Neighborhood radius estimation for variable-neighborhood random fields

We consider random fields defined by finite-region conditional probabilities depending on a neighborhood of the region which changes with the boundary conditions. To predict the symbols within any finite region, it is necessary to inspect a random number of neighborhood symbols which might change according to the value of them. In analogy with the one-dimensional setting we call these neighborhood symbols the context associated to the region at hand. This framework is a natural extension, to d-dimensional fields, of the notion of variable length Markov chains introduced by Rissanen [24] in his classical paper. We define an algorithm to estimate the radius of the smallest ball containing the context based on a realization of the field. We prove the consistency of this estimator. Our proofs are constructive and yield explicit upper bounds for the probability of wrong estimation of the radius of the context.     

Atomistic details of precipitates in lean Al–Mg–Si alloys with trace additions of Ag and Ge studied by HAADF-STEM and DFT

Abstract

Bonding energies and volume misfits for alloying elements and vacancies in multicomponent Al–Mg–Si alloys have been calculated using density functional theory (DFT). A detailed atomic scale analysis has been done for characteristic precipitate structures, using high-angle annular dark-field scanning transmission electron microscopy. Two new stacking configurations of the important strengthening phase β′′ were discovered in the Ge-added alloy. All three stacking variations were found to be energetically favourable to form from DFT calculations. The second stacking configuration, β₂′′, contains vacated columns in its unit cell, consequently requiring less solute to create the same volume fraction of precipitate needles. DFT suggests a lower formation enthalpy per atom for β₂′′ when Si is exchanged with Ge. In the alloy containing Ag additions, a new Q’/C-like local configuration containing Ag instead of Cu was discovered, also this phase was deemed energetically favourable from DFT.     

Multiple periodic solutions in impulsive hybrid neural networks with delays

The existence of multiple periodic solutions and their exponential stability are investigated for impulsive hybrid Hopfield-type neural networks with both time-dependent and distributed delays, using the Leray-Schauder fixed point theorem and Lyapunov functionals. The criteria given are easily verifiable, possess many adjustable parameters, and depend on impulses, providing flexibility for the analysis and design of delayed neural networks with impulse effects. Examples are given.     

Rational Ehrhart quasi-polynomials

Ehrhart?s famous theorem states that the number of integral points in a rational polytope is a quasi-polynomial in the integral dilation factor. We study the case of rational dilation factors. It turns out that the number of integral points can still be written as a rational quasi-polynomial. Furthermore, the coefficients of this rational quasi-polynomial are piecewise polynomial functions and related to each other by derivation.     

Continuous extension operators and convexity

Given a nonempty closed subset A of a Hilbert space X, we denote by L(A) the space of all bounded Lipschitz mappings from A into X, equipped with the supremum norm. We show that there is a continuous mapping F_c:L(A)?L(X) such that for each g∈L(A), F_c(g)|_A=g, , and . We also prove that the corresponding set-valued extension operator is lower semicontinuous.     

A genetic algorithm for the unrelated parallel machine scheduling problem with sequence dependent setup times

In this work a genetic algorithm is presented for the unrelated parallel machine scheduling problem in which machine and job sequence dependent setup times are considered. The proposed genetic algorithm includes a fast local search and a local search enhanced crossover operator. Two versions of the algorithm are obtained after extensive calibrations using the Design of Experiments (DOE) approach. We review, evaluate and compare the proposed algorithm against the best methods known from the literature. We also develop a benchmark of small and large instances to carry out the computational experiments. After an exhaustive computational and statistical analysis we can conclude that the proposed method shows an excellent performance overcoming the rest of the evaluated methods in a comprehensive benchmark set of instances.     

Contactless Conductivity Detection in Capillary Electrophoresis Employing Capillaries with Very Low Inner Diameters

The behaviour of a contactless conductivity detector was studied in its application to capillary electrophoresis employing quartz capillaries with inner diameters (i.d.) of 10 to 75 µm. The detector output signal was measured using KCl as the test electrolyte, within a KCl concentration range from 0 to 100 mmol/L, corresponding to specific conductivities from 0 to 1295 mS/m. When using capillaries with high inner diameters, then the signal‐to‐noise ratio is high in electrolytes of low conductivity. On the other hand, the use of capillaries with low i.d. values is useful in separations employing solutions of high conductivities. The advantages of capillaries with small i.d. values, combined with contactless conductivity detection, are demonstrated on separations of mixtures of inorganic ions and on separations of neutral mono‐ and disaccharides.