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.

Multiple maternal origins and weak phylogeographic structure in domestic goats

Domestic animals have played a key role in human history. Despite their importance, however, the origins of most domestic species remain poorly understood. We assessed the phylogenetic history and population structure of domestic goats by sequencing a hypervariable segment (481 bp) of the mtDNA control region from 406 goats representing 88 breeds distributed across the Old World. Phylogeographic analysis revealed three highly divergent goat lineages (estimated divergence >200,000 years ago), with one lineage occurring only in eastern and southern Asia. A remarkably similar pattern exists in cattle, sheep, and pigs. These results, combined with recent archaeological findings, suggest that goats and other farm animals have multiple maternal origins with a possible center of origin in Asia, as well as in the Fertile Crescent. The pattern of goat mtDNA diversity suggests that all three lineages have undergone population expansions, but that the expansion was relatively recent for two of the lineages (including the Asian lineage). Goat populations are surprisingly less genetically structured than cattle populations. In goats only ≈10% of the mtDNA variation is partitioned among continents. In cattle the amount is ≥50%. This weak structuring suggests extensive intercontinental transportation of goats and has intriguing implications about the importance of goats in historical human migrations and commerce.

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.

Rectification and signal averaging of weak electric fields by biological cells.

Oscillating electric fields can be rectified by proteins in cell membranes to give rise to a dc transport of a substance across the membrane or a net conversion of a substrate to a product. This provides a basis for signal averaging and may be important for understanding the effects of weak extremely low frequency (ELF) electric fields on cellular systems. We consider the limits imposed by thermal and "excess" biological noise on the magnitude and exposure duration of such electric field-induced membrane activity. Under certain circumstances, the excess noise leads to an increase in the signal-to-noise ratio in a manner similar to processes labeled "stochastic resonance." Numerical results indicate that it is difficult to reconcile biological effects with low field strengths.