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Abstract: [E. Steingrímsson, Statistics on ordered partitions of sets, arXiv: math.CO/0605670] introduced several hard statistics on ordered set partitions and conjectured that their generating functions are related to the q-Stirling numbers of the second kind. In a previous paper, half of these conjectures have been proved by Ishikawa, Kasraoui and Zeng using the transfer-matrix method. In this paper, we shall give bijective proofs of all the conjectures of Steingrímsson. Our basic idea is to encode ordered set partitions by a kind of path diagrams and explore the rich combinatorial properties of the latter structure. As a bonus of our approach, we derive two new σ-partition interpretations of the -Stirling numbers of the second kind introduced by Wachs and White. We also discuss the connections with MacMahon''s theorem on the equidistribution of the inversion number and major index on words and give a partition version of his result. [Copyright &y& Elsevier]

Abstract: This paper describes a fast and active texture segmentation approach based on the orientation and the local variance. First, a set of feature images are extracted using the orientation and the local variance. To reduce the computational complexity, a separability measurement method, which is used for selecting four feature images with good separability in four orientations, is proposed in this paper. To improve the segmentation, we adopt a nonlinear diffusion filtering to smooth the four feature images. Finally, a variational framework incorporating these features in a level set based, unsupervised segmentation process is adopted. To improve the computational speed, instead of solving the Euler–Lagrange equation, we calculate the energy, with level set representation, to solve the variational framework. Segmentation results of various synthetic and real textured images has demonstrated that our method has good performance and efficiency. [Copyright &y& Elsevier]

Abstract: This paper distinguishes two categories of questions that the Price equation can help us answer. The two different types of questions require two different disciplines that are related, but nonetheless move in opposite directions. These disciplines are probability theory on the one hand and statistical inference on the other. In the literature on the Price equation this distinction is not made. As a result of this, questions that require a probability model are regularly approached with statistical tools. In this paper, we examine the possibilities of the Price equation for answering questions of either type. By spending extra attention on mathematical formalities, we avoid the two disciplines to get mixed up. After that, we look at some examples, both from kin selection and from group selection, that show how the inappropriate use of statistical terminology can put us on the wrong track. Statements that are ‘derived’ with the help of the Price equation are, therefore, in many cases not the answers they seem to be. Going through the derivations in reverse can, however, be helpful as a guide how to build proper (probabilistic) models that do give answers. [Copyright &y& Elsevier]

Abstract: The theory of quasi-arithmetic means represents a powerful tool in the study of covariance functions across space–time. In the present study we use quasi-arithmetic functionals to make inferences about the permissibility of averages of functions that are not, in general, permissible covariance functions. This is the case, e.g., of the geometric and harmonic averages, for which we obtain permissibility criteria. Also, some important inequalities involving covariance functions and preference relations as well as algebraic properties can be derived by means of the proposed approach. In particular, quasi-arithmetic covariances allow for ordering and preference relations, for a Jensen-type inequality and for a minimal and maximal element of their class. The general results shown in this paper are then applied to the study of spatial and spatio-temporal random fields. In particular, we discuss the representation and smoothness properties of a weakly stationary random field with a quasi-arithmetic covariance function. Also, we show that the generator of the quasi-arithmetic means can be used as a link function in order to build a space–time nonseparable structure starting from the spatial and temporal margins, a procedure that is technically sound for those working with copulas. Several examples of new families of stationary covariances obtainable with this procedure are shown. Finally, we use quasi-arithmetic functionals to generalise existing results concerning the construction of nonstationary spatial covariances, and discuss the applicability and limits of this generalisation. [Copyright &y& Elsevier]

Abstract: Permutation statistics and their connections to Young tableaux have played an important role in enumerative combinatorics. Fibonacci tableaux were defined in 1975 by Stanley, but very few statistics have been defined for these tableaux. In this paper we give definitions for several statistics on Fibonacci tableaux and make connections between these statistics and known statistics for permutations. These connections allow for equidistribution results to be given on the set of standard Fibonacci tableaux. [Copyright &y& Elsevier]

Abstract: The standard mathematical model for stepwise “slow-binding” enzyme inhibition assumes that the initial enzyme–inhibitor complex is always at equilibrium with the free component species and . This assumption implies that the dissociation rate constant is infinitely higher than the isomerization rate constant for . This paper presents a more general mathematical treatment, under the steady state approximation rather than the usual rapid-equilibrium approximation, whereby the two rate constants for the disappearance of are allowed to be comparable in magnitude. Experimentally relevant illustrative examples include discrimination between a single-step and a two-step mechanism for slow-binding inhibition kinetics. [Copyright &y& Elsevier]

Abstract: Autoregressive time series models of order p have parameters, the mean, the variance of the white noise and the p autoregressive parameters. Change in any of these over time is a sign of disturbance that is important to detect. The methods of this paper can test for change in any one of these parameters separately, or in any collection of them. They are available in forms that make one-sided tests possible, furthermore, they can be used to test for a temporary change. The test statistics are based on the efficient score vector. The large sample properties of the change-point estimator are also explored. [Copyright &y& Elsevier]

Abstract: In this paper we provide rather weak conditions on a distribution which would guarantee that the t-statistic of a random vector of order n follows the t-distribution with degrees of freedom. The results sharpen the earlier conclusions of Mauldon [Characterizing properties of statistical distributions, Quart. J. Math. 2(7) (1956) 155–160] and the more recent advances due to Bondesson [When is the t-statistic t-distributed, Sankhyā, Ser. A 45 (1983) 338–345]. The basic tool involved in the derivations is the vertical density representation originally suggested by Troutt [A theorem on the density of the density ordinate and an alternative interpretation of the Box–Muller method, Statistics 22(3) (1991) 463–466; Vertical density representation and a further remark on the Box–Muller method, Statistics 24 (1993) 81–83]. Several illustrative examples are presented. [Copyright &y& Elsevier]

This paper argues that the philosophical tradition of nominalism, as evident in the works of Pierre Gassendi, Thomas Hobbes, Isaac Barrow, and Isaac Newton, played an important role in the history of mathematics during the 17th century. I will argue that nominalist philosophy of mathematics offers new clarification of the development of a “constructivist” tradition in mathematical philosophy. This nominalist and constructivist tradition offered a way for contemporary mathematicians to discuss mathematical objects and magnitudes that did not assume these entities were real in a Platonic sense, and helped lay the groundwork for formalist and instrumentalist approaches in modern mathematics. [Copyright &y& Elsevier]

Cressie and Read (J. Roy. Statist. Soc. B 46 (1984) 440–464) introduced the power divergence statistics, Ra, as multinomial goodness-of-fit statistics. Each Ra has a limiting noncentral chi-square distribution under a local alternative and has a limiting normal distribution under a nonlocal alternative. Taneichi et al. (J. Multivariate Anal. 81 (2002) 335–359) derived an asymptotic approximation for the distribution of Ra under local alternatives. In this paper, using multivariate Edgeworth expansion for a continuous distribution, we show how the approximation based on the limiting normal distribution of Ra under nonlocal alternatives can be improved. We apply the expansion to the power approximation for Ra. The results of numerical investigation show that the proposed power approximation is very effective for the likelihood ratio test. [Copyright &y& Elsevier]

In this paper, we introduce a notion of oblivious keyword search (OKS). Let W be the set of possible keywords. In the commit phase, a database supplier T commits n data. In each transfer subphase, a user U can choose a keyword w∈W adaptively and find Search(w) without revealing w to T, where Search(w) is the set of all data which includes w as a keyword.We then show two efficient protocols such that the size of the commitments is only O(nB) regardless of the size of W, where B is the size of each data. It is formally proved that U learns nothing more than search(w) and T gains no information on the keywords which U searched for. We further present a more efficient adaptive OTkn protocol than the previous one [19] as an application of our first OKS protocol. [Copyright &y& Elsevier]

In this paper, we deal with a class of pseudoparabolic problems with integral boundary conditions. We will first establish an a priori estimate. Then, we prove the existence, uniqueness and continuous dependence of the solution upon the data. Finally, some extensions of the problem are given. [Copyright &y& Elsevier]

This paper deals with the global uniform exponential stability independent of delay of time-delay linear and time-invariant systems subject to point and distributed delays for the initial conditions being continuous real functions except possibly on a set of zero measure of bounded discontinuities. It is assumed that the delay-free system as well as an auxiliary one are globally uniformly exponentially stable and globally uniform exponential stability independent of delay, respectively. The auxiliary system is typically a part of the overall dynamics of the delayed system but not necessarily the isolated undelayed dynamics as usually assumed in the literature. Since there is a great freedom in setting such an auxiliary system, the obtained stability conditions are very useful in a wide class of practical applications. [Copyright &y& Elsevier]