Identifying Isotropic Events using an Improved Regional Moment Tensor Inversion Technique
Energy Technology Data Exchange (ETDEWEB)
Dreger, Douglas S. [Univ. of California, Berkeley, CA (United States); Ford, Sean R. [Univ. of California, Berkeley, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Walter, William R. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2016-12-08
Research was carried out investigating the feasibility of using a regional distance seismic waveform moment tensor inverse procedure to estimate source parameters of nuclear explosions and to use the source inversion results to develop a source-type discrimination capability. The results of the research indicate that it is possible to robustly determine the seismic moment tensor of nuclear explosions, and when compared to natural seismicity in the context of the a Hudson et al. (1989) source-type diagram they are found to separate from populations of earthquakes and underground cavity collapse seismic sources.
Directory of Open Access Journals (Sweden)
Shiann-Jong Lee
2010-01-01
Full Text Available Moment tensor inversion is a routine procedure to obtain information on an earthquake source for moment magnitude and focal mechanism. However, the inversion quality is usually controlled by factors such as knowledge of an earthquake location and the suitability of a 1-D velocity model used. Here we present an improved method to invert the moment tensor solution for local earthquakes. The proposed method differs from routine centroid-moment-tensor inversion of the Broadband Array in Taiwan for Seismology in three aspects. First, the inversion is repeated in the neighborhood of an earthquake_?s hypocenter on a grid basis. Second, it utilizes Green_?s functions based on a true three-dimensional velocity model. And third, it incorporates most of the input waveforms from strong-motion records. The proposed grid-based moment tensor inversion is applied to a local earthquake that occurred near the Taipei basin on 23 October 2004 to demonstrate its effectiveness and superiority over methods used in previous studies. By using the grid-based moment tensor inversion technique and 3-D Green_?s functions, the earthquake source parameters, including earthquake location, moment magnitude and focal mechanism, are accurately found that are sufficiently consistent with regional ground motion observations up to a frequency of 1.0 Hz. This approach can obtain more precise source parameters for other earthquakes in or near a well-modeled basin and crustal structure.
CSIR Research Space (South Africa)
Linzer, LM
2005-04-01
Full Text Available The primary objective of this study was to develop a robust MTI method to estimate the moment tensors of clusters of seismic events recorded in the underground environment. To achieve this, three 'hybrid' MTI methods were developed by the author...
3D Inversion of SQUID Magnetic Tensor Data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2012-01-01
Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...
3D inversion of full tensor magnetic gradiometry (FTMG) data
DEFF Research Database (Denmark)
Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn
2011-01-01
Following recent advances in SQUID technology, full tensor magnetic gradiometry (FTMG) is emerging as a practical exploration method. We introduce 3D regularized focusing inversion for FTMG data. Our model studies show that inversion of magnetic tensor data can significantly improve resolution...
Sampling-free Bayesian inversion with adaptive hierarchical tensor representations
Eigel, Martin; Marschall, Manuel; Schneider, Reinhold
2018-03-01
A sampling-free approach to Bayesian inversion with an explicit polynomial representation of the parameter densities is developed, based on an affine-parametric representation of a linear forward model. This becomes feasible due to the complete treatment in function spaces, which requires an efficient model reduction technique for numerical computations. The advocated perspective yields the crucial benefit that error bounds can be derived for all occuring approximations, leading to provable convergence subject to the discretization parameters. Moreover, it enables a fully adaptive a posteriori control with automatic problem-dependent adjustments of the employed discretizations. The method is discussed in the context of modern hierarchical tensor representations, which are used for the evaluation of a random PDE (the forward model) and the subsequent high-dimensional quadrature of the log-likelihood, alleviating the ‘curse of dimensionality’. Numerical experiments demonstrate the performance and confirm the theoretical results.
Inversion for seismic moment tensors from 6-component waveform data
Donner, Stefanie; Bernauer, Felix; Wassermann, Joachim; Igel, Heiner
2017-04-01
Waveform inversion for the seismic moment tensor nowadays is a well-established standard method in teleseismic distances. Nevertheless, several difficulties remain, especially for shallow and/or regional/local distances. These difficulties include e.g. the resolution of the mechanism, especially the non-double-couple components and the resolution of the centroid depth but also the uncertainty of a determined moment tensor. During the last decade, the observation of rotational ground motions gained increasing attention amongst seismologists. So far, studies were based on one (vertical) component ring laser data but 3-component ring laser data and even data from portable rotation sensors are in reach. These new developments can contribute to solve the difficulties in waveform inversion for moment tensors. Here, we present results for moment tensors, mainly in the regional distance range, derived from collocated translational and rotational ground motion measurements. These results are based on numerical and real-data studies. We inverted the ground motions recorded by a network of stations but also addressed the question of how reliable the inversion for moment tensors is from a single 6-component measurement.
Single-well moment tensor inversion of tensile microseismic events
Czech Academy of Sciences Publication Activity Database
Grechka, V.; Li, Z.; Howell, B.; Vavryčuk, Václav
2016-01-01
Roč. 81, č. 6 (2016), KS219-KS229 ISSN 0016-8033 R&D Projects: GA ČR(CZ) GAP210/12/1491; GA ČR(CZ) GC16-19751J Institutional support: RVO:67985530 Keywords : microseismic events * moment tensor inversion * mathematical formulation Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 2.391, year: 2016
Bayesian ISOLA: new tool for automated centroid moment tensor inversion
Vackář, Jiří; Burjánek, Jan; Gallovič, František; Zahradník, Jiří; Clinton, John
2017-04-01
Focal mechanisms are important for understanding seismotectonics of a region, and they serve as a basic input for seismic hazard assessment. Usually, the point source approximation and the moment tensor (MT) are used. We have developed a new, fully automated tool for the centroid moment tensor (CMT) inversion in a Bayesian framework. It includes automated data retrieval, data selection where station components with various instrumental disturbances and high signal-to-noise are rejected, and full-waveform inversion in a space-time grid around a provided hypocenter. The method is innovative in the following aspects: (i) The CMT inversion is fully automated, no user interaction is required, although the details of the process can be visually inspected latter on many figures which are automatically plotted.(ii) The automated process includes detection of disturbances based on MouseTrap code, so disturbed recordings do not affect inversion.(iii) A data covariance matrix calculated from pre-event noise yields an automated weighting of the station recordings according to their noise levels and also serves as an automated frequency filter suppressing noisy frequencies.(iv) Bayesian approach is used, so not only the best solution is obtained, but also the posterior probability density function.(v) A space-time grid search effectively combined with the least-squares inversion of moment tensor components speeds up the inversion and allows to obtain more accurate results compared to stochastic methods. The method has been tested on synthetic and observed data. It has been tested by comparison with manually processed moment tensors of all events greater than M≥3 in the Swiss catalogue over 16 years using data available at the Swiss data center (http://arclink.ethz.ch). The quality of the results of the presented automated process is comparable with careful manual processing of data. The software package programmed in Python has been designed to be as versatile as possible in
Regional Moment Tensor Inversion for Source Type Identification
Dreger, D. S.; Ford, S. R.; Walter, W. R.
2008-12-01
With Green's functions from calibrated seismic velocity models it is possible to use regional distance moment tensor inversion for source-type identification. The deviatoric and isotropic source components for 17 explosions at the Nevada Test Site, as well as 12 earthquakes and 3 collapses in the surrounding region of the western US, are calculated using a regional time-domain full waveform inversion for the complete moment tensor. The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination between explosions, earthquakes, and collapses. Confidence regions of the model parameters are estimated from the data misfit by assuming normally distributed parameter values. We investigate the sensitivity of the resolved parameters of an explosion to imperfect Earth models, inaccurate event depths, and data with a low signal-to-noise ratio (SNR) assuming a reasonable azimuthal distribution of stations. In the band of interest (0.02-0.10 Hz) the source-type calculated from complete moment tensor inversion is insensitive to velocity models perturbations that cause less than a half-cycle shift (explosion source-type is insensitive to an incorrect depth assumption (for a true depth of 1 km), and the goodness-of-fit of the inversion result cannot be used to resolve the true depth of the explosion. Noise degrades the explosive character of the result, and a good fit and accurate result are obtained when the signal-to-noise ratio (SNR) is greater than 5. We assess the depth and frequency dependence upon the resolved explosive moment. As the depth decreases from 1 km to 200 m, the isotropic moment is no longer accurately resolved and is in error between 50-200%. However, even at the most shallow depth the resultant moment tensor is dominated by the explosive component when the data has a good SNR. Finally, the sensitivity
Moment tensor inversions using strong motion waveforms of Taiwan TSMIP data, 1993–2009
Chang, Kaiwen; Chi, Wu-Cheng; Gung, Yuancheng; Dreger, Douglas; Lee, William H K.; Chiu, Hung-Chie
2011-01-01
Earthquake source parameters are important for earthquake studies and seismic hazard assessment. Moment tensors are among the most important earthquake source parameters, and are now routinely derived using modern broadband seismic networks around the world. Similar waveform inversion techniques can also apply to other available data, including strong-motion seismograms. Strong-motion waveforms are also broadband, and recorded in many regions since the 1980s. Thus, strong-motion data can be used to augment moment tensor catalogs with a much larger dataset than that available from the high-gain, broadband seismic networks. However, a systematic comparison between the moment tensors derived from strong motion waveforms and high-gain broadband waveforms has not been available. In this study, we inverted the source mechanisms of Taiwan earthquakes between 1993 and 2009 by using the regional moment tensor inversion method using digital data from several hundred stations in the Taiwan Strong Motion Instrumentation Program (TSMIP). By testing different velocity models and filter passbands, we were able to successfully derive moment tensor solutions for 107 earthquakes of Mw >= 4.8. The solutions for large events agree well with other available moment tensor catalogs derived from local and global broadband networks. However, for Mw = 5.0 or smaller events, we consistently over estimated the moment magnitudes by 0.5 to 1.0. We have tested accelerograms, and velocity waveforms integrated from accelerograms for the inversions, and found the results are similar. In addition, we used part of the catalogs to study important seismogenic structures in the area near Meishan Taiwan which was the site of a very damaging earthquake a century ago, and found that the structures were dominated by events with complex right-lateral strike-slip faulting during the recent decade. The procedures developed from this study may be applied to other strong-motion datasets to compliment or fill
Thermal measurements and inverse techniques
Orlande, Helcio RB; Maillet, Denis; Cotta, Renato M
2011-01-01
With its uncommon presentation of instructional material regarding mathematical modeling, measurements, and solution of inverse problems, Thermal Measurements and Inverse Techniques is a one-stop reference for those dealing with various aspects of heat transfer. Progress in mathematical modeling of complex industrial and environmental systems has enabled numerical simulations of most physical phenomena. In addition, recent advances in thermal instrumentation and heat transfer modeling have improved experimental procedures and indirect measurements for heat transfer research of both natural phe
Bayesian ISOLA: new tool for automated centroid moment tensor inversion
Vackář, Jiří; Burjánek, Jan; Gallovič, František; Zahradník, Jiří; Clinton, John
2017-08-01
We have developed a new, fully automated tool for the centroid moment tensor (CMT) inversion in a Bayesian framework. It includes automated data retrieval, data selection where station components with various instrumental disturbances are rejected and full-waveform inversion in a space-time grid around a provided hypocentre. A data covariance matrix calculated from pre-event noise yields an automated weighting of the station recordings according to their noise levels and also serves as an automated frequency filter suppressing noisy frequency ranges. The method is tested on synthetic and observed data. It is applied on a data set from the Swiss seismic network and the results are compared with the existing high-quality MT catalogue. The software package programmed in Python is designed to be as versatile as possible in order to be applicable in various networks ranging from local to regional. The method can be applied either to the everyday network data flow, or to process large pre-existing earthquake catalogues and data sets.
Forward modeling and inversion of tensor CSAMT in 3D anisotropic media
Wang, Tao; Wang, Kun-Peng; Tan, Han-Dong
2017-12-01
Tensor controlled-source audio-frequency magnetotellurics (CSAMT) can yield information about electric and magnetic fields owing to its multi-transmitter configuration compared with the common scalar CSAMT. The most current theories, numerical simulations, and inversion of tensor CSAMT are based on far-field measurements and the assumption that underground media have isotropic resistivity. We adopt a three-dimensional (3D) staggered-grid finite difference numerical simulation method to analyze the resistivity in axial anisotropic and isotropic media. We further adopt the limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) method to perform 3D tensor CSAMT axial anisotropic inversion. The inversion results suggest that when the underground structure is anisotropic, the isotropic inversion will introduce errors to the interpretation.
Bayesian ISOLA: new tool for automated centroid moment tensor inversion
Czech Academy of Sciences Publication Activity Database
Vackář, J.; Burjánek, Jan; Gallovič, F.; Zahradník, J.; Clinton, J.
2017-01-01
Roč. 210, č. 2 (2017), s. 693-705 ISSN 0956-540X Institutional support: RVO:67985530 Keywords : inverse theory * waveform inversion * computational seismology * earthquake source observations * seismic noise Subject RIV: DC - Siesmology, Volcanology, Earth Structure OBOR OECD: Volcanology Impact factor: 2.414, year: 2016
Ma, Ju; Dineva, Savka; Cesca, Simone; Heimann, Sebastian
2018-03-01
Mining induced seismicity is an undesired consequence of mining operations, which poses significant hazard to miners and infrastructures and requires an accurate analysis of the rupture process. Seismic moment tensors of mining-induced events help to understand the nature of mining-induced seismicity by providing information about the relationship between the mining, stress redistribution and instabilities in the rock mass. In this work, we adapt and test a waveform-based inversion method on high frequency data recorded by a dense underground seismic system in one of the largest underground mines in the world (Kiruna mine, Sweden). Stable algorithm for moment tensor inversion for comparatively small mining induced earthquakes, resolving both the double couple and full moment tensor with high frequency data is very challenging. Moreover, the application to underground mining system requires accounting for the 3D geometry of the monitoring system. We construct a Green's function database using a homogeneous velocity model, but assuming a 3D distribution of potential sources and receivers. We first perform a set of moment tensor inversions using synthetic data to test the effects of different factors on moment tensor inversion stability and source parameters accuracy, including the network spatial coverage, the number of sensors and the signal-to-noise ratio. The influence of the accuracy of the input source parameters on the inversion results is also tested. Those tests show that an accurate selection of the inversion parameters allows resolving the moment tensor also in presence of realistic seismic noise conditions. Finally, the moment tensor inversion methodology is applied to 8 events chosen from mining block #33/34 at Kiruna mine. Source parameters including scalar moment, magnitude, double couple, compensated linear vector dipole and isotropic contributions as well as the strike, dip, rake configurations of the double couple term were obtained. The orientations
Inverse Filtering Techniques in Speech Analysis | Nwachuku ...
African Journals Online (AJOL)
inverse filtering' has been applied. The unifying features of these techniques are presented, namely: 1. a basis in the source-filter theory of speech production, 2. the use of a network whose transfer function is the inverse of the transfer function of ...
Moment Tensor Inversion of the 1998 Aiquile Earthquake Using Long-period surface waves
Wang, H.
2016-12-01
On 22nd May 1998 at 04:49(GMT), an earthquake of magnitude Mw = 6.6 struck the Aiquile region of Bolivia, causing 105 deaths and significant damage to the nearby towns of Hoyadas and Pampa Grande. This was the largest shallow earthquake (15 km depth) in Bolivia in over 50 years, and was felt as far Sucre, approximately 100 km away. In this report, a centroid moment tensor (CMT) inversion is carried using body waves and surface waves from 1998 Aiquile earthquake with 1-D and 3-D earth models to obtain the source model parameters and moment tensor, which are the values will be subsequently compared against the Global Centroid Moment Tensor Catalog(GCMT). Also, the excitation kernels could be gained and synthetic data can be created with different earth models. The two method for calculating synthetic seismograms are SPECFEM3D Globe which is based on shear wave mantle model S40RTS and crustal model CRUST 2.0, and AxiSEM which is based on PREM 1-D earth Model. Within the report, the theory behind the CMT inversion was explained and the source parameters gained from the inversion can be used to reveal the tectonics of the source of this earthquake, these information could be helpful in assessing seismic hazard and overall tectonic regime of this region. Furthermore, results of synthetic seismograms and the solution of inversion are going to be used to assess two models.
Inverse design technique for cascades
Zannetti, L.; Pandolfi, M.
1984-01-01
A numerical technique to generate cascades is presented. The basic prescribed parameters are: inlet angle, exit pressure, and distribution of blade thickness and lift along a blade. Other sets of parameters are also discussed. The technique is based on the lambda scheme. The problem of stability of the computation as a function of the prescribed set of parameters and the treatment of boundary conditions is discussed. A one dimensional analysis to indicate a possible way for assuring stability for any two dimensional calculation is provided.
Inverse Raman effect: applications and detection techniques
International Nuclear Information System (INIS)
Hughes, L.J. Jr.
1980-08-01
The processes underlying the inverse Raman effect are qualitatively described by comparing it to the more familiar phenomena of conventional and stimulated Raman scattering. An experession is derived for the inverse Raman absorption coefficient, and its relationship to the stimulated Raman gain is obtained. The power requirements of the two fields are examined qualitatively and quantitatively. The assumption that the inverse Raman absorption coefficient is constant over the interaction length is examined. Advantages of the technique are discussed and a brief survey of reported studies is presented
Inverse Raman effect: applications and detection techniques
Energy Technology Data Exchange (ETDEWEB)
Hughes, L.J. Jr.
1980-08-01
The processes underlying the inverse Raman effect are qualitatively described by comparing it to the more familiar phenomena of conventional and stimulated Raman scattering. An experession is derived for the inverse Raman absorption coefficient, and its relationship to the stimulated Raman gain is obtained. The power requirements of the two fields are examined qualitatively and quantitatively. The assumption that the inverse Raman absorption coefficient is constant over the interaction length is examined. Advantages of the technique are discussed and a brief survey of reported studies is presented.
Oil core microcapsules by inverse gelation technique.
Martins, Evandro; Renard, Denis; Davy, Joëlle; Marquis, Mélanie; Poncelet, Denis
2015-01-01
A promising technique for oil encapsulation in Ca-alginate capsules by inverse gelation was proposed by Abang et al. This method consists of emulsifying calcium chloride solution in oil and then adding it dropwise in an alginate solution to produce Ca-alginate capsules. Spherical capsules with diameters around 3 mm were produced by this technique, however the production of smaller capsules was not demonstrated. The objective of this study is to propose a new method of oil encapsulation in a Ca-alginate membrane by inverse gelation. The optimisation of the method leads to microcapsules with diameters around 500 μm. In a search of microcapsules with improved diffusion characteristics, the size reduction is an essential factor to broaden the applications in food, cosmetics and pharmaceuticals areas. This work contributes to a better understanding of the inverse gelation technique and allows the production of microcapsules with a well-defined shell-core structure.
Dettmer, J.; Benavente, R. F.; Cummins, P. R.
2017-12-01
This work considers probabilistic, non-linear centroid moment tensor inversion of data from earthquakes at teleseismic distances. The moment tensor is treated as deviatoric and centroid location is parametrized with fully unknown latitude, longitude, depth and time delay. The inverse problem is treated as fully non-linear in a Bayesian framework and the posterior density is estimated with interacting Markov chain Monte Carlo methods which are implemented in parallel and allow for chain interaction. The source mechanism and location, including uncertainties, are fully described by the posterior probability density and complex trade-offs between various metrics are studied. These include the percent of double couple component as well as fault orientation and the probabilistic results are compared to results from earthquake catalogs. Additional focus is on the analysis of complex events which are commonly not well described by a single point source. These events are studied by jointly inverting for multiple centroid moment tensor solutions. The optimal number of sources is estimated by the Bayesian information criterion to ensure parsimonious solutions. [Supported by NSERC.
Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method
Sun, Yong; Meng, Zhaohai; Li, Fengting
2018-03-01
Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.
Analog fault diagnosis by inverse problem technique
Ahmed, Rania F.
2011-12-01
A novel algorithm for detecting soft faults in linear analog circuits based on the inverse problem concept is proposed. The proposed approach utilizes optimization techniques with the aid of sensitivity analysis. The main contribution of this work is to apply the inverse problem technique to estimate the actual parameter values of the tested circuit and so, to detect and diagnose single fault in analog circuits. The validation of the algorithm is illustrated through applying it to Sallen-Key second order band pass filter and the results show that the detecting percentage efficiency was 100% and also, the maximum error percentage of estimating the parameter values is 0.7%. This technique can be applied to any other linear circuit and it also can be extended to be applied to non-linear circuits. © 2011 IEEE.
International Nuclear Information System (INIS)
Smirnov, Yu.F.; Tolstoi, V.N.; Kharitonov, Yu.I.
1993-01-01
The tree technique for the quantum algebra su q (2) developed in an earlier study is used to construct the q analog of the algebra of irreducible tensor operators. The adjoint action of the algebra su q (2) on irreducible tensor operators is discussed, and the adjoint R matrix is introduced. A set of expressions is obtained for the matrix elements of various irreducible tensor operators and combinations of them. As an application, the recursion relations for the Clebsch-Gordan and Racah coefficients of the algebra su q (2) are derived. 16 refs
Queitsch, M.; Schiffler, M.; Stolz, R.; Meyer, M.; Kukowski, N.
2017-12-01
Measurements of the Earth's magnetic field are one of the most used methods in geophysical exploration. The ambiguity of the method, especially during modeling and inversion of magnetic field data sets, is one of its biggest challenges. Additional directional information, e.g. gathered by gradiometer systems based on Superconducting Quantum Interference Devices (SQUIDs), will positively influence the inversion results and will thus lead to better subsurface magnetization models. This is especially beneficial, regarding the shape and direction of magnetized structures, especially when a significant remanent magnetization of the underlying sources is present. The possibility to separate induced and remanent contributions to the total magnetization may in future also open up advanced ways for geological interpretation of the data, e.g. a first estimation of diagenesis processes. In this study we present the results of airborne full tensor magnetic gradiometry (FTMG) surveys conducted over a dolerite intrusion in central Germany and the results of two magnetization vector inversions (MVI) of the FTMG and a conventional total field anomaly data set. A separation of the two main contributions of the acquired total magnetization will be compared with information of the rock magnetization measured on orientated rock samples. The FTMG inversion results show a much better agreement in direction and strength of both total and remanent magnetization compared to the inversion using only total field anomaly data. To enhance the separation process, the application of additional geophysical methods, i.e. frequency domain electromagnetics (FDEM), in order to gather spatial information of subsurface rock susceptibility will also be discussed. In this approach, we try to extract not only information on subsurface conductivity but also the induced magnetization. Using the total magnetization from the FTMG data and the induced magnetization from the FDEM data, the full separation of
Interferogram analysis using the Abel inversion technique
International Nuclear Information System (INIS)
Yusof Munajat; Mohamad Kadim Suaidi
2000-01-01
High speed and high resolution optical detection system were used to capture the image of acoustic waves propagation. The freeze image in the form of interferogram was analysed to calculate the transient pressure profile of the acoustic waves. The interferogram analysis was based on the fringe shift and the application of the Abel inversion technique. An easier approach was made by mean of using MathCAD program as a tool in the programming; yet powerful enough to make such calculation, plotting and transfer of file. (Author)
Study of the characteristics of crust stress field in East China by inversion of stress tensor
International Nuclear Information System (INIS)
Huilan, Z.; Rugang, D.
1991-12-01
This paper combines the search procedure with the optimization procedure to inverse the average stress tensor, and applies this method to study the crustal stress field using data of the solution of P wave first motion. By dealing with the data of Haicheng, Tangshan, Xingtai, Anyang, Liyang, Taiwan, Fujian and Guangdong areas, we obtain the characteristics of crust stress field of East China. The directions of the principal pressure stress always possess a small dip angle, but the azimuths vary from NEE (in north part of East China) to SEE (in the south part). This frame probably is related to the push-extrusive effects of the northwestern Pacific plate from NEE and the Philippine plate from SEE. (author). 5 refs, 8 figs, 4 tabs
Barth, A.; Wenzel, F.; Giardini, D.
2007-08-01
We provide a procedure for the routine determination of moment tensors from earthquakes with magnitudes as low as M W 4.4 using data recorded by only a few permanent seismic stations at regional to teleseismic distances. Waveforms are inverted for automatically determined frequency pass-bands that depend on source-receiver locations as well as the earthquake magnitude. Inversion results are stable against small variations in the frequency band and provide low data variances, i.e., a good fit between observed and modelled waveform traces. The total frequency band used for our procedure ranges from 10 mHz to 29 mHz (periods of 35 s to 100 s). This enables us to determine focal mechanisms for earthquakes that were not derived previously by routine procedures of CMT or other agencies. As a case study, we determine focal mechanism solutions of 38 light to moderate magnitude earthquakes in eastern Africa between 1995 and 2002.
Centroid Moment Tensor Inversion in a 3D heterogeneous Earth: Application to the Australasian region
Hejrani, B.; Tkalcic, H.; Fichtner, A.
2015-12-01
radially anisotropic structure: new insights into present and past states of the Australasian upper mantle. Earth Planet. Sci. Lett. 290, 270-280. Hingee, M., Tkalčić, H., Fichtner A., Sambridge, M., 2011. Moment tensor inversion using a 3-D structural model: Applications for the Australian region, Geophys. J. Int., 184(2), 949-964.
Czech Academy of Sciences Publication Activity Database
Benetatos, C.; Málek, Jiří; Verga, F.
2013-01-01
Roč. 17, č. 2 (2013), s. 557-577 ISSN 1383-4649 Institutional support: RVO:67985891 Keywords : micro-earthquake * moment-tensor inversion * gas storage * ISOLA Subject RIV: DD - Geochemistry Impact factor: 1.386, year: 2013
CSIR Research Space (South Africa)
Linzer, LM
2002-03-01
Full Text Available could lie in the yield point of the pillar foundation. The aim of this project therefore was to use a moment tensor inversion technique to establish design criteria for the prediction of the yield point of stabilizing pillar/foundation system in deep...
2009-09-30
for earthquakes in southern California, Bull. Seism . Soc. Am. 94: 1748-1761. Liu, Q., and J. Tromp (2006). Finite-frequency kernels based on adjoint...2008a). Component-dependent Frechet sensitivity kernels and utility of three- component seismic records. Bull. Seism . Soc. Am. 98: doi.10.1785/0120070283...L., P. Chen, and T. H. Jordan (2006). Strain Green tensor, reciprocity, and their applications to seismic source and structure studies, Bull. Seism
Convers, Jaime; Custodio, Susana
2016-04-01
Rapid assessment of seismological parameters pertinent to the nucleation and rupture of earthquakes are now routinely calculated by local and regional seismic networks. With the increasing number of stations, fast data transmission, and advanced computer power, we can now go beyond accurate magnitude and epicentral locations, to rapid estimations of other higher-order earthquake parameters such as seismic moment tensor. Although an increased number of stations can minimize azimuthal gaps, it also increases computation time, and potentially introduces poor quality data that often leads to a lower the stability of automated inversions. In this presentation, we focus on moment tensor calculations for earthquakes occurring offshore the southwestern Iberian peninsula. The available regional seismic data in this region has a significant azimuthal gap that results from the geographical setting. In this case, increasing the number of data from stations spanning a small area (and at a small azimuthal angle) increases the calculation time without necessarily improving the accuracy of the inversion. Additionally, limited regional data coverage makes it imperative to exclude poor-quality data, as their negative effect on moment tensor inversions is often significant. In our work, we analyze methods to minimize the effects of large azimuthal gaps in a regional station coverage, of potential bias by uneven station distribution, and of poor data quality in moment tensor inversions obtained for earthquakes offshore the southwestern Iberian peninsula. We calculate moment tensors using the KIWI tools, and we implement different configurations of station-weighing, and cross-correlation of neighboring stations, with the aim of automatically estimating and selecting high-quality data, improving the accuracy of results, and reducing the computation time of moment tensor inversions. As the available recent intermediate-size events offshore the Iberian peninsula is limited due to the long
Planetary radar data inversion techniques improvement
Picardi, G.; Masdea, A.; Mastrogiuseppe, M.; Restano, M.; Seu, R.
2012-04-01
The planetary radar (e.g. MARSIS) data inversion is based on the selection of groups of stationary frames, within the area under investigation, that shall be statistically analyzed after suitable correction. The selection step includes the recovery of bad/poor data and the estimation of the geometrical surface and subsurface features; these feature shall be utilized in order to obtain data that are only dependent by the material nature of the inclusion, within the layer, and of the interface. This paper is addressed to the techniques used for the frames selection, recovery and their geometric estimation content. As first step, frames have been selected in Mars areas where the surface and subsurface have a physical optics behavior (i.e. quite flat); the surface flatness has been estimated according to a simulator based on MOLA (Mars Orbiter Laser Altimeter) data while the subsurface has been estimated taking into account the Doppler filters content (i.e. filter 0, +1, -1). Being the surface and subsurface quite flat only small geometric contribution have been estimated and used for correction of the received echoes. To perform this task surface and subsurface models have been developed, under the Kirchhoff approximation hypothesis, to be compared with the experimental data. A figure showing the different material nature of different areas of the Mars South Pole has been drawn. The discovery of areas with an high dielectric constant led geologists to analyze those areas with other instrument to confirm the results obtained by MARSIS. This paper outlines also the way out for future works in order to analyze more complex surface and subsurface scenarios where conditions for geometric optics or fractal can be present. In this case, it will be mandatory to develop a clutter cancellation technique to avoid the presence of false subsurface echoes generated by surface and subsurface features not immediately below the nadir direction of observation. It will be also necessary
Ford, S. R.; Dreger, D. S.; Walter, W. R.
2006-12-01
Seismic moment tensor analysis at regional distances commonly involves solving for the deviatoric moment tensor and decomposing it to characterize the tectonic earthquake source. The full seismic moment tensor solution can also recover the isotropic component of the seismic source, which is theoretically dominant in explosions and collapses, and present in volcanic events. Analysis of events with demonstrably significant isotropic energy can aid in understanding the source processes of volcanic and geothermal seismic events and the monitoring of nuclear explosions. Using a regional time-domain waveform inversion for the complete moment tensor we calculate the deviatoric and isotropic source components for several explosions at the Nevada Test Site (NTS) and earthquakes, collapses, and volcanic events in the surrounding region of the NTS (Western US). The events separate into specific populations according to their deviation from a pure double-couple and ratio of isotropic to deviatoric energy. The separation allows for anomalous event identification and discrimination of explosions, earthquakes, and collapses. Analysis of the source principal axes can characterize the regional stress field, and tectonic release due to explosions. Error in the moment tensor solutions and source parameters is also calculated. We investigate the sensitivity of the moment tensor solutions to Green's functions calculated with imperfect Earth models, inaccurate event locations, and data with a low signal-to-noise ratio. We also test the performance of the method under a range of recording conditions from excellent azimuthal coverage to cases of sparse coverage as might be expected for smaller events. This analysis will be used to determine the magnitude range where well-constrained solutions can be obtained.
Trimming and procrastination as inversion techniques
Backus, George E.
1996-12-01
By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.
2014-04-30
nodes in numerical methods, we adapt a multigrid/multilevel method ( Briggs , 1987) to solve the wave propagation and inversion problem (Figure 2...passed from coarse to fine grids, and vice versa. Approved for public release; distribution is unlimited. 3 multi-grid scheme ( Briggs , 1987...compressional and shear velocity in the Earth’s mantle, Geophys. J. Int. 153, pp. 443- 466. Antoun, T., D. Harris, T. Lay, S. C. Myers , M. E. Pasyanos
Partitioned Alternating Least Squares Technique for Canonical Polyadic Tensor Decomposition
Czech Academy of Sciences Publication Activity Database
Tichavský, Petr; Phan, A. H.; Cichocki, A.
2016-01-01
Roč. 23, č. 7 (2016), s. 993-997 ISSN 1070-9908 R&D Projects: GA ČR(CZ) GA14-13713S Institutional support: RVO:67985556 Keywords : canonical polyadic decomposition * PARAFAC * tensor decomposition Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 2.528, year: 2016 http://library.utia.cas.cz/separaty/2016/SI/tichavsky-0460710.pdf
DEFF Research Database (Denmark)
Donner, Stefanie; Krüger, Frank; Rössler, Dirk
2014-01-01
In this study, we suggest a novel approach for the retrieval of regional moment tensors for earthquakes with small to moderate magnitudes. The first modification is the combined inversion of broadband and short‐period waveform data. The broadband waveforms are inverted in a frequency range suitable.......1). In this area, several factors exacerbate the difficulty of performing inversion for moment tensors, for example, a heterogeneous station network and large azimuthal gaps. We have demonstrated that our approach supplies reliable moment tensors when inversion from broadband data alone fails. In one case, we...... successfully retrieved a stable solution from short‐period waveform data alone. Thus, our approach enables successful determination of seismic moment tensors wherever a sparse network of broadband stations has thus far prevented it....
Jia, Z.; Ni, S.; Zhan, Z.
2016-12-01
Rapid and accurate determination of full moment tensors plays an important role in seismic source studies. We developed a joint inversion method for full moment tensors that combines both local and teleseismic waveform data. This method, called "gCAPjoint", which is based on the CAP method, enables time shift for synthetics, thus is more robust to inaccuracies in velocity models. Meantime, this method uses both local full waveforms and teleseismic body waves, thus provides enhanced coverage of azimuth and take-off angles of seismic waves, which are critical in constraining focal mechanism and depth. As a case study, we applied the method to two moderate-size intermediate-depth earthquakes (Mw6.3 and Mw6.6) in Hindu Kush. These two earthquakes share very close centroid locations, but the retrieved moment tensors of them are very different. While one event is essentially a pure double-couple thrust earthquake, the other event shows focal mechanism dominated by CLVD component, which can potentially be attributed to multiple double couple sub-events. Such difference for these two events suggests complex faulting geometries in the source region.
Long-Lived Inverse Chirp Signals from Core-Collapse in Massive Scalar-Tensor Gravity.
Sperhake, Ulrich; Moore, Christopher J; Rosca, Roxana; Agathos, Michalis; Gerosa, Davide; Ott, Christian D
2017-11-17
This Letter considers stellar core collapse in massive scalar-tensor theories of gravity. The presence of a mass term for the scalar field allows for dramatic increases in the radiated gravitational wave signal. There are several potential smoking gun signatures of a departure from general relativity associated with this process. These signatures could show up within existing LIGO-Virgo searches.
Shen, Weisen
2016-11-24
Using receiver functions, Rayleigh wave phase velocity dispersion determined from ambient noise and teleseismic earthquakes, and Rayleigh wave horizontal to vertical ground motion amplitude ratios from earthquakes observed across the PLUTONS seismic array, we construct a one-dimensional (1-D) S-wave velocity (Vs) seismic model with uncertainties for Uturuncu volcano, Bolivia, located in the central Andes and overlying the eastward-subducting Nazca plate. We find a fast upper crustal lid placed upon a low-velocity zone (LVZ) in the mid-crust. By incorporating all three types of measurements with complimentary sensitivity, we also explore the average density and Vp/Vs (ratio of P-wave to S-wave velocity) structures beneath the young silicic volcanic field. We observe slightly higher Vp/Vs and a decrease in density near the LVZ, which implies a dacitic source of the partially molten magma body. We exploit the impact of the 1-D model on full moment tensor inversion for the two largest local earthquakes recorded (both magnitude ∼3), demonstrating that the 1-D model influences the waveform fits and the estimated source type for the full moment tensor. Our 1-D model can serve as a robust starting point for future efforts to determine a three-dimensional velocity model for Uturuncu volcano.
Energy Technology Data Exchange (ETDEWEB)
Krapez, J.C. [Office National d' Etudes et de Recherches Aerospatiales (ONERA), Dept. Mecanique du solide et de l' Endommagement, 92 - Chatillon (France); Dubernard, A.; Stachowiak, H. [Universite d' Artois, Lab. d' Artois de Mecanique et Habitat, equipe Materiaux Thermique Instrumentation, 62 - Bethune (France)] (and others)
2000-07-01
This congress, on thermology, took place at Lyon in France, the 15-17 may 2000 with a presentation of 143 papers on the recent researches and specialized discussions. The talks published in this book are sorted out in ten thema. One of the thema concerns the experimental and inverse technics and the data processing. Seventeen talks are presented. They cover the domain of the nondestructive testing of temperature and diffusivity, many studies on the photothermal radiometry and inverse problems as the development of an inverse heat conduction method applied to the interaction flame/wall. This section presents also two papers applied to the energy conservation, one in the buildings sector with the feasibility of a method to separate thermal exchanges by convection and by radiation, the other one to measure the temperature of fuel droplets injected in a combustion chamber. (A.L.B.)
A conditioning technique for matrix inversion for Wilson fermions
International Nuclear Information System (INIS)
DeGrand, T.A.
1988-01-01
I report a simple technique for conditioning conjugate gradient or conjugate residue matrix inversion as applied to the lattice gauge theory problem of computing the propagator of Wilson fermions. One form of the technique provides about a factor of three speedup over an unconditioned algorithm while running at the same speed as an unconditioned algorithm. I illustrate the method as it is applied to a conjugate residue algorithm. (orig.)
Li, Jonathan Y; Middleton, Dana M; Chen, Steven; White, Leonard; Ellinwood, N Matthew; Dickson, Patricia; Vite, Charles; Bradbury, Allison; Provenzale, James M
2017-08-01
Purpose We describe a novel technique for measuring diffusion tensor imaging metrics in the canine brain. We hypothesized that a standard method for region of interest placement could be developed that is highly reproducible, with less than 10% difference in measurements between raters. Methods Two sets of canine brains (three seven-week-old full-brains and two 17-week-old single hemispheres) were scanned ex-vivo on a 7T small-animal magnetic resonance imaging system. Strict region of interest placement criteria were developed and then used by two raters to independently measure diffusion tensor imaging metrics within four different white-matter regions within each specimen. Average values of fractional anisotropy, radial diffusivity, and the three eigenvalues (λ1, λ2, and λ3) within each region in each specimen overall and within each individual image slice were compared between raters by calculating the percentage difference between raters for each metric. Results The mean percentage difference between raters for all diffusion tensor imaging metrics when pooled by each region and specimen was 1.44% (range: 0.01-5.17%). The mean percentage difference between raters for all diffusion tensor imaging metrics when compared by individual image slice was 2.23% (range: 0.75-4.58%) per hemisphere. Conclusion Our results indicate that the technique described is highly reproducible, even when applied to canine specimens of differing age, morphology, and image resolution. We propose this technique for future studies of diffusion tensor imaging analysis in canine brains and for cross-sectional and longitudinal studies of canine brain models of human central nervous system disease.
A New MHD-assisted Stokes Inversion Technique
Riethmüller, T. L.; Solanki, S. K.; Barthol, P.; Gandorfer, A.; Gizon, L.; Hirzberger, J.; van Noort, M.; Blanco Rodríguez, J.; Del Toro Iniesta, J. C.; Orozco Suárez, D.; Schmidt, W.; Martínez Pillet, V.; Knölker, M.
2017-03-01
We present a new method of Stokes inversion of spectropolarimetric data and evaluate it by taking the example of a Sunrise/IMaX observation. An archive of synthetic Stokes profiles is obtained by the spectral synthesis of state-of-the-art magnetohydrodynamics (MHD) simulations and a realistic degradation to the level of the observed data. The definition of a merit function allows the archive to be searched for the synthetic Stokes profiles that best match the observed profiles. In contrast to traditional Stokes inversion codes, which solve the Unno-Rachkovsky equations for the polarized radiative transfer numerically and fit the Stokes profiles iteratively, the new technique provides the full set of atmospheric parameters. This gives us the ability to start an MHD simulation that takes the inversion result as an initial condition. After a relaxation process of half an hour solar time we obtain physically consistent MHD data sets with a target similar to the observation. The new MHD simulation is used to repeat the method in a second iteration, which further improves the match between observation and simulation, resulting in a factor of 2.2 lower mean {χ }2 value. One advantage of the new technique is that it provides the physical parameters on a geometrical height scale. It constitutes a first step toward inversions that give results consistent with the MHD equations.
Formalev, V. F.; Kolesnik, S. A.
2017-11-01
The authors are the first to present a closed procedure for numerical solution of inverse coefficient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identification, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coefficient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed.
Compartmentalization of the Coso East Flank geothermal field imaged by 3-D full-tensor MT inversion
Lindsey, Nathaniel J.; Kaven, Joern; Davatzes, Nicholas C.; Newman, Gregory A.
2017-01-01
Previous magnetotelluric (MT) studies of the high-temperature Coso geothermal system in California identified a subvertical feature of low resistivity (2–5 Ohm m) and appreciable lateral extent (>1 km) in the producing zone of the East Flank field. However, these models could not reproduce gross 3-D effects in the recorded data. We perform 3-D full-tensor inversion and retrieve a resistivity model that out-performs previous 2-D and 3-D off-diagonal models in terms of its fit to the complete 3-D MT data set as well as the degree of modelling bias. Inclusion of secondary Zxx and Zyy data components leads to a robust east-dip (60†) to the previously identified conductive East Flank reservoir feature, which correlates strongly with recently mapped surface faults, downhole well temperatures, 3-D seismic reflection data, and local microseismicity. We perform synthetic forward modelling to test the best-fit dip of this conductor using the response at a nearby MT station. We interpret the dipping conductor as a fractured and fluidized compartment, which is structurally controlled by an unmapped blind East Flank fault zone.
Compartmentalization of the Coso East Flank geothermal field imaged by 3-D full-tensor MT inversion
Lindsey, Nathaniel J.; Kaven, Joern Ole; Davatzes, Nicholas; Newman, Gregory A.
2017-02-01
Previous magnetotelluric (MT) studies of the high-temperature Coso geothermal system in California identified a subvertical feature of low resistivity (2-5 Ohm m) and appreciable lateral extent (>1 km) in the producing zone of the East Flank field. However, these models could not reproduce gross 3-D effects in the recorded data. We perform 3-D full-tensor inversion and retrieve a resistivity model that out-performs previous 2-D and 3-D off-diagonal models in terms of its fit to the complete 3-D MT data set as well as the degree of modelling bias. Inclusion of secondary Zxx and Zyy data components leads to a robust east-dip (60†) to the previously identified conductive East Flank reservoir feature, which correlates strongly with recently mapped surface faults, downhole well temperatures, 3-D seismic reflection data, and local microseismicity. We perform synthetic forward modelling to test the best-fit dip of this conductor using the response at a nearby MT station. We interpret the dipping conductor as a fractured and fluidized compartment, which is structurally controlled by an unmapped blind East Flank fault zone.
Hoy, Andrew R; Kecskemeti, Steven R; Alexander, Andrew L
2015-12-01
White matter tractography reconstructions using conventional diffusion tensor imaging (DTI) near cerebrospinal fluid (CSF) spaces are often adversely affected by CSF partial volume effects (PVEs). This study evaluates the ability of free water elimination (FWE) DTI methods to minimize the PVE of CSF for deterministic tractography applications. Ten healthy individuals were scanned with "traditional," FLAIR (fluid-attenuated inversion recovery), and FWE DTI scans. The fornix, corpus callosum, and cingulum bundles were reconstructed using deterministic tractography. The FWE DTI scan was performed twice to separately match total acquisition time (long FWE) and number of measurements (encoding directions, short FWE) to the FLAIR and "traditional" DTI scans. PVE resolution was determined based on reconstructed tract volume. All reconstructions underwent blinded review for anatomical correctness, symmetry, and completeness. Reconstructions of the fornix demonstrated that the FWE and FLAIR scans produce more complete, anatomically plausible reconstructions than "traditional" DTI. Additionally, the tract reconstructions using FWE-DTI were significantly larger than when FLAIR was used with DTI (P acquisitions did not significantly (P ≥ 0.31) differ from one another for any of the reconstructed tracts. The FWE diffusion model overcomes CSF PVE without the time, SNR, and volumetric coverage penalties inherent to FLAIR DTI. © 2015 Wiley Periodicals, Inc.
Gu, Chen; Marzouk, Youssef M.; Toksöz, M. Nafi
2018-03-01
Small earthquakes occur due to natural tectonic motions and are induced by oil and gas production processes. In many oil/gas fields and hydrofracking processes, induced earthquakes result from fluid extraction or injection. The locations and source mechanisms of these earthquakes provide valuable information about the reservoirs. Analysis of induced seismic events has mostly assumed a double-couple source mechanism. However, recent studies have shown a non-negligible percentage of non-double-couple components of source moment tensors in hydraulic fracturing events, assuming a full moment tensor source mechanism. Without uncertainty quantification of the moment tensor solution, it is difficult to determine the reliability of these source models. This study develops a Bayesian method to perform waveform-based full moment tensor inversion and uncertainty quantification for induced seismic events, accounting for both location and velocity model uncertainties. We conduct tests with synthetic events to validate the method, and then apply our newly developed Bayesian inversion approach to real induced seismicity in an oil/gas field in the sultanate of Oman—determining the uncertainties in the source mechanism and in the location of that event.
Böhm, Karl-Heinz; Auer, Alexander A; Espig, Mike
2016-06-28
In this proof-of-principle study, we apply tensor decomposition techniques to the Full Configuration Interaction (FCI) wavefunction in order to approximate the wavefunction parameters efficiently and to reduce the overall computational effort. For this purpose, the wavefunction ansatz is formulated in an occupation number vector representation that ensures antisymmetry. If the canonical product format tensor decomposition is then applied, the Hamiltonian and the wavefunction can be cast into a multilinear product form. As a consequence, the number of wavefunction parameters does not scale to the power of the number of particles (or orbitals) but depends on the rank of the approximation and linearly on the number of particles. The degree of approximation can be controlled by a single threshold for the rank reduction procedure required in the algorithm. We demonstrate that using this approximation, the FCI Hamiltonian matrix can be stored with N(5) scaling. The error of the approximation that is introduced is below Millihartree for a threshold of ϵ = 10(-4) and no convergence problems are observed solving the FCI equations iteratively in the new format. While promising conceptually, all effort of the algorithm is shifted to the required rank reduction procedure after the contraction of the Hamiltonian with the coefficient tensor. At the current state, this crucial step is the bottleneck of our approach and even for an optimistic estimate, the algorithm scales beyond N(10) and future work has to be directed towards reduction-free algorithms.
Mock, A.; Korlacki, R.; Knight, S.; Schubert, M.
2018-04-01
We determine the frequency dependence of the four independent Cartesian tensor elements of the dielectric function for monoclinic symmetry Y2SiO5 using generalized spectroscopic ellipsometry from 40-1200 cm-1. Three different crystal cuts, each perpendicular to a principle axis, are investigated. We apply our recently described augmentation of lattice anharmonicity onto the eigendielectric displacement vector summation approach [A. Mock et al., Phys. Rev. B 95, 165202 (2017), 10.1103/PhysRevB.95.165202], and we present and demonstrate the application of an eigendielectric displacement loss vector summation approach with anharmonic broadening. We obtain an excellent match between all measured and model-calculated dielectric function tensor elements and all dielectric loss function tensor elements. We obtain 23 Au and 22 Bu symmetry long-wavelength active transverse and longitudinal optical mode parameters including their eigenvector orientation within the monoclinic lattice. We perform density functional theory calculations and obtain 23 Au symmetry and 22 Bu transverse and longitudinal optical mode parameters and their orientation within the monoclinic lattice. We compare our results from ellipsometry and density functional theory and find excellent agreement. We also determine the static and above reststrahlen spectral range dielectric tensor values and find a recently derived generalization of the Lyddane-Sachs-Teller relation for polar phonons in monoclinic symmetry materials satisfied [M. Schubert, Phys Rev. Lett. 117, 215502 (2016), 10.1103/PhysRevLett.117.215502].
SQUIDs and inverse problem techniques in nondestructive evaluation of metals
Bruno, A C
2001-01-01
Superconducting Quantum Interference Devices coupled to gradiometers were used to defect flaws in metals. We detected flaws in aluminium samples carrying current, measuring fields at lift-off distances up to one order of magnitude larger than the size of the flaw. Configured as a susceptometer we detected surface-braking flaws in steel samples, measuring the distortion on the applied magnetic field. We also used spatial filtering techniques to enhance the visualization of the magnetic field due to the flaws. In order to assess its severity, we used the generalized inverse method and singular value decomposition to reconstruct small spherical inclusions in steel. In addition, finite elements and optimization techniques were used to image complex shaped flaws.
Stokes Inversion Techniques for the SOLIS-VSM
Henney, C. J.; Keller, C. U.; Jones, H. P.; SOLIS Team
2002-05-01
The Vector Spectromagnetograph (VSM) instrument of the Synoptic Optical Long-term Investigations of the Sun (SOLIS) project will begin operation in 2002 and provide a 25 year record of synoptic solar observations. The 50-cm aperture VSM will provide daily full-disk photospheric vector and high sensitivity longitudinal magnetograms. In addition, the VSM will produce daily full-disk chormospheric longitudinal magnetograms, along with 1083 nm equivalent width images. Current data transmission and storage resources are such that the reduction of VSM data will be performed at the observing site on Kitt Peak. Reduced data products will be transmitted via a DS3 link from Kitt Peak to the National Solar Observatory's digital archive in Tucson. During a typical observing day, three full-disk photospheric vector magnetograms will be available over the web in two stages: first, as a ``quick-look'' product within 10 minutes of data acquisition, and then as a full Milne-Eddington (ME) inversion product within 24 hours of each observation. The quick-look parameters will include estimates of the magnetic field strength, azimuth and inclination based on Auer, Heasley, House (1977, Solar Physics 55, p. 47). The high-precision vector products will be determined with the High Altitude Observatory ME inversion technique implemented by Skumanich and Lites (1987, ApJ, 322, p.473). The flexible design of the VSM data handling system can incorporate future improvements under consideration (e.g., principal component analysis). However, since the original Stokes profiles observed will not be archived, a retrospective reduction of VSM data will not be possible. Quick-look and full ME inversion results are compared using simulated VSM Stokes profile data based on Kitt Peak Vacuum Telescope magnetograms. This research was supported in part by the Office of Naval Research Grant N00014-91-J-1040.
A technique for measurement of vector and tensor polarization in solid spin one polarized targets
Energy Technology Data Exchange (ETDEWEB)
Kielhorn, W.F.
1991-06-01
Vector and tensor polarizations are explicitly defined and used to characterize the polarization states of spin one polarized targets, and a technique for extracting these polarizations from nuclear magnetic resonance (NMR) data is developed. This technique is independent of assumptions about spin temperature, but assumes the target's crystal structure induces a quadrupole interaction with the spin one particles. Analysis of the NMR signals involves a computer curve fitting algorithm implemented with a fast Fourier transform method which speeds and simplifies curve fitting algorithms used previously. For accurate curve fitting, the NMR electronic circuit must be modeled by the fitting algorithm. Details of a circuit, its model, and data collected from this circuit are given for a solid deuterated ammonia target. 37 refs., 19 figs., 3 tabs.
A technique for measurement of vector and tensor polarization in solid spin one polarized targets
International Nuclear Information System (INIS)
Kielhorn, W.F.
1991-06-01
Vector and tensor polarizations are explicitly defined and used to characterize the polarization states of spin one polarized targets, and a technique for extracting these polarizations from nuclear magnetic resonance (NMR) data is developed. This technique is independent of assumptions about spin temperature, but assumes the target's crystal structure induces a quadrupole interaction with the spin one particles. Analysis of the NMR signals involves a computer curve fitting algorithm implemented with a fast Fourier transform method which speeds and simplifies curve fitting algorithms used previously. For accurate curve fitting, the NMR electronic circuit must be modeled by the fitting algorithm. Details of a circuit, its model, and data collected from this circuit are given for a solid deuterated ammonia target. 37 refs., 19 figs., 3 tabs
Wassermann, J.; Krüger, F.
2001-12-01
In the ongoing Indonesian-German MERAPI project the seismic signals at Merapi volcano are recorded continuously since July 1997 with a combined seismic network-array approach. With this network it was possible to record the seismicity before the onset of the eruption in July 1998 with a high dynamic and broad frequency range. The automatic standard analysis of the recorded seismic data before the first of two larger pyroclastic density flows emphasized the importance of a seismic swarm of VT-B type events in order to forecast the location of the newly formed lava lobe during this eruptive phase. To improve the location accuracy, we relocate these events using an extended cluster analysis technique. We first estimate the amount of events in three different seismic clusters. After this we estimate the relative onset times of all event combinations within one cluster using the SmoothedCOherencyTransform algorithm. Further we use the amplitude of the computed cross-correlation coefficients of each event-event waveform pair to further restrict our hypocenter constrain. In the final step we invert iteratively all estimated travel times, the relative travel times within the different arrays and the correlation coefficients in one single matrix. The resulting high precision hypocenter determination of the distinct clusters indicate a small source volume in the intersection of a old crater floor and the active part of Mt. Merapi. The high precision in hypocenter determination make a detailed analysis of the source mechanisms of these VTB events feasible. We use a point source full moment tensor inversion and simple source time functions to invert for the source mechanism. Greens functions are calculated with the reflectivity method and local 1D models based on refraction on different scales. The bias in the results due to not modelled topography and 3D-structure is estimated using a bootstrap approach.
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.
Parlangeau, Camille; Lacombe, Olivier; Schueller, Sylvie; Daniel, Jean-Marc
2018-01-01
The inversion of calcite twin data is a powerful tool to reconstruct paleostresses sustained by carbonate rocks during their geological history. Following Etchecopar's (1984) pioneering work, this study presents a new technique for the inversion of calcite twin data that reconstructs the 5 parameters of the deviatoric stress tensors from both monophase and polyphase twin datasets. The uncertainties in the parameters of the stress tensors reconstructed by this new technique are evaluated on numerically-generated datasets. The technique not only reliably defines the 5 parameters of the deviatoric stress tensor, but also reliably separates very close superimposed stress tensors (30° of difference in maximum principal stress orientation or switch between σ3 and σ2 axes). The technique is further shown to be robust to sampling bias and to slight variability in the critical resolved shear stress. Due to our still incomplete knowledge of the evolution of the critical resolved shear stress with grain size, our results show that it is recommended to analyze twin data subsets of homogeneous grain size to minimize possible errors, mainly those concerning differential stress values. The methodological uncertainty in principal stress orientations is about ± 10°; it is about ± 0.1 for the stress ratio. For differential stresses, the uncertainty is lower than ± 30%. Applying the technique to vein samples within Mesozoic limestones from the Monte Nero anticline (northern Apennines, Italy) demonstrates its ability to reliably detect and separate tectonically significant paleostress orientations and magnitudes from naturally deformed polyphase samples, hence to fingerprint the regional paleostresses of interest in tectonic studies.
Wéber, Zoltán
2016-01-01
We have successfully estimated the full moment tensors of 22 local earthquakes with local magnitude ranging from 1.2 to 4.8 that occurred in the Hungarian part of the Pannonian basin between 1995 and 2014. We used a probabilistic waveform inversion procedure that takes into account the effects of the random noise contained in the seismograms, the uncertainty of the hypocentre determined from arrival times and the inaccurate knowledge of the velocity structure, while estimating the error affecting the derived focal parameters. The applied probabilistic approach maps the posterior probability density functions (PPDFs) for both the hypocentral coordinates and the moment tensor components. The final estimates are given by the maximum likelihood points of the PPDFs, while solution uncertainties are presented by histogram plots. The estimated uncertainties in the moment tensor components are plotted on the focal sphere in such a way, that the significance of the double couple (DC), the compensated linear vector dipole (CLVD) and the isotropic (ISO) parts of the source can be assessed. We have shown that the applied waveform inversion method is equally suitable to recover the source mechanism for low-magnitude events using short-period local waveforms as well as for moderate-size earthquakes using long-period seismograms. The non-DC components of the retrieved focal mechanisms are statistically insignificant for all the analysed earthquakes. The negligible amount of the ISO component implies the tectonic nature of the investigated events. The moment tensor solutions reported by other agencies for five of the ML > 4 earthquakes studied in this paper are very similar to those calculated by the applied waveform inversion algorithm. We have found only strike-slip and thrust faulting events, giving further support to the hypothesis that the Pannonian basin is currently experiencing a compressional regime of deformation. The orientations of the obtained focal mechanisms are in
Löwer, Alexander; Junge, Andreas
2017-05-01
The influence of anisotropic conductivity structures on magnetotelluric transfer functions is not easy to analyse in its entire complexity. In this study, we investigate the spatial and frequency-dependent behaviour of phase tensors and tipper vectors above a 3D anisotropic conductivity anomaly. The anomaly consists of a simple cubic block embedded in a homogeneous half space. Using a 3D FD code, we compare an isotropic, 2 anisotropic models with an anisotropy factor of 10 and one anisotropic model with the anisotropy factor of 100. The results show characteristic differences between the isotropic and anisotropic cases. For the anisotropic anomalies, the tipper vectors are parallel over the entire area despite the 3D geometry of the anomalous body. The size of the tipper vectors depends on the position of the site relative to the anomaly's boundaries and the direction of the anisotropic strike. Above the anomalous anisotropic body, the main diagonal elements of the phase tensor show the well-known split. Outside the anomaly, the phase tensor principal axis rotates according to the site position in contrast to the constant tipper direction. The 3D inversion of the forward data using an isotropic 3D code (ModEM) yields a very good fit for all cases. Whereas the inversion result matches the isotropic model, wave-like structures with high conductivity contrast occur for the anisotropic models. These structures extend far beyond the extension of the original anomalous body. Thus, the study reveals important indications of the existence of anisotropic conductivity structures for observed magnetotelluric transfer functions.
TensorLy: Tensor Learning in Python
Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja
2016-01-01
Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning. Written in Python, it aims at following the same standard adopted by the main projects of the Python scientific community and fully integrating with these. It allows for fast and straightforward tensor d...
Reconstruction of sound speed profile through natural generalized inverse technique
Digital Repository Service at National Institute of Oceanography (India)
Murty, T.V.R.; Somayajulu, Y.K.; Murty, C.S.
An acoustic model has been developed for reconstruction of vertical sound speed in a near stable or stratified ocean. Generalized inverse method is utilised in the model development. Numerical experiments have been carried out to account...
3D reconstruction of tensors and vectors
Energy Technology Data Exchange (ETDEWEB)
Defrise, Michel; Gullberg, Grant T.
2005-02-17
Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields.
Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Caló, Marco
2017-04-01
Moment tensor inversions for intermediate and small earthquakes (M. < 4.5) are challenging as they principally excite relatively short period seismic waves that interact strongly with local heterogeneities. Incorporating detailed regional 3D velocity models permits obtaining realistic synthetic seismograms and recover the seismic source parameters these smaller events. Two 3D regional velocity models have recently been developed for Mexico, using surface waves and seismic noise tomography (Spica et al., 2016; Gaite et al., 2015), which could be used to model the waveforms of intermediate magnitud earthquakes in this region. Such models are parameterized as layered velocity profiles and for some of the profiles, the velocity difference between two layers are considerable. The "jump" in velocities between two layers is inconvenient for some methods and algorithms that calculate synthetic waveforms, in particular for the method that we are using, the spectral element method (SPECFEM3D GLOBE, Komatitsch y Tromp, 2000), when the mesh does not follow the layer boundaries. In order to make the velocity models more easily implementec in SPECFEM3D GLOBE it is neccesary to apply a homogenization algorithm (Capdeville et al., 2015) such that the (now anisotropic) layer velocities are smoothly varying with depth. In this work, we apply a homogenization algorithm to the regional velocity models in México for implementing them in SPECFEM3D GLOBE, calculate synthetic waveforms for intermediate-magnitude earthquakes in México and invert them for the seismic moment tensor.
Solving Inverse Kinematics – A New Approach to the Extended Jacobian Technique
Directory of Open Access Journals (Sweden)
M. Šoch
2005-01-01
Full Text Available This paper presents a brief summary of current numerical algorithms for solving the Inverse Kinematics problem. Then a new approach based on the Extended Jacobian technique is compared with the current Jacobian Inversion method. The presented method is intended for use in the field of computer graphics for animation of articulated structures.
Applying inversion techniques to understanding nucleus-nucleus potentials
International Nuclear Information System (INIS)
Mackintosh, R.S.; Cooper, S.G.
1996-01-01
The iterative-perturbative (IP) inversion algorithm makes it possible to determine, essentially uniquely, the complex potential, including spin-orbit component, for spin half particles given the elastic scattering S-matrix S lj . We here report an extension of the method to the determination of energy dependent potentials V(r,E) defined over an energy range for which S lj (E) are provided. This is a natural development of the IP algorithm which has previously been applied to fixed energy, fixed partial wave and the intermediate mixed case inversion. The energy range can include negative energies i.e. V(r,E) can reproduce bound state energies. It can also fit the effective range parameter for low energy scattering. We briefly define the classes of cases which can be studied, outline the IP method itself and briefly review the range of applications. We show the power of the method by presenting nucleon-αV(r,E) for S lj (E) derived from experiments above and below the inelastic threshold and relating them to V(r,E) inverted from S lj (E) for RGM theory. Reference is given to the code IMAGO which embodies the IP algorithm. (author). 38 refs., 5 figs., 4 tabs
Techniques and applications of skeletal muscle diffusion tensor imaging: A review
Oudeman, Jos; Nederveen, Aart J.; Strijkers, Gustav J.; Maas, Mario; Luijten, Peter R.; Froeling, Martijn
2016-01-01
Diffusion tensor imaging (DTI) is increasingly applied to study skeletal muscle physiology, anatomy, and pathology. The reason for this growing interest is that DTI offers unique, noninvasive, and potentially diagnostically relevant imaging readouts of skeletal muscle structure that are difficult or
Techniques and applications of skeletal muscle diffusion tensor imaging : A review
Oudeman, Jos; Nederveen, Aart J; Strijkers, Gustav J; Maas, Mario; Luijten, Peter R|info:eu-repo/dai/nl/304821098; Froeling, Martijn|info:eu-repo/dai/nl/413648354
Diffusion tensor imaging (DTI) is increasingly applied to study skeletal muscle physiology, anatomy, and pathology. The reason for this growing interest is that DTI offers unique, noninvasive, and potentially diagnostically relevant imaging readouts of skeletal muscle structure that are difficult or
Development of high energy resolution inverse photoemission technique
International Nuclear Information System (INIS)
Asakura, D.; Fujii, Y.; Mizokawa, T.
2004-01-01
Full text: It is highly important to study occupied and unoccupied electronic states in order to understand electronic properties of strongly correlated electron systems. Photoemission spectroscopy (PES) and inverse photoemission spectroscopy (IPES) are complementary to each other and very powerful experimental methods to study the electronic structure. While PES directly investigates the occupied states below the Fermi level, IPES observes the unoccupied states above it. Although the energy resolution of 2 meV has been achieved for PES, the energy resolution of IPES is still around 200 meV. The poor energy resolution of IPES considerably limits information of unoccupied states. In order to investigate unoccupied states of strongly correlated electron systems, we have designed and constructed a new IPES instrument based on two ideas: off-plane Eagle mounting of the optical system [1, 2] and dispersion matching between incoming electron and outgoing ultraviolet light. In the IPES system, a parallel plate electron analyzer is employed to give the energy dispersion to the incoming electron beam. The outgoing ultraviolet light is monochromatized by a concave grating. The sample, the grating, and the position sensitive detector are arranged in the off-plane Eagle mounting to achieve a good focusing of light. Ray-trace simulations have shown that the energy resolution of 20 meV is expected for the perfect dispersion matching. We will present the principle, mechanism, and current status of our IPES instrument
Hancher, M.
2017-12-01
Recent years have seen promising results from many research teams applying deep learning techniques to geospatial data processing. In that same timeframe, TensorFlow has emerged as the most popular framework for deep learning in general, and Google has assembled petabytes of Earth observation data from a wide variety of sources and made them available in analysis-ready form in the cloud through Google Earth Engine. Nevertheless, developing and applying deep learning to geospatial data at scale has been somewhat cumbersome to date. We present a new set of tools and techniques that simplify this process. Our approach combines the strengths of several underlying tools: TensorFlow for its expressive deep learning framework; Earth Engine for data management, preprocessing, postprocessing, and visualization; and other tools in Google Cloud Platform to train TensorFlow models at scale, perform additional custom parallel data processing, and drive the entire process from a single familiar Python development environment. These tools can be used to easily apply standard deep neural networks, convolutional neural networks, and other custom model architectures to a variety of geospatial data structures. We discuss our experiences applying these and related tools to a range of machine learning problems, including classic problems like cloud detection, building detection, land cover classification, as well as more novel problems like illegal fishing detection. Our improved tools will make it easier for geospatial data scientists to apply modern deep learning techniques to their own problems, and will also make it easier for machine learning researchers to advance the state of the art of those techniques.
Abbas, M. M.; Shapiro, G. L.; Allario, F.; Alvarez, J. M.
1981-01-01
A combination of two different techniques for the inversion of infrared laser heterodyne measurements of tenuous gases in the stratosphere by solar occulation is presented which incorporates the advantages of each technique. An experimental approach and inversion technique are developed which optimize the retrieval of concentration profiles by incorporating the onion peel collection scheme into the spectral inversion technique. A description of an infrared heterodyne spectrometer and the mode of observations for solar occulation measurement is presented, and the results of inversions of some synthetic ClO spectral lines corresponding to solar occulation limb-scans of the stratosphere are examined. A comparison between the new techniques and one of the current techniques indicates that considerable improvement in the accuracy of the retrieved profiles can be achieved. It is found that noise affects the accuracy of both techniques but not in a straightforward manner since there is interaction between the noise level, noise propagation through inversion, and the number of scans leading to an optimum retrieval.
Whalley, Matthew S.
1991-01-01
An inverse solution technique for determining the maximum maneuvering performance of a helicopter using smooth, pilotlike control inputs is presented. Also described is a pilot simulation experiment performed to investigate the accuracy of the solution resulting from this technique. The maneuverability and agility capability of the helicopter math model was varied by varying the pitch and roll damping, the maximum pitch and roll rate, and the maximum load-factor capability. Three maneuvers were investigated: a 180-deg turn, a longitudinal pop-up, and a lateral jink. The inverse solution technique yielded accurate predictions of pilot-in-the-loop maneuvering performance for two of the three maneuvers.
A Highly Efficient Shannon Wavelet Inverse Fourier Technique for Pricing European Options
Ortiz-Gracia, Luis; Oosterlee, C.W.
2016-01-01
In the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of sharp quantitative error
A highly efficient Shannon wavelet inverse Fourier technique for pricing European options
L. Ortiz Gracia (Luis); C.W. Oosterlee (Cornelis)
2016-01-01
htmlabstractIn the search for robust, accurate, and highly efficient financial option valuation techniques, we here present the SWIFT method (Shannon wavelets inverse Fourier technique), based on Shannon wavelets. SWIFT comes with control over approximation errors made by means of
International Nuclear Information System (INIS)
Castaneda M, V. H.; Martinez B, M. R.; Solis S, L. O.; Castaneda M, R.; Leon P, A. A.; Hernandez P, C. F.; Espinoza G, J. G.; Ortiz R, J. M.; Vega C, H. R.; Mendez, R.; Gallego, E.; Sousa L, M. A.
2016-10-01
The Taguchi methodology has proved to be highly efficient to solve inverse problems, in which the values of some parameters of the model must be obtained from the observed data. There are intrinsic mathematical characteristics that make a problem known as inverse. Inverse problems appear in many branches of science, engineering and mathematics. To solve this type of problem, researches have used different techniques. Recently, the use of techniques based on Artificial Intelligence technology is being explored by researches. This paper presents the use of a software tool based on artificial neural networks of generalized regression in the solution of inverse problems with application in high energy physics, specifically in the solution of the problem of neutron spectrometry. To solve this problem we use a software tool developed in the Mat Lab programming environment, which employs a friendly user interface, intuitive and easy to use for the user. This computational tool solves the inverse problem involved in the reconstruction of the neutron spectrum based on measurements made with a Bonner spheres spectrometric system. Introducing this information, the neural network is able to reconstruct the neutron spectrum with high performance and generalization capability. The tool allows that the end user does not require great training or technical knowledge in development and/or use of software, so it facilitates the use of the program for the resolution of inverse problems that are in several areas of knowledge. The techniques of Artificial Intelligence present singular veracity to solve inverse problems, given the characteristics of artificial neural networks and their network topology, therefore, the tool developed has been very useful, since the results generated by the Artificial Neural Network require few time in comparison to other techniques and are correct results comparing them with the actual data of the experiment. (Author)
Inversion of SAR data in active volcanic areas by optimization techniques
Directory of Open Access Journals (Sweden)
G. Nunnari
2005-01-01
Full Text Available The inversion problem concerns the identification of parameters of a volcanic source causing observable changes in ground deformation data recorded in volcanic areas. In particular, this paper deals with the inversion of ground deformation measured by using SAR (Synthetic Aperture Radar interferometry and an inversion approach formulated in terms of an optimization problem is proposed. Based on this inversion scheme, it is shown that the problem of inverting ground deformation data in terms of a single source, of Mogi or Okada type, is numerically well conditioned. In the paper, two case studies of inverting actual SAR data recorded on Mt. Etna during eruptions occurring in 1998 and 2001 are investigated, showing the suitability of the proposed technique.
A comparative study of surface waves inversion techniques at strong motion recording sites in Greece
Panagiotis C. Pelekis,; Savvaidis, Alexandros; Kayen, Robert E.; Vlachakis, Vasileios S.; Athanasopoulos, George A.
2015-01-01
Surface wave method was used for the estimation of Vs vs depth profile at 10 strong motion stations in Greece. The dispersion data were obtained by SASW method, utilizing a pair of electromechanical harmonic-wave source (shakers) or a random source (drop weight). In this study, three inversion techniques were used a) a recently proposed Simplified Inversion Method (SIM), b) an inversion technique based on a neighborhood algorithm (NA) which allows the incorporation of a priori information regarding the subsurface structure parameters, and c) Occam's inversion algorithm. For each site constant value of Poisson's ratio was assumed (ν=0.4) since the objective of the current study is the comparison of the three inversion schemes regardless the uncertainties resulting due to the lack of geotechnical data. A penalty function was introduced to quantify the deviations of the derived Vs profiles. The Vs models are compared as of Vs(z), Vs30 and EC8 soil category, in order to show the insignificance of the existing variations. The comparison results showed that the average variation of SIM profiles is 9% and 4.9% comparing with NA and Occam's profiles respectively whilst the average difference of Vs30 values obtained from SIM is 7.4% and 5.0% compared with NA and Occam's.
International Nuclear Information System (INIS)
Rashad, A.R.M.
1966-01-01
This paper presents a new technique for accurately measuring the scalar and tensor a. c. electrical conductivity of plasmas used in a.c. MHD generators and accelerators. The device consists of a cylindrical plasma column (region 1) moving with a regulated axial velocity. An external magnetic field structure is located outside the plasma, and separated from it by a thin annular homogeneous medium (region 2). The magnetic field system is designed to produce in the plasma a constant axial magnetic field.and a travelling wave magnetic field. The coils of the latter magnetic field system are excited so as to produce radial, azimuthal or axial magnetic field components alone or any combination of them as required. This field design permits measuring the scalar and tensor components of the plasma conductivity directly. The theory of the apparatus is presented analytically in detail. The plasma is described by an accurate set of hydrodynamic-Maxwell equations. The plasma induced magnetic field, pressure variations and velocity profiles are taken into consideration. In region 2, the Maxwell equations are solved exactly. The boundary conditions between regions 1 and 2 are described accurately, and for the boundary conditions between region 2 and the magnetic field system a Fourier synthesis of the travelling magnetic field components is done. An accurate expression for the plasma conductivity shows that o depends upon the Alfvén speed, the slip between the plasma axial speed and the phase velocity of the applied travelling wave magnetic field, the frequency, the plasma current density, the components of the applied travelling wave magnetic field system and the device's cylindrical configuration. The design features are chosen so as to simulate the actual operating conditions of travelling magnetic wave a.c. plasma accelerators and generators. It permits accurate measurements of the plasma conductivity in these specific applications and the results are compared to those of
Metric Tensor Vs. Metric Extensor
Fernández, V. V.; Moya, A. M.; Rodrigues Jr, Waldyr A.
2002-01-01
In this paper we give a comparison between the formulation of the concept of metric for a real vector space of finite dimension in terms of \\emph{tensors} and \\emph{extensors}. A nice property of metric extensors is that they have inverses which are also themselves metric extensors. This property is not shared by metric tensors because tensors do \\emph{not} have inverses. We relate the definition of determinant of a metric extensor with the classical determinant of the corresponding matrix as...
X-ray strain tensor imaging: FEM simulation and experiments with a micro-CT.
Kim, Jae G; Park, So E; Lee, Soo Y
2014-01-01
In tissue elasticity imaging, measuring the strain tensor components is necessary to solve the inverse problem. However, it is impractical to measure all the tensor components in ultrasound or MRI elastography because of their anisotropic spatial resolution. The objective of this study is to compute 3D strain tensor maps from the 3D CT images of a tissue-mimicking phantom. We took 3D micro-CT images of the phantom twice with applying two different mechanical compressions to it. Applying the 3D image correlation technique to the CT images under different compression, we computed 3D displacement vectors and strain tensors at every pixel. To evaluate the accuracy of the strain tensor maps, we made a 3D FEM model of the phantom, and we computed strain tensor maps through FEM simulation. Experimentally obtained strain tensor maps showed similar patterns to the FEM-simulated ones in visual inspection. The correlation between the strain tensor maps obtained from the experiment and the FEM simulation ranges from 0.03 to 0.93. Even though the strain tensor maps suffer from high level noise, we expect the x-ray strain tensor imaging may find some biomedical applications such as malignant tissue characterization and stress analysis inside the tissues.
Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique
Gou, Kun
2012-07-01
An inverse spectral method is developed for recovering a spatially inhomogeneous shear modulus for soft tissue. The study is motivated by a novel use of the intravascular ultrasound technique to image arteries. The arterial wall is idealized as a nonlinear isotropic cylindrical hyperelastic body. A boundary value problem is formulated for the response of the arterial wall within a specific class of quasistatic deformations reflective of the response due to imposed blood pressure. Subsequently, a boundary value problem is developed via an asymptotic construction modeling intravascular ultrasound interrogation which generates small amplitude, high frequency time harmonic vibrations superimposed on the static finite deformation. This leads to a system of second order ordinary Sturm-Liouville boundary value problems that are then employed to reconstruct the shear modulus through a nonlinear inverse spectral technique. Numerical examples are demonstrated to show the viability of the method. © 2012 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Choi, C. Y.
1997-01-01
A geometrical inverse heat conduction problem is solved for the infrared scanning cavity detection by the boundary element method using minimal energy technique. By minimizing the kinetic energy of temperature field, boundary element equations are converted to the quadratic programming problem. A hypothetical inner boundary is defined such that the actual cavity is located interior to the domain. Temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error of surface temperature obtained by infrared scanning, and then boundary element analysis is performed for the position of an unknown boundary (cavity). Cavity detection algorithm is provided, and the effects of minimal energy technique on the inverse solution method are investigated by means of numerical analysis
Kimes, D. S.
1983-01-01
A physically based sensor response model of a row crop was used as the mathematical framework from which several inversion strategies were tested for extracting row structure information and component temperatures using a series of sensor view angles. The technique was evaluated on ground-based radiometric thermal infrared data of a cotton row crop that covered 48 percent of the ground in the vertical projection. The results showed that the accuracies of the predicted row heights and widths, vegetation temperatures, and soil temperatures of the cotton row crop were on the order of 5 cm, 1 deg, and 2 deg C, respectively. The inversion techniques can be applied to directional sensor data from aircraft platforms and even space platforms if the effects of atmospheric absorption and emission can be corrected. In theory, such inversion techniques can be applied to a wide variety of vegetation types and thus can have significant implications for remote sensing research and applications in disciplines that deal with incomplete vegetation canopies.
Directory of Open Access Journals (Sweden)
Marcelo Ribeiro dos Santos
2014-01-01
Full Text Available During machining energy is transformed into heat due to plastic deformation of the workpiece surface and friction between tool and workpiece. High temperatures are generated in the region of the cutting edge, which have a very important influence on wear rate of the cutting tool and on tool life. This work proposes the estimation of heat flux at the chip-tool interface using inverse techniques. Factors which influence the temperature distribution at the AISI M32C high speed steel tool rake face during machining of a ABNT 12L14 steel workpiece were also investigated. The temperature distribution was predicted using finite volume elements. A transient 3D numerical code using irregular and nonstaggered mesh was developed to solve the nonlinear heat diffusion equation. To validate the software, experimental tests were made. The inverse problem was solved using the function specification method. Heat fluxes at the tool-workpiece interface were estimated using inverse problems techniques and experimental temperatures. Tests were performed to study the effect of cutting parameters on cutting edge temperature. The results were compared with those of the tool-work thermocouple technique and a fair agreement was obtained.
Tensor surgery and tensor rank
M. Christandl (Matthias); J. Zuiddam (Jeroen)
2018-01-01
textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices
A gEUD-based inverse planning technique for HDR prostate brachytherapy: Feasibility study
Energy Technology Data Exchange (ETDEWEB)
Giantsoudi, D. [Department of Radiological Sciences, University of Texas Health Sciences Center, San Antonio, Texas 78229 (United States); Department of Radiation Oncology, Francis H. Burr Proton Therapy Center, Boston, Massachusetts 02114 (United States); Baltas, D. [Department of Medical Physics and Engineering, Strahlenklinik, Klinikum Offenbach GmbH, 63069 Offenbach (Germany); Nuclear and Particle Physics Section, Physics Department, University of Athens, 15701 Athens (Greece); Karabis, A. [Pi-Medical Ltd., Athens 10676 (Greece); Mavroidis, P. [Department of Radiological Sciences, University of Texas Health Sciences Center, San Antonio, Texas 78299 and Department of Medical Radiation Physics, Karolinska Institutet and Stockholm University, 17176 (Sweden); Zamboglou, N.; Tselis, N. [Strahlenklinik, Klinikum Offenbach GmbH, 63069 Offenbach (Germany); Shi, C. [St. Vincent' s Medical Center, 2800 Main Street, Bridgeport, Connecticut 06606 (United States); Papanikolaou, N. [Department of Radiological Sciences, University of Texas Health Sciences Center, San Antonio, Texas 78299 (United States)
2013-04-15
Purpose: The purpose of this work was to study the feasibility of a new inverse planning technique based on the generalized equivalent uniform dose for image-guided high dose rate (HDR) prostate cancer brachytherapy in comparison to conventional dose-volume based optimization. Methods: The quality of 12 clinical HDR brachytherapy implants for prostate utilizing HIPO (Hybrid Inverse Planning Optimization) is compared with alternative plans, which were produced through inverse planning using the generalized equivalent uniform dose (gEUD). All the common dose-volume indices for the prostate and the organs at risk were considered together with radiobiological measures. The clinical effectiveness of the different dose distributions was investigated by comparing dose volume histogram and gEUD evaluators. Results: Our results demonstrate the feasibility of gEUD-based inverse planning in HDR brachytherapy implants for prostate. A statistically significant decrease in D{sub 10} or/and final gEUD values for the organs at risk (urethra, bladder, and rectum) was found while improving dose homogeneity or dose conformity of the target volume. Conclusions: Following the promising results of gEUD-based optimization in intensity modulated radiation therapy treatment optimization, as reported in the literature, the implementation of a similar model in HDR brachytherapy treatment plan optimization is suggested by this study. The potential of improved sparing of organs at risk was shown for various gEUD-based optimization parameter protocols, which indicates the ability of this method to adapt to the user's preferences.
Determining the metallicity of the solar envelope using seismic inversion techniques
Buldgen, G.; Salmon, S. J. A. J.; Noels, A.; Scuflaire, R.; Dupret, M. A.; Reese, D. R.
2017-11-01
The solar metallicity issue is a long-lasting problem of astrophysics, impacting multiple fields and still subject to debate and uncertainties. While spectroscopy has mostly been used to determine the solar heavy elements abundance, helioseismologists attempted providing a seismic determination of the metallicity in the solar convective envelope. However, the puzzle remains since two independent groups provided two radically different values for this crucial astrophysical parameter. We aim at providing an independent seismic measurement of the solar metallicity in the convective envelope. Our main goal is to help provide new information to break the current stalemate amongst seismic determinations of the solar heavy element abundance. We start by presenting the kernels, the inversion technique and the target function of the inversion we have developed. We then test our approach in multiple hare-and-hounds exercises to assess its reliability and accuracy. We then apply our technique to solar data using calibrated solar models and determine an interval of seismic measurements for the solar metallicity. We show that our inversion can indeed be used to estimate the solar metallicity thanks to our hare-and-hounds exercises. However, we also show that further dependencies in the physical ingredients of solar models lead to a low accuracy. Nevertheless, using various physical ingredients for our solar models, we determine metallicity values between 0.008 and 0.014.
Whiteside, Leo A
2014-02-01
Avulsion of the abductor muscles of the hip may cause severe limp and pain. Limited literature is available on treatment approaches for this problem, and each has shortcomings. This study describes a muscle transfer technique to treat complete irreparable avulsion of the hip abductor muscles and tendons. Ten adult cadaver specimens were dissected to determine nerve and blood supply point of entry in the gluteus maximus and tensor fascia lata (TFL) and evaluate the feasibility and safety of transferring these muscles to substitute for the gluteus medius and minimus. In this technique, the anterior portion of the gluteus maximus and the entire TFL are mobilized and transferred to the greater trochanter such that the muscle fiber direction of the transferred muscles closely matches that of the gluteus medius and minimus. Five patients (five hips) were treated for primary irreparable disruption of the hip abductor muscles using this technique between January 2008 and April 2011. All patients had severe or moderate pain, severe abductor limp, and positive Trendelenburg sign. Patients were evaluated for pain and function at a mean of 28 months (range, 18-60 months) after surgery. All patients could actively abduct 3 months postoperatively. At 1 year postoperatively, three patients had no hip pain, two had mild pain that did not limit their activity, three had no limp, and one had mild limp. One patient fell, fractured his greater trochanter, and has persistent limp and abduction weakness. The anterior portion of the gluteus maximus and the TFL can be transferred to the greater trochanter to substitute for abductor deficiency. In this small series, the surgical procedure was reproducible and effective; further studies with more patients and longer followup are needed to confirm this.
Directory of Open Access Journals (Sweden)
Andreas Hofmann
2017-10-01
Full Text Available In this study, micron-sized pored membranes, based on the co-polymer polyvinylidene difluoride hexafluoropropylene (PVdF-HFP were prepared via phase inversion techniques. The aim of the approach was to find less harmful and less toxic solvents to fabricate such films. Therefore, the Hansen solubility approach was used to identify safer and less toxic organic solvents for the phase inversion process, relative to present solvent mixtures, based on acetone, dimethyl formamide, dimethyl acetamide or methanol. With this approach, it was possible to identify cyclopentanone, ethylene glycol and benzyl alcohol as suitable solvents for the membrane preparation process. Physicochemical and mechanical properties were analyzed and compared, which revealed a uniform membrane structure through the cross section. Differences were observed at the top surface, in dependence of both preparation approaches, which are described in detail.
Fouda, Ahmed E.
differential TR. This technique provides real-time tracking and exhibits superior clutter rejection at minimal processing costs. It also exploits the distinctive features of time-reversal such as statistical stability and superresolution. Next, we develop an UWB inverse scattering technique for extended targets, with continuous permittivity and/or conductivity fluctuations, based on Bayesian compressive sensing. Bayesian inversion provides means for estimating the confidence level of the inversion, and for adaptively optimizing subsequent measurements. This technique is applied to a wide range of problems of practical interest such as underground crosshole sensing, medical imaging, and rough surface reconstruction. Finally, we develop new TR-based wireless communication techniques for UWB multiple-input single-output (MISO) and multiple-input multiple-output (MIMO) systems. We contrast relative strengths and limitations of those techniques for different scenarios of operation.
Directory of Open Access Journals (Sweden)
J. S. de Villiers
2014-10-01
Full Text Available This research focuses on the inversion of geomagnetic variation field measurement to obtain source currents in the ionosphere. During a geomagnetic disturbance, the ionospheric currents create magnetic field variations that induce geoelectric fields, which drive geomagnetically induced currents (GIC in power systems. These GIC may disturb the operation of power systems and cause damage to grounded power transformers. The geoelectric fields at any location of interest can be determined from the source currents in the ionosphere through a solution of the forward problem. Line currents running east–west along given surface position are postulated to exist at a certain height above the Earth's surface. This physical arrangement results in the fields on the ground having the magnetic north and down components, and the electric east component. Ionospheric currents are modelled by inverting Fourier integrals (over the wavenumber of elementary geomagnetic fields using the Levenberg–Marquardt technique. The output parameters of the inversion model are the current strength, height and surface position of the ionospheric current system. A ground conductivity structure with five layers from Quebec, Canada, based on the Layered-Earth model is used to obtain the complex skin depth at a given angular frequency. This paper presents preliminary and inversion results based on these structures and simulated geomagnetic fields. The results show some interesting features in the frequency domain. Model parameters obtained through inversion are within 2% of simulated values. This technique has applications for modelling the currents of electrojets at the equator and auroral regions, as well as currents in the magnetosphere.
International Nuclear Information System (INIS)
Kravtsov, Y.A.; Kravtsov, Y.A.; Chrzanowski, J.; Mazon, D.
2011-01-01
New procedure for plasma polarimetry data inversion is suggested, which fits two parameter knowledge-based plasma model to the measured parameters (azimuthal and ellipticity angles) of the polarization ellipse. The knowledge-based model is supposed to use the magnetic field and electron density profiles, obtained from magnetic measurements and LIDAR data on the Thomson scattering. In distinction to traditional polarimetry, polarization evolution along the ray is determined on the basis of angular variables technique (AVT). The paper contains a few examples of numerical solutions of these equations, which are applicable in conditions, when Faraday and Cotton-Mouton effects are simultaneously strong. (authors)
Energy Technology Data Exchange (ETDEWEB)
Kawamura, S. [Nippon Geophysical Prospecting Co. Ltd., Tokyo (Japan)
1996-10-01
Smoothness-constrained least-squares technique with ABIC minimization was applied to the inversion of phase velocity of surface waves during geophysical exploration, to confirm its usefulness. Since this study aimed mainly at the applicability of the technique, Love wave was used which is easier to treat theoretically than Rayleigh wave. Stable successive approximation solutions could be obtained by the repeated improvement of velocity model of S-wave, and an objective model with high reliability could be determined. While, for the inversion with simple minimization of the residuals squares sum, stable solutions could be obtained by the repeated improvement, but the judgment of convergence was very hard due to the smoothness-constraint, which might make the obtained model in a state of over-fitting. In this study, Love wave was used to examine the applicability of the smoothness-constrained least-squares technique with ABIC minimization. Applicability of this to Rayleigh wave will be investigated. 8 refs.
Source-jerk analysis using a semi-explicit inverse kinetic technique
International Nuclear Information System (INIS)
Spriggs, G.D.; Pederson, R.A.
1985-01-01
A method is proposed for measuring the effective reproduction factor, k, in subcritical systems. The method uses the transient response of a subcritical system to the sudden removal of an extraneous neutron source (i.e., a source jerk). The response is analyzed using an inverse kinetic technique that least-squares fits the exact analytical solution corresponding to a source-jerk transient as derived from the point-reactor model. It has been found that the technique can provide an accurate means of measuring k in systems that are close to critical (i.e., 0.95 < k < 1.0). As a system becomes more subcritical (i.e., k << 1.0) spatial effects can introduce significant biases depending on the source and detector positions. However, methods are available that can correct for these biases and, hence, can allow measuring subcriticality in systems with k as low as 0.5. 12 refs., 3 figs
Source-jerk analysis using a semi-explicit inverse kinetic technique
International Nuclear Information System (INIS)
Spriggs, G.D.; Pederson, R.A.
1985-01-01
A method is proposed for measuring the effective reproduction factor, k, in subcritical systems. The method uses the transient responses of a subcritical system to the sudden removal of an extraneous neutron source (i.e., a source jerk). The response is analyzed using an inverse kinetic technique that least-squares fits the exact analytical solution corresponding to a source-jerk transient as derived from the point-reactor model. It has been found that the technique can provide an accurate means of measuring k in systems that are close to critical (i.e., 0.95 < k < 1.0). As a system becomes more subcritical (i.e., k << 1.0) spatial effects can introduce significant biases depending on the source and detector positions. However, methods are available that can correct for these biases and, hence, can allow measuring subcriticality in systems with k as low as 0.5
The modified inverse hockey stick technique for adjuvant irradiation after mastectomy
International Nuclear Information System (INIS)
Kukolowicz, P.; Selerski, B.; Kuszewski, T.; Wieczorek, A.
2004-01-01
To present the technique of irradiation of post-mastectomy patients used in the Holycross Cancer Centre in Kielce.The paper presents a detailed description of the technique which is referred to as the 'modified inverse hockey stick technique (MIHS)'. The dosimetric characteristic of dose distribution for the MIHS technique is presented basing on dose distributions calculated for 40 patients. The measurements used to evaluate dose distribution included standard deviation of the dose in the Planning Target Volume (PTV) and the percentage of the PTV volume receiving a dose larger than 110% and smaller than 90%; the lung volume received at least 20 Gy (LV20) and the heart volume received at least 30 Gy (HV30). The distribution of the electron beam energy is also presented. The standard deviation of the dose in the PTV was approx. 10% in a majority of patients. About 12% of the PTV volume received a dose more than 10% smaller than intended and about 10% of the PTV volume received a dose more than 10% greater than intended. For patients irradiated on the left side of the chest wall the LV20 was always lesser than 25% and for patients irradiated on the right side of the chest wall - always less than 35%, except for one patient, in whom it reached 37%. The HV30 was always below 8%. The MIHS technique is a safe and reliable modality. The main advantages of the technique include very convenient and easily repeated positioning of the patient and small doses applied to the organs at risk. The individually calculated bolus plays an important role in diminishing the dose to the lung and heart. The disadvantages of the technique include poor dose homogeneity within the PTV and long matching lines of the electron and photon beams. (author)
Oishi, Masaki; Shinozaki, Tomohisa; Hara, Hikaru; Yamamoto, Kazunuki; Matsusue, Toshio; Bando, Hiroyuki
2018-05-01
The elliptical polarization dependence of the two-photon absorption coefficient β in InP has been measured by the extended Z-scan technique for thick materials in the wavelength range from 1640 to 1800 nm. The analytical formula of the Z-scan technique has been extended with consideration of multiple reflections. The Z-scan results have been fitted very well by the formula and β has been evaluated accurately. The three independent elements of the third-order nonlinear susceptibility tensor in InP have also been determined accurately from the elliptical polarization dependence of β.
Ismail, Zalikha; Kassim, Syara; Harun, Noor Aniza
2017-09-01
The application of biodegradable synthetic polymers become centre of attraction as the versatility structure of polymer itself fascinating with the fact that it can be employed into specific application and requirements. In this study, N-vinylpyrrolidone (NVP) monomer is utilized via inverse miniemulsion polymerization technique to develop aqueous-soluble polymer nanoparticles with lower toxicity. The effects of different molar ratio of water as polar disperse phase in inverse miniemulsion polymerization of poly(N-vinylpyrrolidone) (PNVP) towards their particle sizes, particle size distributions and morphology were discussed. The formation of PNVP nanoparticles was confirmed by Fourier transform infrared (FTIR) and the morphology was determined using scanning electron microscopy (SEM) and transmission electron microscope (TEM). The particle size of PNVP nanoparticles had mean diameters in the range of 100 - 300 nm depending on the reaction conditions, as measured by dynamic light scattering (DLS). The hydrophilic PNVP nanoparticles obtained were expected to be utilized in biological and medical application especially in drugs delivery as well as a new probe in vivo assessment.
Kamali, Arash; Zhang, Caroline C; Riascos, Roy F; Tandon, Nitin; Bonafante-Mejia, Eliana E; Patel, Rajan; Lincoln, John A; Rabiei, Pejman; Ocasio, Laura; Younes, Kyan; Hasan, Khader M
2018-03-27
The mammillary bodies as part of the hypothalamic nuclei are in the central limbic circuitry of the human brain. The mammillary bodies are shown to be directly or indirectly connected to the amygdala, hippocampus, and thalami as the major gray matter structures of the human limbic system. Although it is not primarily considered as part of the human limbic system, the thalamus is shown to be involved in many limbic functions of the human brain. The major direct connection of the thalami with the hypothalamic nuclei is known to be through the mammillothalamic tract. Given the crucial role of the mammillothalamic tracts in memory functions, diffusion tensor imaging may be helpful in better visualizing the surgical anatomy of this pathway noninvasively. This study aimed to investigate the utility of high spatial resolution diffusion tensor tractography for mapping the trajectory of the mammillothalamic tract in the human brain. Fifteen healthy adults were studied after obtaining written informed consent. We used high spatial resolution diffusion tensor imaging data at 3.0 T. We delineated, for the first time, the detailed trajectory of the mammillothalamic tract of the human brain using deterministic diffusion tensor tractography.
Eigenproblem solution by a combined Sturm sequence and inverse iteration technique.
Gupta, K. K.
1973-01-01
Description of an efficient and numerically stable algorithm, along with a complete listing of the associated computer program, developed for the accurate computation of specified roots and associated vectors of the eigenvalue problem Aq = lambda Bq with band symmetric A and B, B being also positive-definite. The desired roots are first isolated by the Sturm sequence procedure; then a special variant of the inverse iteration technique is applied for the individual determination of each root along with its vector. The algorithm fully exploits the banded form of relevant matrices, and the associated program written in FORTRAN V for the JPL UNIVAC 1108 computer proves to be most significantly economical in comparison to similar existing procedures. The program may be conveniently utilized for the efficient solution of practical engineering problems, involving free vibration and buckling analysis of structures. Results of such analyses are presented for representative structures.
Inversion of SAR data in active volcanic areas by optimization techniques
Nunnari, G.; Puglisi, G.; Guglielmino, F.
2005-01-01
International audience; The inversion problem concerns the identification of parameters of a volcanic source causing observable changes in ground deformation data recorded in volcanic areas. In particular, this paper deals with the inversion of ground deformation measured by using SAR (Synthetic Aperture Radar) interferometry and an inversion approach formulated in terms of an optimization problem is proposed. Based on this inversion scheme, it is shown that the problem of inverting ground de...
Robust tensor estimation in diffusion tensor imaging
Maximov, Ivan I.; Grinberg, Farida; Jon Shah, N.
2011-12-01
The signal response measured in diffusion tensor imaging is subject to detrimental influences caused by noise. Noise fields arise due to various contributions such as thermal and physiological noise and sources related to the hardware imperfection. As a result, diffusion tensors estimated by different linear and non-linear least squares methods in absence of a proper noise correction tend to be substantially corrupted. In this work, we propose an advanced tensor estimation approach based on the least median squares method of the robust statistics. Both constrained and non-constrained versions of the method are considered. The performance of the developed algorithm is compared to that of the conventional least squares method and of the alternative robust methods proposed in the literature. Two examples of simulated diffusion attenuations and experimental in vivo diffusion data sets were used as a basis for comparison. The robust algorithms were shown to be advantageous compared to the least squares method in the cases where elimination of the outliers is desirable. Additionally, the constraints were applied in order to prevent generation of the non-positive definite tensors and reduce related artefacts in the maps of fractional anisotropy. The developed method can potentially be exploited also by other MR techniques where a robust regression or outlier localisation is required.
Digital Repository Service at National Institute of Oceanography (India)
Murty, T.V.R.; Rao, M.M.M.; Sadhuram, Y.; Sridevi, B.; Maneesha, K.; SujithKumar, S.; Prasanna, P.L.; Murthy, K.S.R.
of Bengal during south-west monsoon season and explore possibility to reconstruct the acoustic profile of the eddy by Stochastic Inverse Technique. A simulation experiment on forward and inverse problems for observed sound velocity perturbation field has...
Directory of Open Access Journals (Sweden)
Wenz Frederik
2009-09-01
Full Text Available Abstract Background Parameter optimization in the process of inverse treatment planning for intensity modulated radiation therapy (IMRT is mainly conducted by human planners in order to create a plan with the desired dose distribution. To automate this tedious process, an artificial intelligence (AI guided system was developed and examined. Methods The AI system can automatically accomplish the optimization process based on prior knowledge operated by several fuzzy inference systems (FIS. Prior knowledge, which was collected from human planners during their routine trial-and-error process of inverse planning, has first to be "translated" to a set of "if-then rules" for driving the FISs. To minimize subjective error which could be costly during this knowledge acquisition process, it is necessary to find a quantitative method to automatically accomplish this task. A well-developed machine learning technique, based on an adaptive neuro fuzzy inference system (ANFIS, was introduced in this study. Based on this approach, prior knowledge of a fuzzy inference system can be quickly collected from observation data (clinically used constraints. The learning capability and the accuracy of such a system were analyzed by generating multiple FIS from data collected from an AI system with known settings and rules. Results Multiple analyses showed good agreements of FIS and ANFIS according to rules (error of the output values of ANFIS based on the training data from FIS of 7.77 ± 0.02% and membership functions (3.9%, thus suggesting that the "behavior" of an FIS can be propagated to another, based on this process. The initial experimental results on a clinical case showed that ANFIS is an effective way to build FIS from practical data, and analysis of ANFIS and FIS with clinical cases showed good planning results provided by ANFIS. OAR volumes encompassed by characteristic percentages of isodoses were reduced by a mean of between 0 and 28%. Conclusion The
Stieler, Florian; Yan, Hui; Lohr, Frank; Wenz, Frederik; Yin, Fang-Fang
2009-09-25
Parameter optimization in the process of inverse treatment planning for intensity modulated radiation therapy (IMRT) is mainly conducted by human planners in order to create a plan with the desired dose distribution. To automate this tedious process, an artificial intelligence (AI) guided system was developed and examined. The AI system can automatically accomplish the optimization process based on prior knowledge operated by several fuzzy inference systems (FIS). Prior knowledge, which was collected from human planners during their routine trial-and-error process of inverse planning, has first to be "translated" to a set of "if-then rules" for driving the FISs. To minimize subjective error which could be costly during this knowledge acquisition process, it is necessary to find a quantitative method to automatically accomplish this task. A well-developed machine learning technique, based on an adaptive neuro fuzzy inference system (ANFIS), was introduced in this study. Based on this approach, prior knowledge of a fuzzy inference system can be quickly collected from observation data (clinically used constraints). The learning capability and the accuracy of such a system were analyzed by generating multiple FIS from data collected from an AI system with known settings and rules. Multiple analyses showed good agreements of FIS and ANFIS according to rules (error of the output values of ANFIS based on the training data from FIS of 7.77 +/- 0.02%) and membership functions (3.9%), thus suggesting that the "behavior" of an FIS can be propagated to another, based on this process. The initial experimental results on a clinical case showed that ANFIS is an effective way to build FIS from practical data, and analysis of ANFIS and FIS with clinical cases showed good planning results provided by ANFIS. OAR volumes encompassed by characteristic percentages of isodoses were reduced by a mean of between 0 and 28%. The study demonstrated a feasible way to automatically perform
International Nuclear Information System (INIS)
Stieler, Florian; Yan, Hui; Lohr, Frank; Wenz, Frederik; Yin, Fang-Fang
2009-01-01
Parameter optimization in the process of inverse treatment planning for intensity modulated radiation therapy (IMRT) is mainly conducted by human planners in order to create a plan with the desired dose distribution. To automate this tedious process, an artificial intelligence (AI) guided system was developed and examined. The AI system can automatically accomplish the optimization process based on prior knowledge operated by several fuzzy inference systems (FIS). Prior knowledge, which was collected from human planners during their routine trial-and-error process of inverse planning, has first to be 'translated' to a set of 'if-then rules' for driving the FISs. To minimize subjective error which could be costly during this knowledge acquisition process, it is necessary to find a quantitative method to automatically accomplish this task. A well-developed machine learning technique, based on an adaptive neuro fuzzy inference system (ANFIS), was introduced in this study. Based on this approach, prior knowledge of a fuzzy inference system can be quickly collected from observation data (clinically used constraints). The learning capability and the accuracy of such a system were analyzed by generating multiple FIS from data collected from an AI system with known settings and rules. Multiple analyses showed good agreements of FIS and ANFIS according to rules (error of the output values of ANFIS based on the training data from FIS of 7.77 ± 0.02%) and membership functions (3.9%), thus suggesting that the 'behavior' of an FIS can be propagated to another, based on this process. The initial experimental results on a clinical case showed that ANFIS is an effective way to build FIS from practical data, and analysis of ANFIS and FIS with clinical cases showed good planning results provided by ANFIS. OAR volumes encompassed by characteristic percentages of isodoses were reduced by a mean of between 0 and 28%. The study demonstrated a feasible way
Revisiting the time domain induced polarization technique, from linearization to inversion
Kang, S.; Oldenburg, D.
2015-12-01
The induced polarization (IP) technique has been successful in mineral exploration, particularly for finding disseminated sulphide or porphyry deposits, but also in helping solve geotechnical and environmental problems. Electrical induced polarization (EIP) surveys use grounded electrodes and take measurements of the electric field while the current is both "on" and "off". Currently, 2D and 3D inversions of EIP data are generally carried out by first finding a background conductivity from the asymptotic "on-time" measurements. The DC resistivity problem is then linearized about that conductivity to obtain a linear relationship between the off-time data and the "pseudo-chargeability". The distribution of pseudo-chargeability in the earth is then interpreted within the context of the initial geoscience problem pursued. Despite its success, the current EIP implementation does have challenges. A fundamental assumption, that there is no electromagnetic induction (EM) effect, breaks down when the background is conductive. This is especially problematic in regions having conductive overburden. EM induction complicates, and sometimes overwhelms, the IP signal. To ameliorate this effect, we estimate the inductive signal, subtract it from the "off-time" data and invert the resultant IP data using the linearized formulation. We carefully examine the conditions under which this works. We also investigate the potential alterations to the linearized sensitivity function that are needed to allow a linearized inversion to be carried out. Inversions of EIP data recover a "chargeability" but this is not a uniquely defined quantity. There are multiple definitions of this property because there are a diverse number of ways in which an IP datum is defined. In time domain IP surveys, the data might be mV/V or a time-integrated voltage with units of ms. In reality however, data from an EIP survey have many time channels and each one can be inverted separately to produce a chargeability
Directory of Open Access Journals (Sweden)
M. Flórez Méndez
2008-03-01
Full Text Available Presentamos una técnica personal que hemos denominado "Face Up", empleando suturas de poliéster dispuestas a través de incisiones mínimas, que permite lograr un rápido efecto lifting para el rejuvenecimiento de la cara. Nuestra experiencia se basa en los resultados del tratamiento de 600 pacientes intervenidos entre septiembre de 2002 y marzo de 2006. Los resultados fueron evidentes desde el postoperatorio inmediato. Las zonas tratadas quedaron firmemente ligadas al plano de anclaje dentro del cuero cabelludo. Se trataron frente, sienes, cejas, mejillas, pómulos, cuello y regiones paramaxilares adyacentes a la zona de los músculos maseteros y bucinadores, que ceden por efecto de la gravedad y del envejecimiento. En las zonas seleccionadas, las suturas se deslizan a través del tejido subcutáneo, donde la aponeurosis de los músculos implicados está firmemente ligada a este plano. Para la intervención se emplea una aguja, llamada "Demax" (aguja biselada con punta en los dos extremos provista de un orificio en uno de ellos para arrastrar la sutura que se inserta desde la región cefálica temporal hasta el punto distal de la zona de la ptosis, donde se efectúa un cambio de sentido formando un bucle que produce el segundo anclaje del tejido, evitando su desplazamiento. La sutura retorna al punto de entrada para su anudamiento al periostio a fin de conseguir y mantener el levantamiento. Las complicaciones recogidas fueron hematomas leves, equímosis, edema, e infección localizada en la incisión de ingreso y nudo de la sutura. En las evaluaciones efectuadas a corto y largo plazo, los resultados fueron buenos con un índice de satisfacción alto por parte de las pacientes y del médico. La técnica "Face Up" es mínimamente traumática y aporta una alternativa al lifting quirúrgico tradicional para el tratamiento del envejecimiento y de la flacidez faciales.We present a personal technique called "Face Up", using polyester sutures
Directory of Open Access Journals (Sweden)
K. Verbist
2009-10-01
Full Text Available In arid and semi-arid zones, runoff harvesting techniques are often applied to increase the water retention and infiltration on steep slopes. Additionally, they act as an erosion control measure to reduce land degradation hazards. Nevertheless, few efforts were observed to quantify the water harvesting processes of these techniques and to evaluate their efficiency. In this study, a combination of detailed field measurements and modelling with the HYDRUS-2D software package was used to visualize the effect of an infiltration trench on the soil water content of a bare slope in northern Chile. Rainfall simulations were combined with high spatial and temporal resolution water content monitoring in order to construct a useful dataset for inverse modelling purposes. Initial estimates of model parameters were provided by detailed infiltration and soil water retention measurements. Four different measurement techniques were used to determine the saturated hydraulic conductivity (K_{sat} independently. The tension infiltrometer measurements proved a good estimator of the K_{sat} value and a proxy for those measured under simulated rainfall, whereas the pressure and constant head well infiltrometer measurements showed larger variability. Six different parameter optimization functions were tested as a combination of soil-water content, water retention and cumulative infiltration data. Infiltration data alone proved insufficient to obtain high model accuracy, due to large scatter on the data set, and water content data were needed to obtain optimized effective parameter sets with small confidence intervals. Correlation between the observed soil water content and the simulated values was as high as R^{2}=0.93 for ten selected observation points used in the model calibration phase, with overall correlation for the 22 observation points equal to 0.85. The model results indicate that the infiltration trench has a
Czech Academy of Sciences Publication Activity Database
Jechumtálová, Zuzana; Bulant, P.
2014-01-01
Roč. 18, č. 3 (2014), s. 511-531 ISSN 1383-4649 R&D Projects: GA ČR GAP210/10/1728 EU Projects: European Commission(XE) 230669 - AIM Institutional support: RVO:67985530 Keywords : ray tracing * 1-D and 3-D velocity models * earthquake mechanism * amplitude inversion * Dobrá Voda earthquakes Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 1.386, year: 2014
Moran, S.C.
2003-01-01
The volcanological significance of seismicity within Katmai National Park has been debated since the first seismograph was installed in 1963, in part because Katmai seismicity consists almost entirely of high-frequency earthquakes that can be caused by a wide range of processes. I investigate this issue by determining 140 well-constrained first-motion fault-plane solutions for shallow (depth regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a stress field characterized by horizontally oriented ??1 and ??3 axes, with ??1 rotated slightly (12??) relative to the NUVELIA subduction vector, indicating that these earthquakes are occurring in response to regional tectonic forces. On the other hand, stress tensors for earthquake clusters beneath several Katmai cluster volcanoes have vertically oriented ??1 axes, indicating that these events are occuring in response to local, not regional, processes. At Martin-Mageik, vertically oriented ??1 is most consistent with failure under edifice loading conditions in conjunction with localized pore pressure increases associated with hydrothermal circulation cells. At Trident-Novarupta, it is consistent with a number of possible models, including occurence along fractures formed during the 1912 eruption that now serve as horizontal conduits for migrating fluids and/or volatiles from nearby degassing and cooling magma bodies. At Mount Katmai, it is most consistent with continued seismicity along ring-fracture systems created in the 1912 eruption, perhaps enhanced by circulating hydrothermal fluids and/or seepage from the caldera-filling lake.
Inverse kinematics technique for the study of fission-fragment isotopic yields at GANIL energies
International Nuclear Information System (INIS)
Delaune, O.
2012-01-01
The characteristics of the fission-products distributions result of dynamical and quantum properties of the deformation process of the fissioning nucleus. These distributions have also an interest for the conception of new nuclear power plants or for the transmutation of the nuclear wastes. Up to now, our understanding of the nuclear fission remains restricted because of experimental limitations. In particular, yields of the heavy fission products are difficult to get with precision. In this work, an innovative experimental technique is presented. It is based on the use of inverse kinematics coupled to the use of a spectrometer, in which a 238 U beam at 6 or 24 A MeV impinges on light targets. Several actinides, from 238 U to 250 Cf, are produced by transfer or fusion reactions, with an excitation energy ranges from ten to few hundreds MeV depending on the reaction and the beam energy. The fission fragments of these actinides are detected by the VAMOS spectrometer or the LISE separator. The isotopic yields of fission products are completely measured for different fissioning systems. The neutron excess of the fragments is used to characterise the isotopic distributions. Its evolution with excitation energy gives important insights on the mechanisms of the compound-nucleus formation and its deexcitation. Neutron excess is also used to determine the multiplicity of neutrons evaporated by the fragments. The role of the proton and neutron shell effects into the formation of fission fragments is also discussed. (author) [fr
Objective quantification of perturbations produced with a piecewise PV inversion technique
Fita, L.; Romero, R.; Ramis, C.
2007-11-01
PV inversion techniques have been widely used in numerical studies of severe weather cases. These techniques can be applied as a way to study the sensitivity of the responsible meteorological system to changes in the initial conditions of the simulations. Dynamical effects of a collection of atmospheric features involved in the evolution of the system can be isolated. However, aspects, such as the definition of the atmospheric features or the amount of change in the initial conditions, are largely case-dependent and/or subjectively defined. An objective way to calculate the modification of the initial fields is proposed to alleviate this problem. The perturbations are quantified as the mean absolute variations of the total energy between the original and modified fields, and an unique energy variation value is fixed for all the perturbations derived from different PV anomalies. Thus, PV features of different dimensions and characteristics introduce the same net modification of the initial conditions from an energetic point of view. The devised quantification method is applied to study the high impact weather case of 9-11 November 2001 in the Western Mediterranean basin, when a deep and strong cyclone was formed. On the Balearic Islands 4 people died, and sustained winds of 30 ms-1 and precipitation higher than 200 mm/24 h were recorded. Moreover, 700 people died in Algiers during the first phase of the event. The sensitivities to perturbations in the initial conditions of a deep upper level trough, the anticyclonic system related to the North Atlantic high and the surface thermal anomaly related to the baroclinicity of the environment are determined. Results reveal a high influence of the upper level trough and the surface thermal anomaly and a minor role of the North Atlantic high during the genesis of the cyclone.
Objective quantification of perturbations produced with a piecewise PV inversion technique
Directory of Open Access Journals (Sweden)
L. Fita
2007-11-01
Full Text Available PV inversion techniques have been widely used in numerical studies of severe weather cases. These techniques can be applied as a way to study the sensitivity of the responsible meteorological system to changes in the initial conditions of the simulations. Dynamical effects of a collection of atmospheric features involved in the evolution of the system can be isolated. However, aspects, such as the definition of the atmospheric features or the amount of change in the initial conditions, are largely case-dependent and/or subjectively defined. An objective way to calculate the modification of the initial fields is proposed to alleviate this problem. The perturbations are quantified as the mean absolute variations of the total energy between the original and modified fields, and an unique energy variation value is fixed for all the perturbations derived from different PV anomalies. Thus, PV features of different dimensions and characteristics introduce the same net modification of the initial conditions from an energetic point of view. The devised quantification method is applied to study the high impact weather case of 9–11 November 2001 in the Western Mediterranean basin, when a deep and strong cyclone was formed. On the Balearic Islands 4 people died, and sustained winds of 30 ms−1 and precipitation higher than 200 mm/24 h were recorded. Moreover, 700 people died in Algiers during the first phase of the event. The sensitivities to perturbations in the initial conditions of a deep upper level trough, the anticyclonic system related to the North Atlantic high and the surface thermal anomaly related to the baroclinicity of the environment are determined. Results reveal a high influence of the upper level trough and the surface thermal anomaly and a minor role of the North Atlantic high during the genesis of the cyclone.
Tucker Tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander
2018-03-09
In this work, we describe advanced numerical tools for working with multivariate functions and for the analysis of large data sets. These tools will drastically reduce the required computing time and the storage cost, and, therefore, will allow us to consider much larger data sets or finer meshes. Covariance matrices are crucial in spatio-temporal statistical tasks, but are often very expensive to compute and store, especially in 3D. Therefore, we approximate covariance functions by cheap surrogates in a low-rank tensor format. We apply the Tucker and canonical tensor decompositions to a family of Matern- and Slater-type functions with varying parameters and demonstrate numerically that their approximations exhibit exponentially fast convergence. We prove the exponential convergence of the Tucker and canonical approximations in tensor rank parameters. Several statistical operations are performed in this low-rank tensor format, including evaluating the conditional covariance matrix, spatially averaged estimation variance, computing a quadratic form, determinant, trace, loglikelihood, inverse, and Cholesky decomposition of a large covariance matrix. Low-rank tensor approximations reduce the computing and storage costs essentially. For example, the storage cost is reduced from an exponential O(n^d) to a linear scaling O(drn), where d is the spatial dimension, n is the number of mesh points in one direction, and r is the tensor rank. Prerequisites for applicability of the proposed techniques are the assumptions that the data, locations, and measurements lie on a tensor (axes-parallel) grid and that the covariance function depends on a distance, ||x-y||.
International Nuclear Information System (INIS)
Chen, Z.G.; Hindmarsh, T.; Li, T.Q.
2001-01-01
Purpose: To quantify age-related changes of the average diffusion coefficient value in normal adult brain using orientation-independent diffusion tensor trace mapping and to address the methodological influences on diffusion quantification. Material and Methods: Fifty-four normal subjects (aged 20-79 years) were studied on a 1.5-T whole-body MR medical unit using a diffusion-weighted single-shot echo-planar imaging technique. Orientation-independent diffusion tensor trace maps were constructed for each subject using diffusion-weighted MR measurements in four different directions using a tetrahedral gradient combination pattern. The global average (including cerebral spinal fluid) and the tissue average of diffusion coefficients in adult brains were determined by analyzing the diffusion coefficient distribution histogram for the entire brain. Methodological influences on the measured diffusion coefficient were also investigated by comparing the results obtained using different experimental settings. Results: Both global and tissue averages of the diffusion coefficient are significantly correlated with age (p<0.03). The global average of the diffusion coefficient increases 3% per decade after the age of 40, whereas the increase in the tissue average of diffusion coefficient is about 1% per decade. Experimental settings for self-diffusion measurements, such as data acquisition methods and number of b-values, can slightly influence the statistical distribution histogram of the diffusion tensor trace and its average value. Conclusion: Increased average diffusion coefficient in adult brains with aging are consistent with findings regarding structural changes in the brain that have been associated with aging. The study also demonstrates that it is desirable to use the same experimental parameters for diffusion coefficient quantification when comparing between different subjects and groups of interest
Tuning of Block Copolymer Membrane Morphology through Water Induced Phase Inversion Technique
Madhavan, Poornima
2016-06-01
surface and pore walls of PS-b-P4VP block copolymer membranes and then investigated the biocidal activity of the silver nanoparticles grown membranes. Finally, a novel photoresponsive nanostructured triblock copolymer membranes were developed by phase inversion technique. In addition, the photoresponsive behavior on irradiation with light and their membrane flux and retention properties were studied.
International Nuclear Information System (INIS)
Sorokin, O.M.
1984-01-01
The way to obtain energy distribution of electron emission using the method of the inverse function, in which two amplitude pulse analyzers are Used, has been improved. One of them, the flowsheet of which is somewhat changed, is used to obtain the inverse function in the regime of tracing search of channel address of the set ordinate of voltammetric characteristics distribution, and second one - to obtain amplitude distribution of standard pulses, discriminated according to the law of inverse voltammetric characteristics. The distribution function as to the energy which is obtained as a result can have a statistical error of 1-2% at emission currents up to 10-100 electron/s
Aboud, Essam; El-shrief, Adel; Alqahtani, Faisal; Mogren, Saad
2017-04-01
On 19 May, 2009, an earthquake of magnitude (M=5.4) shocked the most volcanically active recent basaltic fields, Luynnier volcanic field, northwestern Saudi Arabia. This event was the largest recorded one since long time ago. Government evacuated the surrounding residents around the epicenter for over 3 months away from any future volcanic activity. The seismic event caused damages to buildings in the village around the epicenter and resulted in surface fissure trending in NNW-SSE direction with about 8 km length. Seismologists from Saudi Geological Survey (SGS) worked out on locating the epicenter and the cause of this earthquake. They collected seismic data from Saudi Geological Surveys Station Network as well as installed broadband seismic stations around the region of the earthquake. They finally concluded that the main cause of the M=5.4 event is dike intrusion at depth of about 5 km (not reached to the surface). In the present work, we carried out detailed ground/airborne gravity survey around the surficial fissure to image the subsurface volcanic structure where about 380 gravity stations were recorded covering the main fissure in an area of 600 km2. Gravity data was analyzed using CET edge detection tools and 3D inversion technique. The results revealed that, there is a magma chamber/body beneath the surface at 5-20 km depth and the main reason for the M=5.4 earthquake is tectonic settings of the Red Sea. Additionally, the area is characterized by set of faults trending in NW direction, parallel to the Red Sea, and most of the volcanic cones were located on faults/contacts implying that, they are structurally controlled. The 8-km surficial crack is extended SE underneath the surface.
International Nuclear Information System (INIS)
Baker, Benjamin A.; Imel, George R.
2013-06-01
This paper presents continuous and discrete equations for the propagation of uncertainty applied to inverse kinetics and shows that the uncertainty of a measurement can be minimized by the proper choice of frequency from the perturbing reactivity waveform. (authors)
Digital Repository Service at National Institute of Oceanography (India)
Rao, M.M.M.; Murty, T.V.R.; Murthy, K.S.R.; Vasudeva, R.Y.
has been performed to build Generalised Inverse Operator (GIO) and it is operated on the observed anomaly with reference to the calculated anomaly to update model parameters. Data and model resolution matrices are computed to check the correctness...
The application of neural network techniques to magnetic and optical inverse problems
International Nuclear Information System (INIS)
Jones, H.V.
2000-12-01
The processing power of the computer has increased at unimaginable rates over the last few decades. However, even today's fastest computer can take several hours to find solutions to some mathematical problems; and there are instances where a high powered supercomputer may be impractical, with the need for near instant solutions just as important (such as in an on-line testing system). This led us to believe that such complex problems could be solved using a novel approach, whereby the system would have prior knowledge about the expected solutions through a process of learning. One method of approaching this kind of problem is through the use of machine learning. Just as a human can be trained and is able to learn from past experiences, a machine is can do just the same. This is the concept of neural networks. The research which was conducted involves the investigation of various neural network techniques, and their applicability to solve some known complex inverse problems in the field of magnetic and optical recording. In some cases a comparison is also made to more conventional methods of solving the problems, from which it was possible to outline some key advantages of using a neural network approach. We initially investigated the application of neural networks to transverse susceptibility data in order to determine anisotropy distributions. This area of research is proving to be very important, as it gives us information about the switching field distribution, which then determines the minimum transition width achievable in a medium, and affects the overwrite characteristics of the media. Secondly, we investigated a similar situation, but applied to an optical problem. This involved the determination of important compact disc parameters from the diffraction pattern of a laser from a disc. This technique was then intended for use in an on-line testing system. Finally we investigated another area of neural networks with the analysis of magnetisation maps and
Energy Technology Data Exchange (ETDEWEB)
Parchevsky, K. V.; Zhao, J.; Hartlep, T.; Kosovichev, A. G., E-mail: akosovichev@solar.stanford.edu [Stanford University, HEPL, Stanford, CA 94305 (United States)
2014-04-10
We performed three-dimensional numerical simulations of the solar surface acoustic wave field for the quiet Sun and for three models with different localized sound-speed perturbations in the interior with deep, shallow, and two-layer structures. We used the simulated data generated by two solar acoustics codes that employ the same standard solar model as a background model, but utilize different integration techniques and different models of stochastic wave excitation. Acoustic travel times were measured using a time-distance helioseismology technique, and compared with predictions from ray theory frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the helioseismic theory for sound-speed perturbations, and for the measurement procedure with and without phase-speed filtering of the oscillation signals. This testing verifies the whole measuring-filtering-inversion procedure for static sound-speed anomalies with small amplitude inside the Sun outside regions of strong magnetic field. It is shown that the phase-speed filtering, frequently used to extract specific wave packets and improve the signal-to-noise ratio, does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the perturbation models in all cases. Due to its smoothing nature, the inversion procedure may overestimate sound-speed variations in regions with sharp gradients of the sound-speed profile.
International Nuclear Information System (INIS)
Parchevsky, K. V.; Zhao, J.; Hartlep, T.; Kosovichev, A. G.
2014-01-01
We performed three-dimensional numerical simulations of the solar surface acoustic wave field for the quiet Sun and for three models with different localized sound-speed perturbations in the interior with deep, shallow, and two-layer structures. We used the simulated data generated by two solar acoustics codes that employ the same standard solar model as a background model, but utilize different integration techniques and different models of stochastic wave excitation. Acoustic travel times were measured using a time-distance helioseismology technique, and compared with predictions from ray theory frequently used for helioseismic travel-time inversions. It is found that the measured travel-time shifts agree well with the helioseismic theory for sound-speed perturbations, and for the measurement procedure with and without phase-speed filtering of the oscillation signals. This testing verifies the whole measuring-filtering-inversion procedure for static sound-speed anomalies with small amplitude inside the Sun outside regions of strong magnetic field. It is shown that the phase-speed filtering, frequently used to extract specific wave packets and improve the signal-to-noise ratio, does not introduce significant systematic errors. Results of the sound-speed inversion procedure show good agreement with the perturbation models in all cases. Due to its smoothing nature, the inversion procedure may overestimate sound-speed variations in regions with sharp gradients of the sound-speed profile.
Wang, Feiyan; Petter Morten, Jan; Spitzer, Klaus
2018-01-01
In this paper, we present a recently developed anisotropic three-dimensional (3-D) inversion framework for interpreting controlled-source electromagnetic (CSEM) data in the frequency domain. The framework integrates a high-order finite element forward operator and a Gauss-Newton inversion algorithm. Conductivity constraints are applied using a parameter transformation. We discretize the continuous forward and inverse problems on unstructured grids for a flexible treatment of arbitrarily complex geometries. Moreover, an unstructured mesh is more desirable in comparison to a single rectilinear mesh for multi-source problems because local grid refinement will not significantly influence the mesh density outside the region of interest. The non-uniform spatial discretization facilitates parameterization of the inversion domain at a suitable scale. For a rapid simulation of multi-source EM data, we opt to use a parallel direct solver. We further accelerate the inversion process by decomposing the entire data set into subsets with respect to frequencies (and transmitters if memory requirement is affordable). The computational tasks associated with each data subset are distributed to different processes and run in parallel. We validate the scheme using a synthetic marine CSEM model with rough bathymetry, and finally, apply it to an industrial-size 3-D data set from the Troll field oil province in the North Sea acquired in 2008 to examine its robustness and practical applicability.
Zhang, Hua; He, Zhen-Hua; Li, Ya-Lin; Li, Rui; He, Guamg-Ming; Li, Zhong
2017-06-01
Multi-wave exploration is an effective means for improving precision in the exploration and development of complex oil and gas reservoirs that are dense and have low permeability. However, converted wave data is characterized by a low signal-to-noise ratio and low resolution, because the conventional deconvolution technology is easily affected by the frequency range limits, and there is limited scope for improving its resolution. The spectral inversion techniques is used to identify λ/8 thin layers and its breakthrough regarding band range limits has greatly improved the seismic resolution. The difficulty associated with this technology is how to use the stable inversion algorithm to obtain a high-precision reflection coefficient, and then to use this reflection coefficient to reconstruct broadband data for processing. In this paper, we focus on how to improve the vertical resolution of the converted PS-wave for multi-wave data processing. Based on previous research, we propose a least squares inversion algorithm with a total variation constraint, in which we uses the total variance as a priori information to solve under-determined problems, thereby improving the accuracy and stability of the inversion. Here, we simulate the Gaussian fitting amplitude spectrum to obtain broadband wavelet data, which we then process to obtain a higher resolution converted wave. We successfully apply the proposed inversion technology in the processing of high-resolution data from the Penglai region to obtain higher resolution converted wave data, which we then verify in a theoretical test. Improving the resolution of converted PS-wave data will provide more accurate data for subsequent velocity inversion and the extraction of reservoir reflection information.
Tensor completion and low-n-rank tensor recovery via convex optimization
International Nuclear Information System (INIS)
Gandy, Silvia; Yamada, Isao; Recht, Benjamin
2011-01-01
In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers
Sparse alignment for robust tensor learning.
Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming
2014-10-01
Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.
Kamson, David O; Juhász, Csaba; Chugani, Harry T; Jeong, Jeong-Won
2015-04-01
Diffusion tensor imaging (DTI) has expanded our knowledge of corticospinal tract (CST) anatomy and development. However, previous developmental DTI studies assessed the CST as a whole, overlooking potential differences in development of its components related to control of the upper and lower extremities. The present cross-sectional study investigated age-related changes, side and gender differences in streamline volume of the leg- and hand-related segments of the CST in children. DTI data of 31 children (1-14 years; mean age: 6±4 years; 17 girls) with normal conventional MRI were analyzed. Leg- and hand-related CST streamline volumes were quantified separately, using a recently validated novel tractography approach. CST streamline volumes on both sides were compared between genders and correlated with age. Higher absolute streamline volumes were found in the left leg-related CST compared to the right (p=0.001) without a gender effect (p=0.4), whereas no differences were found in the absolute hand-related CST volumes (p>0.4). CST leg-related streamline volumes, normalized to hemispheric white matter volumes, declined with age in the right hemisphere only (R=-.51; p=0.004). Absolute leg-related CST streamline volumes showed similar, but slightly weaker correlations. Hand-related absolute or normalized CST streamline volumes showed no age-related variations on either side. These results suggest differential development of CST segments controlling hand vs. leg movements. Asymmetric volume changes in the lower limb motor pathway may be secondary to gradually strengthening left hemispheric dominance and is consistent with previous data suggesting that footedness is a better predictor of hemispheric lateralization than handedness. Copyright © 2014 The Japanese Society of Child Neurology. Published by Elsevier B.V. All rights reserved.
Tensor completion for PDEs with uncertain coefficients and Bayesian Update
Litvinenko, Alexander
2017-03-05
In this work, we tried to show connections between Bayesian update and tensor completion techniques. Usually, only a small/sparse vector/tensor of measurements is available. The typical measurement is a function of the solution. The solution of a stochastic PDE is a tensor, the measurement as well. The idea is to use completion techniques to compute all "missing" values of the measurement tensor and only then apply the Bayesian technique.
Directory of Open Access Journals (Sweden)
A. Stanley Raj
2015-01-01
Full Text Available Soft computing based geoelectrical data inversion differs from conventional computing in fixing the uncertainty problems. It is tractable, robust, efficient, and inexpensive. In this paper, fuzzy logic clustering methods are used in the inversion of geoelectrical resistivity data. In order to characterize the subsurface features of the earth one should rely on the true field oriented data validation. This paper supports the field data obtained from the published results and also plays a crucial role in making an interdisciplinary approach to solve complex problems. Three clustering algorithms of fuzzy logic, namely, fuzzy C-means clustering, fuzzy K-means clustering, and fuzzy subtractive clustering, were analyzed with the help of fuzzy inference system (FIS training on synthetic data. Here in this approach, graphical user interface (GUI was developed with the integration of three algorithms and the input data (AB/2 and apparent resistivity, while importing will process each algorithm and interpret the layer model parameters (true resistivity and depth. A complete overview on the three above said algorithms is presented in the text. It is understood from the results that fuzzy logic subtractive clustering algorithm gives more reliable results and shows efficacy of soft computing tools in the inversion of geoelectrical resistivity data.
The classification of the Ricci tensor in the general theory of relativity
International Nuclear Information System (INIS)
Cormack, W.J.
1979-10-01
A comprehensive classification of the Ricci tensor in General Relativity using several techniques is given and their connection with existing classification studied under the headings; canonical forms for the Ricci tensor, invariant 2-spaces in the classification of the Ricci tensor, Riemannian curvature and the classification of the Riemann and Ricci tensors, and spinor classifications of the Ricci tensor. (U.K.)
Tensor Transpose and Its Properties
Pan, Ran
2014-01-01
Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.
International Nuclear Information System (INIS)
Namatame, Hirofumi; Taniguchi, Masaki
1994-01-01
Photoelectron spectroscopy is regarded as the most powerful means since it can measure almost perfectly the occupied electron state. On the other hand, inverse photoelectron spectroscopy is the technique for measuring unoccupied electron state by using the inverse process of photoelectron spectroscopy, and in principle, the similar experiment to photoelectron spectroscopy becomes feasible. The development of the experimental technology for inverse photoelectron spectroscopy has been carried out energetically by many research groups so far. At present, the heightening of resolution of inverse photoelectron spectroscopy, the development of inverse photoelectron spectroscope in which light energy is variable and so on are carried out. But the inverse photoelectron spectroscope for vacuum ultraviolet region is not on the market. In this report, the principle of inverse photoelectron spectroscopy and the present state of the spectroscope are described, and the direction of the development hereafter is groped. As the experimental equipment, electron guns, light detectors and so on are explained. As the examples of the experiment, the inverse photoelectron spectroscopy of semimagnetic semiconductors and resonance inverse photoelectron spectroscopy are reported. (K.I.)
Note of non-destructive detection of voids by a high frequency inversion technique
International Nuclear Information System (INIS)
Cohen, J.K.; Bleistein, N.
1978-01-01
An inverse method for nondestructive detection of scatterers of high contrast, such as voids or strongly reflecting inclusions, is described. The phase and range normalized far field scattering amplitude is shown to be directly proportional to the Fourier transform of the characteristic function of the scatterer. The characteristic function is equal to unity inside the region occupied by the scatterer and is zero outside. Thus, knowledge of this function provides a description of the scatterer. The method is applied to flaws in a sphere
Gradiometry - an Inverse Problem in Modern Satellite Geodesy
Freeden, Willi; Schneider, F.; Schreiner, Michael
1996-01-01
Satellite gradiometry and its instrumentation is an ultra-sensitive detection technique of the space gravitational gradient (i.e. the Hesse tensor of the gravitational potential). Gradeometry will be of great significance in inertial navigation, gravity survey, geodynamics and earthquake prediction research. In this paper, satellite gradiometry formulated as an inverse problem of satellite geodesy is discussed from two mathematical aspects: Firstly, satellite gradiometry is considered as a co...
Chow, V. Y.; Gerbig, C.; Longo, M.; Koch, F.; Nehrkorn, T.; Eluszkiewicz, J.; Ceballos, J. C.; Longo, K.; Wofsy, S. C.
2012-12-01
The Balanço Atmosférico Regional de Carbono na Amazônia (BARCA) aircraft program spanned the dry to wet and wet to dry transition seasons in November 2008 & May 2009 respectively. It resulted in ~150 vertical profiles covering the Brazilian Amazon Basin (BAB). With the data we attempt to estimate a carbon budget for the BAB, to determine if regional aircraft experiments can provide strong constraints for a budget, and to compare inversion frameworks when optimizing flux estimates. We use a LPDM to integrate satellite-, aircraft-, & surface-data with mesoscale meteorological fields to link bottom-up and top-down models to provide constraints and error bounds for regional fluxes. The Stochastic Time-Inverted Lagrangian Transport (STILT) model driven by meteorological fields from BRAMS, ECMWF, and WRF are coupled to a biosphere model, the Vegetation Photosynthesis Respiration Model (VPRM), to determine regional CO2 fluxes for the BAB. The VPRM is a prognostic biosphere model driven by MODIS 8-day EVI and LSWI indices along with shortwave radiation and temperature from tower measurements and mesoscale meteorological data. VPRM parameters are tuned using eddy flux tower data from the Large-Scale Biosphere Atmosphere experiment. VPRM computes hourly CO2 fluxes by calculating Gross Ecosystem Exchange (GEE) and Respiration (R) for 8 different vegetation types. The VPRM fluxes are scaled up to the BAB by using time-averaged drivers (shortwave radiation & temperature) from high-temporal resolution runs of BRAMS, ECMWF, and WRF and vegetation maps from SYNMAP and IGBP2007. Shortwave radiation from each mesoscale model is validated using surface data and output from GL 1.2, a global radiation model based on GOES 8 visible imagery. The vegetation maps are updated to 2008 and 2009 using landuse scenarios modeled by Sim Amazonia 2 and Sim Brazil. A priori fluxes modeled by STILT-VPRM are optimized using data from BARCA, eddy covariance sites, and flask measurements. The
Directory of Open Access Journals (Sweden)
Qi Hong
2015-01-01
Full Text Available The particle size distribution (PSD plays an important role in environmental pollution detection and human health protection, such as fog, haze and soot. In this study, the Attractive and Repulsive Particle Swarm Optimization (ARPSO algorithm and the basic PSO were applied to retrieve the PSD. The spectral extinction technique coupled with the Anomalous Diffraction Approximation (ADA and the Lambert-Beer Law were employed to investigate the retrieval of the PSD. Three commonly used monomodal PSDs, i.e. the Rosin-Rammer (R-R distribution, the normal (N-N distribution, the logarithmic normal (L-N distribution were studied in the dependent model. Then, an optimal wavelengths selection algorithm was proposed. To study the accuracy and robustness of the inverse results, some characteristic parameters were employed. The research revealed that the ARPSO showed more accurate and faster convergence rate than the basic PSO, even with random measurement error. Moreover, the investigation also demonstrated that the inverse results of four incident laser wavelengths showed more accurate and robust than those of two wavelengths. The research also found that if increasing the interval of the selected incident laser wavelengths, inverse results would show more accurate, even in the presence of random error.
Karunakaran, Madhavan
2016-03-11
In this paper, we demonstrate the formation of nanostructured double hydrophobic poly(styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymer membranes via state-of-the-art phase inversion technique. The nanostructured membrane morphologies are tuned by different solvent and block copolymer compositions. The membrane morphology has been investigated using FESEM, AFM and TEM. Morphological investigation shows the formation of both cylindrical and lamellar structures on the top surface of the block copolymer membranes. The PS-b-PMMA having an equal block length (PS160K-b-PMMA160K) exhibits both cylindrical and lamellar structures on the top layer of the asymmetric membrane. All membranes fabricated from PS160K-b-PMMA160K shows an incomplete pore formation in both cylindrical and lamellar morphologies during the phase inversion process. However, PS-b-PMMA (PS135K-b-PMMA19.5K) block copolymer having a short PMMA block allowed us to produce open pore structures with ordered hexagonal cylindrical pores during the phase inversion process. The resulting PS-b-PMMA nanostructured block copolymer membranes have pure water flux from 105-820 l/m2.h.bar and 95% retention of PEG50K
International Nuclear Information System (INIS)
Lopez, C.; Koski, J.A.; Razani, A.
2000-01-01
A study of the errors introduced when one-dimensional inverse heat conduction techniques are applied to problems involving two-dimensional heat transfer effects was performed. The geometry used for the study was a cylinder with similar dimensions as a typical container used for the transportation of radioactive materials. The finite element analysis code MSC P/Thermal was used to generate synthetic test data that was then used as input for an inverse heat conduction code. Four different problems were considered including one with uniform flux around the outer surface of the cylinder and three with non-uniform flux applied over 360 deg C, 180 deg C, and 90 deg C sections of the outer surface of the cylinder. The Sandia One-Dimensional Direct and Inverse Thermal (SODDIT) code was used to estimate the surface heat flux of all four cases. The error analysis was performed by comparing the results from SODDIT and the heat flux calculated based on the temperature results obtained from P/Thermal. Results showed an increase in error of the surface heat flux estimates as the applied heat became more localized. For the uniform case, SODDIT provided heat flux estimates with a maximum error of 0.5% whereas for the non-uniform cases, the maximum errors were found to be about 3%, 7%, and 18% for the 360 deg C, 180 deg C, and 90 deg C cases, respectively
Inversion for the composite moment tensor
Czech Academy of Sciences Publication Activity Database
Vavryčuk, Václav
2015-01-01
Roč. 105, č. 6 (2015), s. 3024-3035 ISSN 0037-1106 R&D Projects: GA ČR(CZ) GAP210/12/1491; GA ČR GA13-08971S Institutional support: RVO:67985530 Keywords : double-couple earthquakes * West Bohemia * focal mechanisms Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 2.311, year: 2015
Hess, Siegfried
2015-01-01
This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics, at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to tensors of any rank, at graduate level. Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...
Gurau, Razvan
2017-01-01
Written by the creator of the modern theory of random tensors, this book is the first self-contained introductory text to this rapidly developing theory. Starting from notions familiar to the average researcher or PhD student in mathematical or theoretical physics, the book presents in detail the theory and its applications to physics. The recent detections of the Higgs boson at the LHC and gravitational waves at LIGO mark new milestones in Physics confirming long standing predictions of Quantum Field Theory and General Relativity. These two experimental results only reinforce today the need to find an underlying common framework of the two: the elusive theory of Quantum Gravity. Over the past thirty years, several alternatives have been proposed as theories of Quantum Gravity, chief among them String Theory. While these theories are yet to be tested experimentally, key lessons have already been learned. Whatever the theory of Quantum Gravity may be, it must incorporate random geometry in one form or another....
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2018-01-01
textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the
Tensor rank is not multiplicative under the tensor product
M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)
2017-01-01
textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in
Boonyasiriwat, Chaiwoot
2010-11-01
A recently developed time-domain multiscale waveform tomography (MWT) method is applied to synthetic and field marine data. Although the MWT method was already applied to synthetic data, the synthetic data application leads to a development of a hybrid method between waveform tomography and the salt flooding technique commonly use in subsalt imaging. This hybrid method can overcome a convergence problem encountered by inversion with a traveltime velocity tomogram and successfully provides an accurate and highly resolved velocity tomogram for the 2D SEG/EAGE salt model. In the application of MWT to the field data, the inversion process is carried out using a multiscale method with a dynamic early-arrival muting window to mitigate the local minima problem of waveform tomography and elastic effects. With the modified MWT method, reasonably accurate results as verified by comparison of migration images and common image gathers were obtained. The hybrid method with the salt flooding technique is not used in this field data example because there is no salt in the subsurface according to our interpretation. However, we believe it is applicable to field data applications. © 2010 Society of Exploration Geophysicists.
McAlpine, Jerrold D.
In arid regions, mechanical disturbances along the desert floor can result in large fluctuations of dust particles into the atmosphere. Rotorcraft operation near the surface may have the greatest potential for dust entrainment per vehicle. Due to this, there is a need for efficient tools to estimate the risk of air quality and visibility impacts in the neighborhood of rotorcraft operating near the desert surface. In this study, a set of parameterized models were developed to form a multi-component modeling system to simulate the entrainment and dispersion of dust from a rotorcraft wake. A simplified scheme utilizing momentum theory was applied to predict the shear stress at the ground under the rotorcraft. Stochastic dust emission algorithms were used to predict the PM10 emission rate from the wake. The distribution of dust emission from the wake was assigned at the walls of a box-volume that encapsulates the wake. The distribution was determined using the results of an inverse Lagrangian stochastic particle dispersion modeling study, using a dataset from a full-scale experiment. All of the elements were put together into a model that simulates the dispersion of PM10 dust from a rotorcraft wake. Downwind concentrations of PM10 estimated using the multi-component modeling system compared well to a set of experimental measurements.
Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir
2016-08-01
In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.
The Topology of Symmetric Tensor Fields
Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval
1997-01-01
Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.
Tensor rank is not multiplicative under the tensor product
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2017-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...
Tensor Target Polarization at TRIUMF
Energy Technology Data Exchange (ETDEWEB)
Smith, G
2014-10-27
The first measurements of tensor observables in $\\pi \\vec{d}$ scattering experiments were performed in the mid-80's at TRIUMF, and later at SIN/PSI. The full suite of tensor observables accessible in $\\pi \\vec{d}$ elastic scattering were measured: $T_{20}$, $T_{21}$, and $T_{22}$. The vector analyzing power $iT_{11}$ was also measured. These results led to a better understanding of the three-body theory used to describe this reaction. %Some measurements were also made in the absorption and breakup channels. A direct measurement of the target tensor polarization was also made independent of the usual NMR techniques by exploiting the (nearly) model-independent result for the tensor analyzing power at 90$^\\circ _{cm}$ in the $\\pi \\vec{d} \\rightarrow 2p$ reaction. This method was also used to check efforts to enhance the tensor polarization by RF burning of the NMR spectrum. A brief description of the methods developed to measure and analyze these experiments is provided.
Tensor structure for Nori motives
Barbieri-Viale, Luca; Huber, Annette; Prest, Mike
2018-01-01
We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.
Filli, Lukas; Piccirelli, Marco; Kenkel, David; Guggenberger, Roman; Andreisek, Gustav; Beck, Thomas; Runge, Val M; Boss, Andreas
2015-07-01
The aim of this study was to investigate the feasibility of accelerated diffusion tensor imaging (DTI) of skeletal muscle using echo planar imaging (EPI) applying simultaneous multislice excitation with a blipped controlled aliasing in parallel imaging results in higher acceleration unaliasing technique. After federal ethics board approval, the lower leg muscles of 8 healthy volunteers (mean [SD] age, 29.4 [2.9] years) were examined in a clinical 3-T magnetic resonance scanner using a 15-channel knee coil. The EPI was performed at a b value of 500 s/mm2 without slice acceleration (conventional DTI) as well as with 2-fold and 3-fold acceleration. Fractional anisotropy (FA) and mean diffusivity (MD) were measured in all 3 acquisitions. Fiber tracking performance was compared between the acquisitions regarding the number of tracks, average track length, and anatomical precision using multivariate analysis of variance and Mann-Whitney U tests. Acquisition time was 7:24 minutes for conventional DTI, 3:53 minutes for 2-fold acceleration, and 2:38 minutes for 3-fold acceleration. Overall FA and MD values ranged from 0.220 to 0.378 and 1.595 to 1.829 mm2/s, respectively. Two-fold acceleration yielded similar FA and MD values (P ≥ 0.901) and similar fiber tracking performance compared with conventional DTI. Three-fold acceleration resulted in comparable MD (P = 0.199) but higher FA values (P = 0.006) and significantly impaired fiber tracking in the soleus and tibialis anterior muscles (number of tracks, P parallel imaging results in higher acceleration can remarkably reduce acquisition time in DTI of skeletal muscle with similar image quality and quantification accuracy of diffusion parameters. This may increase the clinical applicability of muscle anisotropy measurements.
Tensor eigenvalues and their applications
Qi, Liqun; Chen, Yannan
2018-01-01
This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.
Comon, Pierre
2014-01-01
International audience; Tensor decompositions are at the core of many Blind Source Separation (BSS) algorithms, either explicitly or implicitly. In particular, the Canonical Polyadic (CP) tensor decomposition plays a central role in identification of underdetermined mixtures. Despite some similarities, CP and Singular value Decomposition (SVD) are quite different. More generally, tensors and matrices enjoy different properties, as pointed out in this brief survey.
Parrish, Robert M; Hohenstein, Edward G; Schunck, Nicolas F; Sherrill, C David; Martínez, Todd J
2013-09-27
Configuration-space matrix elements of N-body potentials arise naturally and ubiquitously in the Ritz-Galerkin solution of many-body quantum problems. For the common specialization of local, finite-range potentials, we develop the exact tensor hypercontraction method, which provides a quantized renormalization of the coordinate-space form of the N-body potential, allowing for a highly separable tensor factorization of the configuration-space matrix elements. This representation allows for substantial computational savings in chemical, atomic, and nuclear physics simulations, particularly with respect to difficult "exchangelike" contractions.
International Nuclear Information System (INIS)
Beig, Robert; Krammer, Werner
2004-01-01
For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York
Pajewski, Lara; Giannopoulos, Antonios; Sesnic, Silvestar; Randazzo, Andrea; Lambot, Sébastien; Benedetto, Francesco; Economou, Nikos
2017-04-01
opportunity of testing and validating, against reliable data, their electromagnetic-modelling, inversion, imaging and processing algorithms. One of the most interesting dataset comes from the IFSTTAR Geophysical Test Site, in Nantes (France): this is an open-air laboratory including a large and deep area, filled with various materials arranged in horizontal compacted slices, separated by vertical interfaces and water-tighted in surface; several objects as pipes, polystyrene hollows, boulders and masonry are embedded in the field. Data were collected by using nine different GPR systems and at different frequencies ranging from 200 MHz to 1 GHz. Moreover, some sections of this test site were modelled by using gprMax and the commercial software CST Microwave Studio. Hence, both experimental and synthetic data are available. Further interesting datasets were collected on roads, bridges, concrete cells, columns - and more. (v) WG3 contributed to the TU1208 Education Pack, an open educational package conceived to teach GPR in University courses. (vi) WG3 was very active in offering training activities. The following courses were successfully organised: Training School (TS) "Microwave Imaging and Diagnostics" (in cooperation with the European School of Antennas; 1st edition: Madonna di Campiglio, Italy, March 2014, 2nd edition: Taormina, Italy, October 2016); TS "Numerical modelling of Ground Penetrating Radar using gprMax" (Thessaloniki, Greece, November 2015); TS "Electromagnetic Modelling Techniques for Ground Penetrating Radar" (Split, Croatia, November 2016). Moreover, WG3 organized a workshop on "Electromagnetic modelling with the Finite-Difference Time-Domain technique" (Nantes, France, February 2014) and a workshop on "Electromagnetic modelling and inversion techniques for GPR" (Davos, Switzerland, April 2016) within the 2016 European Conference on Antennas and Propagation (EuCAP). Acknowledgement: The Authors are deeply grateful to COST (European COoperation in Science and
Monte Carlo Volcano Seismic Moment Tensors
Waite, G. P.; Brill, K. A.; Lanza, F.
2015-12-01
Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.
TH-C-12A-06: Feasibility of a MLC-Based Inversely Optimized Multi-Field Grid Therapy Technique
Energy Technology Data Exchange (ETDEWEB)
Jin, J [Georgia Regents University, Augusta, GA (Georgia); Zhao, B; Huang, Y; Kim, J; Qin, Y; Wen, N; Ryu, S; Chetty, I [Henry Ford Health System, Detroit, MI (United States)
2014-06-15
Purpose: Grid therapy (GT), which generates highly spatially modulated dose distributions, can deliver single- or hypo-fractionated radiotherapy for large tumors without causing significant toxicities. GT may be applied in combination with immunotherapy, in light of recent preclinical data of synergetic interaction between radiotherapy and immunotherapy. However, conventional GT uses only one field, which does not have the advantage of multi-fields in 3D conformal-RT or IMRT. We have proposed a novel MLC-based, inverse-planned multi-field 3D GT technique. This study aims to test its deliverability and dosimetric accuracy. Methods: A lattice of small spheres was created as the boost volume within a large target. A simultaneous boost IMRT plan with 8-Gy to the target and 20-Gy to the boost volume was generated in the Eclipse treatment planning system (AAA v10) with a HD120 MLC. Nine beams were used, and the gantry and couch angles were selected so that the spheres were perfectly aligned in every beams eye view. The plan was mapped to a phantom with dose scaled. EBT3 films were calibrated and used to measure the delivered dose. Results: The IMRT plan generated a highly spatially modulated dose distribution in the target. D95%, D50%, D5% for the spheres and the targets in Gy were 18.5, 20.0, 21.4 and 7.9, 9.8, 16.1, respectively. D50% for a 1cm ring 1cm outside the target was 2.9-Gy. Film dosimetry showed good agreement between calculated and delivered dose, with an overall gamma passing rate of 99.6% (3%/1mm). The point dose differences for different spheres varied from 1–6%. Conclusion: We have demonstrated the deliverability and dose calculation accuracy of the MLC-based inversely optimized multi-field GT technique, which achieved a brachytherapy-like dose distribution. Single-fraction high dose can be delivered to the spheres in a large target with minimal dose to the surrounding normal tissue.
The effects of noise over the complete space of diffusion tensor shape.
Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B
2014-01-01
Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved.
Richey, Lauren; Gardner, John; Standing, Michael; Jorgensen, Matthew; Bartl, Michael
2010-10-01
Photonic crystals (PCs) are periodic structures that manipulate electromagnetic waves by defining allowed and forbidden frequency bands known as photonic band gaps. Despite production of PC structures operating at infrared wavelengths, visible counterparts are difficult to fabricate because periodicities must satisfy the diffraction criteria. As part of an ongoing search for naturally occurring PCs [1], a three-dimensional array of nanoscopic spheres in the iridescent scales of the Cerambycidae insects A. elegans and G. celestis has been found. Such arrays are similar to opal gemstones and self-assembled colloidal spheres which can be chemically inverted to create a lattice-like PC. Through a chemical replication process [2], scanning electron microscopy analysis, sequential focused ion beam slicing and three-dimensional modeling, we analyzed the structural arrangement of the nanoscopic spheres. The study of naturally occurring structures and their inversing techniques into PCs allows for diversity in optical PC fabrication. [1] J.W. Galusha et al., Phys. Rev. E 77 (2008) 050904. [2] J.W. Galusha et al., J. Mater. Chem. 20 (2010) 1277.
Directory of Open Access Journals (Sweden)
J Swain
2017-12-01
Full Text Available Indian Space Research Organization had launched Oceansat-2 on 23 September 2009, and the scatterometer onboard was a space-borne sensor capable of providing ocean surface winds (both speed and direction over the globe for a mission life of 5 years. The observations of ocean surface winds from such a space-borne sensor are the potential source of data covering the global oceans and useful for driving the state-of-the-art numerical models for simulating ocean state if assimilated/blended with weather prediction model products. In this study, an efficient interpolation technique of inverse distance and time is demonstrated using the Oceansat-2 wind measurements alone for a selected month of June 2010 to generate gridded outputs. As the data are available only along the satellite tracks and there are obvious data gaps due to various other reasons, Oceansat-2 winds were subjected to spatio-temporal interpolation, and 6-hour global wind fields for the global oceans were generated over 1 × 1 degree grid resolution. Such interpolated wind fields can be used to drive the state-of-the-art numerical models to predict/hindcast ocean-state so as to experiment and test the utility/performance of satellite measurements alone in the absence of blended fields. The technique can be tested for other satellites, which provide wind speed as well as direction data. However, the accuracy of input winds is obviously expected to have a perceptible influence on the predicted ocean-state parameters. Here, some attempts are also made to compare the interpolated Oceansat-2 winds with available buoy measurements and it was found that they are reasonably in good agreement with a correlation coefficient of R > 0.8 and mean deviation 1.04 m/s and 25° for wind speed and direction, respectively.
Feature Surfaces in Symmetric Tensor Fields Based on Eigenvalue Manifold.
Palacios, Jonathan; Yeh, Harry; Wang, Wenping; Zhang, Yue; Laramee, Robert S; Sharma, Ritesh; Schultz, Thomas; Zhang, Eugene
2016-03-01
Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the (topological) analysis of 3D symmetric tensor fields focus on degenerate tensors which form curves. In this paper, we introduce a number of feature surfaces, such as neutral surfaces and traceless surfaces, into tensor field analysis, based on the notion of eigenvalue manifold. Neutral surfaces are the boundary between linear tensors and planar tensors, and the traceless surfaces are the boundary between tensors of positive traces and those of negative traces. Degenerate curves, neutral surfaces, and traceless surfaces together form a partition of the eigenvalue manifold, which provides a more complete tensor field analysis than degenerate curves alone. We also extract and visualize the isosurfaces of tensor modes, tensor isotropy, and tensor magnitude, which we have found useful for domain applications in fluid and solid mechanics. Extracting neutral and traceless surfaces using the Marching Tetrahedra method can cause the loss of geometric and topological details, which can lead to false physical interpretation. To robustly extract neutral surfaces and traceless surfaces, we develop a polynomial description of them which enables us to borrow techniques from algebraic surface extraction, a topic well-researched by the computer-aided design (CAD) community as well as the algebraic geometry community. In addition, we adapt the surface extraction technique, called A-patches, to improve the speed of finding degenerate curves. Finally, we apply our analysis to data from solid and fluid mechanics as well as scalar field analysis.
Kruecken, R; Speidel, K; Voulot, D; Neyens, G; Gernhaeuser, R A; Fraile prieto, L M; Leske, J
We propose to measure the sign and magnitude of the g-factors of the first 2$^{+}$ states in radioactive neutron-rich $^{72,74}$Zn applying the transient field (TF) technique in inverse kinematics. The result of this experiment will allow to probe the $\
Bicanic, D.D.; Neamtu, C.; Manojlovic, M.; Linden, van der D.; Dadarlat, D.; Gijsbertsen, A.; Kurtanjek, Z.; Posavec, K.
2004-01-01
Infrared photothermal radiometry and inverse photopyroelectric method were used to determine thermal effusivity for tomato pastes characterised by a varying dry matter content. Unlike commonly adapted techniques, the two methods used here are reasonably fast and do not require the application of
Tensor rank is not multiplicative under the tensor product
DEFF Research Database (Denmark)
Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen
2018-01-01
The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection...... between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specifically, if a tensor t has border rank strictly smaller than its rank, then the tensor rank of t...... is not multiplicative under taking a sufficiently hight tensor product power. The “tensor Kronecker product” from algebraic complexity theory is related to our tensor product but different, namely it multiplies two k-tensors to get a k-tensor. Nonmultiplicativity of the tensor Kronecker product has been known since...
Cartesian tensors an introduction
Temple, G
2004-01-01
This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t
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
Tensor network method for reversible classical computation
Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.
2018-03-01
We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.
Multiple M2-branes and the embedding tensor
Bergshoeff, Eric A.; de Roo, Mees; Hohm, Olaf
2008-01-01
We show that the Bagger-Lambert theory of multiple M2-branes fits into the general construction of maximally supersymmetric gauge theories using the embedding tensor technique. We apply the embedding tensor technique in order to systematically obtain the consistent gaugings of N = 8 superconformal
Soibelman, Yan
1997-01-01
We introduce the notion of meromorphic tensor category and illustrate it in several examples. They include representations of quantum affine algebras, chiral algebras of Beilinson and Drinfeld, G-vertex algebras of Borcherds, and representations of GL over a local field. Hopefully the formalism will accomodate various tensor structures arising in relation to the quantized Knizhnik-Zamolodchikov equations and deformed CFT
Bayesian approach to magnetotelluric tensor decomposition
Czech Academy of Sciences Publication Activity Database
Červ, Václav; Pek, Josef; Menvielle, M.
2010-01-01
Roč. 53, č. 2 (2010), s. 21-32 ISSN 1593-5213 R&D Projects: GA AV ČR IAA200120701; GA ČR GA205/04/0746; GA ČR GA205/07/0292 Institutional research plan: CEZ:AV0Z30120515 Keywords : galvanic distortion * telluric distortion * impedance tensor * basic procedure * inversion * noise Subject RIV: DE - Earth Magnetism, Geodesy, Geography Impact factor: 0.336, year: 2010
DEFF Research Database (Denmark)
Farahani, Saeed Davoudabadi; Andersen, Michael Skipper; de Zee, Mark
2012-01-01
derived from the detailed musculoskeletal analysis. The technique is demonstrated on a human model pedaling a bicycle. We use a physiology-based cost function expressing the mean square of all muscle activities over the cycle to predict a realistic motion pattern. Posture and motion prediction......, the parameters of these functions are optimized to produce an optimum posture or movement according to a user-defined cost function and constraints. The cost function and the constraints are typically express performance, comfort, injury risk, fatigue, muscle load, joint forces and other physiological properties...
Tensor spherical harmonics and tensor multipoles. II. Minkowski space
International Nuclear Information System (INIS)
Daumens, M.; Minnaert, P.
1976-01-01
The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation
Measuring Nematic Susceptibilities from the Elastoresistivity Tensor
Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian
The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.
Direct tensor rendering using a bidirectional reflectance model
Nagasawa, Mikio; Suzuki, Yoshio
2000-02-01
For the multi variable volumetric tensor field visualization, an efficient direct rendering technique without using geometrical primitive is proposed. The bi- directional reflectance shading model is used to map the anisotropy stress shear tensor components in direct volume rendering. We model the sub-pixel-sized microfacet at tensor sampling points. The nine component of 3D tensor field are mapped onto grid deformation, opacity mapping, color specification, and normal directions of these microfacets. The ray integration is executed though these irregular infinitesimal microfacets distribution. This direct tensor rendering was applied for at-a-glance tensor visualization of earthquake simulation. That realized a view of deformed structure, stress distribution, local shear discontinuity and the shock front, integrated in a single image. The characteristic P- and S-wave modes are distinguished in the rendered earthquake simulations. Compared with the glyph representation of tensor features, the direct tensor rendering gives the general and total image of tensor field even for the low resolution pixel planes, because the sampling object is assumed as infinitesimally small. the computational cost of direct tensor rendering is not so high than that of scalar volume rendering because the modifications are only ins hading calculation but not in the ray integration.
Tensors and their applications
Islam, Nazrul
2006-01-01
About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces
Symmetric Tensor Decomposition
DEFF Research Database (Denmark)
Brachat, Jerome; Comon, Pierre; Mourrain, Bernard
2010-01-01
We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....
International Nuclear Information System (INIS)
Scheunert, M.
1982-10-01
We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)
Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.
Iwasaki, Tohru; Furukawa, Tetsuo
2016-05-01
In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.
Complete algebraic reduction of one-loop tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.; Riemann, T.
2011-01-01
We set up a new, flexible approach for the tensor reduction of one-loop Feynman integrals. The 5-point tensor integrals up to rank R=5 are expressed by 4-point tensor integrals of rank R-1, such that the appearance of the inverse 5-point Gram determinant is avoided. The 4-point tensor coefficients are represented in terms of 4-point integrals, defined in d dimensions, 4-2ε≤d≤4-2ε+2(R-1), with higher powers of the propagators. They can be further reduced to expressions which stay free of the inverse 4-point Gram determinants but contain higher-dimensional 4-point integrals with only the first power of scalar propagators, plus 3-point tensor coefficients. A direct evaluation of the higher-dimensional 4-point functions would avoid the appearance of inverse powers of the Gram determinants completely. The simplest approach, however, is to apply here dimensional recurrence relations in order to reduce them to the familiar 2- to 4-point functions in generic dimension d=4-2ε, introducing thereby coefficients with inverse 4-point Gram determinants up to power R for tensors of rank R. For small or vanishing Gram determinants--where this reduction is not applicable--we use analytic expansions in positive powers of the Gram determinants. Improving the convergence of the expansions substantially with Pade approximants we close up to the evaluation of the 4-point tensor coefficients for larger Gram determinants. Finally, some relations are discussed which may be useful for analytic simplifications of Feynman diagrams.
Pajewski, Lara; Giannopoulos, Antonis; van der Kruk, Jan
2015-04-01
This work aims at presenting the ongoing research activities carried out in Working Group 3 (WG3) 'EM methods for near-field scattering problems by buried structures; data processing techniques' of the COST (European COoperation in Science and Technology) Action TU1208 'Civil Engineering Applications of Ground Penetrating Radar' (www.GPRadar.eu). The principal goal of the COST Action TU1208 is to exchange and increase scientific-technical knowledge and experience of GPR techniques in civil engineering, simultaneously promoting throughout Europe the effective use of this safe and non-destructive technique in the monitoring of infrastructures and structures. WG3 is structured in four Projects. Project 3.1 deals with 'Electromagnetic modelling for GPR applications.' Project 3.2 is concerned with 'Inversion and imaging techniques for GPR applications.' The topic of Project 3.3 is the 'Development of intrinsic models for describing near-field antenna effects, including antenna-medium coupling, for improved radar data processing using full-wave inversion.' Project 3.4 focuses on 'Advanced GPR data-processing algorithms.' Electromagnetic modeling tools that are being developed and improved include the Finite-Difference Time-Domain (FDTD) technique and the spectral domain Cylindrical-Wave Approach (CWA). One of the well-known freeware and versatile FDTD simulators is GprMax that enables an improved realistic representation of the soil/material hosting the sought structures and of the GPR antennas. Here, input/output tools are being developed to ease the definition of scenarios and the visualisation of numerical results. The CWA expresses the field scattered by subsurface two-dimensional targets with arbitrary cross-section as a sum of cylindrical waves. In this way, the interaction is taken into account of multiple scattered fields within the medium hosting the sought targets. Recently, the method has been extended to deal with through-the-wall scenarios. One of the
A Review of Tensors and Tensor Signal Processing
Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.
Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.
Ars, Sébastien; Broquet, Grégoire; Yver Kwok, Camille; Roustan, Yelva; Wu, Lin; Arzoumanian, Emmanuel; Bousquet, Philippe
2017-12-01
This study presents a new concept for estimating the pollutant emission rates of a site and its main facilities using a series of atmospheric measurements across the pollutant plumes. This concept combines the tracer release method, local-scale atmospheric transport modelling and a statistical atmospheric inversion approach. The conversion between the controlled emission and the measured atmospheric concentrations of the released tracer across the plume places valuable constraints on the atmospheric transport. This is used to optimise the configuration of the transport model parameters and the model uncertainty statistics in the inversion system. The emission rates of all sources are then inverted to optimise the match between the concentrations simulated with the transport model and the pollutants' measured atmospheric concentrations, accounting for the transport model uncertainty. In principle, by using atmospheric transport modelling, this concept does not strongly rely on the good colocation between the tracer and pollutant sources and can be used to monitor multiple sources within a single site, unlike the classical tracer release technique. The statistical inversion framework and the use of the tracer data for the configuration of the transport and inversion modelling systems should ensure that the transport modelling errors are correctly handled in the source estimation. The potential of this new concept is evaluated with a relatively simple practical implementation based on a Gaussian plume model and a series of inversions of controlled methane point sources using acetylene as a tracer gas. The experimental conditions are chosen so that they are suitable for the use of a Gaussian plume model to simulate the atmospheric transport. In these experiments, different configurations of methane and acetylene point source locations are tested to assess the efficiency of the method in comparison to the classic tracer release technique in coping with the distances
Directory of Open Access Journals (Sweden)
S. Ars
2017-12-01
Full Text Available This study presents a new concept for estimating the pollutant emission rates of a site and its main facilities using a series of atmospheric measurements across the pollutant plumes. This concept combines the tracer release method, local-scale atmospheric transport modelling and a statistical atmospheric inversion approach. The conversion between the controlled emission and the measured atmospheric concentrations of the released tracer across the plume places valuable constraints on the atmospheric transport. This is used to optimise the configuration of the transport model parameters and the model uncertainty statistics in the inversion system. The emission rates of all sources are then inverted to optimise the match between the concentrations simulated with the transport model and the pollutants' measured atmospheric concentrations, accounting for the transport model uncertainty. In principle, by using atmospheric transport modelling, this concept does not strongly rely on the good colocation between the tracer and pollutant sources and can be used to monitor multiple sources within a single site, unlike the classical tracer release technique. The statistical inversion framework and the use of the tracer data for the configuration of the transport and inversion modelling systems should ensure that the transport modelling errors are correctly handled in the source estimation. The potential of this new concept is evaluated with a relatively simple practical implementation based on a Gaussian plume model and a series of inversions of controlled methane point sources using acetylene as a tracer gas. The experimental conditions are chosen so that they are suitable for the use of a Gaussian plume model to simulate the atmospheric transport. In these experiments, different configurations of methane and acetylene point source locations are tested to assess the efficiency of the method in comparison to the classic tracer release technique in coping
Dark energy in scalar-tensor theories
International Nuclear Information System (INIS)
Moeller, J.
2007-12-01
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of σ-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
Dark energy in scalar-tensor theories
Energy Technology Data Exchange (ETDEWEB)
Moeller, J.
2007-12-15
We investigate several aspects of dynamical dark energy in the framework of scalar-tensor theories of gravity. We provide a classification of scalar-tensor coupling functions admitting cosmological scaling solutions. In particular, we recover that Brans-Dicke theory with inverse power-law potential allows for a sequence of background dominated scaling regime and scalar field dominated, accelerated expansion. Furthermore, we compare minimally and non-minimally coupled models, with respect to the small redshift evolution of the dark energy equation of state. We discuss the possibility to discriminate between different models by a reconstruction of the equation-of-state parameter from available observational data. The non-minimal coupling characterizing scalar-tensor models can - in specific cases - alleviate fine tuning problems, which appear if (minimally coupled) quintessence is required to mimic a cosmological constant. Finally, we perform a phase-space analysis of a family of biscalar-tensor models characterized by a specific type of {sigma}-model metric, including two examples from recent literature. In particular, we generalize an axion-dilaton model of Sonner and Townsend, incorporating a perfect fluid background consisting of (dark) matter and radiation. (orig.)
A moment-tensor catalog for intermediate magnitude earthquakes in Mexico
Rodríguez Cardozo, Félix; Hjörleifsdóttir, Vala; Martínez-Peláez, Liliana; Franco, Sara; Iglesias Mendoza, Arturo
2016-04-01
Located among five tectonic plates, Mexico is one of the world's most seismically active regions. The earthquake focal mechanisms provide important information on the active tectonics. A widespread technique for estimating the earthquake magnitud and focal mechanism is the inversion for the moment tensor, obtained by minimizing a misfit function that estimates the difference between synthetic and observed seismograms. An important element in the estimation of the moment tensor is an appropriate velocity model, which allows for the calculation of accurate Green's Functions so that the differences between observed and synthetics seismograms are due to the source of the earthquake rather than the velocity model. However, calculating accurate synthetic seismograms gets progressively more difficult as the magnitude of the earthquakes decreases. Large earthquakes (M>5.0) excite waves of longer periods that interact weakly with lateral heterogeneities in the crust. For these events, using 1D velocity models to compute Greens functions works well and they are well characterized by seismic moment tensors reported in global catalogs (eg. USGS fast moment tensor solutions and GCMT). The opposite occurs for small and intermediate sized events, where the relatively shorter periods excited interact strongly with lateral heterogeneities in the crust and upper mantle. To accurately model the Green's functions for the smaller events in a large heterogeneous area, requires 3D or regionalized 1D models. To obtain a rapid estimate of earthquake magnitude, the National Seismological Survey in Mexico (Servicio Sismológico Nacional, SSN) automatically calculates seismic moment tensors for events in the Mexican Territory (Franco et al., 2002; Nolasco-Carteño, 2006). However, for intermediate-magnitude and small earthquakes the signal-to-noise ratio could is low for many of the seismic stations, and without careful selection and filtering of the data, obtaining a stable focal mechanism
Tensor analysis for physicists
Schouten, J A
1989-01-01
This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...
Kappadath, S Cheenu; Shaw, Chris C
2003-06-01
Breast cancer may manifest as microcalcifications in x-ray mammography. Small microcalcifications, essential to the early detection of breast cancer, are often obscured by overlapping tissue structures. Dual-energy imaging, where separate low- and high-energy images are acquired and synthesized to cancel the tissue structures, may improve the ability to detect and visualize microcalcifications. Transmission measurements at two different kVp values were made on breast-tissue-equivalent materials under narrow-beam geometry using an indirect flat-panel mammographic imager. The imaging scenario consisted of variable aluminum thickness (to simulate calcifications) and variable glandular ratio (defined as the ratio of the glandular-tissue thickness to the total tissue thickness) for a fixed total tissue thickness--the clinical situation of microcalcification imaging with varying tissue composition under breast compression. The coefficients of the inverse-mapping functions used to determine material composition from dual-energy measurements were calculated by a least-squares analysis. The linear function poorly modeled both the aluminum thickness and the glandular ratio. The inverse-mapping functions were found to vary as analytic functions of second (conic) or third (cubic) order. By comparing the model predictions with the calibration values, the root-mean-square residuals for both the cubic and the conic functions were approximately 50 microm for the aluminum thickness and approximately 0.05 for the glandular ratio.
Joint Tensor Feature Analysis For Visual Object Recognition.
Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po
2015-11-01
Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms.
Killing tensors and conformal Killing tensors from conformal Killing vectors
International Nuclear Information System (INIS)
Rani, Raffaele; Edgar, S Brian; Barnes, Alan
2003-01-01
Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors
International Nuclear Information System (INIS)
Zimmerman, D.A.; Gallegos, D.P.
1992-01-01
The groundwater flow pathway in the Culebra Dolomite aquifer at the Waste Isolation Pilot Plant (WIPP) has been identified a potentially important pathway for radionuclide migration to the accessible environment. Consequently, uncertainties in the models used to describe flow and transport in the Culebra need to be addressed. A ''Geostatistics Test Problem'' is being developed to evaluate a number of inverse techniques that may be used for Dow calculations in the WIPP performance assessment (PA). The Test Problem is actually a series of test cases, each being developed as a highly complex synthetic data sct; the intent is for the ensemble of these data sets span the range of possible conceptual models of groundwater now at the WIPP site. This paper describes the results from Test Case No. 1. Of the five techniques compared, those based on the linearized form of the groundwater flow equation exhibited less bias and less spread in their GWTT distribution functions; the semi-analytical method had the least bias. While the results are not sufficient to make generalizations about which techniques may be better suited for the WIPP PA (only one test case has been exercised), analyses of the data from this test case provides some indication about the relative importance of other aspects of the flow modeling (besides inverse method or geostatistical approach) in PA. Then ancillary analyses examine the effect of gridding an the effect of boundary conditions on the groundwater travel time estimates
Martins, Evandro; Poncelet, Denis; Rodrigues, Ramila Cristiane; Renard, Denis
2017-09-01
In the first part of this article, it was described an innovative method of oil encapsulation from dripping-inverse gelation using water-in-oil (W/O) emulsions. It was noticed that the method of oil encapsulation was quite different depending on the emulsion type (W/O or oil-in-water (O/W)) used and that the emulsion structure (W/O or O/W) had a high impact on the dripping technique and the capsules characteristics. The objective of this article was to elucidate the differences between the dripping techniques using both emulsions and compare the capsule properties (mechanical resistance and release of actives). The oil encapsulation using O/W emulsions was easier to perform and did not require the use of emulsion destabilisers. However, capsules produced from W/O emulsions were more resistant to compression and showed the slower release of actives over time. The findings detailed here widened the knowledge of the inverse gelation and gave opportunities to develop new techniques of oil encapsulation.
Tensors, relativity, and cosmology
Dalarsson, Mirjana
2015-01-01
Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...
DEFF Research Database (Denmark)
Ziegel, Johanna; Nyengaard, Jens Randel; Jensen, Eva B. Vedel
In the present paper, statistical procedures for estimating shape and orientation of arbitrary three-dimensional particles are developed. The focus of this work is on the case where the particles cannot be observed directly, but only via sections. Volume tensors are used for describing particle...... shape and orientation, and stereological estimators of the tensors are derived. It is shown that these estimators can be combined to provide consistent estimators of the moments of the so-called particle cover density. The covariance structure associated with the particle cover density depends...... may be analysed using a generalized methods of moments in which the volume tensors enter. The developed methods are used to study the cell organization in the human brain cortex....
Improving Tensor Based Recommenders with Clustering
DEFF Research Database (Denmark)
Leginus, Martin; Dolog, Peter; Zemaitis, Valdas
2012-01-01
Social tagging systems (STS) model three types of entities (i.e. tag-user-item) and relationships between them are encoded into a 3-order tensor. Latent relationships and patterns can be discovered by applying tensor factorization techniques like Higher Order Singular Value Decomposition (HOSVD...... of the recommendations and execution time are improved and memory requirements are decreased. The clustering is motivated by the fact that many tags in a tag space are semantically similar thus the tags can be grouped. Finally, promising experimental results are presented...
Directory of Open Access Journals (Sweden)
V. Picco
2013-01-01
Full Text Available Radio-frequency tomography was originally proposed to image underground cavities. Its flexible forward model can be used in free-space by choosing an appropriate dyadic Green's function and can be translated in the microwave domain. Experimental data are used to validate a novel inversion scheme, based on the algebraic reconstruction technique. The proposed method is improved by introducing physical bounds on the solution returned. As a result, the images of the dielectric permittivity profiles obtained are superior in quality to the ones obtained using classical regularization approaches such as the truncated singular value decomposition. The results from three experimental case studies are presented and discussed.
Susceptibility tensor imaging (STI) of the brain.
Li, Wei; Liu, Chunlei; Duong, Timothy Q; van Zijl, Peter C M; Li, Xu
2017-04-01
Susceptibility tensor imaging (STI) is a recently developed MRI technique that allows quantitative determination of orientation-independent magnetic susceptibility parameters from the dependence of gradient echo signal phase on the orientation of biological tissues with respect to the main magnetic field. By modeling the magnetic susceptibility of each voxel as a symmetric rank-2 tensor, individual magnetic susceptibility tensor elements as well as the mean magnetic susceptibility and magnetic susceptibility anisotropy can be determined for brain tissues that would still show orientation dependence after conventional scalar-based quantitative susceptibility mapping to remove such dependence. Similar to diffusion tensor imaging, STI allows mapping of brain white matter fiber orientations and reconstruction of 3D white matter pathways using the principal eigenvectors of the susceptibility tensor. In contrast to diffusion anisotropy, the main determinant factor of the susceptibility anisotropy in brain white matter is myelin. Another unique feature of the susceptibility anisotropy of white matter is its sensitivity to gadolinium-based contrast agents. Mechanistically, MRI-observed susceptibility anisotropy is mainly attributed to the highly ordered lipid molecules in the myelin sheath. STI provides a consistent interpretation of the dependence of phase and susceptibility on orientation at multiple scales. This article reviews the key experimental findings and physical theories that led to the development of STI, its practical implementations, and its applications for brain research. Copyright © 2016 John Wiley & Sons, Ltd. Copyright © 2016 John Wiley & Sons, Ltd.
Primordial tensor modes of the early Universe
Martínez, Florencia Benítez; Olmedo, Javier
2016-06-01
We study cosmological tensor perturbations on a quantized background within the hybrid quantization approach. In particular, we consider a flat, homogeneous and isotropic spacetime and small tensor inhomogeneities on it. We truncate the action to second order in the perturbations. The dynamics is ruled by a homogeneous scalar constraint. We carry out a canonical transformation in the system where the Hamiltonian for the tensor perturbations takes a canonical form. The new tensor modes now admit a standard Fock quantization with a unitary dynamics. We then combine this representation with a generic quantum scheme for the homogeneous sector. We adopt a Born-Oppenheimer ansatz for the solutions to the constraint operator, previously employed to study the dynamics of scalar inhomogeneities. We analyze the approximations that allow us to recover, on the one hand, a Schrödinger equation similar to the one emerging in the dressed metric approach and, on the other hand, the ones necessary for the effective evolution equations of these primordial tensor modes within the hybrid approach to be valid. Finally, we consider loop quantum cosmology as an example where these quantization techniques can be applied and compare with other approaches.
A tensor approach to the estimation of hydraulic conductivities in ...
African Journals Online (AJOL)
2006-07-03
Jul 3, 2006 ... coefficients, i.e. the fracture roughness and combined stress conditions, are adapted to calibrate the tensor model application. The application ... Darcy's law is always used to estimate the groundwater flow in both porous and ... Inverse analysis on continuous or discontinuous problems dependent on ...
Inverse problem in transformation optics
Novitsky, Andrey V.
2011-01-01
The straightforward method of transformation optics implies that one starts from the coordinate transformation and determines the Jacobian matrix, the fields and material parameters of the cloak. However, the coordinate transformation appears as an optional function: it is not necessary to know it. We offer the solution of some sort of inverse problem: starting from the fields in the invisibility cloak we directly derive the permittivity and permeability tensors of the cloaking shell. This ap...
-Dimensional Fractional Lagrange's Inversion Theorem
Directory of Open Access Journals (Sweden)
F. A. Abd El-Salam
2013-01-01
Full Text Available Using Riemann-Liouville fractional differential operator, a fractional extension of the Lagrange inversion theorem and related formulas are developed. The required basic definitions, lemmas, and theorems in the fractional calculus are presented. A fractional form of Lagrange's expansion for one implicitly defined independent variable is obtained. Then, a fractional version of Lagrange's expansion in more than one unknown function is generalized. For extending the treatment in higher dimensions, some relevant vectors and tensors definitions and notations are presented. A fractional Taylor expansion of a function of -dimensional polyadics is derived. A fractional -dimensional Lagrange inversion theorem is proved.
Tensor Calculus: Unlearning Vector Calculus
Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita
2018-01-01
Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…
The evolution of tensor polarization
International Nuclear Information System (INIS)
Huang, H.; Lee, S.Y.; Ratner, L.
1993-01-01
By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake
Energy Technology Data Exchange (ETDEWEB)
Sakurai, K.; Shima, H. [OYO Corp., Tokyo (Japan)
1996-10-01
This paper proposes a modeling method of one-dimensional complex resistivity using linear filter technique which has been extended to the complex resistivity. In addition, a numerical test of inversion was conducted using the monitoring results, to discuss the measured frequency band. Linear filter technique is a method by which theoretical potential can be calculated for stratified structures, and it is widely used for the one-dimensional analysis of dc electrical exploration. The modeling can be carried out only using values of complex resistivity without using values of potential. In this study, a bipolar method was employed as a configuration of electrodes. The numerical test of one-dimensional complex resistivity inversion was conducted using the formulated modeling. A three-layered structure model was used as a numerical model. A multi-layer structure with a thickness of 5 m was analyzed on the basis of apparent complex resistivity calculated from the model. From the results of numerical test, it was found that both the chargeability and the time constant agreed well with those of the original model. A trade-off was observed between the chargeability and the time constant at the stage of convergence. 3 refs., 9 figs., 1 tab.
Directory of Open Access Journals (Sweden)
M.A. Nwachukwu
2017-01-01
Full Text Available The use of trial pits as a first step in quarry site development causes land degradation and results in more failure than success for potential quarry investors in some parts of the world. In this paper, resistivity, depth and distance values derived from 26 Vertical Electric Soundings (VES and 2 profiling inversion sections were successfully used to evaluate a quarry site prior to development. The target rock Diabase (Dolerite was observed and it had a resistivity range of 3.0 × 104 –7. 8 × 106 Ω-m, and was clearly distinguishable from associated rocks with its bright red color code on the AGI 1D inversion software. This target rock was overlain by quartzite, indurate shale and mudstone as overburden materials. The quartzite, with its off-red colour, has a resistivity range of 2.0 × 103–2.9 × 105 Ω-m, while the indurate shale, with a yellowish-brown colour, showed resistivity values ranging from 6.1 × 102 – 2.8 × 105 Ω-m. Topsoil was clayey, with a resistivity range from 8 – 8.6 × 102u Ω-m and depths of 0.3–1.8 m, often weathered and replaced by associated rocks outcrops. The diabase rock, in the three prospective pits mapped, showed thicknesses of between 40 and 76 m across the site. The prospective pits were identified to accommodate an estimated 2,569,450 tonnes of diabase with an average quarry pit depth of 50 m. This figure was justified by physical observations made at a nearby quarry pit and from test holes. Communities were able to prepare a geophysical appraisal of the intrusive body in their domain for economic planning and sustainability of the natural resource.
Diffusion tensor image registration using hybrid connectivity and tensor features.
Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang
2014-07-01
Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.
Evaluation of Bayesian tensor estimation using tensor coherence
Kim, Dae-Jin; Kim, In-Young; Jeong, Seok-Oh; Park, Hae-Jeong
2009-06-01
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Evaluation of Bayesian tensor estimation using tensor coherence
Energy Technology Data Exchange (ETDEWEB)
Kim, Dae-Jin; Park, Hae-Jeong [Laboratory of Molecular Neuroimaging Technology, Brain Korea 21 Project for Medical Science, Yonsei University, College of Medicine, Seoul (Korea, Republic of); Kim, In-Young [Department of Biomedical Engineering, Hanyang University, Seoul (Korea, Republic of); Jeong, Seok-Oh [Department of Statistics, Hankuk University of Foreign Studies, Yongin (Korea, Republic of)], E-mail: parkhj@yuhs.ac
2009-06-21
Fiber tractography, a unique and non-invasive method to estimate axonal fibers within white matter, constructs the putative streamlines from diffusion tensor MRI by interconnecting voxels according to the propagation direction defined by the diffusion tensor. This direction has uncertainties due to the properties of underlying fiber bundles, neighboring structures and image noise. Therefore, robust estimation of the diffusion direction is essential to reconstruct reliable fiber pathways. For this purpose, we propose a tensor estimation method using a Bayesian framework, which includes an a priori probability distribution based on tensor coherence indices, to utilize both the neighborhood direction information and the inertia moment as regularization terms. The reliability of the proposed tensor estimation was evaluated using Monte Carlo simulations in terms of accuracy and precision with four synthetic tensor fields at various SNRs and in vivo human data of brain and calf muscle. Proposed Bayesian estimation demonstrated the relative robustness to noise and the higher reliability compared to the simple tensor regression.
Review of diffusion tensor imaging and its application in children
Energy Technology Data Exchange (ETDEWEB)
Vorona, Gregory A. [Children' s Hospital of Richmond at Virginia Commonwealth University, Department of Radiology, Richmond, VA (United States); Berman, Jeffrey I. [Children' s Hospital of Philadelphia, Department of Radiology, Philadelphia, PA (United States)
2015-09-15
Diffusion MRI is an imaging technique that uses the random motion of water to probe tissue microstructure. Diffusion tensor imaging (DTI) can quantitatively depict the organization and connectivity of white matter. Given the non-invasiveness of the technique, DTI has become a widely used tool for researchers and clinicians to examine the white matter of children. This review covers the basics of diffusion-weighted imaging and diffusion tensor imaging and discusses examples of their clinical application in children. (orig.)
Schuh, A. E.; Kawa, S. R.; Crowell, S.; Browell, E. V.; Abshire, J. B.; Ramanathan, A. K.
2015-12-01
Typically more than half of the earth's surface is cloudy at any one point in time. Passive CO2 satellite instruments such as GOSAT and OCO-2 have historically filtered out these scenes, as being too difficult to interpret. However, with the advent of active sensing technologies coupled with ranging capabilities, many of these limitations are being lifted. While, the remote sensing community continues to grapple with the radiative-transfer aspects of the cloud-top CO2 retrieval problem, the carbon cycling community has begun to consider what parts of the carbon cycle might be constrained with this new stream of data. Using cloud data derived from CALIPSO, a simulated carbon cycle, and state of the art atmospheric inversion models, we will investigate the impact of "above cloud" partial-column retrievals of CO2 upon estimates of surface CO2 flux. In particular, we will investigate (1) the general constraint imposed upon surface CO2 fluxes, by retrievals over spatially and time coherent cloud structures around the globe as well as (2) the partitioning of gross primary production and respiration CO2 flux terms by differencing full-column and above-cloud partial column CO2 over scenes with optically thick low clouds.
Li, Xutao; Ng, Michael K; Cong, Gao; Ye, Yunming; Wu, Qingyao
2017-08-01
With the advancement of data acquisition techniques, tensor (multidimensional data) objects are increasingly accumulated and generated, for example, multichannel electroencephalographies, multiview images, and videos. In these applications, the tensor objects are usually nonnegative, since the physical signals are recorded. As the dimensionality of tensor objects is often very high, a dimension reduction technique becomes an important research topic of tensor data. From the perspective of geometry, high-dimensional objects often reside in a low-dimensional submanifold of the ambient space. In this paper, we propose a new approach to perform the dimension reduction for nonnegative tensor objects. Our idea is to use nonnegative Tucker decomposition (NTD) to obtain a set of core tensors of smaller sizes by finding a common set of projection matrices for tensor objects. To preserve geometric information in tensor data, we employ a manifold regularization term for the core tensors constructed in the Tucker decomposition. An algorithm called manifold regularization NTD (MR-NTD) is developed to solve the common projection matrices and core tensors in an alternating least squares manner. The convergence of the proposed algorithm is shown, and the computational complexity of the proposed method scales linearly with respect to the number of tensor objects and the size of the tensor objects, respectively. These theoretical results show that the proposed algorithm can be efficient. Extensive experimental results have been provided to further demonstrate the effectiveness and efficiency of the proposed MR-NTD algorithm.
Mehl, S.; Hill, M.C.
2001-01-01
Five common numerical techniques for solving the advection-dispersion equation (finite difference, predictor corrector, total variation diminishing, method of characteristics, and modified method of characteristics) were tested using simulations of a controlled conservative tracer-test experiment through a heterogeneous, two-dimensional sand tank. The experimental facility was constructed using discrete, randomly distributed, homogeneous blocks of five sand types. This experimental model provides an opportunity to compare the solution techniques: the heterogeneous hydraulic-conductivity distribution of known structure can be accurately represented by a numerical model, and detailed measurements can be compared with simulated concentrations and total flow through the tank. The present work uses this opportunity to investigate how three common types of results - simulated breakthrough curves, sensitivity analysis, and calibrated parameter values - change in this heterogeneous situation given the different methods of simulating solute transport. The breakthrough curves show that simulated peak concentrations, even at very fine grid spacings, varied between the techniques because of different amounts of numerical dispersion. Sensitivity-analysis results revealed: (1) a high correlation between hydraulic conductivity and porosity given the concentration and flow observations used, so that both could not be estimated; and (2) that the breakthrough curve data did not provide enough information to estimate individual values of dispersivity for the five sands. This study demonstrates that the choice of assigned dispersivity and the amount of numerical dispersion present in the solution technique influence estimated hydraulic conductivity values to a surprising degree.
Kern-Steiner, R; Washecheck, H S; Kelsey, D D
1999-05-01
Case study. To demonstrate how an exercise program can be designed with specific sets, repetitions, and rest periods, and to enhance the healing process in early stages of rehabilitation when injured tissues cannot tolerate full body weight. Our goal was to enhance ankle tissue healing by reducing gravitational force through a prescriptive exercise and unloading program. This report describes a treatment method that we used to rehabilitate a collegiate soccer player with a Grade II inversion ankle sprain. This athlete sprained his ankle 6 weeks before the start of rehabilitation and was unable to participate in soccer due to persistent pain and impaired function. A 2-week functional training program was implemented, consisting of exercises chosen for specific task simulation related to soccer. Gravitational force was mechanically altered by suspending the subject or by supporting the subject on a variable incline plane. Weight-bearing was controlled so that the subject could perform exercises without pain. The outcome measures were ankle range of motion (ROM), maximum pain-free isometric strength, vertical force during unilateral squats, and unilateral hop time and distance. Pain-free weight-bearing capacity increased over the 2-week course of rehabilitation and the subject was able to return to playing soccer without pain. The ratios (involved to uninvolved extremity) at time of discharge from physical therapy were 87% to 103% for ankle ROM, 75% to 93% for isometric ankle strength, 91% for unilateral squats, 88% for unilateral hop time, and 86% for unilateral hop distance. Return to function can be achieved in a short period by exercise that is performed with a gradual increase in pain-free weight-bearing capacity.
Gogny interactions with tensor terms
Energy Technology Data Exchange (ETDEWEB)
Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)
2016-07-15
We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)
The geomagnetic field gradient tensor
DEFF Research Database (Denmark)
Kotsiaros, Stavros; Olsen, Nils
2012-01-01
We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...
Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.
Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M
2017-08-01
Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.
Directory of Open Access Journals (Sweden)
C. B. Alden
2018-03-01
Full Text Available Advances in natural gas extraction technology have led to increased activity in the production and transport sectors in the United States and, as a consequence, an increased need for reliable monitoring of methane leaks to the atmosphere. We present a statistical methodology in combination with an observing system for the detection and attribution of fugitive emissions of methane from distributed potential source location landscapes such as natural gas production sites. We measure long (> 500 m, integrated open-path concentrations of atmospheric methane using a dual frequency comb spectrometer and combine measurements with an atmospheric transport model to infer leak locations and strengths using a novel statistical method, the non-zero minimum bootstrap (NZMB. The new statistical method allows us to determine whether the empirical distribution of possible source strengths for a given location excludes zero. Using this information, we identify leaking source locations (i.e., natural gas wells through rejection of the null hypothesis that the source is not leaking. The method is tested with a series of synthetic data inversions with varying measurement density and varying levels of model–data mismatch. It is also tested with field observations of (1 a non-leaking source location and (2 a source location where a controlled emission of 3.1 × 10−5 kg s−1 of methane gas is released over a period of several hours. This series of synthetic data tests and outdoor field observations using a controlled methane release demonstrates the viability of the approach for the detection and sizing of very small leaks of methane across large distances (4+ km2 in synthetic tests. The field tests demonstrate the ability to attribute small atmospheric enhancements of 17 ppb to the emitting source location against a background of combined atmospheric (e.g., background methane variability and measurement uncertainty of 5 ppb (1σ, when
Alden, Caroline B.; Ghosh, Subhomoy; Coburn, Sean; Sweeney, Colm; Karion, Anna; Wright, Robert; Coddington, Ian; Rieker, Gregory B.; Prasad, Kuldeep
2018-03-01
Advances in natural gas extraction technology have led to increased activity in the production and transport sectors in the United States and, as a consequence, an increased need for reliable monitoring of methane leaks to the atmosphere. We present a statistical methodology in combination with an observing system for the detection and attribution of fugitive emissions of methane from distributed potential source location landscapes such as natural gas production sites. We measure long (> 500 m), integrated open-path concentrations of atmospheric methane using a dual frequency comb spectrometer and combine measurements with an atmospheric transport model to infer leak locations and strengths using a novel statistical method, the non-zero minimum bootstrap (NZMB). The new statistical method allows us to determine whether the empirical distribution of possible source strengths for a given location excludes zero. Using this information, we identify leaking source locations (i.e., natural gas wells) through rejection of the null hypothesis that the source is not leaking. The method is tested with a series of synthetic data inversions with varying measurement density and varying levels of model-data mismatch. It is also tested with field observations of (1) a non-leaking source location and (2) a source location where a controlled emission of 3.1 × 10-5 kg s-1 of methane gas is released over a period of several hours. This series of synthetic data tests and outdoor field observations using a controlled methane release demonstrates the viability of the approach for the detection and sizing of very small leaks of methane across large distances (4+ km2 in synthetic tests). The field tests demonstrate the ability to attribute small atmospheric enhancements of 17 ppb to the emitting source location against a background of combined atmospheric (e.g., background methane variability) and measurement uncertainty of 5 ppb (1σ), when measurements are averaged over 2 min. The
Dillon, Joshua V.; Langmore, Ian; Tran, Dustin; Brevdo, Eugene; Vasudevan, Srinivas; Moore, Dave; Patton, Brian; Alemi, Alex; Hoffman, Matt; Saurous, Rif A.
2017-01-01
The TensorFlow Distributions library implements a vision of probability theory adapted to the modern deep-learning paradigm of end-to-end differentiable computation. Building on two basic abstractions, it offers flexible building blocks for probabilistic computation. Distributions provide fast, numerically stable methods for generating samples and computing statistics, e.g., log density. Bijectors provide composable volume-tracking transformations with automatic caching. Together these enable...
The tensor product in Wadler's analysis of lists
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis
1994-01-01
We consider abstract interpretation (in particular strictness analysis) for pairs and lists. We begin by reviewing the well-known fact that the best known description of a pair of elements is obtained using the tensor product rather than the cartesian product. We next present a generalisation...... of Wadler's strictness analysis for lists (1987) using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation...
The tensor product in Wadler's analysis of lists
DEFF Research Database (Denmark)
Nielson, Flemming; Nielson, Hanne Riis
1992-01-01
We consider abstract interpretation (in particular strictness analysis) for pairs and lists. We begin by reviewing the well-known fact that the best known description of a pair of elements is obtained using the tensor product rather than the cartesian product. We next present a generalisation...... of Wadler's strictness analysis for lists using the notion of open set. Finally, we illustrate the intimate connection between the case analysis implicit in Wadler's strictness analysis and the precision that the tensor product allows for modelling the inverse cons operation....
Directory of Open Access Journals (Sweden)
Rex E Jung
Full Text Available That creativity and psychopathology are somehow linked remains a popular but controversial idea in neuroscience research. Brain regions implicated in both psychosis-proneness and creative cognition include frontal projection zones and association fibers. In normal subjects, we have previously demonstrated that a composite measure of divergent thinking (DT ability exhibited significant inverse relationships in frontal lobe areas with both cortical thickness and metabolite concentration of N-acetyl-aspartate (NAA. These findings support the idea that creativity may reside upon a continuum with psychopathology. Here we examine whether white matter integrity, assessed by Fractional Anisotropy (FA, is related to two measures of creativity (Divergent Thinking and Openness to Experience. Based on previous findings, we hypothesize inverse correlations within fronto-striatal circuits. Seventy-two healthy, young adult (18-29 years subjects were scanned on a 3 Tesla scanner with Diffusion Tensor Imaging. DT measures were scored by four raters (alpha = .81 using the Consensual Assessment Technique, from which a composite creativity index (CCI was derived. We found that the CCI was significantly inversely related to FA within the left inferior frontal white matter (t = 5.36, p = .01, and Openness was inversely related to FA within the right inferior frontal white matter (t = 4.61, p = .04. These findings demonstrate an apparent overlap in specific white matter architecture underlying the normal variance of divergent thinking, openness, and psychotic-spectrum traits, consistent with the idea of a continuum.
Tensor Permutation Matrices in Finite Dimensions
Christian, Rakotonirina
2005-01-01
We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...
Effect of cocaine on structural changes in brain: MRI volumetry using tensor-based morphometry.
Narayana, Ponnada A; Datta, Sushmita; Tao, Guozhi; Steinberg, Joel L; Moeller, F Gerard
2010-10-01
Magnetic resonance imaging (MRI) was performed in cocaine-dependent subjects to determine the structural changes in brain compared to non-drug using controls. Cocaine-dependent subjects and controls were carefully screened to rule out brain pathology of undetermined origin. Magnetic resonance images were analyzed using tensor-based morphometry (TBM) and voxel-based morphometry (VBM) without and with modulation to adjust for volume changes during normalization. For TBM analysis, unbiased atlases were generated using two different inverse consistent and diffeomorphic nonlinear registration techniques. Two different control groups were used for generating unbiased atlases. Independent of the nonlinear registration technique and normal cohorts used for creating the unbiased atlases, our analysis failed to detect any statistically significant effect of cocaine on brain volumes. These results show that cocaine-dependent subjects do not show differences in regional brain volumes compared to non-drug using controls. Copyright © 2010 Elsevier Ireland Ltd. All rights reserved.
Genten: Software for Generalized Tensor Decompositions v. 1.0.0
Energy Technology Data Exchange (ETDEWEB)
2017-06-22
Tensors, or multidimensional arrays, are a powerful mathematical means of describing multiway data. This software provides computational means for decomposing or approximating a given tensor in terms of smaller tensors of lower dimension, focusing on decomposition of large, sparse tensors. These techniques have applications in many scientific areas, including signal processing, linear algebra, computer vision, numerical analysis, data mining, graph analysis, neuroscience and more. The software is designed to take advantage of parallelism present emerging computer architectures such has multi-core CPUs, many-core accelerators such as the Intel Xeon Phi, and computation-oriented GPUs to enable efficient processing of large tensors.
Gaudiuso, R; Dell'Aglio, M; De Pascale, O; Loperfido, S; Mangone, A; De Giacomo, A
2014-02-27
A modified version of the calibration-free (CF) method was applied to the analysis of a set of archaeological brooches made of various copper-based alloys and coming from the archaeological site of Egnatia (Apulia, Southern Italy). The developed methodology consists in determining the plasma temperature by reversing the set of equations employed in the usual CF algorithm, and it is thus referred to as "inverse method". The plasma temperature is determined for one certified standard, by using its known elemental composition as an input data, and then applied to the set of unknown samples to evaluate their composition in a CF mode. The feasibility of such an approach is demonstrated by comparing the results obtained with classical LIBS (drawing calibration lines with a series of matrix-matched certified standards) and with independent measurements performed with a conventional technique (LA-ICP-MS). Copyright © 2014 Elsevier B.V. All rights reserved.
Shen, F.; Khodadadi, J. M.
1993-01-01
In order to determine the thermal diffusivity of materials at high temperatures, a two-step extended flash technique, which is applicable to levitated spherical samples, is proposed. The containerless flash method is modeled as an axisymmetric transient conduction heat transfer problem within the sphere subjected to a radiative boundary condition on its surface. The problem of nonlinearity which arises from the radiative heat transfer boundary condition is solved by replacing it with the measured time-dependent surface temperature data, thus giving rise to an 'Inverse Analysis'. Upon obtaining the analytic solution for the temperature field, the determination of the thermal diffusivity turns into a minimization problem, whereby the difference between the actual surface boundary condition and the analytic solution is minimized. In performing the proposed experiments, there is a need to undertake a cool-down experiment which should be governed by the lumped parameter analysis.
International Nuclear Information System (INIS)
Sargent, M.A.; Poskitt, K.J.
1997-01-01
Purpose. To evaluate fast spin-echo and multi-shot echo-planar fluid-attenuated inversion recovery (FLAIR) sequences in paediatric brain imaging. Materials and methods. Matched images from 32 patients with suspected tumour or white matter disease were independently evaluated by two paediatric neuroradiologists. The observer preferences for image quality and lesion detection were analysed for differences between fast spin-echo FLAIR and multi-shot echo-planar FLAIR. Diagnostic quality was compared with that of fast spin-echo T2-weighted images. Results. Images of a diagnostic quality equivalent to that of fast spin-echo T2-weighted images were achieved with both FLAIR techniques. Grey and white matter differentiation and cerebrospinal fluid (CSF) nulling were significantly better on fast spin-echo FLAIR sequences. CSF flow artefact was reduced on multi-shot echo-planar FLAIR. There was no difference in lesion detection. Fast spin-echo FLAIR images were visually preferred at the expense of longer imaging time. Conclusion. Fast FLAIR techniques are complementary to fast spin-echo T2-weighted sequences in imaging of the paediatric brain. We find that the fast spin-echo FLAIR sequence is preferable to the multi-shot echo-planar technique. (orig.). With 5 figs., 2 tabs
International Nuclear Information System (INIS)
Zimmerman, D.A.; Gallegos, D.P.
1993-10-01
The groundwater flow pathway in the Culebra Dolomite aquifer at the Waste Isolation Pilot Plant (WIPP) has been identified as a potentially important pathway for radionuclide migration to the accessible environment. Consequently, uncertainties in the models used to describe flow and transport in the Culebra need to be addressed. A ''Geostatistics Test Problem'' is being developed to evaluate a number of inverse techniques that may be used for flow calculations in the WIPP performance assessment (PA). The Test Problem is actually a series of test cases, each being developed as a highly complex synthetic data set; the intent is for the ensemble of these data sets to span the range of possible conceptual models of groundwater flow at the WIPP site. The Test Problem analysis approach is to use a comparison of the probabilistic groundwater travel time (GWTT) estimates produced by each technique as the basis for the evaluation. Participants are given observations of head and transmissivity (possibly including measurement error) or other information such as drawdowns from pumping wells, and are asked to develop stochastic models of groundwater flow for the synthetic system. Cumulative distribution functions (CDFs) of groundwater flow (computed via particle tracking) are constructed using the head and transmissivity data generated through the application of each technique; one semi-analytical method generates the CDFs of groundwater flow directly. This paper describes the results from Test Case No. 1
Tensor Factorization for Low-Rank Tensor Completion.
Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao
2018-03-01
Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.
Tensor norms and operator ideals
Defant, A; Floret, K
1992-01-01
The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer
Notes on super Killing tensors
Energy Technology Data Exchange (ETDEWEB)
Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)
2016-03-14
The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.
Tensor Train Neighborhood Preserving Embedding
Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin
2018-05-01
In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.
International Nuclear Information System (INIS)
Zimmerman, D.A.; Gallegos, D.P.
1993-01-01
The groundwater flow pathway in the Culebra Dolomite aquifer at the Waste Isolation Pilot Plant (WIPP) has been identified as a potentially important pathway for radionuclide migration to the accessible environment. Consequently, uncertainties in the models used to described flow and transport in the Culebra need to be addressed. A 'Geostatistics Test Problem' is being developed as a highly complex synthetic data set; the intent is for the ensemble of these data sets span the range of possible conceptual models of groundwater flow at the WIPP site. The Test Problem analysis approach is to use a comparison of the probabilistic groundwater travel time (GWTT) estimates produced by each technique as the basis for the evaluation. Participants are given observations of head and transmissivity and are asked to develop stochastic models of groundwater flow for the synthetic system. Cumulative distribution functions (CDFs) of groundwater flow (computed via particle tracking) are constructed using the head and transmissivity data generated through the application of each technique; one semi-analytical method generates the CDFs of groundwater flow directly. This paper describes the results from Test Case No 1. Of the five techniques compared, those based on the linearized form of the groundwater flow equation exhibited less bias and less spread in their GWTT distribution functions; the semi-analytical method had the least bias. While the results are not sufficient to make generalizations about which techniques may be better suited for the WIPP PA (only one test case has been exercised), analysis of the data from this test case provides some indication about the relative importance of other aspects of the flow modeling (besides inverse method or geostatistical approach) in PA. These ancillary analyses examine the effect of gridding and the effect of boundary conditions on the groundwater travel time estimates
High spatial resolution diffusion tensor imaging and its applications
Wang, J J
2002-01-01
Introduction Magnetic Resonance Imaging is at present the only imaging technique available to measure diffusion of water and metabolites in humans. It provides vital insights to brain connectivity and has proved to be an important tool in diagnosis and therapy planning in many neurological diseases such as brain tumour, ischaemia and multiple sclerosis. This project focuses on the development of a high resolution diffusion tensor imaging technique. In this thesis, the basic theory of diffusion tensor MR Imaging is presented. The technical challenges encountered during development of these techniques will be discussed, with proposed solutions. New sequences with high spatial resolution have been developed and the results are compared with the standard technique more commonly used. Overview The project aims at the development of diffusion tensor imaging techniques with a high spatial resolution. Chapter 2 will describe the basic physics of MRI, the phenomenon of diffusion and the measurement of diffusion by MRI...
Directory of Open Access Journals (Sweden)
Seyyed Ghoreishi
2017-09-01
Full Text Available Objective(S: In this work, paclitaxel (PX, a promising anticancer drug, was loaded in the basil seed mucilage (BSM aerogels by implementation of supercritical carbon dioxide (SC-CO2 technology. Then, the effects of operating conditions were studied on the PX mean particle size (MPS, particle size distribution (PSD and drug loading efficiency (DLE. Methods: The employed SC-CO2 process in this research is the combination of phase inversion technique and gas antisolvent (GAS process. The effect of DMSO/water ratio (4 and 6 (v/v, pressure (10-20 MPa, CO2 addition rate (1–3 mL/min and ethanol concentration (5-10% were studied on MPS, PSD and DLE. Scanning electron microscopy (SEM and Zetasizer were used for particle analysis. DLE was investigated by utilizing the high-performance liquid chromatography (HPLC. Results: Nanoparticles of paclitaxel (MPS of 82–131 nm depending on process variables with narrow PSD were successfully loaded in BSM aerogel with DLE of 28–52%. Experimental results indicated that higher DMSO/water ratio, ethanol concentration, pressure and CO2 addition rate reduced MPS and DLE. Conclusions: A modified semi batch SC-CO2 process based on the combination of gas antisolvent process and phase inversion methods using DMSO as co-solvent and ethanol as a secondary solvent was developed for the loading of an anticancer drug, PX, in ocimum basilicum mucilage aerogel. The experimental results determined that the mean particle size, particle size distribution, and drug loading efficiency be controlled with operating conditions.
Asymptotic tensor rank of graph tensors: beyond matrix multiplication
M. Christandl (Matthias); P. Vrana (Péter); J. Zuiddam (Jeroen)
2016-01-01
textabstractWe present an upper bound on the exponent of the asymptotic behaviour of the tensor rank of a family of tensors defined by the complete graph on $k$ vertices. For $k\\geq4$, we show that the exponent per edge is at most 0.77, outperforming the best known upper bound on the exponent per
Ingram, WT
2012-01-01
Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influen
Energy Technology Data Exchange (ETDEWEB)
Castaneda M, V. H.; Martinez B, M. R.; Solis S, L. O.; Castaneda M, R.; Leon P, A. A.; Hernandez P, C. F.; Espinoza G, J. G.; Ortiz R, J. M.; Vega C, H. R. [Universidad Autonoma de Zacatecas, 98000 Zacatecas, Zac. (Mexico); Mendez, R. [CIEMAT, Departamento de Metrologia de Radiaciones Ionizantes, Laboratorio de Patrones Neutronicos, Av. Complutense 22, 28040 Madrid (Spain); Gallego, E. [Universidad Politecnica de Madrid, Departamento de Ingenieria Nuclear, C. Jose Gutierrez Abascal 2, 28006 Madrid (Spain); Sousa L, M. A. [Comision Nacional de Energia Nuclear, Centro de Investigacion de Tecnologia Nuclear, Av. Pte. Antonio Carlos 6627, Pampulha, 31270-901 Belo Horizonte, Minas Gerais (Brazil)
2016-10-15
The Taguchi methodology has proved to be highly efficient to solve inverse problems, in which the values of some parameters of the model must be obtained from the observed data. There are intrinsic mathematical characteristics that make a problem known as inverse. Inverse problems appear in many branches of science, engineering and mathematics. To solve this type of problem, researches have used different techniques. Recently, the use of techniques based on Artificial Intelligence technology is being explored by researches. This paper presents the use of a software tool based on artificial neural networks of generalized regression in the solution of inverse problems with application in high energy physics, specifically in the solution of the problem of neutron spectrometry. To solve this problem we use a software tool developed in the Mat Lab programming environment, which employs a friendly user interface, intuitive and easy to use for the user. This computational tool solves the inverse problem involved in the reconstruction of the neutron spectrum based on measurements made with a Bonner spheres spectrometric system. Introducing this information, the neural network is able to reconstruct the neutron spectrum with high performance and generalization capability. The tool allows that the end user does not require great training or technical knowledge in development and/or use of software, so it facilitates the use of the program for the resolution of inverse problems that are in several areas of knowledge. The techniques of Artificial Intelligence present singular veracity to solve inverse problems, given the characteristics of artificial neural networks and their network topology, therefore, the tool developed has been very useful, since the results generated by the Artificial Neural Network require few time in comparison to other techniques and are correct results comparing them with the actual data of the experiment. (Author)
New results for algebraic tensor reduction of Feynman integrals
Energy Technology Data Exchange (ETDEWEB)
Fleischer, Jochem [Bielefeld Univ. (Germany). Fakultaet fuer Physik; Riemann, Tord [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany); Yundin, Valery [Copenhagen Univ. (Denmark). Niels Bohr International Academy and Discovery Center
2012-02-15
We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2{epsilon}. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)
New results for algebraic tensor reduction of Feynman integrals
International Nuclear Information System (INIS)
Fleischer, Jochem; Yundin, Valery
2012-02-01
We report on some recent developments in algebraic tensor reduction of one-loop Feynman integrals. For 5-point functions, an efficient tensor reduction was worked out recently and is now available as numerical C++ package, PJFry, covering tensor ranks until five. It is free of inverse 5- point Gram determinants and inverse small 4-point Gram determinants are treated by expansions in higher-dimensional 3-point functions. By exploiting sums over signed minors, weighted with scalar products of chords (or, equivalently, external momenta), extremely efficient expressions for tensor integrals contracted with external momenta were derived. The evaluation of 7-point functions is discussed. In the present approach one needs for the reductions a (d +2)-dimensional scalar 5-point function in addition to the usual scalar basis of 1- to 4-point functions in the generic dimension d=4-2ε. When exploiting the four-dimensionality of the kinematics, this basis is sufficient. We indicate how the (d+2)-dimensional 5-point function can be evaluated. (orig.)
Indicial tensor manipulation on MACSYMA
International Nuclear Information System (INIS)
Bogen, R.A.; Pavelle, R.
1977-01-01
A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)
Killing-Yano tensors and Nambu mechanics
International Nuclear Information System (INIS)
Baleanu, D.
1998-01-01
Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3
Diffusion tensor MRI: clinical applications
International Nuclear Information System (INIS)
Meli, Francisco; Romero, Carlos; Carpintiero, Silvina; Salvatico, Rosana; Lambre, Hector; Vila, Jose
2005-01-01
Purpose: To evaluate the usefulness of diffusion-tensor imaging (DTI) on different neurological diseases, and to know if this technique shows additional information than conventional Magnetic Resonance Imaging (MRI). Materials and method: Eight patients, with neurological diseases (five patients with brain tumors, one with multiple sclerosis (MS), one with variant Creutzfeldt-Jakob disease (vCJD) and the other with delayed CO intoxication were evaluated. A MR scanner of 1.5 T was used and conventional sequences and DTI with twenty-five directions were done. Quantitative maps were gotten, where the fractional anisotropy (FA) through regions of interest (ROIs) in specific anatomic area were quantified (i.e.: internal and external capsules, frontal and temporal bundles, corpus fibers). Results: In the patients with brain tumors, there was a decrease of FA on intra and peritumoral fibers. Some of them had a disruption in their pattern. In patients with MS and CO intoxication, partial interruption along white matter bundles was demonstrated. However, a 'mismatch' between the findings of FLAIR, Diffusion-weighted images (DWI) and DTI, in the case of CO intoxication, was seen. Conclusions: DTI gave more information compared to conventional sequences about ultrastructural brain tissue in almost all the diseases above mentioned. Therefore, there is a work in progress about DTI acquisition, to evaluate a new technique, called tractography. (author)
Nonlocal denoising using anisotropic structure tensor for 3D MRI.
Wu, Xi; Liu, Shujuan; Wu, Min; Sun, Huaiqiang; Zhou, Jiliu; Gong, Qiyong; Ding, Zhaohua
2013-10-01
Noise in magnetic resonance imaging (MRI) data is widely recognized to be harmful to image processing and subsequent quantitative analysis. To ameliorate the effects of image noise, the authors present a structure-tensor based nonlocal mean (NLM) denoising technique that can effectively reduce noise in MRI data and improve tissue characterization. The proposed 3D NLM algorithm uses a structure tensor to characterize information around tissue boundaries. The similarity weight of a pixel (or patch), which determines its contribution to the denoising process, is determined by the intensity and structure tensor simultaneously. Meanwhile, similarity of structure tensors is computed using an affine-invariant Riemannian metrics, which compares tensor properties more comprehensively and avoids orientation inaccuracy of structure subsequently. The proposed method is further extended for denoising high dimensional MRI data such as diffusion weighted MRI. It is also extended to handle Rician noise corruption so that denoising effects are further enhanced. The proposed method was implemented in both simulated datasets and multiply modalities of real 3D MRI datasets. Comparisons with related state-of-the-art algorithms demonstrated that this method improves denoising performance qualitatively and quantitatively. In this paper, high order structure information of 3D MRI was characterized by 3D structure tensor and compared for NLM denoising in a Riemannian space. Experiments with simulated and real human MRI data demonstrate a great potential of the proposed technique for routine clinical use.
Local recovery of lithospheric stress tensor from GOCE gravitational tensor
Eshagh, Mehdi
2017-04-01
The sublithospheric stress due to mantle convection can be computed from gravity data and propagated through the lithosphere by solving the boundary-value problem of elasticity for the Earth's lithosphere. In this case, a full tensor of stress can be computed at any point inside this elastic layer. Here, we present mathematical foundations for recovering such a tensor from gravitational tensor measured at satellite altitudes. The mathematical relations will be much simpler in this way than the case of using gravity data as no derivative of spherical harmonics (SHs) or Legendre polynomials is involved in the expressions. Here, new relations between the SH coefficients of the stress and gravitational tensor elements are presented. Thereafter, integral equations are established from them to recover the elements of stress tensor from those of the gravitational tensor. The integrals have no closed-form kernels, but they are easy to invert and their spatial truncation errors are reducible. The integral equations are used to invert the real data of the gravity field and steady-state ocean circulation explorer mission (GOCE), in 2009 November, over the South American plate and its surroundings to recover the stress tensor at a depth of 35 km. The recovered stress fields are in good agreement with the tectonic and geological features of the area.
Reduction method for one-loop tensor 5- and 6-point integrals revisited
International Nuclear Information System (INIS)
Diakonidis, Theodoros
2009-01-01
A complete analytical reduction of general one-loop Feynman integrals with five legs for tensors up to rank R=3 and six legs for tensors up to rank 4 is reviewed. An elegant formalism with extensive use of signed minors was developed for the cancellation of leading inverse Gram determinants. The resulting compact formulae allow both for a study of analytical properties and for efficient numerical programming. Here some special numerical examples are presented. (orig.)
Tensor-GMRES method for large sparse systems of nonlinear equations
Feng, Dan; Pulliam, Thomas H.
1994-01-01
This paper introduces a tensor-Krylov method, the tensor-GMRES method, for large sparse systems of nonlinear equations. This method is a coupling of tensor model formation and solution techniques for nonlinear equations with Krylov subspace projection techniques for unsymmetric systems of linear equations. Traditional tensor methods for nonlinear equations are based on a quadratic model of the nonlinear function, a standard linear model augmented by a simple second order term. These methods are shown to be significantly more efficient than standard methods both on nonsingular problems and on problems where the Jacobian matrix at the solution is singular. A major disadvantage of the traditional tensor methods is that the solution of the tensor model requires the factorization of the Jacobian matrix, which may not be suitable for problems where the Jacobian matrix is large and has a 'bad' sparsity structure for an efficient factorization. We overcome this difficulty by forming and solving the tensor model using an extension of a Newton-GMRES scheme. Like traditional tensor methods, we show that the new tensor method has significant computational advantages over the analogous Newton counterpart. Consistent with Krylov subspace based methods, the new tensor method does not depend on the factorization of the Jacobian matrix. As a matter of fact, the Jacobian matrix is never needed explicitly.
International Nuclear Information System (INIS)
Beleggia, M.; Graef, M. de
2003-01-01
A method is presented to compute the demagnetization tensor field for uniformly magnetized particles of arbitrary shape. By means of a Fourier space approach it is possible to compute analytically the Fourier representation of the demagnetization tensor field for a given shape. Then, specifying the direction of the uniform magnetization, the demagnetizing field and the magnetostatic energy associated with the particle can be evaluated. In some particular cases, the real space representation is computable analytically. In general, a numerical inverse fast Fourier transform is required to perform the inversion. As an example, the demagnetization tensor field for the tetrahedron will be given
Honda, Norihiro; Nanjo, Takuya; Ishii, Katsunori; Awazu, Kunio
2012-03-01
In laser medicine, the accurate knowledge about the optical properties (absorption coefficient; μa, scattering coefficient; μs, anisotropy factor; g) of laser irradiated tissues is important for the prediction of light propagation in tissues, since the efficacy of laser treatment depends on the photon propagation within the irradiated tissues. Thus, it is likely that the optical properties of tissues at near-ultraviolet, visible and near-infrared wavelengths will be more important due to more biomedical applications of lasers will be developed. For improvement of the laser induced thermotherapy, the optical property change during laser treatment should be considered in the wide wavelength range. For estimation of the optical properties of the biological tissues, the optical properties measurement system with a double integrating sphere setup and an inverse Monte Carlo technique was developed. The optical properties of chicken muscle tissue were measured in the native state and after laser coagulation using the optical properties measurement system in the wavelength range from 350 to 2100 nm. A CO2 laser was used for laser coagulation. After laser coagulation, the reduced scattering coefficient of the tissue increased. And, the optical penetration depth decreased. For improvement of the treatment depth during laser coagulation, a quantitative procedure using the treated tissue optical properties for determination of the irradiation power density following light penetration decrease might be important in clinic.
LiFAP-based PVdF-HFP microporous membranes by phase-inversion technique with Li/LiFePO{sub 4} cell
Energy Technology Data Exchange (ETDEWEB)
Aravindan, V.; Vickraman, P. [Gandhigram Rural University, Department of Physics, Gandhigram (India); Sivashanmugam, A.; Thirunakaran, R.; Gopukumar, S. [Central Electrochemical Research Institute, Electrochemical Energy Systems Division, Karaikudi (India)
2009-12-15
Polyvinylidenefluoride-hexafluoropropylene-based (PVdF-HFP-based) gel and composite microporous membranes (GPMs and CPMs) were prepared by phase-inversion technique in the presence 10 wt% of AlO(OH){sub n} nanoparticles. The prepared membranes were gelled with 0.5-M LiPF{sub 3}(CF{sub 2}CF{sub 3}){sub 3} (lithium fluoroalkylphosphate, LiFAP) in EC:DEC (1:1 v/v) and subjected to various characterizations; the AC impedance study shows that CPMs exhibit higher conductivity than GPMs. Mechanical stability measurements on these systems reveal that CPMs exhibit Young's modulus higher than that of bare and GPMs and addition of nanoparticles drastically improves the elongation break was also noted. Transition of the host from {alpha} to {beta} phase after the loading of nanosized filler was confirmed by XRD and Raman studies. Physico-chemical properties, like liquid uptake, porosity, surface area, and activation energy, of the membranes were calculated and results are summarized. Cycling performance of Li/CPM/LiFePO{sub 4} coin cell was fabricated and evaluated at C/10 rate and delivered a discharge capacity of 157 and 148 mAh g {sup -1} respectively for first and tenth cycles. (orig.)
Mishin, V. V.; Mishin, V. M.; Karavaev, Yu.; Han, J. P.; Wang, C.
2016-07-01
We report on novel features of the saturation process of the polar cap magnetic flux and Poynting flux into the magnetosphere from the solar wind during three superstorms. In addition to the well-known effect of the interplanetary electric (Esw) and southward magnetic (interplanetary magnetic field (IMF) Bz) fields, we found that the saturation depends also on the solar wind ram pressure Pd. By means of the magnetogram inversion technique and a global MHD numerical model Piecewise Parabolic Method with a Lagrangian Remap, we explore the dependence of the magnetopause standoff distance on ram pressure and the southward IMF. Unlike earlier studies, in the considered superstorms both Pd and Bz achieve extreme values. As a result, we show that the compression rate of the dayside magnetosphere decreases with increasing Pd and the southward Bz, approaching very small values for extreme Pd ≥ 15 nPa and Bz ≤ -40 nT. This dependence suggests that finite compressibility of the magnetosphere controls saturation of superstorms.
International Nuclear Information System (INIS)
Zhang Lin; Wang Chaoyang; Luo Xuan; Du Kai; Tu Haiyan; Fan Hong; Luo Qing; Yuan Guanghui; Huang Lizhen
2003-01-01
By thermally induced phase-inversion technique, ploy (4-methyl-1-pentene) (PMP) foams are successfully prepared; the density and pore size are 3-80 mg/cm 3 and 1-20 μm respectively. Durene/naphthalene (60/40) is confirmed as the suitable solvent/nonsolvent binary system. The PMP's thermal properties are characterized by TG-DSC system. It is found that the foams thermal properties depend on the density. The thermal analysis method is utilized to measure the gelation of PMP in the binary solvent/nonsolvent system. The range of gelation temperature is preliminarily determined. The influence of mixture system composition and the cooling rate during the making of foams is discussed. TG-DSC is applied to determine the thermal properties of low-density PMP foams prepared in the laboratory. And the effect of density change on the thermal stability of foams are studied. The thermal analysis data play a great role in improving the foam quality. (authors)
Inverse problem in transformation optics
DEFF Research Database (Denmark)
Novitsky, Andrey
2011-01-01
. We offer the solution of some sort of inverse problem: starting from the fields in the invisibility cloak we directly derive the permittivity and permeability tensors of the cloaking shell. This approach can be useful for finding material parameters for the specified electromagnetic fields......The straightforward method of transformation optics implies that one starts from the coordinate transformation and determines the Jacobian matrix, the fields and material parameters of the cloak. However, the coordinate transformation appears as an optional function: it is not necessary to know it...... in the cloaking shell without knowing the coordinate transformation....
Dibb, Russell; Liu, Chunlei
2017-06-01
To develop a susceptibility-based MRI technique for probing microstructure and fiber architecture of magnetically anisotropic tissues-such as central nervous system white matter, renal tubules, and myocardial fibers-in three dimensions using susceptibility tensor imaging (STI) tools. STI can probe tissue microstructure, but is limited by reconstruction artifacts because of absent phase information outside the tissue and noise. STI accuracy may be improved by estimating a joint eigenvector from mutually anisotropic susceptibility and relaxation tensors. Gradient-recalled echo image data were simulated using a numerical phantom and acquired from the ex vivo mouse brain, kidney, and heart. Susceptibility tensor data were reconstructed using STI, regularized STI, and the proposed algorithm of mutually anisotropic and joint eigenvector STI (MAJESTI). Fiber map and tractography results from each technique were compared with diffusion tensor data. MAJESTI reduced the estimated susceptibility tensor orientation error by 30% in the phantom, 36% in brain white matter, 40% in the inner medulla of the kidney, and 45% in myocardium. This improved the continuity and consistency of susceptibility-based fiber tractography in each tissue. MAJESTI estimation of the susceptibility tensors yields lower orientation errors for susceptibility-based fiber mapping and tractography in the intact brain, kidney, and heart. Magn Reson Med 77:2331-2346, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.
MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-10-01
Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.
Random SU(2) invariant tensors
Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei
2018-04-01
SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n = 4. In this paper, we show that for n > 4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.
Full-wave Moment Tensor and Tomographic Inversions Based on 3D Strain Green Tensor
2010-01-31
out on a Beowulf PC cluster purchased with a grant from the National Science Foundation. This work would not be possible without the creativity and...J. Ritsema, and J. Tromp, The spectral-element method, Beowulf computing, and global seismology, Science 298, 1737-1742, 2002. Li, X., and B
Calculating contracted tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.; Riemann, T.
2011-01-01
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this Letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with external momenta. This is based on sums over signed minors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently.
Calculating contracted tensor Feynman integrals
International Nuclear Information System (INIS)
Fleischer, J.
2011-05-01
A recently derived approach to the tensor reduction of 5-point one-loop Feynman integrals expresses the tensor coefficients by scalar 1-point to 4-point Feynman integrals completely algebraically. In this letter we derive extremely compact algebraic expressions for the contractions of the tensor integrals with externalmomenta. This is based on sums over signedminors weighted with scalar products of the external momenta. With these contractions one can construct the invariant amplitudes of the matrix elements under consideration, and the evaluation of one-loop contributions to massless and massive multi-particle production at high energy colliders like LHC and ILC is expected to be performed very efficiently. (orig.)
Tensor Product of Polygonal Cell Complexes
Chien, Yu-Yen
2017-01-01
We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.
A linear support higher-order tensor machine for classification.
Hao, Zhifeng; He, Lifang; Chen, Bingqian; Yang, Xiaowei
2013-07-01
There has been growing interest in developing more effective learning machines for tensor classification. At present, most of the existing learning machines, such as support tensor machine (STM), involve nonconvex optimization problems and need to resort to iterative techniques. Obviously, it is very time-consuming and may suffer from local minima. In order to overcome these two shortcomings, in this paper, we present a novel linear support higher-order tensor machine (SHTM) which integrates the merits of linear C-support vector machine (C-SVM) and tensor rank-one decomposition. Theoretically, SHTM is an extension of the linear C-SVM to tensor patterns. When the input patterns are vectors, SHTM degenerates into the standard C-SVM. A set of experiments is conducted on nine second-order face recognition datasets and three third-order gait recognition datasets to illustrate the performance of the proposed SHTM. The statistic test shows that compared with STM and C-SVM with the RBF kernel, SHTM provides significant performance gain in terms of test accuracy and training speed, especially in the case of higher-order tensors.
Anisotropic conductivity tensor imaging in MREIT using directional diffusion rate of water molecules
International Nuclear Information System (INIS)
Kwon, Oh In; Jeong, Woo Chul; Sajib, Saurav Z K; Kim, Hyung Joong; Woo, Eung Je
2014-01-01
Magnetic resonance electrical impedance tomography (MREIT) is an emerging method to visualize electrical conductivity and/or current density images at low frequencies (below 1 KHz). Injecting currents into an imaging object, one component of the induced magnetic flux density is acquired using an MRI scanner for isotropic conductivity image reconstructions. Diffusion tensor MRI (DT-MRI) measures the intrinsic three-dimensional diffusion property of water molecules within a tissue. It characterizes the anisotropic water transport by the effective diffusion tensor. Combining the DT-MRI and MREIT techniques, we propose a novel direct method for absolute conductivity tensor image reconstructions based on a linear relationship between the water diffusion tensor and the electrical conductivity tensor. We first recover the projected current density, which is the best approximation of the internal current density one can obtain from the measured single component of the induced magnetic flux density. This enables us to estimate a scale factor between the diffusion tensor and the conductivity tensor. Combining these values at all pixels with the acquired diffusion tensor map, we can quantitatively recover the anisotropic conductivity tensor map. From numerical simulations and experimental verifications using a biological tissue phantom, we found that the new method overcomes the limitations of each method and successfully reconstructs both the direction and magnitude of the conductivity tensor for both the anisotropic and isotropic regions. (paper)
Colored Tensor Models - a Review
Directory of Open Access Journals (Sweden)
Razvan Gurau
2012-04-01
Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.
Vilanova, Anna; Burgeth, Bernhard; Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data
2014-01-01
Arising from the fourth Dagstuhl conference entitled Visualization and Processing of Tensors and Higher Order Descriptors for Multi-Valued Data (2011), this book offers a broad and vivid view of current work in this emerging field. Topics covered range from applications of the analysis of tensor fields to research on their mathematical and analytical properties. Part I, Tensor Data Visualization, surveys techniques for visualization of tensors and tensor fields in engineering, discusses the current state of the art and challenges, and examines tensor invariants and glyph design, including an overview of common glyphs. The second Part, Representation and Processing of Higher-order Descriptors, describes a matrix representation of local phase, outlines mathematical morphological operations techniques, extended for use in vector images, and generalizes erosion to the space of diffusion weighted MRI. Part III, Higher Order Tensors and Riemannian-Finsler Geometry, offers powerful mathematical language to model and...
Directory of Open Access Journals (Sweden)
María Fernanda Garcés
2017-04-01
Conclusions: Inversions of intron 22 and 1 were found in half of this group of patients. These results are reproducible and useful to identify the two most frequent mutations in severe hemophilia A patients.
Fast computation of the inverse CMH model
Patel, Umesh D.; Della Torre, Edward
2001-12-01
A fast computational method based on differential equation approach for inverse Della Torre, Oti, Kádár (DOK) model has been extended for the inverse Complete Moving Hysteresis (CMH) model. A cobweb technique for calculating the inverse CMH model is also presented. The two techniques differ from the point of view of flexibility, accuracy, and computation time. Simulation results of the inverse computation for both methods are presented.
Retinal Vessel Segmentation via Structure Tensor Coloring and Anisotropy Enhancement
Directory of Open Access Journals (Sweden)
Mehmet Nergiz
2017-11-01
Full Text Available Retinal vessel segmentation is one of the preliminary tasks for developing diagnosis software systems related to various retinal diseases. In this study, a fully automated vessel segmentation system is proposed. Firstly, the vessels are enhanced using a Frangi Filter. Afterwards, Structure Tensor is applied to the response of the Frangi Filter and a 4-D tensor field is obtained. After decomposing the Eigenvalues of the tensor field, the anisotropy between the principal Eigenvalues are enhanced exponentially. Furthermore, this 4-D tensor field is converted to the 3-D space which is composed of energy, anisotropy and orientation and then a Contrast Limited Adaptive Histogram Equalization algorithm is applied to the energy space. Later, the obtained energy space is multiplied by the enhanced mean surface curvature of itself and the modified 3-D space is converted back to the 4-D tensor field. Lastly, the vessel segmentation is performed by using Otsu algorithm and tensor coloring method which is inspired by the ellipsoid tensor visualization technique. Finally, some post-processing techniques are applied to the segmentation result. In this study, the proposed method achieved mean sensitivity of 0.8123, 0.8126, 0.7246 and mean specificity of 0.9342, 0.9442, 0.9453 as well as mean accuracy of 0.9183, 0.9442, 0.9236 for DRIVE, STARE and CHASE_DB1 datasets, respectively. The mean execution time of this study is 6.104, 6.4525 and 18.8370 s for the aforementioned three datasets respectively.
The energy-momentum tensor of a black hole, or what curves the Schwarzschild geometry?
Balasin, H.; Nachbagauer, H.
1993-11-01
Using distributional techniques we calculate the energy--momentum tensor of the Schwarzschild geometry. It turns out to be a well--defined tensor--distribution concentrated on the $r=0$ region which is usually excluded from space--time. This provides a physical interpretation for the curvature of this geometry.
A simple and accurate technique is described for measuring the uniaxial permittivity tensor of biological materials with a coplanar waveguide transmission-line configuration. Permittivity tensor results are presented for several chicken and beef fresh meat samples at 2.45 GHz....
Renormalized energy-momentum tensor of λΦ4 theory in curved ...
Indian Academy of Sciences (India)
Renormalization of the energy-momentum tensor for λΦΦ4 theory. Our aim is to obtain finite expression for the energy-momentum tensor of a quantized scalar field interacting with classical Einstein gravitational field using momentum cut-off regular- ization technique. We have chosen the λΦ4 model of self-interaction, and ...
Renormalized energy-momentum tensor of λΦ4 theory in curved ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 60; Issue 6. Renormalized energy-momentum tensor of 4 theory in curved space-time. K G Arun Minu Joy ... Divergenceless expression for the energy-momentum tensor of scalar ﬁeld is obtained using the momentum cut-off regularization technique. We consider a ...
Measurement of mean rotation and strain-rate tensors by using stereoscopic PIV
DEFF Research Database (Denmark)
Özcan, Oktay; Meyer, Knud Erik; Larsen, Poul Scheel
2005-01-01
A technique is described for measuring the mean velocity gradient (rate-of-displacement) tensor by using a conventional stereoscopic particle image velocimetry (SPIV) system. Planar measurement of the mean vorticity vector, rate-of-rotation and rate-of-strain tensors and the production of turbule...
Energy Technology Data Exchange (ETDEWEB)
Shin, Chang Soo; Park, Keun Pil [Korea Inst. of Geology Mining and Materials, Taejon (Korea, Republic of); Suh, Jung Hee; Hyun, Byung Koo; Shin, Sung Ryul [Seoul National University, Seoul (Korea, Republic of)
1995-12-01
The seismic reflection exploration technique which is one of the geophysical methods for oil exploration became effectively to image the subsurface structure with rapid development of computer. However, the imagining of subsurface based on the conventional data processing is almost impossible to obtain the information on physical properties of the subsurface such as velocity and density. Since seismic data are implicitly function of velocities of subsurface, it is necessary to develop the inversion method that can delineate the velocity structure using seismic topography and waveform inversion. As a tool to perform seismic inversion, seismic forward modeling program using ray tracing should be developed. In this study, we have developed the algorithm that calculate the travel time of the complex geologic structure using shooting ray tracing by subdividing the geologic model into blocky structure having the constant velocity. With the travel time calculation, the partial derivatives of travel time can be calculated efficiently without difficulties. Since the current ray tracing technique has a limitation to calculate the travel times for extremely complex geologic model, our aim in the future is to develop the powerful ray tracer using the finite element technique. After applying the pseudo waveform inversion to the seismic data of Korea offshore, we can obtain the subsurface velocity model and use the result in bring up the quality of the seismic data processing. If conventional seismic data processing and seismic interpretation are linked with this inversion technique, the high quality of seismic data processing can be expected to image the structure of the subsurface. Future research area is to develop the powerful ray tracer of ray tracing which can calculate the travel times for the extremely complex geologic model. (author). 39 refs., 32 figs., 2 tabs.
Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature
Loveridge, Lee C.
2004-01-01
Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.
A Simplified Algorithm for Inverting Higher Order Diffusion Tensors
Directory of Open Access Journals (Sweden)
Laura Astola
2014-11-01
Full Text Available In Riemannian geometry, a distance function is determined by an inner product on the tangent space. In Riemann–Finsler geometry, this distance function can be determined by a norm. This gives more freedom on the form of the so-called indicatrix or the set of unit vectors. This has some interesting applications, e.g., in medical image analysis, especially in diffusion weighted imaging (DWI. An important application of DWI is in the inference of the local architecture of the tissue, typically consisting of thin elongated structures, such as axons or muscle fibers, by measuring the constrained diffusion of water within the tissue. From high angular resolution diffusion imaging (HARDI data, one can estimate the diffusion orientation distribution function (dODF, which indicates the relative diffusivity in all directions and can be represented by a spherical polynomial. We express this dODF as an equivalent spherical monomial (higher order tensor to directly generalize the (second order diffusion tensor approach. To enable efficient computation of Riemann–Finslerian quantities on diffusion weighted (DW-images, such as the metric/norm tensor, we present a simple and efficient algorithm to invert even order spherical monomials, which extends the familiar inversion of diffusion tensors, i.e., symmetric matrices.
The tensor rank of tensor product of two three-qubit W states is eight
Chen, Lin; Friedland, Shmuel
2017-01-01
We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.
Link prediction via generalized coupled tensor factorisation
DEFF Research Database (Denmark)
Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.
2012-01-01
and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....
The metric theory of tensor products Grothendieck's resume revisited
Diestel, Joe; Swart, Johan; Swarte, Johannes Laurentius; Diestel, Joseph
2008-01-01
Grothendieck's Resumé is a landmark in functional analysis. Despite having appeared more than a half century ago, its techniques and results are still not widely known nor appreciated. This is due, no doubt, to the fact that Grothendieck included practically no proofs, and the presentation is based on the theory of the very abstract notion of tensor products. This book aims at providing the details of Grothendieck's constructions and laying bare how the important classes of operators are a consequence of the abstract operations on tensor norms. Particular attention is paid to how the classical
Seimandi, Mathieu; Bockaert, Joël; Marin, Philippe
2010-01-01
Serotonin (5-HT)(₂C) receptors play a major role in the regulation of mood, and alteration of their functional status has been implicated in the etiology of affect disorders. Correspondingly, they represent an important target for various antidepressant categories, including tricyclics, tetracyclics, mCPP derivatives, specific serotonin reuptake inhibitors, and agomelatine, which exhibit medium to high affinities for 5-HT(₂C) receptors and behave as antagonists. Antidepressant effects of 5-HT(₂C) antagonists have been attributed to a disinhibition of mesocorticolimbic dopaminergic pathways, which exert a beneficial influence upon mood and cognitive functions altered in depression. However, recent experimental evidence revealed a prominent role of constitutive activity in the tonic inhibitory control of dopaminergic transmission exerted by 5-HT(₂C) receptors in specific brain areas such as the nucleus accumbens. Accordingly, alteration in the constitutive activity of 5-HT(₂C) receptors might participate in the induction of depressed states and drugs with inverse agonist properties should themselves be effective antidepressant agents and, possibly, more active than neutral antagonists. This highlights the relevance of systematically evaluating inverse agonist versus neutral antagonist activities of antidepressants acting at 5-HT(₂C) receptors. Here, we provide a detailed description of a palette of cellular assays exploiting constitutive activity of 5-HT(₂C) receptor expressed in heterologous cells (such as HEK-293 cells) toward Gq-operated signaling or their constitutive association with β-arrestins to evaluate inverse agonist activity of antidepressants. We also describe an approach allowing discrimination between inverse agonist and neutral antagonist activities of antidepressants at native constitutively active receptors expressed in cultured cortical neurons, based on previous findings indicating that prolonged treatments with inverse agonists
Tensor product of quantum logics
Pulmannová, Sylvia
1985-01-01
A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch-Piron property in the σ-form is also supposed for any state of M. A ``tensor product'' of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.
Phase transition in tensor models
Energy Technology Data Exchange (ETDEWEB)
Delepouve, Thibault [Laboratoire de Physique Théorique, CNRS UMR 8627, Université Paris Sud,91405 Orsay Cedex (France); Centre de Physique Théorique, CNRS UMR 7644, École Polytechnique,91128 Palaiseau Cedex (France); Gurau, Razvan [Centre de Physique Théorique, CNRS UMR 7644, École Polytechnique,91128 Palaiseau Cedex (France); Perimeter Institute for Theoretical Physics,31 Caroline St. N, N2L 2Y5, Waterloo, ON (Canada)
2015-06-25
Generalizing matrix models, tensor models generate dynamical triangulations in any dimension and support a 1/N expansion. Using the intermediate field representation we explicitly rewrite a quartic tensor model as a field theory for a fluctuation field around a vacuum state corresponding to the resummation of the entire leading order in 1/N (a resummation of the melonic family). We then prove that the critical regime in which the continuum limit in the sense of dynamical triangulations is reached is precisely a phase transition in the field theory sense for the fluctuation field.
Tensor calculus for physics a concise guide
Neuenschwander, Dwight E
2015-01-01
Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...
The 'gravitating' tensor in the dualistic theory
International Nuclear Information System (INIS)
Mahanta, M.N.
1989-01-01
The exact microscopic system of Einstein-type field equations of the dualistic gravitation theory is investigated as well as an analysis of the modified energy-momentum tensor or so called 'gravitating' tensor is presented
Reciprocal mass tensor : a general form
International Nuclear Information System (INIS)
Roy, C.L.
1978-01-01
Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)
A new deteriorated energy-momentum tensor
International Nuclear Information System (INIS)
Duff, M.J.
1982-01-01
The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)
Tensor-based spatiotemporal saliency detection
Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen
2018-03-01
This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.
Akkerman, Erik M.
2010-01-01
Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional
Weyl tensors for asymmetric complex curvatures
International Nuclear Information System (INIS)
Oliveira, C.G.
Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt
Vector and tensor analysis with applications
Borisenko, A I; Silverman, Richard A
1979-01-01
Concise and readable, this text ranges from definition of vectors and discussion of algebraic operations on vectors to the concept of tensor and algebraic operations on tensors. It also includes a systematic study of the differential and integral calculus of vector and tensor functions of space and time. Worked-out problems and solutions. 1968 edition.
Tensor Completion for Estimating Missing Values in Visual Data
Liu, Ji
2012-01-25
In this paper, we propose an algorithm to estimate missing values in tensors of visual data. The values can be missing due to problems in the acquisition process or because the user manually identified unwanted outliers. Our algorithm works even with a small amount of samples and it can propagate structure to fill larger missing regions. Our methodology is built on recent studies about matrix completion using the matrix trace norm. The contribution of our paper is to extend the matrix case to the tensor case by proposing the first definition of the trace norm for tensors and then by building a working algorithm. First, we propose a definition for the tensor trace norm that generalizes the established definition of the matrix trace norm. Second, similarly to matrix completion, the tensor completion is formulated as a convex optimization problem. Unfortunately, the straightforward problem extension is significantly harder to solve than the matrix case because of the dependency among multiple constraints. To tackle this problem, we developed three algorithms: simple low rank tensor completion (SiLRTC), fast low rank tensor completion (FaLRTC), and high accuracy low rank tensor completion (HaLRTC). The SiLRTC algorithm is simple to implement and employs a relaxation technique to separate the dependant relationships and uses the block coordinate descent (BCD) method to achieve a globally optimal solution; the FaLRTC algorithm utilizes a smoothing scheme to transform the original nonsmooth problem into a smooth one and can be used to solve a general tensor trace norm minimization problem; the HaLRTC algorithm applies the alternating direction method of multipliers (ADMMs) to our problem. Our experiments show potential applications of our algorithms and the quantitative evaluation indicates that our methods are more accurate and robust than heuristic approaches. The efficiency comparison indicates that FaLTRC and HaLRTC are more efficient than SiLRTC and between Fa
Interpolation and Inversion - New Features in the Matlab Sesimic Anisotropy Toolbox
Walker, A.; Wookey, J. M.
2015-12-01
A key step in studies of seismic anisotropy in the mantle is often the creation of models designed to explain its physical origin. We previously released MSAT (the Matlab Seismic Anisotropy Toolbox), which includes a range of functions that can be used together to build these models and provide geological or geophysical insight given measurements of, for example, shear-wave splitting. Here we describe some of the new features of MSAT that will be included in a new release timed to coincide with the 2015 Fall Meeting. A critical step in testing models of the origin of seismic anisotropy is the determination of the misfit between shear-wave splitting parameters predicted from a model and measured from seismic observations. Is a model that correctly reproduces the delay time "better" than a model that correctly reproduces the fast polarization? We have introduced several new methods that use both parameters to calculate the misfit in a meaningful way and these can be used as part of an inversion scheme in order to find a model that best matches measured shear wave splitting. Our preferred approach involves the creation, "splitting", and "unsplitting" of a test wavelet. A measure of the misfit is then provided by the normalized second eigenvalue of the covariance matrix of particle motion for the two wavelets in a way similar to that used to find splitting parameters from data. This can be used as part of an inverse scheme to find a model that can reproduce a set of shear-wave splitting observations. A second challenge is the interpolation of elastic constants between two known points. Naive element-by-element interpolation can result in anomalous seismic velocities from the interpolated tensor. We introduce an interpolation technique involving both the orientation (defined in terms of the eigenvectors of the dilatational or Voigt stiffness tensor) and magnitude of the two end-member elastic tensors. This permits changes in symmetry between the end-members and removes
Regional Moment Tensor Source-Type Discrimination Analysis
2015-11-16
66 34: COSO and Amargosa full moment tensor inversion results with 1D and 3D Green’s functions...Md) COSO 1990/03/10, 16:00:00.08 37.104 -116.075 417 4.50 (Md) HOYA 1991/09/14, 19:00:00.08 37.226 -116.429 658 5.40 (Md) JUNCTION 1992/03/26...explosions (METROPOLIS, COSO , HOYA and JUNCTION), we fix the source depth at 1 km for both 1D and 3D GFs. For the comparison at different frequency
Interactive Volume Rendering of Diffusion Tensor Data
Energy Technology Data Exchange (ETDEWEB)
Hlawitschka, Mario; Weber, Gunther; Anwander, Alfred; Carmichael, Owen; Hamann, Bernd; Scheuermann, Gerik
2007-03-30
As 3D volumetric images of the human body become an increasingly crucial source of information for the diagnosis and treatment of a broad variety of medical conditions, advanced techniques that allow clinicians to efficiently and clearly visualize volumetric images become increasingly important. Interaction has proven to be a key concept in analysis of medical images because static images of 3D data are prone to artifacts and misunderstanding of depth. Furthermore, fading out clinically irrelevant aspects of the image while preserving contextual anatomical landmarks helps medical doctors to focus on important parts of the images without becoming disoriented. Our goal was to develop a tool that unifies interactive manipulation and context preserving visualization of medical images with a special focus on diffusion tensor imaging (DTI) data. At each image voxel, DTI provides a 3 x 3 tensor whose entries represent the 3D statistical properties of water diffusion locally. Water motion that is preferential to specific spatial directions suggests structural organization of the underlying biological tissue; in particular, in the human brain, the naturally occuring diffusion of water in the axon portion of neurons is predominantly anisotropic along the longitudinal direction of the elongated, fiber-like axons [MMM+02]. This property has made DTI an emerging source of information about the structural integrity of axons and axonal connectivity between brain regions, both of which are thought to be disrupted in a broad range of medical disorders including multiple sclerosis, cerebrovascular disease, and autism [Mos02, FCI+01, JLH+99, BGKM+04, BJB+03].
Intersections, ideals, and inversion
International Nuclear Information System (INIS)
Vasco, D.W.
1998-01-01
Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly one dimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons
Intersections, ideals, and inversion
Energy Technology Data Exchange (ETDEWEB)
Vasco, D.W.
1998-10-01
Techniques from computational algebra provide a framework for treating large classes of inverse problems. In particular, the discretization of many types of integral equations and of partial differential equations with undetermined coefficients lead to systems of polynomial equations. The structure of the solution set of such equations may be examined using algebraic techniques.. For example, the existence and dimensionality of the solution set may be determined. Furthermore, it is possible to bound the total number of solutions. The approach is illustrated by a numerical application to the inverse problem associated with the Helmholtz equation. The algebraic methods are used in the inversion of a set of transverse electric (TE) mode magnetotelluric data from Antarctica. The existence of solutions is demonstrated and the number of solutions is found to be finite, bounded from above at 50. The best fitting structure is dominantly onedimensional with a low crustal resistivity of about 2 ohm-m. Such a low value is compatible with studies suggesting lower surface wave velocities than found in typical stable cratons.
Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.
Li, Wei; Liu, Chunlei
2013-10-01
Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.
Tensor-Based Methods for Blind Spatial Signature Estimation in Multidimensional Sensor Arrays
Directory of Open Access Journals (Sweden)
Paulo R. B. Gomes
2017-01-01
Full Text Available The estimation of spatial signatures and spatial frequencies is crucial for several practical applications such as radar, sonar, and wireless communications. In this paper, we propose two generalized iterative estimation algorithms to the case in which a multidimensional (R-D sensor array is used at the receiver. The first tensor-based algorithm is an R-D blind spatial signature estimator that operates in scenarios where the source’s covariance matrix is nondiagonal and unknown. The second tensor-based algorithm is formulated for the case in which the sources are uncorrelated and exploits the dual-symmetry of the covariance tensor. Additionally, a new tensor-based formulation is proposed for an L-shaped array configuration. Simulation results show that our proposed schemes outperform the state-of-the-art matrix-based and tensor-based techniques.
The Physical Interpretation of the Lanczos Tensor
Roberts, Mark D.
1999-01-01
The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...
Diffusion tensor imaging of the human skeletal muscle: contributions and applications
International Nuclear Information System (INIS)
Neji, Radhouene
2010-01-01
In this thesis, we present several techniques for the processing of diffusion tensor images. They span a wide range of tasks such as estimation and regularization, clustering and segmentation, as well as registration. The variational framework proposed for recovering a tensor field from noisy diffusion weighted images exploits the fact that diffusion data represent populations of fibers and therefore each tensor can be reconstructed using a weighted combination of tensors lying in its neighborhood. The segmentation approach operates both at the voxel and the fiber tract levels. It is based on the use of Mercer kernels over Gaussian diffusion probabilities to model tensor similarity and spatial interactions, allowing the definition of fiber metrics that combine information from spatial localization and diffusion tensors. Several clustering techniques can be subsequently used to segment tensor fields and fiber tractographies. Moreover, we show how to develop supervised extensions of these algorithms. The registration algorithm uses probability kernels in order to match moving and target images. The deformation consistency is assessed using the distortion induced in the distances between neighboring probabilities. Discrete optimization is used to seek an optimum of the defined objective function. The experimental validation is done over a dataset of manually segmented diffusion images of the lower leg muscle for healthy and diseased subjects. The results of the techniques developed throughout this thesis are promising. (author)
Conformal correlators of mixed-symmetry tensors
Costa, Miguel S
2015-01-01
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to mixed-symmetry tensors by introducing a new commuting or anticommuting polarization vector for each row or column in the Young diagram that describes the index symmetries of the tensor. We determine the tensor structures that are allowed in n-point conformal correlation functions and give an algorithm for counting them in terms of tensor product coefficients. We show, with an example, how the new formalism can be used to compute conformal blocks of arbitrary external fields for the exchange of any conformal primary and its descendants. The matching between the number of tensor structures in conformal field theory correlators of operators in d dimensions and massive scattering amplitudes in d+1 dimensions is also seen to carry over to mixed-symmetry tensors.
Antisymmetric tensor generalizations of affine vector fields.
Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro
2016-02-01
Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.
Analyzing vortex breakdown flow structures by assignment of colors to tensor invariants.
Rütten, Markus; Chong, Min S
2006-01-01
Topological methods are often used to describe flow structures in fluid dynamics and topological flow field analysis usually relies on the invariants of the associated tensor fields. A visual impression of the local properties of tensor fields is often complex and the search of a suitable technique for achieving this is an ongoing topic in visualization. This paper introduces and assesses a method of representing the topological properties of tensor fields and their respective flow patterns with the use of colors. First, a tensor norm is introduced, which preserves the properties of the tensor and assigns the tensor invariants to values of the RGB color space. Secondly, the RGB colors of the tensor invariants are transferred to corresponding hue values as an alternative color representation. The vectorial tensor invariants field is reduced to a scalar hue field and visualization of iso-surfaces of this hue value field allows us to identify locations with equivalent flow topology. Additionally highlighting by the maximum of the eigenvalue difference field reflects the magnitude of the structural change of the flow. The method is applied on a vortex breakdown flow structure inside a cylinder with a rotating lid.
Diffusion tensor imaging and tractography in clinical neuro sciences
International Nuclear Information System (INIS)
Zarei, M.; Johansen-Berg, H.; Matthews, P.M.
2003-01-01
Rapidly evolving MR technology has allowed better understanding of structure and function of the human brain. Diffusion weighted MRI was developed two decades ago and it is now well established in diagnosis of acute ischaemia in patients with stroke. Diffusion tensor MRI uses the same principles but takes a step further allowing US to measure magnitude of the diffusion along different directions. This lead to the development of diffusion tensor tractography, a technique by which major neural pathways in the living brain can be visualized. There is a growing interest in exploring possible use of these techniques in clinical neurology and psychiatry. This article aims to review the principles of this technique and recent discoveries which may help US to better understand neurological and psychiatric disorders
Capdeville, Yann; MÉtivier, Ludovic
2018-02-01
Seismic imaging is an efficient tool to investigate the Earth interior. Many of the different imaging techniques currently used, including the so-called Full Waveform Inversion (FWI), are based on limited frequency band data. Such data are not sensitive to the true earth model, but to a smooth version of it. This smooth version can be related to the true model by the homogenization technique. Homogenization for wave propagation in deterministic media with no scale separation, such as geological media, has been recently developed. With such an asymptotic theory, it is possible to compute an effective medium valid for a given frequency band such that effective waveforms and true waveforms are the same up to a controlled error. In this work we make the link between limited frequency band inversion, mainly FWI, and homogenization. We establish the relation between a true model and a FWI result model. This relation is important for a proper interpretation of FWI images. We numerically illustrate, in the 2-D case, that a FWI result is at best the homogenized version of the true model. Moreover, it appears that the homogenized FWI model is quite independent of the FWI parameterization, as long as it has enough degrees of freedom. In particular, inverting for the full elastic tensor is, in each of our tests, always a good choice. We show how the homogenization can help to understand FWI behavior and help to improve its robustness and convergence by efficiently constraining the solution space of the inverse problem.
Capdeville, Yann; Métivier, Ludovic
2018-05-01
Seismic imaging is an efficient tool to investigate the Earth interior. Many of the different imaging techniques currently used, including the so-called full waveform inversion (FWI), are based on limited frequency band data. Such data are not sensitive to the true earth model, but to a smooth version of it. This smooth version can be related to the true model by the homogenization technique. Homogenization for wave propagation in deterministic media with no scale separation, such as geological media, has been recently developed. With such an asymptotic theory, it is possible to compute an effective medium valid for a given frequency band such that effective waveforms and true waveforms are the same up to a controlled error. In this work we make the link between limited frequency band inversion, mainly FWI, and homogenization. We establish the relation between a true model and an FWI result model. This relation is important for a proper interpretation of FWI images. We numerically illustrate, in the 2-D case, that an FWI result is at best the homogenized version of the true model. Moreover, it appears that the homogenized FWI model is quite independent of the FWI parametrization, as long as it has enough degrees of freedom. In particular, inverting for the full elastic tensor is, in each of our tests, always a good choice. We show how the homogenization can help to understand FWI behaviour and help to improve its robustness and convergence by efficiently constraining the solution space of the inverse problem.
Bayesian seismic AVO inversion
Energy Technology Data Exchange (ETDEWEB)
Buland, Arild
2002-07-01
A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S
Spectral Tensor-Train Decomposition
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.
2016-01-01
discretizations of the target function. We assess the performance of the method on a range of numerical examples: a modified set of Genz functions with dimension up to 100, and functions with mixed Fourier modes or with local features. We observe significant improvements in performance over an anisotropic......The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT.......e., the “cores”) comprising the functional TT decomposition. This result motivates an approximation scheme employing polynomial approximations of the cores. For functions with appropriate regularity, the resulting spectral tensor-train decomposition combines the favorable dimension-scaling of the TT...
Diffusion tensor optical coherence tomography
Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.
2018-01-01
In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.
Transposes, L-Eigenvalues and Invariants of Third Order Tensors
Qi, Liqun
2017-01-01
Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...
International Nuclear Information System (INIS)
Takeuchi, Mitsuo; Wada, Shigeru; Takahashi, Hiroyuki; Hayashi, Kazuhiko; Murayama, Yoji
2000-09-01
At the research reactor such as JRR-3M, the operation management is carried out in order to ensure safe operation, for example, the excess reactivity is measured regularly and confirmed that it satisfies a safety condition. The excess reactivity is calculated using control rod position in criticality and control rod worth measured by a positive period method (P.P method), the conventional inverse kinetic method (IK method) and so on. The neutron source, however, influences measurement results and brings in a measurement error. A new IK method considering the influence of the steady neutron sources is proposed and applied to the JRR-3M. This report shows that the proposed IK method measures control rod worth more precisely than a conventional IK method. (author)
Parameter estimation and inverse problems
Aster, Richard C; Thurber, Clifford H
2005-01-01
Parameter Estimation and Inverse Problems primarily serves as a textbook for advanced undergraduate and introductory graduate courses. Class notes have been developed and reside on the World Wide Web for faciliting use and feedback by teaching colleagues. The authors'' treatment promotes an understanding of fundamental and practical issus associated with parameter fitting and inverse problems including basic theory of inverse problems, statistical issues, computational issues, and an understanding of how to analyze the success and limitations of solutions to these probles. The text is also a practical resource for general students and professional researchers, where techniques and concepts can be readily picked up on a chapter-by-chapter basis.Parameter Estimation and Inverse Problems is structured around a course at New Mexico Tech and is designed to be accessible to typical graduate students in the physical sciences who may not have an extensive mathematical background. It is accompanied by a Web site that...
Statistical perspectives on inverse problems
DEFF Research Database (Denmark)
Andersen, Kim Emil
of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
Schrimpf, Martin
2016-01-01
Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...
Dictionary-Based Tensor Canonical Polyadic Decomposition
Cohen, Jeremy Emile; Gillis, Nicolas
2018-04-01
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.
Bayesian regularization of diffusion tensor images
DEFF Research Database (Denmark)
Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif
2007-01-01
Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...
Inflationary cosmology and 4-index tensor fields
International Nuclear Information System (INIS)
Moorhouse, R.G.; Nixon, J.
1985-01-01
We show how an arbitrarily large expansion of the ordinary dimensions in the very early universe can be achieved in the d=11 supergravity theory where the 4-index anti-symmetric tensor field supplies the energy-momentum tensor. However, the decrease of the extra dimensions is too fast to give a satisfactory inflationary cosmology. If a 4-index tensor field is similar used to provide the energy-momentum tensor in dimensions significantly greater than 11 the inflationary outlook is more hopeful. (orig.)
A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY
SASAKURA, NAOKI
2010-01-01
Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...
Luciani, S.; LeNiliot, C.
2008-11-01
Two-phase and boiling flow instabilities are complex, due to phase change and the existence of several interfaces. To fully understand the high heat transfer potential of boiling flows in microscale's geometry, it is vital to quantify these transfers. To perform this task, an experimental device has been designed to observe flow patterns. Analysis is made up by using an inverse method which allows us to estimate the local heat transfers while boiling occurs inside a microchannel. In our configuration, the direct measurement would impair the accuracy of the searched heat transfer coefficient because thermocouples implanted on the surface minichannels would disturb the established flow. In this communication, we are solving a 3D IHCP which consists in estimating using experimental data measurements the surface temperature and the surface heat flux in a minichannel during convective boiling under several gravity levels (g, 1g, 1.8g). The considered IHCP is formulated as a mathematical optimization problem and solved using the boundary element method (BEM).
DEFF Research Database (Denmark)
Pivnenko, Sergey; Nielsen, Jeppe Majlund; Breinbjerg, Olav
2011-01-01
correction of general high-order probes, including non-symmetric dual-polarized antennas with independent ports. The investigation was carried out by processing with each technique the same measurement data for a challenging case with an antenna under test significantly offset from the center of rotation...
Srivastava, Shalivahan; Agarwal, B. N. P.
2010-08-01
Amplitude of the 2-D analytic signal of the magnetic anomaly profile is independent of the directions of the Earth's magnetic field vector and remnant magnetization of the causative source. It exhibits peaks corresponding to the locations of the corners of a causative source, modelled by say a polygon. It also exhibits a peak corresponding to different idealized source geometries related to the structural indices. This amplitude is computed from the first-order horizontal and vertical derivatives of the observed magnetic anomaly and is relatively less noisy than second-order derivatives. The amplitude can also be computed directly from the measured derivatives. Particle swarm optimization (PSO)-a global optimization technique is applied to interpret this amplitude in terms of the horizontal location and depth, constant (related to magnetization) and various source geometries through structural indices. Applicability of the proposed technique is evaluated through the analyses of simulated magnetic anomalies (noise-free and corrupted with 20 per cent random noise) over different types of source geometries, namely, a thin dyke and a contact with high accuracy in parameter estimation. Studies on the choices of search parameter space reveal that a relatively wide search space can be assigned. Practical applicability of the proposed technique has been demonstrated through three magnetic anomaly profiles digitized from published literature. The results of PSO, Euler deconvolution, enhanced local wavenumber and drill hole are comparable. PSO results also seem to be more stable than other techniques.
Inverse problems of geophysics
International Nuclear Information System (INIS)
Yanovskaya, T.B.
2003-07-01
This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given
Directory of Open Access Journals (Sweden)
Halis Aygün
2008-01-01
Full Text Available We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness.
A Tensor Statistical Model for Quantifying Dynamic Functional Connectivity.
Zhu, Yingying; Zhu, Xiaofeng; Kim, Minjeong; Yan, Jin; Wu, Guorong
2017-06-01
Functional connectivity (FC) has been widely investigated in many imaging-based neuroscience and clinical studies. Since functional Magnetic Resonance Image (MRI) signal is just an indirect reflection of brain activity, it is difficult to accurately quantify the FC strength only based on signal correlation. To address this limitation, we propose a learning-based tensor model to derive high sensitivity and specificity connectome biomarkers at the individual level from resting-state fMRI images. First, we propose a learning-based approach to estimate the intrinsic functional connectivity. In addition to the low level region-to-region signal correlation, latent module-to-module connection is also estimated and used to provide high level heuristics for measuring connectivity strength. Furthermore, sparsity constraint is employed to automatically remove the spurious connections, thus alleviating the issue of searching for optimal threshold. Second, we integrate our learning-based approach with the sliding-window technique to further reveal the dynamics of functional connectivity. Specifically, we stack the functional connectivity matrix within each sliding window and form a 3D tensor where the third dimension denotes for time. Then we obtain dynamic functional connectivity (dFC) for each individual subject by simultaneously estimating the within-sliding-window functional connectivity and characterizing the across-sliding-window temporal dynamics. Third, in order to enhance the robustness of the connectome patterns extracted from dFC, we extend the individual-based 3D tensors to a population-based 4D tensor (with the fourth dimension stands for the training subjects) and learn the statistics of connectome patterns via 4D tensor analysis. Since our 4D tensor model jointly (1) optimizes dFC for each training subject and (2) captures the principle connectome patterns, our statistical model gains more statistical power of representing new subject than current state
Energy Technology Data Exchange (ETDEWEB)
Fiorucci, I.; Muscari, G. [Istituto Nazionale di Geofisica e Vulcanologia, Rome (Italy); De Zafra, R.L. [State Univ. of New York, Stony Brook, NY (United States). Dept. of Physics and Astronomy
2011-07-01
The Ground-Based Millimeter-wave Spectrometer (GBMS) was designed and built at the State University of New York at Stony Brook in the early 1990s and since then has carried out many measurement campaigns of stratospheric O{sub 3}, HNO{sub 3}, CO and N{sub 2}O at polar and mid-latitudes. Its HNO{sub 3} data set shed light on HNO{sub 3} annual cycles over the Antarctic continent and contributed to the validation of both generations of the satellite-based JPL Microwave Limb Sounder (MLS). Following the increasing need for long-term data sets of stratospheric constituents, we resolved to establish a long-term GMBS observation site at the Arctic station of Thule (76.5 N, 68.8 W), Greenland, beginning in January 2009, in order to track the long- and short-term interactions between the changing climate and the seasonal processes tied to the ozone depletion phenomenon. Furthermore, we updated the retrieval algorithm adapting the Optimal Estimation (OE) method to GBMS spectral data in order to conform to the standard of the Network for the Detection of Atmospheric Composition Change (NDACC) microwave group, and to provide our retrievals with a set of averaging kernels that allow more straightforward comparisons with other data sets. The new OE algorithm was applied to GBMS HNO{sub 3} data sets from 1993 South Pole observations to date, in order to produce HNO{sub 3} version 2 (v2) profiles. A sample of results obtained at Antarctic latitudes in fall and winter and at mid-latitudes is shown here. In most conditions, v2 inversions show a sensitivity (i.e., sum of column elements of the averaging kernel matrix) of 100{+-}20% from 20 to 45 km altitude, with somewhat worse (better) sensitivity in the Antarctic winter lower (upper) stratosphere. The 1{sigma} uncertainty on HNO{sub 3} v2 mixing ratio vertical profiles depends on altitude and is estimated at {proportional_to}15% or 0.3 ppbv, whichever is larger. Comparisons of v2 with former (v1) GBMS HNO{sub 3} vertical profiles
Vock, David M; Wolfson, Julian; Bandyopadhyay, Sunayan; Adomavicius, Gediminas; Johnson, Paul E; Vazquez-Benitez, Gabriela; O'Connor, Patrick J
2016-06-01
Models for predicting the probability of experiencing various health outcomes or adverse events over a certain time frame (e.g., having a heart attack in the next 5years) based on individual patient characteristics are important tools for managing patient care. Electronic health data (EHD) are appealing sources of training data because they provide access to large amounts of rich individual-level data from present-day patient populations. However, because EHD are derived by extracting information from administrative and clinical databases, some fraction of subjects will not be under observation for the entire time frame over which one wants to make predictions; this loss to follow-up is often due to disenrollment from the health system. For subjects without complete follow-up, whether or not they experienced the adverse event is unknown, and in statistical terms the event time is said to be right-censored. Most machine learning approaches to the problem have been relatively ad hoc; for example, common approaches for handling observations in which the event status is unknown include (1) discarding those observations, (2) treating them as non-events, (3) splitting those observations into two observations: one where the event occurs and one where the event does not. In this paper, we present a general-purpose approach to account for right-censored outcomes using inverse probability of censoring weighting (IPCW). We illustrate how IPCW can easily be incorporated into a number of existing machine learning algorithms used to mine big health care data including Bayesian networks, k-nearest neighbors, decision trees, and generalized additive models. We then show that our approach leads to better calibrated predictions than the three ad hoc approaches when applied to predicting the 5-year risk of experiencing a cardiovascular adverse event, using EHD from a large U.S. Midwestern healthcare system. Copyright © 2016 Elsevier Inc. All rights reserved.
EDITORIAL: Inverse Problems in Engineering
West, Robert M.; Lesnic, Daniel
2007-01-01
Presented here are 11 noteworthy papers selected from the Fifth International Conference on Inverse Problems in Engineering: Theory and Practice held in Cambridge, UK during 11-15 July 2005. The papers have been peer-reviewed to the usual high standards of this journal and the contributions of reviewers are much appreciated. The conference featured a good balance of the fundamental mathematical concepts of inverse problems with a diverse range of important and interesting applications, which are represented here by the selected papers. Aspects of finite-element modelling and the performance of inverse algorithms are investigated by Autrique et al and Leduc et al. Statistical aspects are considered by Emery et al and Watzenig et al with regard to Bayesian parameter estimation and inversion using particle filters. Electrostatic applications are demonstrated by van Berkel and Lionheart and also Nakatani et al. Contributions to the applications of electrical techniques and specifically electrical tomographies are provided by Wakatsuki and Kagawa, Kim et al and Kortschak et al. Aspects of inversion in optical tomography are investigated by Wright et al and Douiri et al. The authors are representative of the worldwide interest in inverse problems relating to engineering applications and their efforts in producing these excellent papers will be appreciated by many readers of this journal.
Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor
International Nuclear Information System (INIS)
Senovilla, Jose M M
2010-01-01
The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)
Electromagnetic stress tensor for an amorphous metamaterial medium
Wang, Neng; Wang, Shubo; Ng, Jack
2018-03-01
We analytically and numerically investigated the internal optical forces exerted by an electromagnetic wave inside an amorphous metamaterial medium. We derived, by using the principle of virtual work, the Helmholtz stress tensor, which takes into account the electrostriction effect. Several examples of amorphous media are considered, and different electromagnetic stress tensors, such as the Einstein-Laub tensor and Minkowski tensor, are also compared. It is concluded that the Helmholtz stress tensor is the appropriate tensor for such systems.
Unique characterization of the Bel-Robinson tensor
International Nuclear Information System (INIS)
Bergqvist, G; Lankinen, P
2004-01-01
We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors
Differential invariants for higher-rank tensors. A progress report
International Nuclear Information System (INIS)
Tapial, V.
2004-07-01
We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)
Friction tensor concept for textured surfaces
Indian Academy of Sciences (India)
This paper proposes the concept of a friction tensor analogous to the heat conduc- tion tensor in anisotropic media. This implies that there exists two principal friction coefficients μ1,2 analogous to the principal conductivities k1,2. For symmetrically textured surfaces the principal directions are orthogonal with atleast one ...
Gravitational Metric Tensor Exterior to Rotating Homogeneous ...
African Journals Online (AJOL)
The covariant and contravariant metric tensors exterior to a homogeneous spherical body rotating uniformly about a common φ axis with constant angular velocity ω is constructed. The constructed metric tensors in this gravitational field have seven non-zero distinct components.The Lagrangian for this gravitational field is ...
Friction tensor concept for textured surfaces
Indian Academy of Sciences (India)
Depending on the sliding direction the coefﬁcient of friction varies between maximum and minimum for textured surfaces. For random surfaces without any texture the friction coefﬁcient becomes independent of the sliding direction. This paper proposes the concept of a friction tensor analogous to the heat conduction tensor ...
Directory of Open Access Journals (Sweden)
Kuang-dai Leng
2012-01-01
Full Text Available Fabric tensor has proved to be an effective tool statistically characterizing directional data in a smooth and frame-indifferent form. Directional data arising from microscopic physics and mechanics can be summed up as tensor-valued orientation distribution functions (ODFs. Two characterizations of the tensor-valued ODFs are proposed, using the asymmetric and symmetric fabric tensors respectively. The later proves to be nonconvergent and less accurate but still an available solution for where fabric tensors are required in full symmetry. Analytic solutions of the two types of fabric tensors characterizing centrosymmetric and anticentrosymmetric tensor-valued ODFs are presented in terms of orthogonal irreducible decompositions in both two- and three-dimensional (2D and 3D spaces. Accuracy analysis is performed on normally distributed random ODFs to evaluate the approximation quality of the two characterizations, where fabric tensors of higher orders are employed. It is shown that the fitness is dominated by the dispersion degree of the original ODFs rather than the orders of fabric tensors. One application of tensor-valued ODF and fabric tensor in continuum damage mechanics is presented.
White matter injury in newborns with congenital heart disease: a diffusion tensor imaging study.
Mulkey, Sarah B; Ou, Xiawei; Ramakrishnaiah, Raghu H; Glasier, Charles M; Swearingen, Christopher J; Melguizo, Maria S; Yap, Vivien L; Schmitz, Michael L; Bhutta, Adnan T
2014-09-01
Brain injury is observed on cranial magnetic resonance imaging preoperatively in up to 50% of newborns with congenital heart disease. Newer imaging techniques such as diffusion tensor imaging provide sensitive measures of the white matter integrity. The objective of this study was to evaluate the diffusion tensor imaging analysis technique of tract-based spatial statistics in newborns with congenital heart disease. Term newborns with congenital heart disease who would require surgery at less than 1 month of age were prospectively enrolled (n = 19). Infants underwent preoperative and postoperative brain magnetic resonance imaging with diffusion tensor imaging. Tract-based spatial statistics, an objective whole-brain diffusion tensor imaging analysis technique, was used to determine differences in white matter fractional anisotropy between infant groups. Term control infants were also compared with congenital heart disease infants. Postmenstrual age was equivalent between congenital heart disease infant groups and between congenital heart disease and control infants. Ten infants had preoperative brain injury, either infarct or white matter injury, by conventional brain magnetic resonance imaging. The technique of tract-based spatial statistics showed significantly lower fractional anisotropy (P tensor imaging analysis technique that may have better sensitivity in detecting white matter injury compared with conventional brain magnetic resonance imaging in term newborns with congenital heart disease. Copyright © 2014 Elsevier Inc. All rights reserved.
Weyl curvature tensor in static spherical sources
International Nuclear Information System (INIS)
Ponce de Leon, J.
1988-01-01
The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed
A recursive reduction of tensor Feynman integrals
International Nuclear Information System (INIS)
Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.
2009-07-01
We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot......To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... deformations in an attempt to ensure that the local deformations in the warped image remains true to the orientation of the underlying fibers; forward mapping, however, can also create "seams" or gaps and consequently artifacts in the warped image by failing to define accurately the voxels in the template...
On Lovelock analogs of the Riemann tensor
Energy Technology Data Exchange (ETDEWEB)
Camanho, Xian O. [Albert-Einstein-Institut, Max-Planck-Institut fuer Gravitationsphysik, Golm (Germany); Dadhich, Naresh [Jamia Millia Islamia, Centre for Theoretical Physics, New Delhi (India); Inter-University Centre for Astronomy and Astrophysics, Pune (India)
2016-03-15
It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d = 2N + 1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes. (orig.)
Diffusion tensor imaging in spinal cord injury
International Nuclear Information System (INIS)
Kamble, Ravindra B; Venkataramana, Neelam K; Naik, Arun L; Rao, Shailesh V
2011-01-01
To assess the feasibility of spinal tractography in patients of spinal cord injury vs a control group and to compare fractional anisotropy (FA) values between the groups. Diffusion tensor imaging (DTI) was performed in the spinal cord of 29 patients (18 patients and 11 controls). DTI was done in the cervical region if the cord injury was at the dorsal or lumbar region and in the conus region if cord injury was in the cervical or dorsal region. FA was calculated for the patients and the controls and the values were compared. The mean FA value was 0.550±0.09 in the control group and 0.367±0.14 in the patients; this difference was statistically significant (P=0.001). Spinal tractography is a feasible technique to assess the extent of spinal cord injury by FA, which is reduced in patients of spinal cord injury, suggesting possible Wallerian degeneration. In future, this technique may become a useful tool for assessing cord injury patients after stem cell therapy, with improvement in FA values indicating axonal regeneration
Energy Technology Data Exchange (ETDEWEB)
Peng, Bo; Kowalski, Karol
2017-03-01
In this letter, we introduce the reverse Cuthill-McKee (RCM) algorithm, which is often used for the bandwidth reduction of sparse tensors, to transform the two-electron integral tensors to their block diagonal forms. By further applying the pivoted Cholesky decomposition (CD) on each of the diagonal blocks, we are able to represent the high-dimensional two-electron integral tensors in terms of permutation matrices and low-rank Cholesky vectors. This representation facilitates the low-rank factorization of the high-dimensional tensor contractions that are usually encountered in post-Hartree-Fock calculations. In this letter, we discuss the second-order Møller-Plesset (MP2) method and linear coupled- cluster model with doubles (L-CCD) as two simple examples to demonstrate the efficiency of the RCM-CD technique in representing two-electron integrals in a compact form.
Tomographic Image Reconstruction Using Training Images with Matrix and Tensor Formulations
DEFF Research Database (Denmark)
Soltani, Sara
machine learning technique (here, the dictionary learning), prototype elements from the training images are extracted and then incorporated in the tomographic reconstruction problem both with matrix and tensor representations of the training images. First, an algorithm for the tomographic image...... and robustness of the reconstruction to variations of the scale and rotation in the training images is investigated and algorithms to estimate the correct relative scale and orientation of the unknown image to the training images are suggested. Then, a third-order tensor representation for the training images...... images is used. The dictionary and image reconstruction problem are reformulated using the tensor representation. The dictionary learning problem is presented as a nonnegative tensor factorization problem with sparsity constraints and the reconstruction problem is formulated in a convex optimization...
Evidence of tensor correlations in the nuclear many-body system using a modern NN potential
International Nuclear Information System (INIS)
Fiase, J.O.; Nkoma, J.S.; Sharmaand, L.K.; Hosaka, A.
2003-01-01
In this paper we show evidence of the importance of tensor correlations in the nuclear many-body system by calculating the effective two-body nuclear matrix elements in the frame work of the Lowest-Order Constrained Variational (LOCV) technique with two-body correlation functions using the Reid93 potential. We have achieved this by switching on and off the strength of the tensor correlations, α k . We have found that in order to obtain reasonable agreement with earlier calculations based on the G-matrix theory, we must turn on the strength of the tensor correlations especially in the triplet even (TE) and tensor even (TNE) channels to take the value of approximately, 0.05. As an application, we have estimated the value of the Landau - Migdal parameter, g' NN which we found to be g' NN = 0.65. This compares favorably with the G-matrix calculated value of g' NN = 0.54. (author)
Deep Into the Fibers! Postmortem Diffusion Tensor Imaging in Forensic Radiology.
Flach, Patricia Mildred; Schroth, Sarah; Schweitzer, Wolf; Ampanozi, Garyfalia; Slotboom, Johannes; Kiefer, Claus; Germerott, Tanja; Thali, Michael J; El-Koussy, Marwan
2015-09-01
In traumatic brain injury, diffusion-weighted and diffusion tensor imaging of the brain are essential techniques for determining the pathology sustained and the outcome. Postmortem cross-sectional imaging is an established adjunct to forensic autopsy in death investigation. The purpose of this prospective study was to evaluate postmortem diffusion tensor imaging in forensics for its feasibility, influencing factors and correlation to the cause of death compared with autopsy. Postmortem computed tomography, magnetic resonance imaging, and diffusion tensor imaging with fiber tracking were performed in 10 deceased subjects. The Likert scale grading of colored fractional anisotropy maps was correlated to the body temperature and intracranial pathology to assess the diagnostic feasibility of postmortem diffusion tensor imaging and fiber tracking. Optimal fiber tracking (>15,000 fiber tracts) was achieved with a body temperature at 10°C. Likert scale grading showed no linear correlation (P > 0.7) to fiber tract counts. No statistically significant correlation between total fiber count and postmortem interval could be observed (P = 0.122). Postmortem diffusion tensor imaging and fiber tracking allowed for radiological diagnosis in cases with shearing injuries but was impaired in cases with pneumencephalon and intracerebral mass hemorrhage. Postmortem diffusion tensor imaging with fiber tracking provides an exceptional in situ insight "deep into the fibers" of the brain with diagnostic benefit in traumatic brain injury and axonal injuries in the assessment of the underlying cause of death, considering influencing factors for optimal imaging technique.
Third Harmonic Imaging using a Pulse Inversion
DEFF Research Database (Denmark)
Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt
2011-01-01
The pulse inversion (PI) technique can be utilized to separate and enhance harmonic components of a waveform for tissue harmonic imaging. While most ultrasound systems can perform pulse inversion, only few image the 3rd harmonic component. PI pulse subtraction can isolate and enhance the 3rd...
Czech Academy of Sciences Publication Activity Database
Staněk, František; Eisner, Leo; Vesnaver, A.
2017-01-01
Roč. 14, č. 2 (2017), s. 235-240 ISSN 1214-9705 Grant - others:AV ČR(CZ) CNR-16-17 Program:Bilaterální spolupráce Institutional support: RVO:67985891 Keywords : microseismic monitoring * source mechanism * moment tensor * inversion Subject RIV: DC - Siesmology, Volcanology, Earth Structure OBOR OECD: 1.7 Other natural sciences Impact factor: 0.699, year: 2016
Moment Tensor code for the Antelope Environmental Monitoring System
Reyes, J.; Newman, R.; Vernon, F.; van den Hazel, G.
2012-04-01
The time domain seismic moment tensor inversion software package written by Dreger (2003) and updated by Minson & Dreger (2008) has been rewritten for inclusion into the open-source contributed code repository for the Boulder Real Time Technology (BRTT) Antelope Environmental Monitoring System. The new code-base was written natively in the Python language and utilizes the Python interface to Antelope (Lindquist et al., 2008) for data access, Scientific Tools for Python library (Eric Jones et al., 2001) for computation and analysis, and the ObsPy library (Beyreuther et al., 2010) for graphical representation. The new code archives all data products into a Center for Seismic Studies (CSS) 3.0 schema table for easy access and distribution of solutions. Stability of the analysis, verification of results and correlation of solutions with similar methods are discussed in this presentation. Analysis is focused on regional earthquakes recorded by Earthscope's USArray network and event parameters are taken from real time and post-event processed data analysis at the Array Network Facility (ANF). A calibrated velocity model representative of the south-west continental United States is used for the analysis. Beyreuther, M., Barsch, R., Krischer, L., Megies, T., Behr, Y. and Wassermann, J. (2010) ObsPy: A Python Toolbox for Seismology, Seismic Research Letters, 81(3), 530-533. Dreger, D. (2003) TDMT_INV: Time Domain Seismic Moment Tensor INVersion, International Handbook of Earthquake and Engineering Seismology, Volume 81B, p 1627. Eric Jones, Travis Oliphant, Pearu Peterson (2001) SciPy: Open Source Scientific Tools for Python, "http://www.scipy.org/" Lindquist, K.G., Clemesha, A., Newman, R.L. and Vernon, F.L. (2008) The Python Interface to Antelope and Applications. Eos Trans. AGU 89(53), Fall Meet. Suppl., Abstract G43A-0671 Minson, S. & Dreger, D. (2008) Stable inversions for complete moment tensors. Geophys. J. Int., 174, 585-592 Saikia, C. (1994) Modified frequency
Czech Academy of Sciences Publication Activity Database
Kolář, Petr
2008-01-01
Roč. 5, 1 /149/ (2008), s. 31-39 ISSN 1214-9705 R&D Projects: GA AV ČR IAA300120502; GA AV ČR IAA200120701; GA AV ČR(CZ) IAA300120805 Institutional research plan: CEZ:AV0Z30120515 Keywords : seismic moment tensor inversion * error estimation * seismic moment tensor decomposition Subject RIV: DC - Siesmology, Volcanology, Earth Structure
International Nuclear Information System (INIS)
Hicks, H.R.; Dory, R.A.; Holmes, J.A.
1983-01-01
We illustrate in some detail a 2D inverse-equilibrium solver that was constructed to analyze tokamak configurations and stellarators (the latter in the context of the average method). To ensure that the method is suitable not only to determine equilibria, but also to provide appropriately represented data for existing stability codes, it is important to be able to control the Jacobian, tilde J is identical to delta(R,Z)/delta(rho, theta). The form chosen is tilde J = J 0 (rho)R/sup l/rho where rho is a flux surface label, and l is an integer. The initial implementation is for a fixed conducting-wall boundary, but the technique can be extended to a free-boundary model
Inverse photoemission of uranium oxides
International Nuclear Information System (INIS)
Roussel, P.; Morrall, P.; Tull, S.J.
2009-01-01
Understanding the itinerant-localised bonding role of the 5f electrons in the light actinides will afford an insight into their unusual physical and chemical properties. In recent years, the combination of core and valance band electron spectroscopies with theoretic modelling have already made significant progress in this area. However, information of the unoccupied density of states is still scarce. When compared to the forward photoemission techniques, measurements of the unoccupied states suffer from significantly less sensitivity and lower resolution. In this paper, we report on our experimental apparatus, which is designed to measure the inverse photoemission spectra of the light actinides. Inverse photoemission spectra of UO 2 and UO 2.2 along with the corresponding core and valance electron spectra are presented in this paper. UO 2 has been reported previously, although through its inclusion here it allows us to compare and contrast results from our experimental apparatus to the previous Bremsstrahlung Isochromat Spectroscopy and Inverse Photoemission Spectroscopy investigations
Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.
Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N
2017-05-01
This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.
Coupled ADCPs can yield complete Reynolds stress tensor profiles in geophysical surface flows
Vermeulen, B.; Hoitink, A.J.F.; Sassi, M.G.
2011-01-01
We introduce a new technique to measure profiles of each term in the Reynolds stress tensor using coupled acoustic Doppler current profilers (ADCPs). The technique is based on the variance method which is extended to the case with eight acoustic beams. Methods to analyze turbulence from a single
Conformal field theories and tensor categories. Proceedings
Energy Technology Data Exchange (ETDEWEB)
Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics
2014-08-01
First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.
Coupled channels Marchenko inversion for nucleon-nucleon potentials
International Nuclear Information System (INIS)
Kohlhoff, H.; Geramb, H.V. von
1994-01-01
Marchenko inversion is used to determine local energy independent but channel dependent potential matrices from optimum sets of experimental phase shifts. 3 SD 1 and 3 PF 2 channels of nucleon-nucleon systems contain in their off-diagonal potential matrices explicitly the tensor force for T = 0 and 1 isospin. We obtain, together with single channels, complete sets of quantitative nucleon-nucleon potential results which are ready for application in nuclear structure and reaction analyses. The historic coupled channels inversion result of Newton and Fulton is revisited. (orig.)
Local Tensor Radiation Conditions For Elastic Waves
DEFF Research Database (Denmark)
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point....... The tensor relation generalizes the traditional normal incidence impedance condition by accounting for the angle between wave propagation and the surface normal and by including a generalized stiffness term due to spreading of the waves. The effectiveness of the local tensor radiation condition...
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Abelian gauge theories with tensor gauge fields
International Nuclear Information System (INIS)
Kapuscik, E.
1984-01-01
Gauge fields of arbitrary tensor type are introduced. In curved space-time the gravitational field serves as a bridge joining different gauge fields. The theory of second order tensor gauge field is developed on the basis of close analogy to Maxwell electrodynamics. The notion of tensor current is introduced and an experimental test of its detection is proposed. The main result consists in a coupled set of field equations representing a generalization of Maxwell theory in which the Einstein equivalence principle is not satisfied. (author)
Surface tensor estimation from linear sections
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel
2015-01-01
From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....
Why are tensor field theories asymptotically free?
Rivasseau, V.
2015-09-01
In this pedagogic letter we explain the combinatorics underlying the generic asymptotic freedom of tensor field theories. We focus on simple combinatorial models with a 1/p2 propagator and quartic interactions and on the comparison between the intermediate field representations of the vector, matrix and tensor cases. The transition from asymptotic freedom (tensor case) to asymptotic safety (matrix case) is related to the crossing symmetry of the matrix vertex, whereas in the vector case, the lack of asymptotic freedom (“Landau ghost”), as in the ordinary scalar φ^44 case, is simply due to the absence of any wave function renormalization at one loop.
Forward modeling. Route to electromagnetic inversion
Energy Technology Data Exchange (ETDEWEB)
Groom, R.; Walker, P. [PetRos EiKon Incorporated, Ontario (Canada)
1996-05-01
Inversion of electromagnetic data is a topical subject in the literature, and much time has been devoted to understanding the convergence properties of various inverse methods. The relative lack of success of electromagnetic inversion techniques is partly attributable to the difficulties in the kernel forward modeling software. These difficulties come in two broad classes: (1) Completeness and robustness, and (2) convergence, execution time and model simplicity. If such problems exist in the forward modeling kernel, it was demonstrated that inversion can fail to generate reasonable results. It was suggested that classical inversion techniques, which are based on minimizing a norm of the error between data and the simulated data, will only be successful when these difficulties in forward modeling kernels are properly dealt with. 4 refs., 5 figs.
Li, Xu; van Zijl, Peter C M
2014-09-01
An increasing number of studies show that magnetic susceptibility in white matter fibers is anisotropic and may be described by a tensor. However, the limited head rotation possible for in vivo human studies leads to an ill-conditioned inverse problem in susceptibility tensor imaging (STI). Here we suggest the combined use of limiting the susceptibility anisotropy to white matter and imposing morphology constraints on the mean magnetic susceptibility (MMS) for regularizing the STI inverse problem. The proposed MMS regularized STI (MMSR-STI) method was tested using computer simulations and in vivo human data collected at 3T. The fiber orientation estimated from both the STI and MMSR-STI methods was compared to that from diffusion tensor imaging (DTI). Computer simulations show that the MMSR-STI method provides a more accurate estimation of the susceptibility tensor than the conventional STI approach. Similarly, in vivo data show that use of the MMSR-STI method leads to a smaller difference between the fiber orientation estimated from STI and DTI for most selected white matter fibers. The proposed regularization strategy for STI can improve estimation of the susceptibility tensor in white matter. © 2014 Wiley Periodicals, Inc.
Predicting patterns of glioma recurrence using diffusion tensor imaging
International Nuclear Information System (INIS)
Price, Stephen J.; Pickard, John D.; Jena, Rajesh; Burnet, Neil G.; Carpenter, T.A.; Gillard, Jonathan H.
2007-01-01
Although multimodality therapy for high-grade gliomas is making some improvement in outcome, most patients will still die from their disease within a short time. We need tools that allow treatments to be tailored to an individual. In this study we used diffusion tensor imaging (DTI), a technique sensitive to subtle disruption of white-matter tracts due to tumour infiltration, to see if it can be used to predict patterns of glioma recurrence. In this study we imaged 26 patients with gliomas using DTI. Patients were imaged after 2 years or on symptomatic tumour recurrence. The diffusion tensor was split into its isotropic (p) and anisotropic (q) components, and these were plotted on T 2 -weighted images to show the pattern of DTI abnormality. This was compared to the pattern of recurrence. Three DTI patterns could be identified: (a) a diffuse pattern of abnormality where p exceeded q in all directions and was associated with diffuse increase in tumour size; (b) a localised pattern of abnormality where the tumour recurred in one particular direction; and (c) a pattern of minimal abnormality seen in some patients with or without evidence of recurrence. Diffusion tensor imaging is able to predict patterns of tumour recurrence and may allow better individualisation of tumour management and stratification for randomised controlled trials. (orig.)
The gauge-invariant canonical energy-momentum tensor
Lorcé, Cédric
2016-03-01
The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictacted in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMDs and GPDs). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive three similar new sum rules expressing the conservation of transverse momentum.
The gauge-invariant canonical energy-momentum tensor
International Nuclear Information System (INIS)
Lorce, C.
2016-01-01
The canonical energy-momentum tensor is often considered as a purely academic object because of its gauge dependence. However, it has recently been realized that canonical quantities can in fact be defined in a gauge-invariant way provided that strict locality is abandoned, the non-local aspect being dictated in high-energy physics by the factorization theorems. Using the general techniques for the parametrization of non-local parton correlators, we provide for the first time a complete parametrization of the energy-momentum tensor (generalizing the purely local parametrizations of Ji and Bakker-Leader-Trueman used for the kinetic energy-momentum tensor) and identify explicitly the parts accessible from measurable two-parton distribution functions (TMD and GPD). As by-products, we confirm the absence of model-independent relations between TMDs and parton orbital angular momentum, recover in a much simpler way the Burkardt sum rule and derive 3 similar new sum rules expressing the conservation of transverse momentum. (author)
Tucker tensor analysis of Matern functions in spatial statistics
Litvinenko, Alexander
2018-04-20
Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments
Minimal Gersgorin tensor eigenvalue inclusion set and its numerical approximation
Li, Chaoqian; Li, Yaotang
2015-01-01
For a complex tensor A, Minimal Gersgorin tensor eigenvalue inclusion set of A is presented, and its sufficient and necessary condition is given. Furthermore, we study its boundary by the spectrums of the equimodular set and the extended equimodular set for A. Lastly, for an irreducible tensor, a numerical approximation to Minimal Gersgorin tensor eigenvalue inclusion set is given.
Tensor decomposition in electronic structure calculations on 3D Cartesian grids
International Nuclear Information System (INIS)
Khoromskij, B.N.; Khoromskaia, V.; Chinnamsetty, S.R.; Flad, H.-J.
2009-01-01
In this paper, we investigate a novel approach based on the combination of Tucker-type and canonical tensor decomposition techniques for the efficient numerical approximation of functions and operators in electronic structure calculations. In particular, we study applicability of tensor approximations for the numerical solution of Hartree-Fock and Kohn-Sham equations on 3D Cartesian grids. We show that the orthogonal Tucker-type tensor approximation of electron density and Hartree potential of simple molecules leads to low tensor rank representations. This enables an efficient tensor-product convolution scheme for the computation of the Hartree potential using a collocation-type approximation via piecewise constant basis functions on a uniform nxnxn grid. Combined with the Richardson extrapolation, our approach exhibits O(h 3 ) convergence in the grid-size h=O(n -1 ). Moreover, this requires O(3rn+r 3 ) storage, where r denotes the Tucker rank of the electron density with r=O(logn), almost uniformly in n. For example, calculations of the Coulomb matrix and the Hartree-Fock energy for the CH 4 molecule, with a pseudopotential on the C atom, achieved accuracies of the order of 10 -6 hartree with a grid-size n of several hundreds. Since the tensor-product convolution in 3D is performed via 1D convolution transforms, our scheme markedly outperforms the 3D-FFT in both the computing time and storage requirements.
Plaisier, A; Pieterman, K; Lequin, M H; Govaert, P; Heemskerk, A M; Reiss, I K M; Krestin, G P; Leemans, A; Dudink, J
2014-06-01
Neonatal DTI enables quantitative assessment of microstructural brain properties. Although its use is increasing, it is not widely known that vast differences in tractography results can occur, depending on the diffusion tensor estimation methodology used. Current clinical work appears to be insufficiently focused on data quality and processing of neonatal DTI. To raise awareness about this important processing step, we investigated tractography reconstructions of the fornix with the use of several estimation techniques. We hypothesized that the method of tensor estimation significantly affects DTI tractography results. Twenty-eight DTI scans of infants born <29 weeks of gestation, acquired at 30-week postmenstrual age and without intracranial injury observed, were prospectively collected. Four diffusion tensor estimation methods were applied: 1) linear least squares; 2) weighted linear least squares; 3) nonlinear least squares, and 4) robust estimation of tensors by outlier rejection. Quality of DTI data and tractography results were evaluated for each method. With nonlinear least squares and robust estimation of tensors by outlier rejection, significantly lower mean fractional anisotropy values were obtained than with linear least squares and weighted linear least squares. Visualized quality of tract reconstruction was significantly higher by use of robust estimation of tensors by outlier rejection and correlated with quality of DTI data. Quality assessment and choice of processing methodology have considerable impact on neonatal DTI analysis. Dedicated acquisition, quality assessment, and advanced processing of neonatal DTI data must be ensured before performing clinical analyses, such as associating microstructural brain properties with patient outcome. © 2014 by American Journal of Neuroradiology.
TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow
Hafner, Danijar; Davidson, James; Vanhoucke, Vincent
2017-01-01
We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...
Spectra of operators in large N tensor models
Bulycheva, Ksenia; Klebanov, Igor R.; Milekhin, Alexey; Tarnopolsky, Grigory
2018-01-01
We study the operators in the large N tensor models, focusing mostly on the fermionic quantum mechanics with O (N )3 symmetry which may be either global or gauged. In the model with global symmetry, we study the spectra of bilinear operators, which are in either the symmetric traceless or the antisymmetric representation of one of the O (N ) groups. In the symmetric traceless case, the spectrum of scaling dimensions is the same as in the Sachdev-Ye-Kitaev (SYK) model with real fermions; it includes the h =2 zero mode. For the operators antisymmetric in the two indices, the scaling dimensions are the same as in the additional sector found in the complex tensor and SYK models; the lowest h =0 eigenvalue corresponds to the conserved O (N ) charges. A class of singlet operators may be constructed from contracted combinations of m symmetric traceless or antisymmetric two-particle operators. Their two-point functions receive contributions from m melonic ladders. Such multiple ladders are a new phenomenon in the tensor model, which does not seem to be present in the SYK model. The more typical 2 k -particle operators do not receive any ladder corrections and have quantized large N scaling dimensions k /2 . We construct pictorial representations of various singlet operators with low k . For larger k , we use available techniques to count the operators and show that their number grows as 2kk !. As a consequence, the theory has a Hagedorn phase transition at the temperature which approaches zero in the large N limit. We also study the large N spectrum of low-lying operators in the Gurau-Witten model, which has O (N )6 symmetry. We argue that it corresponds to one of the generalized SYK models constructed by Gross and Rosenhaus. Our paper also includes studies of the invariants in large N tensor integrals with various symmetries.
C%2B%2B tensor toolbox user manual.
Energy Technology Data Exchange (ETDEWEB)
Plantenga, Todd D.; Kolda, Tamara Gibson
2012-04-01
The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.
International Nuclear Information System (INIS)
Lorentzen, T.; Christoffersen, J.
1990-01-01
Diffraction techniques such as neutron diffraction allow strain components to be measured in arbitrarily chosen directions in structural components, and hence complete strain tensors can in principle be calculated from any six measured normal strain components. However, in a newly developed technique, whereby a position-sensitive detector is used for simultaneous measurements of chosen strain components at several points along a line through the specimen, there appear to be some limitations on the choice of strain components for strain tensor determination. This note verifies the nature of these limitations. (author)
Unsupervised Tensor Mining for Big Data Practitioners.
Papalexakis, Evangelos E; Faloutsos, Christos
2016-09-01
Multiaspect data are ubiquitous in modern Big Data applications. For instance, different aspects of a social network are the different types of communication between people, the time stamp of each interaction, and the location associated to each individual. How can we jointly model all those aspects and leverage the additional information that they introduce to our analysis? Tensors, which are multidimensional extensions of matrices, are a principled and mathematically sound way of modeling such multiaspect data. In this article, our goal is to popularize tensors and tensor decompositions to Big Data practitioners by demonstrating their effectiveness, outlining challenges that pertain to their application in Big Data scenarios, and presenting our recent work that tackles those challenges. We view this work as a step toward a fully automated, unsupervised tensor mining tool that can be easily and broadly adopted by practitioners in academia and industry.
Potentials for transverse trace-free tensors
International Nuclear Information System (INIS)
Conboye, Rory; Murchadha, Niall Ó
2014-01-01
In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)
Correlators in tensor models from character calculus
Directory of Open Access Journals (Sweden)
A. Mironov
2017-11-01
Full Text Available We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Energy-momentum tensor in scalar QED
International Nuclear Information System (INIS)
Joglekar, S.D.; Misra, A.
1988-01-01
We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
. The output of the reconstruction algorithm is a polytope P, where the surface tensors of P and K are identical up to rank s. We establish a stability result based on a generalization of Wirtinger’s inequality that shows that for large s, two convex bodies are close in shape when they have identical surface...... that are translates of each other. An algorithm for reconstructing an unknown convex body in R 2 from its surface tensors up to a certain rank is presented. Using the reconstruction algorithm, the shape of an unknown convex body can be approximated when only a finite number s of surface tensors are available...... tensors up to rank s. This is used to establish consistency of the developed reconstruction algorithm....
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
2016-01-01
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. When only measurements subject to noise...... of surface tensors are available for reconstruction, we recommend to use certain values of the surface tensors, namely harmonic intrinsic volumes instead of the surface tensors evaluated at the standard basis. The second algorithm we present is based on harmonic intrinsic volumes and allows for noisy...... measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based on measurements subject to noise is established under certain assumptions on the noise...
An introduction to linear algebra and tensors
Akivis, M A; Silverman, Richard A
1978-01-01
Eminently readable, completely elementary treatment begins with linear spaces and ends with analytic geometry, covering multilinear forms, tensors, linear transformation, and more. 250 problems, most with hints and answers. 1972 edition.
Correlators in tensor models from character calculus
Mironov, A.; Morozov, A.
2017-11-01
We explain how the calculations of [20], which provided the first evidence for non-trivial structures of Gaussian correlators in tensor models, are efficiently performed with the help of the (Hurwitz) character calculus. This emphasizes a close similarity between technical methods in matrix and tensor models and supports a hope to understand the emerging structures in very similar terms. We claim that the 2m-fold Gaussian correlators of rank r tensors are given by r-linear combinations of dimensions with the Young diagrams of size m. The coefficients are made from the characters of the symmetric group Sm and their exact form depends on the choice of the correlator and on the symmetries of the model. As the simplest application of this new knowledge, we provide simple expressions for correlators in the Aristotelian tensor model as tri-linear combinations of dimensions.
Shifted power method for computing tensor eigenpairs.
Energy Technology Data Exchange (ETDEWEB)
Mayo, Jackson R.; Kolda, Tamara Gibson
2010-10-01
Recent work on eigenvalues and eigenvectors for tensors of order m {>=} 3 has been motivated by applications in blind source separation, magnetic resonance imaging, molecular conformation, and more. In this paper, we consider methods for computing real symmetric-tensor eigenpairs of the form Ax{sup m-1} = {lambda}x subject to {parallel}x{parallel} = 1, which is closely related to optimal rank-1 approximation of a symmetric tensor. Our contribution is a novel shifted symmetric higher-order power method (SS-HOPM), which we showis guaranteed to converge to a tensor eigenpair. SS-HOPM can be viewed as a generalization of the power iteration method for matrices or of the symmetric higher-order power method. Additionally, using fixed point analysis, we can characterize exactly which eigenpairs can and cannot be found by the method. Numerical examples are presented, including examples from an extension of the method to fnding complex eigenpairs.
Calculus of tensors and differential forms
Sinha, Rajnikant
2014-01-01
Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.
The energy–momentum tensor(s in classical gauge theories
Directory of Open Access Journals (Sweden)
Daniel N. Blaschke
2016-11-01
Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
The Energy-Momentum Tensor(s) in Classical Gauge Theories
Blaschke, Daniel N.; Gieres, Francois; Reboud, Meril; Schweda, Manfred
2016-01-01
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from t...
The energy–momentum tensor(s) in classical gauge theories
Energy Technology Data Exchange (ETDEWEB)
Blaschke, Daniel N., E-mail: dblaschke@lanl.gov [Los Alamos National Laboratory, Los Alamos, NM 87545 (United States); Gieres, François, E-mail: gieres@ipnl.in2p3.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Reboud, Méril, E-mail: meril.reboud@ens-lyon.fr [Institut de Physique Nucléaire de Lyon, Université de Lyon, Université Claude Bernard Lyon 1 and CNRS/IN2P3, Bat. P. Dirac, 4 rue Enrico Fermi, F-69622 Villeurbanne (France); Ecole Normale Supérieure de Lyon, 46 allée d' Italie, F-69364 Lyon CEDEX 07 (France); Schweda, Manfred, E-mail: mschweda@tph.tuwien.ac.at [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstraße 8-10, A-1040 Vienna (Austria)
2016-11-15
We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.
Geometric decomposition of the conformation tensor in viscoelastic turbulence
Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.
2018-05-01
This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.
Extended obstruction tensors and renormalized volume coefficients
Graham, C. Robin
2009-01-01
The behavior under conformal change of the renormalized volume coefficients associated to a pseudo-Riemannian metric is investigated. It is shown that they define second order fully nonlinear operators in the conformal factor whose algebraic structure is elucidated via the introduction of "extended obstruction tensors". These together with the Schouten tensor constitute building blocks for the coefficients in the ambient metric expansion. The renormalized volume coefficients have recently bee...
Higher-Order Tensors in Diffusion Imaging
Schultz, Thomas; Fuster, Andrea; Ghosh, Aurobrata; Deriche, Rachid; Florack, Luc; Lek-Heng, Lim
2013-01-01
International audience; Diffusion imaging is a noninvasive tool for probing the microstructure of fibrous nerve and muscle tissue. Higher-order tensors provide a powerful mathematical language to model and analyze the large and complex data that is generated by its modern variants such as High Angular Resolution Diffusion Imaging (HARDI) or Diffusional Kurtosis Imaging. This survey gives a careful introduction to the foundations of higher-order tensor algebra, and explains how some concepts f...
Goldsborough, Peter
2016-01-01
Deep learning is a branch of artificial intelligence employing deep neural network architectures that has significantly advanced the state-of-the-art in computer vision, speech recognition, natural language processing and other domains. In November 2015, Google released $\\textit{TensorFlow}$, an open source deep learning software library for defining, training and deploying machine learning models. In this paper, we review TensorFlow and put it in context of modern deep learning concepts and ...
Diffusion Tensor Imaging of Pedophilia.
Cantor, James M; Lafaille, Sophie; Soh, Debra W; Moayedi, Massieh; Mikulis, David J; Girard, Todd A
2015-11-01
Pedophilia is a principal motivator of child molestation, incurring great emotional and financial burdens on victims and society. Even among pedophiles who never commit any offense,the condition requires lifelong suppression and control. Previous comparison using voxel-based morphometry (VBM)of MR images from a large sample of pedophiles and controls revealed group differences in white matter. The present study therefore sought to verify and characterize white matter involvement using diffusion tensor imaging (DTI), which better captures the microstructure of white matter than does VBM. Pedophilics ex offenders (n=24) were compared with healthy, age-matched controls with no criminal record and no indication of pedophilia (n=32). White matter microstructure was analyzed with Tract-Based Spatial Statistics, and the trajectories of implicated fiber bundles were identified by probabilistic tractography. Groups showed significant, highly focused differences in DTI parameters which related to participants’ genital responses to sexual depictions of children, but not to measures of psychopathy or to childhood histories of physical abuse, sexual abuse, or neglect. Some previously reported gray matter differences were suggested under highly liberal statistical conditions (p(uncorrected)pedophilia is characterized by neuroanatomical differences in white matter microstructure, over and above any neural characteristics attributable to psychopathy and childhood adversity, which show neuroanatomic footprints of their own. Although some gray matter structures were implicated previously, only few have emerged reliably.
(Ln-bar, g)-spaces. Special tensor fields
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces
On the concircular curvature tensor of Riemannian manifolds
International Nuclear Information System (INIS)
Rahman, M.S.; Lal, S.
1990-06-01
Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs
Tensor Toolbox for MATLAB v. 3.0
Energy Technology Data Exchange (ETDEWEB)
2017-03-07
Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features. It also provides algorithms for tensor decomposition and factorization, algorithms for computing tensor eigenvalues, and methods for visualization of results.
Fourier reconstruction with sparse inversions
Zwartjes, P.M.
2005-01-01
In seismic exploration an image of the subsurface is generated from seismic data through various data processing algorithms. When the data is not acquired on an equidistantly spaced grid, artifacts may result in the final image. Fourier reconstruction is an interpolation technique that can reduce these artifacts by generating uniformly sampled data from such non-uniformly sampled data. The method works by estimating via least-squares inversion the Fourier coefficients that describe the non-un...
Time-reversal and Bayesian inversion
Debski, Wojciech
2017-04-01
Probabilistic inversion technique is superior to the classical optimization-based approach in all but one aspects. It requires quite exhaustive computations which prohibit its use in huge size inverse problems like global seismic tomography or waveform inversion to name a few. The advantages of the approach are, however, so appealing that there is an ongoing continuous afford to make the large inverse task as mentioned above manageable with the probabilistic inverse approach. One of the perspective possibility to achieve this goal relays on exploring the internal symmetry of the seismological modeling problems in hand - a time reversal and reciprocity invariance. This two basic properties of the elastic wave equation when incorporating into the probabilistic inversion schemata open a new horizons for Bayesian inversion. In this presentation we discuss the time reversal symmetry property, its mathematical aspects and propose how to combine it with the probabilistic inverse theory into a compact, fast inversion algorithm. We illustrate the proposed idea with the newly developed location algorithm TRMLOC and discuss its efficiency when applied to mining induced seismic data.
Poya, Roman; Gil, Antonio J.; Ortigosa, Rogelio
2017-07-01
The paper presents aspects of implementation of a new high performance tensor contraction framework for the numerical analysis of coupled and multi-physics problems on streaming architectures. In addition to explicit SIMD instructions and smart expression templates, the framework introduces domain specific constructs for the tensor cross product and its associated algebra recently rediscovered by Bonet et al. (2015, 2016) in the context of solid mechanics. The two key ingredients of the presented expression template engine are as follows. First, the capability to mathematically transform complex chains of operations to simpler equivalent expressions, while potentially avoiding routes with higher levels of computational complexity and, second, to perform a compile time depth-first or breadth-first search to find the optimal contraction indices of a large tensor network in order to minimise the number of floating point operations. For optimisations of tensor contraction such as loop transformation, loop fusion and data locality optimisations, the framework relies heavily on compile time technologies rather than source-to-source translation or JIT techniques. Every aspect of the framework is examined through relevant performance benchmarks, including the impact of data parallelism on the performance of isomorphic and nonisomorphic tensor products, the FLOP and memory I/O optimality in the evaluation of tensor networks, the compilation cost and memory footprint of the framework and the performance of tensor cross product kernels. The framework is then applied to finite element analysis of coupled electro-mechanical problems to assess the speed-ups achieved in kernel-based numerical integration of complex electroelastic energy functionals. In this context, domain-aware expression templates combined with SIMD instructions are shown to provide a significant speed-up over the classical low-level style programming techniques.
International Nuclear Information System (INIS)
Montesinos, M.; Flores, E.
2006-01-01
The symmetric and gauge-invariant energy-momentum tensors for source-free Maxwell and Yang-Mills theories are obtained by means of translations in spacetime via a systematic implementation of Noether's theorem. For the source-free neutral Proca field, the same procedure yields also the symmetric energy-momentum tensor. In all cases, the key point to get the right expressions for the energy-momentum tensors is the appropriate handling of their equations of motion and the Bianchi identities. It must be stressed that these results are obtained without using Belinfante's symmetrization techniques which are usually employed to this end. (Author)
Tensor analysis methods for activity characterization in spatiotemporal data
Energy Technology Data Exchange (ETDEWEB)
Haass, Michael Joseph; Van Benthem, Mark Hilary; Ochoa, Edward M
2014-03-01
Tensor (multiway array) factorization and decomposition offers unique advantages for activity characterization in spatio-temporal datasets because these methods are compatible with sparse matrices and maintain multiway structure that is otherwise lost in collapsing for regular matrix factorization. This report describes our research as part of the PANTHER LDRD Grand Challenge to develop a foundational basis of mathematical techniques and visualizations that enable unsophisticated users (e.g. users who are not steeped in the mathematical details of matrix algebra and mulitway computations) to discover hidden patterns in large spatiotemporal data sets.
Facial Expression Recognition Based on TensorFlow Platform
Directory of Open Access Journals (Sweden)
Xia Xiao-Ling
2017-01-01
Full Text Available Facial expression recognition have a wide range of applications in human-machine interaction, pattern recognition, image understanding, machine vision and other fields. Recent years, it has gradually become a hot research. However, different people have different ways of expressing their emotions, and under the influence of brightness, background and other factors, there are some difficulties in facial expression recognition. In this paper, based on the Inception-v3 model of TensorFlow platform, we use the transfer learning techniques to retrain facial expression dataset (The Extended Cohn-Kanade dataset, which can keep the accuracy of recognition and greatly reduce the training time.
Incremental Tensor Principal Component Analysis for Handwritten Digit Recognition
Directory of Open Access Journals (Sweden)
Chang Liu
2014-01-01
Full Text Available To overcome the shortcomings of traditional dimensionality reduction algorithms, incremental tensor principal component analysis (ITPCA based on updated-SVD technique algorithm is proposed in this paper. This paper proves the relationship between PCA, 2DPCA, MPCA, and the graph embedding framework theoretically and derives the incremental learning procedure to add single sample and multiple samples in detail. The experiments on handwritten digit recognition have demonstrated that ITPCA has achieved better recognition performance than that of vector-based principal component analysis (PCA, incremental principal component analysis (IPCA, and multilinear principal component analysis (MPCA algorithms. At the same time, ITPCA also has lower time and space complexity.
INVERSE FILTERING TECHNIQUES IN SPEECH ANALYSIS
African Journals Online (AJOL)
Dr Obe
features in the speech process: (i) the resonant structure of the vocal-tract transfer function, i.e, formant analysis,. (ii) the glottal wave,. (iii) the fundamental frequency or pitch of the sound. During the production of speech, the configuration of the articulators: the vocal tract tongue, teeth, lips, etc, changes from one sound to.
An Automated Approach for the Determination of the Seismic Moment Tensor in Mining Environments
Wamboldt, Lawrence R.
A study was undertaken to evaluate an automated process to invert for seismic moment tensors from seismic data recorded in mining environments. The data for this study was recorded at Nickel Rim South mine, Sudbury, Ontario. The mine has a seismic monitoring system manufactured by ESG Solutions that performs continuous monitoring of seismicity. On average, approximately 400 seismic events are recorded each day. Currently, data are automatically processed by ESG Solution's software suite during acquisition. The automatic processors pick the P- and/or S-wave arrivals, locate the events and solve for certain source parameters, excluding the seismic moment tensor. In order to solve for the moment tensor, data must be manually processed, which is laborious and therefore seldom performed. This research evaluates an automatic seismic moment tensor inversion method and demonstrates some of the difficulties (through inversions of real and synthetic seismic data) of the inversion process. Results using the method are also compared to the inversion method currently available from ESG Solutions, which requires the manual picking of first-motion polarities for every event. As a result of the extensive synthetic testing of the automatic inversion program, as well as the inversion of real seismic data, it is apparent that there are key parameters requiring greater accuracy in order to increase the reliability of the automation. These parameters include the source time function definition, source location (in turn requiring more accurate and precise knowledge of the earth media), arrival time picks and an attenuation model to account for ray-path dependent filtering of the source time function. In order to improve the automatic method three key pieces of research are needed: (1) studying various location algorithms (and the effects of increasing earth model intricacy) and automatic time picking to improve source location methods, (2) studying how the source time pulse can be
Marin Quintero, Maider J.
2013-01-01
The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…
Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.
Tensor network state correspondence and holography
Singh, Sukhwinder
2018-01-01
In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.
Fast wavelet based sparse approximate inverse preconditioner
Energy Technology Data Exchange (ETDEWEB)
Wan, W.L. [Univ. of California, Los Angeles, CA (United States)
1996-12-31
Incomplete LU factorization is a robust preconditioner for both general and PDE problems but unfortunately not easy to parallelize. Recent study of Huckle and Grote and Chow and Saad showed that sparse approximate inverse could be a potential alternative while readily parallelizable. However, for special class of matrix A that comes from elliptic PDE problems, their preconditioners are not optimal in the sense that independent of mesh size. A reason may be that no good sparse approximate inverse exists for the dense inverse matrix. Our observation is that for this kind of matrices, its inverse entries typically have piecewise smooth changes. We can take advantage of this fact and use wavelet compression techniques to construct a better sparse approximate inverse preconditioner. We shall show numerically that our approach is effective for this kind of matrices.
Solving inverse problems of optical microlithography
Granik, Yuri
2005-05-01
The direct problem of microlithography is to simulate printing features on the wafer under given mask, imaging system, and process characteristics. The goal of inverse problems is to find the best mask and/or imaging system and/or process to print the given wafer features. In this study we will describe and compare solutions of inverse mask problems. Pixel-based inverse problem of mask optimization (or "layout inversion") is harder than inverse source problem, especially for partially-coherent systems. It can be stated as a non-linear constrained minimization problem over complex domain, with large number of variables. We compare method of Nashold projections, variations of Fienap phase-retrieval algorithms, coherent approximation with deconvolution, local variations, and descent searches. We propose electrical field caching technique to substantially speedup the searching algorithms. We demonstrate applications of phase-shifted masks, assist features, and maskless printing.
Jaques, Luís; Pascal, Christophe
2017-09-01
Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal exposures of mineralized quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. The present contribution focuses specifically on the determination of pore pressure. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of ∼300 MPa and formation depths of ∼10 km. Such formation depths are in good agreement with the regional geological evolution. The obtained pore pressure will be merged with vein inversion results, in order to achieve full paleostress tensor restoration, in a forthcoming companion paper.
Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.
Pascal, C.; Jaques Ribeiro, L. M.
2017-12-01
Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal 3D exposures of mineralised quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To further constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of 300 MPa and formation depths of 10 km. As a second step, we measured 600 subhorizontal quartz veins in all the levels of the mine. The inversion of the attitudes of the veins allowed for reconstructing the orientations of the principal axes of stress, the unscaled Mohr circle and the relative pore pressure. After merging these results with the previously obtained absolute pore pressure we reconstructed the six parameters of the paleostress tensor.
International Nuclear Information System (INIS)
Adler, S.L.; Lieberman, J.
1978-01-01
We reanalyze the problem of regularization of the stress-energy tensor for massless vector particles propating in a general background metric, using covariant point separation techniques applied to the Hadamard elementary solution. We correct an error, point out by Wald, in the earlier formulation of Adler, Lieberman, and Ng, and find a stress-energy tensor trace anomaly agreeing with that found by other regularization methods
Diffusion tensor imaging for understanding brain development in early life.
Qiu, Anqi; Mori, Susumu; Miller, Michael I
2015-01-03
The human brain rapidly develops during the final weeks of gestation and in the first two years following birth. Diffusion tensor imaging (DTI) is a unique in vivo imaging technique that allows three-dimensional visualization of the white matter anatomy in the brain. It has been considered to be a valuable tool for studying brain development in early life. In this review, we first introduce the DTI technique. We then review DTI findings on white matter development at the fetal stage and in infancy as well as DTI applications for understanding neurocognitive development and brain abnormalities in preterm infants. Finally, we discuss limitations of DTI and potential valuable imaging techniques for studying white matter myelination.
Source Estimation by Full Wave Form Inversion
Energy Technology Data Exchange (ETDEWEB)
Sjögreen, Björn [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Petersson, N. Anders [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
2013-08-07
Given time-dependent ground motion recordings at a number of receiver stations, we solve the inverse problem for estimating the parameters of the seismic source. The source is modeled as a point moment tensor source, characterized by its location, moment tensor components, the start time, and frequency parameter (rise time) of its source time function. In total, there are 11 unknown parameters. We use a non-linear conjugate gradient algorithm to minimize the full waveform misfit between observed and computed ground motions at the receiver stations. An important underlying assumption of the minimization problem is that the wave propagation is accurately described by the elastic wave equation in a heterogeneous isotropic material. We use a fourth order accurate finite difference method, developed in [12], to evolve the waves forwards in time. The adjoint wave equation corresponding to the discretized elastic wave equation is used to compute the gradient of the misfit, which is needed by the non-linear conjugated minimization algorithm. A new source point moment source discretization is derived that guarantees that the Hessian of the misfit is a continuous function of the source location. An efficient approach for calculating the Hessian is also presented. We show how the Hessian can be used to scale the problem to improve the convergence of the non-linear conjugated gradient algorithm. Numerical experiments are presented for estimating the source parameters from synthetic data in a layer over half-space problem (LOH.1), illustrating rapid convergence of the proposed approach.
International Nuclear Information System (INIS)
Huf, P A; Carminati, J
2015-01-01
In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)
(Ln-bar, g)-spaces. Ordinary and tensor differentials
International Nuclear Information System (INIS)
Manoff, S.; Dimitrov, B.
1998-01-01
Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces
Energy-momentum tensor in the fermion-pairing model
International Nuclear Information System (INIS)
Kawati, S.; Miyata, H.
1980-01-01
The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory
Inverse Kinematics using Quaternions
DEFF Research Database (Denmark)
Henriksen, Knud; Erleben, Kenny; Engell-Nørregård, Morten
In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection....
Inverse logarithmic potential problem
Cherednichenko, V G
1996-01-01
The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Heidsieck, David S P; Smarius, Bram J A; Oomen, Karin P Q; Breugem, Corstiaan C
2016-09-01
Otitis media with effusion is common in infants with an unrepaired cleft palate. Although its prevalence is reduced after cleft surgery, many children continue to suffer from middle ear problems during childhood. While the tensor veli palatini muscle is thought to be involved in middle ear ventilation, evidence about its exact anatomy, function, and role in cleft palate surgery is limited. This study aimed to perform a thorough review of the literature on (1) the role of the tensor veli palatini muscle in the Eustachian tube opening and middle ear ventilation, (2) anatomical anomalies in cleft palate infants related to middle ear disease, and (3) their implications for surgical techniques used in cleft palate repair. A literature search on the MEDLINE database was performed using a combination of the keywords "tensor veli palatini muscle," "Eustachian tube," "otitis media with effusion," and "cleft palate." Several studies confirm the important role of the tensor veli palatini muscle in the Eustachian tube opening mechanism. Maintaining the integrity of the tensor veli palatini muscle during cleft palate surgery seems to improve long-term otological outcome. However, anatomical variations in cleft palate children may alter the effect of the tensor veli palatini muscle on the Eustachian tube's dilatation mechanism. More research is warranted to clarify the role of the tensor veli palatini muscle in cleft palate-associated Eustachian tube dysfunction and development of middle ear problems. Optimized surgical management of cleft palate could potentially reduce associated middle ear problems.
3rd Annual Workshop on Inverse Problem
2015-01-01
This proceeding volume is based on papers presented on the Third Annual Workshop on Inverse Problems which was organized by the Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenburg, and took place in May 2013 in Stockholm. The purpose of this workshop was to present new analytical developments and numerical techniques for solution of inverse problems for a wide range of applications in acoustics, electromagnetics, optical fibers, medical imaging, geophysics, etc. The contributions in this volume reflect these themes and will be beneficial to researchers who are working in the area of applied inverse problems.
Inverse design methods for radiative transfer systems
International Nuclear Information System (INIS)
Daun, K.J.; Howell, J.R.
2005-01-01
Radiant enclosures used in industrial processes have traditionally been designed by trial-and-error, a technique that usually demands considerable time to find a solution of limited quality. As an alternative, designers have recently adopted optimization and inverse methodologies to solve design problems involving radiative transfer; the optimization methodology solves the inverse problem implicitly by transforming it into a multivariable minimization problem, while the inverse design methodology solves the problem explicitly using regularization. This paper presents the details of both methodologies, and demonstrates them by solving for the optimal heater settings in an industrially relevant radiant enclosure design problem
Renormalized energy-momentum tensor of λΦ4 theory in curved ...
Indian Academy of Sciences (India)
Divergenceless expression for the energy-momentum tensor of scalar ﬁeld is obtained using the momentum cut-off regularization technique. We consider a scalar ﬁeld with quartic self-coupling in a spatially ﬂat (3+1)-dimensional Robertson–Walker space-time, having arbitrary mass and coupled to gravity. As special cases ...
Visualizing MR diffusion tensor fields by dynamic fiber tracking and uncertainty mapping
Ehricke, HH; Klose, U; Grodd, W
Recent advances in magnetic resonance imaging have provided methods for the acquisition of high-resolution diffusion tensor fields. Their 3D-visualization with streamline-based techniques-called fiber tracking-allow analysis of cerebral white matter tracts for diagnostic, therapeutic as well as
Two-Dimensional Interactions in a Class of Tensor Gauge Fields from Local BRST Cohomology
Babalic, E M; Cioroianu, E M; Negru, I; Sararu, S C
2003-01-01
Lagrangian interactions in a class of two-dimensional tensor gauge field theory are derived by means of deforming the solution to the master equation with specific cohomological techniques. Both the gauge transformations and their algebra are deformed. The gauge algebra of the coupled model is open.
Encoding !-tensors as !-graphs with neighbourhood orders
Directory of Open Access Journals (Sweden)
David Quick
2015-11-01
Full Text Available Diagrammatic reasoning using string diagrams provides an intuitive language for reasoning about morphisms in a symmetric monoidal category. To allow working with infinite families of string diagrams, !-graphs were introduced as a method to mark repeated structure inside a diagram. This led to !-graphs being implemented in the diagrammatic proof assistant Quantomatic. Having a partially automated program for rewriting diagrams has proven very useful, but being based on !-graphs, only commutative theories are allowed. An enriched abstract tensor notation, called !-tensors, has been used to formalise the notion of !-boxes in non-commutative structures. This work-in-progress paper presents a method to encode !-tensors as !-graphs with some additional structure. This will allow us to leverage the existing code from Quantomatic and quickly provide various tools for non-commutative diagrammatic reasoning.
Federated Tensor Factorization for Computational Phenotyping
Kim, Yejin; Sun, Jimeng; Yu, Hwanjo; Jiang, Xiaoqian
2017-01-01
Tensor factorization models offer an effective approach to convert massive electronic health records into meaningful clinical concepts (phenotypes) for data analysis. These models need a large amount of diverse samples to avoid population bias. An open challenge is how to derive phenotypes jointly across multiple hospitals, in which direct patient-level data sharing is not possible (e.g., due to institutional policies). In this paper, we developed a novel solution to enable federated tensor factorization for computational phenotyping without sharing patient-level data. We developed secure data harmonization and federated computation procedures based on alternating direction method of multipliers (ADMM). Using this method, the multiple hospitals iteratively update tensors and transfer secure summarized information to a central server, and the server aggregates the information to generate phenotypes. We demonstrated with real medical datasets that our method resembles the centralized training model (based on combined datasets) in terms of accuracy and phenotypes discovery while respecting privacy. PMID:29071165
Exploring extra dimensions through inflationary tensor modes
Im, Sang Hui; Nilles, Hans Peter; Trautner, Andreas
2018-03-01
Predictions of inflationary schemes can be influenced by the presence of extra dimensions. This could be of particular relevance for the spectrum of gravitational waves in models where the extra dimensions provide a brane-world solution to the hierarchy problem. Apart from models of large as well as exponentially warped extra dimensions, we analyze the size of tensor modes in the Linear Dilaton scheme recently revived in the discussion of the "clockwork mechanism". The results are model dependent, significantly enhanced tensor modes on one side and a suppression on the other. In some cases we are led to a scheme of "remote inflation", where the expansion is driven by energies at a hidden brane. In all cases where tensor modes are enhanced, the requirement of perturbativity of gravity leads to a stringent upper limit on the allowed Hubble rate during inflation.
Permittivity and permeability tensors for cloaking applications
Choudhury, Balamati; Jha, Rakesh Mohan
2016-01-01
This book is focused on derivations of analytical expressions for stealth and cloaking applications. An optimal version of electromagnetic (EM) stealth is the design of invisibility cloak of arbitrary shapes in which the EM waves can be controlled within the cloaking shell by introducing a prescribed spatial variation in the constitutive parameters. The promising challenge in design of invisibility cloaks lies in the determination of permittivity and permeability tensors for all the layers. This book provides the detailed derivation of analytical expressions of the permittivity and permeability tensors for various quadric surfaces within the eleven Eisenhart co-ordinate systems. These include the cylinders and the surfaces of revolutions. The analytical modeling and spatial metric for each of these surfaces are provided along with their tensors. This mathematical formulation will help the EM designers to analyze and design of various quadratics and their hybrids, which can eventually lead to design of cloakin...
Tensor calculus for engineers and physicists
de Souza Sánchez Filho, Emil
2016-01-01
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of N dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without need...
Tensor pressure tokamak equilibrium and stability
Energy Technology Data Exchange (ETDEWEB)
Cooper, W.A.
1981-03-01
We investigate the equilibrium and magnetohydrodynamic (MHD) stability of tokamaks with tensor pressure and examine, in particular, the effects of anisotropies induced by neutral beam injection. Perpendicular and parallel beam pressure components are evaluated by taking moments of a distribution function obtained from the solution of a Fokker-Planck equation that models the injection of high-energy neutral beams into a tokamak. We numerically generate D-shaped beam-induced tensor pressure equilibria. A double adiabatic energy principle is derived from a modified version of the guiding center plasma energy principle. Finally, we apply the tensor pressure ballooning mode equation to computed equilibria that model experimentally determined ISX-B discharge profiles with high-power neutral beam injection. We predict that the plasma is unstable to flutelike modes in the central core of the discharge as a result of the pressure profile peakedness induced by the beams.
3D structure tensor analysis of light microscopy data for validating diffusion MRI.
Khan, Ahmad Raza; Cornea, Anda; Leigland, Lindsey A; Kohama, Steven G; Jespersen, Sune Nørhøj; Kroenke, Christopher D
2015-05-01
Diffusion magnetic resonance imaging (d-MRI) is a powerful non-invasive and non-destructive technique for characterizing brain tissue on the microscopic scale. However, the lack of validation of d-MRI by independent experimental means poses an obstacle to accurate interpretation of data acquired using this method. Recently, structure tensor analysis has been applied to light microscopy images, and this technique holds promise to be a powerful validation strategy for d-MRI. Advantages of this approach include its similarity to d-MRI in terms of averaging the effects of a large number of cellular structures, and its simplicity, which enables it to be implemented in a high-throughput manner. However, a drawback of previous implementations of this technique arises from it being restricted to 2D. As a result, structure tensor analyses have been limited to tissue sectioned in a direction orthogonal to the direction of interest. Here we describe the analytical framework for extending structure tensor analysis to 3D, and utilize the results to analyze serial image "stacks" acquired with confocal microscopy of rhesus macaque hippocampal tissue. Implementation of 3D structure tensor procedures requires removal of sources of anisotropy introduced in tissue preparation and confocal imaging. This is accomplished with image processing steps to mitigate the effects of anisotropic tissue shrinkage, and the effects of anisotropy in the point spread function (PSF). In order to address the latter confound, we describe procedures for measuring the dependence of PSF anisotropy on distance from the microscope objective within tissue. Prior to microscopy, ex vivo d-MRI measurements performed on the hippocampal tissue revealed three regions of tissue with mutually orthogonal directions of least restricted diffusion that correspond to CA1, alveus and inferior longitudinal fasciculus. We demonstrate the ability of 3D structure tensor analysis to identify structure tensor orientations that
Design of a tensor polarized deuterium target polarized by spin-exchange with optically pumped NA
International Nuclear Information System (INIS)
Green, M.C.
1984-01-01
A proposed design for a tensor polarized deuterium target (approx. 10 15 atoms/cm 2 ) for nuclear physics studies in an electron storage ring accelerator is presented. The deuterium atoms undergo electron spin exchange with a highly polarized sodium vapor; this polarization is transferred to the deuterium nuclei via the hyperfine interaction. The deuterium nuclei obtain their tensor polarization through repeated electron spin exchange/hyperfine interactions. The sodium vapor polarization is maintained by standard optical pumping techniques. Model calculations are presented in detail leading to a discussion of the expected performance and the technical obstacles to be surmounted in the development of such a target
Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.
Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben
2017-08-02
It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.
Diffusion tensor smoothing through weighted Karcher means
Carmichael, Owen; Chen, Jun; Paul, Debashis; Peng, Jie
2014-01-01
Diffusion tensor magnetic resonance imaging (MRI) quantifies the spatial distribution of water Diffusion at each voxel on a regular grid of locations in a biological specimen by Diffusion tensors– 3 × 3 positive definite matrices. Removal of noise from DTI is an important problem due to the high scientific relevance of DTI and relatively low signal to noise ratio it provides. Leading approaches to this problem amount to estimation of weighted Karcher means of Diffusion tensors within spatial neighborhoods, under various metrics imposed on the space of tensors. However, it is unclear how the behavior of these estimators varies with the magnitude of DTI sensor noise (the noise resulting from the thermal e!ects of MRI scanning) as well as the geometric structure of the underlying Diffusion tensor neighborhoods. In this paper, we combine theoretical analysis, empirical analysis of simulated DTI data, and empirical analysis of real DTI scans to compare the noise removal performance of three kernel-based DTI smoothers that are based on Euclidean, log-Euclidean, and affine-invariant metrics. The results suggest, contrary to conventional wisdom, that imposing a simplistic Euclidean metric may in fact provide comparable or superior noise removal, especially in relatively unstructured regions and/or in the presence of moderate to high levels of sensor noise. On the contrary, log-Euclidean and affine-invariant metrics may lead to better noise removal in highly structured anatomical regions, especially when the sensor noise is of low magnitude. These findings emphasize the importance of considering the interplay of sensor noise magnitude and tensor field geometric structure when assessing Diffusion tensor smoothing options. They also point to the necessity for continued development of smoothing methods that perform well across a large range of scenarios. PMID:25419264
Diffusion tensor imaging in spinal cord compression
International Nuclear Information System (INIS)
Wang, Wei; Qin, Wen; Hao, Nanxin; Wang, Yibin; Zong, Genlin
2012-01-01
Background Although diffusion tensor imaging has been successfully applied in brain research for decades, several main difficulties have hindered its extended utilization in spinal cord imaging. Purpose To assess the feasibility and clinical value of diffusion tensor imaging and tractography for evaluating chronic spinal cord compression. Material and Methods Single-shot spin-echo echo-planar DT sequences were scanned in 42 spinal cord compression patients and 49 healthy volunteers. The mean values of the apparent diffusion coefficient and fractional anisotropy were measured in region of interest at the cervical and lower thoracic spinal cord. The patients were divided into two groups according to the high signal on T2WI (the SCC-HI group and the SCC-nHI group for with or without high signal). A one-way ANOVA was used. Diffusion tensor tractography was used to visualize the morphological features of normal and impaired white matter. Results There were no statistically significant differences in the apparent diffusion coefficient and fractional anisotropy values between the different spinal cord segments of the normal subjects. All of the patients in the SCC-HI group had increased apparent diffusion coefficient values and decreased fractional anisotropy values at the lesion level compared to the normal controls. However, there were no statistically significant diffusion index differences between the SCC-nHI group and the normal controls. In the diffusion tensor imaging maps, the normal spinal cord sections were depicted as fiber tracts that were color-encoded to a cephalocaudal orientation. The diffusion tensor images were compressed to different degrees in all of the patients. Conclusion Diffusion tensor imaging and tractography are promising methods for visualizing spinal cord tracts and can provide additional information in clinical studies in spinal cord compression
Tensor network models of multiboundary wormholes
Peach, Alex; Ross, Simon F.
2017-05-01
We study the entanglement structure of states dual to multiboundary wormhole geometries using tensor network models. Perfect and random tensor networks tiling the hyperbolic plane have been shown to provide good models of the entanglement structure in holography. We extend this by quotienting the plane by discrete isometries to obtain models of the multiboundary states. We show that there are networks where the entanglement structure is purely bipartite, extending results obtained in the large temperature limit. We analyse the entanglement structure in a range of examples.
Tensor modes in pure natural inflation
Nomura, Yasunori; Yamazaki, Masahito
2018-05-01
We study tensor modes in pure natural inflation [1], a recently-proposed inflationary model in which an axionic inflaton couples to pure Yang-Mills gauge fields. We find that the tensor-to-scalar ratio r is naturally bounded from below. This bound originates from the finiteness of the number of metastable branches of vacua in pure Yang-Mills theories. Details of the model can be probed by future cosmic microwave background experiments and improved lattice gauge theory calculations of the θ-angle dependence of the vacuum energy.
Reconstruction of convex bodies from surface tensors
DEFF Research Database (Denmark)
Kousholt, Astrid; Kiderlen, Markus
We present two algorithms for reconstruction of the shape of convex bodies in the two-dimensional Euclidean space. The first reconstruction algorithm requires knowledge of the exact surface tensors of a convex body up to rank s for some natural number s. The second algorithm uses harmonic intrinsic...... volumes which are certain values of the surface tensors and allows for noisy measurements. From a generalized version of Wirtinger's inequality, we derive stability results that are utilized to ensure consistency of both reconstruction procedures. Consistency of the reconstruction procedure based...
Bound-Preserving Reconstruction of Tensor Quantities for Remap in ALE Fluid Dynamics
Energy Technology Data Exchange (ETDEWEB)
Klima, Matej [Czech Technical Univ. in Prague, Praha (Czech Republic); Kucharik, MIlan [Czech Technical Univ. in Prague, Praha (Czech Republic); Shashkov, Mikhail Jurievich [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Velechovsky, Jan [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-06
We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables. We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J_{2} invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J_{2} invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.
Morphometric study of tensor of vastus intermedius in South Indian population.
Veeramani, Raveendranath; Gnanasekaran, Dhivyalakshmi
2017-03-01
Tensor of vastus intermedius is a newly discovered muscle located between vastus lateralis and vastus intermedius. The purpose of this study was to investigate the detailed morphology of tensor of vastus intermedius, specifically to provide data pertaining to the attachments, innervations, variation in the types and its morphometry in South Indian population. The tensor of vastus intermedius was studied in thirty six cadaveric lower limbs using macrodissection techniques. The origin of the muscle was from upper part of intertrochanteric line and anterior part of greater trochanter of femur inserted to medial aspect of upper border of patella. The muscle was classified into four types based on the origin and also the aponeurosis course with independent type (type 1) being common. The mean and standard deviation of the length of tensor of vastus intermedius and aponeurosis were 145.40±37.55 mm and 193.55±42.32 mm, respectively. The results of the study suggest that tensor of vastus intermedius is variable and the information provided regarding the attachments, types and quantitative data will contribute to the existing knowledge of the muscle.
Tensor veli palatini electromyography for monitoring Eustachian tube rehabilitation in otitis media.
Picciotti, P M; Della Marca, G; D'Alatri, L; Lucidi, D; Rigante, M; Scarano, E
2017-05-01
The pathogenesis of otitis media is related to Eustachian tube dysfunction. The tensor veli palatini muscle actively opens the Eustachian tube and promotes middle-ear ventilation. This study describes a technique for paratubal electromyography that uses a surface, non-invasive electrode able to record tensor veli palatini muscle activity during swallowing. Twenty otitis media patients and 10 healthy patients underwent tensor veli palatini electromyography. Activity of this muscle before and after Eustachian tube rehabilitation was also assessed. In 78.5 per cent of patients, the electromyography duration phase and/or amplitude were reduced in the affected side. The muscle action potential was impaired in all patients who underwent Eustachian tube rehabilitation. This study confirmed that Eustachian tube muscle dysfunction has a role in otitis media pathogenesis and showed that muscle activity increases after Eustachian tube rehabilitation therapy.
Yao, Xiu-Zhong; Yun, Hong; Zeng, Meng-Su; Wang, He; Sun, Fei; Rao, Sheng-Xiang; Ji, Yuan
2013-05-01
The objective of this paper was to investigate the value of apparent diffusion coefficients (ADCs) for differential diagnosis among solid pancreatic masses using respiratory triggered diffusion-weighted MR imaging with inversion-recovery fat-suppression technique (RT-IR-DWI) at 3.0 T. 20 normal volunteers and 72 patients (Pancreatic ductal adenocarcinoma [PDCA, n=30], mass-forming pancreatitis [MFP, n=15], solid pseudopapillary neoplasm [SPN, n=12], and pancreatic neuroendocrine tumor[PNET, n=15]) underwent RT-IR-DWI (b values: 0 and 600 s/mm(2)) at 3.0 T. Results were correlated with histopathologic data and follow-up imaging. ADC values among different types of pancreatic tissue were statistically analyzed and compared. Statistical difference was noticed in ADC values among normal pancreas, MFP, PDCA, SPN and PNET by ANOVA (pPDCA, MFP and SPN. There was noticeable statistical difference in ADC values among PDCA, MFP and normal pancreas by Least Significant Difference (LSD) (pPDCA (p=0.0300×10(-4)) and normal pancreas (p=0.0007×10(-4)). ADC of PNET was statistically lower than that of normal pancreas (p=0.0360) and higher than that of MFP (p=9.3000×10(-4)). ADC measurements using RT-IR-DWI at 3.0T may aid to disclose the histopathological pattern of normal pancreas and solid pancreatic masses, which may be helpful in characterizing solid pancreatic lesions. Copyright © 2013 Elsevier Inc. All rights reserved.
Observations About the Projective Tensor Product of Banach Spaces
African Journals Online (AJOL)
, 46B, 46E, 47B. Keywords: tensor, Banach, banach space, tensor product, projective norm, greatest crossnorm, semi-embedding, Radon-Nikodym property, absolutely p-summable sequence, strongly p-summable sequence, topological linear ...
Milton, Kimball A.; Fulling, Stephen A.; Parashar, Prachi; Kalauni, Pushpa; Murphy, Taylor
2016-04-01
Motivated by a desire to understand quantum fluctuation energy densities and stress within a spatially varying dielectric medium, we examine the vacuum expectation value for the stress tensor of a scalar field with arbitrary conformal parameter, in the background of a given potential that depends on only one spatial coordinate. We regulate the expressions by incorporating a temporal-spatial cutoff in the (imaginary) time and transverse-spatial directions. The divergences are captured by the zeroth- and second-order WKB approximations. Then the stress tensor is "renormalized" by omitting the terms that depend on the cutoff. The ambiguities that inevitably arise in this procedure are both duly noted and restricted by imposing certain physical conditions; one result is that the renormalized stress tensor exhibits the expected trace anomaly. The renormalized stress tensor exhibits no pressure anomaly, in that the principle of virtual work is satisfied for motions in a transverse direction. We then consider a potential that defines a wall, a one-dimensional potential that vanishes for z 0 , for z >0 . Previously, the stress tensor had been computed outside of the wall, whereas now we compute all components of the stress tensor in the interior of the wall. The full finite stress tensor is computed numerically for the two cases where explicit solutions to the differential equation are available, α =1 and 2. The energy density exhibits an inverse linear divergence as the boundary is approached from the inside for a linear potential, and a logarithmic divergence for a quadratic potential. Finally, the interaction between two such walls is computed, and it is shown that the attractive Casimir pressure between the two walls also satisfies the principle of virtual work (i.e., the pressure equals the negative derivative of the energy with respect to the distance between the walls).
International Nuclear Information System (INIS)
Burkhard, N.R.
1979-01-01
The gravity inversion code applies stabilized linear inverse theory to determine the topography of a subsurface density anomaly from Bouguer gravity data. The gravity inversion program consists of four source codes: SEARCH, TREND, INVERT, and AVERAGE. TREND and INVERT are used iteratively to converge on a solution. SEARCH forms the input gravity data files for Nevada Test Site data. AVERAGE performs a covariance analysis on the solution. This document describes the necessary input files and the proper operation of the code. 2 figures, 2 tables
Social Data Analytics Using Tensors and Sparse Techniques
Zhang, Miao
2014-01-01
The development of internet and mobile technologies is driving an earthshaking social media revolution. They bring the internet world a huge amount of social media content, such as images, videos, comments, etc. Those massive media content and complicate social structures require the analytic expertise to transform those flood of information into…
Bayesian inversion of refraction seismic traveltime data
Ryberg, T.; Haberland, Ch
2018-03-01
We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test
A preliminary report on the development of MATLAB tensor classes for fast algorithm prototyping.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)
2004-07-01
We describe three MATLAB classes for manipulating tensors in order to allow fast algorithm prototyping. A tensor is a multidimensional or N-way array. We present a tensor class for manipulating tensors which allows for tensor multiplication and 'matricization.' We have further added two classes for representing tensors in decomposed format: cp{_}tensor and tucker{_}tensor. We demonstrate the use of these classes by implementing several algorithms that have appeared in the literature.
Probabilistic inversion for chicken processing lines
Energy Technology Data Exchange (ETDEWEB)
Cooke, Roger M. [Department of Mathematics, Delft University of Technology, Delft (Netherlands)]. E-mail: r.m.cooke@ewi.tudelft.nl; Nauta, Maarten [Microbiological Laboratory for Health Protection RIVM, Bilthoven (Netherlands); Havelaar, Arie H. [Microbiological Laboratory for Health Protection RIVM, Bilthoven (Netherlands); Fels, Ine van der [Microbiological Laboratory for Health Protection RIVM, Bilthoven (Netherlands)
2006-10-15
We discuss an application of probabilistic inversion techniques to a model of campylobacter transmission in chicken processing lines. Such techniques are indicated when we wish to quantify a model which is new and perhaps unfamiliar to the expert community. In this case there are no measurements for estimating model parameters, and experts are typically unable to give a considered judgment. In such cases, experts are asked to quantify their uncertainty regarding variables which can be predicted by the model. The experts' distributions (after combination) are then pulled back onto the parameter space of the model, a process termed 'probabilistic inversion'. This study illustrates two such techniques, iterative proportional fitting (IPF) and PARmeter fitting for uncertain models (PARFUM). In addition, we illustrate how expert judgement on predicted observable quantities in combination with probabilistic inversion may be used for model validation and/or model criticism.
Probabilistic inversion for chicken processing lines
International Nuclear Information System (INIS)
Cooke, Roger M.; Nauta, Maarten; Havelaar, Arie H.; Fels, Ine van der
2006-01-01
We discuss an application of probabilistic inversion techniques to a model of campylobacter transmission in chicken processing lines. Such techniques are indicated when we wish to quantify a model which is new and perhaps unfamiliar to the expert community. In this case there are no measurements for estimating model parameters, and experts are typically unable to give a considered judgment. In such cases, experts are asked to quantify their uncertainty regarding variables which can be predicted by the model. The experts' distributions (after combination) are then pulled back onto the parameter space of the model, a process termed 'probabilistic inversion'. This study illustrates two such techniques, iterative proportional fitting (IPF) and PARmeter fitting for uncertain models (PARFUM). In addition, we illustrate how expert judgement on predicted observable quantities in combination with probabilistic inversion may be used for model validation and/or model criticism
Collineations of the curvature tensor in general relativity
Indian Academy of Sciences (India)
physics pp. 43–48. Collineations of the curvature tensor in general relativity. RISHI KUMAR TIWARI. Department of Mathematics and Computer Application, ... and kinematical properties of the models. Keywords. Collineation; Killing vectors; Ricci tensor; Riemannian curvature tensor. PACS No. 98.80. 1. Introduction.
Efficient MATLAB computations with sparse and factored tensors.
Energy Technology Data Exchange (ETDEWEB)
Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)
2006-12-01
In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.
[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.
Tensor based structure estimation in multi-channel images
DEFF Research Database (Denmark)
Schou, Jesper; Dierking, Wolfgang; Skriver, Henning
2000-01-01
. In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...
The nonabelian tensor square of a bieberbach group with ...
African Journals Online (AJOL)
The main objective of this paper is to compute the nonabelian tensor square of one Bieberbach group with elementary abelian 2-group point group of dimension three by using the computational method of the nonabelian tensor square for polycyclic groups. The finding of the computation showed that the nonabelian tensor ...
Relativistic particles with spin and antisymmetric tensor fields
International Nuclear Information System (INIS)
Sandoval Junior, L.
1990-09-01
A study is made on antisymmetric tensor fields particularly on second order tensor field as far as his equivalence to other fields and quantization through the path integral are concerned. Also, a particle model is studied which has been recently proposed and reveals to be equivalent to antisymmetric tensor fields of any order. (L.C.J.A.)
Magnetic hydrodynamics with asymmetric stress tensor
Billig, Yuly
2005-04-01
In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an Abelian extension of the Lie algebra of vector fields with a nontrivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity.
Magnetic hydrodynamics with asymmetric stress tensor
Billig, Yuly
2004-01-01
In this paper we study equations of magnetic hydrodynamics with a stress tensor. We interpret this system as the generalized Euler equation associated with an abelian extension of the Lie algebra of vector fields with a non-trivial 2-cocycle. We use the Lie algebra approach to prove the energy conservation law and the conservation of cross-helicity.
Superstrings with tensor degrees of freedom
Energy Technology Data Exchange (ETDEWEB)
Amorim, R. (Inst. de Fisica, Univ. Federal do Rio de Janeiro, Rio de Janeiro, RJ (Brazil)); Barcelos-Neto, J. (Inst. de Fisica, Univ. Federal do Rio de Janeiro, Rio de Janeiro, RJ (Brazil))
1994-10-01
We add antisymmetric tensor degrees of freedom to the usual superstring coordinates. We show that super and kappa symmetries are only achieved for the spacetime dimension D = 4. We also address problems related to the quantization of the model and discuss the influences of this extended spacetime in the usual quantum field theory. (orig.)
Norm of the Riemannian Curvature Tensor
Indian Academy of Sciences (India)
We consider the Riemannian functional R p ( g ) = ∫ M | R ( g ) | p d v g defined on the space of Riemannian metrics with unit volume on a closed smooth manifold where R ( g ) and d v g denote the corresponding Riemannian curvature tensor and volume form and p ∈ ( 0 , ∞ ) . First we prove that the Riemannian metrics ...
Abelian tensor models on the lattice
Chaudhuri, Soumyadeep; Giraldo-Rivera, Victor I.; Joseph, Anosh; Loganayagam, R.; Yoon, Junggi
2018-04-01
We consider a chain of Abelian Klebanov-Tarnopolsky fermionic tensor models coupled through quartic nearest-neighbor interactions. We characterize the gauge-singlet spectrum for small chains (L =2 ,3 ,4 ,5 ) and observe that the spectral statistics exhibits strong evidence in favor of quasi-many-body localization.
Primordial tensor modes from quantum corrected inflation
DEFF Research Database (Denmark)
Joergensen, Jakob; Sannino, Francesco; Svendsen, Ole
2014-01-01
. Finally we confront these theories with the Planck and BICEP2 data. We demonstrate that the discovery of primordial tensor modes by BICEP2 require the presence of sizable quantum departures from the $\\phi^4$-Inflaton model for the non-minimally coupled scenario which we parametrize and quantify. We...
Magnetotelluric impedance tensor analysis for identification of ...
Indian Academy of Sciences (India)
G Pavan Kumar
2017-07-18
Jul 18, 2017 ... Magnetotelluric impedance tensor analysis for identification of transverse tectonic feature in the Wagad uplift, Kachchh, northwest India. G Pavan Kumar*, Virender Kumar, Mehul Nagar, Dilip Singh,. E Mahendar, Pruthul Patel and P Mahesh. Institute of Seismological Research (ISR), Raisan, Gandhinagar ...
Tensor network methods for invariant theory
Biamonte, Jacob; Bergholm, Ville; Lanzagorta, Marco
2013-11-01
Invariant theory is concerned with functions that do not change under the action of a given group. Here we communicate an approach based on tensor networks to represent polynomial local unitary invariants of quantum states. This graphical approach provides an alternative to the polynomial equations that describe invariants, which often contain a large number of terms with coefficients raised to high powers. This approach also enables one to use known methods from tensor network theory (such as the matrix product state (MPS) factorization) when studying polynomial invariants. As our main example, we consider invariants of MPSs. We generate a family of tensor contractions resulting in a complete set of local unitary invariants that can be used to express the Rényi entropies. We find that the graphical approach to representing invariants can provide structural insight into the invariants being contracted, as well as an alternative, and sometimes much simpler, means to study polynomial invariants of quantum states. In addition, many tensor network methods, such as MPSs, contain excellent tools that can be applied in the study of invariants.
Seamless warping of diffusion tensor fields
DEFF Research Database (Denmark)
Xu, Dongrong; Hao, Xuejun; Bansal, Ravi
2008-01-01
transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...
Visualization and processing of tensor fields
Weickert, Joachim
2007-01-01
Presents information on the visualization and processing of tensor fields. This book serves as an overview for the inquiring scientist, as a basic foundation for developers and practitioners, and as a textbook for specialized classes and seminars for graduate and doctoral students.
Magnetotelluric impedance tensor analysis for identification of ...
Indian Academy of Sciences (India)
We present the results of magnetotelluric (MT) impedance tensors analyses of 18 sites located along a profile cutting various faults in the uplifted Wagad block of the Kachchh basin. The MT time series of 4–5 days recording duration have been processed and the earth response functions are estimated in broad frequency ...
Radiation Forces and Torques without Stress (Tensors)
Bohren, Craig F.
2011-01-01
To understand radiation forces and torques or to calculate them does not require invoking photon or electromagnetic field momentum transfer or stress tensors. According to continuum electromagnetic theory, forces and torques exerted by radiation are a consequence of electric and magnetic fields acting on charges and currents that the fields induce…
Fermionic topological quantum states as tensor networks
Wille, C.; Buerschaper, O.; Eisert, J.
2017-06-01
Tensor network states, and in particular projected entangled pair states, play an important role in the description of strongly correlated quantum lattice systems. They do not only serve as variational states in numerical simulation methods, but also provide a framework for classifying phases of quantum matter and capture notions of topological order in a stringent and rigorous language. The rapid development in this field for spin models and bosonic systems has not yet been mirrored by an analogous development for fermionic models. In this work, we introduce a tensor network formalism capable of capturing notions of topological order for quantum systems with fermionic components. At the heart of the formalism are axioms of fermionic matrix-product operator injectivity, stable under concatenation. Building upon that, we formulate a Grassmann number tensor network ansatz for the ground state of fermionic twisted quantum double models. A specific focus is put on the paradigmatic example of the fermionic toric code. This work shows that the program of describing topologically ordered systems using tensor networks carries over to fermionic models.
Tensor B mode and stochastic Faraday mixing
Giovannini, Massimo
2014-01-01
This paper investigates the Faraday effect as a different source of B mode polarization. The E mode polarization is Faraday rotated provided a stochastic large-scale magnetic field is present prior to photon decoupling. In the first part of the paper we discuss the case where the tensor modes of the geometry are absent and we argue that the B mode recently detected by the Bicep2 collaboration cannot be explained by a large-scale magnetic field rotating, through the Faraday effect, the well established E mode polarization. In this case, the observed temperature autocorrelations would be excessively distorted by the magnetic field. In the second part of the paper the formation of Faraday rotation is treated as a stationary, random and Markovian process with the aim of generalizing a set of scaling laws originally derived in the absence of the tensor modes of the geometry. We show that the scalar, vector and tensor modes of the brightness perturbations can all be Faraday rotated even if the vector and tensor par...
Introduction to vector and tensor analysis
Wrede, Robert C
1972-01-01
A broad introductory treatment, this volume examines general Cartesian coordinates, the cross product, Einstein's special theory of relativity, bases in general coordinate systems, maxima and minima of functions of two variables, line integrals, integral theorems, fundamental notions in n-space, Riemannian geometry, algebraic properties of the curvature tensor, and more. 1963 edition.
Tensor algebra and tensor analysis for engineers with applications to continuum mechanics
Itskov, Mikhail
2015-01-01
This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.
Sharp spatially constrained inversion
DEFF Research Database (Denmark)
Vignoli, Giulio G.; Fiandaca, Gianluca G.; Christiansen, Anders Vest C A.V.C.
2013-01-01
We present sharp reconstruction of multi-layer models using a spatially constrained inversion with minimum gradient support regularization. In particular, its application to airborne electromagnetic data is discussed. Airborne surveys produce extremely large datasets, traditionally inverted...... by using smoothly varying 1D models. Smoothness is a result of the regularization constraints applied to address the inversion ill-posedness. The standard Occam-type regularized multi-layer inversion produces results where boundaries between layers are smeared. The sharp regularization overcomes...... inversions are compared against classical smooth results and available boreholes. With the focusing approach, the obtained blocky results agree with the underlying geology and allow for easier interpretation by the end-user....
International Nuclear Information System (INIS)
Rosenwald, J.-C.
2008-01-01
The lecture addressed the following topics: Optimizing radiotherapy dose distribution; IMRT contributes to optimization of energy deposition; Inverse vs direct planning; Main steps of IMRT; Background of inverse planning; General principle of inverse planning; The 3 main components of IMRT inverse planning; The simplest cost function (deviation from prescribed dose); The driving variable : the beamlet intensity; Minimizing a 'cost function' (or 'objective function') - the walker (or skier) analogy; Application to IMRT optimization (the gradient method); The gradient method - discussion; The simulated annealing method; The optimization criteria - discussion; Hard and soft constraints; Dose volume constraints; Typical user interface for definition of optimization criteria; Biological constraints (Equivalent Uniform Dose); The result of the optimization process; Semi-automatic solutions for IMRT; Generalisation of the optimization problem; Driving and driven variables used in RT optimization; Towards multi-criteria optimization; and Conclusions for the optimization phase. (P.A.)
Submucous Myoma Induces Uterine Inversion
Directory of Open Access Journals (Sweden)
Yu-Li Chen
2006-06-01
Conclusion: Nonpuerperal inversion of the uterus is rarely encountered by gynecologists. Diagnosis of uterine inversion is often not easy and imaging studies might be helpful. Surgical treatment is the method of choice in nonpuerperal uterine inversion.
Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.
2008-01-01
This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...
Inverse problem in hydrogeology
Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.
2005-03-01
cas dans d'autres cas de figure. Par ailleurs, il peut être vu comme une des étapes dans le processus de détermination du comportement de l'aquifère. Il est montré que les méthodes d'évaluation des paramètres actuels ne diffèrent pas si ce n'est dans les détails des calculs informatiques. Il est montré qu'il existe une large panoplie de techniques d'inversion : codes de calcul utilisables par tout-un-chacun, accommodation de la variabilité via la géostatistique, incorporation d'informations géologiques et de différents types de données (température, occurrence, concentration en isotopes, âge, etc.), détermination de l'incertitude. Vu ces développements, la calibration automatique facilite énormément la modélisation. Par ailleurs, il est souhaitable que son utilisation devienne une pratique standardisée. Se sintetiza el estado del problema inverso en aguas subterráneas. El énfasis se ubica en la caracterización de acuíferos, donde los modeladores tienen que enfrentar la incertidumbre del modelo conceptual (principalmente variabilidad temporal y espacial), dependencia de escala, muchos tipos de parámetros desconocidos (transmisividad, recarga, condiciones limitantes, etc), no linealidad, y frecuentemente baja sensibilidad de variables de estado (típicamente presiones y concentraciones) a las propiedades del acuífero. Debido a estas dificultades, no puede separarse la calibración de los procesos de modelado, como frecuentemente se hace en otros campos. En su lugar, debe de visualizarse como un paso en el proceso de enten dimiento del comportamiento del acuífero. En realidad, se muestra que los métodos reales de estimación de parámetros no difieren uno del otro en lo esencial, aunque sí pueden diferir en los detalles computacionales. Se discute que existe amplio espacio para la mejora del problema inverso en aguas subterráneas: desarrollo de códigos amigables alusuario, acomodamiento de variabilidad a través de geoestad
Directory of Open Access Journals (Sweden)
S. Houweling
2004-01-01
Full Text Available Currently two polar orbiting satellite instruments measure CO2 concentrations in the Earth's atmosphere, while other missions are planned for the coming years. In the future such instruments might become powerful tools for monitoring changes in the atmospheric CO2 abundance and to improve our quantitative understanding of the leading processes controlling this. At the moment, however, we are still in an exploratory phase where first experiences are collected and promising new space-based measurement concepts are investigated. This study assesses the potential of some of these concepts to improve CO2 source and sink estimates obtained from inverse modelling. For this purpose the performance of existing and planned satellite instruments is quantified by synthetic simulations of their ability to reduce the uncertainty of the current source and sink estimates in comparison with the existing ground-based network of sampling sites. Our high resolution inversion of sources and sinks (at 8°x10° allows us to investigate the variation of instrument performance in space and time and at various temporal and spatial scales. The results of our synthetic tests clearly indicate that the satellite performance increases with increasing sensitivity of the instrument to CO2 near the Earth's surface, favoring the near infra-red technique. Thermal infrared instruments, on the contrary, reach a better global coverage, because the performance in the near infrared is reduced over the oceans owing to a low surface albedo. Near infra-red sounders can compensate for this by measuring in sun-glint, which will allow accurate measurements over the oceans, at the cost, however, of a lower measurement density. Overall, the sun-glint pointing near infrared instrument is the most promising concept of those tested. We show that the ability of satellite instruments to resolve fluxes at smaller temporal and spatial scales is also related to surface sensitivity. All the satellite
Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Xuqing Zhang
2013-01-01
Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.
Towards overcoming the Monte Carlo sign problem with tensor networks
Energy Technology Data Exchange (ETDEWEB)
Banuls, Mari Carmen; Cirac, J. Ignacio; Kuehn, Stefan [Max-Planck-Institut fuer Quantenoptik (MPQ), Garching (Germany); Cichy, Krzysztof [Frankfurt Univ. (Germany). Inst. fuer Theoretische Physik; Adam Mickiewicz Univ., Poznan (Poland). Faculty of Physics; Jansen, Karl [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC; Saito, Hana [AISIN AW Co., Ltd., Aichi (Japan)
2016-11-15
The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.
Adaptive stochastic Galerkin FEM with hierarchical tensor representations
Eigel, Martin
2016-01-08
PDE with stochastic data usually lead to very high-dimensional algebraic problems which easily become unfeasible for numerical computations because of the dense coupling structure of the discretised stochastic operator. Recently, an adaptive stochastic Galerkin FEM based on a residual a posteriori error estimator was presented and the convergence of the adaptive algorithm was shown. While this approach leads to a drastic reduction of the complexity of the problem due to the iterative discovery of the sparsity of the solution, the problem size and structure is still rather limited. To allow for larger and more general problems, we exploit the tensor structure of the parametric problem by representing operator and solution iterates in the tensor train (TT) format. The (successive) compression carried out with these representations can be seen as a generalisation of some other model reduction techniques, e.g. the reduced basis method. We show that this approach facilitates the efficient computation of different error indicators related to the computational mesh, the active polynomial chaos index set, and the TT rank. In particular, the curse of dimension is avoided.
Structure-adaptive sparse denoising for diffusion-tensor MRI.
Bao, Lijun; Robini, Marc; Liu, Wanyu; Zhu, Yuemin
2013-05-01
Diffusion tensor magnetic resonance imaging (DT-MRI) is becoming a prospective imaging technique in clinical applications because of its potential for in vivo and non-invasive characterization of tissue organization. However, the acquisition of diffusion-weighted images (DWIs) is often corrupted by noise and artifacts, and the intensity of diffusion-weighted signals is weaker than that of classical magnetic resonance signals. In this paper, we propose a new denoising method for DT-MRI, called structure-adaptive sparse denoising (SASD), which exploits self-similarity in DWIs. We define a similarity measure based on the local mean and on a modified structure-similarity index to find sets of similar patches that are arranged into three-dimensional arrays, and we propose a simple and efficient structure-adaptive window pursuit method to achieve sparse representation of these arrays. The noise component of the resulting structure-adaptive arrays is attenuated by Wiener shrinkage in a transform domain defined by two-dimensional principal component decomposition and Haar transformation. Experiments on both synthetic and real cardiac DT-MRI data show that the proposed SASD algorithm outperforms state-of-the-art methods for denoising images with structural redundancy. Moreover, SASD achieves a good trade-off between image contrast and image smoothness, and our experiments on synthetic data demonstrate that it produces more accurate tensor fields from which biologically relevant metrics can then be computed. Copyright © 2013 Elsevier B.V. All rights reserved.
Comparison of quality control software tools for diffusion tensor imaging.
Liu, Bilan; Zhu, Tong; Zhong, Jianhui
2015-04-01
Image quality of diffusion tensor imaging (DTI) is critical for image interpretation, diagnostic accuracy and efficiency. However, DTI is susceptible to numerous detrimental artifacts that may impair the reliability and validity of the obtained data. Although many quality control (QC) software tools are being developed and are widely used and each has its different tradeoffs, there is still no general agreement on an image quality control routine for DTIs, and the practical impact of these tradeoffs is not well studied. An objective comparison that identifies the pros and cons of each of the QC tools will be helpful for the users to make the best choice among tools for specific DTI applications. This study aims to quantitatively compare the effectiveness of three popular QC tools including DTI studio (Johns Hopkins University), DTIprep (University of North Carolina at Chapel Hill, University of Iowa and University of Utah) and TORTOISE (National Institute of Health). Both synthetic and in vivo human brain data were used to quantify adverse effects of major DTI artifacts to tensor calculation as well as the effectiveness of different QC tools in identifying and correcting these artifacts. The technical basis of each tool was discussed, and the ways in which particular techniques affect the output of each of the tools were analyzed. The different functions and I/O formats that three QC tools provide for building a general DTI processing pipeline and integration with other popular image processing tools were also discussed. Copyright © 2015 Elsevier Inc. All rights reserved.
Heriyanto, M.; Srigutomo, W.
2017-07-01
Exploration of natural or energy resources requires geophysical survey to determine the subsurface structure, such as DC resistivity method. In this research, field and synthetic data were used using Schlumberger configuration. One-dimensional (1-D) DC resistivity inversion was carried out using Singular Value Decomposition (SVD) and Levenberg-Marquardt (LM) techniques to obtain layered resistivity structure. We have developed software to perform both inversion methods accompanied by a user-friendly interface. Both of the methods were compared one another to determine the number of iteration, robust to noise, elapsed time of computation, and inversion results. SVD inversion generated faster process and better results than LM did. The inversion showed both of these methods were appropriate to interpret subsurface resistivity structure.
Massless and massive quanta resulting from a mediumlike metric tensor
International Nuclear Information System (INIS)
Soln, J.
1985-01-01
A simple model of the ''primordial'' scalar field theory is presented in which the metric tensor is a generalization of the metric tensor from electrodynamics in a medium. The radiation signal corresponding to the scalar field propagates with a velocity that is generally less than c. This signal can be associated simultaneously with imaginary and real effective (momentum-dependent) masses. The requirement that the imaginary effective mass vanishes, which we take to be the prerequisite for the vacuumlike signal propagation, leads to the ''spontaneous'' splitting of the metric tensor into two distinct metric tensors: one metric tensor gives rise to masslesslike radiation and the other to a massive particle. (author)
Glyph-Based Comparative Visualization for Diffusion Tensor Fields.
Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna
2016-01-01
Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.
Tensoral for post-processing users and simulation authors
Dresselhaus, Eliot
1993-01-01
The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.
Energy-momentum tensor of the electromagnetic field
International Nuclear Information System (INIS)
Horndeski, G.W.; Wainwright, J.
1977-01-01
In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources
Quantum mechanics of Yano tensors: Dirac equation in curved spacetime
International Nuclear Information System (INIS)
Cariglia, Marco
2004-01-01
In spacetimes admitting Yano tensors, the classical theory of the spinning particle possesses enhanced worldline supersymmetry. Quantum mechanically generators of extra supersymmetries correspond to operators that in the classical limit commute with the Dirac operator and generate conserved quantities. We show that the result is preserved in the full quantum theory, that is, Yano symmetries are not anomalous. This was known for Yano tensors of rank 2, but our main result is to show that it extends to Yano tensors of arbitrary rank. We also describe the conformal Yano equation and show that is invariant under Hodge duality. There is a natural relationship between Yano tensors and supergravity theories. As the simplest possible example, we show that when the spacetime admits a Killing spinor then this generates Yano and conformal Yano tensors. As an application, we construct Yano tensors on maximally symmetric spaces: they are spanned by tensor products of Killing vectors
Algebraic and computational aspects of real tensor ranks
Sakata, Toshio; Miyazaki, Mitsuhiro
2016-01-01
This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...
Energy Technology Data Exchange (ETDEWEB)
Lebrun, D.
1997-05-22
The aim of the dissertation is the linearized inversion of multicomponent seismic data for 3D elastic horizontally stratified media, using Born approximation. A Jacobian matrix is constructed; it will be used to model seismic data from elastic parameters. The inversion technique, relying on single value decomposition (SVD) of the Jacobian matrix, is described. Next, the resolution of inverted elastic parameters is quantitatively studies. A first use of the technique is shown in the frame of an evaluation of a sea bottom acquisition (synthetic data). Finally, a real data set acquired with conventional marine technique is inverted. (author) 70 refs.
Fuzzy logic guided inverse treatment planning
International Nuclear Information System (INIS)
Yan Hui; Yin Fangfang; Guan Huaiqun; Kim, Jae Ho
2003-01-01
A fuzzy logic technique was applied to optimize the weighting factors in the objective function of an inverse treatment planning system for intensity-modulated radiation therapy (IMRT). Based on this technique, the optimization of weighting factors is guided by the fuzzy rules while the intensity spectrum is optimized by a fast-monotonic-descent method. The resultant fuzzy logic guided inverse planning system is capable of finding the optimal combination of weighting factors for different anatomical structures involved in treatment planning. This system was tested using one simulated (but clinically relevant) case and one clinical case. The results indicate that the optimal balance between the target dose and the critical organ dose is achieved by a refined combination of weighting factors. With the help of fuzzy inference, the efficiency and effectiveness of inverse planning for IMRT are substantially improved