Search results for "matrices"

Generalized centro-invertible matrices with applications

2014

Centro-invertible matrices are introduced by R.S. Wikramaratna in 2008. For an involutory matrix R, we define the generalized centro-invertible matrices with respect to R to be those matrices A such that RAR = A^−1. We apply these matrices to a problem in modular arithmetic. Specifically, algorithms for image blurring/deblurring are designed by means of generalized centro-invertible matrices. In addition, if R1 and R2 are n × n involutory matrices, then there is a simple bijection between the set of all centro-invertible matrices with respect to R1 and the set with respect to R2.

Comprehensive analysis of forty yeast microarray datasets reveals a novel subset of genes (APha-RiB) consistently negatively associated with ribosome…

2014

Background The scale and complexity of genomic data lend themselves to analysis using sophisticated mathematical techniques to yield information that can generate new hypotheses and so guide further experimental investigations. An ensemble clustering method has the ability to perform consensus clustering over the same set of genes from different microarray datasets by combining results from different clustering methods into a single consensus result. Results In this paper we have performed comprehensive analysis of forty yeast microarray datasets. One recently described Bi-CoPaM method can analyse expressions of the same set of genes from various microarray datasets while using different cl…

Toughened epoxy matrices produced by e-beam irradiation

2009

An Scalable matrix computing unit architecture for FPGA and SCUMO user design interface

2019

High dimensional matrix algebra is essential in numerous signal processing and machine learning algorithms. This work describes a scalable square matrix-computing unit designed on the basis of circulant matrices. It optimizes data flow for the computation of any sequence of matrix operations removing the need for data movement for intermediate results, together with the individual matrix operations’ performance in direct or transposed form (the transpose matrix operation only requires a data addressing modification). The allowed matrix operations are: matrix-by-matrix addition, subtraction, dot product and multiplication, matrix-by-vector multiplication, and matrix by scalar multiplication.…

A saturated strategy robustly ensures stability of the cooperative equilibrium for Prisoner's dilemma

2016

We study diffusion of cooperation in a two-population game in continuous time. At each instant, the game involves two random individuals, one from each population. The game has the structure of a Prisoner's dilemma where each player can choose either to cooperate (c) or to defect (d), and is reframed within the field of approachability in two-player repeated game with vector payoffs. We turn the game into a dynamical system, which is positive, and propose a saturated strategy that ensures local asymptotic stability of the equilibrium (c, c) for any possible choice of the payoff matrix. We show that there exists a rectangle, in the space of payoffs, which is positively invariant for the syst…

Evaluation of the Use of a City Center through the Use of Bluetooth Sensors Network

2019

In order to achieve the objectives of Smart Cities, public administrations need to take measures to regulate mobility, which undoubtedly requires a high level of information and sensorization. Until the implementation of the connected vehicle takes place, it is still necessary to install sensors to obtain information about mobility. Bluetooth sensors are becoming a useful tool due to the low cost of equipment and installation. The use of Bluetooth sensors in cities, with short distances between sensors, makes it necessary to propose new classification algorithms that allow the trips of pedestrians and vehicles to be differentiated. This article presents the study carried out in the city of …

On the accuracy of the fast hierarchical DBEM for the analysis of static and dynamic crack problems

2010

In this paper the main features of a fast dual boundary element method based on the use of hierarchical matrices and iterative solvers are described and its effectiveness for fracture mechanics problems, both in the static and dynamic case, is demonstrated. The fast solver is built by representing the collocation matrix in hierarchical format and by using a preconditioned GMRES for the solution of the algebraic system. The preconditioner is computed in hierarchical format by LU decomposition of a coarse hierarchical representation of the collocation matrix. The method is applied to elastostatic problems and to elastodynamic cases represented in the Laplace transform domain. The application …

Defining relations of minimal degree of the trace algebra of 3×3 matrices

2008

Abstract The trace algebra C n d over a field of characteristic 0 is generated by all traces of products of d generic n × n matrices, n , d ⩾ 2 . Minimal sets of generators of C n d are known for n = 2 and n = 3 for any d as well as for n = 4 and n = 5 and d = 2 . The defining relations between the generators are found for n = 2 and any d and for n = 3 , d = 2 only. Starting with the generating set of C 3 d given by Abeasis and Pittaluga in 1989, we have shown that the minimal degree of the set of defining relations of C 3 d is equal to 7 for any d ⩾ 3 . We have determined all relations of minimal degree. For d = 3 we have also found the defining relations of degree 8. The proofs are based …

On the computational power of affine automata

2017

We investigate the computational power of affine automata (AfAs) introduced in [4]. In particular, we present a simpler proof for how to change the cutpoint for any affine language and a method how to reduce error in bounded error case. Moreover, we address to the question of [4] by showing that any affine language can be recognized by an AfA with certain limitation on the entries of affine states and transition matrices. Lastly, we present the first languages shown to be not recognized by AfAs with bounded-error.

On the ∗-cocharacter sequence of 3×3 matrices

2000

Abstract Let M 3 (F) be the algebra of 3×3 matrices with involution * over a field F of characteristic zero. We study the ∗ -polynomial identities of M 3 (F) , where ∗=t is the transpose involution, through the representation theory of the hyperoctahedral group B n . After decomposing the space of multilinear ∗ -polynomial identities of degree n under the B n -action, we determine which irreducible B n -modules appear with non-zero multiplicity. In symbols, we write the nth ∗ -cocharacter χ n (M 3 (F),*)=∑ r=0 n ∑ λ⊢r,h(λ)⩽6 μ⊢n−r,h(μ)⩽3 m λ,μ χ λ,μ , where λ and μ are partitions of r and n−r , respectively, χ λ,μ is the irreducible B n -character associated to the pair (λ,μ) and m λ,μ ⩾0 i…