Recently, there were several papers on finding good linear codes. Various methods were introduced to make good linear codes. In this paper, we give a simple iterative algorithm to make good linear codes. Using our alg...
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Recently, there were several papers on finding good linear codes. Various methods were introduced to make good linear codes. In this paper, we give a simple iterative algorithm to make good linear codes. Using our algorithm we construct 86 codes which improve the minimum distance of previously best known linear codes for fixed parameters n, k.
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an id...
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An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from other vertices by the set of vertices in C that are at distance at most 1 from x. The problem of finding an identifying code of minimum possible size turned out to be a challenging problem. It was proved by N. Bertrand, I. Charon, O. Hudry and A. Lobstein that if a graph on n vertices with at least one edge admits an identifying code, then a minimal identifying code has size at most n - 1. They introduced classes of graphs whose smallest identifying code is of size n - 1. Few conjectures were formulated to classify the class of all graphs whose minimum identifying code is of size n - 1. In this paper, disproving these conjectures, we classify all finite graphs for which all but one of the vertices are needed to form an identifying code. We classify all infinite graphs needing the whole set of vertices in any identifying code. New upper bounds in terms of the number of vertices and the maximum degree of a graph are also provided. (C) 2011 Elsevier Ltd. All rights reserved.
Many animals use the interaural time differences (ITDs) to locate the source of low frequency sounds. The place coding theory proposed by Jeffress has long been a dominant model to account for the neural mechanisms of...
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Many animals use the interaural time differences (ITDs) to locate the source of low frequency sounds. The place coding theory proposed by Jeffress has long been a dominant model to account for the neural mechanisms of ITD detection. Recent research, however, suggests a wider range of strategies for ITD coding in the binaural auditory brainstem. We discuss how ITD is coded in avian, mammalian, and reptilian nervous systems, and review underlying synaptic and cellular properties that enable precise temporal computation. The latest advances in recording and analysis techniques provide powerful tools for both overcoming and utilizing the large field potentials in these nuclei.
Let (P, L, I) be a partial linear space and X subset of P boolean OR L. Let us denote (X)(I) = U(x is an element of X) {y : y/x) and [X] = (X)(I) boolean OR X. With this terminology a partial linear space (P, L, I) is...
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Let (P, L, I) be a partial linear space and X subset of P boolean OR L. Let us denote (X)(I) = U(x is an element of X) {y : y/x) and [X] = (X)(I) boolean OR X. With this terminology a partial linear space (P, L, I) is said to admit a (1, <= k)-identifying code if and only if the sets [X] are mutually different for all X subset of P boolean OR L with vertical bar X vertical bar <= k. In this paper we give a characterization of k-regular partial linear spaces admitting a (1, <= k)-identifying code. Equivalently, we give a characterization of k-regular bipartite graphs of girth at least six admitting a (1, <= k)-identifying code. Moreover, we present a family of k-regular partial linear spaces on 2(k - 1)(2)+k points and 2(k - 1)(2)+k lines whose incidence graphs do not admit a (1, <= k)-identifying code. Finally, we show that the smallest (k;6)-graphs known up until now for k - 1 where k - 1 is not a prime power, admit a (1, <= k)-identifying code. (C) 2010 Elsevier Ltd. All rights reserved.
We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We study the problem with different measures: volume, diameter and r...
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We address the problem of localizing homology classes, namely, finding the cycle representing a given class with the most concise geometric measure. We study the problem with different measures: volume, diameter and radius. For volume, that is, the 1-norm of a cycle, two main results are presented. First, we prove that the problem is NP-hard to approximate within any constant factor. Second, we prove that for homology of dimension two or higher, the problem is NP-hard to approximate even when the Betti number is O(1). The latter result leads to the inapproximability of the problem of computing the nonbounding cycle with the smallest volume and computing cycles representing a homology basis with the minimal total volume. As for the other two measures defined by pairwise geodesic distance, diameter and radius, we show that the localization problem is NP-hard for diameter but is polynomial for radius. Our work is restricted to homology over the a"currency sign(2) field. Results over other fields have been studied recently by Dey et al.: In STOC, pp. 221-230 (2010).
A systematic strategy for the calculation of density functionals (DFs) consists in coding informations about the density and the energy into polynomials of the degrees of freedom of wave functions. DFs and Kohn-Sham p...
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A systematic strategy for the calculation of density functionals (DFs) consists in coding informations about the density and the energy into polynomials of the degrees of freedom of wave functions. DFs and Kohn-Sham potentials (KSPs) are then obtained by standard elimination procedures of such degrees of freedom between the polynomials. Numerical examples illustrate the formalism. (C) 2011 Elsevier B.V. All rights reserved.
The problem of representation of topological models in the form of triangulation of cubic complexes is related to the character and behaviour of the triangulation in the n-dimensional space. As the base for analysis o...
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The problem of representation of topological models in the form of triangulation of cubic complexes is related to the character and behaviour of the triangulation in the n-dimensional space. As the base for analysis of these characteristics one can take the fundamental statistical information which gives the possibility to synthesise typical features of triangulation in model spaces of various dimensions. In this paper, we suggest an approach to solution of this problems in the case of analysing statistical features of triangulation in the space of dimension at most 4 with the use of binary coding.
We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer t >= 3 is said to be exceptional if f (x) = x(t) is ...
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We prove a conjecture that classifies exceptional numbers. This conjecture arises in two different ways, from cryptography and from coding theory. An odd integer t >= 3 is said to be exceptional if f (x) = x(t) is APN (Almost Perfect Nonlinear) over F(2n) for infinitely many values of n. Equivalently, t is exceptional if the binary cyclic code of length 2(n) - 1 with two zeros omega, omega(t) has minimum distance 5 for infinitely many values of n. The conjecture we prove states that every exceptional number has the form 2(i) 4 + 1 or 4(i) - 2(i) + 1. (C) 2011 Elsevier Inc. All rights reserved.
A performance analysis for a 450 MWth deep burn-high temperature reactor (DB-HTR) fuel was performed using COPA, a fuel performance analysis code of Korea Atomic Energy Research Institute (KAERI). The code computes ga...
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A performance analysis for a 450 MWth deep burn-high temperature reactor (DB-HTR) fuel was performed using COPA, a fuel performance analysis code of Korea Atomic Energy Research Institute (KAERI). The code computes gas pressure buildup in the void volume of a tri-isotropic coated fuel particle (TRISO), temperature distribution in a DB-HTR fuel, thermo-mechanical stress in a coated fuel particle (CFP), failure fractions of a batch of CFPs, and fission product (FP) releases into the coolant. The 350 mu m DB-HTR kernel is composed of 30% UO2 + 70% (5% NpO2 + 95% PuO1.8) mixed with 0.6 moles of silicon carbide (SiC) per mole of heavy metal. The DB-HTR is operated at the constant temperature and power of 858 degrees C and 39.02 mW per CFP for 1395 effective full power days (EFPD) and is subjected to a core heat-up event for 250 h during which the maximum coolant temperature reaches 1548.70 degrees C. Within the normal operating temperature, the fuel showed good thermal and mechanical integrity. At elevated temperatures of the accident event, the failure fraction of CFPs resulted from the mechanical failure (MF) and the thermal decomposition (TD) of the SiC barrier is 3.30 x 10(-3). (C) 2011 Elsevier B.V. All rights reserved.
ODORactor is an open access web server aimed at providing a platform for identifying odorant receptors (ORs) for small molecules and for browsing existing OR-ligand pairs. It enables the prediction of ORs from the mol...
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ODORactor is an open access web server aimed at providing a platform for identifying odorant receptors (ORs) for small molecules and for browsing existing OR-ligand pairs. It enables the prediction of ORs from the molecular structures of arbitrary chemicals by integrating two individual functionalities: odorant verification and OR recognition. The prediction of the ORs for several odorants was experimentally validated in the study. In addition, ODORactor features a comprehensive repertoire of olfactory information that has been manually curated from literature. Therefore, ODORactor may provide an effective way to decipher olfactory coding and could be a useful server tool for both basic olfaction research in academia and for odorant discovery in industry.
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