Analysis of cluster formations on planer cells based on genetic programming

This paper offers an analysis of cluster formations on planer cells comprised of multi-agents utilizing local interactions and state transitions based on Genetic Programming (GP) and its applications. First, we illustrate that if the states of agents are allowed to have continuous values, equilibrium is attained on the basis of the fixed-point theorem. We also show that if the agents are restricted to binary states, equilibrium is attained in an asymptotic sense. However, for agents characterized by more than one state, the attainment of equilibrium is not ensured. We examine our results by using a simulation wherein agents learn from past experiences based on GP. Finally, we demonstrate a system comprised of cluster formations on planer cells comprised of artificial agents, and apply this system to the clustering of employees in firms.     

Clustering and asymptotic behavior in opinion formation

We investigate the long time behavior of models of opinion formation. We consider the case of compactly supported interactions between agents which are also non-symmetric, including for instance the so-called Krause model. Because of the finite range of interaction, convergence to a unique consensus is not expected in general. We are nevertheless able to prove the convergence to a final equilibrium state composed of possibly several local consensus. This result had so far only been conjectured through numerical evidence. Because of the non-symmetry in the model, the analysis is delicate and is performed in two steps: First using entropy estimates to prove the formation of stable clusters and then studying the evolution in each cluster. We study both discrete and continuous in time models and give rates of convergence when those are available.     

混沌中的随机性分析及其在证券中的应用

本通过对混沌的整体秩序与局部随机关系的分析，讨论了当混沌时间序列的自相关函数呈负指数衰减时，我们可以提取混沌中的内在的近似随机的时间序列，并通过运用计量经济中的AR模型进行分析与模拟，模型拟合的结果很理想。由此我们得出对于一类非线性系统同样可以运用一些线性模型来作近似分析。     

Equilibrium States of Random Economies with Locally Interacting Agents and Solutions to Stochastic Variational Inequalities in 〈L1,L∞〉

We study a stochastic model of an economy with locally interacting agents. The basis of the study is a deterministic model of dynamic economic equilibrium proposed by Polterovich. We generalize Polterovich's theory, in particular, in two respects. We introduce stochastics and consider a version of the model with local interactions between the agents. The structure of the interactions is described in terms of random fields on a directed graph. Equilibrium states of the system are solutions to certain variational inequalities in spaces of random vectors. By analyzing these inequalities, we establish an existence theorem for equilibrium, which generalizes and refines a number of previous results.     

Models of shrinking clusters with applications to epidermal wound healing

Models of growing clusters, such as the Eden model and Diffusion Limited Aggregation (DLA), have been widely used to describe a variety of natural growth processes. In this paper, we develop models of shrinking clusters which we use to model epidermal wound healing. We present two approaches to modeling shrinking clusters. In the first approach, which is motivated by the Eden model, every point on the cluster periphery has equal chance of being healed. Noisy and noisefree versions of this model are investigated. In the second approach, DLA is employed in a unique way so that random walkers launched from infinity eventually reach the cluster and contribute to its reduction. Simulation results are presented which illustrate the evolution of the wound healing process for various wound shapes.     

Exploring communication networks to understand organizational crisis using exponential random graph models

In recent social network studies, exponential random graph (ERG) models have been used comprehensively to model global social network structure as a function of their local features. In this study, we describe the ERG models and demonstrate its use in modelling the changing communication network structure at Enron Corporation during the period of its disintegration. We illustrate the modelling on communication networks, and provide a new way of classifying networks and their performance based on the occurrence of their local features. Among several micro-level structures of ERG models, we find significant variation in the appearance of A2P (Alternating k-two-paths) network structure in the communication network during crisis period and non-crisis period. We also notice that the attribute of hierarchical positions of actors (i.e., high rank versus low rank staff) have impact on the evolution process of networks during crisis. These findings could be used in analyzing communication networks of dynamic project groups and their adaptation process during crisis which could lead to an improved understanding how communications network evolve and adapt during crisis.     

Simultaneous Model Selection via Rate-Distortion Theory,With Applications to Cluster and Significance Analysis of Gene Expression Data

High-dimensional data are prevalent across many application areas, and generate an ever-increasing demand for statistical methods of dimension reduction, such as cluster and significance analysis. One application area that has recently received much interest is the analysis of microarray gene expression data.

The results of cluster analysis are open to subjective interpretation. To facilitate the objective inference of such analyses, we use flexible parameterizations of the cluster means, paired with model selection, to generate sparse and easy-to-interpret representations of each cluster. Model selection in cluster analysis is combinatorial in the numbers of clusters and data dimensions, and thus presents a computationally challenging task.

In this article we introduce a model selection method based on rate-distortion theory, which allows us to turn the combinatorial model selection problem into a fast and simultaneous selection across clusters. The method is also applicable to model selection in significance analysis

We show that simultaneous model selection for cluster analysis generates objectively interpretable cluster models, and that the selection performance is competitive with a combinatorial search, at a fraction of the computational cost. Moreover, we show that the rate-distortion based significance analysis substantially increases the power compared with standard methods.

This article has supplementary material online.     

Fast simulation of large‐scale growth models

We give an algorithm that computes the final state of certain growth models without computing all intermediate states. Our technique is based on a “least action principle” which characterizes the odometer function of the growth process. Starting from an approximation for the odometer, we successively correct under‐ and overestimates and provably arrive at the correct final state. Internal diffusion‐limited aggregation (IDLA) is one of the models amenable to our technique. The boundary fluctuations in IDLA were recently proved to be at most logarithmic in the size of the growth cluster, but the constant in front of the logarithm is still not known. As an application of our method, we calculate the size of fluctuations over two orders of magnitude beyond previous simulations, and use the results to estimate this constant. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

Study of discrete automaton models of gene networks of nonregular structure using symbolic calculations

We introduce the discrete automaton models of gene networks with weight functions of vertices accounting for the various forms of the regulatory interaction of agents. We study the discrete mapping that describes the operation of a fragment of the gene network of the bacteria E. coli. For this mapping, we find its fixed points (stationary states) on using the SAT approach. We also study the mappings that are defined by the random graphs of the network which we generate in accordance with the Gilbert-Erdos-Renyi and Watts-Strogatz models. For these mappings, we find the fixed points and the length 2 and 3 cycles. This article can be regarded as a survey of our results on the discrete models of gene networks and the numerical methods for studying their operation.     

A random-key genetic algorithm for the generalized traveling salesman problem

The generalized traveling salesman problem is a variation of the well-known traveling salesman problem in which the set of nodes is divided into clusters; the objective is to find a minimum-cost tour passing through one node from each cluster. We present an effective heuristic for this problem. The method combines a genetic algorithm (GA) with a local tour improvement heuristic. Solutions are encoded using random keys, which circumvent the feasibility problems encountered when using traditional GA encodings. On a set of 41 standard test problems with symmetric distances and up to 442 nodes, the heuristic found solutions that were optimal in most cases and were within 1% of optimality in all but the largest problems, with computation times generally within 10 seconds. The heuristic is competitive with other heuristics published to date in both solution quality and computation time.     

The prize-collecting generalized minimum spanning tree problem

We introduce the prize-collecting generalized minimum spanning tree problem. In this problem a network of node clusters needs to be connected via a tree architecture using exactly one node per cluster. Nodes in each cluster compete by offering a payment for selection. This problem is NP-hard, and we describe several heuristic strategies, including local search and a genetic algorithm. Further, we present a simple and computationally efficient branch-and-cut algorithm. Our computational study indicates that our branch-and-cut algorithm finds optimal solutions for networks with up to 200 nodes within two hours of CPU time, while the heuristic search procedures rapidly find near-optimal solutions for all of the test instances.     

Black swans and white eagles: on mathematics and finance

It is often objected that we cannot use mathematical methods in finance because (1) finance is dominated by unpredictable unique events (the black swans), (2) there are qualitative effects that cannot be quantified, and (3) the laws themselves of finance keep on changing. In this paper we discuss these three objections, offering arguments to reject them. We begin by reviewing the development of the physical sciences, pointing out parallels that are relevant for our discussion. Modern science has abandoned the objective of describing reality and has adopted an operational point of view that regards physical laws as tools to connect observations. Modern science is no longer deterministic, but has accepted a fundamental uncertainty in physical laws both at micro and macroscopic levels. Unpredictable pivotal events exist in the physical sciences as well in finance but this does not lead us to question the use of mathematics in the physical sciences. On the contrary, using principles of safe design, we try to understand how to avoid and contain unpredictability. Financial markets are manmade artifacts with, as actors, a large number of interacting agents. If we so wish, we can reduce the level of uncertainty present in markets: But if we try to do so describing financial markets with simple mathematical laws, we find that these laws are not stable but change over time, eventually with sudden structural breaks. This makes the use of mathematical finance difficult but not impossible. We can forecast human decision-making processes, crucial in forecasting financial markets, at the statistical level in aggregate. From an operational point of view, we have the tools to understand and describe the behavior of large number of interacting agents. At the present stage of development of our science, we need to use the mathematics of adaptive systems, changing mathematical models in function of different market states. However, reductionism to a small number of basic laws remains a fundamental objective of financial economics as it is in the physical sciences.     

Computing the complexity for Schelling segregation models

The Schelling segregation models are “agent based” population models, where individual members of the population (agents) interact directly with other agents and move in space and time. In this note we study one-dimensional Schelling population models as finite dynamical systems. We define a natural notion of entropy which measures the complexity of the family of these dynamical systems. The entropy counts the asymptotic growth rate of the number of limit states. We find formulas and deduce precise asymptotics for the number of limit states, which enable us to explicitly compute the entropy.     

Instantaneous gelation in coagulation dynamics

The coagulation equations are a model for the dynamics of cluster growth in which clusters can coagulate via binary interactions to form larger clusters. For a certain class of rate coefficients we prove that the density is not conserved on any time interval.Dedicated to Klaus Kirchgässner on the occasion of his sixtieth birthday     

Second-order cluster consensus of multi-agent dynamical systems with impulsive effects

This paper discuss the cluster consensus of multi-agent dynamical systems (MADSs) with impulsive effects and coupling delays. Some sufficient conditions that guarantee cluster consensus in MADS are derived. In each cluster, agents update their position and velocity states according to a leader’s instantaneous information, and interactions among agents are uncertain. Furthermore, switching topology problem in MADS is considered by impulsive stability and adaptive strategy. Finally, numerical simulations are given to verify our theoretical analysis.     

Panel‐based stratified cluster sampling and analysis for photovoltaic outdoor measurements

We study a stratified multisite cluster‐sampling panel time series approach in order to analyse and evaluate the quality and reliability of produced items, motivated by the problem to sample and analyse multisite outdoor measurements from photovoltaic systems. The specific stratified sampling in spatial clusters reduces sampling costs and allows for heterogeneity as well as for the analysis of spatial correlations due to defects and damages that tend to occur in clusters. The analysis is based on weighted least squares using data‐dependent weights. We show that this does not affect consistency and asymptotic normality of the least squares estimator under the proposed sampling design under general conditions. The estimation of the relevant variance–covariance matrices is discussed in detail for various models including nested designs and random effects. The strata corresponding to damages or manufacturers are modelled via a quality feature by means of a threshold approach. The analysis of outdoor electroluminescence images shows that spatial correlations and local clusters may arise in such photovoltaic data. Further, relevant statistics such as the mean pixel intensity cannot be assumed to follow a Gaussian law. We investigate the proposed inferential tools in detail by simulations in order to assess the influence of spatial cluster correlations and serial correlations on the test's size and power. ©2016 The Authors. Applied Stochastic Models in Business and Industry published by John Wiley & Sons, Ltd.     

安全疏散模型研究

以四川桑枣中学师生逃生奇迹为背景,用初等数学建模方法建立3种疏散模型对此进行研究,找出人员逃生时间和速度、人与人之间间隙及其他变量之间的关系,并借助实测数据和经验数据对三种模型求解,用于推断四川桑枣中学师生能在1分36秒内成功逃生的可能性.结论是:组织单队(口字模型)疏散是不成功的,组织双队(吕字模型)疏散可以成功,但要把人与人前后之间距离(含人体本身厚度,单位:m)控制在[0.5,0.8]小范围内,速度(单位:m/s)控制在[1.2,1.8]小范围内.而组织三队(品字模型)疏散则更容易成功,控制间距扩大到[0.5,1.3]区间,疏散奔走速度扩大到[0.71,1.72]范围内便可安全疏散.     

Distribution Function of the Blow up Time of the Solution of an Anticipating Random Fatigue Equation

In this paper, we study the distribution function of the time of explosion of a stochastic differential equation modeling the length of the dominant crack due to fatigue.The main novelty is that initial condition is regarded as an anticipating random variable and the stochastic integral is in the forward sense.Under suitable conditions, we use the substitution formula from Russo and Vallois to find the local solution of this equation.Then, we find the law of blow up time by proving some results on barrier crossing probabilities of Brownian bridge.     

盈余管理计量模型效力的实证研究

本文以随机抽取的上海和深圳证券交易所的1000家被并购上市公司为样本,研究了盈余管理计量模型的检验效力问题。本文通过三种验证各模型效力的实证方法比较了6种盈余管理的计量模型。研究发现:第一类误差的方法认为Healy模型、修正的琼斯模型和前瞻性修正的琼斯模型能有效地检验出盈余管理行为:预测误差标准方法则认为前瞻性修正的琼斯模型是最优的模型:而根据对操纵性应计部分的短期效应的实证则认为Healy模型、修正的琼斯模型、KS模型和前瞻性修正的琼斯模型是较优的计量模型。在综合考虑各种实证结果和中国资本市场实际情况的基础上,认为前瞻性修正的琼斯模型在中国证券市场检验盈余管理行为的效力最强。     

The reverse effects of random perturbation on discrete systems for single and multiple population models

The natural species are likely to present several interesting and complex phenomena under random perturbations, which have been confirmed by simple mathematical models. The important questions are: how the random perturbations influence the dynamics of the discrete population models with multiple steady states or multiple species interactions? and is there any different effects for single species and multiple species models with random perturbation? To address those interesting questions, we have proposed the discrete single species model with two stable equilibria and the host-parasitoid model with Holling type functional response functions to address how the random perturbation affects the dynamics. The main results indicate that the random perturbation does not change the number of blurred orbits of the single species model with two stable steady states compared with results for the classical Ricker model with same random perturbation, but it can strength the stability. However, extensive numerical investigations depict that the random perturbation does not influence the complexities of the host-parasitoid models compared with the results for the models without perturbation, while it does increase the period of periodic orbits doubly. All those confirm that the random perturbation has a reverse effect on the dynamics of the discrete single and multiple population models, which could be applied in reality including pest control and resources management.