New techniques for the solution of linear systems by iterative methods

AbstractA new iterative method for the solution of linear systems, based upon a new splitting of the coefficient matrix A, is presented.The method is obtained by considering splittings of the type A = (A − M) + M, where M−1 is a symmetric tridiagonal matrix, and by minimizing the Frobenius norm of the iteration matrix so derived.Numerical examples are provided, showing that our algorithm improves the rate of convergence of Jacobi method, without increasing the order of magnitude of the computational efforts required

Discrete Convex Functions on Graphs and Their Algorithmic Applications

The present article is an exposition of a theory of discrete convex functions on certain graph structures, developed by the author in recent years. This theory is a spin-off of discrete convex analysis by Murota, and is motivated by combinatorial dualities in multiflow problems and the complexity classification of facility location problems on graphs. We outline the theory and algorithmic applications in combinatorial optimization problems

No Association between Personality and Candidate Gene Polymorphisms in a Wild Bird Population

Consistency of between-individual differences in behaviour or personality is a phenomenon in populations that can have ecological consequences and evolutionary potential. One way that behaviour can evolve is to have a genetic basis. Identifying the molecular genetic basis of personality could therefore provide insight into how and why such variation is maintained, particularly in natural populations. Previously identified candidate genes for personality in birds include the dopamine receptor D4 (DRD4), and serotonin transporter (SERT). Studies of wild bird populations have shown that exploratory and bold behaviours are associated with polymorphisms in both DRD4 and SERT. Here we tested for polymorphisms in DRD4 and SERT in the Seychelles warbler (Acrocephalus sechellensis) population on Cousin Island, Seychelles, and then investigated correlations between personality and polymorphisms in these genes. We found no genetic variation in DRD4, but identified four polymorphisms in SERT that clustered into five haplotypes. There was no correlation between bold or exploratory behaviours and SERT polymorphisms/haplotypes. The null result was not due to lack of power, and indicates that there was no association between these behaviours and variation in the candidate genes tested in this population. These null findings provide important data to facilitate representative future meta-analyses on candidate personality genes

Combinatorial integer labeling theorems on finite sets with applications

Tucker’s well-known combinatorial lemma states that, for any given symmetric triangulation of the n-dimensional unit cube and for any integer labeling that assigns to each vertex of the triangulation a label from the set {±1, ±2, · · · , ±n} with the property that antipodal vertices on the boundary of the cube are assigned opposite labels, the triangulation admits a 1-dimensional simplex whose two vertices have opposite labels. In this paper, we are concerned with an arbitrary finite set D of integral vectors in the n-dimensional Euclidean space and an integer labeling that assigns to each element of D a label from the set {±1, ±2, · · · , ±n}. Using a constructive approach, we prove two combinatorial theorems of Tucker type. The theorems state that, under some mild conditions, there exists two integral vectors in D having opposite labels and being cell-connected in the sense that both belong to the set {0, 1} n +q for some integral vector q. These theorems are used to show in a constructive way the existence of an integral solution to a system of nonlinear equations under certain natural conditions. An economic application is provided

Solving certain queueing problems by means of regular splittings

AbstractWe analyze the problem of the computation of the solution of the nonlinear matrix equation X = Σi=0+∞ XiAi, arising in queueing models. We propose a technique based on regular splittings, that on one hand leads to a new method for computing the solution, and on the other hand, it may be used to construct nonlinear matrix equations equivalent to starting one, that can be possibly solved by applying different algorithms

Condizioni Necessarie per Problemi di Ottimizzazione in Presenza di Vincoli

nota indirizzata agli studenti del corso di dottorato, sui moltiplicatori di Lagrange generalizzati e loro applicazioni alla programmazione matematica e al calcolo delle variazion