Estimating spot volatility in the presence of infinite variation jumps

We propose a kernel estimator for the spot volatility of a semi-martingale at a given time point by using high frequency data, where the underlying process accommodates a jump part of infinite variation. The estimator is based on the representation of the characteristic function of Lévy processes. The consistency of the proposed estimator is established under some mild assumptions. By assuming that the jump part of the underlying process behaves like a symmetric stable Lévy process around 0, we establish the asymptotic normality of the proposed estimator. In particular, with a specific kernel function, the estimator is variance efficient. We conduct Monte Carlo simulation studies to assess our theoretical results and compare our estimator with existing ones.     

Kernels and perfectness in arc-local tournament digraphs

In this paper we give a characterization of kernel-perfect (and of critical kernel-imperfect) arc-local tournament digraphs. As a consequence, we prove that arc-local tournament digraphs satisfy a strenghtened form of the following interesting conjecture which constitutes a bridge between kernels and perfectness in digraphs, stated by C. Berge and P. Duchet in 1982: a graph G is perfect if and only if any normal orientation of G is kernel-perfect. We prove a variation of this conjecture for arc-local tournament orientable graphs. Also it is proved that normal arc-local tournament orientable graphs satisfy a stronger form of Berge's strong perfect graph conjecture.     

Information structures in the problem of predicting the outcomes of conflict situations

We consider the content and structure of teaching information in the problem of predicting the outcomes of conflicts, stated as a recognition problem in standard formulation. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 98–103.     

The domination and competition graphs of a tournament

Vertices x and y dominate a tournament T if for all vertices z ≠ x, y, either x beats z or y beats z. Let dom(T) be the graph on the vertices of T with edges between pairs of vertices that dominate T. We show that dom(T) is either an odd cycle with possible pendant vertices or a forest of caterpillars. While this is not a characterization, it does lead to considerable information about dom(T). Since dom(T) is the complement of the competition graph of the tournament formed by reversing the arcs of T, complementary results are obtained for the competition graph of a tournament. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 103–110, 1998     

On the existence of specified cycles in a tournament

For 2 ≦ p ≦n and n ≧ 3, D(n, p) denotes the digraph with n vertices obtained from a directed cycle of length n by changing the orientation of p- 1 consecutives edges. In this paper, we prove that every tournament of order n ≧ 7 contains D(n, p) for p = 2, 3, …, n. Furthermore, we determine the tournaments of order n, 3 ≦ n ≦ 6, which do not contain D(n, p) for some p.     

Undertaking data analysis of student outcomes as professional development for teachers

The study reports on collaborations with practitioners to examine the results of students’ performances on high stakes tests as a means to strengthen practitioners’ knowledge of probability and statistics and to empower their conduct of investigations on student performance. Four issues are summarized: the development of their statistical reasoning, their understanding of the meaning of and relationships among the concepts of validity, reliability and fairness as applied to testing, their introduction to the history of testing and its relationship to science, society and cultural inequality, and their reports of independent inquiries. Data on performance on pre- and post-tests demonstrate growth in teacher reasoning and in their professionalism in raising important issues about testing     

The maximum number of arc-disjoint arborescences in a tournament

In this article, we give the maximum number of arc-disjoint arborescences in a tournament or an oriented complete r-partite graph by means of the indegrees of its vertices.     

Estimating the intensities of harmonic signal sources by the method of L-problem of moments

An optimal estimation algorithm for the intensities of harmonic signal sources is constructed using the L-problem of moments.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 96–98, 1987.     

On the decisiveness of a game in a tournament

In sport tournaments in which teams are matched two at a time, it is useful for a variety of reasons to be able to quantify how important a particular game is. The need for such quantitative information has been addressed in the literature by several more or less simple measures of game importance. In this paper, we point out some of the drawbacks of those measures and we propose a different approach, which rather targets how decisive a game is with respect to the final victory. We give a definition of this idea of game decisiveness in terms of the uncertainty about the eventual winner prevailing in the tournament at the time of the game. As this uncertainty is strongly related to the notion of entropy of a probability distribution, our decisiveness measure is based on entropy-related concepts. We study the suggested decisiveness measure on two real tournaments, the 1988 NBA Championship Series and the UEFA 2012 European Football Championship (Euro 2012), and we show how well it agrees with what intuition suggests. Finally, we also use our decisiveness measure to objectively analyse the recent UEFA decision to expand the European Football Championship from 16 to 24 nations in the future, in terms of the overall attractiveness of the competition.     

Solving soliton equations with self-consistent sources by method of variation of parameters

Starting from the solutions of soliton equations and corresponding eigenfunctions obtained by Darboux transformation, we present a new method to solve soliton equations with self-consistent sources (SESCS) based on method of variation of parameters. The KdV equation with self-consistent sources (KdVSCS) is used as a model to illustrate this new method. In addition, we apply this method to construct some new solutions of the derivative nonlinear Schrödinger equation with self-consistent sources (DNLSSCS) such as phase solution, dark soliton solution, bright soliton solution and breather-type solution.     

多重点源自由面波运动规律数值模拟

基于带耗散源格林函数去奇异积分数值方法,建立了均匀流浸没下双点源自由面波高计算模型,研究在不同耗散系数、弗劳德数及不同点源距离下自由面波高的变化规律以及自由面波形等高线的变化规律.数值模拟结果与前人的数值结果作验证比对,吻合较好.     

Properties of non-simultaneous blow-up in heat equations coupled via different localized sources

This paper deals with u_t = Δu + u^m(x, t)e^pv(0,t), v_t = Δv + u^q(0, t)e^nv(x,t), subject to homogeneous Dirichlet boundary conditions. The complete classification on non-simultaneous and simultaneous blow-up is obtained by four sufficient and necessary conditions. It is interesting that, in some exponent region, large initial data u₀(v₀) leads to the blow-up of u(v), and in some betweenness, simultaneous blow-up occurs. For all of the nonnegative exponents, we find that u(v) blows up only at a single point if m > 1(n > 0), while u(v) blows up everywhere for 0 ? m ? 1 (n = 0). Moreover, blow-up rates are considered for both non-simultaneous and simultaneous blow-up solutions.     

A tournament of order 14 with disjoint Banks and Slater sets

It is shown in this note that there exists a tournament of order 14 with disjoint Banks and Slater sets. Previously, the smallest such tournament was reported to be of order 16. In addition, it is shown that 11 is the minimum order of a tournament in which the Slater set is not a subset of the Banks set.     

Information sources with different cost scales and the principle of conservation of entropy

Summary The aim of this paper is to provide a mathematically rigorous and sufficiently general treatment of the basic information-theoretic problems concerning sources with symbols of different costs and noiseless coding in a general sense. The main new concepts defined in this paper are the entropy rate (entropy per unit cost) of a source with respect to a stochastic cost scale and the encoding (in particular decodable encoding) of a source in a general sense. On the basis of these concepts, we prove some general theorems on the relation of entropy rates with respect to different cost scales and on the effect of encoding to the entropy rate. In particular, the principle of conservation of entropy and the noiseless coding theorem are proved under very general conditions.The main results of this research have been reported at the Second Congress of Bulgarian Mathematicians, Varna, August 1967, at the International Symposium on Information Theory, San Remo, September 1967 and at the Colloquium on Information Theory, Debrecen, September 1967.     

Characterizations of the 3-cycle count and backward length of a tournament

Measures of inconsistency or difference between a set of pairwise comparisons and the final ranking of alternatives, give valuable and useful information. In this paper, we present characterizations of two such measures, the 3-cycle count and the backward length. The characterizations provide insight into what exactly is measured and how measures differ in processing adjustments in a tournament.     

Models and algorithms for the scheduling of a doubles tennis training tournament

We address a doubles tennis scheduling problem in the context of a training tournament, and develop a 0–1 mixed-integer programming model that attempts to balance the partnership and the opponentship pairings among the players. We propose effective symmetry-defeating strategies that impose certain decision hierarchies within the model, which serve to significantly enhance algorithmic performance via their pruning effect. We also discuss the concept of symmetry compatible formulations, and highlight the importance of crafting formulations in discrete optimization in a fashion that enhances the interplay between the original model structure, branch-and-bound algorithms (as implemented in commercial packages such as CPLEX), and the structure of specific symmetry-defeating hierarchical constraints. Finally, various specialized heuristics are devised and are computationally evaluated along with the exact solution schemes using a set of realistic practical test problems.     

The number of pancyclic arcs in a k‐strong tournament

A tournament is a digraph, where there is precisely one arc between every pair of distinct vertices. An arc is pancyclic in a digraph D, if it belongs to a cycle of length l, for all 3 ≤ l ≤ |V (D) |. Let p(D) denote the number of pancyclic arcs in a digraph D and let h(D) denote the maximum number of pancyclic arcs belonging to the same Hamilton cycle of D. Note that p(D) ≥ h(D). Moon showed that h(T) ≥ 3 for all strong non‐trivial tournaments, T, and Havet showed that h(T) ≥ 5 for all 2‐strong tournaments T. We will show that if T is a k‐strong tournament, with k ≥ 2, then p(T) ≥ 1/2, nk and h(T) ≥ (k + 5)/2. This solves a conjecture by Havet, stating that there exists a constant α_k, such that p(T) ≥ α_k n, for all k‐strong tournaments, T, with k ≥ 2. Furthermore, the second results gives support for the conjecture h(T) ≥ 2k + 1, which was also stated by Havet. The previously best‐known bounds when k ≥ 2 were p(T) ≥ 2k + 3 and h(T) ≥ 5. © 2005 Wiley Periodicals, Inc. J Graph Theory     

The number of vertices whose out-arcs are pancyclic in a 2-strong tournament

An arc going out from a vertex x in a digraph is called an out-arc of x. Yao et al. [Discrete Appl. Math. 99 (2000) 245-249] proved that every strong tournament contains a vertex x such that all out-arcs of x are pancyclic. Recently, Yeo [J. Graph Theory 50 (2005) 212-219] proved that each 3-strong tournament contains two such vertices. In this paper, we confirm that Yeo's result is also true for 2-strong tournaments. Our proof implies a polynomial algorithm to find two such vertices.     

On the maximum cardinality of a consistent set of arcs in a random tournament

For any tournament T on n vertices, let h(T) denote the maximum number of edges in the intersection of T with a transitive tournament on the same vertex set. Sharpening a previous result of Spencer, it is proved that, if T_n denotes the random tournament on n vertices, then, $\text{P}$$\text{(h(T}{}_{\mathrm{n}}\text{) ≤}\text{1}\text{2}\text{(}{}_2{}^{\mathrm{n}}\text{) + 1.73n}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{) → 1}$ as n → ∞.