Energy Dispersive X-Ray Spectrometry by Microcalorimetry for the SEM

 Analytical X-ray spectrometry for electron beam instruments has advanced significantly with the development of the microcalorimeter energy dispersive X-ray spectrometer (μcal EDS). The μcal EDS operates by measuring the temperature rise when a single photon is absorbed in a metal target. A cryoelectronic circuit with electrothermal feedback and a superconducting transition edge sensor serves as the thermometer. Spectral resolution approaching 4.5 eV for high energy photons (6000 eV) and 2 eV for low energy photons below 2000 eV has been demonstrated in energy dispersive operation across a photon energy range from 250 eV to 8 keV. Spectra of a variety of materials demonstrate the power of the μcal EDS to solve practical problems while operating on a scanning electron microscope platform.     

On Teichmüller’s theorem on the quasi-invariance of cross ratios

Teichmüller’s theorem gives necessary and sufficient conditions for mapping one ordered quadruple by aK-quasiconformal map onto a second ordered quadruple. We give a simple non-computational proof of the necessity part. We then characterize such extremal mappings, and obtain as a consequence a new formula for the modular function, with leads to a very simple derivation of the known expression for the Poincaré metric on the thrice-punctured sphere. Research partially supported by NSF grant MCS 76-04969A01.     

On the use of loss functions in the changepoint problem

Summary We consider a sequence of independent random variables whose densities depend on a parameter which is subject to a change at an unknown time point. A Bayesian decision-theoretic approach is used to obtain an optimal choice of changepoint. The exponential and multivariate normal models are analyzed, and some numerical examples are given.     

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.