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Random Mapping Statistics
 IN ADVANCES IN CRYPTOLOGY
, 1990
"... Random mappings from a finite set into itself are either a heuristic or an exact model for a variety of applications in random number generation, computational number theory, cryptography, and the analysis of algorithms at large. This paper introduces a general framework in which the analysis of ..."
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Cited by 87 (6 self)
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Random mappings from a finite set into itself are either a heuristic or an exact model for a variety of applications in random number generation, computational number theory, cryptography, and the analysis of algorithms at large. This paper introduces a general framework in which the analysis of about twenty characteristic parameters of random mappings is carried out: These parameters are studied systematically through the use of generating functions and singularity analysis. In particular, an open problem of Knuth is solved, namely that of finding the expected diameter of a random mapping. The same approach is applicable to a larger class of discrete combinatorial models and possibilities of automated analysis using symbolic manipulation systems ("computer algebra") are also briefly discussed.
Wellpoised hypergeometric service for diophantine problems of zeta values
 J. Theorie Nombres Bordeaux
, 2003
"... It is explained how the classical concept of wellpoised hypergeometric series and integrals becomes crucial in studing arithmetic properties of the values of Riemann’s zeta function. By these wellpoised means we obtain: (1) a permutation group for linear forms in 1 and ζ(4) = π 4 /90 yielding a ..."
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Cited by 19 (7 self)
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It is explained how the classical concept of wellpoised hypergeometric series and integrals becomes crucial in studing arithmetic properties of the values of Riemann’s zeta function. By these wellpoised means we obtain: (1) a permutation group for linear forms in 1 and ζ(4) = π 4 /90 yielding a conditional upper bound for the irrationality measure of ζ(4); (2) a secondorder Apérylike recursion for ζ(4) and some loworder recursions for linear forms in odd zeta values; (3) a rich permutation group for a family of certain Eulertype multiple integrals that generalize socalled Beukers’ integrals for ζ(2) and ζ(3).
Combining decision procedures
 In Formal Methods at the Cross Roads: From Panacea to Foundational Support, Lecture Notes in Computer Science
, 2003
"... Abstract. We give a detailed survey of the NelsonOppen method for combining decision procedures, we show how Shostak's method can be seen as an instance of the NelsonOppen method, and we provide a generalization of the NelsonOppen method to the case of nondisjoint theories. 1 Introduction D ..."
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Cited by 10 (0 self)
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Abstract. We give a detailed survey of the NelsonOppen method for combining decision procedures, we show how Shostak's method can be seen as an instance of the NelsonOppen method, and we provide a generalization of the NelsonOppen method to the case of nondisjoint theories. 1 Introduction Decision procedures are algorithms that can reason about the validity or satisfiability of classes of formulae in a given decidable theory, and always terminate with a positive or negative answer.
Iterated Logarithmic Expansions of the Pathwise Code Lengths for Exponential Families
 IEEE Transactions on Information Theory
, 1999
"... Rissanen's Minimum Description Length (MDL) principle is a statistical modeling principle motivated by coding theory. For exponential families we obtain pathwise expansions, to the constant order, of the predictive and mixture code lengths used in MDL. The results are useful for understanding d ..."
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Cited by 7 (2 self)
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Rissanen's Minimum Description Length (MDL) principle is a statistical modeling principle motivated by coding theory. For exponential families we obtain pathwise expansions, to the constant order, of the predictive and mixture code lengths used in MDL. The results are useful for understanding different MDL forms.
Dimensional renormalization in φ 3 theory: ladders and rainbows
, 2008
"... The sum of all the ladder and rainbow diagrams in φ3 theory near 6 dimensions leads to selfconsistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now succeeded in solving these equations, expressing the results in term ..."
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Cited by 1 (0 self)
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The sum of all the ladder and rainbow diagrams in φ3 theory near 6 dimensions leads to selfconsistent higher order differential equations in coordinate space which are not particularly simple for arbitrary dimension D. We have now succeeded in solving these equations, expressing the results in terms of generalized hypergeometric functions; the expansion and representation of these functions can then be used to prove the absence of renormalization factors which are transcendental for this theory and this topology to all orders in perturbation theory. The correct anomalous scaling dimensions of the Green functions are also obtained in the sixdimensional limit.
School of Mathematics, Meteorology and Physics
, 2009
"... On the spectra of certain IntegroDifferentialDelay problems with applications in neurodynamics by Peter Grindrod and Dimitri PinotsisOn the spectra of certain IntegroDifferentialDelay problems with applications in neurodynamics ..."
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On the spectra of certain IntegroDifferentialDelay problems with applications in neurodynamics by Peter Grindrod and Dimitri PinotsisOn the spectra of certain IntegroDifferentialDelay problems with applications in neurodynamics
Durfee Polynomials Extended Abstract
"... Let F(n) be a family of partitions of n and let F(n; d) denote the set of partitions in F(n) with Durfee square of size d. We define the Durfee polynomial of F(n) to be the polynomial PF;n = P jF(n; d)jyd, where 0 ^ d ^ bpnc: This paper describes ongoing efforts to compute statistics associated with ..."
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Let F(n) be a family of partitions of n and let F(n; d) denote the set of partitions in F(n) with Durfee square of size d. We define the Durfee polynomial of F(n) to be the polynomial PF;n = P jF(n; d)jyd, where 0 ^ d ^ bpnc: This paper describes ongoing efforts to compute statistics associated with the Durfee polynomial for various families F.