Stochastic Enumeration Method for Counting NP-Hard Problems

We present a new generic sequential importance sampling algorithm, called stochastic enumeration (SE) for counting #P-complete problems, such as the number of satisfiability assignments and the number of perfect matchings (permanent). We show that SE presents a natural generalization of the classic one-step-look-ahead algorithm in the sense that it: Runs in parallel multiple trajectories instead of a single one; Employs a polynomial time decision making oracle, which can be viewed as an n-step-look-ahead algorithm, where n is the size of the problem. Our simulation studies indicate good performance of SE as compared with the well-known splitting and SampleSearch methods.     

Reducing hypothalamic AGRP by RNA interference increases metabolic rate and decreases body weight without influencing food intake

Background  

Several lines of evidence strongly suggest that agouti-related peptide (AGRP) plays a key role in the regulation of metabolic function but ablation of the AGRP gene has no apparent effect on metabolic function. Since specific pharmacological antagonists of AGRP do not presently exist, we assessed if reduction of hypothalamic AGRP mRNA by RNA interference (RNAI) would influence metabolic function, an outcome suggesting that pharmacological antagonists might constitute useful reagents to treat obesity.     

Velocities, Stresses and Vector Bundle Valued Chains

A mathematical framework for the fundamental objects of continuum mechanics is presented. In the geometric setting of general differentiable manifolds, velocity fields over bodies, modeled as sections of a vector bundle W, are generalized using notions of homological integration theory such as flat chains and cochains. The class of bodies includes fractal sets whose irregular boundaries may have infinite measures. Stresses, initially modeled as smooth differential forms valued in the dual of the jet bundle of W, are generalized to cochains represented by L ^??-sections whose weak divergences are also L ^??. The divergence of a stress field, defined in an earlier work, is generalized to apply to stress cochains. The co-divergence of a velocity field is a weak form of the jet extension mapping and it is the counterpart of the boundary operator for real valued flat chains.     

Exploiting locality: approximating sorting buffers

The sorting buffers problem is motivated by many applications in manufacturing processes and computer science, among them car-painting and file servers architecture. The input is a sequence of items of various types. All the items must be processed, one by one, by a service station. We are given a random-access sorting buffer with a limited capacity. Whenever a new item arrives it may be moved directly to the service station or stored in the buffer. Also, at any time items can be removed from the buffer and assigned to the service station. Our goal is to give the service station a sequence of items with minimum type transitions. We generalize the problem to allow items with different sizes and type transitions with different costs. We give a polynomial-time 9-approximation algorithm for the maximization variant of this problem, which improves the best previously known 20-approximation algorithm.     

Fluorescence Polarization as a Functional Parameter in Monitoring Living Cells: Theory and Practice

The use of fluorescence polarization as a functional parameter in monitoring cellular activation calls for the reliable and accurate measurement of the fluorescence intensity and polarization (FI and FP) of microscopic objects. The relevant experimental parameters that enter such measurements are thoroughly discussed. The possibility of executing FP measurements properly by flow-through systems is compared with that of static cytometry. Remarks on the effects of high-power excitation on markers and cells conclude the paper.     

Generalized Grunsky coefficients and inequalities

The generalized Grunsky coefficients are defined in this paper for all locally univalent meromorphic functions in any domain in the complete complex plane. Various explicit formulas for these coefficients are established. Necessary conditions for univalence are obtained in arbitrary domains and in the unit disc in particular. The first one generalizes Grunsky inequalities and the second one is an extension of the Nehari-Schwarzian derivative condition.     

Hyperbolic metric,curvature of geodesics and hyperbolic discs in hyperbolic plane domains

The purpose of this paper is to investigate the relations among some geometric quantities defined for every hyperbolic plane domain of any connectivity, each of which measures, in some sense, how much the domain deviates either from a disc, convex domain, or simply connected domain on one hand, or a punctured domain on the other hand. Supported by the Landau Center for Mathematical Research in Analysis.     

Molecular-orbital realizations of the bent-bond model: Spiranic derivatives of cyclobutanone

In the frame of our studies on small-ring compounds, we deal here with structures in which a three-membered ring and a carbonylated four-membered ring are fixed in close proximity. The theoretical approach is through an allvalence electron semiempirical method. The experimental background, based on results of other workers, comprises mainly UV and IR spectral data. The main topics to be discussed are: charge-donation and charge-transfer from the 3-ring, hypsochromic and bathochromic shifts of electronic transitions related to the carbonyl, direct substituent effects on the carbonyl stretching frequency, and the across-ring interaction in cyclobutanone.Part XII in series. For previous papers, see Refs. [1, 2].