Results 1  10
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15
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 78 (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.
Varieties of Increasing Trees
, 1992
"... An increasing tree is a labelled rooted tree in which labels along any branch from the root go in increasing order. Under various guises, such trees have surfaced as tree representations of permutations, as data structures in computer science, and as probabilistic models in diverse applications. We ..."
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Cited by 55 (7 self)
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An increasing tree is a labelled rooted tree in which labels along any branch from the root go in increasing order. Under various guises, such trees have surfaced as tree representations of permutations, as data structures in computer science, and as probabilistic models in diverse applications. We present a unified generating function approach to the enumeration of parameters on such trees. The counting generating functions for several basic parameters are shown to be related to a simple ordinary differential equation which is non linear and autonomous. Singularity analysis applied to the intervening generating functions then permits to analyze asymptotically a number of parameters of the trees, like: root degree, number of leaves, path length, and level of nodes. In this way it is found that various models share common features: path length is O(n log n), the distributions of node levels and number of leaves are asymptotically normal, etc.
Stability of the solution to inverse obstacle scattering problem
 J.INVERSE AND ILLPOSED PROBLEMS
, 1994
"... It is proved that if the scattering amplitudes for two obstacles (from a large class of obstacles) differ a little, then the obstacles differ a little, and the rate of convergence is given. An analytical formula for calculating the characteristic function of the obstacle is obtained, given the sca ..."
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Cited by 22 (12 self)
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It is proved that if the scattering amplitudes for two obstacles (from a large class of obstacles) differ a little, then the obstacles differ a little, and the rate of convergence is given. An analytical formula for calculating the characteristic function of the obstacle is obtained, given the scattering amplitude at a fixed frequency. Introduction. Let D ⊂ R 3 be a bounded domain with a smooth boundary Γ, ( ∇ 2 + k 2)u = 0 in D ′: = R 3 \ D, k = const> 0; u = 0 on Γ (1) u = exp(ikα · x) + A(α ′ , α, k)r −1 exp(ikr) + o(r −1), r: = x  → ∞, α ′: = xr −1. (2) Here α ∈ S 2 is a given unit vector, S 2 is the unit sphere in R 3, the function A(α ′ , α, k) is called the
On Stable Compactification With CasimirLike Potential
"... This paper is devoted to the problem of stable compactification of internal spaces in multidimensional cosmological models. This is one of the most important problems in multidimensional cosmology because via stable compactification of the internal dimensions near Planck length we can explain unobse ..."
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This paper is devoted to the problem of stable compactification of internal spaces in multidimensional cosmological models. This is one of the most important problems in multidimensional cosmology because via stable compactification of the internal dimensions near Planck length we can explain unobservability of extra dimensions. With the help of dimensional reduction we obtain an effective D 0 dimensional (usually D 0 = 4) theory in the BransDicke and Einstein frames. The Einstein frame is considered here as the physical one. Stable compactification is achieved here due to the Casimir effect which is induced by the nontrivial topology of the spacetime. The calculation of the Casimir effect in the case of more than one scale factors is a very complicated problem. That is the reason for proposing a Casimirlike ansatz for the energy density of the massless scalar field fluctuations. In this ansatz all internal factors are included on equal footing. The corresponding equation has correct Casimir dimension: [cm]
Stability of the solutions . . . problems with fixedenergy data
, 2002
"... A review of the author’s results is given. Inversion formulas and stability results for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. The inverse potential scattering problem with fixedenergy scattering data is ..."
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A review of the author’s results is given. Inversion formulas and stability results for the solutions to 3D inverse scattering problems with fixed energy data are obtained. Inversion of exact and noisy data is considered. The inverse potential scattering problem with fixedenergy scattering data is discussed in detail, inversion formulas for the exact and for noisy data are derived, error estimates for the inversion formulas are obtained. The inverse obstacle scattering problem is considered for nonsmooth obstacles. Stability estimates are derived for inverse obstacle scattering problem in the class of smooth obstacles. Global estimates for the scttering amplitude are given when the potential grows to infinity in a bounded domain. Inverse geophysical scattering problem is discussed briefly. An algorithm for constructing the DirichlettoNeumann map from the scattering amplitude and vice versa is obtained. An analytical example of nonuniqueness of the solution to a 3D inverse problem of geophysics and a uniqueness theorem for an inverse problem for parabolic equations are given.
Modification of AbelPlana formula for functions with nonintegrable branchpoints
, 710
"... Abstract. The AbelPlana formula is a widely used tool for calculations in Casimir type problems. In this note we present a particular explicit modification of the ..."
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Abstract. The AbelPlana formula is a widely used tool for calculations in Casimir type problems. In this note we present a particular explicit modification of the
Thermal Effects of Rotation in Random Classical ZeroPoint Radiation.
, 704
"... The rotating reference system {µτ}, along with the twopoint correlation functions (CFs) and energy density, is defined and used as the basis for investigating thermal effects observed by a detector rotating through random classical zeropoint radiation. The reference system consists of FrenetSerre ..."
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The rotating reference system {µτ}, along with the twopoint correlation functions (CFs) and energy density, is defined and used as the basis for investigating thermal effects observed by a detector rotating through random classical zeropoint radiation. The reference system consists of FrenetSerret orthogonal tetrads µτ. At each proper time τ the rotating detector is at rest and has a constant acceleration vector at the µτ. The twopoint CFs and the energy density at the rotating reference system should be periodic with the period T = 2π Ω, where Ω is an angular detector velocity, because CF and energy density measurements is one of the tools the detector can use to justify the periodicity of its motion. The CFs have been calculated for both electromagnetic and massless scalar fields in two cases, with and without taking this periodicity into consideration. It turned out that only periodic CFs have some thermal features and particularly the Planck’s factor with the temperature Trot = ¯hΩ
Consistent Model Specification Tests Against Smooth Transition Alternatives ∗
, 2005
"... In this paper we develop tests of functional form that are consistent against a class of nonlinear "smooth transition " models of the conditional mean. Our method is an extension of the consistent model specification tests developed by Bierens (1990), de Jong (1996) and Bierens and Ploberger (1997), ..."
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In this paper we develop tests of functional form that are consistent against a class of nonlinear "smooth transition " models of the conditional mean. Our method is an extension of the consistent model specification tests developed by Bierens (1990), de Jong (1996) and Bierens and Ploberger (1997), provides maximal power against nonlinear smooth transition ARX specifications, and is consistent against any deviation from the null hypothesis. Of separate interest, we provide substantial detail regarding when and whether Bierenstype tests are asymptotically degenerate. In a simulation experiment in which all parameters are randomly selected, and a linear AR null model is selected by minimizing the AIC, the proposed test has power nearly identical to a most powerful test for true STAR processes, and dominates popular tests. 1. Introduction Smooth Transition Threshold Autoregressive (STAR)