global mean interpolation, as judged by both SNR rate-distortion performance and low-rate artifact mitigation, for data distributions whose histograms do not take the form of sharply peaked, symmetric, unimodal probability density functions. These performance advantages can hold even for data whose distribution differs only moderately from the peaked unimodal case, as demonstrated by POP salinity data. The interpolation method is very general and is not tied to any particular class of applications, could be used for more generic smooth interpolation.
Precipitation interpolation in mountainous areas
Kolberg, Sjur
2015-04-01
Different precipitation interpolation techniques as well as external drift covariates are tested and compared in a 26000 km2 mountainous area in Norway, using daily data from 60 stations. The main method of assessment is cross-validation. Annual precipitation in the area varies from below 500 mm to more than 2000 mm. The data were corrected for wind-driven undercatch according to operational standards. While temporal evaluation produce seemingly acceptable at-station correlation values (on average around 0.6), the average daily spatial correlation is less than 0.1. Penalising also bias, Nash-Sutcliffe R2 values are negative for spatial correspondence, and around 0.15 for temporal. Despite largely violated assumptions, plain Kriging produces better results than simple inverse distance weighting. More surprisingly, the presumably 'worst-case' benchmark of no interpolation at all, simply averaging all 60 stations for each day, actually outperformed the standard interpolation techniques. For logistic reasons, high altitudes are under-represented in the gauge network. The possible effect of this was investigated by a) fitting a precipitation lapse rate as an external drift, and b) applying a linear model of orographic enhancement (Smith and Barstad, 2004). These techniques improved the results only marginally. The gauge density in the region is one for each 433 km2; higher than the overall density of the Norwegian national network. Admittedly the cross-validation technique reduces the gauge density, still the results suggest that we are far from able to provide hydrological models with adequate data for the main driving force.
Interpolation algorithm for asynchronous ADC-data
Directory of Open Access Journals (Sweden)
S. Bramburger
2017-09-01
Full Text Available This paper presents a modified interpolation algorithm for signals with variable data rate from asynchronous ADCs. The Adaptive weights Conjugate gradient Toeplitz matrix (ACT algorithm is extended to operate with a continuous data stream. An additional preprocessing of data with constant and linear sections and a weighted overlap of step-by-step into spectral domain transformed signals improve the reconstruction of the asycnhronous ADC signal. The interpolation method can be used if asynchronous ADC data is fed into synchronous digital signal processing.
Parris, B. A.; Egbert, G. D.; Key, K.; Livelybrooks, D.
2016-12-01
Magnetotellurics (MT) is an electromagnetic technique used to model the inner Earth's electrical conductivity structure. MT data can be analyzed using iterative, linearized inversion techniques to generate models imaging, in particular, conductive partial melts and aqueous fluids that play critical roles in subduction zone processes and volcanism. For example, the Magnetotelluric Observations of Cascadia using a Huge Array (MOCHA) experiment provides amphibious data useful for imaging subducted fluids from trench to mantle wedge corner. When using MOD3DEM(Egbert et al. 2012), a finite difference inversion package, we have encountered problems inverting, particularly, sea floor stations due to the strong, nearby conductivity gradients. As a work-around, we have found that denser, finer model grids near the land-sea interface produce better inversions, as characterized by reduced data residuals. This is partly to be due to our ability to more accurately capture topography and bathymetry. We are experimenting with improved interpolation schemes that more accurately track EM fields across cell boundaries, with an eye to enhancing the accuracy of the simulated responses and, thus, inversion results. We are adapting how MOD3DEM interpolates EM fields in two ways. The first seeks to improve weighting functions for interpolants to better address current continuity across grid boundaries. Electric fields are interpolated using a tri-linear spline technique, where the eight nearest electrical field estimates are each given weights determined by the technique, a kind of weighted average. We are modifying these weights to include cross-boundary conductivity ratios to better model current continuity. We are also adapting some of the techniques discussed in Shantsev et al (2014) to enhance the accuracy of the interpolated fields calculated by our forward solver, as well as to better approximate the sensitivities passed to the software's Jacobian that are used to generate a new
Woźniak, M.; Smołka, M.; Cortes, Adriano Mauricio; Paszyński, M.; Schaefer, R.
2016-01-01
We study the features of a new mixed integration scheme dedicated to solving the non-stationary variational problems. The scheme is composed of the FEM approximation with respect to the space variable coupled with a 3-leveled time integration scheme
International Nuclear Information System (INIS)
Maysonnave, T.; Bayol, F.; Demol, G.; Almeida, T. d'; Lassalle, F.; Morell, A.; Grunenwald, J.; Chuvatin, A.S.; Pecastaing, L.; De Ferron, A.S.
2014-01-01
SPHINX is a microsecond linear transformer driver LTD, used essentially for implosion of Z-pinch loads in direct drive mode. It can deliver a 6-MA current pulse within 800 ns into a Z-pinch load. The dynamic load current multiplier concept enables the current pulse to be modified by increasing its amplitude while reducing its rise time before being delivered to the load. This compact system is made up of concentric electrodes (auto transformer), a dynamic flux extruder (cylindrical wire array), a vacuum convolute (eight post-holes), and a vacuum closing switch, which is the key component of the system. Several different schemes are investigated for designing a vacuum switch suitable for operating the dynamic load current multiplier on the SPHINX generator for various applications, including isentropic compression experiments and Z-pinch radiation effects studies. In particular, the design of a compact vacuum surface switch and a multichannel vacuum switch, located upstream of the load are studied. Electrostatic simulations supporting the switch designs are presented along with test bed experiments. Initial results from shots on the SPHINX driver are also presented. (authors)
International Nuclear Information System (INIS)
Blok, M. de; Nationaal Inst. voor Kernfysica en Hoge-Energiefysica
1990-01-01
This report describes a time-interpolator with which time differences can be measured using digital and analog techniques. It concerns a maximum measuring time of 6.4 μs with a resolution of 100 ps. Use is made of Emitter Coupled Logic (ECL) and analogues of high-frequency techniques. The difficulty which accompanies the use of ECL-logic is keeping as short as possible the mutual connections and closing properly the outputs in order to avoid reflections. The digital part of the time-interpolator consists of a continuous running clock and logic which converts an input signal into a start- and stop signal. The analog part consists of a Time to Amplitude Converter (TAC) and an analog to digital converter. (author). 3 refs.; 30 figs
Interpolative Boolean Networks
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Vladimir Dobrić
2017-01-01
Full Text Available Boolean networks are used for modeling and analysis of complex systems of interacting entities. Classical Boolean networks are binary and they are relevant for modeling systems with complex switch-like causal interactions. More descriptive power can be provided by the introduction of gradation in this model. If this is accomplished by using conventional fuzzy logics, the generalized model cannot secure the Boolean frame. Consequently, the validity of the model’s dynamics is not secured. The aim of this paper is to present the Boolean consistent generalization of Boolean networks, interpolative Boolean networks. The generalization is based on interpolative Boolean algebra, the [0,1]-valued realization of Boolean algebra. The proposed model is adaptive with respect to the nature of input variables and it offers greater descriptive power as compared with traditional models. For illustrative purposes, IBN is compared to the models based on existing real-valued approaches. Due to the complexity of the most systems to be analyzed and the characteristics of interpolative Boolean algebra, the software support is developed to provide graphical and numerical tools for complex system modeling and analysis.
Directory of Open Access Journals (Sweden)
Pang Fubin
2015-09-01
Full Text Available In this paper the origin problem of data synchronization is analyzed first, and then three common interpolation methods are introduced to solve the problem. Allowing for the most general situation, the paper divides the interpolation error into harmonic and transient interpolation error components, and the error expression of each method is derived and analyzed. Besides, the interpolation errors of linear, quadratic and cubic methods are computed at different sampling rates, harmonic orders and transient components. Further, the interpolation accuracy and calculation amount of each method are compared. The research results provide theoretical guidance for selecting the interpolation method in the data synchronization application of electronic transformer.
Efficient GPU-based texture interpolation using uniform B-splines
Ruijters, D.; Haar Romenij, ter B.M.; Suetens, P.
2008-01-01
This article presents uniform B-spline interpolation, completely contained on the graphics processing unit (GPU). This implies that the CPU does not need to compute any lookup tables or B-spline basis functions. The cubic interpolation can be decomposed into several linear interpolations [Sigg and
A parameterization of observer-based controllers: Bumpless transfer by covariance interpolation
DEFF Research Database (Denmark)
Stoustrup, Jakob; Komareji, Mohammad
2009-01-01
This paper presents an algorithm to interpolate between two observer-based controllers for a linear multivariable system such that the closed loop system remains stable throughout the interpolation. The method interpolates between the inverse Lyapunov functions for the two original state feedback...
Interpolating string field theories
International Nuclear Information System (INIS)
Zwiebach, B.
1992-01-01
This paper reports that a minimal area problem imposing different length conditions on open and closed curves is shown to define a one-parameter family of covariant open-closed quantum string field theories. These interpolate from a recently proposed factorizable open-closed theory up to an extended version of Witten's open string field theory capable of incorporating on shell closed strings. The string diagrams of the latter define a new decomposition of the moduli spaces of Riemann surfaces with punctures and boundaries based on quadratic differentials with both first order and second order poles
Scalable Intersample Interpolation Architecture for High-channel-count Beamformers
DEFF Research Database (Denmark)
Tomov, Borislav Gueorguiev; Nikolov, Svetoslav I; Jensen, Jørgen Arendt
2011-01-01
Modern ultrasound scanners utilize digital beamformers that operate on sampled and quantized echo signals. Timing precision is of essence for achieving good focusing. The direct way to achieve it is through the use of high sampling rates, but that is not economical, so interpolation between echo...... samples is used. This paper presents a beamformer architecture that combines a band-pass filter-based interpolation algorithm with the dynamic delay-and-sum focusing of a digital beamformer. The reduction in the number of multiplications relative to a linear perchannel interpolation and band-pass per......-channel interpolation architecture is respectively 58 % and 75 % beamformer for a 256-channel beamformer using 4-tap filters. The approach allows building high channel count beamformers while maintaining high image quality due to the use of sophisticated intersample interpolation....
Fast image interpolation via random forests.
Huang, Jun-Jie; Siu, Wan-Chi; Liu, Tian-Rui
2015-10-01
This paper proposes a two-stage framework for fast image interpolation via random forests (FIRF). The proposed FIRF method gives high accuracy, as well as requires low computation. The underlying idea of this proposed work is to apply random forests to classify the natural image patch space into numerous subspaces and learn a linear regression model for each subspace to map the low-resolution image patch to high-resolution image patch. The FIRF framework consists of two stages. Stage 1 of the framework removes most of the ringing and aliasing artifacts in the initial bicubic interpolated image, while Stage 2 further refines the Stage 1 interpolated image. By varying the number of decision trees in the random forests and the number of stages applied, the proposed FIRF method can realize computationally scalable image interpolation. Extensive experimental results show that the proposed FIRF(3, 2) method achieves more than 0.3 dB improvement in peak signal-to-noise ratio over the state-of-the-art nonlocal autoregressive modeling (NARM) method. Moreover, the proposed FIRF(1, 1) obtains similar or better results as NARM while only takes its 0.3% computational time.
Convergence of trajectories in fractal interpolation of stochastic processes
International Nuclear Information System (INIS)
MaIysz, Robert
2006-01-01
The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation
Quasi interpolation with Voronoi splines.
Mirzargar, Mahsa; Entezari, Alireza
2011-12-01
We present a quasi interpolation framework that attains the optimal approximation-order of Voronoi splines for reconstruction of volumetric data sampled on general lattices. The quasi interpolation framework of Voronoi splines provides an unbiased reconstruction method across various lattices. Therefore this framework allows us to analyze and contrast the sampling-theoretic performance of general lattices, using signal reconstruction, in an unbiased manner. Our quasi interpolation methodology is implemented as an efficient FIR filter that can be applied online or as a preprocessing step. We present visual and numerical experiments that demonstrate the improved accuracy of reconstruction across lattices, using the quasi interpolation framework. © 2011 IEEE
Research of Cubic Bezier Curve NC Interpolation Signal Generator
Directory of Open Access Journals (Sweden)
Shijun Ji
2014-08-01
Full Text Available Interpolation technology is the core of the computer numerical control (CNC system, and the precision and stability of the interpolation algorithm directly affect the machining precision and speed of CNC system. Most of the existing numerical control interpolation technology can only achieve circular arc interpolation, linear interpolation or parabola interpolation, but for the numerical control (NC machining of parts with complicated surface, it needs to establish the mathematical model and generate the curved line and curved surface outline of parts and then discrete the generated parts outline into a large amount of straight line or arc to carry on the processing, which creates the complex program and a large amount of code, so it inevitably introduce into the approximation error. All these factors affect the machining accuracy, surface roughness and machining efficiency. The stepless interpolation of cubic Bezier curve controlled by analog signal is studied in this paper, the tool motion trajectory of Bezier curve can be directly planned out in CNC system by adjusting control points, and then these data were put into the control motor which can complete the precise feeding of Bezier curve. This method realized the improvement of CNC trajectory controlled ability from the simple linear and circular arc to the complex project curve, and it provides a new way for economy realizing the curve surface parts with high quality and high efficiency machining.
Mintěl, Tomáš
2009-01-01
Tato diplomová práce se zabývá akcelerací interpolačních metod s využitím GPU a architektury NVIDIA (R) CUDA TM. Grafický výstup je reprezentován demonstrační aplikací pro transformaci obrazu nebo videa s použitím vybrané interpolace. Časově kritické části kódu jsou přesunuty na GPU a vykonány paralelně. Pro práci s obrazem a videem jsou použity vysoce optimalizované algoritmy z knihovny OpenCV, od firmy Intel. This master's thesis deals with acceleration of pixel interpolation methods usi...
Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf
2018-06-01
For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.
Köbler, Jonathan; Schneider, Matti; Ospald, Felix; Andrä, Heiko; Müller, Ralf
2018-04-01
For short fiber reinforced plastic parts the local fiber orientation has a strong influence on the mechanical properties. To enable multiscale computations using surrogate models we advocate a two-step identification strategy. Firstly, for a number of sample orientations an effective model is derived by numerical methods available in the literature. Secondly, to cover a general orientation state, these effective models are interpolated. In this article we develop a novel and effective strategy to carry out this interpolation. Firstly, taking into account symmetry arguments, we reduce the fiber orientation phase space to a triangle in R^2 . For an associated triangulation of this triangle we furnish each node with an surrogate model. Then, we use linear interpolation on the fiber orientation triangle to equip each fiber orientation state with an effective stress. The proposed approach is quite general, and works for any physically nonlinear constitutive law on the micro-scale, as long as surrogate models for single fiber orientation states can be extracted. To demonstrate the capabilities of our scheme we study the viscoelastic creep behavior of short glass fiber reinforced PA66, and use Schapery's collocation method together with FFT-based computational homogenization to derive single orientation state effective models. We discuss the efficient implementation of our method, and present results of a component scale computation on a benchmark component by using ABAQUS ®.
Interpolant tree automata and their application in Horn clause verification
DEFF Research Database (Denmark)
Kafle, Bishoksan; Gallagher, John Patrick
2016-01-01
This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this ......This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way...... clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead....
International Nuclear Information System (INIS)
Sergienko, I.V.; Golodnikov, A.N.
1984-01-01
This article applies the methods of decompositions, which are used to solve continuous linear problems, to integer and partially integer problems. The fall-vector method is used to solve the obtained coordinate problems. An algorithm of the fall-vector is described. The Kornai-Liptak decomposition principle is used to reduce the integer linear programming problem to integer linear programming problems of a smaller dimension and to a discrete coordinate problem with simple constraints
Fuzzy linguistic model for interpolation
International Nuclear Information System (INIS)
Abbasbandy, S.; Adabitabar Firozja, M.
2007-01-01
In this paper, a fuzzy method for interpolating of smooth curves was represented. We present a novel approach to interpolate real data by applying the universal approximation method. In proposed method, fuzzy linguistic model (FLM) applied as universal approximation for any nonlinear continuous function. Finally, we give some numerical examples and compare the proposed method with spline method
A disposition of interpolation techniques
Knotters, M.; Heuvelink, G.B.M.
2010-01-01
A large collection of interpolation techniques is available for application in environmental research. To help environmental scientists in choosing an appropriate technique a disposition is made, based on 1) applicability in space, time and space-time, 2) quantification of accuracy of interpolated
Shape-based interpolation of multidimensional grey-level images
International Nuclear Information System (INIS)
Grevera, G.J.; Udupa, J.K.
1996-01-01
Shape-based interpolation as applied to binary images causes the interpolation process to be influenced by the shape of the object. It accomplishes this by first applying a distance transform to the data. This results in the creation of a grey-level data set in which the value at each point represents the minimum distance from that point to the surface of the object. (By convention, points inside the object are assigned positive values; points outside are assigned negative values.) This distance transformed data set is then interpolated using linear or higher-order interpolation and is then thresholded at a distance value of zero to produce the interpolated binary data set. In this paper, the authors describe a new method that extends shape-based interpolation to grey-level input data sets. This generalization consists of first lifting the n-dimensional (n-D) image data to represent it as a surface, or equivalently as a binary image, in an (n + 1)-dimensional [(n + 1)-D] space. The binary shape-based method is then applied to this image to create an (n + 1)-D binary interpolated image. Finally, this image is collapsed (inverse of lifting) to create the n-D interpolated grey-level data set. The authors have conducted several evaluation studies involving patient computed tomography (CT) and magnetic resonance (MR) data as well as mathematical phantoms. They all indicate that the new method produces more accurate results than commonly used grey-level linear interpolation methods, although at the cost of increased computation
Contrast-guided image interpolation.
Wei, Zhe; Ma, Kai-Kuang
2013-11-01
In this paper a contrast-guided image interpolation method is proposed that incorporates contrast information into the image interpolation process. Given the image under interpolation, four binary contrast-guided decision maps (CDMs) are generated and used to guide the interpolation filtering through two sequential stages: 1) the 45(°) and 135(°) CDMs for interpolating the diagonal pixels and 2) the 0(°) and 90(°) CDMs for interpolating the row and column pixels. After applying edge detection to the input image, the generation of a CDM lies in evaluating those nearby non-edge pixels of each detected edge for re-classifying them possibly as edge pixels. This decision is realized by solving two generalized diffusion equations over the computed directional variation (DV) fields using a derived numerical approach to diffuse or spread the contrast boundaries or edges, respectively. The amount of diffusion or spreading is proportional to the amount of local contrast measured at each detected edge. The diffused DV fields are then thresholded for yielding the binary CDMs, respectively. Therefore, the decision bands with variable widths will be created on each CDM. The two CDMs generated in each stage will be exploited as the guidance maps to conduct the interpolation process: for each declared edge pixel on the CDM, a 1-D directional filtering will be applied to estimate its associated to-be-interpolated pixel along the direction as indicated by the respective CDM; otherwise, a 2-D directionless or isotropic filtering will be used instead to estimate the associated missing pixels for each declared non-edge pixel. Extensive simulation results have clearly shown that the proposed contrast-guided image interpolation is superior to other state-of-the-art edge-guided image interpolation methods. In addition, the computational complexity is relatively low when compared with existing methods; hence, it is fairly attractive for real-time image applications.
International Nuclear Information System (INIS)
Garcia-Santos, J. M.; Cejudo, J.
2002-01-01
In contrast to conventional computed tomography (CT), helical CT requires the application of interpolators to achieve image reconstruction. This is because the projections processed by the computer are not situated in the same plane. Since the introduction of helical CT. a number of interpolators have been designed in the attempt to maintain the thickness of the reconstructed section as close as possible to the thickness of the X-ray beam. The purpose of this article is to discuss the function of these interpolators, stressing the advantages and considering the possible inconveniences of high-grade curved interpolators with respect to standard linear interpolators. (Author) 7 refs
Reaction schemes of immunoanalysis
International Nuclear Information System (INIS)
Delaage, M.; Barbet, J.
1991-01-01
The authors apply a general theory for multiple equilibria to the reaction schemes of immunoanalysis, competition and sandwich. This approach allows the manufacturer to optimize the system and provide the user with interpolation functions for the standard curve and its first derivative as well, thus giving access to variance [fr
Occlusion-Aware View Interpolation
Directory of Open Access Journals (Sweden)
Janusz Konrad
2009-01-01
Full Text Available View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.
Occlusion-Aware View Interpolation
Directory of Open Access Journals (Sweden)
Ince Serdar
2008-01-01
Full Text Available Abstract View interpolation is an essential step in content preparation for multiview 3D displays, free-viewpoint video, and multiview image/video compression. It is performed by establishing a correspondence among views, followed by interpolation using the corresponding intensities. However, occlusions pose a significant challenge, especially if few input images are available. In this paper, we identify challenges related to disparity estimation and view interpolation in presence of occlusions. We then propose an occlusion-aware intermediate view interpolation algorithm that uses four input images to handle the disappearing areas. The algorithm consists of three steps. First, all pixels in view to be computed are classified in terms of their visibility in the input images. Then, disparity for each pixel is estimated from different image pairs depending on the computed visibility map. Finally, luminance/color of each pixel is adaptively interpolated from an image pair selected by its visibility label. Extensive experimental results show striking improvements in interpolated image quality over occlusion-unaware interpolation from two images and very significant gains over occlusion-aware spline-based reconstruction from four images, both on synthetic and real images. Although improvements are obvious only in the vicinity of object boundaries, this should be useful in high-quality 3D applications, such as digital 3D cinema and ultra-high resolution multiview autostereoscopic displays, where distortions at depth discontinuities are highly objectionable, especially if they vary with viewpoint change.
BIMOND3, Monotone Bivariate Interpolation
International Nuclear Information System (INIS)
Fritsch, F.N.; Carlson, R.E.
2001-01-01
1 - Description of program or function: BIMOND is a FORTRAN-77 subroutine for piecewise bi-cubic interpolation to data on a rectangular mesh, which reproduces the monotonousness of the data. A driver program, BIMOND1, is provided which reads data, computes the interpolating surface parameters, and evaluates the function on a mesh suitable for plotting. 2 - Method of solution: Monotonic piecewise bi-cubic Hermite interpolation is used. 3 - Restrictions on the complexity of the problem: The current version of the program can treat data which are monotone in only one of the independent variables, but cannot handle piecewise monotone data
The research on NURBS adaptive interpolation technology
Zhang, Wanjun; Gao, Shanping; Zhang, Sujia; Zhang, Feng
2017-04-01
In order to solve the problems of Research on NURBS Adaptive Interpolation Technology, such as interpolation time bigger, calculation more complicated, and NURBS curve step error are not easy changed and so on. This paper proposed a study on the algorithm for NURBS adaptive interpolation method of NURBS curve and simulation. We can use NURBS adaptive interpolation that calculates (xi, yi, zi). Simulation results show that the proposed NURBS curve interpolator meets the high-speed and high-accuracy interpolation requirements of CNC systems. The interpolation of NURBS curve should be finished. The simulation results show that the algorithm is correct; it is consistent with a NURBS curve interpolation requirements.
CANONICAL BACKWARD DIFFERENTIATION SCHEMES FOR ...
African Journals Online (AJOL)
This paper describes a new nonlinear backward differentiation schemes for the numerical solution of nonlinear initial value problems of first order ordinary differential equations. The schemes are based on rational interpolation obtained from canonical polynomials. They are A-stable. The test problems show that they give ...
COMPARISONS BETWEEN DIFFERENT INTERPOLATION TECHNIQUES
Directory of Open Access Journals (Sweden)
G. Garnero
2014-01-01
In the present study different algorithms will be analysed in order to spot an optimal interpolation methodology. The availability of the recent digital model produced by the Regione Piemonte with airborne LIDAR and the presence of sections of testing realized with higher resolutions and the presence of independent digital models on the same territory allow to set a series of analysis with consequent determination of the best methodologies of interpolation. The analysis of the residuals on the test sites allows to calculate the descriptive statistics of the computed values: all the algorithms have furnished interesting results; all the more interesting, notably for dense models, the IDW (Inverse Distance Weighing algorithm results to give best results in this study case. Moreover, a comparative analysis was carried out by interpolating data at different input point density, with the purpose of highlighting thresholds in input density that may influence the quality reduction of the final output in the interpolation phase.
A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum
Chou, Jack C. K.
1989-01-01
The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.
Threshold Signature Schemes Application
Directory of Open Access Journals (Sweden)
Anastasiya Victorovna Beresneva
2015-10-01
Full Text Available This work is devoted to an investigation of threshold signature schemes. The systematization of the threshold signature schemes was done, cryptographic constructions based on interpolation Lagrange polynomial, elliptic curves and bilinear pairings were examined. Different methods of generation and verification of threshold signatures were explored, the availability of practical usage of threshold schemes in mobile agents, Internet banking and e-currency was shown. The topics of further investigation were given and it could reduce a level of counterfeit electronic documents signed by a group of users.
Directory of Open Access Journals (Sweden)
B. M. Monge-Sanz
2013-09-01
Full Text Available This study evaluates effects and applications of a new linear parameterisation for stratospheric methane and water vapour. The new scheme (CoMeCAT is derived from a 3-D full-chemistry-transport model (CTM. It is suitable for any global model, and is shown here to produce realistic profiles in the TOMCAT/SLIMCAT 3-D CTM and the ECMWF (European Centre for Medium-Range Weather Forecasts general circulation model (GCM. Results from the new scheme are in good agreement with the full-chemistry CTM CH4 field and with observations from the Halogen Occultation Experiment (HALOE. The scheme is also used to derive stratospheric water increments, which in the CTM produce vertical and latitudinal H2O variations in fair agreement with satellite observations. Stratospheric H2O distributions in the ECMWF GCM show realistic overall features, although concentrations are smaller than in the CTM run (up to 0.5 ppmv smaller above 10 hPa. The potential of the new CoMeCAT tracer for evaluating stratospheric transport is exploited to assess the impacts of nudging the free-running GCM to ERA-40 and ERA-Interim reanalyses. The nudged GCM shows similar transport patterns to the offline CTM forced by the corresponding reanalysis data. The new scheme also impacts radiation and temperature in the model. Compared to the default CH4 climatology and H2O used by the ECMWF radiation scheme, the main effect on ECMWF temperatures when considering both CH4 and H2O from CoMeCAT is a decrease of up to 1.0 K over the tropical mid/low stratosphere. The effect of using the CoMeCAT scheme for radiative forcing (RF calculations is investigated using the offline Edwards–Slingo radiative transfer model. Compared to the default model option of a tropospheric global 3-D CH4 value, the CoMeCAT distribution produces an overall change in the annual mean net RF of up to −30 mW m−2.
Gaussian Process Interpolation for Uncertainty Estimation in Image Registration
Wachinger, Christian; Golland, Polina; Reuter, Martin; Wells, William
2014-01-01
Intensity-based image registration requires resampling images on a common grid to evaluate the similarity function. The uncertainty of interpolation varies across the image, depending on the location of resampled points relative to the base grid. We propose to perform Bayesian inference with Gaussian processes, where the covariance matrix of the Gaussian process posterior distribution estimates the uncertainty in interpolation. The Gaussian process replaces a single image with a distribution over images that we integrate into a generative model for registration. Marginalization over resampled images leads to a new similarity measure that includes the uncertainty of the interpolation. We demonstrate that our approach increases the registration accuracy and propose an efficient approximation scheme that enables seamless integration with existing registration methods. PMID:25333127
Permanently calibrated interpolating time counter
International Nuclear Information System (INIS)
Jachna, Z; Szplet, R; Kwiatkowski, P; Różyc, K
2015-01-01
We propose a new architecture of an integrated time interval counter that provides its permanent calibration in the background. Time interval measurement and the calibration procedure are based on the use of a two-stage interpolation method and parallel processing of measurement and calibration data. The parallel processing is achieved by a doubling of two-stage interpolators in measurement channels of the counter, and by an appropriate extension of control logic. Such modification allows the updating of transfer characteristics of interpolators without the need to break a theoretically infinite measurement session. We describe the principle of permanent calibration, its implementation and influence on the quality of the counter. The precision of the presented counter is kept at a constant level (below 20 ps) despite significant changes in the ambient temperature (from −10 to 60 °C), which can cause a sevenfold decrease in the precision of the counter with a traditional calibration procedure. (paper)
Reducing Interpolation Artifacts for Mutual Information Based Image Registration
Soleimani, H.; Khosravifard, M.A.
2011-01-01
Medical image registration methods which use mutual information as similarity measure have been improved in recent decades. Mutual Information is a basic concept of Information theory which indicates the dependency of two random variables (or two images). In order to evaluate the mutual information of two images their joint probability distribution is required. Several interpolation methods, such as Partial Volume (PV) and bilinear, are used to estimate joint probability distribution. Both of these two methods yield some artifacts on mutual information function. Partial Volume-Hanning window (PVH) and Generalized Partial Volume (GPV) methods are introduced to remove such artifacts. In this paper we show that the acceptable performance of these methods is not due to their kernel function. It's because of the number of pixels which incorporate in interpolation. Since using more pixels requires more complex and time consuming interpolation process, we propose a new interpolation method which uses only four pixels (the same as PV and bilinear interpolations) and removes most of the artifacts. Experimental results of the registration of Computed Tomography (CT) images show superiority of the proposed scheme. PMID:22606673
Interpolation decoding method with variable parameters for fractal image compression
International Nuclear Information System (INIS)
He Chuanjiang; Li Gaoping; Shen Xiaona
2007-01-01
The interpolation fractal decoding method, which is introduced by [He C, Yang SX, Huang X. Progressive decoding method for fractal image compression. IEE Proc Vis Image Signal Process 2004;3:207-13], involves generating progressively the decoded image by means of an interpolation iterative procedure with a constant parameter. It is well-known that the majority of image details are added at the first steps of iterations in the conventional fractal decoding; hence the constant parameter for the interpolation decoding method must be set as a smaller value in order to achieve a better progressive decoding. However, it needs to take an extremely large number of iterations to converge. It is thus reasonable for some applications to slow down the iterative process at the first stages of decoding and then to accelerate it afterwards (e.g., at some iteration as we need). To achieve the goal, this paper proposed an interpolation decoding scheme with variable (iteration-dependent) parameters and proved the convergence of the decoding process mathematically. Experimental results demonstrate that the proposed scheme has really achieved the above-mentioned goal
Directory of Open Access Journals (Sweden)
Buscaglia Gustavo C.
2001-01-01
Full Text Available A new numerical approach is proposed to alleviate the computational cost of solving non-linear non-uniform homogenized problems. The article details the application of the proposed approach to lubrication problems with roughness effects. The method is based on a two-parameter Taylor expansion of the implicit dependence of the homogenized coefficients on the average pressure and on the local value of the air gap thickness. A fourth-order Taylor expansion provides an approximation that is accurate enough to be used in the global problem solution instead of the exact dependence, without introducing significant errors. In this way, when solving the global problem, the solution of local problems is simply replaced by the evaluation of a polynomial. Moreover, the method leads naturally to Newton-Raphson nonlinear iterations, that further reduce the cost. The overall efficiency of the numerical methodology makes it feasible to apply rigorous homogenization techniques in the analysis of compressible fluid contact considering roughness effects. Previous work makes use of an heuristic averaging technique. Numerical comparison proves that homogenization-based methods are superior when the roughness is strongly anisotropic and not aligned with the flow direction.
Convexity-preserving Bernstein–Bézier quartic scheme
Directory of Open Access Journals (Sweden)
Maria Hussain
2014-07-01
Full Text Available A C1 convex surface data interpolation scheme is presented to preserve the shape of scattered data arranged over a triangular grid. Bernstein–Bézier quartic function is used for interpolation. Lower bound of the boundary and inner Bézier ordinates is determined to guarantee convexity of surface. The developed scheme is flexible and involves more relaxed constraints.
Can a polynomial interpolation improve on the Kaplan-Yorke dimension?
International Nuclear Information System (INIS)
Richter, Hendrik
2008-01-01
The Kaplan-Yorke dimension can be derived using a linear interpolation between an h-dimensional Lyapunov exponent λ (h) >0 and an h+1-dimensional Lyapunov exponent λ (h+1) <0. In this Letter, we use a polynomial interpolation to obtain generalized Lyapunov dimensions and study the relationships among them for higher-dimensional systems
Kriging interpolation in seismic attribute space applied to the South Arne Field, North Sea
DEFF Research Database (Denmark)
Hansen, Thomas Mejer; Mosegaard, Klaus; Schiøtt, Christian
2010-01-01
Seismic attributes can be used to guide interpolation in-between and extrapolation away from well log locations using for example linear regression, neural networks, and kriging. Kriging-based estimation methods (and most other types of interpolation/extrapolation techniques) are intimately linke...
Directory of Open Access Journals (Sweden)
Mingjian Sun
2015-01-01
Full Text Available Photoacoustic imaging is an innovative imaging technique to image biomedical tissues. The time reversal reconstruction algorithm in which a numerical model of the acoustic forward problem is run backwards in time is widely used. In the paper, a time reversal reconstruction algorithm based on particle swarm optimization (PSO optimized support vector machine (SVM interpolation method is proposed for photoacoustics imaging. Numerical results show that the reconstructed images of the proposed algorithm are more accurate than those of the nearest neighbor interpolation, linear interpolation, and cubic convolution interpolation based time reversal algorithm, which can provide higher imaging quality by using significantly fewer measurement positions or scanning times.
International Nuclear Information System (INIS)
Chan, C.T.; Vanderbilt, D.; Louie, S.G.; Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720)
1986-01-01
We present a general self-consistency procedure formulated in momentum space for electronic structure and total-energy calculations of crystalline solids. It is shown that both the charge density and the change in the Hamiltonian matrix elements in each iteration can be calculated in a straight-forward fashion once a set of overlap matrices is computed. The present formulation has the merit of bringing the self-consistency problem for different basis sets to the same footing. The scheme is used to extend a first-principles pseudopotential linear combination of Gaussian orbitals method to full point-by-point self-consistency, without refitting of potentials. It is shown that the set of overlap matrices can be calculated very efficiently if we exploit the translational and space-group symmetries of the system under consideration. This scheme has been applied to study the structural and electronic properties of Si and W, prototypical systems of very different bonding properties. The results agree well with experiment and other calculations. The fully self-consistent results are compared with those obtained by a variational procedure [J. R. Chelikowsky and S. G. Louie, Phys. Rev. B 29, 3470 (1984)]. We find that the structural properties for bulk Si and W (both systems have no interatomic charge transfer) can be treated accurately by the variational procedure. However, full self-consistency is needed for an accurate description of the band energies
Directory of Open Access Journals (Sweden)
Kowal Robert
2016-12-01
Full Text Available A simple linear regression model is one of the pillars of classic econometrics. Multiple areas of research function within its scope. One of the many fundamental questions in the model concerns proving the efficiency of the most commonly used OLS estimators and examining their properties. In the literature of the subject one can find taking back to this scope and certain solutions in that regard. Methodically, they are borrowed from the multiple regression model or also from a boundary partial model. Not everything, however, is here complete and consistent. In the paper a completely new scheme is proposed, based on the implementation of the Cauchy-Schwarz inequality in the arrangement of the constraint aggregated from calibrated appropriately secondary constraints of unbiasedness which in a result of choice the appropriate calibrator for each variable directly leads to showing this property. A separate range-is a matter of choice of such a calibrator. These deliberations, on account of the volume and kinds of the calibration, were divided into a few parts. In the one the efficiency of OLS estimators is proven in a mixed scheme of the calibration by averages, that is preliminary, and in the most basic frames of the proposed methodology. In these frames the future outlines and general premises constituting the base of more distant generalizations are being created.
Effect of interpolation on parameters extracted from seating interface pressure arrays.
Wininger, Michael; Crane, Barbara
2014-01-01
Interpolation is a common data processing step in the study of interface pressure data collected at the wheelchair seating interface. However, there has been no focused study on the effect of interpolation on features extracted from these pressure maps, nor on whether these parameters are sensitive to the manner in which the interpolation is implemented. Here, two different interpolation paradigms, bilinear versus bicubic spline, are tested for their influence on parameters extracted from pressure array data and compared against a conventional low-pass filtering operation. Additionally, analysis of the effect of tandem filtering and interpolation, as well as the interpolation degree (interpolating to 2, 4, and 8 times sampling density), was undertaken. The following recommendations are made regarding approaches that minimized distortion of features extracted from the pressure maps: (1) filter prior to interpolate (strong effect); (2) use of cubic interpolation versus linear (slight effect); and (3) nominal difference between interpolation orders of 2, 4, and 8 times (negligible effect). We invite other investigators to perform similar benchmark analyses on their own data in the interest of establishing a community consensus of best practices in pressure array data processing.
Generation of nuclear data banks through interpolation
International Nuclear Information System (INIS)
Castillo M, J.A.
1999-01-01
Nuclear Data Bank generation, is a process in which a great amount of resources is required, both computing and humans. If it is taken into account that at some times it is necessary to create a great amount of those, it is convenient to have a reliable tool that generates Data Banks with the lesser resources, in the least possible time and with a very good approximation. In this work are shown the results obtained during the development of INTPOLBI code, used to generate Nuclear Data Banks employing bi cubic polynomial interpolation, taking as independent variables the uranium and gadolinium percents. Two proposals were worked, applying in both cases the finite element method, using one element with 16 nodes to carry out the interpolation. In the first proposals the canonic base was employed to obtain the interpolating polynomial and later, the corresponding linear equations system. In the solution of this system the Gaussian elimination method with partial pivot was applied. In the second case, the Newton base was used to obtain the mentioned system, resulting in a triangular inferior matrix, which structure, applying elemental operations, to obtain a blocks diagonal matrix, with special characteristics and easier to work with. For the validations test, a comparison was made between the values obtained with INTPOLBI and INTERTEG (created at the Instituto de Investigaciones Electricas with the same purpose) codes, and Data Banks created through the conventional process, that is, with nuclear codes normally used. Finally, it is possible to conclude that the Nuclear Data Banks generated with INTPOLBI code constitute a very good approximation that, even though do not wholly replace conventional process, however are helpful in cases when it is necessary to create a great amount of Data Banks. (Author)
Nuclear data banks generation by interpolation
International Nuclear Information System (INIS)
Castillo M, J. A.
1999-01-01
Nuclear Data Bank generation, is a process in which a great amount of resources is required, both computing and humans. If it is taken into account that at some times it is necessary to create a great amount of those, it is convenient to have a reliable tool that generates Data Banks with the lesser resources, in the least possible time and with a very good approximation. In this work are shown the results obtained during the development of INTPOLBI code, use to generate Nuclear Data Banks employing bicubic polynominal interpolation, taking as independent variables the uranium and gadolinia percents. Two proposal were worked, applying in both cases the finite element method, using one element with 16 nodes to carry out the interpolation. In the first proposals the canonic base was employed, to obtain the interpolating polynomial and later, the corresponding linear equation systems. In the solution of this systems the Gaussian elimination methods with partial pivot was applied. In the second case, the Newton base was used to obtain the mentioned system, resulting in a triangular inferior matrix, which structure, applying elemental operations, to obtain a blocks diagonal matrix, with special characteristics and easier to work with. For the validation tests, a comparison was made between the values obtained with INTPOLBI and INTERTEG (create at the Instituto de Investigaciones Electricas (MX) with the same purpose) codes, and Data Banks created through the conventional process, that is, with nuclear codes normally used. Finally, it is possible to conclude that the Nuclear Data Banks generated with INTPOLBI code constitute a very good approximation that, even though do not wholly replace conventional process, however are helpful in cases when it is necessary to create a great amount of Data Banks
CSIR Research Space (South Africa)
Van den Bergh, F
2006-01-01
Full Text Available This paper presents two new schemes for interpolating missing samples in satellite diurnal temperature cycles (DTCs). The first scheme, referred to here as the cosine model, is an improvement of the model proposed in [2] and combines a cosine...
Navon, M. I.; Stefanescu, R.; Fuelberg, H. E.; Marchand, M.
2012-12-01
NASA's launch of the GOES-R Lightning Mapper (GLM) in 2015 will provide continuous, full disc, high resolution total lightning (IC + CG) data. The data will be available at a horizontal resolution of approximately 9 km. Compared to other types of data, the assimilation of lightning data into operational numerical models has received relatively little attention. Previous efforts of lightning assimilation mostly have employed nudging. This paper will describe the implementation of 1D+3D/4D Var assimilation schemes of existing ground-based WTLN (Worldwide Total Lightning Network) lightning observations using non-linear observation operators in the incremental WRFDA system. To mimic the expected output of GLM, the WTLN data were used to generate lightning super-observations characterized by flash rates/81 km2/20 min. A major difficulty associated with variational approaches is the complexity of the observation operator that defines the model equivalent of lightning. We use Convective Available Potential Energy (CAPE) as a proxy between lightning data and model variables. This operator is highly nonlinear. Marecal and Mahfouf (2003) have shown that nonlinearities can prevent direct assimilation of rainfall rates in the ECMWF 4D-VAR (using the incremental formulation proposed by Courtier et al. (1994)) from being successful. Using data from the 2011 Tuscaloosa, AL tornado outbreak, we have proved that the direct assimilation of lightning data into the WRF 3D/4D - Var systems is limited due to this incremental approach. Severe threshold limits must be imposed on the innovation vectors to obtain an improved analysis. We have implemented 1D+3D/4D Var schemes to assimilate lightning observations into the WRF model. Their use avoids innovation vector constrains from preventing the inclusion of a greater number of lightning observations Their use also minimizes the problem that nonlinearities in the moist convective scheme can introduce discontinuities in the cost function
An integral conservative gridding--algorithm using Hermitian curve interpolation.
Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K
2008-11-07
The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to
An integral conservative gridding-algorithm using Hermitian curve interpolation
International Nuclear Information System (INIS)
Volken, Werner; Frei, Daniel; Manser, Peter; Mini, Roberto; Born, Ernst J; Fix, Michael K
2008-01-01
The problem of re-sampling spatially distributed data organized into regular or irregular grids to finer or coarser resolution is a common task in data processing. This procedure is known as 'gridding' or 're-binning'. Depending on the quantity the data represents, the gridding-algorithm has to meet different requirements. For example, histogrammed physical quantities such as mass or energy have to be re-binned in order to conserve the overall integral. Moreover, if the quantity is positive definite, negative sampling values should be avoided. The gridding process requires a re-distribution of the original data set to a user-requested grid according to a distribution function. The distribution function can be determined on the basis of the given data by interpolation methods. In general, accurate interpolation with respect to multiple boundary conditions of heavily fluctuating data requires polynomial interpolation functions of second or even higher order. However, this may result in unrealistic deviations (overshoots or undershoots) of the interpolation function from the data. Accordingly, the re-sampled data may overestimate or underestimate the given data by a significant amount. The gridding-algorithm presented in this work was developed in order to overcome these problems. Instead of a straightforward interpolation of the given data using high-order polynomials, a parametrized Hermitian interpolation curve was used to approximate the integrated data set. A single parameter is determined by which the user can control the behavior of the interpolation function, i.e. the amount of overshoot and undershoot. Furthermore, it is shown how the algorithm can be extended to multidimensional grids. The algorithm was compared to commonly used gridding-algorithms using linear and cubic interpolation functions. It is shown that such interpolation functions may overestimate or underestimate the source data by about 10-20%, while the new algorithm can be tuned to
Ding, Qian; Wang, Yong; Zhuang, Dafang
2018-04-15
The appropriate spatial interpolation methods must be selected to analyze the spatial distributions of Potentially Toxic Elements (PTEs), which is a precondition for evaluating PTE pollution. The accuracy and effect of different spatial interpolation methods, which include inverse distance weighting interpolation (IDW) (power = 1, 2, 3), radial basis function interpolation (RBF) (basis function: thin-plate spline (TPS), spline with tension (ST), completely regularized spline (CRS), multiquadric (MQ) and inverse multiquadric (IMQ)) and ordinary kriging interpolation (OK) (semivariogram model: spherical, exponential, gaussian and linear), were compared using 166 unevenly distributed soil PTE samples (As, Pb, Cu and Zn) in the Suxian District, Chenzhou City, Hunan Province as the study subject. The reasons for the accuracy differences of the interpolation methods and the uncertainties of the interpolation results are discussed, then several suggestions for improving the interpolation accuracy are proposed, and the direction of pollution control is determined. The results of this study are as follows: (i) RBF-ST and OK (exponential) are the optimal interpolation methods for As and Cu, and the optimal interpolation method for Pb and Zn is RBF-IMQ. (ii) The interpolation uncertainty is positively correlated with the PTE concentration, and higher uncertainties are primarily distributed around mines, which is related to the strong spatial variability of PTE concentrations caused by human interference. (iii) The interpolation accuracy can be improved by increasing the sample size around the mines, introducing auxiliary variables in the case of incomplete sampling and adopting the partition prediction method. (iv) It is necessary to strengthen the prevention and control of As and Pb pollution, particularly in the central and northern areas. The results of this study can provide an effective reference for the optimization of interpolation methods and parameters for
Randomized interpolative decomposition of separated representations
Biagioni, David J.; Beylkin, Daniel; Beylkin, Gregory
2015-01-01
We introduce an algorithm to compute tensor interpolative decomposition (dubbed CTD-ID) for the reduction of the separation rank of Canonical Tensor Decompositions (CTDs). Tensor ID selects, for a user-defined accuracy ɛ, a near optimal subset of terms of a CTD to represent the remaining terms via a linear combination of the selected terms. CTD-ID can be used as an alternative to or in combination with the Alternating Least Squares (ALS) algorithm. We present examples of its use within a convergent iteration to compute inverse operators in high dimensions. We also briefly discuss the spectral norm as a computational alternative to the Frobenius norm in estimating approximation errors of tensor ID. We reduce the problem of finding tensor IDs to that of constructing interpolative decompositions of certain matrices. These matrices are generated via randomized projection of the terms of the given tensor. We provide cost estimates and several examples of the new approach to the reduction of separation rank.
Size-Dictionary Interpolation for Robot's Adjustment
Directory of Open Access Journals (Sweden)
Morteza eDaneshmand
2015-05-01
Full Text Available This paper describes the classification and size-dictionary interpolation of the three-dimensional data obtained by a laser scanner to be used in a realistic virtual fitting room, where automatic activation of the chosen mannequin robot, while several mannequin robots of different genders and sizes are simultaneously connected to the same computer, is also considered to make it mimic the body shapes and sizes instantly. The classification process consists of two layers, dealing, respectively, with gender and size. The interpolation procedure tries to find out which set of the positions of the biologically-inspired actuators for activation of the mannequin robots could lead to the closest possible resemblance of the shape of the body of the person having been scanned, through linearly mapping the distances between the subsequent size-templates and the corresponding position set of the bioengineered actuators, and subsequently, calculating the control measures that could maintain the same distance proportions, where minimizing the Euclidean distance between the size-dictionary template vectors and that of the desired body sizes determines the mathematical description. In this research work, the experimental results of the implementation of the proposed method on Fits.me's mannequin robots are visually illustrated, and explanation of the remaining steps towards completion of the whole realistic online fitting package is provided.
Impact of gridpoint statistical interpolation scheme over Indian region
Indian Academy of Sciences (India)
An analysis system experiment was conducted for the month of June 2008 with Gridpoint ... ance in spectral space (in SSI) allows little control .... Conventional aircraft observations (AIREP) ...... Environmental Prediction (NCEP) for sharing.
AN INTERPOLATING CURVE SUBDIVISION SCHEME BASED ON DISCRETE FIRST DERIVATIVE
Directory of Open Access Journals (Sweden)
ALBEIRO ESPINOSA BEDOYA
2013-01-01
tortuosidad. Un análisis de las distribuciones de frecuencia obtenidas para esta propiedad, empleando la prueba de KruskalWallis, revela que el esquema DFDS posee los menores valores de tortuosidad en un rango más estrecho.
Fast digital zooming system using directionally adaptive image interpolation and restoration.
Kang, Wonseok; Jeon, Jaehwan; Yu, Soohwan; Paik, Joonki
2014-01-01
This paper presents a fast digital zooming system for mobile consumer cameras using directionally adaptive image interpolation and restoration methods. The proposed interpolation algorithm performs edge refinement along the initially estimated edge orientation using directionally steerable filters. Either the directionally weighted linear or adaptive cubic-spline interpolation filter is then selectively used according to the refined edge orientation for removing jagged artifacts in the slanted edge region. A novel image restoration algorithm is also presented for removing blurring artifacts caused by the linear or cubic-spline interpolation using the directionally adaptive truncated constrained least squares (TCLS) filter. Both proposed steerable filter-based interpolation and the TCLS-based restoration filters have a finite impulse response (FIR) structure for real time processing in an image signal processing (ISP) chain. Experimental results show that the proposed digital zooming system provides high-quality magnified images with FIR filter-based fast computational structure.
A Parallel Strategy for High-speed Interpolation of CNC Using Data Space Constraint Method
Directory of Open Access Journals (Sweden)
Shuan-qiang Yang
2013-12-01
Full Text Available A high-speed interpolation scheme using parallel computing is proposed in this paper. The interpolation method is divided into two tasks, namely, the rough task executing in PC and the fine task in the I/O card. During the interpolation procedure, the double buffers are constructed to exchange the interpolation data between the two tasks. Then, the data space constraint method is adapted to ensure the reliable and continuous data communication between the two buffers. Therefore, the proposed scheme can be realized in the common distribution of the operation systems without real-time performance. The high-speed and high-precision motion control can be achieved as well. Finally, an experiment is conducted on the self-developed CNC platform, the test results are shown to verify the proposed method.
Node insertion in Coalescence Fractal Interpolation Function
International Nuclear Information System (INIS)
Prasad, Srijanani Anurag
2013-01-01
The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed
New analytic unitarization schemes
International Nuclear Information System (INIS)
Cudell, J.-R.; Predazzi, E.; Selyugin, O. V.
2009-01-01
We consider two well-known classes of unitarization of Born amplitudes of hadron elastic scattering. The standard class, which saturates at the black-disk limit includes the standard eikonal representation, while the other class, which goes beyond the black-disk limit to reach the full unitarity circle, includes the U matrix. It is shown that the basic properties of these schemes are independent of the functional form used for the unitarization, and that U matrix and eikonal schemes can be extended to have similar properties. A common form of unitarization is proposed interpolating between both classes. The correspondence with different nonlinear equations are also briefly examined.
Pricing and simulation for real estate index options: Radial basis point interpolation
Gong, Pu; Zou, Dong; Wang, Jiayue
2018-06-01
This study employs the meshfree radial basis point interpolation (RBPI) for pricing real estate derivatives contingent on real estate index. This method combines radial and polynomial basis functions, which can guarantee the interpolation scheme with Kronecker property and effectively improve accuracy. An exponential change of variables, a mesh refinement algorithm and the Richardson extrapolation are employed in this study to implement the RBPI. Numerical results are presented to examine the computational efficiency and accuracy of our method.
Bayer Demosaicking with Polynomial Interpolation.
Wu, Jiaji; Anisetti, Marco; Wu, Wei; Damiani, Ernesto; Jeon, Gwanggil
2016-08-30
Demosaicking is a digital image process to reconstruct full color digital images from incomplete color samples from an image sensor. It is an unavoidable process for many devices incorporating camera sensor (e.g. mobile phones, tablet, etc.). In this paper, we introduce a new demosaicking algorithm based on polynomial interpolation-based demosaicking (PID). Our method makes three contributions: calculation of error predictors, edge classification based on color differences, and a refinement stage using a weighted sum strategy. Our new predictors are generated on the basis of on the polynomial interpolation, and can be used as a sound alternative to other predictors obtained by bilinear or Laplacian interpolation. In this paper we show how our predictors can be combined according to the proposed edge classifier. After populating three color channels, a refinement stage is applied to enhance the image quality and reduce demosaicking artifacts. Our experimental results show that the proposed method substantially improves over existing demosaicking methods in terms of objective performance (CPSNR, S-CIELAB E, and FSIM), and visual performance.
Interpolant Tree Automata and their Application in Horn Clause Verification
Directory of Open Access Journals (Sweden)
Bishoksan Kafle
2016-07-01
Full Text Available This paper investigates the combination of abstract interpretation over the domain of convex polyhedra with interpolant tree automata, in an abstraction-refinement scheme for Horn clause verification. These techniques have been previously applied separately, but are combined in a new way in this paper. The role of an interpolant tree automaton is to provide a generalisation of a spurious counterexample during refinement, capturing a possibly infinite set of spurious counterexample traces. In our approach these traces are then eliminated using a transformation of the Horn clauses. We compare this approach with two other methods; one of them uses interpolant tree automata in an algorithm for trace abstraction and refinement, while the other uses abstract interpretation over the domain of convex polyhedra without the generalisation step. Evaluation of the results of experiments on a number of Horn clause verification problems indicates that the combination of interpolant tree automaton with abstract interpretation gives some increase in the power of the verification tool, while sometimes incurring a performance overhead.
A temporal interpolation approach for dynamic reconstruction in perfusion CT
International Nuclear Information System (INIS)
Montes, Pau; Lauritsch, Guenter
2007-01-01
This article presents a dynamic CT reconstruction algorithm for objects with time dependent attenuation coefficient. Projection data acquired over several rotations are interpreted as samples of a continuous signal. Based on this idea, a temporal interpolation approach is proposed which provides the maximum temporal resolution for a given rotational speed of the CT scanner. Interpolation is performed using polynomial splines. The algorithm can be adapted to slow signals, reducing the amount of data acquired and the computational cost. A theoretical analysis of the approximations made by the algorithm is provided. In simulation studies, the temporal interpolation approach is compared with three other dynamic reconstruction algorithms based on linear regression, linear interpolation, and generalized Parker weighting. The presented algorithm exhibits the highest temporal resolution for a given sampling interval. Hence, our approach needs less input data to achieve a certain quality in the reconstruction than the other algorithms discussed or, equivalently, less x-ray exposure and computational complexity. The proposed algorithm additionally allows the possibility of using slow rotating scanners for perfusion imaging purposes
2016-02-11
experiments were then conducted on the same BABEL task. The acoustic models were trained on 46 hours of speech. Tan - dem and hybrid DNN systems were...interpolation gave a comparable WER score of 46.9%. A fur - ther linear interpolation using equation (11) between the back-off based interpolated LM and the
Application of ordinary kriging for interpolation of micro-structured technical surfaces
International Nuclear Information System (INIS)
Raid, Indek; Kusnezowa, Tatjana; Seewig, Jörg
2013-01-01
Kriging is an interpolation technique used in geostatistics. In this paper we present kriging applied in the field of three-dimensional optical surface metrology. Technical surfaces are not always optically cooperative, meaning that measurements of technical surfaces contain invalid data points because of different effects. These data points need to be interpolated to obtain a complete area in order to fulfil further processing. We present an elementary type of kriging, known as ordinary kriging, and apply it to interpolate measurements of different technical surfaces containing different kinds of realistic defects. The result of the interpolation with kriging is compared to six common interpolation techniques: nearest neighbour, natural neighbour, inverse distance to a power, triangulation with linear interpolation, modified Shepard's method and radial basis function. In order to quantify the results of different interpolations, the topographies are compared to defect-free reference topographies. Kriging is derived from a stochastic model that suggests providing an unbiased, linear estimation with a minimized error variance. The estimation with kriging is based on a preceding statistical analysis of the spatial structure of the surface. This comprises the choice and adaptation of specific models of spatial continuity. In contrast to common methods, kriging furthermore considers specific anisotropy in the data and adopts the interpolation accordingly. The gained benefit requires some additional effort in preparation and makes the overall estimation more time-consuming than common methods. However, the adaptation to the data makes this method very flexible and accurate. (paper)
A rational function based scheme for solving advection equation
International Nuclear Information System (INIS)
Xiao, Feng; Yabe, Takashi.
1995-07-01
A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in surpressinging overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily swicthed as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme. (author)
Potential problems with interpolating fields
Energy Technology Data Exchange (ETDEWEB)
Birse, Michael C. [The University of Manchester, Theoretical Physics Division, School of Physics and Astronomy, Manchester (United Kingdom)
2017-11-15
A potential can have features that do not reflect the dynamics of the system it describes but rather arise from the choice of interpolating fields used to define it. This is illustrated using a toy model of scattering with two coupled channels. A Bethe-Salpeter amplitude is constructed which is a mixture of the waves in the two channels. The potential derived from this has a strong repulsive core, which arises from the admixture of the closed channel in the wave function and not from the dynamics of the model. (orig.)
Directory of Open Access Journals (Sweden)
Huiqing Fang
2016-01-01
Full Text Available Based on geometrically exact beam theory, a hybrid interpolation is proposed for geometric nonlinear spatial Euler-Bernoulli beam elements. First, the Hermitian interpolation of the beam centerline was used for calculating nodal curvatures for two ends. Then, internal curvatures of the beam were interpolated with a second interpolation. At this point, C1 continuity was satisfied and nodal strain measures could be consistently derived from nodal displacement and rotation parameters. The explicit expression of nodal force without integration, as a function of global parameters, was founded by using the hybrid interpolation. Furthermore, the proposed beam element can be degenerated into linear beam element under the condition of small deformation. Objectivity of strain measures and patch tests are also discussed. Finally, four numerical examples are discussed to prove the validity and effectivity of the proposed beam element.
Conformal Interpolating Algorithm Based on Cubic NURBS in Aspheric Ultra-Precision Machining
International Nuclear Information System (INIS)
Li, C G; Zhang, Q R; Cao, C G; Zhao, S L
2006-01-01
Numeric control machining and on-line compensation for aspheric surface are key techniques in ultra-precision machining. In this paper, conformal cubic NURBS interpolating curve is applied to fit the character curve of aspheric surface. Its algorithm and process are also proposed and imitated by Matlab7.0 software. To evaluate the performance of the conformal cubic NURBS interpolation, we compare it with the linear interpolations. The result verifies this method can ensure smoothness of interpolating spline curve and preserve original shape characters. The surface quality interpolated by cubic NURBS is higher than by line. The algorithm is benefit to increasing the surface form precision of workpieces in ultra-precision machining
Interpolation of rational matrix functions
Ball, Joseph A; Rodman, Leiba
1990-01-01
This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an indepe...
Evaluation of various interpolants available in DICE
Energy Technology Data Exchange (ETDEWEB)
Turner, Daniel Z. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Reu, Phillip L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Crozier, Paul [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-02-01
This report evaluates several interpolants implemented in the Digital Image Correlation Engine (DICe), an image correlation software package developed by Sandia. By interpolants we refer to the basis functions used to represent discrete pixel intensity data as a continuous signal. Interpolation is used to determine intensity values in an image at non - pixel locations. It is also used, in some cases, to evaluate the x and y gradients of the image intensities. Intensity gradients subsequently guide the optimization process. The goal of this report is to inform analysts as to the characteristics of each interpolant and provide guidance towards the best interpolant for a given dataset. This work also serves as an initial verification of each of the interpolants implemented.
Data interpolation for vibration diagnostics using two-variable correlations
International Nuclear Information System (INIS)
Branagan, L.
1991-01-01
This paper reports that effective machinery vibration diagnostics require a clear differentiation between normal vibration changes caused by plant process conditions and those caused by degradation. The normal relationship between vibration and a process parameter can be quantified by developing the appropriate correlation. The differences in data acquisition requirements between dynamic signals (vibration spectra) and static signals (pressure, temperature, etc.) result in asynchronous data acquisition; the development of any correlation must then be based on some form of interpolated data. This interpolation can reproduce or distort the original measured quantity depending on the characteristics of the data and the interpolation technique. Relevant data characteristics, such as acquisition times, collection cycle times, compression method, storage rate, and the slew rate of the measured variable, are dependent both on the data handling and on the measured variable. Linear and staircase interpolation, along with the use of clustering and filtering, provide the necessary options to develop accurate correlations. The examples illustrate the appropriate application of these options
Research on interpolation methods in medical image processing.
Pan, Mei-Sen; Yang, Xiao-Li; Tang, Jing-Tian
2012-04-01
Image interpolation is widely used for the field of medical image processing. In this paper, interpolation methods are divided into three groups: filter interpolation, ordinary interpolation and general partial volume interpolation. Some commonly-used filter methods for image interpolation are pioneered, but the interpolation effects need to be further improved. When analyzing and discussing ordinary interpolation, many asymmetrical kernel interpolation methods are proposed. Compared with symmetrical kernel ones, the former are have some advantages. After analyzing the partial volume and generalized partial volume estimation interpolations, the new concept and constraint conditions of the general partial volume interpolation are defined, and several new partial volume interpolation functions are derived. By performing the experiments of image scaling, rotation and self-registration, the interpolation methods mentioned in this paper are compared in the entropy, peak signal-to-noise ratio, cross entropy, normalized cross-correlation coefficient and running time. Among the filter interpolation methods, the median and B-spline filter interpolations have a relatively better interpolating performance. Among the ordinary interpolation methods, on the whole, the symmetrical cubic kernel interpolations demonstrate a strong advantage, especially the symmetrical cubic B-spline interpolation. However, we have to mention that they are very time-consuming and have lower time efficiency. As for the general partial volume interpolation methods, from the total error of image self-registration, the symmetrical interpolations provide certain superiority; but considering the processing efficiency, the asymmetrical interpolations are better.
Cardinal Basis Piecewise Hermite Interpolation on Fuzzy Data
Directory of Open Access Journals (Sweden)
H. Vosoughi
2016-01-01
Full Text Available A numerical method along with explicit construction to interpolation of fuzzy data through the extension principle results by widely used fuzzy-valued piecewise Hermite polynomial in general case based on the cardinal basis functions, which satisfy a vanishing property on the successive intervals, has been introduced here. We have provided a numerical method in full detail using the linear space notions for calculating the presented method. In order to illustrate the method in computational examples, we take recourse to three prime cases: linear, cubic, and quintic.
Generalization of binary tensor product schemes depends upon four parameters
International Nuclear Information System (INIS)
Bashir, R.; Bari, M.; Mustafa, G.
2018-01-01
This article deals with general formulae of parametric and non parametric bivariate subdivision scheme with four parameters. By assigning specific values to those parameters we get some special cases of existing tensor product schemes as well as a new proposed scheme. The behavior of schemes produced by the general formulae is interpolating, approximating and relaxed. Approximating bivariate subdivision schemes produce some other surfaces as compared to interpolating bivariate subdivision schemes. Polynomial reproduction and polynomial generation are desirable properties of subdivision schemes. Capability of polynomial reproduction and polynomial generation is strongly connected with smoothness, sum rules, convergence and approximation order. We also calculate the polynomial generation and polynomial reproduction of 9-point bivariate approximating subdivision scheme. Comparison of polynomial reproduction, polynomial generation and continuity of existing and proposed schemes has also been established. Some numerical examples are also presented to show the behavior of bivariate schemes. (author)
Differential Interpolation Effects in Free Recall
Petrusic, William M.; Jamieson, Donald G.
1978-01-01
Attempts to determine whether a sufficiently demanding and difficult interpolated task (shadowing, i.e., repeating aloud) would decrease recall for earlier-presented items as well as for more recent items. Listening to music was included as a second interpolated task. Results support views that serial position effects reflect a single process.…
Analysis of velocity planning interpolation algorithm based on NURBS curve
Zhang, Wanjun; Gao, Shanping; Cheng, Xiyan; Zhang, Feng
2017-04-01
To reduce interpolation time and Max interpolation error in NURBS (Non-Uniform Rational B-Spline) inter-polation caused by planning Velocity. This paper proposed a velocity planning interpolation algorithm based on NURBS curve. Firstly, the second-order Taylor expansion is applied on the numerator in NURBS curve representation with parameter curve. Then, velocity planning interpolation algorithm can meet with NURBS curve interpolation. Finally, simulation results show that the proposed NURBS curve interpolator meet the high-speed and high-accuracy interpolation requirements of CNC systems. The interpolation of NURBS curve should be finished.
An Improved Rotary Interpolation Based on FPGA
Directory of Open Access Journals (Sweden)
Mingyu Gao
2014-08-01
Full Text Available This paper presents an improved rotary interpolation algorithm, which consists of a standard curve interpolation module and a rotary process module. Compared to the conventional rotary interpolation algorithms, the proposed rotary interpolation algorithm is simpler and more efficient. The proposed algorithm was realized on a FPGA with Verilog HDL language, and simulated by the ModelSim software, and finally verified on a two-axis CNC lathe, which uses rotary ellipse and rotary parabolic as an example. According to the theoretical analysis and practical process validation, the algorithm has the following advantages: firstly, less arithmetic items is conducive for interpolation operation; and secondly the computing time is only two clock cycles of the FPGA. Simulations and actual tests have proved that the high accuracy and efficiency of the algorithm, which shows that it is highly suited for real-time applications.
Dynamic Stability Analysis Using High-Order Interpolation
Directory of Open Access Journals (Sweden)
Juarez-Toledo C.
2012-10-01
Full Text Available A non-linear model with robust precision for transient stability analysis in multimachine power systems is proposed. The proposed formulation uses the interpolation of Lagrange and Newton's Divided Difference. The High-Order Interpolation technique developed can be used for evaluation of the critical conditions of the dynamic system.The technique is applied to a 5-area 45-machine model of the Mexican interconnected system. As a particular case, this paper shows the application of the High-Order procedure for identifying the slow-frequency mode for a critical contingency. Numerical examples illustrate the method and demonstrate the ability of the High-Order technique to isolate and extract temporal modal behavior.
Gridded precipitation dataset for the Rhine basin made with the genRE interpolation method
Osnabrugge, van B.; Uijlenhoet, R.
2017-01-01
A high resolution (1.2x1.2km) gridded precipitation dataset with hourly time step that covers the whole Rhine basin for the period 1997-2015. Made from gauge data with the genRE interpolation scheme. See "genRE: A method to extend gridded precipitation climatology datasets in near real-time for
Spatiotemporal video deinterlacing using control grid interpolation
Venkatesan, Ragav; Zwart, Christine M.; Frakes, David H.; Li, Baoxin
2015-03-01
With the advent of progressive format display and broadcast technologies, video deinterlacing has become an important video-processing technique. Numerous approaches exist in the literature to accomplish deinterlacing. While most earlier methods were simple linear filtering-based approaches, the emergence of faster computing technologies and even dedicated video-processing hardware in display units has allowed higher quality but also more computationally intense deinterlacing algorithms to become practical. Most modern approaches analyze motion and content in video to select different deinterlacing methods for various spatiotemporal regions. We introduce a family of deinterlacers that employs spectral residue to choose between and weight control grid interpolation based spatial and temporal deinterlacing methods. The proposed approaches perform better than the prior state-of-the-art based on peak signal-to-noise ratio, other visual quality metrics, and simple perception-based subjective evaluations conducted by human viewers. We further study the advantages of using soft and hard decision thresholds on the visual performance.
Interferometric interpolation of sparse marine data
Hanafy, Sherif M.
2013-10-11
We present the theory and numerical results for interferometrically interpolating 2D and 3D marine surface seismic profiles data. For the interpolation of seismic data we use the combination of a recorded Green\\'s function and a model-based Green\\'s function for a water-layer model. Synthetic (2D and 3D) and field (2D) results show that the seismic data with sparse receiver intervals can be accurately interpolated to smaller intervals using multiples in the data. An up- and downgoing separation of both recorded and model-based Green\\'s functions can help in minimizing artefacts in a virtual shot gather. If the up- and downgoing separation is not possible, noticeable artefacts will be generated in the virtual shot gather. As a partial remedy we iteratively use a non-stationary 1D multi-channel matching filter with the interpolated data. Results suggest that a sparse marine seismic survey can yield more information about reflectors if traces are interpolated by interferometry. Comparing our results to those of f-k interpolation shows that the synthetic example gives comparable results while the field example shows better interpolation quality for the interferometric method. © 2013 European Association of Geoscientists & Engineers.
Vedadi, Farhang; Shirani, Shahram
2014-01-01
A new method of image resolution up-conversion (image interpolation) based on maximum a posteriori sequence estimation is proposed. Instead of making a hard decision about the value of each missing pixel, we estimate the missing pixels in groups. At each missing pixel of the high resolution (HR) image, we consider an ensemble of candidate interpolation methods (interpolation functions). The interpolation functions are interpreted as states of a Markov model. In other words, the proposed method undergoes state transitions from one missing pixel position to the next. Accordingly, the interpolation problem is translated to the problem of estimating the optimal sequence of interpolation functions corresponding to the sequence of missing HR pixel positions. We derive a parameter-free probabilistic model for this to-be-estimated sequence of interpolation functions. Then, we solve the estimation problem using a trellis representation and the Viterbi algorithm. Using directional interpolation functions and sequence estimation techniques, we classify the new algorithm as an adaptive directional interpolation using soft-decision estimation techniques. Experimental results show that the proposed algorithm yields images with higher or comparable peak signal-to-noise ratios compared with some benchmark interpolation methods in the literature while being efficient in terms of implementation and complexity considerations.
Computationally efficient real-time interpolation algorithm for non-uniform sampled biosignals.
Guven, Onur; Eftekhar, Amir; Kindt, Wilko; Constandinou, Timothy G
2016-06-01
This Letter presents a novel, computationally efficient interpolation method that has been optimised for use in electrocardiogram baseline drift removal. In the authors' previous Letter three isoelectric baseline points per heartbeat are detected, and here utilised as interpolation points. As an extension from linear interpolation, their algorithm segments the interpolation interval and utilises different piecewise linear equations. Thus, the algorithm produces a linear curvature that is computationally efficient while interpolating non-uniform samples. The proposed algorithm is tested using sinusoids with different fundamental frequencies from 0.05 to 0.7 Hz and also validated with real baseline wander data acquired from the Massachusetts Institute of Technology University and Boston's Beth Israel Hospital (MIT-BIH) Noise Stress Database. The synthetic data results show an root mean square (RMS) error of 0.9 μV (mean), 0.63 μV (median) and 0.6 μV (standard deviation) per heartbeat on a 1 mVp-p 0.1 Hz sinusoid. On real data, they obtain an RMS error of 10.9 μV (mean), 8.5 μV (median) and 9.0 μV (standard deviation) per heartbeat. Cubic spline interpolation and linear interpolation on the other hand shows 10.7 μV, 11.6 μV (mean), 7.8 μV, 8.9 μV (median) and 9.8 μV, 9.3 μV (standard deviation) per heartbeat.
DATASPACE - A PROGRAM FOR THE LOGARITHMIC INTERPOLATION OF TEST DATA
Ledbetter, F. E.
1994-01-01
Scientists and engineers work with the reduction, analysis, and manipulation of data. In many instances, the recorded data must meet certain requirements before standard numerical techniques may be used to interpret it. For example, the analysis of a linear visoelastic material requires knowledge of one of two time-dependent properties, the stress relaxation modulus E(t) or the creep compliance D(t), one of which may be derived from the other by a numerical method if the recorded data points are evenly spaced or increasingly spaced with respect to the time coordinate. The problem is that most laboratory data are variably spaced, making the use of numerical techniques difficult. To ease this difficulty in the case of stress relaxation data analysis, NASA scientists developed DATASPACE (A Program for the Logarithmic Interpolation of Test Data), to establish a logarithmically increasing time interval in the relaxation data. The program is generally applicable to any situation in which a data set needs increasingly spaced abscissa values. DATASPACE first takes the logarithm of the abscissa values, then uses a cubic spline interpolation routine (which minimizes interpolation error) to create an evenly spaced array from the log values. This array is returned from the log abscissa domain to the abscissa domain and written to an output file for further manipulation. As a result of the interpolation in the log abscissa domain, the data is increasingly spaced. In the case of stress relaxation data, the array is closely spaced at short times and widely spaced at long times, thus avoiding the distortion inherent in evenly spaced time coordinates. The interpolation routine gives results which compare favorably with the recorded data. The experimental data curve is retained and the interpolated points reflect the desired spacing. DATASPACE is written in FORTRAN 77 for IBM PC compatibles with a math co-processor running MS-DOS and Apple Macintosh computers running MacOS. With
NOAA Optimum Interpolation (OI) SST V2
National Oceanic and Atmospheric Administration, Department of Commerce — The optimum interpolation (OI) sea surface temperature (SST) analysis is produced weekly on a one-degree grid. The analysis uses in situ and satellite SST's plus...
Kuu plaat : Interpol Antics. Plaadid kauplusest Lasering
2005-01-01
Heliplaatidest: "Interpol Antics", Scooter "Mind the Gap", Slide-Fifty "The Way Ahead", Psyhhoterror "Freddy, löö esimesena!", Riho Sibul "Must", Bossacucanova "Uma Batida Diferente", "Biscantorat - Sound of the spirit from Glenstal Abbey"
NOAA Daily Optimum Interpolation Sea Surface Temperature
National Oceanic and Atmospheric Administration, Department of Commerce — The NOAA 1/4° daily Optimum Interpolation Sea Surface Temperature (or daily OISST) is an analysis constructed by combining observations from different platforms...
Integration and interpolation of sampled waveforms
International Nuclear Information System (INIS)
Stearns, S.D.
1978-01-01
Methods for integrating, interpolating, and improving the signal-to-noise ratio of digitized waveforms are discussed with regard to seismic data from underground tests. The frequency-domain integration method and the digital interpolation method of Schafer and Rabiner are described and demonstrated using test data. The use of bandpass filtering for noise reduction is also demonstrated. With these methods, a backlog of seismic test data has been successfully processed
Wideband DOA Estimation through Projection Matrix Interpolation
Selva, J.
2017-01-01
This paper presents a method to reduce the complexity of the deterministic maximum likelihood (DML) estimator in the wideband direction-of-arrival (WDOA) problem, which is based on interpolating the array projection matrix in the temporal frequency variable. It is shown that an accurate interpolator like Chebyshev's is able to produce DML cost functions comprising just a few narrowband-like summands. Actually, the number of such summands is far smaller (roughly by factor ten in the numerical ...
Interpolation for a subclass of H
Indian Academy of Sciences (India)
|g(zm)| ≤ c |zm − zm |, ∀m ∈ N. Thus it is natural to pose the following interpolation problem for H. ∞. : DEFINITION 4. We say that (zn) is an interpolating sequence in the weak sense for H. ∞ if given any sequence of complex numbers (λn) verifying. |λn| ≤ c ψ(zn,z. ∗ n) |zn − zn |, ∀n ∈ N,. (4) there exists a product fg ∈ H.
Workload Balancing on Heterogeneous Systems: A Case Study of Sparse Grid Interpolation
Muraraşu, Alin
2012-01-01
Multi-core parallelism and accelerators are becoming common features of today’s computer systems, as they allow for computational power without sacrificing energy efficiency. Due to heterogeneity, tuning for each type of compute unit and adequate load balancing is essential. This paper proposes static and dynamic solutions for load balancing in the context of an application for visualizing high-dimensional simulation data. The application relies on the sparse grid technique for data compression. Its performance critical part is the interpolation routine used for decompression. Results show that our load balancing scheme allows for an efficient acceleration of interpolation on heterogeneous systems containing multi-core CPUs and GPUs.
Reconstruction of reflectance data using an interpolation technique.
Abed, Farhad Moghareh; Amirshahi, Seyed Hossein; Abed, Mohammad Reza Moghareh
2009-03-01
A linear interpolation method is applied for reconstruction of reflectance spectra of Munsell as well as ColorChecker SG color chips from the corresponding colorimetric values under a given set of viewing conditions. Hence, different types of lookup tables (LUTs) have been created to connect the colorimetric and spectrophotometeric data as the source and destination spaces in this approach. To optimize the algorithm, different color spaces and light sources have been used to build different types of LUTs. The effects of applied color datasets as well as employed color spaces are investigated. Results of recovery are evaluated by the mean and the maximum color difference values under other sets of standard light sources. The mean and the maximum values of root mean square (RMS) error between the reconstructed and the actual spectra are also calculated. Since the speed of reflectance reconstruction is a key point in the LUT algorithm, the processing time spent for interpolation of spectral data has also been measured for each model. Finally, the performance of the suggested interpolation technique is compared with that of the common principal component analysis method. According to the results, using the CIEXYZ tristimulus values as a source space shows priority over the CIELAB color space. Besides, the colorimetric position of a desired sample is a key point that indicates the success of the approach. In fact, because of the nature of the interpolation technique, the colorimetric position of the desired samples should be located inside the color gamut of available samples in the dataset. The resultant spectra that have been reconstructed by this technique show considerable improvement in terms of RMS error between the actual and the reconstructed reflectance spectra as well as CIELAB color differences under the other light source in comparison with those obtained from the standard PCA technique.
Image interpolation via graph-based Bayesian label propagation.
Xianming Liu; Debin Zhao; Jiantao Zhou; Wen Gao; Huifang Sun
2014-03-01
In this paper, we propose a novel image interpolation algorithm via graph-based Bayesian label propagation. The basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices, then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones. This process can be posed as a Bayesian inference, in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation. Specially, our algorithm first constructs a set of local interpolation models, which predict the intensity labels of all image samples, and a loss term will be minimized to keep the predicted labels of the available low-resolution (LR) samples sufficiently close to the original ones. Then, all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples. Moreover, a graph-Laplacian-based manifold regularization term is incorporated to penalize the global smoothness of intensity labels, such smoothing can alleviate the insufficient training of the local models and make them more robust. Finally, we construct a unified objective function to combine together the global loss of the locally linear regression, square error of prediction bias on the available LR samples, and the manifold regularization term. It can be solved with a closed-form solution as a convex optimization problem. Experimental results demonstrate that the proposed method achieves competitive performance with the state-of-the-art image interpolation algorithms.
Calculation of electromagnetic parameter based on interpolation algorithm
International Nuclear Information System (INIS)
Zhang, Wenqiang; Yuan, Liming; Zhang, Deyuan
2015-01-01
Wave-absorbing material is an important functional material of electromagnetic protection. The wave-absorbing characteristics depend on the electromagnetic parameter of mixed media. In order to accurately predict the electromagnetic parameter of mixed media and facilitate the design of wave-absorbing material, based on the electromagnetic parameters of spherical and flaky carbonyl iron mixture of paraffin base, this paper studied two different interpolation methods: Lagrange interpolation and Hermite interpolation of electromagnetic parameters. The results showed that Hermite interpolation is more accurate than the Lagrange interpolation, and the reflectance calculated with the electromagnetic parameter obtained by interpolation is consistent with that obtained through experiment on the whole. - Highlights: • We use interpolation algorithm on calculation of EM-parameter with limited samples. • Interpolation method can predict EM-parameter well with different particles added. • Hermite interpolation is more accurate than Lagrange interpolation. • Calculating RL based on interpolation is consistent with calculating RL from experiment
MODIS Snow Cover Recovery Using Variational Interpolation
Tran, H.; Nguyen, P.; Hsu, K. L.; Sorooshian, S.
2017-12-01
Cloud obscuration is one of the major problems that limit the usages of satellite images in general and in NASA's Moderate Resolution Imaging Spectroradiometer (MODIS) global Snow-Covered Area (SCA) products in particular. Among the approaches to resolve the problem, the Variational Interpolation (VI) algorithm method, proposed by Xia et al., 2012, obtains cloud-free dynamic SCA images from MODIS. This method is automatic and robust. However, computational deficiency is a main drawback that degrades applying the method for larger scales (i.e., spatial and temporal scales). To overcome this difficulty, this study introduces an improved version of the original VI. The modified VI algorithm integrates the MINimum RESidual (MINRES) iteration (Paige and Saunders., 1975) to prevent the system from breaking up when applied to much broader scales. An experiment was done to demonstrate the crash-proof ability of the new algorithm in comparison with the original VI method, an ability that is obtained when maintaining the distribution of the weights set after solving the linear system. After that, the new VI algorithm was applied to the whole Contiguous United States (CONUS) over four winter months of 2016 and 2017, and validated using the snow station network (SNOTEL). The resulting cloud free images have high accuracy in capturing the dynamical changes of snow in contrast with the MODIS snow cover maps. Lastly, the algorithm was applied to create a Cloud free images dataset from March 10, 2000 to February 28, 2017, which is able to provide an overview of snow trends over CONUS for nearly two decades. ACKNOWLEDGMENTSWe would like to acknowledge NASA, NOAA Office of Hydrologic Development (OHD) National Weather Service (NWS), Cooperative Institute for Climate and Satellites (CICS), Army Research Office (ARO), ICIWaRM, and UNESCO for supporting this research.
Bonus schemes and trading activity
Pikulina, E.S.; Renneboog, L.D.R.; ter Horst, J.R.; Tobler, P.N.
2014-01-01
Little is known about how different bonus schemes affect traders' propensity to trade and which bonus schemes improve traders' performance. We study the effects of linear versus threshold bonus schemes on traders' behavior. Traders buy and sell shares in an experimental stock market on the basis of
Energy Technology Data Exchange (ETDEWEB)
Clarisse, J.M
2007-07-01
A numerical scheme for computing linear Lagrangian perturbations of spherically symmetric flows of gas dynamics is proposed. This explicit first-order scheme uses the Roe method in Lagrangian coordinates, for computing the radial spherically symmetric mean flow, and its linearized version, for treating the three-dimensional linear perturbations. Fulfillment of the geometric conservation law discrete formulations for both the mean flow and its perturbation is ensured. This scheme capabilities are illustrated by the computation of free-surface mode evolutions at the boundaries of a spherical hollow shell undergoing an homogeneous cumulative compression, showing excellent agreement with reference results. (author)
A Hybrid Method for Interpolating Missing Data in Heterogeneous Spatio-Temporal Datasets
Directory of Open Access Journals (Sweden)
Min Deng
2016-02-01
Full Text Available Space-time interpolation is widely used to estimate missing or unobserved values in a dataset integrating both spatial and temporal records. Although space-time interpolation plays a key role in space-time modeling, existing methods were mainly developed for space-time processes that exhibit stationarity in space and time. It is still challenging to model heterogeneity of space-time data in the interpolation model. To overcome this limitation, in this study, a novel space-time interpolation method considering both spatial and temporal heterogeneity is developed for estimating missing data in space-time datasets. The interpolation operation is first implemented in spatial and temporal dimensions. Heterogeneous covariance functions are constructed to obtain the best linear unbiased estimates in spatial and temporal dimensions. Spatial and temporal correlations are then considered to combine the interpolation results in spatial and temporal dimensions to estimate the missing data. The proposed method is tested on annual average temperature and precipitation data in China (1984–2009. Experimental results show that, for these datasets, the proposed method outperforms three state-of-the-art methods—e.g., spatio-temporal kriging, spatio-temporal inverse distance weighting, and point estimation model of biased hospitals-based area disease estimation methods.
Directory of Open Access Journals (Sweden)
Mauricio Castro Franco
2017-07-01
Full Text Available Context: Interpolating soil properties at field-scale in the Colombian piedmont eastern plains is challenging due to: the highly and complex variable nature of some processes; the effects of the soil; the land use; and the management. While interpolation techniques are being adapted to include auxiliary information of these effects, the soil data are often difficult to predict using conventional techniques of spatial interpolation. Method: In this paper, we evaluated and compared six spatial interpolation techniques: Inverse Distance Weighting (IDW, Spline, Ordinary Kriging (KO, Universal Kriging (UK, Cokriging (Ckg, and Residual Maximum Likelihood-Empirical Best Linear Unbiased Predictor (REML-EBLUP, from conditioned Latin Hypercube as a sampling strategy. The ancillary information used in Ckg and REML-EBLUP was indexes calculated from a digital elevation model (MDE. The “Random forest” algorithm was used for selecting the most important terrain index for each soil properties. Error metrics were used to validate interpolations against cross validation. Results: The results support the underlying assumption that HCLc captured adequately the full distribution of variables of ancillary information in the Colombian piedmont eastern plains conditions. They also suggest that Ckg and REML-EBLUP perform best in the prediction in most of the evaluated soil properties. Conclusions: Mixed interpolation techniques having auxiliary soil information and terrain indexes, provided a significant improvement in the prediction of soil properties, in comparison with other techniques.
Interpolated sagittal and coronal reconstruction of CT images in the screening of neck abnormalities
International Nuclear Information System (INIS)
Koga, Issei
1983-01-01
Recontructed sagittal and coronal images were analyzed for their usefulness during clinical applications and to determine the correct use of recontruction techniques. Recontructed stereoscopic images can be formed by continuous or interrupted image reconstruction using interpolation. This study showed that lesions less than 10 mm in diameter should be made continuously and recontructed with uninterrupted technique. However, 5 mm interrupted distances are acceptable for interpolated reconstruction except in cases of lesions less than 10 mm in diameter. Clinically, interpolated reconstruction is not adequated for semicircular lesions less than 10 mm. Blood vessels and linear lesions are good condiated for the application of interpolated recontruction. Reconstruction of images using interrupted interpolation is therefore recommended for screening and for demonstrating correct stereoscopic information, except cases of small lesions less than 10 mm in diameter. Results of this study underscore the fact that obscure information in transverse CT images should be routinely utilized by interporating recontruction techniques, if transverse images are not made continuously. Interpolated recontruction may be helpful in obtaining stereoscopic information. (author)
Finite-dimensional linear algebra
Gockenbach, Mark S
2010-01-01
Some Problems Posed on Vector SpacesLinear equationsBest approximationDiagonalizationSummaryFields and Vector SpacesFields Vector spaces Subspaces Linear combinations and spanning sets Linear independence Basis and dimension Properties of bases Polynomial interpolation and the Lagrange basis Continuous piecewise polynomial functionsLinear OperatorsLinear operatorsMore properties of linear operatorsIsomorphic vector spaces Linear operator equations Existence and uniqueness of solutions The fundamental theorem; inverse operatorsGaussian elimination Newton's method Linear ordinary differential eq
Discrete Orthogonal Transforms and Neural Networks for Image Interpolation
Directory of Open Access Journals (Sweden)
J. Polec
1999-09-01
Full Text Available In this contribution we present transform and neural network approaches to the interpolation of images. From transform point of view, the principles from [1] are modified for 1st and 2nd order interpolation. We present several new interpolation discrete orthogonal transforms. From neural network point of view, we present interpolation possibilities of multilayer perceptrons. We use various configurations of neural networks for 1st and 2nd order interpolation. The results are compared by means of tables.
Motion compensated frame interpolation with a symmetric optical flow constraint
DEFF Research Database (Denmark)
Rakêt, Lars Lau; Roholm, Lars; Bruhn, Andrés
2012-01-01
We consider the problem of interpolating frames in an image sequence. For this purpose accurate motion estimation can be very helpful. We propose to move the motion estimation from the surrounding frames directly to the unknown frame by parametrizing the optical flow objective function such that ......We consider the problem of interpolating frames in an image sequence. For this purpose accurate motion estimation can be very helpful. We propose to move the motion estimation from the surrounding frames directly to the unknown frame by parametrizing the optical flow objective function...... methods. The proposed reparametrization is generic and can be applied to almost every existing algorithm. In this paper we illustrate its advantages by considering the classic TV-L1 optical flow algorithm as a prototype. We demonstrate that this widely used method can produce results that are competitive...... with current state-of-the-art methods. Finally we show that the scheme can be implemented on graphics hardware such that it be- comes possible to double the frame rate of 640 × 480 video footage at 30 fps, i.e. to perform frame doubling in realtime....
New families of interpolating type IIB backgrounds
Minasian, Ruben; Petrini, Michela; Zaffaroni, Alberto
2010-04-01
We construct new families of interpolating two-parameter solutions of type IIB supergravity. These correspond to D3-D5 systems on non-compact six-dimensional manifolds which are mathbb{T}2 fibrations over Eguchi-Hanson and multi-center Taub-NUT spaces, respectively. One end of the interpolation corresponds to a solution with only D5 branes and vanishing NS three-form flux. A topology changing transition occurs at the other end, where the internal space becomes a direct product of the four-dimensional surface and the two-torus and the complexified NS-RR three-form flux becomes imaginary self-dual. Depending on the choice of the connections on the torus fibre, the interpolating family has either mathcal{N}=2 or mathcal{N}=1 supersymmetry. In the mathcal{N}=2 case it can be shown that the solutions are regular.
Interpolation of quasi-Banach spaces
International Nuclear Information System (INIS)
Tabacco Vignati, A.M.
1986-01-01
This dissertation presents a method of complex interpolation for familities of quasi-Banach spaces. This method generalizes the theory for families of Banach spaces, introduced by others. Intermediate spaces in several particular cases are characterized using different approaches. The situation when all the spaces have finite dimensions is studied first. The second chapter contains the definitions and main properties of the new interpolation spaces, and an example concerning the Schatten ideals associated with a separable Hilbert space. The case of L/sup P/ spaces follows from the maximal operator theory contained in Chapter III. Also introduced is a different method of interpolation for quasi-Banach lattices of functions, and conditions are given to guarantee that the two techniques yield the same result. Finally, the last chapter contains a different, and more direct, approach to the case of Hardy spaces
Single-Image Super-Resolution Based on Rational Fractal Interpolation.
Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming
2018-08-01
This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.
The effect of interpolation methods in temperature and salinity trends in the Western Mediterranean
Directory of Open Access Journals (Sweden)
M. VARGAS-YANEZ
2012-04-01
Full Text Available Temperature and salinity data in the historical record are scarce and unevenly distributed in space and time and the estimation of linear trends is sensitive to different factors. In the case of the Western Mediterranean, previous works have studied the sensitivity of these trends to the use of bathythermograph data, the averaging methods or the way in which gaps in time series are dealt with. In this work, a new factor is analysed: the effect of data interpolation. Temperature and salinity time series are generated averaging existing data over certain geographical areas and also by means of interpolation. Linear trends from both types of time series are compared. There are some differences between both estimations for some layers and geographical areas, while in other cases the results are consistent. Those results which do not depend on the use of interpolated or non-interpolated data, neither are influenced by data analysis methods can be considered as robust ones. Those results influenced by the interpolation process or the factors analysed in previous sensitivity tests are not considered as robust results.
Treatment of Outliers via Interpolation Method with Neural Network Forecast Performances
Wahir, N. A.; Nor, M. E.; Rusiman, M. S.; Gopal, K.
2018-04-01
Outliers often lurk in many datasets, especially in real data. Such anomalous data can negatively affect statistical analyses, primarily normality, variance, and estimation aspects. Hence, handling the occurrences of outliers require special attention. Therefore, it is important to determine the suitable ways in treating outliers so as to ensure that the quality of the analyzed data is indeed high. As such, this paper discusses an alternative method to treat outliers via linear interpolation method. In fact, assuming outlier as a missing value in the dataset allows the application of the interpolation method to interpolate the outliers thus, enabling the comparison of data series using forecast accuracy before and after outlier treatment. With that, the monthly time series of Malaysian tourist arrivals from January 1998 until December 2015 had been used to interpolate the new series. The results indicated that the linear interpolation method, which was comprised of improved time series data, displayed better results, when compared to the original time series data in forecasting from both Box-Jenkins and neural network approaches.
The interpolation method based on endpoint coordinate for CT three-dimensional image
International Nuclear Information System (INIS)
Suto, Yasuzo; Ueno, Shigeru.
1997-01-01
Image interpolation is frequently used to improve slice resolution to reach spatial resolution. Improved quality of reconstructed three-dimensional images can be attained with this technique as a result. Linear interpolation is a well-known and widely used method. The distance-image method, which is a non-linear interpolation technique, is also used to convert CT value images to distance images. This paper describes a newly developed method that makes use of end-point coordinates: CT-value images are initially converted to binary images by thresholding them and then sequences of pixels with 1-value are arranged in vertical or horizontal directions. A sequence of pixels with 1-value is defined as a line segment which has starting and end points. For each pair of adjacent line segments, another line segment was composed by spatial interpolation of the start and end points. Binary slice images are constructed from the composed line segments. Three-dimensional images were reconstructed from clinical X-ray CT images, using three different interpolation methods and their quality and processing speed were evaluated and compared. (author)
Convection-diffusion lattice Boltzmann scheme for irregular lattices
Sman, van der R.G.M.; Ernst, M.H.
2000-01-01
In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the
Lattice Boltzmann scheme for diffusion on triangular grids
Sman, van der R.G.M.
2003-01-01
In this paper we present a Lattice Boltzmann scheme for diffusion on it unstructured triangular grids. In this formulation of a LB for irregular grids there is no need for interpolation, which is required in other LB schemes on irregular grids. At the end of the propagation step the lattice gas
BV-norm convergence of interpolation approximations for Frobenius-Perron operators
International Nuclear Information System (INIS)
Ding, J; Rhee, N
2008-01-01
Let S be a chaotic transformation from an interval into itself and let P be the corresponding Frobenius-Perron operator associated with S. In this paper we prove the convergence under the variation norm for a piecewise linear interpolation method that was recently proposed by the authors for computing a stationary density of P
Energy Technology Data Exchange (ETDEWEB)
Park, Jae Woo; Rhee, Young Min, E-mail: ymrhee@postech.ac.kr [Center for Self-assembly and Complexity, Institute for Basic Science (IBS), Pohang 790-784 (Korea, Republic of); Department of Chemistry, Pohang University of Science and Technology (POSTECH), Pohang 790-784 (Korea, Republic of)
2014-04-28
Simulating molecular dynamics directly on quantum chemically obtained potential energy surfaces is generally time consuming. The cost becomes overwhelming especially when excited state dynamics is aimed with multiple electronic states. The interpolated potential has been suggested as a remedy for the cost issue in various simulation settings ranging from fast gas phase reactions of small molecules to relatively slow condensed phase dynamics with complex surrounding. Here, we present a scheme for interpolating multiple electronic surfaces of a relatively large molecule, with an intention of applying it to studying nonadiabatic behaviors. The scheme starts with adiabatic potential information and its diabatic transformation, both of which can be readily obtained, in principle, with quantum chemical calculations. The adiabatic energies and their derivatives on each interpolation center are combined with the derivative coupling vectors to generate the corresponding diabatic Hamiltonian and its derivatives, and they are subsequently adopted in producing a globally defined diabatic Hamiltonian function. As a demonstration, we employ the scheme to build an interpolated Hamiltonian of a relatively large chromophore, para-hydroxybenzylidene imidazolinone, in reference to its all-atom analytical surface model. We show that the interpolation is indeed reliable enough to reproduce important features of the reference surface model, such as its adiabatic energies and derivative couplings. In addition, nonadiabatic surface hopping simulations with interpolation yield population transfer dynamics that is well in accord with the result generated with the reference analytic surface. With these, we conclude by suggesting that the interpolation of diabatic Hamiltonians will be applicable for studying nonadiabatic behaviors of sizeable molecules.
Multiscale empirical interpolation for solving nonlinear PDEs
Calo, Victor M.; Efendiev, Yalchin R.; Galvis, Juan; Ghommem, Mehdi
2014-01-01
residuals and Jacobians on the fine grid. We use empirical interpolation concepts to evaluate these residuals and Jacobians of the multiscale system with a computational cost which is proportional to the size of the coarse-scale problem rather than the fully
Spectral Compressive Sensing with Polar Interpolation
DEFF Research Database (Denmark)
Fyhn, Karsten; Dadkhahi, Hamid; F. Duarte, Marco
2013-01-01
. In this paper, we introduce a greedy recovery algorithm that leverages a band-exclusion function and a polar interpolation function to address these two issues in spectral compressive sensing. Our algorithm is geared towards line spectral estimation from compressive measurements and outperforms most existing...
Technique for image interpolation using polynomial transforms
Escalante Ramírez, B.; Martens, J.B.; Haskell, G.G.; Hang, H.M.
1993-01-01
We present a new technique for image interpolation based on polynomial transforms. This is an image representation model that analyzes an image by locally expanding it into a weighted sum of orthogonal polynomials. In the discrete case, the image segment within every window of analysis is
Mansilha, C; Melo, A; Rebelo, H; Ferreira, I M P L V O; Pinho, O; Domingues, V; Pinho, C; Gameiro, P
2010-10-22
A multi-residue methodology based on a solid phase extraction followed by gas chromatography-tandem mass spectrometry was developed for trace analysis of 32 compounds in water matrices, including estrogens and several pesticides from different chemical families, some of them with endocrine disrupting properties. Matrix standard calibration solutions were prepared by adding known amounts of the analytes to a residue-free sample to compensate matrix-induced chromatographic response enhancement observed for certain pesticides. Validation was done mainly according to the International Conference on Harmonisation recommendations, as well as some European and American validation guidelines with specifications for pesticides analysis and/or GC-MS methodology. As the assumption of homoscedasticity was not met for analytical data, weighted least squares linear regression procedure was applied as a simple and effective way to counteract the greater influence of the greater concentrations on the fitted regression line, improving accuracy at the lower end of the calibration curve. The method was considered validated for 31 compounds after consistent evaluation of the key analytical parameters: specificity, linearity, limit of detection and quantification, range, precision, accuracy, extraction efficiency, stability and robustness. Copyright © 2010 Elsevier B.V. All rights reserved.
A Study on the Improvement of Digital Periapical Images using Image Interpolation Methods
International Nuclear Information System (INIS)
Song, Nam Kyu; Koh, Kwang Joon
1998-01-01
Image resampling is of particular interest in digital radiology. When resampling an image to a new set of coordinate, there appears blocking artifacts and image changes. To enhance image quality, interpolation algorithms have been used. Resampling is used to increase the number of points in an image to improve its appearance for display. The process of interpolation is fitting a continuous function to the discrete points in the digital image. The purpose of this study was to determine the effects of the seven interpolation functions when image resampling in digital periapical images. The images were obtained by Digora, CDR and scanning of Ektaspeed plus periapical radiograms on the dry skull and human subject. The subjects were exposed to intraoral X-ray machine at 60 kVp and 70 kVp with exposure time varying between 0.01 and 0.50 second. To determine which interpolation method would provide the better image, seven functions were compared ; (1) nearest neighbor (2) linear (3) non-linear (4) facet model (5) cubic convolution (6) cubic spline (7) gray segment expansion. And resampled images were compared in terms of SNR (Signal to Noise Ratio) and MTF (Modulation Transfer Function) coefficient value. The obtained results were as follows ; 1. The highest SNR value (75.96 dB) was obtained with cubic convolution method and the lowest SNR value (72.44 dB) was obtained with facet model method among seven interpolation methods. 2. There were significant differences of SNR values among CDR, Digora and film scan (P 0.05). 4. There were significant differences of MTF coefficient values between linear interpolation method and the other six interpolation methods (P<0.05). 5. The speed of computation time was the fastest with nearest neighbor method and the slowest with non-linear method. 6. The better image was obtained with cubic convolution, cubic spline and gray segment method in ROC analysis. 7. The better sharpness of edge was obtained with gray segment expansion method
A Spatial Interpolation Framework for Efficient Valuation of Large Portfolios of Variable Annuities
Directory of Open Access Journals (Sweden)
Seyed Amir Hejazi
2017-07-01
Full Text Available Variable Annuity (VA products expose insurance companies to considerable risk becauseof the guarantees they provide to buyers of these products. Managing and hedging these risks requireinsurers to find the values of key risk metrics for a large portfolio of VA products. In practice, manycompanies rely on nested Monte Carlo (MC simulations to find key risk metrics. MC simulations arecomputationally demanding, forcing insurance companies to invest hundreds of thousands of dollars incomputational infrastructure per year. Moreover, existing academic methodologies are focused on fairvaluation of a single VA contract, exploiting ideas in option theory and regression. In most cases, thecomputational complexity of these methods surpasses the computational requirements of MC simulations.Therefore, academic methodologies cannot scale well to large portfolios of VA contracts. In thispaper, we present a framework for valuing such portfolios based on spatial interpolation. We providea comprehensive study of this framework and compare existing interpolation schemes. Our numericalresults show superior performance, in terms of both computational effciency and accuracy, for thesemethods compared to nested MC simulations. We also present insights into the challenge of findingan effective interpolation scheme in this framework, and suggest guidelines that help us build a fullyautomated scheme that is effcient and accurate.
Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
Lu, Jianfeng; Thicke, Kyle
2017-12-01
We present a new cubic scaling algorithm for the calculation of the RPA correlation energy. Our scheme splits up the dependence between the occupied and virtual orbitals in χ0 by use of Cauchy's integral formula. This introduces an additional integral to be carried out, for which we provide a geometrically convergent quadrature rule. Our scheme also uses the newly developed Interpolative Separable Density Fitting algorithm to further reduce the computational cost in a way analogous to that of the Resolution of Identity method.
Institute of Scientific and Technical Information of China (English)
ZHENG Guangguo; ZHOU Dongsheng; WEI Xiaopeng; ZHANG Qiang
2012-01-01
Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.
International Nuclear Information System (INIS)
Palau, J.M.; Cathalau, S.; Hudelot, J.P.; Barran, F.; Bellanger, V.; Magnaud, C.; Moreau, F.
2011-01-01
Burnable poisons are extensively used by Light Water Reactor designers in order to preserve the fuel reactivity potential and increase the cycle length (without increasing the uranium enrichment). In the industrial two-steps (assembly 2D transport-core 3D diffusion) calculation schemes these heterogeneities yield to strong flux and cross-sections perturbations that have to be taken into account in the final 3D burn-up calculations. This paper presents the application of an enhanced cross-section interpolation model (implemented in the French CRONOS2 code) to LWR (highly poisoned) depleted core calculations. The principle is to use the absorbers (or actinide) concentrations as the new interpolation parameters instead of the standard local burnup/fluence parameters. It is shown by comparing the standard (burnup/fluence) and new (concentration) interpolation models and using the lattice transport code APOLLO2 as a numerical reference that reactivity and local reaction rate prediction of a 2x2 LWR assembly configuration (slab geometry) is significantly improved with the concentration interpolation model. Gains on reactivity and local power predictions (resp. more than 1000 pcm and 20 % discrepancy reduction compared to the reference APOLLO2 scheme) are obtained by using this model. In particular, when epithermal absorbers are inserted close to thermal poison the 'shadowing' ('screening') spectral effects occurring during control operations are much more correctly modeled by concentration parameters. Through this outstanding example it is highlighted that attention has to be paid to the choice of cross-section interpolation parameters (burnup 'indicator') in core calculations with few energy groups and variable geometries all along the irradiation cycle. Actually, this new model could be advantageously applied to steady-state and transient LWR heterogeneous core computational analysis dealing with strong spectral-history variations under
Generation of response functions of a NaI detector by using an interpolation technique
International Nuclear Information System (INIS)
Tominaga, Shoji
1983-01-01
A computer method is developed for generating response functions of a NaI detector to monoenergetic γ-rays. The method is based on an interpolation between measured response curves by a detector. The computer programs are constructed for Heath's response spectral library. The principle of the basic mathematics used for interpolation, which was reported previously by the author, et al., is that response curves can be decomposed into a linear combination of intrinsic-component patterns, and thereby the interpolation of curves is reduced to a simple interpolation of weighting coefficients needed to combine the component patterns. This technique has some advantages of data compression, reduction in computation time, and stability of the solution, in comparison with the usual functional fitting method. The processing method of segmentation of a spectrum is devised to generate useful and precise response curves. A spectral curve, obtained for each γ-ray source, is divided into some regions defined by the physical processes, such as the photopeak area, the Compton continuum area, the backscatter peak area, and so on. Each segment curve then is processed separately for interpolation. Lastly the estimated curves to the respective areas are connected on one channel scale. The generation programs are explained briefly. It is shown that the generated curve represents the overall shape of a response spectrum including not only its photopeak but also the corresponding Compton area, with a sufficient accuracy. (author)
Zhang, Liping; Zhang, Shiwen; Huang, Yajie; Cao, Meng; Huang, Yuanfang; Zhang, Hongyan
2016-03-24
Understanding abandoned mine land (AML) changes during land reclamation is crucial for reusing damaged land resources and formulating sound ecological restoration policies. This study combines the linear programming (LP) model and the CLUE-S model to simulate land-use dynamics in the Mentougou District (Beijing, China) from 2007 to 2020 under three reclamation scenarios, that is, the planning scenario based on the general land-use plan in study area (scenario 1), maximal comprehensive benefits (scenario 2), and maximal ecosystem service value (scenario 3). Nine landscape-scale graph metrics were then selected to describe the landscape characteristics. The results show that the coupled model presented can simulate the dynamics of AML effectively and the spatially explicit transformations of AML were different. New cultivated land dominates in scenario 1, while construction land and forest land account for major percentages in scenarios 2 and 3, respectively. Scenario 3 has an advantage in most of the selected indices as the patches combined most closely. To conclude, reclaiming AML by transformation into more forest can reduce the variability and maintain the stability of the landscape ecological system in study area. These findings contribute to better mapping AML dynamics and providing policy support for the management of AML.
SAR image formation with azimuth interpolation after azimuth transform
Doerry,; Armin W. , Martin; Grant D. , Holzrichter; Michael, W [Albuquerque, NM
2008-07-08
Two-dimensional SAR data can be processed into a rectangular grid format by subjecting the SAR data to a Fourier transform operation, and thereafter to a corresponding interpolation operation. Because the interpolation operation follows the Fourier transform operation, the interpolation operation can be simplified, and the effect of interpolation errors can be diminished. This provides for the possibility of both reducing the re-grid processing time, and improving the image quality.
Interpolation of fuzzy data | Khodaparast | Journal of Fundamental ...
African Journals Online (AJOL)
Considering the many applications of mathematical functions in different ways, it is essential to have a defining function. In this study, we used Fuzzy Lagrangian interpolation and natural fuzzy spline polynomials to interpolate the fuzzy data. In the current world and in the field of science and technology, interpolation issues ...
Interpolation of diffusion weighted imaging datasets
DEFF Research Database (Denmark)
Dyrby, Tim B; Lundell, Henrik; Burke, Mark W
2014-01-01
anatomical details and signal-to-noise-ratio for reliable fibre reconstruction. We assessed the potential benefits of interpolating DWI datasets to a higher image resolution before fibre reconstruction using a diffusion tensor model. Simulations of straight and curved crossing tracts smaller than or equal......Diffusion weighted imaging (DWI) is used to study white-matter fibre organisation, orientation and structural connectivity by means of fibre reconstruction algorithms and tractography. For clinical settings, limited scan time compromises the possibilities to achieve high image resolution for finer...... interpolation methods fail to disentangle fine anatomical details if PVE is too pronounced in the original data. As for validation we used ex-vivo DWI datasets acquired at various image resolutions as well as Nissl-stained sections. Increasing the image resolution by a factor of eight yielded finer geometrical...
International Nuclear Information System (INIS)
Cullen, D.E.
1979-01-01
Program LINEAR converts evaluated cross sections in the ENDF/B format into a tabular form that is subject to linear-linear interpolation in energy and cross section. The code also thins tables of cross sections already in that form (i.e., removes points not needed for linear interpolability). The main advantage of the code is that it allows subsequent codes to consider only linear-linear data. A listing of the source deck is available on request
Some splines produced by smooth interpolation
Czech Academy of Sciences Publication Activity Database
Segeth, Karel
2018-01-01
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.sciencedirect.com/science/article/pii/S0096300317302746?via%3Dihub
Some splines produced by smooth interpolation
Czech Academy of Sciences Publication Activity Database
Segeth, Karel
2018-01-01
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 direct.com/ science /article/pii/S0096300317302746?via%3Dihub
An algorithm for centerline extraction using natural neighbour interpolation
DEFF Research Database (Denmark)
Mioc, Darka; Antón Castro, Francesc/François; Dharmaraj, Girija
2004-01-01
, especially due to the lack of explicit topology in commercial GIS systems. Indeed, each map update might require the batch processing of the whole map. Currently, commercial GIS do not offer completely automatic raster/vector conversion even for simple scanned black and white maps. Various commercial raster...... they need user defined tolerances settings, what causes difficulties in the extraction of complex spatial features, for example: road junctions, curved or irregular lines and complex intersections of linear features. The approach we use here is based on image processing filtering techniques to extract...... to the improvement of data caption and conversion in GIS and to develop a software toolkit for automated raster/vector conversion. The approach is based on computing the skeleton from Voronoi diagrams using natural neighbour interpolation. In this paper we present the algorithm for skeleton extraction from scanned...
Differential maps, difference maps, interpolated maps, and long term prediction
International Nuclear Information System (INIS)
Talman, R.
1988-06-01
Mapping techniques may be thought to be attractive for the long term prediction of motion in accelerators, especially because a simple map can approximately represent an arbitrarily complicated lattice. The intention of this paper is to develop prejudices as to the validity of such methods by applying them to a simple, exactly solveable, example. It is shown that a numerical interpolation map, such as can be generated in the accelerator tracking program TEAPOT, predicts the evolution more accurately than an analytically derived differential map of the same order. Even so, in the presence of ''appreciable'' nonlinearity, it is shown to be impractical to achieve ''accurate'' prediction beyond some hundreds of cycles of oscillation. This suggests that the value of nonlinear maps is restricted to the parameterization of only the ''leading'' deviation from linearity. 41 refs., 6 figs
High Order Semi-Lagrangian Advection Scheme
Malaga, Carlos; Mandujano, Francisco; Becerra, Julian
2014-11-01
In most fluid phenomena, advection plays an important roll. A numerical scheme capable of making quantitative predictions and simulations must compute correctly the advection terms appearing in the equations governing fluid flow. Here we present a high order forward semi-Lagrangian numerical scheme specifically tailored to compute material derivatives. The scheme relies on the geometrical interpretation of material derivatives to compute the time evolution of fields on grids that deform with the material fluid domain, an interpolating procedure of arbitrary order that preserves the moments of the interpolated distributions, and a nonlinear mapping strategy to perform interpolations between undeformed and deformed grids. Additionally, a discontinuity criterion was implemented to deal with discontinuous fields and shocks. Tests of pure advection, shock formation and nonlinear phenomena are presented to show performance and convergence of the scheme. The high computational cost is considerably reduced when implemented on massively parallel architectures found in graphic cards. The authors acknowledge funding from Fondo Sectorial CONACYT-SENER Grant Number 42536 (DGAJ-SPI-34-170412-217).
Quadratic polynomial interpolation on triangular domain
Li, Ying; Zhang, Congcong; Yu, Qian
2018-04-01
In the simulation of natural terrain, the continuity of sample points are not in consonance with each other always, traditional interpolation methods often can't faithfully reflect the shape information which lie in data points. So, a new method for constructing the polynomial interpolation surface on triangular domain is proposed. Firstly, projected the spatial scattered data points onto a plane and then triangulated them; Secondly, A C1 continuous piecewise quadric polynomial patch was constructed on each vertex, all patches were required to be closed to the line-interpolation one as far as possible. Lastly, the unknown quantities were gotten by minimizing the object functions, and the boundary points were treated specially. The result surfaces preserve as many properties of data points as possible under conditions of satisfying certain accuracy and continuity requirements, not too convex meantime. New method is simple to compute and has a good local property, applicable to shape fitting of mines and exploratory wells and so on. The result of new surface is given in experiments.
Trace interpolation by slant-stack migration
International Nuclear Information System (INIS)
Novotny, M.
1990-01-01
The slant-stack migration formula based on the radon transform is studied with respect to the depth steep Δz of wavefield extrapolation. It can be viewed as a generalized trace-interpolation procedure including wave extrapolation with an arbitrary step Δz. For Δz > 0 the formula yields the familiar plane-wave decomposition, while for Δz > 0 it provides a robust tool for migration transformation of spatially under sampled wavefields. Using the stationary phase method, it is shown that the slant-stack migration formula degenerates into the Rayleigh-Sommerfeld integral in the far-field approximation. Consequently, even a narrow slant-stack gather applied before the diffraction stack can significantly improve the representation of noisy data in the wavefield extrapolation process. The theory is applied to synthetic and field data to perform trace interpolation and dip reject filtration. The data examples presented prove that the radon interpolator works well in the dip range, including waves with mutual stepouts smaller than half the dominant period
Image Interpolation with Geometric Contour Stencils
Directory of Open Access Journals (Sweden)
Pascal Getreuer
2011-09-01
Full Text Available We consider the image interpolation problem where given an image vm,n with uniformly-sampled pixels vm,n and point spread function h, the goal is to find function u(x,y satisfying vm,n = (h*u(m,n for all m,n in Z. This article improves upon the IPOL article Image Interpolation with Contour Stencils. In the previous work, contour stencils are used to estimate the image contours locally as short line segments. This article begins with a continuous formulation of total variation integrated over a collection of curves and defines contour stencils as a consistent discretization. This discretization is more reliable than the previous approach and can effectively distinguish contours that are locally shaped like lines, curves, corners, and circles. These improved contour stencils sense more of the geometry in the image. Interpolation is performed using an extension of the method described in the previous article. Using the improved contour stencils, there is an increase in image quality while maintaining similar computational efficiency.
Delimiting areas of endemism through kernel interpolation.
Oliveira, Ubirajara; Brescovit, Antonio D; Santos, Adalberto J
2015-01-01
We propose a new approach for identification of areas of endemism, the Geographical Interpolation of Endemism (GIE), based on kernel spatial interpolation. This method differs from others in being independent of grid cells. This new approach is based on estimating the overlap between the distribution of species through a kernel interpolation of centroids of species distribution and areas of influence defined from the distance between the centroid and the farthest point of occurrence of each species. We used this method to delimit areas of endemism of spiders from Brazil. To assess the effectiveness of GIE, we analyzed the same data using Parsimony Analysis of Endemism and NDM and compared the areas identified through each method. The analyses using GIE identified 101 areas of endemism of spiders in Brazil GIE demonstrated to be effective in identifying areas of endemism in multiple scales, with fuzzy edges and supported by more synendemic species than in the other methods. The areas of endemism identified with GIE were generally congruent with those identified for other taxonomic groups, suggesting that common processes can be responsible for the origin and maintenance of these biogeographic units.
Delimiting areas of endemism through kernel interpolation.
Directory of Open Access Journals (Sweden)
Ubirajara Oliveira
Full Text Available We propose a new approach for identification of areas of endemism, the Geographical Interpolation of Endemism (GIE, based on kernel spatial interpolation. This method differs from others in being independent of grid cells. This new approach is based on estimating the overlap between the distribution of species through a kernel interpolation of centroids of species distribution and areas of influence defined from the distance between the centroid and the farthest point of occurrence of each species. We used this method to delimit areas of endemism of spiders from Brazil. To assess the effectiveness of GIE, we analyzed the same data using Parsimony Analysis of Endemism and NDM and compared the areas identified through each method. The analyses using GIE identified 101 areas of endemism of spiders in Brazil GIE demonstrated to be effective in identifying areas of endemism in multiple scales, with fuzzy edges and supported by more synendemic species than in the other methods. The areas of endemism identified with GIE were generally congruent with those identified for other taxonomic groups, suggesting that common processes can be responsible for the origin and maintenance of these biogeographic units.
Evaluation of Teeth and Supporting Structures on Digital Radiograms using Interpolation Methods
International Nuclear Information System (INIS)
Koh, Kwang Joon; Chang, Kee Wan
1999-01-01
To determine the effect of interpolation functions when processing the digital periapical images. The digital images were obtained by Digora and CDR system on the dry skull and human subject. 3 oral radiologists evaluated the 3 portions of each processed image using 7 interpolation methods and ROC curves were obtained by trapezoidal methods. The highest Az value(0.96) was obtained with cubic spline method and the lowest Az value(0.03) was obtained with facet model method in Digora system. The highest Az value(0.79) was obtained with gray segment expansion method and the lowest Az value(0.07) was obtained with facet model method in CDR system. There was significant difference of Az value in original image between Digora and CDR system at alpha=0.05 level. There were significant differences of Az values between Digora and CDR images with cubic spline method, facet model method, linear interpolation method and non-linear interpolation method at alpha= 0.1 level.
Interpolation functions and the Lions-Peetre interpolation construction
International Nuclear Information System (INIS)
Ovchinnikov, V I
2014-01-01
The generalization of the Lions-Peetre interpolation method of means considered in the present survey is less general than the generalizations known since the 1970s. However, our level of generalization is sufficient to encompass spaces that are most natural from the point of view of applications, like the Lorentz spaces, Orlicz spaces, and their analogues. The spaces φ(X 0 ,X 1 ) p 0 ,p 1 considered here have three parameters: two positive numerical parameters p 0 and p 1 of equal standing, and a function parameter φ. For p 0 ≠p 1 these spaces can be regarded as analogues of Orlicz spaces under the real interpolation method. Embedding criteria are established for the family of spaces φ(X 0 ,X 1 ) p 0 ,p 1 , together with optimal interpolation theorems that refine all the known interpolation theorems for operators acting on couples of weighted spaces L p and that extend these theorems beyond scales of spaces. The main specific feature is that the function parameter φ can be an arbitrary natural functional parameter in the interpolation. Bibliography: 43 titles
DEFF Research Database (Denmark)
van Leeuwen, Theo
2013-01-01
This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation.......This chapter presents a framework for analysing colour schemes based on a parametric approach that includes not only hue, value and saturation, but also purity, transparency, luminosity, luminescence, lustre, modulation and differentiation....
Research progress and hotspot analysis of spatial interpolation
Jia, Li-juan; Zheng, Xin-qi; Miao, Jin-li
2018-02-01
In this paper, the literatures related to spatial interpolation between 1982 and 2017, which are included in the Web of Science core database, are used as data sources, and the visualization analysis is carried out according to the co-country network, co-category network, co-citation network, keywords co-occurrence network. It is found that spatial interpolation has experienced three stages: slow development, steady development and rapid development; The cross effect between 11 clustering groups, the main convergence of spatial interpolation theory research, the practical application and case study of spatial interpolation and research on the accuracy and efficiency of spatial interpolation. Finding the optimal spatial interpolation is the frontier and hot spot of the research. Spatial interpolation research has formed a theoretical basis and research system framework, interdisciplinary strong, is widely used in various fields.
Discontinuous nodal schemes applied to the bidimensional neutron transport equation
International Nuclear Information System (INIS)
Delfin L, A.; Valle G, E. Del; Hennart B, J.P.
1996-01-01
In this paper several strong discontinuous nodal schemes are described, starting from the one that has only two interpolation parameters per cell to the one having ten. Their application to the spatial discretization of the neutron transport equation in X-Y geometry is also described, giving, for each one of the nodal schemes, the approximation for the angular neutron flux that includes the set of interpolation parameters and the corresponding polynomial space. Numerical results were obtained for several test problems presenting here the problem with the highest degree of difficulty and their comparison with published results 1,2 . (Author)
Gorji, Taha; Sertel, Elif; Tanik, Aysegul
2017-12-01
Soil management is an essential concern in protecting soil properties, in enhancing appropriate soil quality for plant growth and agricultural productivity, and in preventing soil erosion. Soil scientists and decision makers require accurate and well-distributed spatially continuous soil data across a region for risk assessment and for effectively monitoring and managing soils. Recently, spatial interpolation approaches have been utilized in various disciplines including soil sciences for analysing, predicting and mapping distribution and surface modelling of environmental factors such as soil properties. The study area selected in this research is Tuz Lake Basin in Turkey bearing ecological and economic importance. Fertile soil plays a significant role in agricultural activities, which is one of the main industries having great impact on economy of the region. Loss of trees and bushes due to intense agricultural activities in some parts of the basin lead to soil erosion. Besides, soil salinization due to both human-induced activities and natural factors has exacerbated its condition regarding agricultural land development. This study aims to compare capability of Local Polynomial Interpolation (LPI) and Radial Basis Functions (RBF) as two interpolation methods for mapping spatial pattern of soil properties including organic matter, phosphorus, lime and boron. Both LPI and RBF methods demonstrated promising results for predicting lime, organic matter, phosphorous and boron. Soil samples collected in the field were used for interpolation analysis in which approximately 80% of data was used for interpolation modelling whereas the remaining for validation of the predicted results. Relationship between validation points and their corresponding estimated values in the same location is examined by conducting linear regression analysis. Eight prediction maps generated from two different interpolation methods for soil organic matter, phosphorus, lime and boron parameters
Calculation of reactivity without Lagrange interpolation
International Nuclear Information System (INIS)
Suescun D, D.; Figueroa J, J. H.; Rodriguez R, K. C.; Villada P, J. P.
2015-09-01
A new method to solve numerically the inverse equation of punctual kinetics without using Lagrange interpolating polynomial is formulated; this method uses a polynomial approximation with N points based on a process of recurrence for simulating different forms of nuclear power. The results show a reliable accuracy. Furthermore, the method proposed here is suitable for real-time measurements of reactivity, with step sizes of calculations greater that Δt = 0.3 s; due to its precision can be used to implement a digital meter of reactivity in real time. (Author)
Solving the Schroedinger equation using Smolyak interpolants
International Nuclear Information System (INIS)
Avila, Gustavo; Carrington, Tucker Jr.
2013-01-01
In this paper, we present a new collocation method for solving the Schroedinger equation. Collocation has the advantage that it obviates integrals. All previous collocation methods have, however, the crucial disadvantage that they require solving a generalized eigenvalue problem. By combining Lagrange-like functions with a Smolyak interpolant, we device a collocation method that does not require solving a generalized eigenvalue problem. We exploit the structure of the grid to develop an efficient algorithm for evaluating the matrix-vector products required to compute energy levels and wavefunctions. Energies systematically converge as the number of points and basis functions are increased
Topics in multivariate approximation and interpolation
Jetter, Kurt
2005-01-01
This book is a collection of eleven articles, written by leading experts and dealing with special topics in Multivariate Approximation and Interpolation. The material discussed here has far-reaching applications in many areas of Applied Mathematics, such as in Computer Aided Geometric Design, in Mathematical Modelling, in Signal and Image Processing and in Machine Learning, to mention a few. The book aims at giving a comprehensive information leading the reader from the fundamental notions and results of each field to the forefront of research. It is an ideal and up-to-date introduction for gr
A multistage motion vector processing method for motion-compensated frame interpolation.
Huang, Ai- Mei; Nguyen, Truong Q
2008-05-01
In this paper, a novel, low-complexity motion vector processing algorithm at the decoder is proposed for motion-compensated frame interpolation or frame rate up-conversion. We address the problems of having broken edges and deformed structures in an interpolated frame by hierarchically refining motion vectors on different block sizes. Our method explicitly considers the reliability of each received motion vector and has the capability of preserving the structure information. This is achieved by analyzing the distribution of residual energies and effectively merging blocks that have unreliable motion vectors. The motion vector reliability information is also used as a prior knowledge in motion vector refinement using a constrained vector median filter to avoid choosing identical unreliable one. We also propose using chrominance information in our method. Experimental results show that the proposed scheme has better visual quality and is also robust, even in video sequences with complex scenes and fast motion.
Energy Technology Data Exchange (ETDEWEB)
Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.
2014-07-25
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
Air Quality Assessment Using Interpolation Technique
Directory of Open Access Journals (Sweden)
Awkash Kumar
2016-07-01
Full Text Available Air pollution is increasing rapidly in almost all cities around the world due to increase in population. Mumbai city in India is one of the mega cities where air quality is deteriorating at a very rapid rate. Air quality monitoring stations have been installed in the city to regulate air pollution control strategies to reduce the air pollution level. In this paper, air quality assessment has been carried out over the sample region using interpolation techniques. The technique Inverse Distance Weighting (IDW of Geographical Information System (GIS has been used to perform interpolation with the help of concentration data on air quality at three locations of Mumbai for the year 2008. The classification was done for the spatial and temporal variation in air quality levels for Mumbai region. The seasonal and annual variations of air quality levels for SO2, NOx and SPM (Suspended Particulate Matter have been focused in this study. Results show that SPM concentration always exceeded the permissible limit of National Ambient Air Quality Standard. Also, seasonal trends of pollutant SPM was low in monsoon due rain fall. The finding of this study will help to formulate control strategies for rational management of air pollution and can be used for many other regions.
J.K. Hoogland (Jiri); C.D.D. Neumann
2000-01-01
textabstractIn this article we present a new approach to the numerical valuation of derivative securities. The method is based on our previous work where we formulated the theory of pricing in terms of tradables. The basic idea is to fit a finite difference scheme to exact solutions of the pricing
Multiresolution Motion Estimation for Low-Rate Video Frame Interpolation
Directory of Open Access Journals (Sweden)
Hezerul Abdul Karim
2004-09-01
Full Text Available Interpolation of video frames with the purpose of increasing the frame rate requires the estimation of motion in the image so as to interpolate pixels along the path of the objects. In this paper, the specific challenges of low-rate video frame interpolation are illustrated by choosing one well-performing algorithm for high-frame-rate interpolation (Castango 1996 and applying it to low frame rates. The degradation of performance is illustrated by comparing the original algorithm, the algorithm adapted to low frame rate, and simple averaging. To overcome the particular challenges of low-frame-rate interpolation, two algorithms based on multiresolution motion estimation are developed and compared on objective and subjective basis and shown to provide an elegant solution to the specific challenges of low-frame-rate video interpolation.
An Improved Minimum Error Interpolator of CNC for General Curves Based on FPGA
Directory of Open Access Journals (Sweden)
Jiye HUANG
2014-05-01
Full Text Available This paper presents an improved minimum error interpolation algorithm for general curves generation in computer numerical control (CNC. Compared with the conventional interpolation algorithms such as the By-Point Comparison method, the Minimum- Error method and the Digital Differential Analyzer (DDA method, the proposed improved Minimum-Error interpolation algorithm can find a balance between accuracy and efficiency. The new algorithm is applicable for the curves of linear, circular, elliptical and parabolic. The proposed algorithm is realized on a field programmable gate array (FPGA with Verilog HDL language, and simulated by the ModelSim software, and finally verified on a two-axis CNC lathe. The algorithm has the following advantages: firstly, the maximum interpolation error is only half of the minimum step-size; and secondly the computing time is only two clock cycles of the FPGA. Simulations and actual tests have proved that the high accuracy and efficiency of the algorithm, which shows that it is highly suited for real-time applications.
Systems and methods for interpolation-based dynamic programming
Rockwood, Alyn
2013-01-03
Embodiments of systems and methods for interpolation-based dynamic programming. In one embodiment, the method includes receiving an object function and a set of constraints associated with the objective function. The method may also include identifying a solution on the objective function corresponding to intersections of the constraints. Additionally, the method may include generating an interpolated surface that is in constant contact with the solution. The method may also include generating a vector field in response to the interpolated surface.
Systems and methods for interpolation-based dynamic programming
Rockwood, Alyn
2013-01-01
Embodiments of systems and methods for interpolation-based dynamic programming. In one embodiment, the method includes receiving an object function and a set of constraints associated with the objective function. The method may also include identifying a solution on the objective function corresponding to intersections of the constraints. Additionally, the method may include generating an interpolated surface that is in constant contact with the solution. The method may also include generating a vector field in response to the interpolated surface.
International Nuclear Information System (INIS)
Yun, Sung Hwan
2004-02-01
Radiative transfer is a complex phenomenon in which radiation field interacts with material. This thermal radiative transfer phenomenon is composed of two equations which are the balance equation of photons and the material energy balance equation. The two equations involve non-linearity due to the temperature and that makes the radiative transfer equation more difficult to solve. During the last several years, there have been many efforts to solve the non-linear radiative transfer problems by Monte Carlo method. Among them, it is known that Semi-Analog Monte Carlo (SMC) method developed by Ahrens and Larsen is accurate regard-less of the time step size in low temperature region. But their works are limited to one-dimensional, low temperature problems. In this thesis, we suggest some method to remove their limitations in the SMC method and apply to the more realistic problems. An initially cold problem was solved over entire temperature region by using piecewise linear interpolation of the heat capacity, while heat capacity is still fitted as a cubic curve within the lowest temperature region. If we assume the heat capacity to be linear in each temperature region, the non-linearity still remains in the radiative transfer equations. We then introduce the first-order Taylor expansion to linearize the non-linear radiative transfer equations. During the linearization procedure, absorption-reemission phenomena may be described by a conventional reemission time sampling scheme which is similar to the repetitive sampling scheme in particle transport Monte Carlo method. But this scheme causes significant stochastic errors, which necessitates many histories. Thus, we present a new reemission time sampling scheme which reduces stochastic errors by storing the information of absorption times. The results of the comparison of the two schemes show that the new scheme has less stochastic errors. Therefore, the improved SMC method is able to solve more realistic problems with
Directory of Open Access Journals (Sweden)
Shaofeng Wang
2017-05-01
Full Text Available Mineral reserve estimation and mining design depend on a precise modeling of the mineralized deposit. A multi-step interpolation algorithm, including 1D biharmonic spline estimator for interpolating floor altitudes, 2D nearest neighbor, linear, natural neighbor, cubic, biharmonic spline, inverse distance weighted, simple kriging, and ordinary kriging interpolations for grade distribution on the two vertical sections at roadways, and 3D linear interpolation for grade distribution between sections, was proposed to build a 3D grade distribution model of the mineralized seam in a longwall mining panel with a U-shaped layout having two roadways at both sides. Compared to field data from exploratory boreholes, this multi-step interpolation using a natural neighbor method shows an optimal stability and a minimal difference between interpolation and field data. Using this method, the 97,576 m3 of bauxite, in which the mass fraction of Al2O3 (Wa and the mass ratio of Al2O3 to SiO2 (Wa/s are 61.68% and 27.72, respectively, was delimited from the 189,260 m3 mineralized deposit in the 1102 longwall mining panel in the Wachangping mine, Southwest China. The mean absolute errors, the root mean squared errors and the relative standard deviations of errors between interpolated data and exploratory grade data at six boreholes are 2.544, 2.674, and 32.37% of Wa; and 1.761, 1.974, and 67.37% of Wa/s, respectively. The proposed method can be used for characterizing the grade distribution in a mineralized seam between two roadways at both sides of a longwall mining panel.
Distance-two interpolation for parallel algebraic multigrid
International Nuclear Information System (INIS)
Sterck, H de; Falgout, R D; Nolting, J W; Yang, U M
2007-01-01
In this paper we study the use of long distance interpolation methods with the low complexity coarsening algorithm PMIS. AMG performance and scalability is compared for classical as well as long distance interpolation methods on parallel computers. It is shown that the increased interpolation accuracy largely restores the scalability of AMG convergence factors for PMIS-coarsened grids, and in combination with complexity reducing methods, such as interpolation truncation, one obtains a class of parallel AMG methods that enjoy excellent scalability properties on large parallel computers
Comparison of Interpolation Methods as Applied to Time Synchronous Averaging
National Research Council Canada - National Science Library
Decker, Harry
1999-01-01
Several interpolation techniques were investigated to determine their effect on time synchronous averaging of gear vibration signals and also the effects on standard health monitoring diagnostic parameters...
Measurement and tricubic interpolation of the magnetic field for the OLYMPUS experiment
Energy Technology Data Exchange (ETDEWEB)
Bernauer, J.C. [Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, MA (United States); Diefenbach, J. [Hampton University, Hampton, VA (United States); Elbakian, G. [Alikhanyan National Science Laboratory (Yerevan Physics Institute), Yerevan (Armenia); Gavrilov, G. [Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); Goerrissen, N. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Hasell, D.K.; Henderson, B.S. [Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, MA (United States); Holler, Y. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Karyan, G. [Alikhanyan National Science Laboratory (Yerevan Physics Institute), Yerevan (Armenia); Ludwig, J. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Marukyan, H. [Alikhanyan National Science Laboratory (Yerevan Physics Institute), Yerevan (Armenia); Naryshkin, Y. [Petersburg Nuclear Physics Institute, Gatchina (Russian Federation); O' Connor, C.; Russell, R.L.; Schmidt, A. [Massachusetts Institute of Technology, Laboratory for Nuclear Science, Cambridge, MA (United States); Schneekloth, U. [Deutsches Elektronen-Synchrotron DESY, Hamburg (Germany); Suvorov, K.; Veretennikov, D. [Petersburg Nuclear Physics Institute, Gatchina (Russian Federation)
2016-07-01
The OLYMPUS experiment used a 0.3 T toroidal magnetic spectrometer to measure the momenta of outgoing charged particles. In order to accurately determine particle trajectories, knowledge of the magnetic field was needed throughout the spectrometer volume. For that purpose, the magnetic field was measured at over 36,000 positions using a three-dimensional Hall probe actuated by a system of translation tables. We used these field data to fit a numerical magnetic field model, which could be employed to calculate the magnetic field at any point in the spectrometer volume. Calculations with this model were computationally intensive; for analysis applications where speed was crucial, we pre-computed the magnetic field and its derivatives on an evenly spaced grid so that the field could be interpolated between grid points. We developed a spline-based interpolation scheme suitable for SIMD implementations, with a memory layout chosen to minimize space and optimize the cache behavior to quickly calculate field values. This scheme requires only one-eighth of the memory needed to store necessary coefficients compared with a previous scheme (Lekien and Marsden, 2005 [1]). This method was accurate for the vast majority of the spectrometer volume, though special fits and representations were needed to improve the accuracy close to the magnet coils and along the toroidal axis.
Shape Preserving Interpolatory Subdivision Schemes for Nonuniform Data
Kuijt, F.; van Damme, Rudolf M.J.
2002-01-01
This article is concerned with a class of shape preserving four-point subdivision schemes which are stationary and which interpolate nonuniform univariate data {(xi, fi)}. These data are functional data, i.e., xi≠xj if i≠j. Subdivision for the strictly monotone x-values is performed by a subdivision
Shape-based grey-level image interpolation
International Nuclear Information System (INIS)
Keh-Shih Chuang; Chun-Yuan Chen; Ching-Kai Yeh
1999-01-01
The three-dimensional (3D) object data obtained from a CT scanner usually have unequal sampling frequencies in the x-, y- and z-directions. Generally, the 3D data are first interpolated between slices to obtain isotropic resolution, reconstructed, then operated on using object extraction and display algorithms. The traditional grey-level interpolation introduces a layer of intermediate substance and is not suitable for objects that are very different from the opposite background. The shape-based interpolation method transfers a pixel location to a parameter related to the object shape and the interpolation is performed on that parameter. This process is able to achieve a better interpolation but its application is limited to binary images only. In this paper, we present an improved shape-based interpolation method for grey-level images. The new method uses a polygon to approximate the object shape and performs the interpolation using polygon vertices as references. The binary images representing the shape of the object were first generated via image segmentation on the source images. The target object binary image was then created using regular shape-based interpolation. The polygon enclosing the object for each slice can be generated from the shape of that slice. We determined the relative location in the source slices of each pixel inside the target polygon using the vertices of a polygon as the reference. The target slice grey-level was interpolated from the corresponding source image pixels. The image quality of this interpolation method is better and the mean squared difference is smaller than with traditional grey-level interpolation. (author)
Mayne, Terence P; Paskaranandavadivel, Niranchan; Erickson, Jonathan C; OGrady, Gregory; Cheng, Leo K; Angeli, Timothy R
2018-02-01
High-resolution mapping of gastrointestinal (GI) slow waves is a valuable technique for research and clinical applications. Interpretation of high-resolution GI mapping data relies on animations of slow wave propagation, but current methods remain as rudimentary, pixelated electrode activation animations. This study aimed to develop improved methods of visualizing high-resolution slow wave recordings that increases ease of interpretation. The novel method of "wavefront-orientation" interpolation was created to account for the planar movement of the slow wave wavefront, negate any need for distance calculations, remain robust in atypical wavefronts (i.e., dysrhythmias), and produce an appropriate interpolation boundary. The wavefront-orientation method determines the orthogonal wavefront direction and calculates interpolated values as the mean slow wave activation-time (AT) of the pair of linearly adjacent electrodes along that direction. Stairstep upsampling increased smoothness and clarity. Animation accuracy of 17 human high-resolution slow wave recordings (64-256 electrodes) was verified by visual comparison to the prior method showing a clear improvement in wave smoothness that enabled more accurate interpretation of propagation, as confirmed by an assessment of clinical applicability performed by eight GI clinicians. Quantitatively, the new method produced accurate interpolation values compared to experimental data (mean difference 0.02 ± 0.05 s) and was accurate when applied solely to dysrhythmic data (0.02 ± 0.06 s), both within the error in manual AT marking (mean 0.2 s). Mean interpolation processing time was 6.0 s per wave. These novel methods provide a validated visualization platform that will improve analysis of high-resolution GI mapping in research and clinical translation.
Input variable selection for interpolating high-resolution climate ...
African Journals Online (AJOL)
Although the primary input data of climate interpolations are usually meteorological data, other related (independent) variables are frequently incorporated in the interpolation process. One such variable is elevation, which is known to have a strong influence on climate. This research investigates the potential of 4 additional ...
An efficient interpolation filter VLSI architecture for HEVC standard
Zhou, Wei; Zhou, Xin; Lian, Xiaocong; Liu, Zhenyu; Liu, Xiaoxiang
2015-12-01
The next-generation video coding standard of High-Efficiency Video Coding (HEVC) is especially efficient for coding high-resolution video such as 8K-ultra-high-definition (UHD) video. Fractional motion estimation in HEVC presents a significant challenge in clock latency and area cost as it consumes more than 40 % of the total encoding time and thus results in high computational complexity. With aims at supporting 8K-UHD video applications, an efficient interpolation filter VLSI architecture for HEVC is proposed in this paper. Firstly, a new interpolation filter algorithm based on the 8-pixel interpolation unit is proposed in this paper. It can save 19.7 % processing time on average with acceptable coding quality degradation. Based on the proposed algorithm, an efficient interpolation filter VLSI architecture, composed of a reused data path of interpolation, an efficient memory organization, and a reconfigurable pipeline interpolation filter engine, is presented to reduce the implement hardware area and achieve high throughput. The final VLSI implementation only requires 37.2k gates in a standard 90-nm CMOS technology at an operating frequency of 240 MHz. The proposed architecture can be reused for either half-pixel interpolation or quarter-pixel interpolation, which can reduce the area cost for about 131,040 bits RAM. The processing latency of our proposed VLSI architecture can support the real-time processing of 4:2:0 format 7680 × 4320@78fps video sequences.
Some observations on interpolating gauges and non-covariant gauges
Indian Academy of Sciences (India)
We discuss the viability of using interpolating gauges to deﬁne the non-covariant gauges starting from the covariant ones. We draw attention to the need for a very careful treatment of boundary condition deﬁning term. We show that the boundary condition needed to maintain gauge-invariance as the interpolating parameter ...
Improved Interpolation Kernels for Super-resolution Algorithms
DEFF Research Database (Denmark)
Rasti, Pejman; Orlova, Olga; Tamberg, Gert
2016-01-01
Super resolution (SR) algorithms are widely used in forensics investigations to enhance the resolution of images captured by surveillance cameras. Such algorithms usually use a common interpolation algorithm to generate an initial guess for the desired high resolution (HR) image. This initial guess...... when their original interpolation kernel is replaced by the ones introduced in this work....
Directory of Open Access Journals (Sweden)
Aihua Liu
2017-01-01
Full Text Available A method of direction-of-arrival (DOA estimation using array interpolation is proposed in this paper to increase the number of resolvable sources and improve the DOA estimation performance for coprime array configuration with holes in its virtual array. The virtual symmetric nonuniform linear array (VSNLA of coprime array signal model is introduced, with the conventional MUSIC with spatial smoothing algorithm (SS-MUSIC applied on the continuous lags in the VSNLA; the degrees of freedom (DoFs for DOA estimation are obviously not fully exploited. To effectively utilize the extent of DoFs offered by the coarray configuration, a compressing sensing based array interpolation algorithm is proposed. The compressing sensing technique is used to obtain the coarse initial DOA estimation, and a modified iterative initial DOA estimation based interpolation algorithm (IMCA-AI is then utilized to obtain the final DOA estimation, which maps the sample covariance matrix of the VSNLA to the covariance matrix of a filled virtual symmetric uniform linear array (VSULA with the same aperture size. The proposed DOA estimation method can efficiently improve the DOA estimation performance. The numerical simulations are provided to demonstrate the effectiveness of the proposed method.
Phase Center Interpolation Algorithm for Airborne GPS through the Kalman Filter
Directory of Open Access Journals (Sweden)
Edson A. Mitishita
2005-12-01
Full Text Available The aerial triangulation is a fundamental step in any photogrammetric project. The surveying of the traditional control points, depending on region to be mapped, still has a high cost. The distribution of control points at the block, and its positional quality, influence directly in the resulting precisions of the aero triangulation processing. The airborne GPS technique has as key objectives cost reduction and quality improvement of the ground control in the modern photogrammetric projects. Nowadays, in Brazil, the greatest photogrammetric companies are acquiring airborne GPS systems, but those systems are usually presenting difficulties in the operation, due to the need of human resources for the operation, because of the high technology involved. Inside the airborne GPS technique, one of the fundamental steps is the interpolation of the position of the phase center of the GPS antenna, in the photo shot instant. Traditionally, low degree polynomials are used, but recent studies show that those polynomials is reduced in turbulent flights, which are quite common, mainly in great scales flights. This paper has as objective to present a solution for that problem, through an algorithm based on the Kalman Filter, which takes into account the dynamic aspect of the problem. At the end of the paper, the results of a comparison between experiments done with the proposed methodology and a common linear interpolator are shown. These results show a significant accuracy gain at the procedure of linear interpolation, when the Kalman filter is used.
Comparison of LHC collimator beam-based alignment to BPM-Interpolated centers
Valentino, G; Assmann, R W; Bruce, R; Muller, G J; Redaelli, S; Rossi, A; Lari, L
2012-01-01
The beam centers at the Large Hadron Collider collimators are determined by beam-based alignment, where both jaws of a collimator are moved in separately until a loss spike is detected on a Beam LossMonitor downstream. Orbit drifts of more than a few hundred micrometers cannot be tolerated, as they would compromise the performance of the collimation system. Beam Position Monitors (BPMs) are installed at various locations around the LHC ring, and a linear interpolation of the orbit can be obtained at the collimator positions. In this paper, the results obtained from beam-based alignment are compared with the orbit interpolated from the BPM data throughout the 2011 and 2012 LHC proton runs.
Directory of Open Access Journals (Sweden)
Meiling Cheng
2017-11-01
Full Text Available Accurate assessment of spatial and temporal precipitation is crucial for simulating hydrological processes in basins, but is challenging due to insufficient rain gauges. Our study aims to analyze different precipitation interpolation schemes and their performances in runoff simulation during light and heavy rain periods. In particular, combinations of different interpolation estimates are explored and their performances in runoff simulation are discussed. The study was carried out in the Pengxi River basin of the Three Gorges Basin. Precipitation data from 16 rain gauges were interpolated using the Thiessen Polygon (TP, Inverse Distance Weighted (IDW, and Co-Kriging (CK methods. Results showed that streamflow predictions employing CK inputs demonstrated the best performance in the whole process, in terms of the Nash–Sutcliffe Coefficient (NSE, the coefficient of determination (R2, and the Root Mean Square Error (RMSE indices. The TP, IDW, and CK methods showed good performance in the heavy rain period but poor performance in the light rain period compared with the default method (least sophisticated nearest neighbor technique in Soil and Water Assessment Tool (SWAT. Furthermore, the correlation between the dynamic weight of one method and its performance during runoff simulation followed a parabolic function. The combination of CK and TP achieved a better performance in decreasing the largest and lowest absolute errors compared to any single method, but the IDW method outperformed all methods in terms of the median absolute error. However, it is clear from our findings that interpolation methods should be chosen depending on the amount of precipitation, adaptability of the method, and accuracy of the estimate in different rain periods.
Lamb, David W.; Mengersen, Kerrie
2016-01-01
Modern soil mapping is characterised by the need to interpolate point referenced (geostatistical) observations and the availability of large numbers of environmental characteristics for consideration as covariates to aid this interpolation. Modelling tasks of this nature also occur in other fields such as biogeography and environmental science. This analysis employs the Least Angle Regression (LAR) algorithm for fitting Least Absolute Shrinkage and Selection Operator (LASSO) penalized Multiple Linear Regressions models. This analysis demonstrates the efficiency of the LAR algorithm at selecting covariates to aid the interpolation of geostatistical soil carbon observations. Where an exhaustive search of the models that could be constructed from 800 potential covariate terms and 60 observations would be prohibitively demanding, LASSO variable selection is accomplished with trivial computational investment. PMID:27603135
Computing Diffeomorphic Paths for Large Motion Interpolation.
Seo, Dohyung; Jeffrey, Ho; Vemuri, Baba C
2013-06-01
In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms. Direct computation of a geodesic path on the space of diffeomorphisms Diff (Ω) is difficult, and it can be attributed mainly to the infinite dimensionality of Diff (Ω). Our proposed framework, to some degree, bypasses this difficulty using the quotient map of Diff (Ω) to the quotient space Diff ( M )/ Diff ( M ) μ obtained by quotienting out the subgroup of volume-preserving diffeomorphisms Diff ( M ) μ . This quotient space was recently identified as the unit sphere in a Hilbert space in mathematics literature, a space with well-known geometric properties. Our framework leverages this recent result by computing the diffeomorphic path in two stages. First, we project the given diffeomorphism pair onto this sphere and then compute the geodesic path between these projected points. Second, we lift the geodesic on the sphere back to the space of diffeomerphisms, by solving a quadratic programming problem with bilinear constraints using the augmented Lagrangian technique with penalty terms. In this way, we can estimate the path of diffeomorphisms, first, staying in the space of diffeomorphisms, and second, preserving shapes/volumes in the deformed images along the path as much as possible. We have applied our framework to interpolate intermediate frames of frame-sub-sampled video sequences. In the reported experiments, our approach compares favorably with the popular Large Deformation Diffeomorphic Metric Mapping framework (LDDMM).
Functions with disconnected spectrum sampling, interpolation, translates
Olevskii, Alexander M
2016-01-01
The classical sampling problem is to reconstruct entire functions with given spectrum S from their values on a discrete set L. From the geometric point of view, the possibility of such reconstruction is equivalent to determining for which sets L the exponential system with frequencies in L forms a frame in the space L^2(S). The book also treats the problem of interpolation of discrete functions by analytic ones with spectrum in S and the problem of completeness of discrete translates. The size and arithmetic structure of both the spectrum S and the discrete set L play a crucial role in these problems. After an elementary introduction, the authors give a new presentation of classical results due to Beurling, Kahane, and Landau. The main part of the book focuses on recent progress in the area, such as construction of universal sampling sets, high-dimensional and non-analytic phenomena. The reader will see how methods of harmonic and complex analysis interplay with various important concepts in different areas, ...
Gülşen, Esra; Kurtulus, Bedri; Necati Yaylim, Tolga; Avsar, Ozgur
2017-04-01
In groundwater studies, quantification and detection of fluid flows in borehole is an important part of assessment aquifer characteristic at different depths. Monitoring wells disturbs the natural flow field and this disturbance creates different flow paths to an aquifer. Vertical flow fluid analyses are one of the important techniques to deal with the detection and quantification of these vertical flows in borehole/monitoring wells. Liwa region is located about 146 km to the south west of Abu Dhabi city and about 36 km southwest of Madinat Zayed. SWSR (Strategic Water Storage & Recovery Project) comprises three Schemes (A, B and C) and each scheme contains an infiltration basin in the center, 105 recovery wells, 10 clusters and each cluster comprises 3 monitoring wells with different depths; shallow ( 50 m), intermediate ( 75 m) and deep ( 100 m). The scope of this study is to calculate the transmissivity values at different depth and evaluate the Fluid Flow Log (FFL) data for Scheme A (105 recovery wells) in order to understand the aquifer characteristic at different depths. The transmissivity values at different depth levels are calculated using Razack and Huntley (1991) equation for vertical flow rates of 30 m3 /h, 60 m3 /h, 90 m3 /h, 120 m3 /h and then Empirical Bayesian Kriging is used for interpolation in Scheme A using ArcGIS 10.2 software. FFL are drawn by GeODin software. Derivative analysis of fluid flow data are done by Microsoft Office: Excel software. All statistical analyses are calculated by IBMSPSS software. The interpolation results show that the transmissivity values are higher at the top of the aquifer. In other word, the aquifer is found more productive at the upper part of the Liwa aquifer. We are very grateful for financial support and providing us the data to ZETAS Dubai Inc.
Roy, Subrata P.
2014-01-28
The method of moments with interpolative closure (MOMIC) for soot formation and growth provides a detailed modeling framework maintaining a good balance in generality, accuracy, robustness, and computational efficiency. This study presents several computational issues in the development and implementation of the MOMIC-based soot modeling for direct numerical simulations (DNS). The issues of concern include a wide dynamic range of numbers, choice of normalization, high effective Schmidt number of soot particles, and realizability of the soot particle size distribution function (PSDF). These problems are not unique to DNS, but they are often exacerbated by the high-order numerical schemes used in DNS. Four specific issues are discussed in this article: the treatment of soot diffusion, choice of interpolation scheme for MOMIC, an approach to deal with strongly oxidizing environments, and realizability of the PSDF. General, robust, and stable approaches are sought to address these issues, minimizing the use of ad hoc treatments such as clipping. The solutions proposed and demonstrated here are being applied to generate new physical insight into complex turbulence-chemistry-soot-radiation interactions in turbulent reacting flows using DNS. © 2014 Copyright Taylor and Francis Group, LLC.
[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].
Xu, Yonghong; Gao, Shangce; Hao, Xiaofei
2016-04-01
Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.
On Multiple Interpolation Functions of the -Genocchi Polynomials
Directory of Open Access Journals (Sweden)
Jin Jeong-Hee
2010-01-01
Full Text Available Abstract Recently, many mathematicians have studied various kinds of the -analogue of Genocchi numbers and polynomials. In the work (New approach to q-Euler, Genocchi numbers and their interpolation functions, "Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105–112, 2009.", Kim defined new generating functions of -Genocchi, -Euler polynomials, and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz type -zeta function. This function interpolates -Genocchi polynomials at negative integers. Finally, we also give some identities related to these polynomials.
Spectral interpolation - Zero fill or convolution. [image processing
Forman, M. L.
1977-01-01
Zero fill, or augmentation by zeros, is a method used in conjunction with fast Fourier transforms to obtain spectral spacing at intervals closer than obtainable from the original input data set. In the present paper, an interpolation technique (interpolation by repetitive convolution) is proposed which yields values accurate enough for plotting purposes and which lie within the limits of calibration accuracies. The technique is shown to operate faster than zero fill, since fewer operations are required. The major advantages of interpolation by repetitive convolution are that efficient use of memory is possible (thus avoiding the difficulties encountered in decimation in time FFTs) and that is is easy to implement.
Steady State Stokes Flow Interpolation for Fluid Control
DEFF Research Database (Denmark)
Bhatacharya, Haimasree; Nielsen, Michael Bang; Bridson, Robert
2012-01-01
— suffer from a common problem. They fail to capture the rotational components of the velocity field, although extrapolation in the normal direction does consider the tangential component. We address this problem by casting the interpolation as a steady state Stokes flow. This type of flow captures......Fluid control methods often require surface velocities interpolated throughout the interior of a shape to use the velocity as a feedback force or as a boundary condition. Prior methods for interpolation in computer graphics — velocity extrapolation in the normal direction and potential flow...
C1 Rational Quadratic Trigonometric Interpolation Spline for Data Visualization
Directory of Open Access Journals (Sweden)
Shengjun Liu
2015-01-01
Full Text Available A new C1 piecewise rational quadratic trigonometric spline with four local positive shape parameters in each subinterval is constructed to visualize the given planar data. Constraints are derived on these free shape parameters to generate shape preserving interpolation curves for positive and/or monotonic data sets. Two of these shape parameters are constrained while the other two can be set free to interactively control the shape of the curves. Moreover, the order of approximation of developed interpolant is investigated as O(h3. Numeric experiments demonstrate that our method can construct nice shape preserving interpolation curves efficiently.
Chiral properties of baryon interpolating fields
International Nuclear Information System (INIS)
Nagata, Keitaro; Hosaka, Atsushi; Dmitrasinovic, V.
2008-01-01
We study the chiral transformation properties of all possible local (non-derivative) interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We derive and use the relations/identities among the baryon operators with identical quantum numbers that follow from the combined color, Dirac and isospin Fierz transformations. These relations reduce the number of independent baryon operators with any given spin and isospin. The Fierz identities also effectively restrict the allowed baryon chiral multiplets. It turns out that the non-derivative baryons' chiral multiplets have the same dimensionality as their Lorentz representations. For the two independent nucleon operators the only permissible chiral multiplet is the fundamental one, ((1)/(2),0)+(0,(1)/(2)). For the Δ, admissible Lorentz representations are (1,(1)/(2))+((1)/(2),1) and ((3)/(2),0)+(0,(3)/(2)). In the case of the (1,(1)/(2))+((1)/(2),1) chiral multiplet, the I(J)=(3)/(2)((3)/(2)) Δ field has one I(J)=(1)/(2)((3)/(2)) chiral partner; otherwise it has none. We also consider the Abelian (U A (1)) chiral transformation properties of the fields and show that each baryon comes in two varieties: (1) with Abelian axial charge +3; and (2) with Abelian axial charge -1. In case of the nucleon these are the two Ioffe fields; in case of the Δ, the (1,(1)/(2))+((1)/(2),1) multiplet has an Abelian axial charge -1 and the ((3)/(2),0)+(0,(3)/(2)) multiplet has an Abelian axial charge +3. (orig.)
Comparison of two fractal interpolation methods
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme
Rõõm, Rein; Männik, Aarne; Luhamaa, Andres
2007-10-01
Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.
An Energy Decaying Scheme for Nonlinear Dynamics of Shells
Bottasso, Carlo L.; Bauchau, Olivier A.; Choi, Jou-Young; Bushnell, Dennis M. (Technical Monitor)
2000-01-01
A novel integration scheme for nonlinear dynamics of geometrically exact shells is developed based on the inextensible director assumption. The new algorithm is designed so as to imply the strict decay of the system total mechanical energy at each time step, and consequently unconditional stability is achieved in the nonlinear regime. Furthermore, the scheme features tunable high frequency numerical damping and it is therefore stiffly accurate. The method is tested for a finite element spatial formulation of shells based on mixed interpolations of strain tensorial components and on a two-parameter representation of director rotations. The robustness of the, scheme is illustrated with the help of numerical examples.
Brantson, Eric Thompson; Ju, Binshan; Wu, Dan; Gyan, Patricia Semwaah
2018-04-01
This paper proposes stochastic petroleum porous media modeling for immiscible fluid flow simulation using Dykstra-Parson coefficient (V DP) and autocorrelation lengths to generate 2D stochastic permeability values which were also used to generate porosity fields through a linear interpolation technique based on Carman-Kozeny equation. The proposed method of permeability field generation in this study was compared to turning bands method (TBM) and uniform sampling randomization method (USRM). On the other hand, many studies have also reported that, upstream mobility weighting schemes, commonly used in conventional numerical reservoir simulators do not accurately capture immiscible displacement shocks and discontinuities through stochastically generated porous media. This can be attributed to high level of numerical smearing in first-order schemes, oftentimes misinterpreted as subsurface geological features. Therefore, this work employs high-resolution schemes of SUPERBEE flux limiter, weighted essentially non-oscillatory scheme (WENO), and monotone upstream-centered schemes for conservation laws (MUSCL) to accurately capture immiscible fluid flow transport in stochastic porous media. The high-order schemes results match well with Buckley Leverett (BL) analytical solution without any non-oscillatory solutions. The governing fluid flow equations were solved numerically using simultaneous solution (SS) technique, sequential solution (SEQ) technique and iterative implicit pressure and explicit saturation (IMPES) technique which produce acceptable numerical stability and convergence rate. A comparative and numerical examples study of flow transport through the proposed method, TBM and USRM permeability fields revealed detailed subsurface instabilities with their corresponding ultimate recovery factors. Also, the impact of autocorrelation lengths on immiscible fluid flow transport were analyzed and quantified. A finite number of lines used in the TBM resulted into visual
Directory of Open Access Journals (Sweden)
Annalisa Di Piazza
2015-04-01
Full Text Available An exhaustive comparison among different spatial interpolation algorithms was carried out in order to derive annual and monthly air temperature maps for Sicily (Italy. Deterministic, data-driven and geostatistics algorithms were used, in some cases adding the elevation information and other physiographic variables to improve the performance of interpolation techniques and the reconstruction of the air temperature field. The dataset is given by air temperature data coming from 84 stations spread around the island of Sicily. The interpolation algorithms were optimized by using a subset of the available dataset, while the remaining subset was used to validate the results in terms of the accuracy and bias of the estimates. Validation results indicate that univariate methods, which neglect the information from physiographic variables, significantly entail the largest errors, while performances improve when such parameters are taken into account. The best results at the annual scale have been obtained using the the ordinary kriging of residuals from linear regression and from the artificial neural network algorithm, while, at the monthly scale, a Fourier-series algorithm has been used to downscale mean annual temperature to reproduce monthly values in the annual cycle.
Additive operator-difference schemes splitting schemes
Vabishchevich, Petr N
2013-01-01
Applied mathematical modeling isconcerned with solving unsteady problems. This bookshows how toconstruct additive difference schemes to solve approximately unsteady multi-dimensional problems for PDEs. Two classes of schemes are highlighted: methods of splitting with respect to spatial variables (alternating direction methods) and schemes of splitting into physical processes. Also regionally additive schemes (domain decomposition methods)and unconditionally stable additive schemes of multi-component splitting are considered for evolutionary equations of first and second order as well as for sy
Rhie-Chow interpolation in strong centrifugal fields
Bogovalov, S. V.; Tronin, I. V.
2015-10-01
Rhie-Chow interpolation formulas are derived from the Navier-Stokes and continuity equations. These formulas are generalized to gas dynamics in strong centrifugal fields (as high as 106 g) occurring in gas centrifuges.
Efficient Algorithms and Design for Interpolation Filters in Digital Receiver
Directory of Open Access Journals (Sweden)
Xiaowei Niu
2014-05-01
Full Text Available Based on polynomial functions this paper introduces a generalized design method for interpolation filters. The polynomial-based interpolation filters can be implemented efficiently by using a modified Farrow structure with an arbitrary frequency response, the filters allow many pass- bands and stop-bands, and for each band the desired amplitude and weight can be set arbitrarily. The optimization coefficients of the interpolation filters in time domain are got by minimizing the weighted mean squared error function, then converting to solve the quadratic programming problem. The optimization coefficients in frequency domain are got by minimizing the maxima (MiniMax of the weighted mean squared error function. The degree of polynomials and the length of interpolation filter can be selected arbitrarily. Numerical examples verified the proposed design method not only can reduce the hardware cost effectively but also guarantee an excellent performance.
[Multimodal medical image registration using cubic spline interpolation method].
He, Yuanlie; Tian, Lianfang; Chen, Ping; Wang, Lifei; Ye, Guangchun; Mao, Zongyuan
2007-12-01
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.
Interpolating and sampling sequences in finite Riemann surfaces
Ortega-Cerda, Joaquim
2007-01-01
We provide a description of the interpolating and sampling sequences on a space of holomorphic functions on a finite Riemann surface, where a uniform growth restriction is imposed on the holomorphic functions.
Illumination estimation via thin-plate spline interpolation.
Shi, Lilong; Xiong, Weihua; Funt, Brian
2011-05-01
Thin-plate spline interpolation is used to interpolate the chromaticity of the color of the incident scene illumination across a training set of images. Given the image of a scene under unknown illumination, the chromaticity of the scene illumination can be found from the interpolated function. The resulting illumination-estimation method can be used to provide color constancy under changing illumination conditions and automatic white balancing for digital cameras. A thin-plate spline interpolates over a nonuniformly sampled input space, which in this case is a training set of image thumbnails and associated illumination chromaticities. To reduce the size of the training set, incremental k medians are applied. Tests on real images demonstrate that the thin-plate spline method can estimate the color of the incident illumination quite accurately, and the proposed training set pruning significantly decreases the computation.
Fast image interpolation for motion estimation using graphics hardware
Kelly, Francis; Kokaram, Anil
2004-05-01
Motion estimation and compensation is the key to high quality video coding. Block matching motion estimation is used in most video codecs, including MPEG-2, MPEG-4, H.263 and H.26L. Motion estimation is also a key component in the digital restoration of archived video and for post-production and special effects in the movie industry. Sub-pixel accurate motion vectors can improve the quality of the vector field and lead to more efficient video coding. However sub-pixel accuracy requires interpolation of the image data. Image interpolation is a key requirement of many image processing algorithms. Often interpolation can be a bottleneck in these applications, especially in motion estimation due to the large number pixels involved. In this paper we propose using commodity computer graphics hardware for fast image interpolation. We use the full search block matching algorithm to illustrate the problems and limitations of using graphics hardware in this way.
3D Medical Image Interpolation Based on Parametric Cubic Convolution
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In the process of display, manipulation and analysis of biomedical image data, they usually need to be converted to data of isotropic discretization through the process of interpolation, while the cubic convolution interpolation is widely used due to its good tradeoff between computational cost and accuracy. In this paper, we present a whole concept for the 3D medical image interpolation based on cubic convolution, and the six methods, with the different sharp control parameter, which are formulated in details. Furthermore, we also give an objective comparison for these methods using data sets with the different slice spacing. Each slice in these data sets is estimated by each interpolation method and compared with the original slice using three measures: mean-squared difference, number of sites of disagreement, and largest difference. According to the experimental results, we present a recommendation for 3D medical images under the different situations in the end.
Interpolation and sampling in spaces of analytic functions
Seip, Kristian
2004-01-01
The book is about understanding the geometry of interpolating and sampling sequences in classical spaces of analytic functions. The subject can be viewed as arising from three classical topics: Nevanlinna-Pick interpolation, Carleson's interpolation theorem for H^\\infty, and the sampling theorem, also known as the Whittaker-Kotelnikov-Shannon theorem. The book aims at clarifying how certain basic properties of the space at hand are reflected in the geometry of interpolating and sampling sequences. Key words for the geometric descriptions are Carleson measures, Beurling densities, the Nyquist rate, and the Helson-Szegő condition. The book is based on six lectures given by the author at the University of Michigan. This is reflected in the exposition, which is a blend of informal explanations with technical details. The book is essentially self-contained. There is an underlying assumption that the reader has a basic knowledge of complex and functional analysis. Beyond that, the reader should have some familiari...
Energy-Driven Image Interpolation Using Gaussian Process Regression
Directory of Open Access Journals (Sweden)
Lingling Zi
2012-01-01
Full Text Available Image interpolation, as a method of obtaining a high-resolution image from the corresponding low-resolution image, is a classical problem in image processing. In this paper, we propose a novel energy-driven interpolation algorithm employing Gaussian process regression. In our algorithm, each interpolated pixel is predicted by a combination of two information sources: first is a statistical model adopted to mine underlying information, and second is an energy computation technique used to acquire information on pixel properties. We further demonstrate that our algorithm can not only achieve image interpolation, but also reduce noise in the original image. Our experiments show that the proposed algorithm can achieve encouraging performance in terms of image visualization and quantitative measures.
Spatial interpolation of point velocities in stream cross-section
Directory of Open Access Journals (Sweden)
Hasníková Eliška
2015-03-01
Full Text Available The most frequently used instrument for measuring velocity distribution in the cross-section of small rivers is the propeller-type current meter. Output of measuring using this instrument is point data of a tiny bulk. Spatial interpolation of measured data should produce a dense velocity profile, which is not available from the measuring itself. This paper describes the preparation of interpolation models.
The Convergence Acceleration of Two-Dimensional Fourier Interpolation
Directory of Open Access Journals (Sweden)
Anry Nersessian
2008-07-01
Full Text Available Hereby, the convergence acceleration of two-dimensional trigonometric interpolation for a smooth functions on a uniform mesh is considered. Together with theoretical estimates some numerical results are presented and discussed that reveal the potential of this method for application in image processing. Experiments show that suggested algorithm allows acceleration of conventional Fourier interpolation even for sparse meshes that can lead to an efficient image compression/decompression algorithms and also to applications in image zooming procedures.
Survey: interpolation methods for whole slide image processing.
Roszkowiak, L; Korzynska, A; Zak, J; Pijanowska, D; Swiderska-Chadaj, Z; Markiewicz, T
2017-02-01
Evaluating whole slide images of histological and cytological samples is used in pathology for diagnostics, grading and prognosis . It is often necessary to rescale whole slide images of a very large size. Image resizing is one of the most common applications of interpolation. We collect the advantages and drawbacks of nine interpolation methods, and as a result of our analysis, we try to select one interpolation method as the preferred solution. To compare the performance of interpolation methods, test images were scaled and then rescaled to the original size using the same algorithm. The modified image was compared to the original image in various aspects. The time needed for calculations and results of quantification performance on modified images were also compared. For evaluation purposes, we used four general test images and 12 specialized biological immunohistochemically stained tissue sample images. The purpose of this survey is to determine which method of interpolation is the best to resize whole slide images, so they can be further processed using quantification methods. As a result, the interpolation method has to be selected depending on the task involving whole slide images. © 2016 The Authors Journal of Microscopy © 2016 Royal Microscopical Society.
Surface interpolation with radial basis functions for medical imaging
International Nuclear Information System (INIS)
Carr, J.C.; Beatson, R.K.; Fright, W.R.
1997-01-01
Radial basis functions are presented as a practical solution to the problem of interpolating incomplete surfaces derived from three-dimensional (3-D) medical graphics. The specific application considered is the design of cranial implants for the repair of defects, usually holes, in the skull. Radial basis functions impose few restrictions on the geometry of the interpolation centers and are suited to problems where interpolation centers do not form a regular grid. However, their high computational requirements have previously limited their use to problems where the number of interpolation centers is small (<300). Recently developed fast evaluation techniques have overcome these limitations and made radial basis interpolation a practical approach for larger data sets. In this paper radial basis functions are fitted to depth-maps of the skull's surface, obtained from X-ray computed tomography (CT) data using ray-tracing techniques. They are used to smoothly interpolate the surface of the skull across defect regions. The resulting mathematical description of the skull's surface can be evaluated at any desired resolution to be rendered on a graphics workstation or to generate instructions for operating a computer numerically controlled (CNC) mill
Monolithic front-end ICs for interpolating cathode pad and strip detectors for GEM
International Nuclear Information System (INIS)
O'Connor, P.
1993-05-01
We are developing CMOS circuits for readout of interpolating cathode strip and pad chambers for the GEM experiment at the SSC. Because these detectors require position resolution of about 1% of the strip pitch, the electronic noise level must be less than 2000 electrons. Several test chips have been fabricated to demonstrate the feasibility of achieving the combination of low noise, speed, and wide dynamic range in CMOS. Results to date show satisfactory noise and linearity performance. Future development will concentrate on radiation-hardening the central tracker ASIC design, optimizing the shaper peaking time and noise contribution, providing more user-configurable output options, and packaging and test issues
Maximum Feedrate Interpolator for Multi-axis CNC Machining with Jerk Constraints
Beudaert , Xavier; Lavernhe , Sylvain; Tournier , Christophe
2012-01-01
A key role of the CNC is to perform the feedrate interpolation which means to generate the setpoints for each machine tool axis. The aim of the VPOp algorithm is to make maximum use of the machine tool respecting both tangential and axis jerk on rotary and linear axes. The developed algorithm uses an iterative constraints intersection approach. At each sampling period, all the constraints given by each axis are expressed and by intersecting all of them the allowable interval for the next poin...
Directory of Open Access Journals (Sweden)
Elmira Ashpazzadeh
2018-04-01
Full Text Available A numerical technique based on the Hermite interpolant multiscaling functions is presented for the solution of Convection-diusion equations. The operational matrices of derivative, integration and product are presented for multiscaling functions and are utilized to reduce the solution of linear Convection-diusion equation to the solution of algebraic equations. Because of sparsity of these matrices, this method is computationally very attractive and reduces the CPU time and computer memory. Illustrative examples are included to demonstrate the validity and applicability of the new technique.
5-D interpolation with wave-front attributes
Xie, Yujiang; Gajewski, Dirk
2017-11-01
Most 5-D interpolation and regularization techniques reconstruct the missing data in the frequency domain by using mathematical transforms. An alternative type of interpolation methods uses wave-front attributes, that is, quantities with a specific physical meaning like the angle of emergence and wave-front curvatures. In these attributes structural information of subsurface features like dip and strike of a reflector are included. These wave-front attributes work on 5-D data space (e.g. common-midpoint coordinates in x and y, offset, azimuth and time), leading to a 5-D interpolation technique. Since the process is based on stacking next to the interpolation a pre-stack data enhancement is achieved, improving the signal-to-noise ratio (S/N) of interpolated and recorded traces. The wave-front attributes are determined in a data-driven fashion, for example, with the Common Reflection Surface (CRS method). As one of the wave-front-attribute-based interpolation techniques, the 3-D partial CRS method was proposed to enhance the quality of 3-D pre-stack data with low S/N. In the past work on 3-D partial stacks, two potential problems were still unsolved. For high-quality wave-front attributes, we suggest a global optimization strategy instead of the so far used pragmatic search approach. In previous works, the interpolation of 3-D data was performed along a specific azimuth which is acceptable for narrow azimuth acquisition but does not exploit the potential of wide-, rich- or full-azimuth acquisitions. The conventional 3-D partial CRS method is improved in this work and we call it as a wave-front-attribute-based 5-D interpolation (5-D WABI) as the two problems mentioned above are addressed. Data examples demonstrate the improved performance by the 5-D WABI method when compared with the conventional 3-D partial CRS approach. A comparison of the rank-reduction-based 5-D seismic interpolation technique with the proposed 5-D WABI method is given. The comparison reveals that
Malvar-He-Cutler Linear Image Demosaicking
Directory of Open Access Journals (Sweden)
Pascal Getreuer
2011-08-01
Full Text Available Image demosaicking (or demosaicing is the interpolation problem of estimating complete color information for an image that has been captured through a color filter array (CFA, particularly on the Bayer pattern. In this paper we review a simple linear method using 5 x 5 filters, proposed by Malvar, He, and Cutler in 2004, that shows surprisingly good results.
International Nuclear Information System (INIS)
Ganesan, S.; Gopalakrishnan, V.; Ramanadhan, M.M.; Cullan, D.E.
1986-01-01
We investigate the effect of interpolation error in the pre-processing codes LINEAR, RECENT and SIGMA1 on calculations of self-shielding factors and their temperature derivatives. We consider the 2.0347 to 3.3546 keV energy region for 238 U capture, which is the NEACRP benchmark exercise on unresolved parameters. The calculated values of temperature derivatives of self-shielding factors are significantly affected by interpolation error. The sources of problems in both evaluated data and codes are identified and eliminated in the 1985 version of these codes. This paper helps to (1) inform code users to use only 1985 versions of LINEAR, RECENT, and SIGMA1 and (2) inform designers of other code systems where they may have problems and what to do to eliminate their problems. (author)
International Nuclear Information System (INIS)
Ganesan, S.; Gopalakrishnan, V.; Ramanadhan, M.M.; Cullen, D.E.
1985-01-01
The authors investigate the effect of interpolation error in the pre-processing codes LINEAR, RECENT and SIGMA1 on calculations of self-shielding factors and their temperature derivatives. They consider the 2.0347 to 3.3546 keV energy region for /sup 238/U capture, which is the NEACRP benchmark exercise on unresolved parameters. The calculated values of temperature derivatives of self-shielding factors are significantly affected by interpolation error. The sources of problems in both evaluated data and codes are identified and eliminated in the 1985 version of these codes. This paper helps to (1) inform code users to use only 1985 versions of LINEAR, RECENT, and SIGMA1 and (2) inform designers of other code systems where they may have problems and what to do to eliminate their problems
International Nuclear Information System (INIS)
T Sutton; T Trumbull
2005-01-01
Secondary neutron energy spectra used by Monte Carlo codes are often provided in tabular format. Examples are the spectra obtained from ENDF/B-VI File 5 when the LF parameter has the value 1. These secondary spectra are tabulated on an incident energy mesh, and in a Monte Carlo calculation the tabulated spectra are generally interpolated to the energy of the incident neutron. A common method of interpolation involves the use of the unit base transformation. The details of the implementation vary from code to code, so here we will simply focus on the mathematics of the method. Given an incident neutron with energy E, the bracketing points E i and E i+1 on the incident energy mesh are determined. The corresponding secondary energy spectra are transformed to a dimensionless energy coordinate system in which the secondary energies lie between zero and one. A dimensionless secondary energy is then sampled from a spectrum obtained by linearly interpolating the transformed spectra--often using the method of statistical interpolation. Finally, the sampled secondary energy is transformed back into the normal energy coordinate system. For this inverse transformation, the minimum and maximum energies are linearly interpolated from the values given in the non-transformed secondary spectra. The purpose of the unit base transformation is to preserve (as nearly as possible) the physics of the secondary distribution--in particular the minimum and maximum energies possible for the secondary neutron. This method is used by several codes including MCNP and the new MC21 code that is the subject of this paper. In comparing MC21 results to those of MCNP, it was discovered that the nuclear data supplied to MCNP is structured in such a way that the code may not be doing the best possible job of preserving the physics of certain nuclear interactions. In this paper, we describe the problem and explain how it may be avoided
Study on Scattered Data Points Interpolation Method Based on Multi-line Structured Light
International Nuclear Information System (INIS)
Fan, J Y; Wang, F G; W, Y; Zhang, Y L
2006-01-01
Aiming at the range image obtained through multi-line structured light, a regional interpolation method is put forward in this paper. This method divides interpolation into two parts according to the memory format of the scattered data, one is interpolation of the data on the stripes, and the other is interpolation of data between the stripes. Trend interpolation method is applied to the data on the stripes, and Gauss wavelet interpolation method is applied to the data between the stripes. Experiments prove regional interpolation method feasible and practical, and it also promotes the speed and precision
A Meshfree Cell-based Smoothed Point Interpolation Method for Solid Mechanics Problems
International Nuclear Information System (INIS)
Zhang Guiyong; Liu Guirong
2010-01-01
In the framework of a weakened weak (W 2 ) formulation using a generalized gradient smoothing operation, this paper introduces a novel meshfree cell-based smoothed point interpolation method (CS-PIM) for solid mechanics problems. The W 2 formulation seeks solutions from a normed G space which includes both continuous and discontinuous functions and allows the use of much more types of methods to create shape functions for numerical methods. When PIM shape functions are used, the functions constructed are in general not continuous over the entire problem domain and hence are not compatible. Such an interpolation is not in a traditional H 1 space, but in a G 1 space. By introducing the generalized gradient smoothing operation properly, the requirement on function is now further weakened upon the already weakened requirement for functions in a H 1 space and G 1 space can be viewed as a space of functions with weakened weak (W 2 ) requirement on continuity. The cell-based smoothed point interpolation method (CS-PIM) is formulated based on the W 2 formulation, in which displacement field is approximated using the PIM shape functions, which possess the Kronecker delta property facilitating the enforcement of essential boundary conditions [3]. The gradient (strain) field is constructed by the generalized gradient smoothing operation within the cell-based smoothing domains, which are exactly the triangular background cells. A W 2 formulation of generalized smoothed Galerkin (GS-Galerkin) weak form is used to derive the discretized system equations. It was found that the CS-PIM possesses the following attractive properties: (1) It is very easy to implement and works well with the simplest linear triangular mesh without introducing additional degrees of freedom; (2) it is at least linearly conforming; (3) this method is temporally stable and works well for dynamic analysis; (4) it possesses a close-to-exact stiffness, which is much softer than the overly-stiff FEM model and
Liu, Shulun; Li, Yuan; Pauwels, Valentijn R. N.; Walker, Jeffrey P.
2017-12-01
Rain gauges are widely used to obtain temporally continuous point rainfall records, which are then interpolated into spatially continuous data to force hydrological models. However, rainfall measurements and interpolation procedure are subject to various uncertainties, which can be reduced by applying quality control and selecting appropriate spatial interpolation approaches. Consequently, the integrated impact of rainfall quality control and interpolation on streamflow simulation has attracted increased attention but not been fully addressed. This study applies a quality control procedure to the hourly rainfall measurements obtained in the Warwick catchment in eastern Australia. The grid-based daily precipitation from the Australian Water Availability Project was used as a reference. The Pearson correlation coefficient between the daily accumulation of gauged rainfall and the reference data was used to eliminate gauges with significant quality issues. The unrealistic outliers were censored based on a comparison between gauged rainfall and the reference. Four interpolation methods, including the inverse distance weighting (IDW), nearest neighbors (NN), linear spline (LN), and ordinary Kriging (OK), were implemented. The four methods were firstly assessed through a cross-validation using the quality-controlled rainfall data. The impacts of the quality control and interpolation on streamflow simulation were then evaluated through a semi-distributed hydrological model. The results showed that the Nash–Sutcliffe model efficiency coefficient (NSE) and Bias of the streamflow simulations were significantly improved after quality control. In the cross-validation, the IDW and OK methods resulted in good interpolation rainfall, while the NN led to the worst result. In term of the impact on hydrological prediction, the IDW led to the most consistent streamflow predictions with the observations, according to the validation at five streamflow-gauged locations. The OK method
Simple Numerical Schemes for the Korteweg-deVries Equation
International Nuclear Information System (INIS)
McKinstrie, C. J.; Kozlov, M.V.
2000-01-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves
Simple Numerical Schemes for the Korteweg-deVries Equation
Energy Technology Data Exchange (ETDEWEB)
C. J. McKinstrie; M. V. Kozlov
2000-12-01
Two numerical schemes, which simulate the propagation of dispersive non-linear waves, are described. The first is a split-step Fourier scheme for the Korteweg-de Vries (KdV) equation. The second is a finite-difference scheme for the modified KdV equation. The stability and accuracy of both schemes are discussed. These simple schemes can be used to study a wide variety of physical processes that involve dispersive nonlinear waves.
Sparse representation based image interpolation with nonlocal autoregressive modeling.
Dong, Weisheng; Zhang, Lei; Lukac, Rastislav; Shi, Guangming
2013-04-01
Sparse representation is proven to be a promising approach to image super-resolution, where the low-resolution (LR) image is usually modeled as the down-sampled version of its high-resolution (HR) counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e., the LR image is directly down-sampled from its HR counterpart without blurring, the super-resolution problem becomes an image interpolation problem. In such cases, however, the conventional sparse representation models (SRM) become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, fortunately, many nonlocal similar patches to a given patch could provide nonlocal constraint to the local structure. In this paper, we incorporate the image nonlocal self-similarity into SRM for image interpolation. More specifically, a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in SRM. We show that the NARM-induced sampling matrix is less coherent with the representation dictionary, and consequently makes SRM more effective for image interpolation. Our extensive experimental results demonstrate that the proposed NARM-based image interpolation method can effectively reconstruct the edge structures and suppress the jaggy/ringing artifacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as SSIM and FSIM.
A hybrid Lagrangian Voronoi-SPH scheme
Fernandez-Gutierrez, D.; Souto-Iglesias, A.; Zohdi, T. I.
2017-11-01
A hybrid Lagrangian Voronoi-SPH scheme, with an explicit weakly compressible formulation for both the Voronoi and SPH sub-domains, has been developed. The SPH discretization is substituted by Voronoi elements close to solid boundaries, where SPH consistency and boundary conditions implementation become problematic. A buffer zone to couple the dynamics of both sub-domains is used. This zone is formed by a set of particles where fields are interpolated taking into account SPH particles and Voronoi elements. A particle may move in or out of the buffer zone depending on its proximity to a solid boundary. The accuracy of the coupled scheme is discussed by means of a set of well-known verification benchmarks.
Spatio-Temporal Interpolation of Cloudy SST Fields Using Conditional Analog Data Assimilation
Directory of Open Access Journals (Sweden)
Ronan Fablet
2018-02-01
Full Text Available The ever increasing geophysical data streams pouring from earth observation satellite missions and numerical simulations along with the development of dedicated big data infrastructure advocate for truly exploiting the potential of these datasets, through novel data-driven strategies, to deliver enhanced satellite-derived gapfilled geophysical products from partial satellite observations. We here demonstrate the relevance of the analog data assimilation (AnDA for an application to the reconstruction of cloud-free level-4 gridded Sea Surface Temperature (SST. We propose novel AnDA models which exploit auxiliary variables such as sea surface currents and significantly reduce the computational complexity of AnDA. Numerical experiments benchmark the proposed models with respect to state-of-the-art interpolation techniques such as optimal interpolation and EOF-based schemes. We report relative improvement up to 40%/50% in terms of RMSE and also show a good parallelization performance, which supports the feasibility of an upscaling on a global scale.
International Nuclear Information System (INIS)
Magnusson Seger, Maria
1998-01-01
We here present LINCON FAST which is an exact method for 3D reconstruction from cone-beam projection data. The new method is compared to the LINCON method which is known to be fast and to give good image quality. Both methods have O(N 3 log N) complexity and are based on Grangeat's result which states that the derivative of the Radon transform of the object function can be obtained from cone-beam projections. One disadvantage with LINCON is that the rather computationally intensive chirp z-transform is frequently used. In LINCON FAST , FFT and interpolation in the Fourier domain are used instead, which are less computationally demanding. The computation tools involved in LINCON FAST are solely FFT, 1D eight-point interpolation, multiplicative weighting and tri-linear interpolation. We estimate that LINCON FAST will be 2-2.5 times faster than LINCON. The interpolation filter belongs to a special class of filters developed by us. It turns out that the filter must be very carefully designed to keep a good image quality. Visual inspection of experimental results shows that the image quality is almost the same for LINCON and the new method LINCON FAST . However, it should be remembered that LINCON FAST can never give better image quality than LINCON, since LINCON FAST is designed to approximate LINCON as well as possible. (author)
Zhu, Mengchen; Salcudean, Septimiu E
2011-07-01
In this paper, we propose an interpolation-based method for simulating rigid needles in B-mode ultrasound images in real time. We parameterize the needle B-mode image as a function of needle position and orientation. We collect needle images under various spatial configurations in a water-tank using a needle guidance robot. Then we use multidimensional tensor-product interpolation to simulate images of needles with arbitrary poses and positions using collected images. After further processing, the interpolated needle and seed images are superimposed on top of phantom or tissue image backgrounds. The similarity between the simulated and the real images is measured using a correlation metric. A comparison is also performed with in vivo images obtained during prostate brachytherapy. Our results, carried out for both the convex (transverse plane) and linear (sagittal/para-sagittal plane) arrays of a trans-rectal transducer indicate that our interpolation method produces good results while requiring modest computing resources. The needle simulation method we present can be extended to the simulation of ultrasound images of other wire-like objects. In particular, we have shown that the proposed approach can be used to simulate brachytherapy seeds.
Gas proportional detectors with interpolating cathode pad readout for high track multiplicities
International Nuclear Information System (INIS)
Yu, Bo.
1991-12-01
New techniques for position encoding in very high rate particle and photon detectors will be required in experiments planned for future particle accelerators such as the Superconducting Super Collider and new, high intensity, synchrotron sources. Studies of two interpolating cathode ''pad'' readout systems are described in this thesis. They are well suited for high multiplicity, two dimensional unambiguous position sensitive detection of minimum ionizing particles and heavy ions as well as detection of x-rays at high counting rates. One of the readout systems uses subdivided rows of pads interconnected by resistive strips as the cathode of a multiwire proportional chamber (MWPC). A position resolution of less than 100 μm rms, for 5.4 keV x-rays, and differential non-linearity of 12% have been achieved. Low mass (∼0.6% of a radiation length) detector construction techniques have been developed. The second readout system uses rows of chevron shaped cathode pads to perform geometrical charge division. Position resolution (FWHM) of about 1% of the readout spacing and differential non-linearity of 10% for 5.4 keV x-rays have been achieved. A review of other interpolating methods is included. Low mass cathode construction techniques are described. In conclusion, applications and future developments are discussed. 54 refs
Interpolation of vector fields from human cardiac DT-MRI
International Nuclear Information System (INIS)
Yang, F; Zhu, Y M; Rapacchi, S; Robini, M; Croisille, P; Luo, J H
2011-01-01
There has recently been increased interest in developing tensor data processing methods for the new medical imaging modality referred to as diffusion tensor magnetic resonance imaging (DT-MRI). This paper proposes a method for interpolating the primary vector fields from human cardiac DT-MRI, with the particularity of achieving interpolation and denoising simultaneously. The method consists of localizing the noise-corrupted vectors using the local statistical properties of vector fields, removing the noise-corrupted vectors and reconstructing them by using the thin plate spline (TPS) model, and finally applying global TPS interpolation to increase the resolution in the spatial domain. Experiments on 17 human hearts show that the proposed method allows us to obtain higher resolution while reducing noise, preserving details and improving direction coherence (DC) of vector fields as well as fiber tracking. Moreover, the proposed method perfectly reconstructs azimuth and elevation angle maps.
Inoculating against eyewitness suggestibility via interpolated verbatim vs. gist testing.
Pansky, Ainat; Tenenboim, Einat
2011-01-01
In real-life situations, eyewitnesses often have control over the level of generality in which they choose to report event information. In the present study, we adopted an early-intervention approach to investigate to what extent eyewitness memory may be inoculated against suggestibility, following two different levels of interpolated reporting: verbatim and gist. After viewing a target event, participants responded to interpolated questions that required reporting of target details at either the verbatim or the gist level. After 48 hr, both groups of participants were misled about half of the target details and were finally tested for verbatim memory of all the details. The findings were consistent with our predictions: Whereas verbatim testing was successful in completely inoculating against suggestibility, gist testing did not reduce it whatsoever. These findings are particularly interesting in light of the comparable testing effects found for these two modes of interpolated testing.
Image interpolation used in three-dimensional range data compression.
Zhang, Shaoze; Zhang, Jianqi; Huang, Xi; Liu, Delian
2016-05-20
Advances in the field of three-dimensional (3D) scanning have made the acquisition of 3D range data easier and easier. However, with the large size of 3D range data comes the challenge of storing and transmitting it. To address this challenge, this paper presents a framework to further compress 3D range data using image interpolation. We first use a virtual fringe-projection system to store 3D range data as images, and then apply the interpolation algorithm to the images to reduce their resolution to further reduce the data size. When the 3D range data are needed, the low-resolution image is scaled up to its original resolution by applying the interpolation algorithm, and then the scaled-up image is decoded and the 3D range data are recovered according to the decoded result. Experimental results show that the proposed method could further reduce the data size while maintaining a low rate of error.
Importance of interpolation and coincidence errors in data fusion
Ceccherini, Simone; Carli, Bruno; Tirelli, Cecilia; Zoppetti, Nicola; Del Bianco, Samuele; Cortesi, Ugo; Kujanpää, Jukka; Dragani, Rossana
2018-02-01
The complete data fusion (CDF) method is applied to ozone profiles obtained from simulated measurements in the ultraviolet and in the thermal infrared in the framework of the Sentinel 4 mission of the Copernicus programme. We observe that the quality of the fused products is degraded when the fusing profiles are either retrieved on different vertical grids or referred to different true profiles. To address this shortcoming, a generalization of the complete data fusion method, which takes into account interpolation and coincidence errors, is presented. This upgrade overcomes the encountered problems and provides products of good quality when the fusing profiles are both retrieved on different vertical grids and referred to different true profiles. The impact of the interpolation and coincidence errors on number of degrees of freedom and errors of the fused profile is also analysed. The approach developed here to account for the interpolation and coincidence errors can also be followed to include other error components, such as forward model errors.
An improved local radial point interpolation method for transient heat conduction analysis
Wang, Feng; Lin, Gao; Zheng, Bao-Jing; Hu, Zhi-Qiang
2013-06-01
The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions.
An improved local radial point interpolation method for transient heat conduction analysis
International Nuclear Information System (INIS)
Wang Feng; Lin Gao; Hu Zhi-Qiang; Zheng Bao-Jing
2013-01-01
The smoothing thin plate spline (STPS) interpolation using the penalty function method according to the optimization theory is presented to deal with transient heat conduction problems. The smooth conditions of the shape functions and derivatives can be satisfied so that the distortions hardly occur. Local weak forms are developed using the weighted residual method locally from the partial differential equations of the transient heat conduction. Here the Heaviside step function is used as the test function in each sub-domain to avoid the need for a domain integral. Essential boundary conditions can be implemented like the finite element method (FEM) as the shape functions possess the Kronecker delta property. The traditional two-point difference method is selected for the time discretization scheme. Three selected numerical examples are presented in this paper to demonstrate the availability and accuracy of the present approach comparing with the traditional thin plate spline (TPS) radial basis functions
Amir, Sahar Z.
2013-05-01
We introduce an efficient thermodynamically consistent technique to extrapolate and interpolate normalized Canonical NVT ensemble averages like pressure and energy for Lennard-Jones (L-J) fluids. Preliminary results show promising applicability in oil and gas modeling, where accurate determination of thermodynamic properties in reservoirs is challenging. The thermodynamic interpolation and thermodynamic extrapolation schemes predict ensemble averages at different thermodynamic conditions from expensively simulated data points. The methods reweight and reconstruct previously generated database values of Markov chains at neighboring temperature and density conditions. To investigate the efficiency of these methods, two databases corresponding to different combinations of normalized density and temperature are generated. One contains 175 Markov chains with 10,000,000 MC cycles each and the other contains 3000 Markov chains with 61,000,000 MC cycles each. For such massive database creation, two algorithms to parallelize the computations have been investigated. The accuracy of the thermodynamic extrapolation scheme is investigated with respect to classical interpolation and extrapolation. Finally, thermodynamic interpolation benefiting from four neighboring Markov chains points is implemented and compared with previous schemes. The thermodynamic interpolation scheme using knowledge from the four neighboring points proves to be more accurate than the thermodynamic extrapolation from the closest point only, while both thermodynamic extrapolation and thermodynamic interpolation are more accurate than the classical interpolation and extrapolation. The investigated extrapolation scheme has great potential in oil and gas reservoir modeling.That is, such a scheme has the potential to speed up the MCMC thermodynamic computation to be comparable with conventional Equation of State approaches in efficiency. In particular, this makes it applicable to large-scale optimization of L
Estimating monthly temperature using point based interpolation techniques
Saaban, Azizan; Mah Hashim, Noridayu; Murat, Rusdi Indra Zuhdi
2013-04-01
This paper discusses the use of point based interpolation to estimate the value of temperature at an unallocated meteorology stations in Peninsular Malaysia using data of year 2010 collected from the Malaysian Meteorology Department. Two point based interpolation methods which are Inverse Distance Weighted (IDW) and Radial Basis Function (RBF) are considered. The accuracy of the methods is evaluated using Root Mean Square Error (RMSE). The results show that RBF with thin plate spline model is suitable to be used as temperature estimator for the months of January and December, while RBF with multiquadric model is suitable to estimate the temperature for the rest of the months.
Multi-dimensional cubic interpolation for ICF hydrodynamics simulation
International Nuclear Information System (INIS)
Aoki, Takayuki; Yabe, Takashi.
1991-04-01
A new interpolation method is proposed to solve the multi-dimensional hyperbolic equations which appear in describing the hydrodynamics of inertial confinement fusion (ICF) implosion. The advection phase of the cubic-interpolated pseudo-particle (CIP) is greatly improved, by assuming the continuities of the second and the third spatial derivatives in addition to the physical value and the first derivative. These derivatives are derived from the given physical equation. In order to evaluate the new method, Zalesak's example is tested, and we obtain successfully good results. (author)
Oversampling of digitized images. [effects on interpolation in signal processing
Fischel, D.
1976-01-01
Oversampling is defined as sampling with a device whose characteristic width is greater than the interval between samples. This paper shows why oversampling should be avoided and discusses the limitations in data processing if circumstances dictate that oversampling cannot be circumvented. Principally, oversampling should not be used to provide interpolating data points. Rather, the time spent oversampling should be used to obtain more signal with less relative error, and the Sampling Theorem should be employed to provide any desired interpolated values. The concepts are applicable to single-element and multielement detectors.
Scientific data interpolation with low dimensional manifold model
Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley
2018-01-01
We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
Scientific data interpolation with low dimensional manifold model
International Nuclear Information System (INIS)
Zhu, Wei; Wang, Bao; Barnard, Richard C.; Hauck, Cory D.
2017-01-01
Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.
SYNTHESIS OF VISCOELASTIC MATERIAL MODELS (SCHEMES
Directory of Open Access Journals (Sweden)
V. Bogomolov
2014-10-01
Full Text Available The principles of structural viscoelastic schemes construction for materials with linear viscoelastic properties in accordance with the given experimental data on creep tests are analyzed. It is shown that there can be only four types of materials with linear visco-elastic properties.
Review and Analysis of Cryptographic Schemes Implementing Threshold Signature
Directory of Open Access Journals (Sweden)
Anastasiya Victorovna Beresneva
2015-03-01
Full Text Available This work is devoted to the study of threshold signature schemes. The systematization of the threshold signature schemes was done, cryptographic constructions based on interpolation Lagrange polynomial, ellipt ic curves and bilinear pairings were investigated. Different methods of generation and verification of threshold signatures were explored, e.g. used in a mobile agents, Internet banking and e-currency. The significance of the work is determined by the reduction of the level of counterfeit electronic documents, signed by certain group of users.
Directory of Open Access Journals (Sweden)
Kresno Wikan Sadono
2016-12-01
Full Text Available Persamaan differensial banyak digunakan untuk menggambarkan berbagai fenomena dalam bidang sains dan rekayasa. Berbagai masalah komplek dalam kehidupan sehari-hari dapat dimodelkan dengan persamaan differensial dan diselesaikan dengan metode numerik. Salah satu metode numerik, yaitu metode meshfree atau meshless berkembang akhir-akhir ini, tanpa proses pembuatan elemen pada domain. Penelitian ini menggabungkan metode meshless yaitu radial basis point interpolation method (RPIM dengan integrasi waktu discontinuous Galerkin method (DGM, metode ini disebut RPIM-DGM. Metode RPIM-DGM diaplikasikan pada advection equation pada satu dimensi. RPIM menggunakan basis function multiquadratic function (MQ dan integrasi waktu diturunkan untuk linear-DGM maupun quadratic-DGM. Hasil simulasi menunjukkan, metode ini mendekati hasil analitis dengan baik. Hasil simulasi numerik dengan RPIM DGM menunjukkan semakin banyak node dan semakin kecil time increment menunjukkan hasil numerik semakin akurat. Hasil lain menunjukkan, integrasi numerik dengan quadratic-DGM untuk suatu time increment dan jumlah node tertentu semakin meningkatkan akurasi dibandingkan dengan linear-DGM. [Title: Numerical solution of advection equation with radial basis interpolation method and discontinuous Galerkin method for time integration] Differential equation is widely used to describe a variety of phenomena in science and engineering. A variety of complex issues in everyday life can be modeled with differential equations and solved by numerical method. One of the numerical methods, the method meshfree or meshless developing lately, without making use of the elements in the domain. The research combines methods meshless, i.e. radial basis point interpolation method with discontinuous Galerkin method as time integration method. This method is called RPIM-DGM. The RPIM-DGM applied to one dimension advection equation. The RPIM using basis function multiquadratic function and time
Biased motion vector interpolation for reduced video artifacts.
2011-01-01
In a video processing system where motion vectors are estimated for a subset of the blocks of data forming a video frame, and motion vectors are interpolated for the remainder of the blocks of the frame, a method includes determining, for at least at least one block of the current frame for which a
A Note on Interpolation of Stable Processes | Nassiuma | Journal of ...
African Journals Online (AJOL)
Interpolation procedures tailored for gaussian processes may not be applied to infinite variance stable processes. Alternative techniques suitable for a limited set of stable case with index α∈(1,2] were initially studied by Pourahmadi (1984) for harmonizable processes. This was later extended to the ARMA stable process ...
Analysis of Spatial Interpolation in the Material-Point Method
DEFF Research Database (Denmark)
Andersen, Søren; Andersen, Lars
2010-01-01
are obtained using quadratic elements. It is shown that for more complex problems, the use of partially negative shape functions is inconsistent with the material-point method in its current form, necessitating other types of interpolation such as cubic splines in order to obtain smoother representations...
Fast interpolation for Global Positioning System (GPS) satellite orbits
Clynch, James R.; Sagovac, Christopher Patrick; Danielson, D. A. (Donald A.); Neta, Beny
1995-01-01
In this report, we discuss and compare several methods for polynomial interpolation of Global Positioning Systems ephemeris data. We show that the use of difference tables is more efficient than the method currently in use to construct and evaluate the Lagrange polynomials.
Interpolation in computing science : the semantics of modularization
Renardel de Lavalette, Gerard R.
2008-01-01
The Interpolation Theorem, first formulated and proved by W. Craig fifty years ago for predicate logic, has been extended to many other logical frameworks and is being applied in several areas of computer science. We give a short overview, and focus on the theory of software systems and modules. An
Parallel optimization of IDW interpolation algorithm on multicore platform
Guan, Xuefeng; Wu, Huayi
2009-10-01
Due to increasing power consumption, heat dissipation, and other physical issues, the architecture of central processing unit (CPU) has been turning to multicore rapidly in recent years. Multicore processor is packaged with multiple processor cores in the same chip, which not only offers increased performance, but also presents significant challenges to application developers. As a matter of fact, in GIS field most of current GIS algorithms were implemented serially and could not best exploit the parallelism potential on such multicore platforms. In this paper, we choose Inverse Distance Weighted spatial interpolation algorithm (IDW) as an example to study how to optimize current serial GIS algorithms on multicore platform in order to maximize performance speedup. With the help of OpenMP, threading methodology is introduced to split and share the whole interpolation work among processor cores. After parallel optimization, execution time of interpolation algorithm is greatly reduced and good performance speedup is achieved. For example, performance speedup on Intel Xeon 5310 is 1.943 with 2 execution threads and 3.695 with 4 execution threads respectively. An additional output comparison between pre-optimization and post-optimization is carried out and shows that parallel optimization does to affect final interpolation result.
LIP: The Livermore Interpolation Package, Version 1.6
Energy Technology Data Exchange (ETDEWEB)
Fritsch, F. N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-01-04
This report describes LIP, the Livermore Interpolation Package. LIP was totally rewritten from the package described in [1]. In particular, the independent variables are now referred to as x and y, since it is a general-purpose package that need not be restricted to equation of state data, which uses variables ρ (density) and T (temperature).
Functional Commutant Lifting and Interpolation on Generalized Analytic Polyhedra
Czech Academy of Sciences Publication Activity Database
Ambrozie, Calin-Grigore
2008-01-01
Roč. 34, č. 2 (2008), s. 519-543 ISSN 0362-1588 R&D Projects: GA ČR(CZ) GA201/06/0128 Institutional research plan: CEZ:AV0Z10190503 Keywords : intertwining lifting * interpolation * analytic functions Subject RIV: BA - General Mathematics Impact factor: 0.327, year: 2008
Interpolation solution of the single-impurity Anderson model
International Nuclear Information System (INIS)
Kuzemsky, A.L.
1990-10-01
The dynamical properties of the single-impurity Anderson model (SIAM) is studied using a novel Irreducible Green's Function method (IGF). The new solution for one-particle GF interpolating between the strong and weak correlation limits is obtained. The unified concept of relevant mean-field renormalizations is indispensable for strong correlation limit. (author). 21 refs
Two-dimensional interpolation with experimental data smoothing
International Nuclear Information System (INIS)
Trejbal, Z.
1989-01-01
A method of two-dimensional interpolation with smoothing of time statistically deflected points is developed for processing of magnetic field measurements at the U-120M field measurements at the U-120M cyclotron. Mathematical statement of initial requirements and the final result of relevant algebraic transformations are given. 3 refs
Recent developments in free-viewpoint interpolation for 3DTV
Zinger, S.; Do, Q.L.; With, de P.H.N.
2012-01-01
Current development of 3D technologies brings 3DTV within reach for the customers. We discuss in this article the recent advancements in free-viewpoint interpolation for 3D video. This technology is still a research topic and many efforts are dedicated to creation, evaluation and improvement of new
Twitch interpolation technique in testing of maximal muscle strength
DEFF Research Database (Denmark)
Bülow, P M; Nørregaard, J; Danneskiold-Samsøe, B
1993-01-01
The aim was to study the methodological aspects of the muscle twitch interpolation technique in estimating the maximal force of contraction in the quadriceps muscle utilizing commercial muscle testing equipment. Six healthy subjects participated in seven sets of experiments testing the effects...
Limiting reiteration for real interpolation with slowly varying functions
Czech Academy of Sciences Publication Activity Database
Gogatishvili, Amiran; Opic, Bohumír; Trebels, W.
2005-01-01
Roč. 278, 1-2 (2005), s. 86-107 ISSN 0025-584X R&D Projects: GA ČR(CZ) GA201/01/0333 Institutional research plan: CEZ:AV0Z10190503 Keywords : real interpolation * K-functional * limiting reiteration Subject RIV: BA - General Mathematics Impact factor: 0.465, year: 2005
Approximating Exponential and Logarithmic Functions Using Polynomial Interpolation
Gordon, Sheldon P.; Yang, Yajun
2017-01-01
This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…
Blind Authentication Using Periodic Properties ofInterpolation
Czech Academy of Sciences Publication Activity Database
Mahdian, Babak; Saic, Stanislav
2008-01-01
Roč. 3, č. 3 (2008), s. 529-538 ISSN 1556-6013 R&D Projects: GA ČR GA102/08/0470 Institutional research plan: CEZ:AV0Z10750506 Keywords : image forensics * digital forgery * image tampering * interpolation detection * resampling detection Subject RIV: IN - Informatics, Computer Science Impact factor: 2.230, year: 2008
Interpolation Inequalities and Spectral Estimates for Magnetic Operators
Dolbeault, Jean; Esteban, Maria J.; Laptev, Ari; Loss, Michael
2018-05-01
We prove magnetic interpolation inequalities and Keller-Lieb-Thir-ring estimates for the principal eigenvalue of magnetic Schr{\\"o}dinger operators. We establish explicit upper and lower bounds for the best constants and show by numerical methods that our theoretical estimates are accurate.
Nonlinear secret image sharing scheme.
Shin, Sang-Ho; Lee, Gil-Je; Yoo, Kee-Young
2014-01-01
Over the past decade, most of secret image sharing schemes have been proposed by using Shamir's technique. It is based on a linear combination polynomial arithmetic. Although Shamir's technique based secret image sharing schemes are efficient and scalable for various environments, there exists a security threat such as Tompa-Woll attack. Renvall and Ding proposed a new secret sharing technique based on nonlinear combination polynomial arithmetic in order to solve this threat. It is hard to apply to the secret image sharing. In this paper, we propose a (t, n)-threshold nonlinear secret image sharing scheme with steganography concept. In order to achieve a suitable and secure secret image sharing scheme, we adapt a modified LSB embedding technique with XOR Boolean algebra operation, define a new variable m, and change a range of prime p in sharing procedure. In order to evaluate efficiency and security of proposed scheme, we use the embedding capacity and PSNR. As a result of it, average value of PSNR and embedding capacity are 44.78 (dB) and 1.74t⌈log2 m⌉ bit-per-pixel (bpp), respectively.
Energy Technology Data Exchange (ETDEWEB)
Castillo M, J A
1999-07-01
Nuclear Data Bank generation, is a process in which a great amount of resources is required, both computing and humans. If it is taken into account that at some times it is necessary to create a great amount of those, it is convenient to have a reliable tool that generates Data Banks with the lesser resources, in the least possible time and with a very good approximation. In this work are shown the results obtained during the development of INTPOLBI code, use to generate Nuclear Data Banks employing bicubic polynominal interpolation, taking as independent variables the uranium and gadolinia percents. Two proposal were worked, applying in both cases the finite element method, using one element with 16 nodes to carry out the interpolation. In the first proposals the canonic base was employed, to obtain the interpolating polynomial and later, the corresponding linear equation systems. In the solution of this systems the Gaussian elimination methods with partial pivot was applied. In the second case, the Newton base was used to obtain the mentioned system, resulting in a triangular inferior matrix, which structure, applying elemental operations, to obtain a blocks diagonal matrix, with special characteristics and easier to work with. For the validation tests, a comparison was made between the values obtained with INTPOLBI and INTERTEG (create at the Instituto de Investigaciones Electricas (MX) with the same purpose) codes, and Data Banks created through the conventional process, that is, with nuclear codes normally used. Finally, it is possible to conclude that the Nuclear Data Banks generated with INTPOLBI code constitute a very good approximation that, even though do not wholly replace conventional process, however are helpful in cases when it is necessary to create a great amount of Data Banks.
Comparison of the nuclear code systems LINEAR-RECENT-NJOY and NJOY
International Nuclear Information System (INIS)
Seehusen, J.
1983-07-01
The reconstructed cross sections of the code systems LINEAR-RECENT-GROUPIE (Version 1982) and NJOY (Version 1982) have been compared for several materials. Some fuel cycle isotopes and structural materials of the ENDF/B-4 general purpose and ENDF/B-5 dosimetry files have been choosen. The reconstructed total, capture and fission cross sections calculated by LINEAR-RECENT and NJOY have been analized. The two sets of pointwise cross sections differ significantly. Another disagreement was found in the transformation of ENDF/B-4 and 5 files into data with a linear interpolation scheme. Unshielded multigroup constants at O 0 K (620 groups, SANDII) have been calculated by the three code systems LINEAR-RECENT-GROUPIE, NJOY and RESEND5-INTEND. The code system RESEND5-INTEND calculates wrong group constants and should not be used any more. The two sets of group constants obtained from ENDF/B-4 data using GROUPIE and NJOY differ for some group constants by more than 2%. Some disagreements at low energies (10 -3 -eV) of the total cross section of Na-23 and Al-27 are difficult to understand. For ENDF/B-5 dosimetry data the capture group constants differ significantly. (Author) [pt
Shilov, Georgi E
1977-01-01
Covers determinants, linear spaces, systems of linear equations, linear functions of a vector argument, coordinate transformations, the canonical form of the matrix of a linear operator, bilinear and quadratic forms, Euclidean spaces, unitary spaces, quadratic forms in Euclidean and unitary spaces, finite-dimensional space. Problems with hints and answers.
High-Dimensional Intrinsic Interpolation Using Gaussian Process Regression and Diffusion Maps
International Nuclear Information System (INIS)
Thimmisetty, Charanraj A.; Ghanem, Roger G.; White, Joshua A.; Chen, Xiao
2017-01-01
This article considers the challenging task of estimating geologic properties of interest using a suite of proxy measurements. The current work recast this task as a manifold learning problem. In this process, this article introduces a novel regression procedure for intrinsic variables constrained onto a manifold embedded in an ambient space. The procedure is meant to sharpen high-dimensional interpolation by inferring non-linear correlations from the data being interpolated. The proposed approach augments manifold learning procedures with a Gaussian process regression. It first identifies, using diffusion maps, a low-dimensional manifold embedded in an ambient high-dimensional space associated with the data. It relies on the diffusion distance associated with this construction to define a distance function with which the data model is equipped. This distance metric function is then used to compute the correlation structure of a Gaussian process that describes the statistical dependence of quantities of interest in the high-dimensional ambient space. The proposed method is applicable to arbitrarily high-dimensional data sets. Here, it is applied to subsurface characterization using a suite of well log measurements. The predictions obtained in original, principal component, and diffusion space are compared using both qualitative and quantitative metrics. Considerable improvement in the prediction of the geological structural properties is observed with the proposed method.
Interpolation approach to Hamiltonian-varying quantum systems and the adiabatic theorem
International Nuclear Information System (INIS)
Pan, Yu; James, Matthew R.; Miao, Zibo; Amini, Nina H.; Ugrinovskii, Valery
2015-01-01
Quantum control could be implemented by varying the system Hamiltonian. According to adiabatic theorem, a slowly changing Hamiltonian can approximately keep the system at the ground state during the evolution if the initial state is a ground state. In this paper we consider this process as an interpolation between the initial and final Hamiltonians. We use the mean value of a single operator to measure the distance between the final state and the ideal ground state. This measure resembles the excitation energy or excess work performed in thermodynamics, which can be taken as the error of adiabatic approximation. We prove that under certain conditions, this error can be estimated for an arbitrarily given interpolating function. This error estimation could be used as guideline to induce adiabatic evolution. According to our calculation, the adiabatic approximation error is not linearly proportional to the average speed of the variation of the system Hamiltonian and the inverse of the energy gaps in many cases. In particular, we apply this analysis to an example in which the applicability of the adiabatic theorem is questionable. (orig.)
Directory of Open Access Journals (Sweden)
Kurt James Werner
2016-10-01
Full Text Available The magnitude of the Discrete Fourier Transform (DFT of a discrete-time signal has a limited frequency definition. Quadratic interpolation over the three DFT samples surrounding magnitude peaks improves the estimation of parameters (frequency and amplitude of resolved sinusoids beyond that limit. Interpolating on a rescaled magnitude spectrum using a logarithmic scale has been shown to improve those estimates. In this article, we show how to heuristically tune a power scaling parameter to outperform linear and logarithmic scaling at an equivalent computational cost. Although this power scaling factor is computed heuristically rather than analytically, it is shown to depend in a structured way on window parameters. Invariance properties of this family of estimators are studied and the existence of a bias due to noise is shown. Comparing to two state-of-the-art estimators, we show that an optimized power scaling has a lower systematic bias and lower mean-squared-error in noisy conditions for ten out of twelve common windowing functions.
F. Pan; M. Stieglitz; R.B. McKane
2012-01-01
Digital elevation model (DEM) data are essential to hydrological applications and have been widely used to calculate a variety of useful topographic characteristics, e.g., slope, flow direction, flow accumulation area, stream channel network, topographic index, and others. Except for slope, none of the other topographic characteristics can be calculated until the flow...
Building Input Adaptive Parallel Applications: A Case Study of Sparse Grid Interpolation
Murarasu, Alin; Weidendorfer, Josef
2012-01-01
bring a substantial contribution to the speedup. By identifying common patterns in the input data, we propose new algorithms for sparse grid interpolation that accelerate the state-of-the-art non-specialized version. Sparse grid interpolation
Coupled electrostatic-elastic analysis for topology optimization using material interpolation
International Nuclear Information System (INIS)
Alwan, A; Ananthasuresh, G K
2006-01-01
In this paper, we present a novel analytical formulation for the coupled partial differential equations governing electrostatically actuated constrained elastic structures of inhomogeneous material composition. We also present a computationally efficient numerical framework for solving the coupled equations over a reference domain with a fixed finiteelement mesh. This serves two purposes: (i) a series of problems with varying geometries and piece-wise homogeneous and/or inhomogeneous material distribution can be solved with a single pre-processing step (ii) topology optimization methods can be easily implemented by interpolating the material at each point in the reference domain from a void to a dielectric or a conductor. This is attained by considering the steady-state electrical current conduction equation with a 'leaky capacitor' model instead of the usual electrostatic equation. This formulation is amenable for both static and transient problems in the elastic domain coupled with the quasi-electrostatic electric field. The procedure is numerically implemented on the COMSOL Multiphysics (registered) platform using the weak variational form of the governing equations. Examples have been presented to show the accuracy and versatility of the scheme. The accuracy of the scheme is validated for the special case of piece-wise homogeneous material in the limit of the leaky-capacitor model approaching the ideal case
Effect of interpolation on parameters extracted from seating interface pressure arrays
Michael Wininger, PhD; Barbara Crane, PhD, PT
2015-01-01
Interpolation is a common data processing step in the study of interface pressure data collected at the wheelchair seating interface. However, there has been no focused study on the effect of interpolation on features extracted from these pressure maps, nor on whether these parameters are sensitive to the manner in which the interpolation is implemented. Here, two different interpolation paradigms, bilinear versus bicubic spline, are tested for their influence on parameters extracted from pre...
International Nuclear Information System (INIS)
Casa, L D C; Krueger, P S
2013-01-01
Unstructured three-dimensional fluid velocity data were interpolated using Gaussian radial basis function (RBF) interpolation. Data were generated to imitate the spatial resolution and experimental uncertainty of a typical implementation of defocusing digital particle image velocimetry. The velocity field associated with a steadily rotating infinite plate was simulated to provide a bounded, fully three-dimensional analytical solution of the Navier–Stokes equations, allowing for robust analysis of the interpolation accuracy. The spatial resolution of the data (i.e. particle density) and the number of RBFs were varied in order to assess the requirements for accurate interpolation. Interpolation constraints, including boundary conditions and continuity, were included in the error metric used for the least-squares minimization that determines the interpolation parameters to explore methods for improving RBF interpolation results. Even spacing and logarithmic spacing of RBF locations were also investigated. Interpolation accuracy was assessed using the velocity field, divergence of the velocity field, and viscous torque on the rotating boundary. The results suggest that for the present implementation, RBF spacing of 0.28 times the boundary layer thickness is sufficient for accurate interpolation, though theoretical error analysis suggests that improved RBF positioning may yield more accurate results. All RBF interpolation results were compared to standard Gaussian weighting and Taylor expansion interpolation methods. Results showed that RBF interpolation improves interpolation results compared to the Taylor expansion method by 60% to 90% based on the average squared velocity error and provides comparable velocity results to Gaussian weighted interpolation in terms of velocity error. RMS accuracy of the flow field divergence was one to two orders of magnitude better for the RBF interpolation compared to the other two methods. RBF interpolation that was applied to
Analysis of Program Obfuscation Schemes with Variable Encoding Technique
Fukushima, Kazuhide; Kiyomoto, Shinsaku; Tanaka, Toshiaki; Sakurai, Kouichi
Program analysis techniques have improved steadily over the past several decades, and software obfuscation schemes have come to be used in many commercial programs. A software obfuscation scheme transforms an original program or a binary file into an obfuscated program that is more complicated and difficult to analyze, while preserving its functionality. However, the security of obfuscation schemes has not been properly evaluated. In this paper, we analyze obfuscation schemes in order to clarify the advantages of our scheme, the XOR-encoding scheme. First, we more clearly define five types of attack models that we defined previously, and define quantitative resistance to these attacks. Then, we compare the security, functionality and efficiency of three obfuscation schemes with encoding variables: (1) Sato et al.'s scheme with linear transformation, (2) our previous scheme with affine transformation, and (3) the XOR-encoding scheme. We show that the XOR-encoding scheme is superior with regard to the following two points: (1) the XOR-encoding scheme is more secure against a data-dependency attack and a brute force attack than our previous scheme, and is as secure against an information-collecting attack and an inverse transformation attack as our previous scheme, (2) the XOR-encoding scheme does not restrict the calculable ranges of programs and the loss of efficiency is less than in our previous scheme.
On the linear programming bound for linear Lee codes.
Astola, Helena; Tabus, Ioan
2016-01-01
Based on an invariance-type property of the Lee-compositions of a linear Lee code, additional equality constraints can be introduced to the linear programming problem of linear Lee codes. In this paper, we formulate this property in terms of an action of the multiplicative group of the field [Formula: see text] on the set of Lee-compositions. We show some useful properties of certain sums of Lee-numbers, which are the eigenvalues of the Lee association scheme, appearing in the linear programming problem of linear Lee codes. Using the additional equality constraints, we formulate the linear programming problem of linear Lee codes in a very compact form, leading to a fast execution, which allows to efficiently compute the bounds for large parameter values of the linear codes.
Single image interpolation via adaptive nonlocal sparsity-based modeling.
Romano, Yaniv; Protter, Matan; Elad, Michael
2014-07-01
Single image interpolation is a central and extensively studied problem in image processing. A common approach toward the treatment of this problem in recent years is to divide the given image into overlapping patches and process each of them based on a model for natural image patches. Adaptive sparse representation modeling is one such promising image prior, which has been shown to be powerful in filling-in missing pixels in an image. Another force that such algorithms may use is the self-similarity that exists within natural images. Processing groups of related patches together exploits their correspondence, leading often times to improved results. In this paper, we propose a novel image interpolation method, which combines these two forces-nonlocal self-similarities and sparse representation modeling. The proposed method is contrasted with competitive and related algorithms, and demonstrated to achieve state-of-the-art results.
Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery.
Ratliff, Bradley M; LaCasse, Charles F; Tyo, J Scott
2009-05-25
Microgrid polarimeters are composed of an array of micro-polarizing elements overlaid upon an FPA sensor. In the past decade systems have been designed and built in all regions of the optical spectrum. These systems have rugged, compact designs and the ability to obtain a complete set of polarimetric measurements during a single image capture. However, these systems acquire the polarization measurements through spatial modulation and each measurement has a varying instantaneous field-of-view (IFOV). When these measurements are combined to estimate the polarization images, strong edge artifacts are present that severely degrade the estimated polarization imagery. These artifacts can be reduced when interpolation strategies are first applied to the intensity data prior to Stokes vector estimation. Here we formally study IFOV error and the performance of several bilinear interpolation strategies used for reducing it.
Bi-local baryon interpolating fields with two flavors
Energy Technology Data Exchange (ETDEWEB)
Dmitrasinovic, V. [Belgrade University, Institute of Physics, Pregrevica 118, Zemun, P.O. Box 57, Beograd (RS); Chen, Hua-Xing [Institutos de Investigacion de Paterna, Departamento de Fisica Teorica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Valencia (Spain); Peking University, Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Beijing (China)
2011-02-15
We construct bi-local interpolating field operators for baryons consisting of three quarks with two flavors, assuming good isospin symmetry. We use the restrictions following from the Pauli principle to derive relations/identities among the baryon operators with identical quantum numbers. Such relations that follow from the combined spatial, Dirac, color, and isospin Fierz transformations may be called the (total/complete) Fierz identities. These relations reduce the number of independent baryon operators with any given spin and isospin. We also study the Abelian and non-Abelian chiral transformation properties of these fields and place them into baryon chiral multiplets. Thus we derive the independent baryon interpolating fields with given values of spin (Lorentz group representation), chiral symmetry (U{sub L}(2) x U{sub R}(2) group representation) and isospin appropriate for the first angular excited states of the nucleon. (orig.)
Kriging for interpolation of sparse and irregularly distributed geologic data
Energy Technology Data Exchange (ETDEWEB)
Campbell, K.
1986-12-31
For many geologic problems, subsurface observations are available only from a small number of irregularly distributed locations, for example from a handful of drill holes in the region of interest. These observations will be interpolated one way or another, for example by hand-drawn stratigraphic cross-sections, by trend-fitting techniques, or by simple averaging which ignores spatial correlation. In this paper we consider an interpolation technique for such situations which provides, in addition to point estimates, the error estimates which are lacking from other ad hoc methods. The proposed estimator is like a kriging estimator in form, but because direct estimation of the spatial covariance function is not possible the parameters of the estimator are selected by cross-validation. Its use in estimating subsurface stratigraphy at a candidate site for geologic waste repository provides an example.
A scheme for the hadron spectrum
International Nuclear Information System (INIS)
Hoyer, P.
1978-03-01
A theoretically self-consistent dual scheme is proposed for the hadron spectrum, which follows naturally from basic requirements and phenomenology. All resonance properties and couplings are calculable in terms of a limited number of input parameters. A first application to ππ→ππ explains the linear trajectory and small daughter couplings. The Zweig rule and the decoupling of baryonium from mesons are expected to be consequences of the scheme. (Auth.)
An Optimization Scheme for ProdMod
International Nuclear Information System (INIS)
Gregory, M.V.
1999-01-01
A general purpose dynamic optimization scheme has been devised in conjunction with the ProdMod simulator. The optimization scheme is suitable for the Savannah River Site (SRS) High Level Waste (HLW) complex operations, and able to handle different types of optimizations such as linear, nonlinear, etc. The optimization is performed in the stand-alone FORTRAN based optimization deliver, while the optimizer is interfaced with the ProdMod simulator for flow of information between the two
Sman, van der R.G.M.
2006-01-01
In the special case of relaxation parameter = 1 lattice Boltzmann schemes for (convection) diffusion and fluid flow are equivalent to finite difference/volume (FD) schemes, and are thus coined finite Boltzmann (FB) schemes. We show that the equivalence is inherent to the homology of the
The interpolation method of stochastic functions and the stochastic variational principle
International Nuclear Information System (INIS)
Liu Xianbin; Chen Qiu
1993-01-01
Uncertainties have been attaching more importance to increasingly in modern engineering structural design. Viewed on an appropriate scale, the inherent physical attributes (material properties) of many structural systems always exhibit some patterns of random variation in space and time, generally the random variation shows a small parameter fluctuation. For a linear mechanical system, the random variation is modeled as a random one of a linear partial differential operator and, in stochastic finite element method, a random variation of a stiffness matrix. Besides the stochasticity of the structural physical properties, the influences of random loads which always represent themselves as the random boundary conditions bring about much more complexities in structural analysis. Now the stochastic finite element method or the probabilistic finite element method is used to study the structural systems with random physical parameters, whether or not the loads are random. Differing from the general finite element theory, the main difficulty which the stochastic finite element method faces is the inverse operation of stochastic operators and stochastic matrices, since the inverse operators and the inverse matrices are statistically correlated to the random parameters and random loads. So far, many efforts have been made to obtain the reasonably approximate expressions of the inverse operators and inverse matrices, such as Perturbation Method, Neumann Expansion Method, Galerkin Method (in appropriate Hilbert Spaces defined for random functions), Orthogonal Expansion Method. Among these methods, Perturbation Method appear to be the most available. The advantage of these methods is that the fairly accurate response statistics can be obtained under the condition of the finite information of the input. However, the second-order statistics obtained by use of Perturbation Method and Neumann Expansion Method are not always the appropriate ones, because the relevant second
The modal surface interpolation method for damage localization
Pina Limongelli, Maria
2017-05-01
The Interpolation Method (IM) has been previously proposed and successfully applied for damage localization in plate like structures. The method is based on the detection of localized reductions of smoothness in the Operational Deformed Shapes (ODSs) of the structure. The IM can be applied to any type of structure provided the ODSs are estimated accurately in the original and in the damaged configurations. If the latter circumstance fails to occur, for example when the structure is subjected to an unknown input(s) or if the structural responses are strongly corrupted by noise, both false and missing alarms occur when the IM is applied to localize a concentrated damage. In order to overcome these drawbacks a modification of the method is herein investigated. An ODS is the deformed shape of a structure subjected to a harmonic excitation: at resonances the ODS are dominated by the relevant mode shapes. The effect of noise at resonance is usually lower with respect to other frequency values hence the relevant ODS are estimated with higher reliability. Several methods have been proposed to reliably estimate modal shapes in case of unknown input. These two circumstances can be exploited to improve the reliability of the IM. In order to reduce or eliminate the drawbacks related to the estimation of the ODSs in case of noisy signals, in this paper is investigated a modified version of the method based on a damage feature calculated considering the interpolation error relevant only to the modal shapes and not to all the operational shapes in the significant frequency range. Herein will be reported the comparison between the results of the IM in its actual version (with the interpolation error calculated summing up the contributions of all the operational shapes) and in the new proposed version (with the estimation of the interpolation error limited to the modal shapes).
Direct Trajectory Interpolation on the Surface using an Open CNC
Beudaert , Xavier; Lavernhe , Sylvain; Tournier , Christophe
2014-01-01
International audience; Free-form surfaces are used for many industrial applications from aeronautical parts, to molds or biomedical implants. In the common machining process, computer-aided manufacturing (CAM) software generates approximated tool paths because of the limitation induced by the input tool path format of the industrial CNC. Then, during the tool path interpolation, marks on finished surfaces can appear induced by non smooth feedrate planning. Managing the geometry of the tool p...
Strip interpolation in silicon and germanium strip detectors
International Nuclear Information System (INIS)
Wulf, E. A.; Phlips, B. F.; Johnson, W. N.; Kurfess, J. D.; Lister, C. J.; Kondev, F.; Physics; Naval Research Lab.
2004-01-01
The position resolution of double-sided strip detectors is limited by the strip pitch and a reduction in strip pitch necessitates more electronics. Improved position resolution would improve the imaging capabilities of Compton telescopes and PET detectors. Digitizing the preamplifier waveform yields more information than can be extracted with regular shaping electronics. In addition to the energy, depth of interaction, and which strip was hit, the digitized preamplifier signals can locate the interaction position to less than the strip pitch of the detector by looking at induced signals in neighboring strips. This allows the position of the interaction to be interpolated in three dimensions and improve the imaging capabilities of the system. In a 2 mm thick silicon strip detector with a strip pitch of 0.891 mm, strip interpolation located the interaction of 356 keV gamma rays to 0.3 mm FWHM. In a 2 cm thick germanium detector with a strip pitch of 5 mm, strip interpolation of 356 keV gamma rays yielded a position resolution of 1.5 mm FWHM
Importance of interpolation and coincidence errors in data fusion
Directory of Open Access Journals (Sweden)
S. Ceccherini
2018-02-01
Full Text Available The complete data fusion (CDF method is applied to ozone profiles obtained from simulated measurements in the ultraviolet and in the thermal infrared in the framework of the Sentinel 4 mission of the Copernicus programme. We observe that the quality of the fused products is degraded when the fusing profiles are either retrieved on different vertical grids or referred to different true profiles. To address this shortcoming, a generalization of the complete data fusion method, which takes into account interpolation and coincidence errors, is presented. This upgrade overcomes the encountered problems and provides products of good quality when the fusing profiles are both retrieved on different vertical grids and referred to different true profiles. The impact of the interpolation and coincidence errors on number of degrees of freedom and errors of the fused profile is also analysed. The approach developed here to account for the interpolation and coincidence errors can also be followed to include other error components, such as forward model errors.
Interpolation of daily rainfall using spatiotemporal models and clustering
Militino, A. F.
2014-06-11
Accumulated daily rainfall in non-observed locations on a particular day is frequently required as input to decision-making tools in precision agriculture or for hydrological or meteorological studies. Various solutions and estimation procedures have been proposed in the literature depending on the auxiliary information and the availability of data, but most such solutions are oriented to interpolating spatial data without incorporating temporal dependence. When data are available in space and time, spatiotemporal models usually provide better solutions. Here, we analyse the performance of three spatiotemporal models fitted to the whole sampled set and to clusters within the sampled set. The data consists of daily observations collected from 87 manual rainfall gauges from 1990 to 2010 in Navarre, Spain. The accuracy and precision of the interpolated data are compared with real data from 33 automated rainfall gauges in the same region, but placed in different locations than the manual rainfall gauges. Root mean squared error by months and by year are also provided. To illustrate these models, we also map interpolated daily precipitations and standard errors on a 1km2 grid in the whole region. © 2014 Royal Meteorological Society.
Interpolation of daily rainfall using spatiotemporal models and clustering
Militino, A. F.; Ugarte, M. D.; Goicoa, T.; Genton, Marc G.
2014-01-01
Accumulated daily rainfall in non-observed locations on a particular day is frequently required as input to decision-making tools in precision agriculture or for hydrological or meteorological studies. Various solutions and estimation procedures have been proposed in the literature depending on the auxiliary information and the availability of data, but most such solutions are oriented to interpolating spatial data without incorporating temporal dependence. When data are available in space and time, spatiotemporal models usually provide better solutions. Here, we analyse the performance of three spatiotemporal models fitted to the whole sampled set and to clusters within the sampled set. The data consists of daily observations collected from 87 manual rainfall gauges from 1990 to 2010 in Navarre, Spain. The accuracy and precision of the interpolated data are compared with real data from 33 automated rainfall gauges in the same region, but placed in different locations than the manual rainfall gauges. Root mean squared error by months and by year are also provided. To illustrate these models, we also map interpolated daily precipitations and standard errors on a 1km2 grid in the whole region. © 2014 Royal Meteorological Society.
Global sensitivity analysis using sparse grid interpolation and polynomial chaos
International Nuclear Information System (INIS)
Buzzard, Gregery T.
2012-01-01
Sparse grid interpolation is widely used to provide good approximations to smooth functions in high dimensions based on relatively few function evaluations. By using an efficient conversion from the interpolating polynomial provided by evaluations on a sparse grid to a representation in terms of orthogonal polynomials (gPC representation), we show how to use these relatively few function evaluations to estimate several types of sensitivity coefficients and to provide estimates on local minima and maxima. First, we provide a good estimate of the variance-based sensitivity coefficients of Sobol' (1990) [1] and then use the gradient of the gPC representation to give good approximations to the derivative-based sensitivity coefficients described by Kucherenko and Sobol' (2009) [2]. Finally, we use the package HOM4PS-2.0 given in Lee et al. (2008) [3] to determine the critical points of the interpolating polynomial and use these to determine the local minima and maxima of this polynomial. - Highlights: ► Efficient estimation of variance-based sensitivity coefficients. ► Efficient estimation of derivative-based sensitivity coefficients. ► Use of homotopy methods for approximation of local maxima and minima.
Adaptive Residual Interpolation for Color and Multispectral Image Demosaicking.
Monno, Yusuke; Kiku, Daisuke; Tanaka, Masayuki; Okutomi, Masatoshi
2017-12-01
Color image demosaicking for the Bayer color filter array is an essential image processing operation for acquiring high-quality color images. Recently, residual interpolation (RI)-based algorithms have demonstrated superior demosaicking performance over conventional color difference interpolation-based algorithms. In this paper, we propose adaptive residual interpolation (ARI) that improves existing RI-based algorithms by adaptively combining two RI-based algorithms and selecting a suitable iteration number at each pixel. These are performed based on a unified criterion that evaluates the validity of an RI-based algorithm. Experimental comparisons using standard color image datasets demonstrate that ARI can improve existing RI-based algorithms by more than 0.6 dB in the color peak signal-to-noise ratio and can outperform state-of-the-art algorithms based on training images. We further extend ARI for a multispectral filter array, in which more than three spectral bands are arrayed, and demonstrate that ARI can achieve state-of-the-art performance also for the task of multispectral image demosaicking.
On removing interpolation and resampling artifacts in rigid image registration.
Aganj, Iman; Yeo, Boon Thye Thomas; Sabuncu, Mert R; Fischl, Bruce
2013-02-01
We show that image registration using conventional interpolation and summation approximations of continuous integrals can generally fail because of resampling artifacts. These artifacts negatively affect the accuracy of registration by producing local optima, altering the gradient, shifting the global optimum, and making rigid registration asymmetric. In this paper, after an extensive literature review, we demonstrate the causes of the artifacts by comparing inclusion and avoidance of resampling analytically. We show the sum-of-squared-differences cost function formulated as an integral to be more accurate compared with its traditional sum form in a simple case of image registration. We then discuss aliasing that occurs in rotation, which is due to the fact that an image represented in the Cartesian grid is sampled with different rates in different directions, and propose the use of oscillatory isotropic interpolation kernels, which allow better recovery of true global optima by overcoming this type of aliasing. Through our experiments on brain, fingerprint, and white noise images, we illustrate the superior performance of the integral registration cost function in both the Cartesian and spherical coordinates, and also validate the introduced radial interpolation kernel by demonstrating the improvement in registration.
Directory of Open Access Journals (Sweden)
José Machado
2016-04-01
the MDT interpolation of measured points is required. The use of TDM, 3D surfaces and contours in moving fast computer programs and can create some problems, such as the type of interpolation used. This work aims to analyze the interpolation methods in points quoted from an irregular geometric figure generated by the Surfer program. They used 12 interpolations available (Data Metrics, Inverse Distance, Kriging, Local Polynomial, Minimum Curvature, Modified Shepard Method, Moving Average, Natural Neighbor, Nearest Neighbor, Polynomial Regression, Radial fuction and Triangulation with Linear Interpolation and analyzed the generated topographic maps. The relief was generated graphical representation via the MDT. They were awarded the excellent concepts, excellent, good, average and bad representation of relief and discussed according Relief representations to the listed geometric image. Data Metrics, Polynomial Regression, Moving Average e Local Polynomial (bad; Moving Average e Modified Shepard Method (regular; Nearest Neighbor (media; Inverse Distance (good; Kriging e Radial Function (great e Triangulation With Linear Interpolation e Natural Neighbor (excellent conditions to representation presented dates.
Similarities and Differences Between Warped Linear Prediction and Laguerre Linear Prediction
Brinker, Albertus C. den; Krishnamoorthi, Harish; Verbitskiy, Evgeny A.
2011-01-01
Linear prediction has been successfully applied in many speech and audio processing systems. This paper presents the similarities and differences between two classes of linear prediction schemes, namely, Warped Linear Prediction (WLP) and Laguerre Linear Prediction (LLP). It is shown that both
Directory of Open Access Journals (Sweden)
S.M. Green
2017-03-01
Full Text Available Flux-chamber measurements of greenhouse gas exchanges between the soil and the atmosphere represent a snapshot of the conditions on a particular site and need to be combined or used in some way to provide integrated fluxes for the longer time periods that are often of interest. In contrast to carbon dioxide (CO2, most studies that have estimated the time-integrated flux of CH4 on ombrotrophic peatlands have not used models. Typically, linear interpolation is used to estimate CH4 fluxes during the time periods between flux-chamber measurements. CH4 fluxes generally show a rise followed by a fall through the growing season that may be captured reasonably well by interpolation, provided there are sufficiently frequent measurements. However, day-to-day and week-to-week variability is also often evident in CH4 flux data, and will not necessarily be properly represented by interpolation. Using flux chamber data from a UK blanket peatland, we compared annualised CH4 fluxes estimated by interpolation with those estimated using linear models and found that the former tended to be higher than the latter. We consider the implications of these results for the calculation of the radiative forcing effect of ombrotrophic peatlands.
Impact of the updating scheme on stationary states of networks
International Nuclear Information System (INIS)
Radicchi, F; Ahn, Y Y; Meyer-Ortmanns, H
2008-01-01
From Boolean networks it is well known that the number of attractors as a function of the system size depends on the updating scheme which is chosen either synchronously or asynchronously. In this contribution, we report on a systematic interpolation between synchronous and asynchronous updating in a one-dimensional chain of Ising spins. The stationary state for fully synchronous updating is antiferromagnetic. The interpolation allows us to locate a phase transition between phases with an absorbing and a fluctuating stationary state. The associated universality class is that of parity conservation. We also report on a more recent study of asynchronous updates applied to the yeast cell-cycle network. Compared to the synchronous update, the basin of attraction of the largest attractor considerably shrinks and the convergence to the biological pathway slows down and is less dominant. Both examples illustrate how sensitively the stationary states and the properties of attractors can depend on the updating mode of the algorithm
Study on the algorithm for Newton-Rapson iteration interpolation of NURBS curve and simulation
Zhang, Wanjun; Gao, Shanping; Cheng, Xiyan; Zhang, Feng
2017-04-01
In order to solve the problems of Newton-Rapson iteration interpolation method of NURBS Curve, Such as interpolation time bigger, calculation more complicated, and NURBS curve step error are not easy changed and so on. This paper proposed a study on the algorithm for Newton-Rapson iteration interpolation method of NURBS curve and simulation. We can use Newton-Rapson iterative that calculate (xi, yi, zi). Simulation results show that the proposed NURBS curve interpolator meet the high-speed and high-accuracy interpolation requirements of CNC systems. The interpolation of NURBS curve should be finished. The simulation results show that the algorithm is correct; it is consistent with a NURBS curve interpolation requirements.
Prediction of selected Indian stock using a partitioning–interpolation based ARIMA–GARCH model
Directory of Open Access Journals (Sweden)
C. Narendra Babu
2015-07-01
Full Text Available Accurate long-term prediction of time series data (TSD is a very useful research challenge in diversified fields. As financial TSD are highly volatile, multi-step prediction of financial TSD is a major research problem in TSD mining. The two challenges encountered are, maintaining high prediction accuracy and preserving the data trend across the forecast horizon. The linear traditional models such as autoregressive integrated moving average (ARIMA and generalized autoregressive conditional heteroscedastic (GARCH preserve data trend to some extent, at the cost of prediction accuracy. Non-linear models like ANN maintain prediction accuracy by sacrificing data trend. In this paper, a linear hybrid model, which maintains prediction accuracy while preserving data trend, is proposed. A quantitative reasoning analysis justifying the accuracy of proposed model is also presented. A moving-average (MA filter based pre-processing, partitioning and interpolation (PI technique are incorporated by the proposed model. Some existing models and the proposed model are applied on selected NSE India stock market data. Performance results show that for multi-step ahead prediction, the proposed model outperforms the others in terms of both prediction accuracy and preserving data trend.
Systems of Inhomogeneous Linear Equations
Scherer, Philipp O. J.
Many problems in physics and especially computational physics involve systems of linear equations which arise e.g. from linearization of a general nonlinear problem or from discretization of differential equations. If the dimension of the system is not too large standard methods like Gaussian elimination or QR decomposition are sufficient. Systems with a tridiagonal matrix are important for cubic spline interpolation and numerical second derivatives. They can be solved very efficiently with a specialized Gaussian elimination method. Practical applications often involve very large dimensions and require iterative methods. Convergence of Jacobi and Gauss-Seidel methods is slow and can be improved by relaxation or over-relaxation. An alternative for large systems is the method of conjugate gradients.
Directory of Open Access Journals (Sweden)
Makram J. Geha
2011-01-01
Full Text Available Milk yield records (305d, 2X, actual milk yield of 123,639 registered first lactation Holstein cows were used to compare linear regression (y = β0 + β1X + e ,quadratic regression, (y = β0 + β1X + β2X2 + e cubic regression (y = β0 + β1X + β2X2 + β3X3 + e and fixed factor models, with cubic-spline interpolation models, for estimating the effects of inbreeding on milk yield. Ten animal models, all with herd-year-season of calving as fixed effect, were compared using the Akaike corrected-Information Criterion (AICc. The cubic-spline interpolation model with seven knots had the lowest AICc, whereas for all those labeled as "traditional", AICc was higher than the best model. Results from fitting inbreeding using a cubic-spline with seven knots were compared to results from fitting inbreeding as a linear covariate or as a fixed factor with seven levels. Estimates of inbreeding effects were not significantly different between the cubic-spline model and the fixed factor model, but were significantly different from the linear regression model. Milk yield decreased significantly at inbreeding levels greater than 9%. Variance component estimates were similar for the three models. Ranking of the top 100 sires with daughter records remained unaffected by the model used.
International Nuclear Information System (INIS)
Suwono.
1978-01-01
A linear gate providing a variable gate duration from 0,40μsec to 4μsec was developed. The electronic circuity consists of a linear circuit and an enable circuit. The input signal can be either unipolar or bipolar. If the input signal is bipolar, the negative portion will be filtered. The operation of the linear gate is controlled by the application of a positive enable pulse. (author)
International Nuclear Information System (INIS)
Vretenar, M
2014-01-01
The main features of radio-frequency linear accelerators are introduced, reviewing the different types of accelerating structures and presenting the main characteristics aspects of linac beam dynamics
Scheme Program Documentation Tools
DEFF Research Database (Denmark)
Nørmark, Kurt
2004-01-01
are separate and intended for different documentation purposes they are related to each other in several ways. Both tools are based on XML languages for tool setup and for documentation authoring. In addition, both tools rely on the LAML framework which---in a systematic way---makes an XML language available...... as named functions in Scheme. Finally, the Scheme Elucidator is able to integrate SchemeDoc resources as part of an internal documentation resource....
Linearization Method and Linear Complexity
Tanaka, Hidema
We focus on the relationship between the linearization method and linear complexity and show that the linearization method is another effective technique for calculating linear complexity. We analyze its effectiveness by comparing with the logic circuit method. We compare the relevant conditions and necessary computational cost with those of the Berlekamp-Massey algorithm and the Games-Chan algorithm. The significant property of a linearization method is that it needs no output sequence from a pseudo-random number generator (PRNG) because it calculates linear complexity using the algebraic expression of its algorithm. When a PRNG has n [bit] stages (registers or internal states), the necessary computational cost is smaller than O(2n). On the other hand, the Berlekamp-Massey algorithm needs O(N2) where N(≅2n) denotes period. Since existing methods calculate using the output sequence, an initial value of PRNG influences a resultant value of linear complexity. Therefore, a linear complexity is generally given as an estimate value. On the other hand, a linearization method calculates from an algorithm of PRNG, it can determine the lower bound of linear complexity.
Optimal interpolation method for intercomparison of atmospheric measurements.
Ridolfi, Marco; Ceccherini, Simone; Carli, Bruno
2006-04-01
Intercomparison of atmospheric measurements is often a difficult task because of the different spatial response functions of the experiments considered. We propose a new method for comparison of two atmospheric profiles characterized by averaging kernels with different vertical resolutions. The method minimizes the smoothing error induced by the differences in the averaging kernels by exploiting an optimal interpolation rule to map one profile into the retrieval grid of the other. Compared with the techniques published so far, this method permits one to retain the vertical resolution of the less-resolved profile involved in the intercomparison.
Advantage of Fast Fourier Interpolation for laser modeling
International Nuclear Information System (INIS)
Epatko, I.V.; Serov, R.V.
2006-01-01
The abilities of a new algorithm: the 2-dimensional Fast Fourier Interpolation (FFI) with magnification factor (zoom) 2 n whose purpose is to improve the spatial resolution when necessary, are analyzed in details. FFI procedure is useful when diaphragm/aperture size is less than half of the current simulation scale. The computation noise due to FFI procedure is less than 10 -6 . The additional time for FFI is approximately equal to one Fast Fourier Transform execution time. For some applications using FFI procedure, the execution time decreases by a 10 4 factor compared with other laser simulation codes. (authors)
Rate of convergence of Bernstein quasi-interpolants
International Nuclear Information System (INIS)
Diallo, A.T.
1995-09-01
We show that if f is an element of C[0,1] and B (2r-1) n f (r integer ≥ 1) is the Bernstein Quasi-Interpolant defined by Sablonniere, then parallel B (2r-1) n f - f parallel C[0,1] ≤ ω 2r φ (f, 1/√n) where ω 2r φ is the Ditzian-Totik modulus of smoothness with φ(x) = √ x(1-x), x is an element of [0,1]. (author). 6 refs
Data mining techniques in sensor networks summarization, interpolation and surveillance
Appice, Annalisa; Fumarola, Fabio; Malerba, Donato
2013-01-01
Sensor networks comprise of a number of sensors installed across a spatially distributed network, which gather information and periodically feed a central server with the measured data. The server monitors the data, issues possible alarms and computes fast aggregates. As data analysis requests may concern both present and past data, the server is forced to store the entire stream. But the limited storage capacity of a server may reduce the amount of data stored on the disk. One solution is to compute summaries of the data as it arrives, and to use these summaries to interpolate the real data.
Hörmander spaces, interpolation, and elliptic problems
Mikhailets, Vladimir A; Malyshev, Peter V
2014-01-01
The monograph gives a detailed exposition of the theory of general elliptic operators (scalar and matrix) and elliptic boundary value problems in Hilbert scales of Hörmander function spaces. This theory was constructed by the authors in a number of papers published in 2005-2009. It is distinguished by a systematic use of the method of interpolation with a functional parameter of abstract Hilbert spaces and Sobolev inner product spaces. This method, the theory and their applications are expounded for the first time in the monographic literature. The monograph is written in detail and in a
Acceleration of Meshfree Radial Point Interpolation Method on Graphics Hardware
International Nuclear Information System (INIS)
Nakata, Susumu
2008-01-01
This article describes a parallel computational technique to accelerate radial point interpolation method (RPIM)-based meshfree method using graphics hardware. RPIM is one of the meshfree partial differential equation solvers that do not require the mesh structure of the analysis targets. In this paper, a technique for accelerating RPIM using graphics hardware is presented. In the method, the computation process is divided into small processes suitable for processing on the parallel architecture of the graphics hardware in a single instruction multiple data manner.
Calibration method of microgrid polarimeters with image interpolation.
Chen, Zhenyue; Wang, Xia; Liang, Rongguang
2015-02-10
Microgrid polarimeters have large advantages over conventional polarimeters because of the snapshot nature and because they have no moving parts. However, they also suffer from several error sources, such as fixed pattern noise (FPN), photon response nonuniformity (PRNU), pixel cross talk, and instantaneous field-of-view (IFOV) error. A characterization method is proposed to improve the measurement accuracy in visible waveband. We first calibrate the camera with uniform illumination so that the response of the sensor is uniform over the entire field of view without IFOV error. Then a spline interpolation method is implemented to minimize IFOV error. Experimental results show the proposed method can effectively minimize the FPN and PRNU.
New extended interpolating operators for hadron correlation functions
Energy Technology Data Exchange (ETDEWEB)
Scardino, Francesco; Papinutto, Mauro [Roma ' ' Sapienza' ' Univ. (Italy). Dipt. di Fisica; INFN, Sezione di Roma (Italy); Schaefer, Stefan [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2016-12-22
New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators with the states of interest. The extended operators have good renormalisation properties and are easy to control when taking the continuum limit. Moreover the short distance behaviour of the two point functions built from these operators is greatly improved. The operators have been numerically implemented and a comparison to point sources and Jacobi smeared sources has been performed on the new CLS configurations.
New extended interpolating operators for hadron correlation functions
International Nuclear Information System (INIS)
Scardino, Francesco; Papinutto, Mauro; Schaefer, Stefan
2016-01-01
New extended interpolating operators made of quenched three dimensional fermions are introduced in the context of lattice QCD. The mass of the 3D fermions can be tuned in a controlled way to find a better overlap of the extended operators with the states of interest. The extended operators have good renormalisation properties and are easy to control when taking the continuum limit. Moreover the short distance behaviour of the two point functions built from these operators is greatly improved. The operators have been numerically implemented and a comparison to point sources and Jacobi smeared sources has been performed on the new CLS configurations.
Interpolation Error Estimates for Mean Value Coordinates over Convex Polygons.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2013-08-01
In a similar fashion to estimates shown for Harmonic, Wachspress, and Sibson coordinates in [Gillette et al., AiCM, to appear], we prove interpolation error estimates for the mean value coordinates on convex polygons suitable for standard finite element analysis. Our analysis is based on providing a uniform bound on the gradient of the mean value functions for all convex polygons of diameter one satisfying certain simple geometric restrictions. This work makes rigorous an observed practical advantage of the mean value coordinates: unlike Wachspress coordinates, the gradient of the mean value coordinates does not become large as interior angles of the polygon approach π.
Geometries and interpolations for symmetric positive definite matrices
DEFF Research Database (Denmark)
Feragen, Aasa; Fuster, Andrea
2017-01-01
. In light of the simulation results, we discuss the mathematical and qualitative properties of these new metrics in comparison with the classical ones. Finally, we explore the nonlinear variation of properties such as shape and scale throughout principal geodesics in different metrics, which affects...... the visualization of scale and shape variation in tensorial data. With the paper, we will release a software package with Matlab scripts for computing the interpolations and statistics used for the experiments in the paper (Code is available at https://sites.google.com/site/aasaferagen/home/software)....
Trends in Continuity and Interpolation for Computer Graphics.
Gonzalez Garcia, Francisco
2015-01-01
In every computer graphics oriented application today, it is a common practice to texture 3D models as a way to obtain realistic material. As part of this process, mesh texturing, deformation, and visualization are all key parts of the computer graphics field. This PhD dissertation was completed in the context of these three important and related fields in computer graphics. The article presents techniques that improve on existing state-of-the-art approaches related to continuity and interpolation in texture space (texturing), object space (deformation), and screen space (rendering).
International Nuclear Information System (INIS)
Cai, Ailong; Wang, Linyuan; Yan, Bin; Zhang, Hanming; Li, Lei; Xi, Xiaoqi; Li, Jianxin
2015-01-01
In this study, we consider a novel form of computed tomography (CT), that is, linear scan CT (LCT), which applies a straight line trajectory. Furthermore, an iterative algorithm is proposed for pseudo-polar Fourier reconstruction through total variation minimization (PPF-TVM). Considering that the sampled Fourier data are distributed in pseudo-polar coordinates, the reconstruction model minimizes the TV of the image subject to the constraint that the estimated 2D Fourier data for the image are consistent with the 1D Fourier transform of the projection data. PPF-TVM employs the alternating direction method (ADM) to develop a robust and efficient iteration scheme, which ensures stable convergence provided that appropriate parameter values are given. In the ADM scheme, PPF-TVM applies the pseudo-polar fast Fourier transform and its adjoint to iterate back and forth between the image and frequency domains. Thus, there is no interpolation in the Fourier domain, which makes the algorithm both fast and accurate. PPF-TVM is particularly useful for limited angle reconstruction in LCT and it appears to be robust against artifacts. The PPF-TVM algorithm was tested with the FORBILD head phantom and real data in comparisons with state-of-the-art algorithms. Simulation studies and real data verification suggest that PPF-TVM can reconstruct higher accuracy images with lower time consumption
Expressions for linearized perturbations in ideal-fluid cosmological models
International Nuclear Information System (INIS)
Ratra, B.
1988-01-01
We present closed-form solutions of the relativistic linear perturbation equations (in synchronous gauge) that govern the evolution of inhomogeneities in homogeneous, spatially flat, ideal-fluid, cosmological models. These expressions, which are valid for irregularities on any scale, allow one to analytically interpolate between the known approximate solutions which are valid at early times and at late times
Said-Houari, Belkacem
2017-01-01
This self-contained, clearly written textbook on linear algebra is easily accessible for students. It begins with the simple linear equation and generalizes several notions from this equation for the system of linear equations and introduces the main ideas using matrices. It then offers a detailed chapter on determinants and introduces the main ideas with detailed proofs. The third chapter introduces the Euclidean spaces using very simple geometric ideas and discusses various major inequalities and identities. These ideas offer a solid basis for understanding general Hilbert spaces in functional analysis. The following two chapters address general vector spaces, including some rigorous proofs to all the main results, and linear transformation: areas that are ignored or are poorly explained in many textbooks. Chapter 6 introduces the idea of matrices using linear transformation, which is easier to understand than the usual theory of matrices approach. The final two chapters are more advanced, introducing t...
Sahabiev, I. A.; Ryazanov, S. S.; Kolcova, T. G.; Grigoryan, B. R.
2018-03-01
The three most common techniques to interpolate soil properties at a field scale—ordinary kriging (OK), regression kriging with multiple linear regression drift model (RK + MLR), and regression kriging with principal component regression drift model (RK + PCR)—were examined. The results of the performed study were compiled into an algorithm of choosing the most appropriate soil mapping technique. Relief attributes were used as the auxiliary variables. When spatial dependence of a target variable was strong, the OK method showed more accurate interpolation results, and the inclusion of the auxiliary data resulted in an insignificant improvement in prediction accuracy. According to the algorithm, the RK + PCR method effectively eliminates multicollinearity of explanatory variables. However, if the number of predictors is less than ten, the probability of multicollinearity is reduced, and application of the PCR becomes irrational. In that case, the multiple linear regression should be used instead.
Energy Technology Data Exchange (ETDEWEB)
Mueller, Kerstin; Schwemmer, Chris; Hornegger, Joachim [Pattern Recognition Lab, Department of Computer Science, Erlangen Graduate School in Advanced Optical Technologies (SAOT), Friedrich-Alexander-Universitaet Erlangen-Nuernberg, Erlangen 91058 (Germany); Zheng Yefeng; Wang Yang [Imaging and Computer Vision, Siemens Corporate Research, Princeton, New Jersey 08540 (United States); Lauritsch, Guenter; Rohkohl, Christopher; Maier, Andreas K. [Siemens AG, Healthcare Sector, Forchheim 91301 (Germany); Schultz, Carl [Thoraxcenter, Erasmus MC, Rotterdam 3000 (Netherlands); Fahrig, Rebecca [Department of Radiology, Stanford University, Stanford, California 94305 (United States)
2013-03-15
all experiments showed that TPS interpolation provided the best results. The quantitative results in the phantom experiments showed comparable nRMSE of Almost-Equal-To 0.047 {+-} 0.004 for the TPS and Shepard's method. Only slightly inferior results for the smoothed weighting function and the linear approach were achieved. The UQI resulted in a value of Almost-Equal-To 99% for all four interpolation methods. On clinical human data sets, the best results were clearly obtained with the TPS interpolation. The mean contour deviation between the TPS reconstruction and the standard FDK reconstruction improved in the three human cases by 1.52, 1.34, and 1.55 mm. The Dice coefficient showed less sensitivity with respect to variations in the ventricle boundary. Conclusions: In this work, the influence of different motion interpolation methods on left ventricle motion compensated tomographic reconstructions was investigated. The best quantitative reconstruction results of a phantom, a porcine, and human clinical data sets were achieved with the TPS approach. In general, the framework of motion estimation using a surface model and motion interpolation to a dense MVF provides the ability for tomographic reconstruction using a motion compensation technique.
International Nuclear Information System (INIS)
Müller, Kerstin; Schwemmer, Chris; Hornegger, Joachim; Zheng Yefeng; Wang Yang; Lauritsch, Günter; Rohkohl, Christopher; Maier, Andreas K.; Schultz, Carl; Fahrig, Rebecca
2013-01-01
experiments showed that TPS interpolation provided the best results. The quantitative results in the phantom experiments showed comparable nRMSE of ≈0.047 ± 0.004 for the TPS and Shepard's method. Only slightly inferior results for the smoothed weighting function and the linear approach were achieved. The UQI resulted in a value of ≈ 99% for all four interpolation methods. On clinical human data sets, the best results were clearly obtained with the TPS interpolation. The mean contour deviation between the TPS reconstruction and the standard FDK reconstruction improved in the three human cases by 1.52, 1.34, and 1.55 mm. The Dice coefficient showed less sensitivity with respect to variations in the ventricle boundary. Conclusions: In this work, the influence of different motion interpolation methods on left ventricle motion compensated tomographic reconstructions was investigated. The best quantitative reconstruction results of a phantom, a porcine, and human clinical data sets were achieved with the TPS approach. In general, the framework of motion estimation using a surface model and motion interpolation to a dense MVF provides the ability for tomographic reconstruction using a motion compensation technique.
Multiresolution signal decomposition schemes
J. Goutsias (John); H.J.A.M. Heijmans (Henk)
1998-01-01
textabstract[PNA-R9810] Interest in multiresolution techniques for signal processing and analysis is increasing steadily. An important instance of such a technique is the so-called pyramid decomposition scheme. This report proposes a general axiomatic pyramid decomposition scheme for signal analysis
Two-Beam Linear Colliders - Special Issues
Corsini, Roberto
2010-01-01
The path towards a multi-TeV e+e- linear collider proposed by the CLIC study is based on the Two-Beam Acceleration (TBA) scheme. Such a scheme is promising in term of efficiency, reliability and cost. The rationale behind the two-beam scheme is discussed in the paper, together with the special issues related to this technology and the R&D needed to demonstrate its feasibility.
THE EFFECT OF STIMULUS ANTICIPATION ON THE INTERPOLATED TWITCH TECHNIQUE
Directory of Open Access Journals (Sweden)
Duane C. Button
2008-12-01
Full Text Available The objective of this study was to investigate the effect of expected and unexpected interpolated stimuli (IT during a maximum voluntary contraction on quadriceps force output and activation. Two groups of male subjects who were either inexperienced (MI: no prior experience with IT tests or experienced (ME: previously experienced 10 or more series of IT tests received an expected or unexpected IT while performing quadriceps isometric maximal voluntary contractions (MVCs. Measurements included MVC force, quadriceps and hamstrings electromyographic (EMG activity, and quadriceps inactivation as measured by the interpolated twitch technique (ITT. When performing MVCs with the expectation of an IT, the knowledge or lack of knowledge of an impending IT occurring during a contraction did not result in significant overall differences in force, ITT inactivation, quadriceps or hamstrings EMG activity. However, the expectation of an IT significantly (p < 0.0001 reduced MVC force (9.5% and quadriceps EMG activity (14.9% when compared to performing MVCs with prior knowledge that stimulation would not occur. While ME exhibited non-significant decreases when expecting an IT during a MVC, MI force and EMG activity significantly decreased 12.4% and 20.9% respectively. Overall, ME had significantly (p < 0.0001 higher force (14.5% and less ITT inactivation (10.4% than MI. The expectation of the noxious stimuli may account for the significant decrements in force and activation during the ITT
Flip-avoiding interpolating surface registration for skull reconstruction.
Xie, Shudong; Leow, Wee Kheng; Lee, Hanjing; Lim, Thiam Chye
2018-03-30
Skull reconstruction is an important and challenging task in craniofacial surgery planning, forensic investigation and anthropological studies. Existing methods typically reconstruct approximating surfaces that regard corresponding points on the target skull as soft constraints, thus incurring non-zero error even for non-defective parts and high overall reconstruction error. This paper proposes a novel geometric reconstruction method that non-rigidly registers an interpolating reference surface that regards corresponding target points as hard constraints, thus achieving low reconstruction error. To overcome the shortcoming of interpolating a surface, a flip-avoiding method is used to detect and exclude conflicting hard constraints that would otherwise cause surface patches to flip and self-intersect. Comprehensive test results show that our method is more accurate and robust than existing skull reconstruction methods. By incorporating symmetry constraints, it can produce more symmetric and normal results than other methods in reconstructing defective skulls with a large number of defects. It is robust against severe outliers such as radiation artifacts in computed tomography due to dental implants. In addition, test results also show that our method outperforms thin-plate spline for model resampling, which enables the active shape model to yield more accurate reconstruction results. As the reconstruction accuracy of defective parts varies with the use of different reference models, we also study the implication of reference model selection for skull reconstruction. Copyright © 2018 John Wiley & Sons, Ltd.
3D Interpolation Method for CT Images of the Lung
Directory of Open Access Journals (Sweden)
Noriaki Asada
2003-06-01
Full Text Available A 3-D image can be reconstructed from numerous CT images of the lung. The procedure reconstructs a solid from multiple cross section images, which are collected during pulsation of the heart. Thus the motion of the heart is a special factor that must be taken into consideration during reconstruction. The lung exhibits a repeating transformation synchronized to the beating of the heart as an elastic body. There are discontinuities among neighboring CT images due to the beating of the heart, if no special techniques are used in taking CT images. The 3-D heart image is reconstructed from numerous CT images in which both the heart and the lung are taken. Although the outline shape of the reconstructed 3-D heart is quite unnatural, the envelope of the 3-D unnatural heart is fit to the shape of the standard heart. The envelopes of the lung in the CT images are calculated after the section images of the best fitting standard heart are located at the same positions of the CT images. Thus the CT images are geometrically transformed to the optimal CT images fitting best to the standard heart. Since correct transformation of images is required, an Area oriented interpolation method proposed by us is used for interpolation of transformed images. An attempt to reconstruct a 3-D lung image by a series of such operations without discontinuity is shown. Additionally, the same geometrical transformation method to the original projection images is proposed as a more advanced method.
Interpolation methods for creating a scatter radiation exposure map
Energy Technology Data Exchange (ETDEWEB)
Gonçalves, Elicardo A. de S., E-mail: elicardo.goncalves@ifrj.edu.br [Instituto Federal do Rio de Janeiro (IFRJ), Paracambi, RJ (Brazil); Gomes, Celio S.; Lopes, Ricardo T. [Coordenacao de Pos-Graduacao e Pesquisa de Engenharia (PEN/COPPE/UFRJ), Rio de Janeiro, RJ (Brazil). Programa de Engenharia Nuclear; Oliveira, Luis F. de; Anjos, Marcelino J. dos; Oliveira, Davi F. [Universidade do Estado do Rio de Janeiro (UFRJ), RJ (Brazil). Instituto de Física
2017-07-01
A well know way for best comprehension of radiation scattering during a radiography is to map exposure over the space around the source and sample. This map is done measuring exposure in points regularly spaced, it means, measurement will be placed in localization chosen by increasing a regular steps from a starting point, along the x, y and z axes or even radial and angular coordinates. However, it is not always possible to maintain the accuracy of the steps throughout the entire space, or there will be regions of difficult access where the regularity of the steps will be impaired. This work intended to use some interpolation techniques that work with irregular steps, and to compare their results and their limits. It was firstly done angular coordinates, and tested in lack of some points. Later, in the same data was performed the Delaunay tessellation interpolation ir order to compare. Computational and graphic treatments was done with the GNU OCTAVE software and its image-processing package. Real data was acquired from a bunker where a 6 MeV betatron can be used to produce radiation scattering. (author)
Interpolation on the manifold of K component GMMs.
Kim, Hyunwoo J; Adluru, Nagesh; Banerjee, Monami; Vemuri, Baba C; Singh, Vikas
2015-12-01
Probability density functions (PDFs) are fundamental objects in mathematics with numerous applications in computer vision, machine learning and medical imaging. The feasibility of basic operations such as computing the distance between two PDFs and estimating a mean of a set of PDFs is a direct function of the representation we choose to work with. In this paper, we study the Gaussian mixture model (GMM) representation of the PDFs motivated by its numerous attractive features. (1) GMMs are arguably more interpretable than, say, square root parameterizations (2) the model complexity can be explicitly controlled by the number of components and (3) they are already widely used in many applications. The main contributions of this paper are numerical algorithms to enable basic operations on such objects that strictly respect their underlying geometry. For instance, when operating with a set of K component GMMs, a first order expectation is that the result of simple operations like interpolation and averaging should provide an object that is also a K component GMM. The literature provides very little guidance on enforcing such requirements systematically. It turns out that these tasks are important internal modules for analysis and processing of a field of ensemble average propagators (EAPs), common in diffusion weighted magnetic resonance imaging. We provide proof of principle experiments showing how the proposed algorithms for interpolation can facilitate statistical analysis of such data, essential to many neuroimaging studies. Separately, we also derive interesting connections of our algorithm with functional spaces of Gaussians, that may be of independent interest.
MAGIC: A Tool for Combining, Interpolating, and Processing Magnetograms
Allred, Joel
2012-01-01
Transients in the solar coronal magnetic field are ultimately the source of space weather. Models which seek to track the evolution of the coronal field require magnetogram images to be used as boundary conditions. These magnetograms are obtained by numerous instruments with different cadences and resolutions. A tool is required which allows modelers to fmd all available data and use them to craft accurate and physically consistent boundary conditions for their models. We have developed a software tool, MAGIC (MAGnetogram Interpolation and Composition), to perform exactly this function. MAGIC can manage the acquisition of magneto gram data, cast it into a source-independent format, and then perform the necessary spatial and temporal interpolation to provide magnetic field values as requested onto model-defined grids. MAGIC has the ability to patch magneto grams from different sources together providing a more complete picture of the Sun's field than is possible from single magneto grams. In doing this, care must be taken so as not to introduce nonphysical current densities along the seam between magnetograms. We have designed a method which minimizes these spurious current densities. MAGIC also includes a number of post-processing tools which can provide additional information to models. For example, MAGIC includes an interface to the DA VE4VM tool which derives surface flow velocities from the time evolution of surface magnetic field. MAGIC has been developed as an application of the KAMELEON data formatting toolkit which has been developed by the CCMC.
Image re-sampling detection through a novel interpolation kernel.
Hilal, Alaa
2018-06-01
Image re-sampling involved in re-size and rotation transformations is an essential element block in a typical digital image alteration. Fortunately, traces left from such processes are detectable, proving that the image has gone a re-sampling transformation. Within this context, we present in this paper two original contributions. First, we propose a new re-sampling interpolation kernel. It depends on five independent parameters that controls its amplitude, angular frequency, standard deviation, and duration. Then, we demonstrate its capacity to imitate the same behavior of the most frequent interpolation kernels used in digital image re-sampling applications. Secondly, the proposed model is used to characterize and detect the correlation coefficients involved in re-sampling transformations. The involved process includes a minimization of an error function using the gradient method. The proposed method is assessed over a large database of 11,000 re-sampled images. Additionally, it is implemented within an algorithm in order to assess images that had undergone complex transformations. Obtained results demonstrate better performance and reduced processing time when compared to a reference method validating the suitability of the proposed approaches. Copyright © 2018 Elsevier B.V. All rights reserved.
Interpolation methods for creating a scatter radiation exposure map
International Nuclear Information System (INIS)
Gonçalves, Elicardo A. de S.; Gomes, Celio S.; Lopes, Ricardo T.; Oliveira, Luis F. de; Anjos, Marcelino J. dos; Oliveira, Davi F.
2017-01-01
A well know way for best comprehension of radiation scattering during a radiography is to map exposure over the space around the source and sample. This map is done measuring exposure in points regularly spaced, it means, measurement will be placed in localization chosen by increasing a regular steps from a starting point, along the x, y and z axes or even radial and angular coordinates. However, it is not always possible to maintain the accuracy of the steps throughout the entire space, or there will be regions of difficult access where the regularity of the steps will be impaired. This work intended to use some interpolation techniques that work with irregular steps, and to compare their results and their limits. It was firstly done angular coordinates, and tested in lack of some points. Later, in the same data was performed the Delaunay tessellation interpolation ir order to compare. Computational and graphic treatments was done with the GNU OCTAVE software and its image-processing package. Real data was acquired from a bunker where a 6 MeV betatron can be used to produce radiation scattering. (author)
Some observations on interpolating gauges and non-covariant gauges
International Nuclear Information System (INIS)
Joglekar, Satish D.
2003-01-01
We discuss the viability of using interpolating gauges to define the non-covariant gauges starting from the covariant ones. We draw attention to the need for a very careful treatment of boundary condition defining term. We show that the boundary condition needed to maintain gauge invariance as the interpolating parameter θ varies, depends very sensitively on the parameter variation. We do this with a gauge used by Doust. We also consider the Lagrangian path-integrals in Minkowski space for gauges with a residual gauge-invariance. We point out the necessity of inclusion of an ε-term (even) in the formal treatments, without which one may reach incorrect conclusions. We, further, point out that the ε-term can contribute to the BRST WT-identities in a non-trivial way (even as ε → 0). We point out that these contributions lead to additional constraints on Green's function that are not normally taken into account in the BRST formalism that ignores the ε-term, and that they are characteristic of the way the singularities in propagators are handled. We argue that a prescription, in general, will require renormalization; if at all it is to be viable. (author)
Anisotropic interpolation theorems of Musielak-Orlicz type
Directory of Open Access Journals (Sweden)
Jinxia Li
2016-10-01
Full Text Available Abstract Anisotropy is a common attribute of Nature, which shows different characterizations in different directions of all or part of the physical or chemical properties of an object. The anisotropic property, in mathematics, can be expressed by a fairly general discrete group of dilations { A k : k ∈ Z } $\\{A^{k}: k\\in\\mathbb{Z}\\}$ , where A is a real n × n $n\\times n$ matrix with all its eigenvalues λ satisfy | λ | > 1 $|\\lambda|>1$ . Let φ : R n × [ 0 , ∞ → [ 0 , ∞ $\\varphi: \\mathbb{R}^{n}\\times[0, \\infty\\to[0,\\infty$ be an anisotropic Musielak-Orlicz function such that φ ( x , ⋅ $\\varphi(x,\\cdot$ is an Orlicz function and φ ( ⋅ , t $\\varphi(\\cdot,t$ is a Muckenhoupt A ∞ ( A $\\mathbb {A}_{\\infty}(A$ weight. The aim of this article is to obtain two anisotropic interpolation theorems of Musielak-Orlicz type, which are weighted anisotropic extension of Marcinkiewicz interpolation theorems. The above results are new even for the isotropic weighted settings.
Directory of Open Access Journals (Sweden)
R. Sitharthan
2016-09-01
Full Text Available This paper aims at modelling an electronically coupled distributed energy resource with an adaptive protection scheme. The electronically coupled distributed energy resource is a microgrid framework formed by coupling the renewable energy source electronically. Further, the proposed adaptive protection scheme provides a suitable protection to the microgrid for various fault conditions irrespective of the operating mode of the microgrid: namely, grid connected mode and islanded mode. The outstanding aspect of the developed adaptive protection scheme is that it monitors the microgrid and instantly updates relay fault current according to the variations that occur in the system. The proposed adaptive protection scheme also employs auto reclosures, through which the proposed adaptive protection scheme recovers faster from the fault and thereby increases the consistency of the microgrid. The effectiveness of the proposed adaptive protection is studied through the time domain simulations carried out in the PSCAD⧹EMTDC software environment.
Stoll, R R
1968-01-01
Linear Algebra is intended to be used as a text for a one-semester course in linear algebra at the undergraduate level. The treatment of the subject will be both useful to students of mathematics and those interested primarily in applications of the theory. The major prerequisite for mastering the material is the readiness of the student to reason abstractly. Specifically, this calls for an understanding of the fact that axioms are assumptions and that theorems are logical consequences of one or more axioms. Familiarity with calculus and linear differential equations is required for understand
Implementation and analysis of trajectory schemes for informate: a serial link robot manipulator
International Nuclear Information System (INIS)
Rauf, A.; Ahmed, S.M.; Asif, M.; Ahmad, M.
1997-01-01
Trajectory planning schemes generally interpolate or approximate the desired path by a class of polynomial functions and generate a sequence of time based control set points for the control of the manipulator movement from certain initial configuration to final configuration. Schemes for trajectory generation can be implemented in Joint space and in Cartesian space. This paper describes Joint Space trajectory schemes and Cartesian Space trajectory schemes and their implementation for Infomate, a six degrees of freedom serial link robot manipulator. LSPBs and cubic Spline are chosen as interpolating functions of time for each type of schemes. Modules developed have been incorporated in an OLP system for Infomate. Trajectory planning Schemes discussed in this paper incorporate the constraints of velocities and accelerations of the actuators. comparison with respect to computation and motion time is presented for above mentioned trajectory schemes. Algorithms have been developed that enable the end effector to follow a straight line; other paths like circle, ellipse, etc. can be approximated by straight line segments. (author)
International Nuclear Information System (INIS)
Zhou, Yongxi; Ernzerhof, Matthias; Bahmann, Hilke
2015-01-01
Drawing on the adiabatic connection of density functional theory, exchange-correlation functionals of Kohn-Sham density functional theory are constructed which interpolate between the extreme limits of the electron-electron interaction strength. The first limit is the non-interacting one, where there is only exchange. The second limit is the strong correlated one, characterized as the minimum of the electron-electron repulsion energy. The exchange-correlation energy in the strong-correlation limit is approximated through a model for the exchange-correlation hole that is referred to as nonlocal-radius model [L. O. Wagner and P. Gori-Giorgi, Phys. Rev. A 90, 052512 (2014)]. Using the non-interacting and strong-correlated extremes, various interpolation schemes are presented that yield new approximations to the adiabatic connection and thus to the exchange-correlation energy. Some of them rely on empiricism while others do not. Several of the proposed approximations yield the exact exchange-correlation energy for one-electron systems where local and semi-local approximations often fail badly. Other proposed approximations generalize existing global hybrids by using a fraction of the exchange-correlation energy in the strong-correlation limit to replace an equal fraction of the semi-local approximation to the exchange-correlation energy in the strong-correlation limit. The performance of the proposed approximations is evaluated for molecular atomization energies, total atomic energies, and ionization potentials
Solow, Daniel
2014-01-01
This text covers the basic theory and computation for a first course in linear programming, including substantial material on mathematical proof techniques and sophisticated computation methods. Includes Appendix on using Excel. 1984 edition.
Liesen, Jörg
2015-01-01
This self-contained textbook takes a matrix-oriented approach to linear algebra and presents a complete theory, including all details and proofs, culminating in the Jordan canonical form and its proof. Throughout the development, the applicability of the results is highlighted. Additionally, the book presents special topics from applied linear algebra including matrix functions, the singular value decomposition, the Kronecker product and linear matrix equations. The matrix-oriented approach to linear algebra leads to a better intuition and a deeper understanding of the abstract concepts, and therefore simplifies their use in real world applications. Some of these applications are presented in detailed examples. In several ‘MATLAB-Minutes’ students can comprehend the concepts and results using computational experiments. Necessary basics for the use of MATLAB are presented in a short introduction. Students can also actively work with the material and practice their mathematical skills in more than 300 exerc...
Berberian, Sterling K
2014-01-01
Introductory treatment covers basic theory of vector spaces and linear maps - dimension, determinants, eigenvalues, and eigenvectors - plus more advanced topics such as the study of canonical forms for matrices. 1992 edition.
Searle, Shayle R
2012-01-01
This 1971 classic on linear models is once again available--as a Wiley Classics Library Edition. It features material that can be understood by any statistician who understands matrix algebra and basic statistical methods.
International Nuclear Information System (INIS)
Hardy, David J.; Schulten, Klaus; Wolff, Matthew A.; Skeel, Robert D.; Xia, Jianlin
2016-01-01
The multilevel summation method for calculating electrostatic interactions in molecular dynamics simulations constructs an approximation to a pairwise interaction kernel and its gradient, which can be evaluated at a cost that scales linearly with the number of atoms. The method smoothly splits the kernel into a sum of partial kernels of increasing range and decreasing variability with the longer-range parts interpolated from grids of increasing coarseness. Multilevel summation is especially appropriate in the context of dynamics and minimization, because it can produce continuous gradients. This article explores the use of B-splines to increase the accuracy of the multilevel summation method (for nonperiodic boundaries) without incurring additional computation other than a preprocessing step (whose cost also scales linearly). To obtain accurate results efficiently involves technical difficulties, which are overcome by a novel preprocessing algorithm. Numerical experiments demonstrate that the resulting method offers substantial improvements in accuracy and that its performance is competitive with an implementation of the fast multipole method in general and markedly better for Hamiltonian formulations of molecular dynamics. The improvement is great enough to establish multilevel summation as a serious contender for calculating pairwise interactions in molecular dynamics simulations. In particular, the method appears to be uniquely capable for molecular dynamics in two situations, nonperiodic boundary conditions and massively parallel computation, where the fast Fourier transform employed in the particle–mesh Ewald method falls short.
Christofilos, N.C.; Polk, I.J.
1959-02-17
Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.
An application of gain-scheduled control using state-space interpolation to hydroactive gas bearings
DEFF Research Database (Denmark)
Theisen, Lukas Roy Svane; Camino, Juan F.; Niemann, Hans Henrik
2016-01-01
with a gain-scheduling strategy using state-space interpolation, which avoids both the performance loss and the increase of controller order associated to the Youla parametrisation. The proposed state-space interpolation for gain-scheduling is applied for mass imbalance rejection for a controllable gas...... bearing scheduled in two parameters. Comparisons against the Youla-based scheduling demonstrate the superiority of the state-space interpolation....
Lusine Poghosyan
2014-01-01
The paper considers convergence acceleration of the quasi-periodic and the quasi-periodic-rational interpolations by application of polynomial corrections. We investigate convergence of the resultant quasi-periodic-polynomial and quasi-periodic-rational-polynomial interpolations and derive exact constants of the main terms of asymptotic errors in the regions away from the endpoints. Results of numerical experiments clarify behavior of the corresponding interpolations for moderate number of in...
Pujades-Claumarchirant, Ma Carmen; Granero, Domingo; Perez-Calatayud, Jose; Ballester, Facundo; Melhus, Christopher; Rivard, Mark
2010-03-01
The aim of this work was to determine dose distributions for high-energy brachytherapy sources at spatial locations not included in the radial dose function g L ( r ) and 2D anisotropy function F ( r , θ ) table entries for radial distance r and polar angle θ . The objectives of this study are as follows: 1) to evaluate interpolation methods in order to accurately derive g L ( r ) and F ( r , θ ) from the reported data; 2) to determine the minimum number of entries in g L ( r ) and F ( r , θ ) that allow reproduction of dose distributions with sufficient accuracy. Four high-energy photon-emitting brachytherapy sources were studied: 60 Co model Co0.A86, 137 Cs model CSM-3, 192 Ir model Ir2.A85-2, and 169 Yb hypothetical model. The mesh used for r was: 0.25, 0.5, 0.75, 1, 1.5, 2-8 (integer steps) and 10 cm. Four different angular steps were evaluated for F ( r , θ ): 1°, 2°, 5° and 10°. Linear-linear and logarithmic-linear interpolation was evaluated for g L ( r ). Linear-linear interpolation was used to obtain F ( r , θ ) with resolution of 0.05 cm and 1°. Results were compared with values obtained from the Monte Carlo (MC) calculations for the four sources with the same grid. Linear interpolation of g L ( r ) provided differences ≤ 0.5% compared to MC for all four sources. Bilinear interpolation of F ( r , θ ) using 1° and 2° angular steps resulted in agreement ≤ 0.5% with MC for 60 Co, 192 Ir, and 169 Yb, while 137 Cs agreement was ≤ 1.5% for θ energy brachytherapy sources, and was similar to commonly found examples in the published literature. For F ( r , θ ) close to the source longitudinal-axis, polar angle step sizes of 1°-2° were sufficient to provide 2% accuracy for all sources.
A repeat-until-success quantum computing scheme
Energy Technology Data Exchange (ETDEWEB)
Beige, A [School of Physics and Astronomy, University of Leeds, Leeds LS2 9JT (United Kingdom); Lim, Y L [DSO National Laboratories, 20 Science Park Drive, Singapore 118230, Singapore (Singapore); Kwek, L C [Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore (Singapore)
2007-06-15
Recently we proposed a hybrid architecture for quantum computing based on stationary and flying qubits: the repeat-until-success (RUS) quantum computing scheme. The scheme is largely implementation independent. Despite the incompleteness theorem for optical Bell-state measurements in any linear optics set-up, it allows for the implementation of a deterministic entangling gate between distant qubits. Here we review this distributed quantum computation scheme, which is ideally suited for integrated quantum computation and communication purposes.
A repeat-until-success quantum computing scheme
International Nuclear Information System (INIS)
Beige, A; Lim, Y L; Kwek, L C
2007-01-01
Recently we proposed a hybrid architecture for quantum computing based on stationary and flying qubits: the repeat-until-success (RUS) quantum computing scheme. The scheme is largely implementation independent. Despite the incompleteness theorem for optical Bell-state measurements in any linear optics set-up, it allows for the implementation of a deterministic entangling gate between distant qubits. Here we review this distributed quantum computation scheme, which is ideally suited for integrated quantum computation and communication purposes
A morphing-based scheme for large deformation analysis with stereo-DIC
Genovese, Katia; Sorgente, Donato
2018-05-01
A key step in the DIC-based image registration process is the definition of the initial guess for the non-linear optimization routine aimed at finding the parameters describing the pixel subset transformation. This initialization may result very challenging and possibly fail when dealing with pairs of largely deformed images such those obtained from two angled-views of not-flat objects or from the temporal undersampling of rapidly evolving phenomena. To address this problem, we developed a procedure that generates a sequence of intermediate synthetic images for gradually tracking the pixel subset transformation between the two extreme configurations. To this scope, a proper image warping function is defined over the entire image domain through the adoption of a robust feature-based algorithm followed by a NURBS-based interpolation scheme. This allows a fast and reliable estimation of the initial guess of the deformation parameters for the subsequent refinement stage of the DIC analysis. The proposed method is described step-by-step by illustrating the measurement of the large and heterogeneous deformation of a circular silicone membrane undergoing axisymmetric indentation. A comparative analysis of the results is carried out by taking as a benchmark a standard reference-updating approach. Finally, the morphing scheme is extended to the most general case of the correspondence search between two largely deformed textured 3D geometries. The feasibility of this latter approach is demonstrated on a very challenging case: the full-surface measurement of the severe deformation (> 150% strain) suffered by an aluminum sheet blank subjected to a pneumatic bulge test.
Directory of Open Access Journals (Sweden)
Mathieu Lepot
2017-10-01
Full Text Available A thorough review has been performed on interpolation methods to fill gaps in time-series, efficiency criteria, and uncertainty quantifications. On one hand, there are numerous available methods: interpolation, regression, autoregressive, machine learning methods, etc. On the other hand, there are many methods and criteria to estimate efficiencies of these methods, but uncertainties on the interpolated values are rarely calculated. Furthermore, while they are estimated according to standard methods, the prediction uncertainty is not taken into account: a discussion is thus presented on the uncertainty estimation of interpolated/extrapolated data. Finally, some suggestions for further research and a new method are proposed.
[Research on fast implementation method of image Gaussian RBF interpolation based on CUDA].
Chen, Hao; Yu, Haizhong
2014-04-01
Image interpolation is often required during medical image processing and analysis. Although interpolation method based on Gaussian radial basis function (GRBF) has high precision, the long calculation time still limits its application in field of image interpolation. To overcome this problem, a method of two-dimensional and three-dimensional medical image GRBF interpolation based on computing unified device architecture (CUDA) is proposed in this paper. According to single instruction multiple threads (SIMT) executive model of CUDA, various optimizing measures such as coalesced access and shared memory are adopted in this study. To eliminate the edge distortion of image interpolation, natural suture algorithm is utilized in overlapping regions while adopting data space strategy of separating 2D images into blocks or dividing 3D images into sub-volumes. Keeping a high interpolation precision, the 2D and 3D medical image GRBF interpolation achieved great acceleration in each basic computing step. The experiments showed that the operative efficiency of image GRBF interpolation based on CUDA platform was obviously improved compared with CPU calculation. The present method is of a considerable reference value in the application field of image interpolation.
Compressive Parameter Estimation for Sparse Translation-Invariant Signals Using Polar Interpolation
DEFF Research Database (Denmark)
Fyhn, Karsten; Duarte, Marco F.; Jensen, Søren Holdt
2015-01-01
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non...... to attain good estimation precision and keep the computational complexity low. Our numerical experiments show that the proposed algorithms outperform existing approaches that either leverage polynomial interpolation or are based on a conversion to a frequency-estimation problem followed by a super...... interpolation increases the estimation precision....
Xie, Lizhe; Hu, Yining; Chen, Yang; Shi, Luyao
2015-03-01
Projection and back-projection are the most computational consuming parts in Computed Tomography (CT) reconstruction. Parallelization strategies using GPU computing techniques have been introduced. We in this paper present a new parallelization scheme for both projection and back-projection. The proposed method is based on CUDA technology carried out by NVIDIA Corporation. Instead of build complex model, we aimed on optimizing the existing algorithm and make it suitable for CUDA implementation so as to gain fast computation speed. Besides making use of texture fetching operation which helps gain faster interpolation speed, we fixed sampling numbers in the computation of projection, to ensure the synchronization of blocks and threads, thus prevents the latency caused by inconsistent computation complexity. Experiment results have proven the computational efficiency and imaging quality of the proposed method.
ANGELO-LAMBDA, Covariance matrix interpolation and mathematical verification
International Nuclear Information System (INIS)
Kodeli, Ivo
2007-01-01
1 - Description of program or function: The codes ANGELO-2.3 and LAMBDA-2.3 are used for the interpolation of the cross section covariance data from the original to a user defined energy group structure, and for the mathematical tests of the matrices, respectively. The LAMBDA-2.3 code calculates the eigenvalues of the matrices (both for the original or the converted) and lists them accordingly into positive and negative matrices. This verification is strongly recommended before using any covariance matrices. These versions of the two codes are the extended versions of the previous codes available in the Packages NEA-1264 - ZZ-VITAMIN-J/COVA. They were specifically developed for the purposes of the OECD LWR UAM benchmark, in particular for the processing of the ZZ-SCALE5.1/COVA-44G cross section covariance matrix library retrieved from the SCALE-5.1 package. Either the original SCALE-5.1 libraries or the libraries separated into several files by Nuclides can be (in principle) processed by ANGELO/LAMBDA codes, but the use of the one-nuclide data is strongly recommended. Due to large deviations of the correlation matrix terms from unity observed in some SCALE5.1 covariance matrices, the previous more severe acceptance condition in the ANGELO2.3 code was released. In case the correlation coefficients exceed 1.0, only a warning message is issued, and coefficients are replaced by 1.0. 2 - Methods: ANGELO-2.3 interpolates the covariance matrices to a union grid using flat weighting. LAMBDA-2.3 code includes the mathematical routines to calculate the eigenvalues of the covariance matrices. 3 - Restrictions on the complexity of the problem: The algorithm used in ANGELO is relatively simple, therefore the interpolations involving energy group structure which are very different from the original (e.g. large difference in the number of energy groups) may not be accurate. In particular in the case of the MT=1018 data (fission spectra covariances) the algorithm may not be
Monotone difference schemes for weakly coupled elliptic and parabolic systems
P. Matus (Piotr); F.J. Gaspar Lorenz (Franscisco); L. M. Hieu (Le Minh); V.T.K. Tuyen (Vo Thi Kim)
2017-01-01
textabstractThe present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is
Diabat Interpolation for Polymorph Free-Energy Differences.
Kamat, Kartik; Peters, Baron
2017-02-02
Existing methods to compute free-energy differences between polymorphs use harmonic approximations, advanced non-Boltzmann bias sampling techniques, and/or multistage free-energy perturbations. This work demonstrates how Bennett's diabat interpolation method ( J. Comput. Phys. 1976, 22, 245 ) can be combined with energy gaps from lattice-switch Monte Carlo techniques ( Phys. Rev. E 2000, 61, 906 ) to swiftly estimate polymorph free-energy differences. The new method requires only two unbiased molecular dynamics simulations, one for each polymorph. To illustrate the new method, we compute the free-energy difference between face-centered cubic and body-centered cubic polymorphs for a Gaussian core solid. We discuss the justification for parabolic models of the free-energy diabats and similarities to methods that have been used in studies of electron transfer.
Basis set approach in the constrained interpolation profile method
International Nuclear Information System (INIS)
Utsumi, T.; Koga, J.; Yabe, T.; Ogata, Y.; Matsunaga, E.; Aoki, T.; Sekine, M.
2003-07-01
We propose a simple polynomial basis-set that is easily extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution by the constraints from the spatial derivative of the original equation. Thus the solution even on the subgrid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges. 3rd and 5th order polynomials are tested on the one-dimensional Schroedinger equation and are proved to give solutions a few orders of magnitude higher in accuracy than conventional methods for lower-lying eigenstates. (author)
Interpolation method by whole body computed tomography, Artronix 1120
International Nuclear Information System (INIS)
Fujii, Kyoichi; Koga, Issei; Tokunaga, Mitsuo
1981-01-01
Reconstruction of the whole body CT images by interpolation method was investigated by rapid scanning. Artronix 1120 with fixed collimator was used to obtain the CT images every 5 mm. X-ray source was circully movable to obtain perpendicular beam to the detector. A length of 150 mm was scanned in about 15 min., with the slice width of 5 mm. The images were reproduced every 7.5 mm, which was able to reduce every 1.5 mm when necessary. Out of 420 inspection in the chest, abdomen, and pelvis, 5 representative cases for which this method was valuable were described. The cases were fibrous histiocytoma of upper mediastinum, left adrenal adenoma, left ureter fibroma, recurrence of colon cancer in the pelvis, and abscess around the rectum. This method improved the image quality of lesions in the vicinity of the ureters, main artery, and rectum. The time required and exposure dose were reduced to 50% by this method. (Nakanishi, T.)