1. 


2. 
 Ahmad, M. Rauf
(författare)

A twosample test statistic for highdimensional multivariate data under nonnormality
 2011

Rapport (övrigt vetenskapligt)abstract
 Ahmad, Ohlson, and von Rosen (2011a) present asymptotic distribution of a onesample test statistic under nonnormality, when the data are high dimensional, i.e., when the dimension of the vector, p, may exceed the sample size, n. This paper extends the case to a twosample statistic to test the difference of mean vectors of two independent multivariate distributions, again under highdimensional set up. Using the asymptotic theory of Ustatistics, and under mild assumptions on the traces of the unknown covariance matrices, the statistic is shown to follow an approximate normal distribution when n and p are large. However, no relationship between n and p is assumed. An extension to the paired case is given, which, being essentially a onesample statistic, supplements the asymptotic results obtained in Ahmad, Ohlson, and von Rosen (2011a).


3. 
 Ahmad, M. Rauf, et al.
(författare)

A Ustatistics Based Approach to Mean Testing for High Dimensional Multivariate Data Under Nonnormality
 2011

Rapport (övrigt vetenskapligt)abstract
 A test statistic is considered for testing a hypothesis for the mean vector for multivariate data, when the dimension of the vector, p, may exceed the number of vectors, n, and the underlying distribution need not necessarily be normal. With n, p large, and under mild assumptions, the statistic is shown to asymptotically follow a normal distribution. A by product of the paper is the approximate distribution of a quadratic form, based on the reformulation of wellknown Box's approximation, under highdimensional set up.


4. 


5. 
 Ahmad, M. Rauf, et al.
(författare)

Some Tests of Covariance Matrices for High Dimensional Multivariate Data
 2011

Rapport (övrigt vetenskapligt)abstract
 Test statistics for sphericity and identity of the covariance matrix are presented, when the data are multivariate normal and the dimension, p, can exceed the sample size, n. Using the asymptotic theory of Ustatistics, the test statistics are shown to follow an approximate normal distribution for large p, also when p >> n. The statistics are derived under very general conditions, particularly avoiding any strict assumptions on the traces of the unknown covariance matrix. Neither any relationship between n and p is assumed. The accuracy of the statistics is shown through simulation results, particularly emphasizing the case when p can be much larger than n. The validity of the commonly used assumptions for highdimensional set up is also briefly discussed.


6. 
 Amsallem, David, et al.
(författare)

Highorder accurate difference schemes for the HodgkinHuxley equations
 2012

Rapport (övrigt vetenskapligt)abstract
 A novel approach for simulating potential propagation in neuronal branches with high accuracy is developed. The method relies on highorder accurate dierence schemes using the SummationByParts operators with weak boundary and interface conditions applied to the HodgkinHuxley equations. This work is the rst demonstrating high accuracy for that equation. Several boundary conditions are considered including the nonstandard one accounting for the soma presence, which is characterized by its own partial dierential equation. Wellposedness for the continuous problem as well as stability of the discrete approximation is proved for all the boundary conditions. Gains in terms of CPU times are observed when highorder operators are used, demonstrating the advantage of the highorder schemes for simulating potential propagation in large neuronal trees.


7. 
 Andersson, LarsErik, 19422014
(författare)

Quasistatic frictional contact problems with finitely many degrees of freedom.
 1999

Rapport (övrigt vetenskapligt)abstract
 In the present paper results on existence and uniqueness of solutions to discrete frictional quasistatic unilateral contact problems are given under a condition that the coefficients of friction are smaller than a certain upper bound. This upper bound is defined in terms of an influence matrix for the contact nodes. The results of existence and uniqueness may be ordered into two classes depending on whether regularity conditions for the applied forces are imposed or not. For general loading which has a time derivative almost everywhere it is shown that a solution exists which satisfies governing equations for almost all times. Uniqueness of the solution has been shown only when the problem is restricted to two degrees of freedom. For a loading which is right piecewise analytic, additional results can be obtained. For instance, if each contact node has only two degrees of freedom a unique solution which satisfies governing equeations for all times exists. For the constructed solutions a priori estimates of the displacement field and its time derivate in terms of the applied forces are also given.


8. 
 Andersson, Mats, et al.
(författare)

Global Search Strategies for Solving Multilinear Leastsquares Problems
 2011

Rapport (övrigt vetenskapligt)abstract
 The multilinear leastsquares (MLLS) problem is an extension of the linear leastsquares problem. The difference is that a multilinearoperator is used in place of a matrixvector product. The MLLS istypically a largescale problem characterized by a large number of local minimizers. It originates, for instance, from the design of filter networks. We present a global search strategy that allows formoving from one local minimizer to a better one. The efficiencyof this strategy isillustrated by results of numerical experiments performed forsome problems related to the design of filter networks.


9. 
 Andersson, Mats, et al.
(författare)

Sparsity Optimization in Design of Multidimensional Filter Networks
 2013

Rapport (övrigt vetenskapligt)abstract
 Filter networks is a powerful tool used for reducing the image processing time, while maintaining its reasonably high quality.They are composed of sparse subfilters whose low sparsity ensures fast image processing.The filter network design is related to solvinga sparse optimization problem where a cardinality constraint bounds above the sparsity level.In the case of sequentially connected subfilters, which is the simplest network structure of those considered in this paper, a cardinalityconstrained multilinear leastsquares (MLLS) problem is to be solved. If to disregard the cardinality constraint, the MLLS is typically a largescale problem characterized by a large number of local minimizers. Each of the local minimizers is singular and nonisolated.The cardinality constraint makes the problem even more difficult to solve.An approach for approximately solving the cardinalityconstrained MLLS problem is presented.It is then applied to solving a bicriteria optimization problem in which both thetime and quality of image processing are optimized. The developed approach is extended to designing filter networks of a more general structure. Its efficiency is demonstrated by designing certain 2D and 3D filter networks. It is also compared with the existing approaches.


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