Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models

The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event.

RECURRENCE FOR THE GENERALIZED BIRTH-DEATH CHAINS IN A RANDOM ENVIRONMENT

This is a study of one dimensional generalized birth-death chains in a random environment (GBDIRE). We give two sufficient conditions of recurrence for GBDIRE.

On Kendall's Conjecture for an Extended Birth-death Q-processes with Instantaneous State and Catastrophes

A new structure with the special property that instantaneous state and catas-trophes is imposed to ordinary birth-death processes is considered. Kendall's conjecture forthe processes is proved to be right.

Logarithmic Sobolev Inequalities for Two-Sided Birth-Death Processes

In this paper, we study the logarithmic Sobolev inequalities for two-sided birth-death processes. An estimate of the logarithmic Sobolev constant α for a two-sided birth-death process is obtained by the Hardy-type inequality and a criteria for a is also presented.

Inferring Multi-Type Birth-Death Parameters for a Structured Host Population with Application to HIV Epidemic in Africa

Human Immunodeficiency Virus (HIV) dynamics in Africa are purely characterised by sparse sampling of DNA sequences for individuals who are infected. There are some sub-groups that are more at risk than the general population. These sub-groups have higher infectivity rates. We came up with a likelihood inference model of multi-type birth-death process that can be used to make inference for HIV epidemic in an African setting. We employ a likelihood inference that incorporates a probability of removal from infectious pool in the model. We have simulated trees and made parameter inference on the simulated trees as well as investigating whether the model distinguishes between heterogeneous and homogeneous dynamics. The model makes fairly good parameter inference. It distinguishes between heterogeneous and homogeneous dynamics well. Parameter estimation was also performed under sparse sampling scenario. We investigated whether trees obtained from a structured population are more balanced than those from a non-structured host population using tree statistics that measure tree balance and imbalance. Trees from non-structured population were more balanced basing on Colless and Sackin indices.

A Linear Immigration-Birth-Death Model and Its Statistical Inference

formula of simulation proccss by In this paper, we employ monmnt generating function to obtain some exact transition probability of inlmigration-birth-death（IBD） model and discuss the of sample path and statistical inference with complete observations of the IBD the exact transition density formula.

一类二次矩阵方程的牛顿迭代法及其收敛性

二次矩阵方程是科学与工程计算中一类重要的方程,探讨有效的数值方法是一项有意义的工作,拟生灭过程在股价模拟、库存控制、排队论等很多领域都有着重要的应用,对一类来源于拟生灭过程的特殊的二次矩阵方程进行了研究。在最小非负解存在且唯一的假设条件下,提出了牛顿迭代法并证明其收敛性。当初始矩阵取零矩阵时,牛顿迭代法产生的矩阵列收敛到方程的唯一最小非负解。最后通过数值例子验证算法的有效性与可行性。

清代诗人生卒年丛考——以湖北梅钺、李中黄等七位诗人为中心

中国古典诗歌按照加速度的原理发展,至清代而达到极度繁荣。迄今仍有作品传世的清代诗人,少说也在十万人以上,超过此前历代诗人总和的若干倍。但他们的生卒年,目前能够现成查到的,仅仅只有很少的一部分。日后像编纂《全清诗》以及其他诸多诗歌文献,这都会成为一个棘手的问题。因此,在学术界既有的相关工具书之外,从各种原始资料不断补充考察清代诗人生卒年,的确很有必要。这里就湖北梅钺、李中黄,浙江张懋忠、钟氏(海宁徐濬妻),河南郜献珂,山东刘士聪,云南李凤彩,以及江苏易震吉等诗人,对他们的生卒年做些探讨。

基于飞机状态的备件动态规划技术

伴随民航业的竞争日趋激烈,航空公司迫切需要控制成本以提升效益。民机备件既是直接影响飞行安全的关键因素,备件成本又在航空公司可控成本中占比最高。因此,在保证飞行安全的前提下做好备件规划,对航空公司有至关重要的意义。根据民机备件的安全级别、故障修复时限等对备件分级设置保障率水平,采用符合备件故障特性的马尔可夫生灭过程,建立满足给定保障率水平的备件量计算模型,并在此基础上建立以保障成本最低为目标函数,满足保障率水平为约束函数的备件量动态规划模型。基于飞机状态分析历史故障数据、季节性、日利用率、机队规模对备件保障的影响,在所建模型中将故障率季节性差异、日利用率和飞机停场损失淡旺季差异进行评估以减小计算结果与实际需求的偏差。以H航空公司ERJ-190机型显示组件为例,对所建模型进行应用验证,计算结果与H航空公司运营实际相吻合,证明所建模型可为航空公司备件规划提供技术方法支持。

Variational Formulas of Poincaré-type Inequalities for Birth-Death Processes

In author's one previous paper, the same topic was studied for onedimensional diffusions. As a continuation, this paper studies the discrete case, that is thebirth-death processes. The explicit criteria for the inequalities, the variational formulas andexplicit bounds of the corresponding constants in the inequalities are presented. As typicalapplications, the Nash inequalities and logarithmic Sobolev inequalities are examined.

基于任务生灭过程模型的边缘计算批处理调度算法分析与设计

移动边缘计算技术为低时延要求、资源敏感的计算任务需求提供解决方案,通过研究任务请求特征以提高调度算法效率是边缘计算的重要研究方向。不同于现有研究将任务请求特征建模为单一随机变量的做法,提出基于任务请求生灭过程模型的边缘计算架构,将求解最优调度决策的过程建模为无限期平均成本马尔可夫决策过程。在使用贝尔曼方程分析问题的过程中,利用任务的生灭特性对未来的请求到达做出估计以判断当前决策对未来系统时延能耗成本的影响,进而辅助确定当前状态的最优决策,并结合任务相关性感知提出批处理任务调度控制算法。所提算法根据生灭状态信息对策略迭代的状态空间和决策空间进行剪枝以降低策略改进的复杂度,突破了策略迭代算法的复杂度瓶颈。仿真结果表明,所提算法相较于传统的策略迭代算法具有明显的低复杂度优势,且能在不同系统条件下保持低时延、能耗成本。

Birth-death processes on trees

In this paper, we consider birth-death processes on a tree T and we are interested when it is regular, recurrent and ergodic (strongly, exponentially). By constructing two corresponding birth death processes on Z+, we obtain computable conditions sufficient or necessary for that (in many cases, these two conditions coincide). With the help of these constructions, we give explicit upper and lower bounds for the Dirichlet eigenvalue λ0. At last, some examples are investigated to justify our results.

部分服务台同步多重休假的排队库存系统

本文研究了(s,S)库存策略的多服务台排队库存系统,其中库存为空时有部分服务台同步多重休假,休假时间服从指数分布。顾客到达为泊松过程,每个服务台的服务时间和补货时间均服从指数分布。利用拟生灭过程和矩阵几何解法,计算了系统稳态概率和一些性能指标,并给出了系统单位时间的平均费用函数。最后,通过数值算例分析了参数对费用函数的影响,并得到最优库存策略和最优平均费用。

博世扇贝纹对亚微米硅通孔中应力的影响

硅通孔(TSV)是三维(3D)集成中的关键互连技术。采用博世(Bosch)工艺刻蚀TSV,尤其是亚微米直径的TSV时,侧壁产生的扇贝纹会引起TSV中的应力集中。利用有限元单元生死技术分析亚微米TSV制备过程中的应力变化,并对应力的影响因素进行了分析。研究了TSV节距、扇贝纹高度和宽度、阻挡层材料参数、工艺温度和工作温度等因素对TSV内部应力的影响,并选择了4个主要因素进行正交实验分析。研究结果表明,减小扇贝纹宽度、增大扇贝纹高度、降低工艺温度均能有效缓解扇贝纹附近的应力波动幅度,其中扇贝纹宽度对应力波动的影响最大。通过上述分析,对影响亚微米TSV应力的主要因素进行了排序,从而为TSV制备过程中的参数优化提供了指导。

整体式闸首底板施工宽缝位置及合缝时间对底板的受力影响

针对我国船闸规范中未对闸首底板设置施工宽缝的相关理论进行规定的问题,本文通过对浙江某船闸工程的案例进行研究,采用ANSYS有限元软件,对设置施工宽缝和未设置施工宽缝两种结构模型进行数值分析,研究施工宽缝的位置及合缝时间对底板受力的影响。研究结果表明:底板的负弯矩随宽缝位置由底板两侧向中间变化而减小,底板的负弯矩随合缝时间的推迟而减小,在设计中应在考虑施工便利等相关因素前提下,尽量使宽缝靠近底板中间轴线,并选择在边墩完成总沉降的60%~80%时进行合缝,以降低弯矩,实现最大的综合效益。为施工宽缝的底板理论研究提供有益的参考,有助于规范设计和施工实践。

Numerical simulation of slag layer and its distribution on hot surface of copper stave based on ANSYS birth-death element technology

The core of the long-life copper stave was to ensure the stability of the slag layer,and the uniform distribution of the slag layer was beneficial to restrict the generation of the overthick slag layer.A novel model for calculating the thickness and distribution of the slag layer in the part of copper stave was established based on the finite element theory through the ANSYS birth-death element technology.The distribution and thickness of the slag layer on the hot surface of copper stave were calculated and analyzed when the gas temperature and slag properties tended to be changed,which was applied to characterize the slag-hanging capability of copper stave with the changes of furnace conditions.It was shown that the thickness of hot surface slag layer in the part of copper stave decreased obviously while the temperature of stave body raised rapidly with increasing gas temperature.When the gas temperature was 1400℃,the inlaid slag layer was gradually melted,and the maximum temperature of the stave body was closed to 120℃.The change of gas temperature was very sensitive to the adherent dross capability of copper stave which would be enhanced by the promotion of slag-hanging temperature.However,when the slag-hanging temperature was 1150℃and the gas temperature was lower than 1250℃,the overlhick slag layer was easily formed on the hot surface of the copper stave,and its stability was poor.The improvement in the thermal conductivity of slag could be conducive to the formation of the uniform and stable slag layer on the hot surface of copper stave,especially in the dovetail groove.When the thermal conductivity of the slag was greater than 1.8 W m^(-2)℃^(-1),the inlaid slag layer in the dovetail groove was not melted,although the gas temperature reached 1500℃.

First eigenvalue of birth-death processes with killing

In this paper, we present an explicit and computable lower bound for the first eigenvalue of birth-death processes with killing. This estimate is qualitatively sharp for birth-death processes without killing. We also establish an approximation procedure for the first eigenvalue of the birth-death process with killing by an increasing principal eigenvalue sequence of some birth-death processes without killing. Some applications of our results are illustrated by many examples.

L^2-Algebraic Decay Rate for Transient Birth-Death Processes

This paper is a continuation of the study of the algebraic speed for Markov processes. The authors concentrate on algebraic decay rate for the transient birth-death processes. According to the classification of the boundaries, a series of the sufficient conditions for algebraic decay is presented. To illustrate the power of the results, some examples are included.

从“作者之死”到“文本之生”——罗兰·巴特“作者之死”观念的理论呼唤

“作者之死”是罗兰·巴特文本理论中极具破坏力和感召力的一个理论观点,“文本之生”是罗兰·巴特通过对参与文学活动的读者的呼唤所期冀的新的文学氛围和文论环境。对写作本身的讨论表现了罗兰·巴特对写作者和作者这两种身份的理论认识,进而也为其连接写作实践与接受实践的文本概念的建立奠定了基础。“作者之死”理论在今天的文论构建过程中具有理论层和实践层的意义,不同于作品的文本概念不仅能够将“作者之死”和“文本之生”统一在整体的文学活动中,也实证了作者和读者围绕文本展开的文学实践的延续性与同一性。

New point view of spectral gap in functional spaces for birth-death processes

Constructing some proper functional spaces, we obtain the corresponding norm for the operator （-.L）^-1, and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5（3）： 379-515], for transient birth-death processes.