Optimality principles and uniqueness for Bellman equations of unbounded control problems with discontinuous running cost

We study viscosity solutions of Hamilton-Jacobi equations that arise in optimal control problems with unbounded controls and discontinuous Lagrangian. In our assumptions, the comparison principle will not hold, in general. We prove optimality principles that extend the scope of the results of [23] under very general assumptions, allowing unbounded controls. In particular, our results apply to calculus of variations problems under Tonelli type coercivity conditions. Optimality principles can be applied to obtain necessary and sufficient conditions for uniqueness in boundary value problems, and to characterize minimal and maximal solutions when uniqueness fails. We give examples of applications of our results in this direction.     

Lyapunov Functions for Infinite-Dimensional Systems

We study Lyapunov functions for infinite-dimensional dynamical systems governed by general maximal monotone operators. We obtain a characterization of Lyapunov pairs by means of the associated Hamilton-Jacobi partial differential equations, whose solutions are meant in the viscosity sense, as evolved in works of Tataru and Crandall-Lions. Our approach also leads to a new sufficient condition for Lyapunov pairs, generalizing a classical result of Pazy.     

An Iterative Variant of the Degenerate Kernel Method for Solving Fredholm Integral Equations

An iterative variant of the classical degenerate kernel method for solving Fredholm integral equations of the second kind is presented and its convergence properties are studied.     

Rate determining factors in protein model structures

Previous research has shown a strong correlation of protein folding rates to the native state geometry, yet a complete explanation for this dependence is still lacking. Here we study the rate-geometry relationship with a simple statistical physics model, and focus on two classes of model geometries, representing ideal parallel and antiparallel structures. We find that the logarithm of the rate shows an almost perfect linear correlation with the "absolute contact order", but the slope depends on the particular class considered. We discuss these findings in the light of experimental results.     

Determination of organic acids in urine by solid-phase microextraction and gas chromatography-ion trap tandem mass spectrometry previous 'in sample' derivatization with trimethyloxonium tetrafluoroborate

A method for the determination of the organic acids directly in the urine employing derivatization with trimethyloxonium tetrafluoroborate as a methylating agent and sequential extraction by head space and direct immersion/solid phase microextraction is reported. Furoic acid, hippuric acid, methylhippuric acid, mandelic acid, phenylglyoxylic acid and trans, trans muconic acid contained in urine and proposed by the American Conference of Governmental Industrial Hygienists as biological exposure indices were determined after a fast and economically convenient preparation step and sensitive gas chromatography-ion trap-mass spectrometry/tandem mass spectrometry analysis. Urine is rather a complex sample and hence the acquisition method required specific GC-MS instrumentation capable of supporting the changeover, fully automated during a single chromatographic separation, from mass to tandem mass spectrometry and both chemical and electron ionization modes. The automation of the analytical method provides a number of advantages, including reduced analysis time for both routine analysis and method development, and greater reproducibility. The equilibrium and kinetics of this substances vs head space/direct immersion-solid phase microextraction were investigated and evaluated theoretically.     

Asymptotic behavior of the number of distinct values in a sample from the geometric stick-breaking process

Discrete random probability measures are a key ingredient of Bayesian nonparametric inference. A sample generates ties with positive probability and a fundamental object of both theoretical and applied interest is the corresponding number of distinct values. The growth rate can be determined from the rate of decay of the small frequencies implying that, when the decreasingly ordered frequencies admit a tractable form, the asymptotics of the number of distinct values can be conveniently assessed. We focus on the geometric stick-breaking process and we investigate the effect of the distribution for the success probability on the asymptotic behavior of the number of distinct values. A whole range of logarithmic behaviors are obtained by appropriately tuning the prior. A two-term expansion is also derived and illustrated in a comparison with a larger family of discrete random probability measures having an additional parameter given by the scale of the negative binomial distribution.

     

ACCDB: A collection of chemistry databases for broad computational purposes

The importance of databases of reliable and accurate data in chemistry has substantially increased in the past two decades. Their main usage is to parametrize electronic structure theory methods, and to assess their capabilities and accuracy for a broad set of chemical problems. The collection we present here—ACCDB—includes data from 16 different research groups, for a total of 44,931 unique reference data points, all at a level of theory significantly higher than density functional theory, and covering most of the periodic table. It is composed of five databases taken from literature (GMTKN, MGCDB84, Minnesota2015, DP284, and W4-17), two newly developed reaction energy databases (W4-17-RE and MN-RE), and a new collection of databases containing transition metals. A set of expandable software tools for its manipulation is also presented here for the first time, as well as a case study where ACCDB is used for benchmarking commercial CPUs for chemistry calculations. © 2018 Wiley Periodicals, Inc.