Sufficient Conditions for a Digraph to be Supereulerian

A (di)graph is supereulerian if it contains a spanning eulerian sub(di)graph. This property is a relaxation of hamiltonicity. Inspired by this analogy with hamiltonian cycles and by similar results in supereulerian graph theory, we analyze a number of sufficient Ore type conditions for a digraph to be supereulerian. Furthermore, we study the following conjecture due to Thomassé and the first author: if the arc‐connectivity of a digraph is not smaller than its independence number, then the digraph is supereulerian. As a support for this conjecture we prove it for digraphs that are semicomplete multipartite or quasitransitive and verify the analogous statement for undirected graphs.     

On the core of cost-revenue games: Minimum cost spanning tree games with revenues

In this paper, we analyze cost sharing problems arising from a general service by explicitly taking into account the generated revenues. To this cost-revenue sharing problem, we associate a cooperative game with transferable utility, called cost-revenue game. By considering cooperation among the agents using the general service, the value of a coalition is defined as the maximum net revenues that the coalition may obtain by means of cooperation. As a result, a coalition may profit from not allowing all its members to get the service that generates the revenues. We focus on the study of the core of cost-revenue games. Under the assumption that cooperation among the members of the grand coalition grants the use of the service under consideration to all its members, it is shown that a cost-revenue game has a nonempty core for any vector of revenues if, and only if, the dual game of the cost game has a large core. Using this result, we investigate minimum cost spanning tree games with revenues. We show that if every connection cost can take only two values (low or high cost), then, the corresponding minimum cost spanning tree game with revenues has a nonempty core. Furthermore, we provide an example of a minimum cost spanning tree game with revenues with an empty core where every connection cost can take only one of three values (low, medium, or high cost).     

改进的生成树遗传算法及其在物流配送成本优化中的应用

针对物流配送成本优化问题的特点,建立了数学模型,并对基本的生成树遗传算法进行了改进,同时详细阐述了改进的生成树编码的遗传算法在物流配送成本优化问题中的运用等关键技术.最后根据此算法设计了一个物流配送优化系统,解决了一个物流配送成本优化问题,效果良好.此系统对于中小型物流公司设计最优物流策略和降低物流成本有着很大的应用前景.     

Intraday volatility and network topological properties in the Korean stock market

We examine whether the relationship between market volatility and network properties in the low-frequency level can be applied to the high-frequency level. For the analysis, we use the minimum spanning tree (MST) method constructed from intraday Korean stock market data. The results show that the higher the market volatility is, the denser the MST of stocks becomes. The normalized tree length shows a strong negative relationship with market volatility, indicating that the distances between nodes are shorter when the market volatility is high. The mean occupation layer shows the tendency of having a smaller value in a higher volatility market. The maximum number of links becomes larger when the market volatility increases. All these network properties support the network being dense and shrinking in high market volatility conditions; that is, the degree of co-movement in financial market is reinforced in the intraday high-frequency level.     

Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

Generalized nonlinear master equations for local fluctuations: Dimensionality expansions and augmented mean field theory

By application of a projection operator technique we derive a formally exact generalization of the nonlinear mean field master equation introduced recently for the study of local fluctuations in a reacting medium. Our starting point is a phenomenological cell master equation. The results of our theory are applicable to the theory of a fluctuating hydrodynamic reacting system. The mean field equation is placed on a firm theoretical foundation by showing it to be the lowest order approximation in an expansion in the dimensionality of the physical space keeping the product of the number of nearest neighbors (an increasing function of dimensionality) and the typical diffusion coefficient constant. A more accurate nonlinear master equation that allows for the correlation and fluctuations in the environment of a given volume element is derived in the form of an augmented mean field equation.Work supported in part by a grant from the National Science Foundation.     

一种基于图论与熵的专家判断客观可信度的确定方法

本文给出一种群决策中确定专家判断可信度的方法，其主要思路是首先通过图论中最小生成树的方法提取专家判断矩阵的全部信息，其次，使用相对熵指标确定获得专家判断的最终结果，并同时衡量专家自身判断的统一程度，从而确定专家判断的相对客观可信度。最后，文章给出一个典型的算例以说明该方法的可行性和有效性。     

The expectation hypothesis of interest rates and network theory: The case of Brazil

This paper investigates the topological properties of the Brazilian term structure of interest rates network. We build the minimum spanning tree (MST), which is based on the concept of ultrametricity, using the correlation matrix for interest rates of different maturities. We show that the short-term interest rate is the most important within the interest rates network, which is in line with the Expectation Hypothesis of interest rates. Furthermore, we find that the Brazilian interest rates network forms clusters by maturity.     

The Lindblad and Redfield forms derived from the Born–Markov master equation without secular approximation and their applications

In this paper, we derive the Lindblad and Redfield forms of the master equation based on the Born–Markov master equation with and without the secular approximation for open multi-level quantum systems. The coefficients of the equations are re-evaluated according to the scheme in[(2019), Phys. Rev. A 99, 022118]. They are complex numbers rather than the real numbers obtained from traditional simplified methods. The dynamics of two models(one is an open threelevel quantum system model, and the other is the model of phycoerythrin 545(PE545) in a photosynthesis system) are studied. It is shown that the secular approximation and the simplified real coefficients may cause a small distortion of the dynamics in some environments, but a large distortion of the dynamics in others. These effects are discussed and characterized by studying the dynamics of nontrivial instances of multi-level systems in the presence of dissipation.     

高功率准分子激光主振荡功率放大系统光学元件的稳定性

为了分析高功率准分子激光主振荡功率放大(MOPA)系统中各光学元件稳定性对靶面光斑定位精度的影响,建立了分析模型,利用分析结果指导高稳定性镜架设计以满足系统实验需求。根据高功率准分子激光MOPA系统特点,有效地简化了系统光路,建立了系统光路模型;按照系统打靶精度要求,利用三维坐标变换和光线追迹法,计算得到了系统单个光学元件稳定性对靶面光斑定位精度的影响规律;最后,对自行设计的镜架进行了稳定性测量。计算结果表明,反射镜的旋转变化和透镜垂直光轴的平移变化是影响靶面光斑定位精度的主要因素,且主放大光路中反射镜在X方向和Y方向上最大的变化范围分别不能超过0.8和1.6μrad。实际测量结果表明,设计的镜架在X方向和Y方向最大的变化范围分别为0.6和0.81μrad,满足系统实验要求。