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Modeling Billiards Games
"... Twoplayer games of billiards, of the sort seen in recent Computer Olympiads held by the International Computer Games Association, are an emerging area with unique challenges for A.I. research. Complementing the heuristic/algorithmic aspect of billiards, of the sort brought to the fore in the ICGA b ..."
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Cited by 11 (4 self)
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Twoplayer games of billiards, of the sort seen in recent Computer Olympiads held by the International Computer Games Association, are an emerging area with unique challenges for A.I. research. Complementing the heuristic/algorithmic aspect of billiards, of the sort brought to the fore in the ICGA billiards tournaments, we investigate formal models of such games. The modeling is surprisingly subtle. While sharing features with existing models (including stochastic games, games on a square, recursive games, and extensive form games), our model is distinct, and consequently requires novel analysis. We focus on the basic question of whether the game has an equilibrium. For finite versions of the game it is not hard to show the existence of a pure strategy Markov perfect Nash equilibrium. In the infinite case, it can be shown that under certain conditions a stationary pure strategy Markov perfect Nash equilibrium is guaranteed to exist.
Effective uniform bounds from proofs in abstract functional analysis
 CIE 2005 NEW COMPUTATIONAL PARADIGMS: CHANGING CONCEPTIONS OF WHAT IS COMPUTABLE
, 2005
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Proof Interpretations and the Computational Content of Proofs. Draft of book in preparation
, 2007
"... This survey reports on some recent developments in the project of applying proof theory to proofs in core mathematics. The historical roots, however, go back to Hilbert’s central theme in the foundations of mathematics which can be paraphrased by the following question ..."
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Cited by 9 (1 self)
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This survey reports on some recent developments in the project of applying proof theory to proofs in core mathematics. The historical roots, however, go back to Hilbert’s central theme in the foundations of mathematics which can be paraphrased by the following question
On stability and convergence of the populationdynamics in differential evolution
 AI COMMUN
"... Theoretical analysis of the dynamics of evolutionary algorithms is believed to be very important to understand the search behavior of evolutionary algorithms and to develop more efficient algorithms. In this paper we investigate the dynamics of a canonical Differential Evolution (DE) algorithm with ..."
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Cited by 5 (2 self)
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Theoretical analysis of the dynamics of evolutionary algorithms is believed to be very important to understand the search behavior of evolutionary algorithms and to develop more efficient algorithms. In this paper we investigate the dynamics of a canonical Differential Evolution (DE) algorithm with DE/rand/1 type mutation and binomial crossover. Differential Evolution (DE) is wellknown as a simple and efficient algorithm for global optimization over continuous spaces. Since its inception in 1995, DE has been finding many important applications in realworld optimization problems from diverse domains of science and engineering. The paper proposes a simple mathematical model of the underlying evolutionary dynamics of a onedimensional DEpopulation. The model shows that the fundamental dynamics of each searchagent (parameter vector) in DE employs the gradientdescent type search strategy (although it uses no analytical expression for the gradient itself), with a learning rate parameter that depends on control parameters like scale factor F and crossover rate CR of DE. The stability and convergencebehavior of the proposed dynamics is analyzed in the light of Lyapunov’s stability theorems very near to the islolated equilibrium points during the final stages of the search. Empirical studies over simple objective functions are conducted in order to validate the theoretical analysis.
ON FIXEDPOINTS OF MULTIVALUED FUNCTIONS ON COMPLETE LATTICES AND THEIR APPLICATION TO GENERALIZED LOGIC PROGRAMS
"... Abstract. Unlike monotone singlevalued functions, multivalued mappings may have none, one or (possibly infinitely) many minimal fixedpoints. The contribution of this work is twofold. At first we overview and investigate about the existence and computation of minimal fixedpoints of multivalued m ..."
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Abstract. Unlike monotone singlevalued functions, multivalued mappings may have none, one or (possibly infinitely) many minimal fixedpoints. The contribution of this work is twofold. At first we overview and investigate about the existence and computation of minimal fixedpoints of multivalued mappings, whose domain is a complete lattice and whose range is its power set. Second, we show how these results are applied to a general form of logic programs, where the truth space is a complete lattice. We show that a multivalued operator can be defined whose fixedpoints are in onetoone correspondence with the models of the logic program. Key words. Fixedpoints; multivalued functions; complete lattices; logic programming AMS subject classifications. 47H10, 06B23 68N17, 68Q55, 1. Introduction. It
Classifying Coding DNA with Nucleotide Statistics
"... Abstract: In this report, we compared the success rate of classification of coding sequences (CDS) vs. introns by Codon Structure Factor (CSF) and by a method that we called Universal Feature Method (UFM). UFM is based on the scoring of purine bias (Rrr) and stop codon frequency. We show that the su ..."
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Abstract: In this report, we compared the success rate of classification of coding sequences (CDS) vs. introns by Codon Structure Factor (CSF) and by a method that we called Universal Feature Method (UFM). UFM is based on the scoring of purine bias (Rrr) and stop codon frequency. We show that the success rate of CDS/intron classification by UFM is higher than by CSF. UFM classifies ORFs as coding or noncoding through a score based on (i) the stop codon distribution, (ii) the product of purine probabilities in the three positions of nucleotide triplets, (iii) the product of Cytosine (C), Guanine (G), and Adenine (A) probabilities in the 1st, 2nd, and 3rd positions of triplets, respectively, (iv) the probabilities of G in 1st and 2nd position of triplets and (v) the distance of their GC3 vs. GC2 levels to the regression line of the universal correlation. More than 80 % of CDSs (true positives) of Homo sapiens (�250 bp), Drosophila melanogaster (�250 bp) and Arabidopsis thaliana (�200 bp) are successfully classified with a false positive rate lower or equal to 5%. The method releases coding sequences in their coding strand and coding frame, which allows their automatic translation into protein sequences with 95 % confidence. The method is a natural consequence of the compositional bias of nucleotides in coding sequences.
Academy of Sciences
"... Abstract. First the characteristic of monotonicity of any Banach lattice X is expressed in terms of the left limit of the modulus of monotonicity of X at the point 1. It is also shown that for Köthe spaces the classical coefficient of monotonicity is the same as the characteristic of monotonicity co ..."
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Abstract. First the characteristic of monotonicity of any Banach lattice X is expressed in terms of the left limit of the modulus of monotonicity of X at the point 1. It is also shown that for Köthe spaces the classical coefficient of monotonicity is the same as the characteristic of monotonicity corresponding to another modulus of monotonicity ̂ δm,E. The characteristic of monotonicity of Orlicz function spaces and Orlicz sequence spaces equipped with the Luxemburg norm, are calculated. In the first case the characteristic is expressed in terms of the generating Orlicz function only, but in the sequence case the formula is not so direct. Three examples show why in the sequence case so direct formula is rather impossible. Some other auxiliary and complemented results are also presented. By the result of BetiukPilarska and Prus [2] which establish that Banach lattices X with ε0,m(X) < 1 and weak orthogonality property have the weak fixed point property our results are related to the fixed point theory [15]. 1. Preliminaries Let us denote S+(X) = S(X) ∩ X+, where S(X) is the unit sphere of a Banach lattice X (for its definition see [3], [14] and [21]) and X+ is the positive cone of X. A Banach lattice X is said to be strictly monotone (X ∈ (SM)) if for all x, y ∈ X+ such that y ≤ x and y ̸ = x, we have ‖y ‖ < ‖x‖. A Banach lattice X is said to be uniformly monotone (X ∈ (UM)) if for any ε ∈ (0, 1) there is δ(ε) ∈ (0, 1) such that ‖x − y ‖ ≤ 1 − δ(ε) whenever 0 ≤ y ≤ x, ‖x ‖ = 1 and ‖y ‖ ≥ ε (see [3]). For a given Banach lattice X, the function δm,X: [0, 1] → [0, 1] defined by δm,X(ε) = inf{1 − ‖x − y ‖ : 0 ≤ y ≤ x, ‖x ‖ = 1, ‖y ‖ ≥ ε} 2000 Mathematics Subject Classification. 46B42,46B20,46A80,46E30. Key words and phrases. Banach lattice, Köthe space, Orlicz space, Lorentz space, Luxemburg norm,
COMMON FIXED POINTS FOR THREE MAPPINGS USING GFUNCTIONS AND THE PROPERTY (E.A)
"... Abstract. Here, using the property (E.A) (see [1]) and the class of Gfunctions, we provide an extension to a result recently obtained by P. N. Dutta and Binayak S. Choudhury in [3]. ..."
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Abstract. Here, using the property (E.A) (see [1]) and the class of Gfunctions, we provide an extension to a result recently obtained by P. N. Dutta and Binayak S. Choudhury in [3].