Diagonal F-Thresholds on Binomial Hypersurfaces

In this article, we study the diagonal F-threshold, that is, the F-threshold of the maximal ideal with respect to the maximal ideal itself. In particular, we give a formula of the diagonal F-thresholds for binomial hypersurfaces, and compare the diagonal F-thresholds with F-pure thresholds for strongly F-regular binomial hypersurfaces.

As a result, we prove that those diagonal F-thresholds always exist and they are rational numbers in that case.     

Binomial arithmetical rank of lattice ideals

 In this paper, we will show that a lattice ideal is a complete intersection if and only if its binomial arithmetical rank equals its height, if the characteristic of the base field k is zero. And we will give the condition that a binomial ideal equals a lattice ideal up to radical in the case of char k=0. Further, we will study the upper bound of the binomial arithmetical rank of lattice ideals and give a sharp bound for the lattice ideals of codimension two. Received: 12 June 2001 / Revised version: 22 July 2002     

The Symplectic Monoid

In this paper, we describe explicitly the symplectic monoid ? and its Renner monoid ? using elementary methods. We refine the Bruhat–Renner decomposition of ? and analyze in detail the length function on ?. We then show that every element of ? has a unique canonical form decomposition, which is an analogue of the canonical form of elements in Chevalley groups. We also compute the order of ? over a finite field, and as a consequence we obtain a new combinatorial identity.     

Triangular Decomposition of Composition Algebras of Domestic Canonical Algebras

Let A be a domestic canonical algebra over a finite field. In this article, we prove that the composition algebra C(A) of A has a triangular decomposition 𝒫·𝒯·? corresponding to the division of the indecomposable modules into the preprojectives, the regulars, and the preinjectives.     

Finiteness of polyhedral decompositions of cusped hyperbolic manifolds obtained by the Epstein-Penner's method

Epstein and Penner give a canonical method of decomposing a cusped hyperbolic manifold into ideal polyhedra. The decomposition depends on arbitrarily specified weights for the cusps. From the construction, it is rather obvious that there appear at most a finite number of decompositions if the given weights are slightly changed. However, since the space of weights is not compact, it is not clear whether the total number of such decompositions is finite. In this paper we prove that the number of polyhedral decompositions of a cusped hyperbolic manifold obtained by the Epstein-Penner's method is finite.

     

具有常红利边界的复合马尔可夫二项模型

主要讨论复合马尔可夫二项模型.在模型中引进一个常数红利边界策略,得到了Gerber-Shiu罚金函数所满足的线性方程组,且证明该方程组存在唯一解.最后,作为罚金函数的一些应用实例给出了一些具体风险量的计算公式.     

基于二项分布随机增长的无标度网络

提出—个具有随机增长的无标度网络模型．该模型的演化规则仍然是BA模型的增长和择优连接,但是每一时间间隔添加到网络中的边数是—个具有二项分布的随机变量．通过率方程方法,本文证明了该网络的度分布具有幂律尾部,该模型生成了—个无标度网络．     

Circuit decompositions of join‐covered graphs

In this paper, we focus our attention on join‐covered graphs, that is, ±1‐weighted graphs, without negative circuits, in which every edge lies in a zero‐weight circuit. Join covered graphs are a natural generalization of matching‐covered graphs. Many important properties of matching covered graphs, such as the existence of a canonical partition, tight cut decomposition and ear decomposition, have been generalized to join covered graphs by A. Seb? [5]. In this paper we prove that any two edges of a join‐covered graph lie on a zero‐weight circuit (under an equivalent weighting), generalize this statement to an arbitrary number of edges, and characterize minimal bipartite join‐covered graphs. © 2009 Wiley Periodicals, Inc. J Graph Theory 62, 220–233, 2009     

Epstein–Penner Decompositions and Thrice Punctured Spheres in Hyperbolic 3-Manifolds

Let M be a cusped hyperbolic 3-manifold containing an incompressible thrice punctured sphere S. Suppose that M is not the Whitehead link complement. We prove that a certain arc on S is isotopic to an edge of a Euclidean decomposition of M. By using the above result, we relate alternating knot diagrams and the canonical decompositions. Let K be an alternating hyperbolic knot. On a reduced alternating knot diagram of K, if we replace one of the crossings with a large number of half twists, the polar axis of the crossing is isotopic to an edge of the canonical decomposition for the resulting knot.     

Permutation Binomial Functions over Finite Fields

We consider binomial functions over a finite field of order 2ⁿ. Some necessary condition is found for such a binomial function to be a permutation. It is proved that there are no permutation binomial functions in the case that 2ⁿ ? 1 is prime. Permutation binomial functions are constructed in the case when n is composite and found for n ≥ 8.     

On the Canonical Decomposition of Quiver Representations

Kac introduced the notion of the canonical decomposition for a dimension vector of a quiver. Here we will give an efficient algorithm to compute the canonical decomposition. Our study of the canonical decomposition for quivers with three vertices gives us fractal-like pictures.     

Probabilistic inference with noisy-threshold models based on a CP tensor decomposition

The specification of conditional probability tables (CPTs) is a difficult task in the construction of probabilistic graphical models. Several types of canonical models have been proposed to ease that difficulty. Noisy-threshold models generalize the two most popular canonical models: the noisy-or and the noisy-and. When using the standard inference techniques the inference complexity is exponential with respect to the number of parents of a variable. More efficient inference techniques can be employed for CPTs that take a special form. CPTs can be viewed as tensors. Tensors can be decomposed into linear combinations of rank-one tensors, where a rank-one tensor is an outer product of vectors. Such decomposition is referred to as Canonical Polyadic (CP) or CANDECOMP-PARAFAC (CP) decomposition. The tensor decomposition offers a compact representation of CPTs which can be efficiently utilized in probabilistic inference. In this paper we propose a CP decomposition of tensors corresponding to CPTs of threshold functions, exactly ℓ-out-of-k functions, and their noisy counterparts. We prove results about the symmetric rank of these tensors in the real and complex domains. The proofs are constructive and provide methods for CP decomposition of these tensors. An analytical and experimental comparison with the parent-divorcing method (which also has a polynomial complexity) shows superiority of the CP decomposition-based method. The experiments were performed on subnetworks of the well-known QMRT-DT network generalized by replacing noisy-or by noisy-threshold models.     

Binomial and factorial congruences for Fq[t]

We present several elementary theorems, observations and questions related to the theme of congruences satisfied by binomial coefficients and factorials modulo primes (or prime powers) in the setting of polynomial ring over a finite field. When we look at the factorial of n or the binomial coefficient ‘n choose m’ in this setting, though the values are in a function field, n and m can be usual integers, polynomials or mixed. Thus there are several interesting analogs of the well-known theorems of Lucas, Wilson etc. with quite different proofs and new phenomena.     

负二项分布随机变量的分解定理

给出了负二项分布的分解定理,并进一步研究了负二项分布的有关性质和近似计算公式.在复杂排队系统中离散状态下顾客等待时间分布的概率计算中起到了重要作用.     

Binomial edge ideals and bounds for their regularity

Journal of Algebraic Combinatorics - Let G be a simple graph on n vertices and $$J_G$$ denote the corresponding binomial edge ideal in $$S = K[x_1, \ldots , x_n, y_1, \ldots , y_n].$$ We prove that...     

双二项风险模型的破产概率

首先将经典的复合二项风险模型推广到保费到达过程与个体索赔过程是两个相互独立的二项过程的一种新模型，然后运用两种方法得出破产概率满足的一般公式和Lundberg不等式．     

关于二项分布的强偏差定理

利用分析方法建立了用不等式表示的用渐近平均对数似然比刻划的服从二项分布的随机变量序列的强偏差定理,作为推论得到了服从二项分布的相依随机变量序列的强大数定律.     

Two-Parametric Compound Binomial Approximations

We consider two-parametric compound binomial approximation of the generalized Poisson binomial distribution. We show that the accuracy of approximation essentially depends on the symmetry or shifting of distributions and construct asymptotic expansions. For the proofs, we combine the properties of norms with the results for convolutions of symmetric and shifted distributions. In the lattice case, we use the characteristic function method. In the case of almost binomial approximation, we apply Steins method.__________Published in Lietuvos Matematikos Rinkinys, Vol. 44, No. 4, pp. 443–466, October–December, 2004.     

A Remark on the Fourier Pairing and the Binomial Formula for the Macdonald Polynomials

We concisely and directly prove that the interpolation Macdonald polynomials are orthogonal with respect to the Fourier pairing and briefly discuss immediate applications of this fact, in particular, to the symmetry of the Fourier pairing and to the binomial formula.     

Log canonical thresholds of binomial ideals

We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming. Dedicated to Professor Toshiyuki Katsura on the occasion of his sixtieth birthday