A stochastic approximation algorithm with Markov chain Monte-Carlo method for incomplete data estimation problems

We propose a general procedure for solving incomplete data estimation problems. The procedure can be used to find the maximum likelihood estimate or to solve estimating equations in difficult cases such as estimation with the censored or truncated regression model, the nonlinear structural measurement error model, and the random effects model. The procedure is based on the general principle of stochastic approximation and the Markov chain Monte-Carlo method. Applying the theory on adaptive algorithms, we derive conditions under which the proposed procedure converges. Simulation studies also indicate that the proposed procedure consistently converges to the maximum likelihood estimate for the structural measurement error logistic regression model.

Suppressor T cells regulate the nonanergic cell population that remains after peripheral tolerance is induced to the Mls-1 antigen in T cell receptor Vβ8.1 transgenic mice

We have found suppressor T cells that inhibit the proliferative response of naive CD4+ T cells in T cell receptor (TCR) Vβ8.1 transgenic mice rendered tolerant in vivo by inoculation of Mls-1a-positive cells. This suppression was mediated by CD4+ T cells but not by CD8+ T cells or double-negative (DN) cells, and splenic CD4+ T cells from tolerant mice displayed a greater suppression than lymph node CD4+ T cells. Cell contact was required for efficient suppression, and known inhibitory cytokines such as IL-4, IL-10, and transforming growth factor β were not involved. Suppressor T cells inhibited IL-2 production by naive CD4+ T cells, and the addition of exogenous IL-2 diminished the suppressed activity while having little activity on tolerant T cells. Suppression was abolished by the elimination of CD25+ T cells in the tolerant CD4+ T cell subset. CD25+CD4+ T cells suppressed the proliferative response of the residual fraction of the nonanergic population, namely, 6C10+CD4+ T cells still present in the tolerant mice. However, 6C10−CD4+ T cells still had reduced reactivity to Mls-1a even after CD25+CD4+ T cells were removed and exogenous IL-2 was added. Suppressor cells appear to affect only residual nonanergic cells in situ, thereby facilitating the maintenance of the unresponsive state in vivo. These data provide a framework for understanding suppressor T cells and explain the difficulties and variables in defining their activity in other systems, because suppressor T cells apparently control only a small population of nonanergic cells in the periphery and may be viewed as a homeostatic mechanism.

Approximation algorithms

Increasing global competition, rapidly changing markets, and greater consumer awareness have altered the way in which corporations do business. To become more efficient, many industries have sought to model some operational aspects by gigantic optimization problems. It is not atypical to encounter models that capture 106 separate “yes” or “no” decisions to be made. Although one could, in principle, try all 2106 possible solutions to find the optimal one, such a method would be impractically slow. Unfortunately, for most of these models, no algorithms are known that find optimal solutions with reasonable computation times. Typically, industry must rely on solutions of unguaranteed quality that are constructed in an ad hoc manner. Fortunately, for some of these models there are good approximation algorithms: algorithms that produce solutions quickly that are provably close to optimal. Over the past 6 years, there has been a sequence of major breakthroughs in our understanding of the design of approximation algorithms and of limits to obtaining such performance guarantees; this area has been one of the most flourishing areas of discrete mathematics and theoretical computer science.

Motor learning by field approximation.

We investigated how human subjects adapt to forces perturbing the motion of their ams. We found that this kind of learning is based on the capacity of the central nervous system (CNS) to predict and therefore to cancel externally applied perturbing forces. Our experimental results indicate: (i) that the ability of the CNS to compensate for the perturbing forces is restricted to those spatial locations where the perturbations have been experienced by the moving arm. The subjects also are able to compensate for forces experienced at neighboring workspace locations. However, adaptation decays smoothly and quickly with distance from the locations where disturbances had been sensed by the moving limb. (ii) Our experiments also how that the CNS builds an internal model of the external perturbing forces in intrinsic (muscles and / or joints) coordinates.