Sensitivity analysis and model optimization for reaction-diffusion systems

This paper presents a computational framework for the optimization and sensitivity analysis of a process whose state depends upon several parameter functions. Assuming that the process is described by a system of quasilinear, parabolic, partial differential equations, we show how determining the problem parameters so as to improve an associated objective functional is directly related to knowing the state function sensitivities. An expression for the gradient of the objective functional in terms of the solutions of an adjoint system enables one to bypass the calculation of state function sensitivities. These concepts are illustrated for a simple model of cooperative processes in chemical kinetics. Since sensitivity analysis and model optimization are important tools for investigating parameter dependence and validating mathematical models, research developments in such diverse fields as optimal design theory, chemical kinetics, and parameter identification are important motivations for this paper.This author would like to gratefully acknowledge Dr. M. Delle Donne, EGG, for several helpful discussions.This author was partially supported by NSF Grant No. CMS-80-05677.     

Orientational sampling and rigid-body minimization in molecular docking revisited: On-the-fly optimization and degeneracy removal

Summary Strategies for computational association of molecular components entail a compromise between configurational exploration and accurate evaluation. Following the work of Meng et al. [Proteins, 17 (1993) 266], we investigate issues related to sampling and optimization in molecular docking within the context of the DOCK program. An extensive analysis of diverse sampling conditions for six receptor-ligand complexes has enabled us to evaluate the tractability and utility of on-the-fly force-field score minimization, as well as the method for configurational exploration. We find that the sampling scheme in DOCK is extremely robust in its ability to produce configurations near to those experimentally observed. Furthermore, despite the heavy resource demands of refinement, the incorporation of a rigid-body, grid-based simplex minimizer directly into the docking process results in a docking strategy that is more efficient at retrieving experimentally observed configurations than docking in the absence of optimization. We investigate the capacity for further performance enhancement by implementing a degeneracy checking protocol aimed at circumventing redundant optimizations of geometrically similar orientations. Finally, we present methods that assist in the selection of sampling levels appropriate to desired result quality and available computational resources.     

Transient absorption from the relaxed excited state of the F center in KF

The infrared absorption spectrum from the relaxed excited state of the F center reported for KF is found to be qualitatively similar to that for the other potassium halides and lies at energies which suggest a 2s-2p transition, as predicted by Ham and Grevsmühl.     

Stochastic theory of nonlinear rate processes with multiple stationary states

A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of $\text{O}$(N⁰) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is $\text{O}$(e^N). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.     

S-wave ππ scattering from the reaction π+p → π+pπ0π0 at 3.5 GeV/c

We have studied the 2π⁰ system produced in the reaction π⁺p → π⁺pπ⁰π⁰ at 3.5 GeV/c, using the heavy-liquid bubble chamber technique. The cross section of the reaction π⁺π^? → π⁰π⁰ saturates the S-wave unitarity limit around 750 MeV/c² and near threshold is indicative of an I=0 S-wave scaterring length larger than expected.     

Functors whose domain is a category of morphisms

Summary Connected sequences of functors whose domain, is the category of morphisms of an arbitrary abelian categoryA and whose range categoryB is also abelian are compared with the composition functors of Eckmann and Hilton acting between the same categories Sequences of functors of both types are obtained from any half-exact functorA→B ifA has enough injectives and projectives. This revised version was published online in November 2006 with corrections to the Cover Date.     

Finite dimensional approximation in infinite dimensional mathematical programming

We consider the problem of approximating an optimal solution to a separable, doubly infinite mathematical program (P) with lower staircase structure by solutions to the programs (P(N)) obtained by truncating after the firstN variables andN constraints of (P). Viewing the surplus vector variable associated with theNth constraint as a state, and assuming that all feasible states are eventually reachable from any feasible state, we show that the efficient set of all solutions optimal to all possible feasible surplus states for (P(N)) converges to the set of optimal solutions to (P). A tie-breaking algorithm which selects a nearest-point efficient solution for (P(N)) is shown (for convex programs) to converge to an optimal solution to (P). A stopping rule is provided for discovering a value ofN sufficiently large to guarantee any prespecified level of accuracy. The theory is illustrated by an application to production planning.The work of Robert L. Smith was partially supported by the National Science Foundation under Grant ECS-8700836.     

Capacitive Discharge Graphite Furnace Laser-Excited Atomic Fluorescence of Thallium

For the first time, an anisotropic graphite furnace heated by capacitive discharge was used for laser-excited atomic fluorescence spectrometry. A detection limit of 5 fg for thallium was obtained with a laser repetition rate of 500 Hz and a peak integration time of 80 ms. The use of a capacitive discharge furnace allows for a shorter integration time, which in turn should allow for integration of less background noise, and improved detection limits. Theoretically, the magnitude of the shot noise should be proportional to the square root of the integration time, and inversely proportional to the square root of the laser repetition rate. Experimental data illustrated the effect of laser repetition rate, but were inconclusive with respect to integration time. The linear dynamic range of the calibration curve was six orders of magnitude, which was comparable to that normally obtained for laser-excited atomic fluorescence in modern commercial graphite furnaces. Thallium was accurately determined in NIST biological samples at levels one to two orders of magnitude below the detection limit of electrothermal atomic absorption spectrometry, with an analytical precision between 8 and 20%. The interference effects of calcium, sodium chloride, and potassium chloride on the thallium signal were investigated and shown to be similar to both laser-excited atomic fluorescence in a conventional furnace and capacitive discharge furnace atomic absorption results reported in the literature.     

Chemical shift nonequivalence of sulfinates: Structural,solvent and temperature effects

The structural, solvent and temperature effects on the PMR spectra of several alkyl alkanesulfinates and arenesulfinates are discussed. A low order intrinsic nonequivalence was observed in substituents alpha to the sulfinate sulfur atom, the nonequivalence being significantly less than in sulfoxides, and solvent and temperature dependent. Nonequivalence of diastereotopic substituents on the ester oxygen exceeded nonequivalence in similar sulfoxides and is largely insensitive to temperatures from 25° to 120°C. Benzene complexes with sulfinates greatly enhancing the proton nonequivalence of alpha substituents apparently by causing a further shielding of the already more shielded nonequivalent protons.     

On new kinds of Teichmüller spaces

We introduce a Teichmüller space for a Riemann surface withn distinguished points. Ifn=0 this is the ordinary Teichmüller space. Forn=1, in special cases, it represents the Teichmüller curve and the universal covering space of the Teichmüller curve. The corresponding modular groups and Riemann spaces are investigated. Some purely topological applications on homotopy of self-maps of surfaces are obtained. Research partially supported by NSF Grant GP-19572. The author is currently a Guggenheim Memorial Fellow.