面向SNS大数据的捕获移出模型抽样估计

捕获移出模型起源于生物种群调查和特殊社会网络的研究,是一种复杂抽样方法,一般用于对不确定群体的总量规模和方差进行估计。本文将改进的捕获移出模型应用到社交网络传播规模的抽样估计中,对网络信息的传播范围和波及人群进行了初步估计,并以近期北京频繁出现的"雾霾"事件的自由传播为例进行了实证分析。研究表明,捕获移出模型可以对社交网络中的热点事件的传播规模和再传播的概率进行有效估计,从而说明社交网络已逐渐成为公共话语空间的重要传播路径和传播方式。面对社交网络的迅速蔓延,本文对大数据环境下的抽样估计方法也进行了初步的探索和实践。     

互惠系统的最优脉冲捕获

对两种群互惠系统的脉冲捕获问题进行了全面的研究.确定了在被捕获种群达到一定数量时,再进行脉冲捕获的最优捕获策略.这样既维持了种群的生态平衡,又使我们在捕获过程中的获利最大.     

自治单种群模型及其最优捕获策略

本文用一种新的方法,讨论了单种群生物资源的捕获优化问题.分别以单位时间最大可持续捕获量和单位时间最大净利润为管理目标,得到一类自治单种群捕获模型的最优捕获策略,所得结果包括了文献中研究过的几乎所有自治单种群捕获模型的相应研究结果.     

一类随机模型的最优捕获问题研究

在Volterra两种群竞争模型的基础上,构造了随机的具有捕获的两种群竞争模型,研究讨论了捕获对种群生长过程的影响和如何实现最优捕获等问题.从确定性模型入手,深入讨论随机竞争模型的收获最优问题.通过对捕获强度E和贴现率等的估计与讨论,计算出了最优捕获强度最优捕获量最优经济收益.     

一类自治单种群模型及其最优捕获策略

用一种新的方法,讨论了单种群生物资源的捕获优化问题.分别以单位时间最大可持续捕获量和单位时间最大净利润为管理目标,得到一类自治单种群捕获模型的最优捕获策略,所得结果包括了文献中研究过的几乎所有自治单种群捕获模型的相应研究结果.     

具周期系数的单种群模型及其最优捕获策略

该文用一种新的方法, 讨论了单种群生物资源的捕获优化问题.以最大的可持续单位时间捕获量为管理目标, 得到一类非自治单种群捕获模型的最优捕获策略, 所得结果包括了文献中研究过的几乎所有单种群捕获模型的相应研究结果.     

一种特殊分形网络的平均加权捕获时间[英文]

本文构造一个具有分形几何特点的特殊网络.将网络中心层中的节点作为陷阱点,选择节点和边都加权的方法来研究陷阱捕获问题,并得出的加权平均捕获时间的精确解析公式.     

数值分析在波束扫描与捕获问题中的应用研究

建立了雷达波束扫描与捕获问题的运动学模型和方程,通过计算得到一组密集的数据.对这组数据进行数值分析,得到飞机被捕获的最大捕获半径.采用正交多项式对这组数据进行拟合,得到一个光滑的拟合曲面,同时给出被捕获次数和时间随飞行状态变化趋势的近似解析表达式.     

广义Richards-Gilpin-Ayala模型的捕获优化问题

在Richards-Gilpin-Ayala模型的基础上,提出了一类更广泛的数学模型—广义Richards-Gilpin-Ayala模型.进而讨论该模型单种群生物资源的捕获优化问题,分析了被开发生物种群的动力学性质.在单位捕获努力量假定下,以最大可持续捕获量为管理目标,确定了线性捕获下的最优捕获策略,得到了最优捕获努力量,最大可持续收获及相应的最优种群水平的显式表达式.这些结果推广了相关文献中关于Schaefer模型、广义Logistic模型的相应结果.     

动态价格下Logistic生长模型的捕获问题

基于市场价格受供给和需求影响,建立一种新型的动态价格下的捕获模型,并对此模型进行了动力学分析.在经济意义下,如果捕获相同数量的生物种群,那么在均衡价格下的捕获努力量会低于常数价格下的捕获努力量,这将为如何降低捕捞成本提供有价值的理论借鉴.     

Lincoln-Petersen模型中群体大小的置信限和置信区间

对于Lincoln-Petersen模型,基于捕获-再捕获方法得到的数据,我们给出了群体大小的置信限和置信区间的有效计算方法.     

Population size estimation with covariate values missing non-ignorable

The main purpose of this paper is using capture-recapture data to estimate the population size when some covariate values are missing, possibly non-ignorable. Conditional likelihood method is adopted, with a sub-model describing various missing mechanisms. The derived estimate is proved to be asymptotically normal, and simulation studies via a version of EM algorithm show that it is approximately unbiased. The proposed method is applied to a real example, and the result is compared with previous ones.     

Total domination changing and stable graphs upon vertex removal

A set S of vertices in a graph G is a total dominating set if every vertex of G is adjacent to some vertex in S. The minimum cardinality of a total dominating set of G is the total domination number of G. A graph is total domination vertex removal stable if the removal of an arbitrary vertex leaves the total domination number unchanged. On the other hand, a graph is total domination vertex removal changing if the removal of an arbitrary vertex changes the total domination number. In this paper, we study total domination vertex removal changing and stable graphs.     

A correspondence principle between (hyper)graph theory and probability theory,and the (hyper)graph removal lemma

We introduce a correspondence principle (analogous to the Furstenberg Correspondence Principle) that allows one to extract an infinite random graph or hypergraph from a sequence of increasingly large deterministic graphs or hypergraphs. As an application we present a new (infinitary) proof of the hypergraph removal lemma of Nagle-Schacht-Rödl-Skokan and Gowers, which does not require the hypergraph regularity lemma and requires significantly less computation. This in turn gives new proofs of several corollaries of the hypergraph removal lemma, such as Szemerédi’s Theorem on arithmetic progressions.     

Solving influence diagrams with fuzzy chance and value nodes

In this paper we discuss how influence diagrams are affected by the presence of fuzziness in chance and value nodes. In this way, by modelling fuzzy-valued random variables and utilities in terms of fuzzy random variables, we analyze the statistical rules corresponding to the affected value-preserving transformations, namely: chance node removal and decision node removal. Some supporting results on fuzzy random variables introduced in this paper will provide us with the required mathematical tool to formalize the new statistical rules. Finally, an example is included to illustrate the study in the paper.     

Utilization of mathematical models to investigate the bifurcation and chaotic behavior of ethanol fermentors

This paper uses an experimentally verified model to explore the conditions for increasing productivity and yield of the ethanol fermentation process. Detailed bifurcation analysis is carried out to uncover the rich static and dynamic behavior of the fermentor with/without ethanol removal membranes. The emphasis is on producing higher ethanol yield and productivity through unconventional modes of operation. Possible increase of sugar conversion and ethanol productivity using periodic and chaotic operation at high sugar concentrations is investigated for continuous stirred tank fermentors with/without ethanol removal membranes. This study is the prelude to an extensive experimental program to investigate the chaotic behavior of an experimental fermentor with/without ethanol selective membrane leading to scaling up the experimental fermentor to an industrial sized fermentor.     

Complexity and exact algorithms for vertex multicut in interval and bounded treewidth graphs

Multicut is a fundamental network communication and connectivity problem. It is defined as: given an undirected graph and a collection of pairs of terminal vertices, find a minimum set of edges or vertices whose removal disconnects each pair. We mainly focus on the case of removing vertices, where we distinguish between allowing or disallowing the removal of terminal vertices. Complementing and refining previous results from the literature, we provide several NP-completeness and (fixed-parameter) tractability results for restricted classes of graphs such as trees, interval graphs, and graphs of bounded treewidth.     

A mathematical model of infectious diseases

In the formulation of models for the spread of communicable diseases which include removal and population dynamics, it is necessary to distinguish between removal through recovery with immunity and removal by death due to disease. This distinction must be made because of the difference in the effect on the population dynamics of the different kinds of removal and because there are significant differences in the behavior of the models. We have formulated a class of models which allow recovery with immunity for a fraction of the infective and permanent removal by death from disease for the remainder. Earlier models of this type have postulated an increased death rate for infective, but such models are restricted to exponentially distributed-infective periods. Because of the differences in behavior between models with recovery and models with permanent removal do not arise when the infective period is exponentially distributed, we have chosen to formulate a different type of model which is sufficiently general to admit qualitative differences.     

UNSTEADY STATE DISPERSION OF AIR POLLUTANTS UNDER THE EFFECTS OF DELAYED AND NONDELAYED REMOVAL MECHANISMS

Abstract In this paper, we present a two‐dimensional time‐dependent mathematical model for studying the unsteady state dispersion of air pollutants emitted from an elevated line source in the atmosphere under the simultaneous effects of delayed (slow) and nondelayed (instantaneous) removal mechanisms. The wind speed and coefficient of diffusion are taken as functions of the vertical height above the ground. The deposition of pollutants on the absorptive ground and leakage into the atmosphere at the inversion layer are also included in the model by applying appropriate boundary conditions. The model is solved numerically by the fractional step method. The Lagrangian approach is used to solve the advection part, whereas the Eulerian finite difference scheme is applied to solve the part with the diffusion and removal processes. The solutions are analyzed to observe the effects of coexisting delayed and nondelayed removal mechanisms on overall dispersion. Comparison of delayed and nondelayed removal processes of equal capacity shows that the latter (nondelayed) process is more effective than the former (delayed removal) in the removal of pollutants from the atmosphere.     

Improved Harmonic Incompatibility Removal for Susceptibility Mapping via Reduction of Basis Mismatch

In quantitative susceptibility mapping (QSM), the background field removal is an essential data acquisition step because it has a significant effect on the restoration quality by generating a harmonic incompatibility in the measured local field data. Even though the sparsity based first generation harmonic incompatibility removal (1GHIRE) model has achieved the performance gain over the traditional approaches, the 1GHIRE model has to be further improved as there is a basis mismatch underlying in numerically solving Poisson’s equation for the background removal. In this paper, we propose the second generation harmonic incompatibility removal (2GHIRE) model to reduce a basis mismatch, inspired by the balanced approach in the tight frame based image restoration. Experimental results shows the superiority of the proposed 2GHIRE model both in the restoration qualities and the computational efficiency.