Minimum energy configurations on a toric lattice as a quadratic assignment problem

We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex quadratic programming (CQP), and a semidefinite programming (SDP) bound. Since the last two bounds were not compared directly before, we prove that the SDP bound is stronger than the CQP bound. We then apply these to improve known bounds on a discrete energy minimization problem, reformulated as a QAP, which aims to minimize the potential energy between repulsive particles on a toric grid. Thus we are able to prove optimality for several configurations of particles and grid sizes, complementing earlier results by Bouman et al. (2013). The semidefinite programs in question are too large to solve without pre-processing, and we use a symmetry reduction method by Permenter and Parrilo (2020) to make computation of the SDP bounds possible.     

Massively time-parallel,approximate simulation of loss queueing systems

A time-parallel simulation obtains parallelism by partitioning the time domain of the simulation. An approximate time-parallel simulation algorithm named GG1K is developed for acyclic networks of loss FCFSG/G/1/K queues. The GG1K algorithm requires two phases. In the first phase, a similar system (i.e. aG/G/1/ queue) is simulated using the GLM algorithm. Then the resultant trajectory is transformed into an approximateG/G/1/K trajectory in the second phase. The closeness of the approximation is investigated theoretically and experimentally. Our results show that the approximation is highly accurate except whenK is very small (e.g. 5) in certain models. The algorithm exploits unbounded parallelism and can achieve near-linear speedup when the number of arrivals simulated is sufficiently large.     

Spectrally determined growth is generic

Let be the infinitesimal generator of a -semigroup of operators in a Hilbert space. We consider the class of operators , where is bounded. It is proved that the spectrum of determines the growth of the associated semigroup for ``most" operators (in the sense of Baire category).

     

A characterization of discrete unimodality with applications to variance upper bounds

Bertin and Theodorescu (1984,Statist. Probab. Lett.,2, 23–30) developed a characterization of discrete unimodality based on convexity properties of a discretization of distribution functions. We offer a new characterization of discrete unimodality based on convexity properties of a piecewise linear extension of distribution functions. This reliance on functional convexity, as in Khintchine's classic definition, leads to variance dilations and upper bounds on variance for a large class of discrete unimodal distributions. These bounds are compared to existing inequalities due to Muilwijk (1966,Sankhy, Ser. B,28, p. 183), Moors and Muilwijk (1971,Sankhy, Ser. B,33, 385–388), and Rayner (1975,Sankhy, Ser. B,37, 135–138), and are found to be generally tighter, thus illustrating the power of unimodality assumptions.     

Solvent effects on 17O nuclear magnetic shielding: N-methylformamide in polar and apolar solutions

The solvent effect on ¹⁷O isotropic shielding was computed by different methods: the polarizable continuum model and a mixed approach, including a few real solvent molecules treated as the solute. The experimental data show that the behavior of protic and aprotic solvents is markedly different: we found that the continuum approach describes well the observed shielding at various dielectric constants for aprotic solvents, while the mixed procedure is needed when hydrogen bonds to the magnetic centre are present.Contribution to the Jacopo Tomasi Honorary Issue     

Analyzing functional similarity of protein sequences with discrete wavelet transform

This paper applies discrete wavelet transform (DWT) with various protein substitution models to find functional similarity of proteins with low identity. A new metric, 'S' function, based on the DWT is proposed to measure the pair-wise similarity. We also develop a segmentation technique, combined with DWT, to handle long protein sequences. The results are compared with those using the pair-wise alignment and PSI-BLAST.     

Discrete Fourier Transform Analysis of Chronoamperometric Currents Obtained Under Ultrasound

A discrete Fourier transform (DFT) technique was used to analyze chronoamperometric currents at a Pt microdisk electrode (Ø=15 μm) in an electrolyte containing [Fe(CN)₆]^3?/[Fe(CN)₆]^4? under ultrasound at a frequency of 26.3 kHz and the powers of 0–50 W. The currents were measured by a high‐speed data acquisition card. Considering the effects of acoustic vibrations and cavitations on the limiting currents, a microdisk electrode and a high frequency sampling (10 MHz) were used to collect the current signals to restrain the deviation of average from sampling period in other methods. The results show that the amplitudes at 0 Hz and 26.3 kHz are related to the decay of ultrasound at constant power output when the separation between sono‐horn and electrode increases, and also related to the reactant concentration at the same ultrasonic conditions. The frequency signals are always shown in frequency spectrum despite different ultrasonic conditions. The amplitudes reflect the intensity of ultrasound and the concentration of reactant in solution, so they can be called specific frequencies. This method can be used to analyze quantitatively the effects of ultrasound on electrochemical reaction, determine the reactant concentration and measure the distribution of ultrasonic intensity in a solution.     

Statistical mechanics of a dynamical system based on Conway's game of Life

We study a discrete dynamical system whose evolution is governed by rules similar to those of Conway's game of Life but also include a stochastic element (parametrized by a temperature). Statistical properties that are examined are density as a function of temperature and entropy (suitably defined). A phase transition and a certain thermodynamic constant of the motion are observed.Lady Davis Visiting Scientist at the Technion 1974–75.     

Computer-assisted choice of discrete spacers for anionic isotachophoresis separations

In isotachophoresis (ITP), the sample constituents migrate, depending on their concentrations in the loaded sample, either in fully developed zones or in the boundary layers between the zones of constituents of the corresponding effective mobilities. The latter (spike) migration mode is analytically beneficial in selective detections of trace analytes, especially, when appropriately chosen discrete spacers minimize detection interferences due to matrix constituents. To facilitate a search for suitable mixtures of discrete spacers, a two-step calculation procedure was developed in this work. Using a pool of discrete spacers consisting of 42 anionic and zwitterionic constituents, this procedure was shown effective in the anionic ITP separations performed at pH = 6.5-10.0. Besides the predictions of the migration orders, it was helpful in identifying the spacing constituents that could cause resolution problems due to an uncertainty with which pH of the leading electrolyte solution is known. The ionic mobility and pKa data, taken for the spacing constituents from the literature and the ones obtained from the ITP experiments carried out in this work, were used in the calculations performed in a context with the choice of spacers. Although the data obtained from the ITP experiments provided better results, small uncertainties with which they were acquired (attributable to fluctuations in the experimental conditions) set practical limits in the calculation based choice of multi-component mixtures of the spacing constituents.     

Value function and optimality conditions for semilinear control problems

This paper is concerned with optimal control problems of Mayer and Bolza type for systems governed by a semilinear state equationx(t)=Ax(t) + f(t, x(t), u(t)), u(t) U, whereA is the infinitesimal generator of a strongly continuous semigroup in a Banach spaceX. We prove necessary and sufficient conditions for optimality and then use these conditions to investigate properties of the value function related to superdifferentials. Conversely, we use the value function to obtain criteria for optimality and feedback systems.Work (partially) supported by the Research Project Equazioni di evoluzione e applicazioni fisicomatematiche (M.U.R.S.T.-Italy).