Previously, we have discussed a recursive solution to the vector normal equation utilizing the recursive Cholesky and Modified Gram-Schmidt Orthogonalization (MGSO) algorithms. Previously, we have also discussed a blind adaptive approach for detection and extraction of signals of interest in the presence of noise and interference without relying on preamble or training sequences. The heart of t...

The prediction of drug-target interactions is a key step in the drug discovery process, which serves to identify new drugs or novel targets for existing drugs. However, experimental methods for predicting drug-target interactions are expensive and time-consuming. Therefore, the in silico prediction of drug-target interactions has recently attracted increasing attention. In this study, we propos...

The sup norm problem has been an active area and now there exist non-trivial estimates for cusp forms of large level, on higher rank groups, and for half-integral weight forms [BH] [T1] [HT1] [HT2] [T2] [HRR] [BP] [BM] [M] [K]. Nevertheless, the basic estimate for Γ = PSL2(Z) in the eigenvalue aspect has not been improved. The case of Eisenstein series seems to have been largely neglected up to...

Let $D \subset \mathbb{R}^d$ be a bounded, connected domain with smooth boundary, and let $-\Delta u = \mu\_1 u$ the first nontrivial eigenfunction of Laplace operator Neumann boundary conditions. We prove that $$ \max\_{x \in D} \~u(x) \leq 60 \cdot \partial we emphasize this constant is uniform among all domains in dimensions. In particular, hot spots conjecture cannot fail by an arbitrarily ...

This paper develops the necessary tools to understand the relationship between eigenvalues of the Laplacian matrix of a graph and the connectedness of the graph. First we prove that a graph has k connected components if and only if the algebraic multiplicity of eigenvalue 0 for the graph’s Laplacian matrix is k. We then prove Cheeger’s inequality (for dregular graphs) which bounds the number of...

In matrix computations, such as in factoring matrices, Hermitian and, preferably, positive definite elements are occasionally required. Related problems can often be cast as that of existence of respective elements in a matrix subspace. For two dimensional matrix subspaces, first results in this regard are due to Finsler. To assess positive definiteness in larger dimensional cases, the task bec...

A natural question in the study of geometric operators is that of how much information is needed to estimate the eigenvalues of an operator. For the square of the Dirac operator, such a question has at least peripheral physical import. When coupled to gauge fields, the lowest eigenvalue is related to chiral symmetry breaking. In the pure metric case, lower eigenvalue estimates may help to give ...

Let λ1 be the greatest eigenvalue and λn the least eigenvalue of the adjacency matrix of a connected graph G with n vertices, m edges and diameter D. We prove that if G is nonregular, then Δ− λ1 > nΔ− 2m n(D(nΔ− 2m)+ 1) 1 n(D + 1) , where Δ is the maximum degree of G. The inequality improves previous bounds of Stevanović and of Zhang. It also implies that a lower bound on λn obtained by Alon an...

In this paper we concentrate on the problem of comparing the effectiveness of the Darwinian, and Least Square methods, with the influence of the input signal (statistics) spreadness highlighted. Our approach in this paper is to carry out an extensive suite of simulations for both the Darwinian algorithm and LMS algorithm under varying initial conditions and eigenvalue spread of the signal autoc...