Equilibrium in semimonotone market games

This paper analyzes the existence of equilibrium for a class of market games in which agents are allowed to follow different patterns of behaviour, including cases where the strategy sets are neither compact nor convex. Agent’s behaviour is modelled in terms of “inverse reply correspondences” (mappings that associate to each agent’s strategy those outcomes that she finds acceptable). Sufficient conditions for an equilibrium to exist are provided     

A packet filter placement problem with application to defense against spoofed denial of service attacks

We analyze a problem in computer network security, wherein packet filters are deployed to defend a network against spoofed denial of service attacks. Information on the Internet is transmitted by the exchange of IP packets, which must declare their origin and destination addresses. A route-based packet filter verifies whether the purported origin of a packet is correct with respect to the current route map. We examine the optimization problem of finding a minimum cardinality set of nodes to filter in the network such that no spoofed packet can reach its destination. We prove that this problem is NP-hard, and derive properties that explicitly relate the filter placement problem to the vertex cover problem. We identify topologies and routing policies for which a polynomial-time solution to the minimum filter placement problem exists, and prove that under certain routing conditions a greedy heuristic for the filter placement problem yields an optimal solution.     

Minimum entropy orientations

We study graph orientations that minimize the entropy of the in-degree sequence. We prove that the minimum entropy orientation problem is NP-hard even if the graph is planar, and that there exists a simple linear-time algorithm that returns an approximate solution with an additive error guarantee of 1 bit.     

极大全控点临界图

图G的点集S如果满足:VG-S(或VG)中每个点相邻于S中的某个点(或而不是它本身),则称点集S是一个控制集(或全控制集).图G的所有控制集(或全控制集)中最小基数的控制集(或全控制集)中的点数,称为控制数(或全控数),记为γ(G)(或γt(G)).在这篇文章中我们特征化γt-临界图且满足γt(G)=n-Δ(G)的图特征,这回答了Goddard等人提出的一个问题.     

Numerical simulation of two-dimensional soap froth

The temporal evolution of two-dimensional foam is studied by event-driven numerical simulations based on different types of models. It is shown that most of the dynamical and topological features seen in experimental measurements can be reproduced. The average area of cells scales linearly with time and the distribution of n-sided cells can be compared with known results. The topological models regarding the lengths of the boundaries yield the best results among the models studied.     

Two-loop vertices in quantum field theory: infrared convergent scalar configurations

A comprehensive study is performed of general massive, scalar, two-loop Feynman diagrams with three external legs. Algorithms for their numerical evaluation are introduced and discussed, numerical results are shown for all different topologies and comparisons with analytical results, whenever available, are performed. An internal cross-check, based on alternative procedures, is also applied. The analysis of infrared divergent configurations, as well as the treatment of tensor integrals, will be discussed in two forthcoming papers.     

Uncountable families of vertex-transitive graphs of finite degree

We prove that the set of vertex-transitive graphs of finite degree is uncountably large.     

Laplacian integral graphs in S(a, b)

Let G_n,m be the family of graphs with n vertices and m edges, when n and m are previously given. It is well-known that there is a subset of G_n,m constituted by graphs G such that the vertex connectivity, the edge connectivity, and the minimum degree are all equal. In this paper, S(a, b)-classes of connected (a, b)-linear graphs with n vertices and m edges are described, where m is given as a function of a,b∈N/2. Some of them have extremal graphs for which the equalities above are extended to algebraic connectivity. These graphs are Laplacian integral although they are not threshold graphs. However, we do build threshold graphs in S(a, b).     

环烷烃及烷烃的折光指数与结构的关系研究

以分子拓扑学点价和自相关函数研究为基础,设计开发出一种新的以点价计算为基础的结构信息自相关拓扑指数tX.基于多元线性回归技术建立了对环烷烃及其烷烃的折光指数作出估算的定量结构性质关系.点价被定义为βi,由βi建构结构信息自相关拓扑指数tX.得到了它们与64种环烷烃的折光指数(nD)的二元回归方程和与27种烷烃的折光指数的二元回归方程.对环烷烃和烷烃折光指数的计算结果表明,计算值与实验值的一致性令人满意,平均误差为0. 25% .利用建立的模型,对另外5种烷烃的折光指数进行了预测.