Global convergence of the Euler‐Poisson system for ion dynamics

We consider smooth solutions of the Euler‐Poisson system for ion dynamics in which the electron density is replaced by a Boltzmann relation. The system arises in the modeling of plasmas, where appear two small parameters, the relaxation time and the Debye length. When the initial data are sufficiently close to constant equilibrium states, we prove the convergence of the system for all time, as each of the parameters goes to zero. The limit systems are drift‐diffusion equations and compressible Euler equations. The proof is based on uniform energy estimates and compactness arguments.     

Proof of the local REM conjecture for number partitioning. II. Growing energy scales

We continue our analysis of the number partitioning problem with n weights chosen i.i.d. from some fixed probability distribution with density ρ. In Part I of this work, we established the so‐called local REM conjecture of Bauke, Franz and Mertens. Namely, we showed that, as n → ∞, the suitably rescaled energy spectrum above some fixed scale α tends to a Poisson process with density one, and the partitions corresponding to these energies become asymptotically uncorrelated. In this part, we analyze the number partitioning problem for energy scales α_n that grow with n, and show that the local REM conjecture holds as long as n^‐1/4α_n → 0, and fails if α_n grows like κn^1/4 with κ > 0. We also consider the SK‐spin glass model, and show that it has an analogous threshold: the local REM conjecture holds for energies of order o(n), and fails if the energies grow like κn with κ > 0. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2009     

Compound Poisson Approximation of the Number of Exceedances in Gaussian Sequences

Consider a finite sequence of Gaussian random variables. Count the number of exceedances of some level a, i.e. the number of values exceeding the level. Let this level and the length of the sequence increase simultaneously so that the expected number of exceedances remains fixed. It is well-known that if the long-range dependence is not too strong, the number of exceeding points converges in distribution to a Poisson distribution. However, for sequences with some individual large correlations, the Poisson convergence is slow due to clumping. Using Steins method we show that, at least for m-dependent sequences, the rate of convergence is improved by using compound Poisson as approximating distribution. An explicit bound for the convergence rate is derived for the compound Poisson approximation, and also for a subclass of the compound Poisson distribution, where only clumps of size two are considered. Results from numerical calculations and simulations are also presented.     

Co‐existence of Poisson and non‐Poisson processes in ordered parallel multilane pedestrian traffic

We show that non‐Poisson and Poisson processes can coexist in ordered parallel multilane pedestrian traffic, in the presence of lane switching which asymmetrically benefits the switchers and nonswitchers. Pedestrians join at the tail end of a queue and transact at the opposite front end. Their aim is to complete a transaction within the shortest possible time, and they can transfer to a shorter queue with probability p_s. Traffic is described by the utilization parameter U = λ〈t_s〉/N, where λ is the average rate of pedestrians entering the system, 〈t_s〉 is the average transaction time, and N is the number of lanes. Using an agent‐based model, we investigate the dependence of the average completion time 〈t_c〉 with variable K = 1 + (1 ? U)^?1 for different N and 〈t_s〉 values. In the absence of switching (p_s = 0), we found that 〈t_c〉 ∝ K^τ, where τ ≈ 1 regardless of N and 〈t_s〉. Lane switching (p_s = 1) reduces 〈t_c〉 for a given K, but its characteristic dependence with K differs for nonswitchers and switchers in the same traffic system. For the nonswitchers, 〈t_c〉 ∝ K^τ, where τ < 1. At low K values, switchers have a larger 〈t_c〉 that also increases more rapidly with K. At large K, the increase rates become equal for both. For nonswitchers, the possible t_c values obey an exponentially decaying probability density function p(t_c). The switchers on the other hand, are described by a fat‐tailed p(t_c) implying that a few are penalized with t_c values that are considerably longer than any of those experienced by nonswitchers. © 2006 Wiley Periodicals, Inc. Complexity 11: 35–42, 2006     

Boundary value problem for the N‐dimensional time periodic Vlasov–Poisson system

In this work, we study the existence of time periodic weak solution for the N‐dimensional Vlasov–Poisson system with boundary conditions. We start by constructing time periodic solutions with compact support in momentum and bounded electric field for a regularized system. Then, the a priori estimates follow by computations involving the conservation laws of mass, momentum and energy. One of the key point is to impose a geometric hypothesis on the domain: we suppose that its boundary is strictly star‐shaped with respect to some point of the domain. These results apply for both classical or relativistic case and for systems with several species of particles. Copyright © 2006 John Wiley & Sons, Ltd.     

Poisson evolution in word selection

This paper presents the finding that the invocation of new words in human language samples is governed by a slowly changing Poisson process. The time dependent rate constant for this process has the form

λ(t) = λ₁(1−λ₂t)e^-λ₂t+λ₃(1−λ₄t)e^-λ₄t+λ₅

, where

λ_i > 0, I=1,…,5

.

This form implies that there are opening, middle and final phases to the introduction of new words, each distinguished by a dominant rate constant, or equivalently, rate of decay. With the occasional exception of the phase transition from beginning to middle, the rate λ(t) decays monotonically. Thus, λ(t) quantifies how the penchant of humans to introduce new words declines with the progression of their narratives, written or spoken.     

Estimating retail demand with Poisson mixtures and out‐of‐sample likelihood

Estimation of retail demand is critical to decisions about procuring, shipping, and shelving. The idea of Poisson demand process is central to retail inventory management and numerous studies suggest that negative binomial (NB) distribution characterize retail demand well. In this study, we reassess the adequacy of estimating retail demand with the NB distribution. We propose two Poisson mixtures—the Poisson–Tweedie family (PTF) and the Conway–Maxwell–Poisson distribution—as generic alternatives to the NB distribution. On the basis of the principle of likelihood and information theory, we adopt out‐of‐sample likelihood as a metric for model selection. We test the procedure on consumer demand for 580 stock‐keeping unit store sales datasets. Overall the PTF and the Conway–Maxwell–Poisson distribution outperform the NB distribution for 70% of the tested samples. As a general case of the NB model, the PTF has particularly strong performance for datasets with relatively small means and high dispersion. Our finding carries useful implications for researchers and practitioners who seek for flexible alternatives to the oft‐used NB distribution in characterizing retail demand. Copyright © 2013 John Wiley & Sons, Ltd.     

Random k‐SAT and the power of two choices

We study an Achlioptas‐process version of the random k‐SAT process: a bounded number of k‐clauses are drawn uniformly at random at each step, and exactly one added to the growing formula according to a particular rule. We prove the existence of a rule that shifts the satisfiability threshold. This extends a well‐studied area of probabilistic combinatorics (Achlioptas processes) to random CSP's. In particular, while a rule to delay the 2‐SAT threshold was known previously, this is the first proof of a rule to shift the threshold of k‐SAT for . We then propose a gap decision problem based upon this semi‐random model. The aim of the problem is to investigate the hardness of the random k‐SAT decision problem, as opposed to the problem of finding an assignment or certificate of unsatisfiability. Finally, we discuss connections to the study of Achlioptas random graph processes. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 163–173, 2015     

Distribution free tests for comparing trends in Poisson series

Tests are presented for comparing trends in the rate of occurence of events for two Poisson series. The tests are based on a product model which is similar to the one proposed by Cox [2]. The model allows arbitrary trends in the individual series. Although the density function of the observable variables does not belong to the exponential family, the method often used for exponential families is shown to be applicable for constructing the tests.     

On the central limit theorem for the stationary Poisson process of compact sets

Stochastic geometry models based on a stationary Poisson point process of compact subsets of the Euclidean space are examined. Random measures on ?^d, derived from these processes using Hausdorff and projection measures are studied. The central limit theorem is formulated in a way which enables comparison of the various estimators of the intensity of the produced random measures. Approximate confidence intervals for the intensity are constructed. Their use is demonstrated in an example of length intensity estimation for the segment processes. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Extremal graphs for the k‐flower

The Turán number of a graph H, , is the maximum number of edges in any graph of order n that does not contain an H as a subgraph. A graph on vertices consisting of k triangles that intersect in exactly one common vertex is called a k‐fan, and a graph consisting of k cycles that intersect in exactly one common vertex is called a k‐flower. In this article, we determine the Turán number of any k‐flower containing at least one odd cycle and characterize all extremal graphs provided n is sufficiently large. Erdős, Füredi, Gould, and Gunderson determined the Turán number for the k‐fan. Our result is a generalization of their result. The addition aim of this article is to draw attention to a powerful tool, the so‐called progressive induction lemma of Simonovits.     

Packing k‐edge trees in graphs of restricted vertex degrees

Let denote the set of graphs with each vertex of degree at least r and at most s, v(G) the number of vertices, and τ_k (G) the maximum number of disjoint k‐edge trees in G. In this paper we show that

• (a1) if G ∈ and s ≥ 4, then τ₂(G) ≥ v(G)/(s + 1),
• (a2) if G ∈ and G has no 5‐vertex components, then τ₂(G) ≥ v(G)4,
• (a3) if G ∈ and G has no k‐vertex component, where k ≥ 2 and s ≥ 3, then τ_k(G) ≥ (v(G) ‐k)/(sk ‐ k + 1), and
• (a4) the above bounds are attained for infinitely many connected graphs.

Our proofs provide polynomial time algorithms for finding the corresponding packings in a graph. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 306–324, 2007     

Inside the critical window for cohomology of random k‐complexes

We prove sharper versions of theorems of Linial–Meshulam and Meshulam–Wallach which describe the behavior for ‐cohomology of a random k‐dimensional simplicial complex within a narrow transition window. In particular, we show that if Y is a random k‐dimensional simplicial complex with each k‐simplex appearing i.i.d. with probability with and fixed, then the dimension of cohomology is asymptotically Poisson distributed with mean . In the k = 2 case we also prove that in an accompanying growth process, with high probability, vanishes exactly at the moment when the last ‐simplex gets covered by a k‐simplex, a higher‐dimensional analogue of a “stopping time” theorem about connectivity of random graphs due to Bollobás and Thomason. Random Struct. Alg., 2015 © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 102–124, 2016     

Two Tikhonov‐type regularization methods for inverse source problem on the Poisson equation

In this paper, we investigate a problem of the identification of an unknown source on Poisson equation from some fixed location. A conditional stability estimate for an inverse heat source problem is proved. We show that such a problem is mildly ill‐posed and further present two Tikhonov‐type regularization methods (a generalized Tikhonov regularization method and a simplified generalized Tikhonov regularization method) to deal with this problem. Convergence estimates are presented under the a priori choice of the regularization parameter. Numerical results are presented to illustrate the accuracy and efficiency of our methods. Copyright © 2012 John Wiley & Sons, Ltd.     

A fourth‐order Hermitian box‐scheme with fast solver for the Poisson problem in a cube

We present a fourth‐order Hermitian box‐scheme (HB‐scheme) for the Poisson problem in a cube. A single‐nonstaggered regular grid is used supporting the discrete unknowns u and . The scheme is fourth‐order accurate for u and in norm. The fast numerical resolution uses a matrix capacitance method, resulting in a computational complexity of . Numerical results are reported on several examples including nonseparable problems. The present scheme is the extension to the three‐dimensional case of the HB‐scheme presented in Abbas and Croisille [J Sci Comp 49 (2011), 239–267]. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 609–629, 2015     

Coupling methods in connection with Poisson process approximation

Motivated by a simple probabilistic model for the radioactive decay, we show thatSerfling's [1978] approach to Poisson approximation using coupling techniques can in a natural way also be applied to Poisson process approximation. This provides at the same time uniform estimations for the deviation of a Markov-Bernoulli process from the approximating Poisson process with respect to the total variation distance. An application to quasirandom input queuing models is also given.     

Cycles with two blocks in k‐chromatic digraphs

Let k and ℓ be positive integers. A cycle with two blocks is a digraph obtained by an orientation of an undirected cycle, which consists of two internally (vertex) disjoint paths of lengths at least k and ℓ, respectively, from a vertex to another one. A problem of Addario‐Berry, Havet and Thomassé [J. Combin. Theory Ser. B 97 (2007), 620–626] asked if, given positive integers k and ℓ such that , any strongly connected digraph D containing no has chromatic number at most . In this article, we show that such digraph D has chromatic number at most , improving the previous upper bound of Cohen et al. [Subdivisions of oriented cycles in digraphs with large chromatic number, to appear]. We also show that if in addition D is Hamiltonian, then its underlying simple graph is ‐degenerate and thus the chromatic number of D is at most , which is tight.     

防洪风险分析中的一个二元标值犘狅犻狊狊狅狀点过程模型

该文将洪水的大小和持续时间作为防洪设施的工程风险中不可忽略的因素,提出了以洪水的大小和持续时间为标值的二元标值Ｐｏｉｓｓｏｎ点过程模型,给出了防洪综合风险率的计算公式,并进行了实例计算．     

Existence of global weak solutions for Navier‐Stokes‐Poisson equations with quantum effect and convergence to incompressible Navier‐Stokes equations

In this paper, we consider a three dimensional quantum Navier‐Stokes‐Poisson equations. Existence of global weak solutions is obtained, and convergence toward the classical solution of the incompressible Navier‐Stokes equation is rigorously proven for well prepared initial data. Furthermore, the associated convergence rates are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.