Tree-valued resampling dynamics Martingale problems and applications

The measure-valued Fleming–Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the “individuals” in the population at a fixed time. The goal of the present paper is to replace this static point of view on the genealogies by an analysis of the evolution of genealogies. We encode the genealogy of the population as an (isometry class of an) ultra-metric space which is equipped with a probability measure. The space of ultra-metric measure spaces together with the Gromov-weak topology serves as state space for tree-valued processes. We use well-posed martingale problems to construct the tree-valued resampling dynamics of the evolving genealogies for both the finite population Moran model and the infinite population Fleming–Viot diffusion. We show that sufficient information about any ultra-metric measure space is contained in the distribution of the vector of subtree lengths obtained by sequentially sampled “individuals”. We give explicit formulas for the evolution of the Laplace transform of the distribution of finite subtrees under the tree-valued Fleming–Viot dynamics.     

Agent-based modelling and simulation of urban evacuation: relative effectiveness of simultaneous and staged evacuation strategies

This study investigates the effectiveness of simultaneous and staged evacuation strategies using agent-based simulation. In the simultaneous strategy, all residents are informed to evacuate simultaneously, whereas in the staged evacuation strategy, residents in different zones are organized to evacuate in an order based on different sequences of the zones within the affected area. This study uses an agent-based technique to model traffic flows at the level of individual vehicles and investigates the collective behaviours of evacuating vehicles. We conducted simulations using a microscopic simulation system called Paramics on three types of road network structures under different population densities. The three types of road network structures include a grid road structure, a ring road structure, and a real road structure from the City of San Marcos, Texas. Default rules in Paramics were used for trip generation, destination choice, and route choice. Simulation results indicate that (1) there is no evacuation strategy that can be considered as the best strategy across different road network structures, and the performance of the strategies depends on both road network structure and population density; (2) if the population density in the affected area is high and the underlying road network structure is a grid structure, then a staged evacuation strategy that alternates non-adjacent zones in the affected area is effective in reducing the overall evacuation time.     

随机交通网络渐近连通可靠性分析

应用原有拓扑法获得城市交通网络的拓扑结构图,利用对偶拓扑法得到交通网络的对偶图,建立交通网络的随机网络模型。定义交通网络的渐近连通可靠性,得到路段连通可靠性、路网规模及整个路网连通可靠性之间的定量关系,结合随机图论、大数定律、渐近方法等证明所得结论;通过实例说明结论的应用价值。     

Modeling the effects of variable external influences and demographic processes on innovation diffusion

In this paper, a nonlinear mathematical model for innovation diffusion is proposed and analyzed by considering the effects of variable external influences (cumulative marketing efforts) and human population (variable marketing potential) in a society. The change in the population density is caused by various demographic processes such as immigration, emigration, intrinsic growth rate, death rate, etc.Thus, the problem of innovation diffusion is governed by three dynamic variables, namely, non adopters’ density, adopters’ density and the cumulative density of external influences. The model is analyzed by using the stability theory of differential equations and computer simulation.The model analysis shows that the main effect of the increase in cumulative density of external influences is to make the adopter population density reach its equilibrium at a much faster rate. It further shows that the density of adopters’ population increases as the parameters related to increase in non adopters’ population density increase. The effects of various parameters in the model on the nature of existing single equilibrium have also been discussed by using numerical simulation. It is shown that parameters related to the growth of non adopters’ population density have stabilizing effects on the system.     

An analytical process of the spatio-temporal evolution of urban systems based on allometric and fractal ideas

This paper presents a computer-based analytical framework for the spatio-temporal evolution of urban systems using the ideas from the allometric growth associated with fractals. Both cities as systems and systems of cities follow the law of allometric growth, and the scaling factors of the allometric relations can compose the matrix equations as eigenfunctions. The fractal dimension arrays are just the eigenvectors of the scaling factor matrices while the numbers of variables are the greatest eigenvalues. The solutions of matrix equations can be employed to analyse city systems and evaluate relative levels of urban development. The method is applied to Hangzhou urban system of China. The results reveal clearly an urbanization process characterized as population concentration and an industrialization process characterized as industrial diffusion. The computation results are consistent with the reality, which indicate that the method is available for analyzing the spatio-temporal evolution of complex systems such as cities.     

An allometric scaling relation based on logistic growth of cities

The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed “exponential allometry”, which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the above mentioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed “logistic allometry”. The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.     

A REACTION–DIFFUSION EQUATION MODELING THE INVASION OF THE ARGENTINE ANT POPULATION,LINEPITHEMA HUMILE,AT JASPER RIDGE BIOLOGICAL PRESERVE

Abstract A continuous reaction–diffusion model is developed for the invasive Argentine ant population within a preserve in northern California. The model is a second‐order partial differential equation incorporating a logistic growth term. The dispersal distance traveled during the reproductive process of budding is used to estimate the diffusion coefficient. The model has two homogeneous steady states, one occurring at the propagation front where the Argentine ant population does not yet exist and one occurring where the population has reached carrying capacity. The traveling wave solutions of the model depict the population density for a given time and location. Using current research, parameter values for the model are estimated and a traveling wave solution for the average parameter values is numerically demonstrated.     

基于深度学习LSTM对交通流状态的预测

当今道路交通状态对城市管理和人们出行愈加重要,影响着人类生活的方方面面.以深圳交通为研究对象,由基础车辆数据和道路坐标构建了路网系统,从车辆速度和密度两个方面导出了交通流状态评价指数TSI.利用深度学习长短期记忆神经网络(LSTM)对车辆速度和密度两个指标进行预测,并通过对比极限学习机(ELM),时间序列(ARMA)和BP神经网络,进行仿真实验,结果表明相对于传统预测模型,所采用的LSTM网络具有更优的预测精确度和对远期预测的稳定性.最后利用预测结果计算出更能直观反映出道路交通拥堵情况的TSI指数,为人们提供了准确的交通状态预测.     

Concurrency and Commitment: Network Scheduling and Its Consequences for Diffusion 1

Network ties are thought to be concurrent—one can “have” many friends at once, for instance—but their concrete enactment is largely serial and episodic, guided by priorities that steer a person from one encounter to the next. Further, dyadic encounters require that two people be simultaneously available to interact, creating the need for coordinated scheduling. Here I study the consequences of scheduling for network diffusion, using a computer simulation that interposes a scheduling process between a pre-existing network and instances of contagion. The pace and extent of diffusion are shown to depend upon the interaction of network topology, contagion rule (on first-contact versus at some threshold), and whether actors try to remedy past scheduling imperfections. Scheduling turns central actors into diffusion bottlenecks, but can also trigger early adoption by giving actors false readings on the status of their network alters. The implications of scheduling extend beyond diffusion, to other outcomes such as decision-making, as well as to network evolution.     

面向集群创新网络异质企业的知识扩散建模及仿真研究

基于合作的集群创新网络知识扩散已经成为企业实现知识创新的重要手段,而集群创新网络知识扩散的动力学过程强烈依赖于异质企业间知识扩散能力的影响,为此,本文综合考虑了企业间不同接触数量、知识吸收和传播能力、知识淘汰率等异质性因素,建立了基于传染病理论的知识扩散模型,验证了由各异质因素构成的知识扩散再生数对知识扩散均衡和扩散效果的影响,并结合仿真实验进一步得出:在知识扩散前期,集群创新网络应发挥hub节点及异质网络的优势加快知识扩散,在中后期应注意企业关系发展的均衡性及企业接触邻居的规模性;相比过于强调知识交流的广泛性,加强企业传播能力和吸收能力的培养对网络知识扩散效果的提升更具意义;随着时间演化,企业知识淘汰率也会影响网络知识扩散的收敛情况。     

Mutation and recombination in a model of phenotype evolution

A model of phenotype evolution incorporating mutation and recombination is investigated. The model consists of an ordinary differential equation for the population density with respect to a continuous variable representing phenotype diversity. We prove that each solution converges for the weak^* topology to a Radon measure. Received November 29, 2000; accepted August 30, 2001.     

Optimizing winter road maintenance operations under real-time information

This paper introduces a real-time optimization model that can be used by maintenance managers to develop and evaluate alternative resources allocation plans for winter road maintenance operations. The model takes into account a wide range of road and weather condition factors such as road network topology, road class, weather forecasts, and contractual service levels, and produces a vehicle dispatch schedule that is optimal with respect to operating costs and quality of service. The model is then used in an analysis on a realistic case to illustrate the potential impact of improved information on winter maintenance operations.     

Fractal-based exponential distribution of urban density and self-affine fractal forms of cities

Urban population density always follows the exponential distribution and can be described with Clark’s model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark’s model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark’s model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.     

An evolution equation based approach to topology optimization

The objective of topology optimization is to find a mechanical structure with maximum stiffness and minimal amount of used material for given boundary conditions [2]. There are different approaches. Either the structure mass is held constant and the structure stiffness is increased or the amount of used material is constantly reduced while specific conditions are fulfilled. In contrast, we focus on the growth of a optimal structure from a void model space and solve this problem by introducing a variational problem considering the spatial distribution of structure mass (or density field) as variable [3]. By minimizing the Gibbs free energy according to Hamilton's principle in dynamics for dissipative processes, we are able to find an evolution equation for the internal variable describing the density field. Hence, our approach belongs to the growth strategies used for topology optimization. We introduce a Lagrange multiplier to control the total mass within the model space [1]. Thus, the numerical solution can be provided in a single finite element environment as known from material modeling. A regularization with a discontinuous Galerkin approach for the density field enables us to suppress the well-known checkerboarding phenomena while evaluating the evolution equation within each finite element separately [4]. Therefore, the density field is no additional field unknown but a Gauß-point quantity and the calculation effort is strongly reduced. Finally, we present solutions of optimized structures for different boundary problems. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nodal distance distributions in cluster flight spacecraft network

The high-speed flight of cluster flight spacecraft modules increases the uncertainty of network topology. In order to better design the orbital of the cluster flight spacecraft and improve the performance of cluster flight spacecraft network (CFSN), this paper studies the nodal distance distributions (NDDs). First, based on twin-satellites mode, the mobility model of nodes is established. And then by adopting empirical statistical method and curve fitting method, the solution of the nodal distance density function in the CFSN is obtained. Second, the probability density function is applied to the model distance-dependent path loss, and the probability density of path loss under the model is analyzed. Finally, the distributions of maximum and minimum distance among multiple nodes and the threshold range of nodal connection distance are derived, and the probabilistic connectivity matrix of any time slot in the orbital hyper-period and spatial–temporal evolution graphs under different thresholds is obtained. The analytical results verify the feasibility of the model and the approximate solution of the NDDs in this paper. This method also provides a theoretical reference for the nodal connection in irregular wireless networks.     

关于圆形和方形城市工作区道路交通面积的解析与比较

对于城市规划来讲，事先预测其工作区内所需道路面积，以尽量避免实际交通网络中发生拥挤阻塞，具有重要意义，在本文，我们通过考虑一个城市通勤高峰时期的车辆交通情况，并通过利用走行中的车辆占用道路面积这一概念，基于一个相对现实的模型，从理论上对圆形方形城市工作区推导了所需的道路面积，并将两者加以比较，以发现与其交通网络结构相关的工作区的相对有效形状。     

A personalized kinetic model of traffic flow

A kinetic model of traffic flow on roads is developed which takes into account not only the multilane structure of the road, but also the multifaced aspect of traffic in which different kinds of vehicles and of drivers interact together. Differentiation among the various types of individuals is accomplished by introducing, in the traffic simulation, a modeling methodology proper of sociobiological population dynamics. In particular, the evolution is described by a generalized Boltzmann model for several population density functions. On the other hand, the intrinsic character of the individual driver-vehicle, that is free to autonomously decide about his future, justifies the introduction of an independent linear stochastic term in the evolution equation, in addition tto the quadratic interaction one, that is uncommon in these models.     

基于网络等级特征与VMS的交叉巢式Logit模型

基于等级特征与可变信息板(VMS)研究了交叉巢式Logit(CNL)模型及网络交通流分配。综合幂函数与指数函数表示方法给出新的信息效用衰减因子,结合道路等级特征表示VMS对车流的影响系数及CNL模型的分配系数;给出等级结构道路网络的随机用户均衡条件下的交叉巢式Logit路径选择模型及其等价数学规划,并设计网络流分配算法。通过实例网络的计算与分析,得到一些有意义的结论:等级结构越显著的路网总出行时间费用越低且其分散参数(θ)弹性绝对值越大;对具有较强随机性的实际路网,若增加一定的确定性则节省更多网络总出行时间;道路网络中设置了VMS时总出行时间受分散参数的影响更小。     

A NUMERICAL STUDY OF THE SPRUCE BUDWORM REACTION‐DIFFUSION EQUATION WITH HOSTILE BOUNDARIES

ABSTRACT. One of the interesting single species reaction diffusion problems is the spruce budworm model describing insect dispersal behavior. In an earlier study, Singh et al. [7] considered the two‐dimensional spruce budworm model with density dependent diffusion balanced by an artificial wind equal to the population gradient. Here we extend the model by considering more realistic density dependent diffusion and advection with hostile boundaries. We solve this model using a splitting method in which advection, diffusion and reaction processes are separated. Various hostility conditions have been used at the boundary. The numerical results show that the population moves quickly to a steady state outbreak situation when the advective components due to the density dependent diffusion are included.     

Network modeling of chromatography by stochastic phenomena of adsorption,diffusion and convection

The limitation of macroscopic models to represent structural parameters, such as topology and morphology, as well as population effects, i.e. multi-molecules movement, in the modeling of chromatography systems has implications on the understanding of the phenomenological aspects that contribute to the separation mechanisms in porous media. The representation of the porous structure of chromatographic columns by a three-dimensional cubic network of interconnected sites allows a better analysis of the structural characteristics of the porous column and its connection with the phenomena of adsorption, diffusion and convection. In the present work the application of an interconnected cubic network model associated with a stochastic modeling of the adsorption, diffusion and convection phenomena leads to the proper representation of the dynamic aspects of the breakthrough curves related to separation processes in chromatographic columns. Therefore, it is possible to study the dynamics of solute retention from the molecules distribution in the separation processes throughout the column. Among the mass transfer mechanisms investigated, the convection showed to be closely related to the separation dynamics of chromatography, with the diffusion having little effects. The adsorption influenced both the separation dynamics and solute retention.