Archetypical Conductive Polymer Structure for Specific Interaction with Proteins

A series of 2,4-dinitrophenyl (DNP) functionalized polypyrrole terpolymers, capable of specific binding to IgE antibodies (proteins), have been synthesized using oxidizing initiator, ammonium persulfate and were characterized by ¹H-NMR, IR, DSC, Light Scattering etc. The terpolymers were composed of monomers and macromonomers: monomer (pyrrole), macromonomer A (pyrrole with pendant ethylene glycol) and macromonomer B (pyrrole with pendant DNP) with specific functionality of conductance, processiblity and binding, respectively. The terpolymers are found to be semiconductive, (5 × 10^?6 S cm^?1) by itself without the addition of doping agents. Molecular dynamics simulation of terpolymer shows that the DNP-(2,4-dinitrophenyl) functional group extends out from the polymer backbone and thus, is available for binding. The DNP functional groups on the terpolymer achieve steady state binding with anti-DNP IgE proteins at nanomolar concentrations in solution. The terpolymer was blended with sulfonated polystyrene and processed in fibers which exhibited effective specific binding to fluorescently tagged IgE proteins and therefore, possessed the potential to be an active component in biosensor.     

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.     

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.     

Error analysis for regenerative queueing estimators with special reference to gradient estimators via likelihood ratio

The performance of telecommunications systems is typically estimated (either analytically or by simulation) via queueing theoretic models. The gradient of the expected performance with respect to the various parameters (such as arrival rate or service rate) is very important as it not only measures the sensitivity to change, but is also needed for the solution of optimization problems. While the estimator for the expected performance is the sample mean of the simulation experiment, there are several possibilities for the estimator of the gradient. They include the obvious finite difference approximation, but also other recently advocated techniques, such as estimators derived from likelihood ratio transformations or from infinitesimal perturbations. A major problem in deciding upon which estimator to use and in planning the length of the simulation has been the scarcity of analytical error calculations for estimators of queueing models. It is this question that we answer in this paper for the waiting time moments (of arbitrary order) of theM / G / 1 queue by using the queueing analysis technique developed by Shalmon. We present formulas for the error variance of the estimators of expectation and of its gradient as a function of the simulation length; at arbitrary traffic intensity the formulas are recursive, while the heavy traffic approximations are explicit and of very simple form. For the gradient of the mean waiting time with respect to the arrival (or service) rate, and at 1 percent relative precision, the heavy traffic formulas show that the likelihood ratio estimator for the gradient reduces the length of the simulation required by the finite difference estimator by about one order of magnitude; further increasing the relative precision by a factor increases the reduction advantage by the same factor. At any relative precision, it exceeds the length of the simulation required for the estimation of the mean with the same relative precision by about one order of magnitude. While strictly true for theM / G / 1 queue, the formulas can also be used as guidelines in the planning of queueing simulations and of stochastic optimizations of complex queueing systems, particularly those with Poisson arivals.     

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.