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.

Filamentary microstructure and linear temperature dependence of normal state transport in optimized high temperature superconductors

A filamentary model of “metallic” conduction in layered high temperature superconductive cuprates explains the concurrence of normal state resistivities (Hall mobilities) linear in T (T−2) with optimized superconductivity. The model predicts the lowest temperature T0 for which linearity holds and it also predicts the maximum superconductive transition temperature Tc. The theory abandons the effective medium approximation that includes Fermi liquid as well as all other nonpercolative models in favor of countable smart basis states.

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.

DNA-protein binding assays from a single sea urchin egg: a high-sensitivity capillary electrophoresis method.

A capillary electrophoresis method has been developed to study DNA-protein complexes by mobility-shift assay. This method is at least 100 times more sensitive than conventional gel mobility-shift procedures. Key features of the technique include the use of a neutral coated capillary, a small amount of linear polymer in the separation medium, and use of covalently dye-labeled DNA probes that can be detected with a commercially available laser-induced fluorescence monitor. The capillary method provides quantitative data in runs requiring < 20 min, from which dissociation constants are readily determined. As a test case we studied interactions of a developmentally important sea urchin embryo transcription factor, SpP3A2. As little as 2-10 x 10(6) molecules of specific SpP3A2-oligonucleotide complex were reproducibly detected, using recombinant SpP3A2, crude nuclear extract, egg lysates, and even a single sea urchin egg lysed within the capillary column.