Realization of long exact sequences of abelian groups

Given a long exact sequence of abelian groups [fórmula disponible al document original] a short exact sequence of complexes of free abelian groups is constructed whose cohomology long exact sequence is precisely L. In this sense, L is realized . Two techniques which are introduced to reduce or replace lengthy diagram chasing arguments may be of interest to some readers. One is an arithmetic of bicartesian squares; the other is the use of the fact that categories of morphisms of abelian categories are themselves abelian

Monte Carlo algorithms for the detection of necessary linear matrix inequality constraints

We reduce the size of large semidefinite programming problems by identifying necessary linear matrix inequalities (LMI's) using Monte Carlo techniques. We describe three algorithms for detecting necessary LMI constraints that extend algorithms used in linear programming to semidefinite programming. We demonstrate that they are beneficial and could serve as tools for a semidefinite programming preprocessor. A necessary LMI is one whose removal changes the feasible region defined by all the LMI constraints. The general problem of checking whether or not a particular LMI is necessary is NP-complete. However, the methods we describe are polynomial in each iteration, and the number of iterations can be limited by stopping rules. This provides a practical method for reducing the size of some large Semidefinite Programming problems before one attempts to solve them. We demonstrate the applicability of this approach to solving instances of the Lowner ellipsoid problem. We also consider the problem of classification of all the constraints of a semidefinite programming problem as redundant or necessary

A probabilistic method for detecting multivariate extreme outliers

Given a data set arising from a series of observations, an outlier is a value that deviates substantially from the natural variability of the data set as to arouse suspicions that it was generated by a different mechanism. We call an observation an extreme outlier if it lies at an abnormal distance from the "center" of the data set. We introduce the Monte Carlo SCD algorithm for detecting extreme outliers. The algorithm finds extreme outliers in terms of a subset of the data set called the outer shell. Each iteration of the algorithm is polynomial. This could be reduced by preprocessing the data to reduce its size. This approach has an interesting new feature. It estimates a relative measure of the degree to which a data point on the outer shell is an outlier (its "outlierness"). This measure has potential for serendipitous discoveries in data mining where unusual or special behavior is of interest. Other applications include spatial filtering and smoothing in digital image processing. We apply this method to baseball data and identify the ten most exceptional pitchers of the 1998 American League. To illustrate another useful application, we also show that the SCD can be used to reduce the solution time of the D-optimal experimental design problem

Stress, ageing and their influence on functional, cellular and molecular aspects of the immune system

The immune response is essential for keeping an organism healthy and for defending it from different types of pathogens. It is a complex system that consists of a large number of components performing different functions. The adequate and controlled interaction between these components is necessary for a robust and strong immune response. There are, however, many factors that interfere with the way the immune response functions. Stress and ageing now consistently appear in the literature as factors that act upon the immune system in the way that is often damaging. This review focuses on the role of stress and ageing in altering the robustness of the immune response first separately, and then simultaneously, discussing the effects that emerge from their interplay. The special focus is on the psychological stress and the impact that it has at different levels, from the whole system to the individual molecules, resulting in consequences for physical health

The Vaccination Model in Psychoneuroimmunology Research: A Review

This chapter explores the reasoning behind using the vaccination model to examine the influence of psychosocial factors on immunity. It then briefly discusses the mechanics of the vaccination response and the protocols used in psychoneuroimmunology vaccine research, before giving examples from the research literature of the studies examining relationships such as the association between stress and vaccination response. It also explores the ways the vaccination model can be used to answer key questions in psychoneuroimmunology, such as the following: “Does it matter when stressful life events occur relative to when the vaccine is received?” “What are the effects of prior exposure to the antigen?” “Do other psychosocial factors influence vaccine response besides stress?” Finally, it briefly considers the mechanisms underlying psychosocial factors and vaccination response associations and the future research needed to understand these better, and indeed to use current and future knowledge to improve and enhance vaccine responses in key at-risk populations

The replica location problem and Chebyshev polynomials of the second kind

We study the optimal placement of replicas of data objects in a connected network with the topology of a straight-line segment. This special case of a NP-complete location problem has a remarkably attractive algebraic solution. The minimum cost problem gives rise to tridiagonal matrices that are both persymmetric and symmetric and these are used to prove the symmetry of the optimal solution. The eigenvalues and eigenvectors of these matrices are completely described by Chebyshev polynomials of the second kind to give a complete solution to the replica location problem. We denote the kth Chebyshev polynomials of the second kind by Uk. The Chebyshev identity U2m+1 = 2(x-1) × ((U0 + U1)2 + (U1+U2)2+ ⋯ +(Um-1 + Um)2) + 2(x+m)arises naturally in examining the norms of the eigenvectors that occur

Functors whose domain is a category of morphisms

Connected sequences of functors whose domain, is the category of morphisms of an arbitrary abelian category A and whose range category B is also abelian are compared with the composition functors of Eckmann and Hilton acting between the same categories Sequences of functors of both types are obtained from any half-exact functor A→B if A has enough injectives and projectives