A generalized Pólya's urn with graph based interactions

Given a finite connected graph G, place a bin at each vertex. Two bins are called a pair if they share an edge of G. At discrete times, a ball is added to each pair of bins. In a pair of bins, one of the bins gets the ball with probability proportional to its current number of balls raised by some fixed power . We characterize the limiting behavior of the proportion of balls in the bins. The proof uses a dynamical approach to relate the proportion of balls to a vector field. Our main result is that the limit set of the proportion of balls is contained in the equilibria set of the vector field. We also prove that if then there is a single point with non‐zero entries such that the proportion converges to v almost surely. A special case is when G is regular and . We show e.g. that if G is non‐bipartite then the proportion of balls in the bins converges to the uniform measure almost surely.Copyright © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,614–634, 2015     

Temperature-programmed ESDIAD/TOF system as a new technique for characterization of adsorbed molecules and reaction intermediates

A temperature-programmed (TP-) electron stimulated desorption ion angular distribution (ESDIAD)/time-of-flight (TOF) system was developed to monitor changes in adsorbed layers in real time. This system can measure ESDIAD images and TOF spectra of desorbing ions stimulated by pulsed electron beam in temperature programmed surface processes. The coadsorption layers of CO and ammonia, the coadsorption layers of CO and methylamine, and the coadsorption layer of CO and acetylene on Ru(001), which were previously studied by our group using LEED, TPD and HREELS, have been observed by this system. The change in configuration of admolecules, the change in site occupation and the thermal evolution of adspecies can be monitored.     

Noise sensitivity of Boolean functions and applications to percolation

It is shown that a large class of events in a product probability space are highly sensitive to noise, in the sense that with high probability, the configuration with an arbitrary small percent of random errors gives almost no prediction whether the event occurs. On the other hand, weighted majority functions are shown to be noise-stable. Several necessary and sufficient conditions for noise sensitivity and stability are given. Consider, for example, bond percolation on ann+1 byn grid. A configuration is a function that assigns to every edge the value 0 or 1. Let ω be a random configuration, selected according to the uniform measure. A crossing is a path that joins the left and right sides of the rectangle, and consists entirely of edges ℓ with ω(ℓ)=1. By duality, the probability for having a crossing is 1/2. Fix an ɛ ∈ (0, 1). For each edge ℓ, let ω′(ℓ)=ω(ℓ) with probability 1 − ɛ, and ω′(ℓ)=1 − ω(ℓ) with probability ɛ, independently of the other edges. Letp(τ) be the probability for having a crossing in ω, conditioned on ω′ = τ. Then for alln sufficiently large,P{τ : |p(τ) − 1/2| > ɛ}<ɛ.     

Tumor promoters exist in two conformational states in solution. st]Stereochemistry of (3)-indolactam-V.

¹H-Nmr study and force field calculation of conformational Isomerism in (±)-indolactam-V which is a biologically active fragment of tumor promoter, teleocidin B, are described.     

Three tree-paths

Itai and Rodeh [3] have proved that for any 2-connected graph G and any vertex s ∈ G there are two spanning trees such that the paths from any other vertex to s on the trees are disjoint. In this paper the result is generalized to 3-connected graphs.     

A comparison of the on-top dissociation of H2 on Ni(100) and Cu(100)

The on-top dissociations of H₂ on Ni(100) and Cu(100) are studied using a cluster approach. Correlation effects are accounted for through the use of CASSCF and CCI methods. The central metal atom is treated with all its electrons whereas the other cluster atoms are described by recently developed one electron ECP's. A molecular chemisorbed H₂ state on nickel, similar to that recently observed experimentally, was identified in the cluster calculations and also for the triatomic NiH₂. No such state was found on copper. The large differences found for the on top dissociation of H₂ on nickel and copper are attributed solely to the difference in 3d orbital occupation. The parallel between the on top dissociation reaction on the cluster and the dissociation on a single atom is also studied. While the neutral triatomic NiH₂ represents a qualitatively correct model in the nickel case, the negatively charged CuH ₂ ^– is required as a model in the copper case.     

Automatic superposition of drug molecules based on their common receptor site

Summary We have prevously developed a new rational method for superposing molecules in terms of submolecular physical and chemical properties, but not in terms of atom positions or chemical structures as has been done in the conventional methods. The program was originally developed for interactive use on a three-dimensional graphic display, providing goodness-of-fit indices on molecular shape, hydrogen bonds, electrostatic interactions and others.Here, we report a new unbiased searching method for the best superposition of molecules, covering all the superposing modes and conformational freedom, as an additional function of the program. The function is based on a novel least-squares method which superposes the expected positions and orientations of hydrogen bonding partners in the receptor that are deduced from both molecules. The method not only gives reliability and reproducibility to the result of the superposition, but also allows us to save labor and time. It is demonstrated that this method is very efficient for finding the correct superposing mode in such systems where hydrogen bonds play important roles.     

Effective dynamic correlation in multiconfigurational wave-function calculations on atoms and molecules

An intuitive understanding of dynamic correlation in terms of a regularized electron repulsion expression is outlined. Expressions for cusp kinetic energy corrected regularized electron repulsion integrals are deduced and implemented in a multiconfigurational wave-function framework. A regularized complete active space self-consistent field (reg-CASSCF) technique is suggested and tested on atomic total energies, molecular structures and binding energies. Received: 26 November 1996 / Accepted: 21 April 1997