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 tha...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.展开更多
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.
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 f...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℃.展开更多
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.
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 in...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.展开更多
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 pop...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.展开更多
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 ...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.展开更多
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 in...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.展开更多
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...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.展开更多
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 ...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.展开更多
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 [Fr...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.展开更多
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 bo...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.展开更多
基金supported in part by the NIH grant R01CA241134supported in part by the NSF grant CMMI-1552764+3 种基金supported in part by the NSF grants DMS-1349724 and DMS-2052465supported in part by the NSF grant CCF-1740761supported in part by the U.S.-Norway Fulbright Foundation and the Research Council of Norway R&D Grant 309273supported in part by the Norwegian Centennial Chair grant and the Doctoral Dissertation Fellowship from the University of Minnesota.
文摘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.
文摘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.
基金The authors were especially grateful to the National Natural Science Foundation of China(No.51904063)Fundamental Research Funds for the Central Universities(Nos.N172503016,N172502005,and N172506011)China Postdoctoral Science Foundation(No.2018M640259).
文摘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℃.
基金Supported by the Guangxi Science Foundation(0339071)
文摘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.
基金the National Natural Science Foundation of China(10271091)
文摘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.
文摘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.
基金Supported by the Fundamental Research Funds for the Central Universities(JBK120405)
文摘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.
文摘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.
基金supported by National Natural Science Foundation of China (Grant No.10721091)
文摘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.
文摘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.
基金Acknowledgements This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11101040, 11131003）, the 985 Project, the 973 Project （No. 2011CB808000）, the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20100003110005）, and the Fundamental Research Funds for the Central Universities.
文摘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.
基金supported by the National Natural Science Foundation of China (No. 10721091)
文摘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.
