Search results for "Linear Algebra."
showing 10 items of 552 documents
On stability of generic subriemannian caustic in the three-space
2000
Abstract The singularities of exponential mappings in subriemannian geometry are interesting objects, that are already non-trivial at the local level, contrarily to their Riemannian analogs. The simplest case is the three-dimensional contact case. Here we show that the corresponding generic caustics have moduli at the origin, and the first module that occurs has a simple geometric interpretation. On the contrary, we prove a stability result of the “big wave front”, that is, of the graph of the multivalued arclength function, reparametrized in a certain way. This object is a three-dimensional surface, which has also the natural structure of a wave front. The projection on the three-dimension…
Land surface emissivity retrieval from satellite data
2012
As an intrinsic property of natural materials, land surface emissivity LSE is an important surface parameter and can be derived from the emitted radiance measured from space. Besides radiometric calibration and cloud detection, two main problems need to be resolved to obtain LSE values from space measurements. These problems are often referred to as land surface temperature LST and emissivity separation from radiance at ground level and as atmospheric corrections in the literature. To date, many LSE retrieval methods have been proposed with the same goal but different application conditions, advantages, and limitations. The aim of this article is to review these LSE retrieval methods and to…
MULTIPLICITIES IN THE MIXED TRACE COCHARACTER SEQUENCE OF TWO 3 × 3 MATRICES
2006
We find explicitly the multiplicities in the (mixed) trace cocharacter sequence of two 3 × 3 matrices over a field of characteristic 0 and show that asymptotically they behave as polynomials of seventh degree. As a consequence we obtain also the multiplicities of certain irreducible characters in the cocharacter sequence of the polynomial identities of 3 × 3 matrices.
Visual Discrimination of the 17 Plane Symmetry Groups
2011
Within most of the 17 plane symmetry groups, individual symmetry operations act in multiple, nonequivalent ways. This, and the fact that many groups can be realized on the basis of different unit cells and generating regions, poses difficulties for visual discrimination and identification. Because of inherent confounds, only few of the groups can be studied by traditional experimental methodology. The use of an oddity paradigm and specific tiling patterns that camouflage groups in complex textures are recommended as partial remedy to this impasse. In order to prepare readers for an appreciation of the aforementioned issues and to provide a rationale for their investigation, the reporting of…
On the classification of visual patterns: systems analysis using detection experiments.
1977
Behavioral experiments are indispensable for the analysis of biological systems for cognition and recognition. When these are carried out as detection experiments three types of description can be used for the problem of visual pattern recognition which allow conclusions to be drawn on the operating function of the system. Provided that the signals to be recognized have additive noise superimposed on them, system description is possible: 1. on the basis on the probabilities of recognition and of mix-up,--2. through the analysis of the transformation of distribution densities of the noise,--3. by means of the measurable distances of the patterns from each other in feature space.-The analysis…
Empirical Autotuning of Two-level Parallel Linear Algebra Routines on Large cc-NUMA Systems
2012
In large cc-NUMA systems the efficient use of the different levels of the memory hierarchy is not an easy task, and the performance of multithreading implementations of the libraries decreases when the number of cores used increases, so producing an important lost of efficiency. To alleviate this problem, routines with multilevel parallelism can be developed by combining OpenMP and BLAS parallelism. In that way, higher performance can be achieved, but it is necessary to develop some autotuning technique for the appropriate selection of the number of threads to use at each level. The selection can be made through theoretical models of the execution time or some installation methodology. This…
Parallel Calculation of CCSDT and Mk-MRCCSDT Energies.
2010
A scheme for the parallel calculation of energies at the coupled-cluster singles, doubles, and triples (CCSDT) level of theory, several approximate iterative CCSDT schemes (CCSDT-1a, CCSDT-1b, CCSDT-2, CCSDT-3, and CC3), and for the state-specific multireference coupled-cluster ansatz suggested by Mukherjee with a full treatment of triple excitations (Mk-MRCCSDT) is presented. The proposed scheme is based on the adaptation of a highly efficient serial coupled-cluster code leading to a communication-minimized implementation by parallelizing the time-determining steps. The parallel algorithm is tailored for affordable cluster architectures connected by standard communication networks such as …
"Master-Slave" Biological Network Alignment
2010
Performing global alignment between protein-protein interaction (PPI) networks of different organisms is important to infer knowledge about conservation across species. Known methods that perform this task operate symmetrically, that is to say, they do not assign a distinct role to the input PPI networks. However, in most cases, the input networks are indeed distinguishable on the basis of how well the corresponding organism is biologically well-characterized. For well-characterized organisms the associated PPI network supposedly encode in a sound manner all the information about their proteins and associated interactions, which is far from being the case for not well characterized ones. He…
Extracting string motif bases for quorum higher than two
2012
Bases of generators of motifs consisting of strings in which some positions can be occupied by a don’t care provide a useful conceptual tool for their description and a way to reduce the time and space involved in the discovery process. In the last few years, a few algorithms have been proposed for the extraction of a basis, building in large part on combinatorial properties of strings and their autocorrelations. Currently, the most efficient techniques for binary alphabets and quorum q = 2 require time quadratic in the length of the host string. The present paper explores properties of motif bases for quorum q ≥ 2, both with binary and general alphabets, by also showing that important resu…
Clarkson-McCarthy inequalities with unitary and isometry orbits
2020
Abstract A refinement of a trace inequality of McCarthy establishing the uniform convexity of the Schatten p-classes for p > 2 is proved: if A , B are two n-by-n matrices, then there exists some pair of n-by-n unitary matrices U , V such that U | A + B 2 | p U ⁎ + V | A − B 2 | p V ⁎ ≤ | A | p + | B | p 2 . A similar statement holds for compact Hilbert space operators. Another improvement of McCarthy's inequality is given via the new operator parallelogramm law, | A + B | 2 ⊕ | A − B | 2 = U 0 ( | A | 2 + | B | 2 ) U 0 ⁎ + V 0 ( | A | 2 + | B | 2 ) V 0 ⁎ for some pair of 2n-by-n isometry matrices U 0 , V 0 .