This paper proposes a framework for the handling of spatio-temporal queries with inexact matches, using the concept of relation similarity. We initially describe a binary string encoding for 1D relations that permits ...
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This paper proposes a framework for the handling of spatio-temporal queries with inexact matches, using the concept of relation similarity. We initially describe a binary string encoding for 1D relations that permits the automatic derivation of similarity measures. We then extend this model to various granularity levels and many dimensions, and show that reasoning on spatio-temporal structure is significantly facilitated in the new framework. Finally, we provide algorithms and optimization methods for four types of queries: (i) object retrieval based on some spatio-temporal relations with respect to a reference object, (ii) spatial joins, i.e., retrieval of object pairs that satisfy some input relation, (iii) structural queries, which retrieve configurations matching a particular spatio-temporal structure, and (iv) special cases of motion queries. Considering the current large availability of multidimensional data and the increasing need for flexible query-answering mechanisms, our techniques can be used as the core of spatio-temporal query processors.
The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA). Unfortunately, there exists no one-dimensional two-state CA which...
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The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA). Unfortunately, there exists no one-dimensional two-state CA which classifies binary strings according to their densities. If, however, in place of simple cells one uses agents which change their behaviour from one rule to another after a fixed number of iterations, the classification can be performed by the traffic rule 184 and the majority rule 232. This two-rule solution cannot be easily generalized to two (or higher) dimensions, because it critically depends on a kinetic phase transition occurring in the rule 184. No rule exhibiting analogous transition is known in two dimensions, most likely because no such rule exists. We propose, therefore, to approach this problem form a slightly different angle, namely by introducing a stochastic component into each of the two rules. If one precedes each iteration of rule 184 by the stochastic "lane changing rule", and each iteration of rule 232 by the stochastic "crowd avoidance" rule, in the limit of infinitely many iterations the classification can be performed correctly with probability 1. This solution can be described either in the language of CA, or using the paradigm of agents which move and proliferate on the 2D lattice, following probabilistic rules.
Assume that a tuple of binary strings (a) over bar = has negligible mutual information with another string b. Does this mean that properties of the Kolmogorov complexity of (a) over bar do not change significantly if...
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Assume that a tuple of binary strings (a) over bar = < a(1), ..., a(n)> has negligible mutual information with another string b. Does this mean that properties of the Kolmogorov complexity of (a) over bar do not change significantly if we relativize them to b? This question becomes very nontrivial when we try to formalize it. In this paper we investigate this problem for a special class of properties (for properties that can be expressed by an there exists-formula). In particular, we show that a random (conditional on (a) over bar) oracle b does not help to extract common information from the strings a(i).
Energy minimization studies were carried out for a number of Cu clusters using binary and Gray-coded genetic algorithms along with real coded differential evolution, and their optimized ground state geometries are pre...
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Energy minimization studies were carried out for a number of Cu clusters using binary and Gray-coded genetic algorithms along with real coded differential evolution, and their optimized ground state geometries are presented. The potential energy function is constructed using a two-body interaction methodology, involving both attractive and repulsive pair-potential terms. The results obtained through the evolutionary algorithms are compared against those obtained earlier using a Monte Carlo technique.
The Collatz function can be stated as 'for any odd positive integer x, calculate 3x + 1 and then divide by 2 until the result is odd'. Colussi (2011) discovered and proved that if x attains 1 on the kth iterat...
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The Collatz function can be stated as 'for any odd positive integer x, calculate 3x + 1 and then divide by 2 until the result is odd'. Colussi (2011) discovered and proved that if x attains 1 on the kth iteration of the Collatz function, then its binary representation can be written as the concatenation of strings SkSk-1 ... s(1) where each s(h) is a finite and contiguous extract from the representation of We provide an elementary confirmation of Colussi's finding, and comment on how working in binary 'protects' the repetends of 1/3(h) as formed into each sh. Crown Copyright (C) 2016 Published by Elsevier B.V. All rights reserved.
A genetic algorithm for testing isomorphism among kinematic chains and to select the best frame and input links is presented. The computational effort involved is minimum and the method is unique as it satisfies bath ...
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A genetic algorithm for testing isomorphism among kinematic chains and to select the best frame and input links is presented. The computational effort involved is minimum and the method is unique as it satisfies bath the necessary aid sufficient requirements. Fitness of a binary string corresponding to a link is indicative of its design parameters. Consequently the Jit,less of a chain indicates the number of design parameters active in motion generation. Chains are compared for function generation on the basis of the 'fitness' of first generation nod second generation 'fitness,' etc., in that order. [S1050-0472(00)00801-1].
The Carlson-Simpson lemma is a combinatorial statement occurring in the proof of the Dual Ramsey theorem. Formulated in terms of variable words, it informally asserts that given any finite coloring of the strings, the...
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The Carlson-Simpson lemma is a combinatorial statement occurring in the proof of the Dual Ramsey theorem. Formulated in terms of variable words, it informally asserts that given any finite coloring of the strings, there is an infinite sequence with infinitely many variables such that for every valuation, some specific set of initial segments is homogeneous. Friedman, Simpson, and Montalban asked about its reverse mathematical strength. We study the computability-theoretic properties and the reverse mathematics of this statement, and relate it to the finite union theorem. In particular, we prove the Ordered Variable word for binary strings in ACA(0).
We show that almost all binary strings of length n contain all blocks of size (1-ε)log2 n a close to uniform number of times. From this, we derive tight bounds on the discrepancy of random infinite strings. Our resul...
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We show that almost all binary strings of length n contain all blocks of size (1-ε)log2 n a close to uniform number of times. From this, we derive tight bounds on the discrepancy of random infinite strings. Our results are obtained through explicit generating function expressions and contour integration estimates.
A Steinhaus matrix is a symmetric 0-1 matrix [a(i,j)](nxn) such that a(i,i) = 0 for 0 less than or equal to i less than or equal to n - 1 and a(i,j) = (a(i-1,j-1) + a(i-1,j)) (mod 2) for 1 less than or equal to i <...
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A Steinhaus matrix is a symmetric 0-1 matrix [a(i,j)](nxn) such that a(i,i) = 0 for 0 less than or equal to i less than or equal to n - 1 and a(i,j) = (a(i-1,j-1) + a(i-1,j)) (mod 2) for 1 less than or equal to i < j less than or equal to n-1. A Steinhaus graph is a graph whose adjacency matrix is a Steinhaus matrix. In this paper, we present a new characterization of bipartite Steinhaus graphs.
Biometric discretization extracts a binary string from a set of real-valued features per user. This representative string can be used as a cryptographic key in many security applications upon error correction. Discret...
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Biometric discretization extracts a binary string from a set of real-valued features per user. This representative string can be used as a cryptographic key in many security applications upon error correction. Discretization performance should not degrade from the actual continuous features-based classification performance significantly. However, numerous discretization approaches based on ineffective encoding schemes have been put forward. Therefore, the correlation between such discretization and classification has never been made clear. In this article, we aim to bridge the gap between continuous and Hamming domains, and provide a revelation upon how discretization based on equal-width quantization and linearly separable subcode encoding could affect the classification performance in the Hamming domain. We further illustrate how such discretization can be applied in order to obtain a highly resembled classification performance under the general Lp distance and the inner product metrics. Finally, empirical studies conducted on two benchmark face datasets vindicate our analysis results.
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