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For expansive continuous maps with the specification property, we compute the topological entropy of the irregular set for the Birkhoff averages of a continuous function. This is the set of points for which the Birkhoff averages do not converge. The entropy is expressed in terms of a conditional variational principle. We also consider the general case of irregular sets obtained from ratios of Birkhoff averages of continuous functions. Moreover, we obtain a conditional variational principle for the topological entropy of the family of subsets of the irregular set formed by the points such that the set of accumulation points of the ratio of Birkhoff averages is a given interval. As nontrivial applications, we obtain conditional variational principles for the topological entropy of the level sets of local entropies, pointwise dimensions and Lyapunov exponents both on repellers and hyperbolic sets. [ABSTRACT FROM AUTHOR]

This paper features a method to synthesize the track irregularities, by which the alignment may be analytically represented by a pseudo-stochastic function, as well as the implementation of such method in the numerical simulation of the dynamic behaviour of the railway vehicles. The method thus suggested allows a convenient formulation of the limits of the interval specific to the wavelengths of the track lateral irregularities, so that it will be representative for the frequency range of the vehicle lateral vibrations. The Part I of this paper demonstrates the method to synthesize the track alignment and its basic elements - the power spectral density of the track irregularities, as per ORE B176 and the values associated with the track quality levels, mentioned in the UIC 518 Leaflet. The Part II introduces the results of the numerical simulations regarding the dynamic behaviour of the railway vehicle during the circulation on a tangent track with lateral irregularities, synthesized as in the method herein. [ABSTRACT FROM AUTHOR]

In this paper, we derive the asymptotic statistical properties of a class of generalized discrepancies introduced by Cui and Freeden (SIAM J. Sci. Comput., 1997) to test equidistribution on the sphere. We show that they have highly desirable properties and encompass several statistics already proposed in the literature. In particular, it turns out that the limiting distribution is an (infinite) weighted sum of chi-squared random variables. Issues concerning the approximation of this distribution are considered in detail and explicit bounds for the approximation error are given. The statistics are then applied to assess the equidistribution of Hammersley low discrepancy sequences on the sphere and the uniformity of a dataset concerning magnetic orientations. [ABSTRACT FROM AUTHOR]

The total edge irregular k-labeling of a graph G=(V,E) is the labeling of vertices and edges of G in such a way that for any different edges their weights are distinct. The total edge irregularity strength, tes (G), is defined as the minimum k for which G has a total edge irregular k-labeling. In this paper, we consider the total edge irregularity strength of the disjoint union of m special types of helm graphs. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we study certain weighted Sobolev spaces defined on an open subset of (not necessarily bounded or regular) when the weight is a function related to the distance from a subset of . As an application, we prove boundedness and compactness results for operators in such weighted Sobolev spaces. [Copyright &y& Elsevier]

Nested and co-nested formulas are two classes of CNF instances that can be characterized in terms of outerplanar graphs. For these classes, linear time algorithms are known for SAT and (unweighted) Max-SAT. In this paper we devise linear time algorithms for a general optimization version of SAT. Moreover, we show that a general probabilistic version of SAT reduces to solving a system of linear inequalities where the number of variables and constraints is linear in the size of the formula. [ABSTRACT FROM AUTHOR]

Abstract: Let be the sum-of-digits function of in base . Newman (1969) has shown the surprising phenomenon that for all (with some ). Motivated by investigations of distribution properties of Niederreiter–Halton sequences we study for and , where is the -weighted sum-of-digits function of in base 2. We completely classify all and for which Newman-type results hold, thereby generalising the result of Newman and results given by Drmota and Stoll (2008) . We point out consequences of our results for the distribution of Niederreiter–Halton sequences (). [ABSTRACT FROM AUTHOR]

Abstract: The conceptual predictive statistic, C p , is a widely used criterion for model selection in linear regression. C p serves as an estimator of a discrepancy, a measure that reflects the disparity between the generating model and a fitted candidate model. This discrepancy, based on scaled squared error loss, is asymmetric: an alternate measure is obtained by reversing the roles of the two models in the definition of the measure. We propose a variant of the C p statistic based on estimating a symmetrized version of the discrepancy targeted by C p . We claim that the resulting criterion provides better protection against overfitting than C p , since the symmetric discrepancy is more sensitive towards detecting overspecification than its asymmetric counterpart. We illustrate our claim by presenting simulation results. Finally, we demonstrate the practical utility of the new criterion by discussing a modeling application based on data collected in a cardiac rehabilitation program at University of Iowa Hospitals and Clinics. [Copyright &y& Elsevier]

We show a construction of a PCP with both sub-constant error and almost-linear size. Specifically, for some constant 0 < α < 1, we construct a PCP verifier for checking satisfiability of Boolean formulas that on input of size n uses $$\log\, n+O((\log\, n)^{1-\alpha})$$ random bits to make 7 queries to a proof of size $$n·2^{O((\log\, n)^{1-\alpha})}$$, where each query is answered by $$O((\log\, n)^{1-\alpha})$$ bit long string, and the verifier has perfect completeness and error $$2^{-\Omega((\log\, n)^{\alpha})}$$. The construction is by a new randomness-efficient version of the aggregation through curves technique. Its main ingredients are a recent low degree test with both sub-constant error and almost-linear size and a new method for constructing a short list of balanced curves. [ABSTRACT FROM AUTHOR]

Les auteurs s'intéressent au problème d'estimation des fonctions de régression qui présentent des discontinuités dans la première dérivée. Ils analysent le biais de l'estimateur de régression linéaire locale et de ses versions à noyau unilatéral droite et gauche afin de proposer une procédure d'estimation améliorée, fondée sur la sélection automatique du meilleur estimateur basé sur la somme des résidus carrés. Les auteurs fournissent des résultats théoriques ainsi qu'une étude numérique sur des données simulées et réelles. La revue canadienne de statistique 37: 453-475; 2009 © 2009 Société statistique du Canada [ABSTRACT FROM AUTHOR]

A class of approximate methods to solve operator equations of first kind with not exactly given input data is constructed. For involved methods their optimality by the order on sets of sourcewise represented solutions is proved and the bound of informational expenses is obtained. These algorithms are numerically implemented in an efficient way. An example of application of two such algorithms is given. [ABSTRACT FROM AUTHOR]

Abstract: We study the problem of discrepancy of finite point sets in the unit square with respect to convex polygons, when the directions of the edges are fixed, when the number of edges is bounded, as well as when no such restrictions are imposed. In all three cases, we obtain estimates for the supremum norm that are very close to best possible. [Copyright &y& Elsevier]

Assume that α is an irrational number with continued fraction expansion [ a 0; a 1, . . .] and convergents [InlineMediaObject not available: see fulltext.], n= 0, 1 . . . . Every positive integer N has a unique expansion N= b 0 q 0+ b 1 q 1+ . . . + b m q m , where the digits b i are nonnegative integers with b 0< a 1, b i ≤ a i +1 and such that b i = a i +1 implies b i −1=0, the so-called Ostrowski expansion of N to base α. On the other hand let c [0, x ) be the characteristic function of the half-open interval [0, x) and let [InlineMediaObject not available: see fulltext.] be the L 2-discrepancy of the sequence ( n α) mod 1, where { y} denotes the fractional part of the real number y. In this paper, we give an explicit formula for D*(2) N(α) entirely in terms of the digits b 0, . . . , b m . This formula enables one to compute the L 2-discrepancy in at most O(log4 N) steps, where the O-constant does not depend on α, while in the classical formulae for the L 2-discrepancy N 2/2 calculation steps are necessary. The fastest algorithm so far was found by S. Heinrich [3] and works (for all sequences) in O( N log N) steps. [ABSTRACT FROM AUTHOR]

A lower bound is established for the strip discrepancy of a broad class of point distributions. The bound implies unbounded strip discrepancy for equally weighted point distributions under favorable conditions. The methods of proof use notions from integral geometry. [ABSTRACT FROM AUTHOR]

We show that the graph isomorphism problem is hard under DLOGTIME uniform AC0 many-one reductions for the complexity classes NL, PL (probabilistic logarithmic space) for every logarithmic space modular class ModκL and for the class DET of problems NC1 reducible to the determinant. These are the strongest known hardness results for the graph isomorphism problem and imply a randomized logarithmic space reduction from the perfect matching problem to graph isomorphism. We also investigate hardness results for the graph automorphism problem. [ABSTRACT FROM AUTHOR]

We have computed true star-discrepancies D*(N) for Halton and Niederreiter point sequences in dimensions s=2, 3, 4, and 6 with N up to 250 000, 10 000, 2000 and 300, respectively. For comparison, we also calculated some L2 discrepancies T*. The mean behaviour of D*(N) can well be approximated by power laws with an exponent between about -0.7 and -0.9, which slowly decreases with N. This behaviour is far from the generally assumed asymptotic one ∼C(s)(logN)s/N. The factor between the true and the asymptotic behaviour increases strongly with s and reaches many orders of magnitude for large s. The ratios of D*(N) for different low discrepancy sequences are not proportional to the presumed asymptotic pre-factors C(s). Especially for the range of bases investigated, Niederreiter sequences have about the same D* as Halton ones in a range of N, which we conjecture to be at least of the order of 1010. [Copyright &y& Elsevier]

In this note we construct certain sequences of finite point sets in [0, 1)s(s ≥ 1) and give the upper bounds of their discrepancy. Furthermore we prove that these sequences are uniformly distrbuted in [0, 1)s. [ABSTRACT FROM AUTHOR]

A stochastic model for the generation of observed income distributions is used to provide an explanation for the Pareto law of incomes. The basic assumptions of the model are that the evolution of individual incomes follows Gibrat's law and that the population or workforce is growing at a fixed (probabilistic) rate. Analysis of the model suggests that Paretian behavior can occur in either or both tails of an income distribution. It is shown that the magnitude of the upper-tail Pareto exponent depends on the interaction between the distribution of the growth in incomes and the growth in the size of the earning population. In particular a small Pareto exponent can be expected to occur for a population exhibiting fast or highly variable growth in incomes coupled with relatively slow population growth. [ABSTRACT FROM AUTHOR]

Provides a way to compute minimal log discrepancies using arcs and jets. Definition and the basic properties of log discrepancies; Theorems of the proposed operation for computing log discrepancies; Definitions and properties of jet schemes.

We study distributions $\{\backslash Cal\; D\}\_N$ of N points in the unit square U2 with minimal order of L2-discrepancy ℒ2[$\{\backslash Cal\; D\}\_N$] < C(log N)1/2, where the constant C is independent of N. We present an approach that uses Walsh functions and can be generalized to higher dimensions. Bibliography: 19 titles. [ABSTRACT FROM AUTHOR]

Pereverzev (1995) consider ed Tikhonov regularization combined with a modified form of a projection method for obtaining stable approximate solutions for ill-posed operator equations. He showed, under a certain a priori choice of the regularization parameter and a specific smoothness assumption on the solution, that the method yields the optimal order with less computational information, in the sense of complexity, than the projection method considered by Plato and Vainikko (1990). In this paper we apply a modified form of the Arcangeli's discrepancy principle for choosing the regularization parameter, and show that the conclusions of Pereverzev still hold. In fact, we do the analysis using a modified form of the generalized Arcangeli's method suggested by Schock (1984) under more flexible smoothness assumption on the solution, as has been done by George and Nair (1998), and derive the optimal result as a special case. Moreover, we compare the computational complexity of the present method with two traditional projection methods in the case of a priori parameter choice, and also discuss the computational complexity required to implement the suggested discrepancy principle. [ABSTRACT FROM AUTHOR]

The article presents a micro-lesson on probability and symmetry, with regards to harmonic divergence, h = the summation of 1/n = infinity. It declares that the harmonic divergence has several perfect proofs. It suggests that the probabilistic micro-lesson in this article was not conceived as a proof of the harmonic divergence, it is just a fragment of discussion about records. It also presents an exercise to prove that P(Y =X) = 0. assuming that X and Y are independent random variables and the Y takes values in [0, q) and is uniformly distributed over that interval. It suggests that equation could be solved by using the symmetry.