Asymptotics in the random assignment problem

Summary We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve on the known numerical bounds for the limit.Research supported by NSF Grant MCS90-01710     

Fragmentation during the formic acid/formaldehyde (eschweiler-clarke) methylation of polyamines

Eschweiler-Clarke methylations of both acyclic and cyclic polyamines can lead to methylation products of fragments of the original polyamine; thus 1,5,9,13-tetra-azatridecane yields 1,1,3,3-tetramethylpropanediamine exclusively and 1,5,9-triazacyclododecane gives 45% 1,5,9-trimethyl-1,5,9-triazacyclodecane and 45% 2,6,10-trimethyl-2,6,10-triazaundecane.     

A Maximum Entropy Approach for Collaborative Filtering

Collaborative filtering (CF) involves predicting the preferences of a user for a set of items given partial knowledge of the user's preferences for other items, while leveraging a database of profiles for other users. CF has applications e.g. in predicting Web sites a person will visit and in recommending products. Fundamentally, CF is a pattern recognition task, but a formidable one, often involving a huge feature space, a large data set, and many missing features. Even more daunting is the fact that a CF inference engine must be capable of predicting any (user-selected) items, given any available set of partial knowledge on the user's other preferences. In other words, the model must be designed to solve any of a huge (combinatoric) set of possible inference tasks. CF techniques include memory-based, classification-based, and statistical modelling approaches. Among these, modelling approaches scale best with large data sets and are the most adept at handling missing features. The disadvantage of these methods lies in the statistical assumptions (e.g. feature independence), which may be unjustified. To address this shortcoming we propose a new model-based CF method, based on the maximum entropy principle. For the MS Web application, the new method is demonstrated to outperform a number of CF approaches, including naive Bayes and latent variable (cluster) models, support vector machines (SVMs), and the (Pearson) correlation method.     

Nonequilibrium Statistical Mechanics and Entropy Production in a Classical Infinite System of Rotators

We analyze the dynamics of a simple but nontrivial classical Hamiltonian system of infinitely many coupled rotators. We assume that this infinite system is driven out of thermal equilibrium either because energy is injected by an external force (Case I), or because heat flows between two thermostats at different temperatures (Case II). We discuss several possible definitions of the entropy production associated with a finite or infinite region, or with a partition of the system into a finite number of pieces. We show that these definitions satisfy the expected bounds in terms of thermostat temperatures and energy flow.     

Catalytic partial oxidation of methane using RhSr- and Ni-substituted hexaaluminates

This paper reports the results of experimental and modeling efforts to characterize partial oxidation of methane to produce synthesis gas (H₂ and CO) using metal-substituted hexaaluminate catalysts in short-contact-time reactors. Hexaaluminate catalysts offer excellent high-temperature stability compared to the equivalent metal-based catalysts. The hexaaluminates are synthesized by a metal-exchange process using alumoxane precursors that enable a wide range of metal substitutions. Of all the combinations tested, RhSr-substituted hexaaluminates yielded the best performance. The catalysts are supported on alumina porous-foam structures, which are positioned within a tube furnace to control the operating temperature. Two-stage combinations of RhSr- and Ni-substituted hexaaluminates are shown to improve conversion activity and selectivity compared to a single-catalyst system.     

Radical Couplings as Key Steps for the Preparation of Derivatives of Nonactic Acid

Summary. Free radical couplings from furan, as cheap starting material, were studied in view of developing a rapid strategy en route to the synthesis of derivatives of nonactin. The chain containing the alcohol function was introduced in one or two steps in 86% yield. For the introduction of the second chain with the ester function two different coupling methods were tested. Starting from the advanced intermediates obtained nonactin derivatives can be prepared by catalytic hydrogenation of the furan ring.