Search results for "Linear Algebra."
showing 10 items of 552 documents
Nucleotide's bilinear indices: Novel bio-macromolecular descriptors for bioinformatics studies of nucleic acids. I. Prediction of paromomycin's affin…
2009
A new set of nucleotide-based bio-macromolecular descriptors are presented. This novel approach to bio-macromolecular design from a linear algebra point of view is relevant to nucleic acids quantitative structure-activity relationship (QSAR) studies. These bio-macromolecular indices are based on the calculus of bilinear maps on Re(n)[b(mk)(x (m),y (m)):Re(n) x Re(n)--Re] in canonical basis. Nucleic acid's bilinear indices are calculated from kth power of non-stochastic and stochastic nucleotide's graph-theoretic electronic-contact matrices, M(m)(k) and (s)M(m)(k), respectively. That is to say, the kth non-stochastic and stochastic nucleic acid's bilinear indices are calculated using M(m)(k)…
Catalan Morphology and Low-level Patterns in a Network Model
2005
The fact that more specific or low-level morphological patterns may coexist with the most general or abstract ones is a characteristic insight of Cognitive Morphology. According to the bottom-up approach of the model, it is even to be expected that low-level patterns may have a more relevant role than the most inclusive and abstract ones. On the basis of the analysis of an aspect of Catalan inflection (velar verbs of the second conjugation) and one aspect of Catalan word-formation (complex words with the prefixoid radio-), we will show the advantages of incorporating to the model salient low-level patterns and the local paradigmatic relations in which they are based. info:eu-repo/semantics/…
Experimental Study of Six Different Implementations of Parallel Matrix Multiplication on Heterogeneous Computational Clusters of Multicore Processors
2010
Two strategies of distribution of computations can be used to implement parallel solvers for dense linear algebra problems for Heterogeneous Computational Clusters of Multicore Processors (HCoMs). These strategies are called Heterogeneous Process Distribution Strategy (HPS) and Heterogeneous Data Distribution Strategy (HDS). They are not novel and have been researched thoroughly. However, the advent of multicores necessitates enhancements to them. In this paper, we present these enhancements. Our study is based on experiments using six applications to perform Parallel Matrix-matrix Multiplication (PMM) on an HCoM employing the two distribution strategies.
On Discovering Low Order Models in Biochemical Reaction Kinetics
2007
We develop a method by which a large number of differential equations representing biochemical reaction kinetics may be represented by a smaller number of differential equations. The basis of our technique is a conjecture that the high dimension equations of biochemical kinetics, which involve reaction terms of specific forms, are actually implementing a low dimension system whose behavior requires right hand sides that can not be biochemically implemented. For systems that satisfy this conjecture, we develop a simple approximation scheme based on multilinear algebra that extracts the low dimensional system from simulations of the high dimension system. We demonstrate this technique on a st…
Cocharacters of Bilinear Mappings and Graded Matrices
2012
Let Mk(F) be the algebra of k ×k matrices over a field F of characteristic 0. If G is any group, we endow Mk(F) with the elementary grading induced by the k-tuple (1,...,1,g) where g ∈ G, g2 ≠ 1. Then the graded identities of Mk(F) depending only on variables of homogeneous degree g and g − 1 are obtained by a natural translation of the identities of bilinear mappings (see Bahturin and Drensky, Linear Algebra Appl 369:95–112, 2003). Here we study such identities by means of the representation theory of the symmetric group. We act with two copies of the symmetric group on a space of multilinear graded polynomials of homogeneous degree g and g − 1 and we find an explicit decomposition of the …
Computation of the Multivariate Oja Median
2003
The multivariate Oja median (Oja, 1983) is an affine equivariant multivariate location estimate with high efficiency. This estimate has a bounded influence function but zero breakdown. The computation of the estimate appears to be highly intensive. We consider different, exact and stochastic, algorithms for the calculation of the value of the estimate. In the stochastic algorithms, the gradient of the objective function, the rank function, is estimated by sampling observation. hyperplanes. The estimated rank function with its estimated accuracy then yields a confidence region for the true sample Oja median, and the confidence region shrinks to the sample median with the increasing number of…
The evolution of COVID-19: A discontinuous approach.
2021
The evolution of the COVID-19 disease is monitored on the basis of the daily number of infected patients and the daily number of deaths provided from national health agencies. The variation of such parameters with time parallels that described for the growth/decay of historic transportation systems revealing the appearance of discontinuities. The evolution of the pandemic disease is represented in terms of two nominally equivalent formulations: a logistic model with sharp changes in its rate parameters, and in topological terms resulting in 2nd order phase transitions in the infected patients/time space.
Unitarity of the SoV Transform for the Toda Chain
2014
The quantum separation of variables method consists in mapping the original Hilbert space where a spectral problem is formulated onto one where the spectral problem takes a simpler "separated" form. In order to realise such a program, one should construct the map explicitly and then show that it is unitary. In the present paper, we develop a technique which allows one to prove the unitarity of this map in the case of the quantum Toda chain. Our proof solely builds on objects and relations naturally arising in the framework of the so-called quantum inverse scattering method. Hence, with minor modifications, it should be readily transposable to other quantum integrable models solvable by the …
A taxonomy for wavelet neural networks applied to nonlinear modelling
2008
This article presents a novel classification of wavelet neural networks based on the orthogonality/non-orthogonality of neurons and the type of nonlinearity employed. On the basis of this classification different network types are studied and their characteristics illustrated by means of simple one-dimensional nonlinear examples. For multidimensional problems, which are affected by the curse of dimensionality, the idea of spherical wavelet functions is considered. The behaviour of these networks is also studied for modelling of a low-dimension map.
Mirror and triplet displacement energies within nuclear DFT: : numerical stability
2017
Isospin-symmetry-violating class II and III contact terms are introduced into the Skyrme energy density functional to account for charge dependence of the strong nuclear interaction. The two new coupling constants are adjusted to available experimental data on triplet and mirror displacement energies, respectively. We present preliminary results of the fit, focusing on its numerical stability with respect to the basis size.