Perfectly Matched Layers for Time-Harmonic Second Order Elliptic Problems

The main goal of this work is to give a review of the Perfectly Matched Layer (PML) technique for time-harmonic problems. Precisely, we focus our attention on problems stated in unbounded domains, which involve second order elliptic equations writing in divergence form and, in particular, on the Helmholtz equation at low frequency regime. Firstly, the PML technique is introduced by means of a simple porous model in one dimension. It is emphasized that an adequate choice of the so called complex absorbing function in the PML yields to accurate numerical results. Then, in the two-dimensional case, the PML governing equation is described for second order partial differential equations by using a smooth complex change of variables. Its mathematical analysis and some particular examples are also included. Numerical drawbacks and optimal choice of the PML absorbing function are studied in detail. In fact, theoretical and numerical analysis show the advantages of using non-integrable absorbing functions. Finally, we present some relevant real life numerical simulations where the PML technique is widely and successfully used although they are not covered by the standard theoretical framework.     

The use of lexical semantics in interlingual machine translation

This paper describes the lexical-semantic basis for UNITRAN, an implemented scheme for translating Spanish, English, and German bidirectionally. Two claims made here are that the current representation handles many distinctions (or divergences) across languages without recourse to language-specific rules and that the lexical-semantic framework provides the basis for a systematic mapping between the interlingua and the syntactic structure. The representation adopted is an extended version of lexical conceptual structure which is suitable to the task of translating between divergent structures for two reasons: (1) it provides an abstraction of language-independent properties from structural idiosyncrasies; and (2) it is compositional in nature. The lexical-semantic approach addresses the divergence problem by using a linguistically grounded mapping that has access to parameter settings in the lexicon. We will examine a number of relevant issues including the problem of defining primitives, the issue of interlinguality, the cross-linguistic coverage of the system, and the mapping between the syntactic structure and the interlingua. A detailed example of lexical-semantic composition will be presented.     

Group-Wise Point-Set Registration Using a Novel CDF-Based Havrda-Charvát Divergence

This paper presents a novel and robust technique for group-wise registration of point sets with unknown correspondence. We begin by defining a Havrda-Charvát (HC) entropy valid for cumulative distribution functions (CDFs) which we dub the HC Cumulative Residual Entropy (HC-CRE). Based on this definition, we propose a new measure called the CDF-HC divergence which is used to quantify the dis-similarity between CDFs estimated from each point-set in the given population of point sets. This CDF-HC divergence generalizes the CDF Jensen-Shannon (CDF-JS) divergence introduced earlier in the literature, but is much simpler in implementation and computationally more efficient. A closed-form formula for the analytic gradient of the cost function with respect to the non-rigid registration parameters has been derived, which is conducive for efficient quasi-Newton optimization. Our CDF-HC algorithm is especially useful for unbiased point-set atlas construction and can do so without the need to establish correspondences. Mathematical analysis and experimental results indicate that this CDF-HC registration algorithm outperforms the previous group-wise point-set registration algorithms in terms of efficiency, accuracy and robustness.     

On the representation of McCarthy's in the -calculus

We study the encoding of , the call-by-name λ-calculus enriched with McCarthy's amb operator, into the π-calculus. Semantically, amb is a challenging operator, for the fairness constraints that it expresses. We prove that, under a certain interpretation of divergence in the λ-calculus (weak divergence), a faithful encoding is impossible. However, with a different interpretation of divergence (strong divergence), the encoding is possible, and for this case we derive results and coinductive proof methods to reason about that are similar to those for the encoding of pure λ-calculi. We then use these methods to derive the most important laws concerning amb. We take bisimilarity as behavioural equivalence on the π-calculus, which sheds some light on the relationship between fairness and bisimilarity.     

Multiple attribute group decision-making based on order-α divergence and entropy measures under q-rung orthopair fuzzy environment

The q-rung orthopair fuzzy set (^qROPFS), proposed by Yager, is a more effective and proficient tool to represent uncertain or vague information in real-life situations. Divergence and entropy are two important measures, which have been extensively studied in different information environments, including fuzzy, intuitionistic fuzzy, interval-valued fuzzy, and Pythagorean fuzzy. In the present communication, we study the divergence and entropy measures under the q-rung orthopair fuzzy environment. First, the work defines two new order-α divergence measures for ^qROPFSs to quantify the information of discrimination between two ^qROPFSs. We also examine several mathematical properties associated with order-α ^qROPF divergence measures in detail. Second, the paper introduces two new parametric entropy functions called “order-α ^qROPF entropy measures” to measure the degree of fuzziness associated with a ^qROPFS. We show that the proposed order-α divergence and entropy measures include several existing divergence and entropy measures as their particular cases. Further, the paper develops a new decision-making approach to solve multiple attribute group decision-making problems under the ^qROPF environment where the information about the attribute weights is completely unknown or partially known. Finally, an example of selecting the best enterprise resource planning system is provided to illustrate the decision-making steps and effectiveness of the proposed approach.     

Algorithm for spline-based elastic registration in application to confocal images of gene expression

We perform elastic registration by an algorithm based on a pixelwise and regularized optimization criterion. We express the deformation field thanks to B-splines, which allows us to deal with a rich variety of deformations. The algorithm is able to handle soft landmark constraints, which is particularly useful when parts of the images contain very little information, or when it is unevenly distributed. We solve the problem by minimizing the distance between the target image and the warped source. We regularize this minimization problem by divergence and curl. We apply the proposed algorithm to the registration of the confocal scanning microscopy images of Drosophila embryos. The text was submitted by the authors in English.     

Molecular surfaces on proteins via beta shapes

A protein consists of linearly combined amino acids via peptide bonds, and an amino acid consists of atoms. It is known that the geometric structure of a protein is the primary factor which determines the functions of the protein.Given the atomic complex of a protein, one of the most important geometric structures of a protein is its molecular surface since this distinguishes between the interior and exterior of the protein and plays an important role in protein folding, docking, interactions between proteins, and other functions.This paper presents an algorithm for the precise and efficient computation of the molecular surface of a protein, using a recently proposed geometric construct called the β-shape based on the Voronoi diagram of atoms in a protein. Given a Voronoi diagram of atoms, based on the Euclidean distance from the atom surfaces, the proposed algorithm first computes the β-shape with an appropriate sized probe. Then, the molecular surface is computed by employing a blending operation on the atomic complex of the protein. In this paper, it is also shown that for a given Voronoi diagram of atoms, the multiple molecular surfaces can be computed by using various sized probes.     

蝶形天线的计算机仿真设计

蝶形天线是在脉冲型探地雷达中广泛采用的一种宽带天线。本文采用时域有限差分算法(FDTD)结合PML吸收边界条件分析了蝶形天线在高斯脉冲激励下的时域特性,通过傅立叶变换,计算出天线的方向图和在不同频率下的输入阻抗,结果表明FDTD算法用于分析蝶形天线是有效的。     

Infinitary Logic and Inductive Definability over Finite Structures

The extensions of first-order logic with a least fixed point operator (FO + LFP) and with a partial fixed point operator (FO + PFP) are known to capture the complexity classes P and PSPACE respectively in the presence of an ordering relation over finite structures. Recently, Abiteboul and Vianu (in "Proceedings of the 23rd ACM Symposium on the Theory of Computing," 1991) investigated the relationship of these two logics in the absence of an ordering, using a machine model of generic computation. In particular, they showed that the two languages have equivalent expressive power if and only if P = PSPACE. These languages can also be seen as fragments of an infinitary logic where each formula has a bounded number of variables, L^ω_∞ω, (see, for instance, Kolaitis and Vardi, in "Proceedings of the 5th IEEE Symposium on Logic in Computer Science," pp. 156-167, 1990). We investigate this logic on finite structures and provide a normal form for it. We also present a treatment of Abiteboul and Vianu′s results from this point of view. In particular, we show that we can write a formula of FO + LFP that defines an ordering of the L^k_∞ω, types uniformly over all finite structures. One consequence of this is a generalization of the equivalence of FO + LFP and P from ordered structures to classes of structures where every element is definable. We also settle a conjecture mentioned by Abiteboul and Vianu by showing that FO + LFP is properly contained in the polynomial time computable fragment of L^ω_∞ω, raising the question of whether the latter fragment is a recursively enumerable class.     

Nash Stability in Additively Separable Hedonic Games and Community Structures

We prove that the problem of deciding whether a Nash stable partition exists in an Additively Separable Hedonic Game is NP-complete. We also show that the problem of deciding whether a non trivial Nash stable partition exists in an Additively Separable Hedonic Game with non-negative and symmetric preferences is NP-complete. We motivate our study of the computational complexity by linking Nash stable partitions in Additively Separable Hedonic Games to community structures in networks. Our results formally justify that computing community structures in general is hard. The research is partly sponsored by the company Cofman ().     

High Order Weighted Essentially Non-oscillation Schemes for Two-Dimensional Detonation Wave Simulations

In this paper, we demonstrate the detailed numerical studies of three classical two dimensional detonation waves by solving the two dimensional reactive Euler equations with species with the fifth order WENO-Z finite difference scheme (Borges et al. in J. Comput. Phys. 227:3101?C3211, 2008) with various grid resolutions. To reduce the computational cost and to avoid wave reflection from the artificial computational boundary of a truncated physical domain, we derive an efficient and easily implemented one dimensional Perfectly Matched Layer (PML) absorbing boundary condition (ABC) for the two dimensional unsteady reactive Euler equation when one of the directions of domain is periodical and inflow/outflow in the other direction. The numerical comparison among characteristic, free stream, extrapolation and PML boundary conditions are conducted for the detonation wave simulations. The accuracy and efficiency of four mentioned boundary conditions are verified against the reference solutions which are obtained from using a large computational domain. Numerical schemes for solving the system of hyperbolic conversation laws with a single-mode sinusoidal perturbed ZND analytical solution as initial conditions are presented. Regular rectangular combustion cell, pockets of unburned gas and bubbles and spikes are generated and resolved in the simulations. It is shown that large amplitude of perturbation wave generates more fine scale structures within the detonation waves and the number of cell structures depends on the wave number of sinusoidal perturbation.     

Separation of Synchronous and Asynchronous Communication Via Testing

One of the early results about the asynchronous π-calculus which significantly contributed to its popularity is the capability of encoding the output prefix of the (choiceless) π-calculus in a natural and elegant way. Encodings of this kind were proposed by Honda and Tokoro, by Nestmann and (independently) by Boudol. We investigate whether the above encodings preserve De Nicola and Hennessy's testing semantics. In this sense, it turns out that, under some general conditions, no encoding of output prefix is able to preserve the must testing. This negative result is due to (a) the non atomicity of the sequences of steps which are necessary in the asynchronous π-calculus to mimic synchronous communication, and (b) testing semantics's sensitivity to divergence.     

Efficient Randomized Algorithms for the Repeated Median Line Estimator

The problem of fitting a straight line to a finite collection of points in the plane is an important problem in statistical estimation. Recently there has been a great deal of interest is robust estimators, because of their lack of sensitivity to outlying data points. The basic measure of the robustness of an estimator is its breakdown point, that is, the fraction (up to 50%) of outlying data points that can corrupt the estimator. One problem with robust estimators is that achieving high breakdown points (near 50%) has proved to be computationally demanding. In this paper we present the best known theoretical algorithm and a practical subquadratic algorithm for computing a 50% breakdown point line estimator, the Siegel or repeated median line estimator. We first present an O(n\log n) randomized expected-time algorithm, where n is the number of given points. This algorithm relies, however, on sophisticated data structures. We also present a very simple O(n log ² n) randomized algorithm for this problem, which uses no complex data structures. We provide empirical evidence that, for many realistic input distributions, the running time of this second algorithm is actually O(n log n) expected time. Received January 25, 1995; revised May 17, 1996. Communciated by L. J. Guibas.     

A novel view of the variational Bayesian clustering

We prove that the evaluation function of variational Bayesian (VB) clustering algorithms can be described as the log likelihood of given data minus the Kullback–Leibler (KL) divergence between the prior and the posterior of model parameters. In this novel formalism of VB, the evaluation functions can be explicitly interpreted as information criteria for model selection and the KL divergence imposes a heavy penalty on the posterior far from the prior. We derive the update process of the variational Bayesian clustering with finite mixture Student's t-distribution, taking the penalty term for the degree of freedoms into account.     

Coalgebraic Semantics for Positive Modal Logic

Positive Modal Logic is the restriction of the modal local consequence relation defined by the class of all Kripke models to the propositional negation-free modal language. The class of positive modal algebras is the one canonically associated with PML according to the theory of the algebraization of logics. In [4], a Priestley-style duality is established between the category of positive modal algebras and the category of K⁺-spaces. In this paper, we establish a categorical equivalence between the category K⁺ of K⁺-spaces and the category Coalg(V) of coalgebras of a suitable endofunctor V on the category of Priestley spaces.     

Distribution of Lattice Points

We discuss the lattice structure of congruential random number generators and examine figures of merit. Distribution properties of lattice measures in various dimensions are demonstrated by using large numerical data. Systematic search methods are introduced to diagnose multiplier areas exhibiting good, bad and worst lattice structures. We present two formulae to express multipliers producing worst and bad laice points. The conventional criterion of normalised lattice rule is also questioned and it is shown that this measure used with a fixed threshold is not suitable for an effective discrimination of lattice structures. Usage of percentiles represents different dimensions in a fair fashion and provides consistency for different figures of merits.     

Coordination by Timers for Channel-Based Anonymous Communications

In this paper we present a new model for timed coordination of communicating distributed processes. The proposed model is an extension of the π-calculus with locations, types, and timers. Types are used to express restricted access to distributed resources. Timers define timeouts for both communication channels and resources. We define the syntax of the model and its operational semantics and provide a few results regarding the typing system and the timers. A timed barbed bisimulation relation is defined to compare the processes. Coordination is given in two stages: by strategically assigning values to timers, and then by employing a set of additional coordination rules. The timed coordination aspects are given through a coordinator pair. It consists of a timers assigning function which can be changed dynamically, and a set of coordination rules. As an illustrating example, we relate our model with the channels of the Reo coordination model.