Photoionization dynamics of glycine adsorbed on a silicon cluster: "on-the-fly" simulations

Dynamics of glycine chemisorbed on the surface of a silicon cluster is studied for a process that involves single-photon ionization, followed by recombination with the electron after a selected time delay. The process is studied by "on-the-fly" molecular dynamics simulations, using the semiempirical parametric method number 3 (PM3) potential energy surface. The system is taken to be in the ground state prior to photoionization, and time delays from 5 to 50 fs before the recombination are considered. The time evolution is computed over 10 ps. The main findings are (1) the positive charge after ionization is initially mostly distributed on the silicon cluster. (2) After ionization the major structural changes are on the silicon cluster. These include Si-Si bond breaking and formation and hydrogen transfer between different silicon atoms. (3) The transient ionization event gives rise to dynamical behavior that depends sensitively on the ion state lifetime. Subsequent to 45 fs evolution in the charged state, the glycine molecule starts to rotate on the silicon cluster. Implications of the results to various processes that are induced by transient transition to a charged state are discussed. These include inelastic tunneling in molecular devices, photochemistry on conducting surfaces, and electron-molecule scattering.     

The primes contain arbitrarily long polynomial progressions

We establish the existence of infinitely many polynomial progressions in the primes; more precisely, given any integer-valued polynomials P ₁, …, P _k  ∈ Z[m] in one unknown m with P ₁(0) = … = P _k (0) = 0, and given any ε > 0, we show that there are infinitely many integers x and m, with 1 \leqslant m \leqslant x^e1 \leqslant m \leqslant x^\varepsilon, such that x + P ₁(m), …, x + P _k (m) are simultaneously prime. The arguments are based on those in [18], which treated the linear case P _j  = (j − 1)m and ε = 1; the main new features are a localization of the shift parameters (and the attendant Gowers norm objects) to both coarse and fine scales, the use of PET induction to linearize the polynomial averaging, and some elementary estimates for the number of points over finite fields in certain algebraic varieties.     

Statistical quality control for ternary ordinal quality data

The paper considers various aspects of statistical quality control by means of sample data received on a ternary ordinal scale. A new method for evaluating quality level and dispersion, free of any latent numerical scale assumptions, is proposed. The emphasis is on working with large samples, which enable the statistical analysis, estimation and control by the use of approximate analytical expressions of these measures to be considerably simplified. Two complementary studies demonstrate the usage of the proposed approach. Copyright © 2010 John Wiley & Sons, Ltd.     

Categorical (binary) difference terms and protomodularity

In this paper we obtain an intrinsic syntactical characterization of protomodularity, via so-called categorical difference terms, similar to the one known in the case of varieties involving binary terms d satisfying d(x, x) = d(y, y). We also show that purely categorical modifications of the condition in the characterization give characterizations of Mal’tsev and additive categories, thus revealing a new conceptual link between these three classes of categories, and hence, also between the corresponding classes of varieties.     

Facets of Descent III: Monadic Descent for Rings and Algebras

We develop an elementary approach to the classical descent problems for modules and algebras, and their generalizations, based on the theory of monads.     

Guidelines for choosing molecular "alligator clip" binding motifs in electron transport devices

We employ a one-electron, tight-binding model of an electrode-molecule-electrode junction to explore the fundamental relationship between adsorption geometry and electron transport, producing exact results (within this model). By varying the chemisorption location (e.g., atop a surface atom or in a hollow site between surface atoms) and the molecule-electrode coupling, we find that the largest currents are realized when the molecule (i) is highly coordinated by the surface and (ii) has favorable overlap with electrode states near the Fermi level. We also show the importance of electrode-induced molecular level shifting for certain adsorption geometries, which can cause molecular levels far from the Fermi level to conduct better than those near the Fermi level. Since all of these factors are greatly influenced by the chemical moiety used to link the molecule to an electrode, these results present a set of guidelines to help choose "alligator clips" for molecular electronic devices.     

Decidable (= separable) objects and morphisms in lextensive categories

After investigating all conceivable properties of decidable objects and maps in left exact categories with well-behaved finite sums (‘lextensive categories’), we give a characterization in such categories of decidable morphisms which are (finite) coverings (in an appropriate sense). Finally, we give two applications of this result, to separable algebras and to local homeomorphisms. In both cases it explains categorically the advantage of two well-known notions — strongly separable algebras and local homeomorphisms with path lifting property, respectively.     

Principal component analysis combined with truncated-Newton minimization for dimensionality reduction of chemical databases

 The similarity and diversity sampling problems are two challenging optimization tasks that arise in the analysis of chemical databases. As a first step to their solution, we propose an efficient projection/ refinement protocol based on the principal component analysis (PCA) and the truncated-Newton minimization method implemented by our package TNPACK (PCA/TNPACK). We show that PCA can provide the same initial guess as the singular value decomposition (SVD) for the optimization task of solving the distance-geometry optimization problem if each column of a database matrix has a mean of zero. Hence, our PCA/TNPACK approach is analogous to the SVD/TNPACK projection/refinement protocol that we developed recently for visualizing large chemical databases. Using PCA/TNPACK and the Merck MDDR database (MDL Drug Data Report), we further investigate the projection/refinement procedure with regards to the preservation of the original clusters of chemical compounds, the accuracy of similarity and diversity sampling of chemical compounds, and the potential application in the study of structure activity relationships. We also explore by simple experiments accuracy and efficiency aspects of the PCA/TNPACK procedure compared to those of a global optimization algorithm (simulated annealing, as implemented by the program package SIMANN) in terms of producing the projection mapping of a database. Numerical results show that the 2D PCA/TNPACK mapping can preserve the distance relationships of the original database and is thus valuable as a first step in similarity and diversity applications. Of course, the generation of a global rather than local minimizer and its interpretation in terms of pharameceutical applications remains a challenge. Since all numerical tests are performed on the Merck MDDR database, results are representative of realistic cases encountered in the field of drug design, and may help analyze properties of medicinal compounds. Received: December 21, 2000 / Accepted: August 19, 2002 Published online: September 27, 2002 Mathematics Subject Classification (2000): 65K10, 62H25, 92C50     

Cellular properties and population asymptotics in the population balance equation

Proliferating cell populations at steady-state growth often exhibit broad protein distributions with exponential tails. The sources of this variation and its universality are of much theoretical interest. Here we address the problem by asymptotic analysis of the population balance equation. We show that the steady-state distribution tail is determined by a combination of protein production and cell division and is insensitive to other model details. Under general conditions this tail is exponential with a dependence on parameters consistent with experiment. We discuss the conditions for this effect to be dominant over other sources of variation and the relation to experiments.     

Theory of three-dimensional alignment by intense laser pulses

We introduce a theoretical framework for study of three-dimensional alignment by moderately intense laser pulses and discuss it at an elementary level. Several features of formal interest are noted and clarified. Our approach is nonperturbative, treating the laser field within classical and the material system within quantum mechanics. The theory is implemented numerically using a basis set of rotational eigenstates, transforming the time-dependent Schrodinger equation to a set of coupled differential equations where all matrix elements are analytically soluble. The approach was applied over the past few years to explore different adiabatic and nonadiabatic three-dimensional alignment approaches in conjunction with experiments, but its formal details and numerical implementation were not reported in previous studies. Although we provide simple numerical examples to illustrate the content of the equations, our main goal is to complement previous reports through an introductory discussion of the underlying theory.