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.
This paper aims at two problems which exist in most of repairable spare part demand models at present: the exponential distribution as the basic assumption and one typical distribution corresponding to a model. A gene...This paper aims at two problems which exist in most of repairable spare part demand models at present: the exponential distribution as the basic assumption and one typical distribution corresponding to a model. A general repairable spare part demand model built on quasi birth-and-death process is developed. This model assumes that both the operational time of the unit and the maintenance time of the unit follow the continuous time phase type distributions. The first passage time distribution to be out of spares, the first mean time to be out of spares, and an algorithm to get the minimal amount of spares under certain restrictions are obtained. At the end of this paper, a numerical example is given.展开更多
In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-death network(RBDN) with network size decline.First,by stochastic process rules,the steady state ...In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-death network(RBDN) with network size decline.First,by stochastic process rules,the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0 < p < 1/2,then the average degree of network with n nodes is introduced to calculate the degree distributions.Specifically,taking m = 3 for example,we explain the detailed solving process,in which computer simulation is used to verify our degree distribution solutions.In addition,the tail characteristics of the degree distribution are discussed.Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN.展开更多
At first, the concept of bridge reliability is given, followed with its mathematic model. Then, based on the analysis about the mechanism of the damage and repair of bridges, and the state diversion of bridge network,...At first, the concept of bridge reliability is given, followed with its mathematic model. Then, based on the analysis about the mechanism of the damage and repair of bridges, and the state diversion of bridge network, the state diversion process is proved to be birth-and-death process. In the end, the state diversion balance equation of bridge network is built, and the evaluation model of wartime bridge reliability is got. The model is used in a certain example, and it is proved to be precise and credible.展开更多
In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for ...In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.展开更多
Objectives: Current study sought to determine an association between Low Birth Weight (LBW) and early neonatal mortality at a resource limited country’s referral hospital and to determine relationship between materna...Objectives: Current study sought to determine an association between Low Birth Weight (LBW) and early neonatal mortality at a resource limited country’s referral hospital and to determine relationship between maternal age and birth outcomes. Method: A retrospective study analyzing data on births in the Volta Regional Hospital, Ghana from the period of November 2011 to June 2016. A total of 8279 births were analyzed. Results: Results suggest that teenage mothers (8.60%) are more likely to give birth to pre-term babies than the elderly (6.60%) and the adult mothers (4.61%). LBW is highest among the teenage mothers (12.69%) followed by the elderly mothers (7.87%) and then the least among the adult mothers (6.48%). Extremely Low Birth Weight (ELBW) and Macrosomia births were more observed among the elderly mothers (0.90%;2.17%) than the teenage (0.28%;0.14%) and adult mothers (0.34%;1.61%) respectively. Data suggest that 100% of the ELBW were pre-term birth, 88.28% Very Low Birth Weight (VLBW), 34.56% LBW and only 1.06% of the pre-term birth were with Normal Birth Weight (NBW). Death rate ranges from 50% for ELBW, 33.59% for VLBW, 8.22% for LBW, 5.43% for Macrosomia and 1.5% for NBW. However, death rate distribution among the various age groups was statistically not significant (P 0.106). Conclusions: Our study suggests that early neonatal death, especially deaths among ELBW and VLBW is still high at the VRH of Ghana and therefore there is the need for further studies into interventions to reduce death among neonates born with VLBW and ELBW.展开更多
Background: It is yet a controversy subject whether low birth weight and infant death are associated to human immunodeficiency virus-1 infection. Objective: To appreciate association between low birth weights, mother ...Background: It is yet a controversy subject whether low birth weight and infant death are associated to human immunodeficiency virus-1 infection. Objective: To appreciate association between low birth weights, mother to child HIV transmission and infant mortality in HIV-1 infected pregnant women delivering between 2011 and 2016. Materials: We conducted 6 years cohort study in urban Mali. Outcome included preterm delivery, small for gestational age, infant survival status and HIV transmission. Comparison concerned women clinical WHO stage, mother viro-immunological status, and newborn anthropometric parameters. Results: HIV-1 infected women who delivered low birth weight newborn were 20.9% (111/531) versus 16.5% (1910/11.546) in HIV negative patients (p = 0.016). CD4 T cell counts low than 350 T cells count were strongly associated to LBW (p = 0.000;RR = 3.03;95% CI [1.89 - 3.16]). There is no significant association between ART that was initiated during pregnancy (p = 0.061, RR = 0.02;CI 95% (1.02 - 1.99)) or during delivery (p = 0.571;RR = 1.01;CI 95% (0.10 - 3.02)) and LBW delivery. In multivariate analysis ART regimens containing protease inhibitor (PI) were lone regimens associated with LBW ((p = 0.030;RR = 1.001;95% confidence interval [1.28 - 3.80]). Very low birth weight was statistically associated to women HIV infection (adjusted relative risk, 2.02;p = 0.000;95% confidence interval (2.17 - 4.10)). There is no significant difference between mother to child HIV transmission rate in the two HIV-infected pregnant women (10 infected children in group 2: MTCT rate 4.5%) and 3 infected children in group 1 (MTCT rate: 2.7%) (p = 0.56;RR, 0.59;CI 95% (0.18 - 4.39)). In multivariate analysis, LBW was associated with infant death (p = 0.001;RR = 2.04;CI 95% [1.04 - 5.05]). The median weight of infant at the moment of death in group 1 was 851 g (IQR: 520 - 1833 g). Significant relationship was found between infant death among LBW newborn with mother WHO stage 2 (p = 0.004;adjusted RR = 3.22;CI 95% [2.25 - 6.00]), CD4 T cells count 3 (p = 0.005;RR = 2.81;CI 95% [1.20 - 4.11]), PI regimens (p = 0.030;RR = 1.00;CI 95% [1.28 - 3.80]). Conclusion: We confirm increased risk of low birth weight and mother HIV-1 infection and we identified strongest association between mortality in infant born to HIV-1 infected mother and LBW.展开更多
Introduction: Our aim was to identify the risk factors of clinical birth asphyxia and subsequent newborn death in the presence of nuchal cord in a sub-Saharan Africa setting. Methodology: It was a six-months’ case-co...Introduction: Our aim was to identify the risk factors of clinical birth asphyxia and subsequent newborn death in the presence of nuchal cord in a sub-Saharan Africa setting. Methodology: It was a six-months’ case-control study involving 117 parturients whose babies presented with a nuchal cord at delivery. The study was carried out at the Yaoundé Gyneco-Obstetric and Pediatric Hospital, Cameroon, from January 1st to June 30th 2013. Results: The risk factors of clinical birth asphyxia identified were: first delivery, absence of obstetrical ultrasound during pregnancy, nuchal cord with more than one loop, duration of second stage of labor more than 30 minutes during vaginal delivery. The risk factors for newborn death from clinical birth asphyxia in the presence of nuchal cord were: maternal age Conclusion: We recommend a systematic obstetrical ultrasound before labor, so as to detect the presence of a nuchal cord, its tightness and the number of loops. Also, cesarean section should be considered when a nuchal cord is associated with first delivery, tightness or multiple looping.展开更多
A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the...A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.展开更多
我们与随机的移动，尺寸 k 的一个总数能以时间依赖者率在生产新单体建议一个单体出生死亡模型我(t) k 或在率 J (t) k 失去一单体，并且与概率 P (t) ，任何尺寸的一个总数随机被移开。我们然后经分解借助于率方程调查模型的运动进化...我们与随机的移动，尺寸 k 的一个总数能以时间依赖者率在生产新单体建议一个单体出生死亡模型我(t) k 或在率 J (t) k 失去一单体，并且与概率 P (t) ，任何尺寸的一个总数随机被移开。我们然后经分解借助于率方程调查模型的运动进化。结果证明总数尺寸分发的可伸缩的行为关键地依赖于网出生率我(t)—象出生率一样的 J (t) 我(t) 。总数尺寸分发能在一些情况中接近一张标准或修改的可伸缩的表格，但是它可以在另外的情况中拿一张没有规模的表格。而且，种类能最后幸存仅当也我(t)—J (t)≥
P (t) 或[J (t)+ P (t)−
我(t)] t 0 在 t 1；否则，它将变得绝灭。展开更多
We propose a two-species infection model,in which an infected aggregate can gain one monomer from ahealthy one due to infection when they meet together.Moreover,both the healthy and infected aggregates may lose onemon...We propose a two-species infection model,in which an infected aggregate can gain one monomer from ahealthy one due to infection when they meet together.Moreover,both the healthy and infected aggregates may lose onemonomer because of self-death,but a healthy aggregate can spontaneously yield a new monomer.Consider a simplesystem in which the birth/death rates are directly proportional to the aggregate size,namely,the birth and death ratesof the healthy aggregate of size k are Jx k and J_2k while the self-death rate of the infected aggregate of size k is J_3k.Wethen investigate the kinetics of such a system by means of rate equation approach.For the J_1>J_2 case,the aggregatesize distribution of either species approaches the generalized scaling form and the typical size of either species increaseswavily at large times.For the J_1=J_2 case,the size distribution of healthy aggregates approaches the generalized scalingform while that of infected aggregates satisfies the modified scaling form.For the J_1<J_2 case,the size distribution ofhealthy aggregates satisfies the modified scaling form,but that of infected aggregates does not scale.展开更多
An aggregation growth model of three species A,B and C with the competition between catalyzed birth and catalyzed death is proposed.Irreversible aggregation occurs between any two aggregates of the like species with t...An aggregation growth model of three species A,B and C with the competition between catalyzed birth and catalyzed death is proposed.Irreversible aggregation occurs between any two aggregates of the like species with the constant rate kernels I n (n=1,2,3).Meanwhile,a monomer birth of an A species aggregate of size k occurs under the catalysis of a B species aggregate of size j with the catalyzed birth rate kernel K(k,j)=Kkj υ,and a monomer death of an A species aggregate of size k occurs under the catalysis of a C species aggregate of size j with the catalyzed death rate kernel L(k,j)=Lkj υ,where υ is a parameter reflecting the dependence of the catalysis reaction rates of birth and death on the size of catalyst aggregate.The kinetic evolution behaviours of the three species are investigated by the rate equation approach based on the mean-field theory.The form of the aggregate size distribution of A species a k (t) is found to be dependent crucially on the competition between the catalyzed birth and death of A species,as well as the irreversible aggregation processes of the three species:(1) In the υ < 0 case,the irreversible aggregation dominates the process,and a k (t) satisfies the conventional scaling form;(2) In the υ≥ 0 case,the competition between the catalyzed birth and death dominates the process.When the catalyzed birth controls the process,a k (t) takes the conventional or generalized scaling form.While the catalyzed death controls the process,the scaling description of the aggregate size distribution breaks down completely.展开更多
In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death(IBD) model and discuss the simulation of sample path and statistical inference with...In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death(IBD) model and discuss the simulation of sample path and statistical inference with complete observations of the IBD process by the exact transition density formula.展开更多
In this paper,we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended W...In this paper,we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state.The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process.We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth.Furthermore,the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure.In particular,a critical purity of the initial mixed entangled state exists,above which entanglement sudden birth vanishes while entanglement sudden death appears.It is also noticed that stable entanglement,which is independent of different initial states of the qubits (pure or mixed state),occurs even in the presence of decoherence.These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth,death and revival.展开更多
In recent years some interrelationships between time of birth and longevity were published. Concomitant publications appeared demonstrating links between Space Weather and the timing of medical events;in part of both ...In recent years some interrelationships between time of birth and longevity were published. Concomitant publications appeared demonstrating links between Space Weather and the timing of medical events;in part of both these studies it was shown that Space Weather indices are stronger connected with the time of conception as with the birth time. The aim of these study was to consider birth and conception month of patients suffering from a number of “big killer” pathologies, affecting human longevity and comparing with published data on centenarians—100 - 112 years old persons in the USA. Patients and Methods: We included monthly births distribution of our four papers including patients with Acute Myocardial Infarction undergoing Percutaneous Coronary Intervention (PCI)—n-3765, and admitted in another tertiary medical facility for AMI—n-22,047, and, also patients suffering Rapid—n-1239 and Sudden Cardiac Death—n-327 and, also, patients with oncologic malignancies—n-44587. At all in this group 71,965 patients were included. Their birth and conception months were compared with analogical data of 1574 people of 100 - 112 years old using data of L.A. and N.S. Gavrilov for USA centenarians. Results: The birth months of the cardiovascular and oncology patients were maximal in January, March and April (above 10% at each of these months);their conception was maximal in April, June and July. The monthly distribution of conception and birth of the studied population is presented in Tables 1-3. The maximal birth months of the centenarians were November, September, and October;the maximal conception months were December, January, and February. Conclusion: People suffering Myocardial Infarction, Sudden Cardiac Death and Oncologic Malignancies are in higher numbers born in the first four months of the year and conception in April, June and July. The maximal birth months of the very old people were November, September and October and conception were December, January and February.展开更多
We further study the kinetic behavior of the exchange-driven growth with birth and death for the case of birth rate kernel being less than that of death based on the mean-field theory. The symmetric exchange rate kern...We further study the kinetic behavior of the exchange-driven growth with birth and death for the case of birth rate kernel being less than that of death based on the mean-field theory. The symmetric exchange rate kernel is K(k,j) = K'(k,j) = Ikjv, and the birth and death rates are proportional to the aggregate's size. The long time asymptotic behavior of the aggregate size distribution ak(t) is found to obey a much unusual scaling law with an exponentially growing scaling function φ(x) = exp(x).展开更多
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 α 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
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Supported by National Defense Foundation of P. R. China (41319060206)
文摘This paper aims at two problems which exist in most of repairable spare part demand models at present: the exponential distribution as the basic assumption and one typical distribution corresponding to a model. A general repairable spare part demand model built on quasi birth-and-death process is developed. This model assumes that both the operational time of the unit and the maintenance time of the unit follow the continuous time phase type distributions. The first passage time distribution to be out of spares, the first mean time to be out of spares, and an algorithm to get the minimal amount of spares under certain restrictions are obtained. At the end of this paper, a numerical example is given.
基金Project supported by the National Natural Science Foundation of China(Grant No.61273015)the Chinese Scholarship Council
文摘In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-death network(RBDN) with network size decline.First,by stochastic process rules,the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0 < p < 1/2,then the average degree of network with n nodes is introduced to calculate the degree distributions.Specifically,taking m = 3 for example,we explain the detailed solving process,in which computer simulation is used to verify our degree distribution solutions.In addition,the tail characteristics of the degree distribution are discussed.Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN.
文摘At first, the concept of bridge reliability is given, followed with its mathematic model. Then, based on the analysis about the mechanism of the damage and repair of bridges, and the state diversion of bridge network, the state diversion process is proved to be birth-and-death process. In the end, the state diversion balance equation of bridge network is built, and the evaluation model of wartime bridge reliability is got. The model is used in a certain example, and it is proved to be precise and credible.
基金The Fundamental Research Funds for the Central Universities,CHD (300102129202)the NSF (11701041) of China+1 种基金the Natural Science Basic Research Plan (2018JM1011) in Shaanxi Province of ChinaScientific Innovation Practice Project (300103002110) of Postgraduates of Chang’an University
文摘In this paper, we propose an SIRS epidemic model with pulse vaccination, birth pulse and Logistic death rate. By using the stroboscopic map of a discrete dynamical system, the disease-free periodic solution (DFPS for short) of the model under pulse vaccination and birth pulse is obtained. Based on the Floquet theory and comparison theorem of impulsive differential equations, the global asymptotic stability of the DFPS is given, and sufficient conditions for the permanence of the model are obtained. In addition, numerical simulations are done to confirm our theoretical results.
文摘Objectives: Current study sought to determine an association between Low Birth Weight (LBW) and early neonatal mortality at a resource limited country’s referral hospital and to determine relationship between maternal age and birth outcomes. Method: A retrospective study analyzing data on births in the Volta Regional Hospital, Ghana from the period of November 2011 to June 2016. A total of 8279 births were analyzed. Results: Results suggest that teenage mothers (8.60%) are more likely to give birth to pre-term babies than the elderly (6.60%) and the adult mothers (4.61%). LBW is highest among the teenage mothers (12.69%) followed by the elderly mothers (7.87%) and then the least among the adult mothers (6.48%). Extremely Low Birth Weight (ELBW) and Macrosomia births were more observed among the elderly mothers (0.90%;2.17%) than the teenage (0.28%;0.14%) and adult mothers (0.34%;1.61%) respectively. Data suggest that 100% of the ELBW were pre-term birth, 88.28% Very Low Birth Weight (VLBW), 34.56% LBW and only 1.06% of the pre-term birth were with Normal Birth Weight (NBW). Death rate ranges from 50% for ELBW, 33.59% for VLBW, 8.22% for LBW, 5.43% for Macrosomia and 1.5% for NBW. However, death rate distribution among the various age groups was statistically not significant (P 0.106). Conclusions: Our study suggests that early neonatal death, especially deaths among ELBW and VLBW is still high at the VRH of Ghana and therefore there is the need for further studies into interventions to reduce death among neonates born with VLBW and ELBW.
文摘Background: It is yet a controversy subject whether low birth weight and infant death are associated to human immunodeficiency virus-1 infection. Objective: To appreciate association between low birth weights, mother to child HIV transmission and infant mortality in HIV-1 infected pregnant women delivering between 2011 and 2016. Materials: We conducted 6 years cohort study in urban Mali. Outcome included preterm delivery, small for gestational age, infant survival status and HIV transmission. Comparison concerned women clinical WHO stage, mother viro-immunological status, and newborn anthropometric parameters. Results: HIV-1 infected women who delivered low birth weight newborn were 20.9% (111/531) versus 16.5% (1910/11.546) in HIV negative patients (p = 0.016). CD4 T cell counts low than 350 T cells count were strongly associated to LBW (p = 0.000;RR = 3.03;95% CI [1.89 - 3.16]). There is no significant association between ART that was initiated during pregnancy (p = 0.061, RR = 0.02;CI 95% (1.02 - 1.99)) or during delivery (p = 0.571;RR = 1.01;CI 95% (0.10 - 3.02)) and LBW delivery. In multivariate analysis ART regimens containing protease inhibitor (PI) were lone regimens associated with LBW ((p = 0.030;RR = 1.001;95% confidence interval [1.28 - 3.80]). Very low birth weight was statistically associated to women HIV infection (adjusted relative risk, 2.02;p = 0.000;95% confidence interval (2.17 - 4.10)). There is no significant difference between mother to child HIV transmission rate in the two HIV-infected pregnant women (10 infected children in group 2: MTCT rate 4.5%) and 3 infected children in group 1 (MTCT rate: 2.7%) (p = 0.56;RR, 0.59;CI 95% (0.18 - 4.39)). In multivariate analysis, LBW was associated with infant death (p = 0.001;RR = 2.04;CI 95% [1.04 - 5.05]). The median weight of infant at the moment of death in group 1 was 851 g (IQR: 520 - 1833 g). Significant relationship was found between infant death among LBW newborn with mother WHO stage 2 (p = 0.004;adjusted RR = 3.22;CI 95% [2.25 - 6.00]), CD4 T cells count 3 (p = 0.005;RR = 2.81;CI 95% [1.20 - 4.11]), PI regimens (p = 0.030;RR = 1.00;CI 95% [1.28 - 3.80]). Conclusion: We confirm increased risk of low birth weight and mother HIV-1 infection and we identified strongest association between mortality in infant born to HIV-1 infected mother and LBW.
文摘Introduction: Our aim was to identify the risk factors of clinical birth asphyxia and subsequent newborn death in the presence of nuchal cord in a sub-Saharan Africa setting. Methodology: It was a six-months’ case-control study involving 117 parturients whose babies presented with a nuchal cord at delivery. The study was carried out at the Yaoundé Gyneco-Obstetric and Pediatric Hospital, Cameroon, from January 1st to June 30th 2013. Results: The risk factors of clinical birth asphyxia identified were: first delivery, absence of obstetrical ultrasound during pregnancy, nuchal cord with more than one loop, duration of second stage of labor more than 30 minutes during vaginal delivery. The risk factors for newborn death from clinical birth asphyxia in the presence of nuchal cord were: maternal age Conclusion: We recommend a systematic obstetrical ultrasound before labor, so as to detect the presence of a nuchal cord, its tightness and the number of loops. Also, cesarean section should be considered when a nuchal cord is associated with first delivery, tightness or multiple looping.
文摘A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.
基金supported by National Natural Science Foundation of China under Grant Nos. 10775104 and 10305009
文摘我们与随机的移动，尺寸 k 的一个总数能以时间依赖者率在生产新单体建议一个单体出生死亡模型我(t) k 或在率 J (t) k 失去一单体，并且与概率 P (t) ，任何尺寸的一个总数随机被移开。我们然后经分解借助于率方程调查模型的运动进化。结果证明总数尺寸分发的可伸缩的行为关键地依赖于网出生率我(t)—象出生率一样的 J (t) 我(t) 。总数尺寸分发能在一些情况中接近一张标准或修改的可伸缩的表格，但是它可以在另外的情况中拿一张没有规模的表格。而且，种类能最后幸存仅当也我(t)—J (t)≥
P (t) 或[J (t)+ P (t)−
我(t)] t 0 在 t 1；否则，它将变得绝灭。
基金National Natural Science Foundation of China under Grant Nos.10775104 and 10305009
文摘We propose a two-species infection model,in which an infected aggregate can gain one monomer from ahealthy one due to infection when they meet together.Moreover,both the healthy and infected aggregates may lose onemonomer because of self-death,but a healthy aggregate can spontaneously yield a new monomer.Consider a simplesystem in which the birth/death rates are directly proportional to the aggregate size,namely,the birth and death ratesof the healthy aggregate of size k are Jx k and J_2k while the self-death rate of the infected aggregate of size k is J_3k.Wethen investigate the kinetics of such a system by means of rate equation approach.For the J_1>J_2 case,the aggregatesize distribution of either species approaches the generalized scaling form and the typical size of either species increaseswavily at large times.For the J_1=J_2 case,the size distribution of healthy aggregates approaches the generalized scalingform while that of infected aggregates satisfies the modified scaling form.For the J_1<J_2 case,the size distribution ofhealthy aggregates satisfies the modified scaling form,but that of infected aggregates does not scale.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10275048 and 10305009)the Zhejiang Provincial Natural Science Foundation of China (Grant No 102067)
文摘An aggregation growth model of three species A,B and C with the competition between catalyzed birth and catalyzed death is proposed.Irreversible aggregation occurs between any two aggregates of the like species with the constant rate kernels I n (n=1,2,3).Meanwhile,a monomer birth of an A species aggregate of size k occurs under the catalysis of a B species aggregate of size j with the catalyzed birth rate kernel K(k,j)=Kkj υ,and a monomer death of an A species aggregate of size k occurs under the catalysis of a C species aggregate of size j with the catalyzed death rate kernel L(k,j)=Lkj υ,where υ is a parameter reflecting the dependence of the catalysis reaction rates of birth and death on the size of catalyst aggregate.The kinetic evolution behaviours of the three species are investigated by the rate equation approach based on the mean-field theory.The form of the aggregate size distribution of A species a k (t) is found to be dependent crucially on the competition between the catalyzed birth and death of A species,as well as the irreversible aggregation processes of the three species:(1) In the υ < 0 case,the irreversible aggregation dominates the process,and a k (t) satisfies the conventional scaling form;(2) In the υ≥ 0 case,the competition between the catalyzed birth and death dominates the process.When the catalyzed birth controls the process,a k (t) takes the conventional or generalized scaling form.While the catalyzed death controls the process,the scaling description of the aggregate size distribution breaks down completely.
基金Supported by the Fundamental Research Funds for the Central Universities(JBK120405)
文摘In this paper, we employ moment generating function to obtain some exact formula of transition probability of immigration-birth-death(IBD) model and discuss the simulation of sample path and statistical inference with complete observations of the IBD process by the exact transition density formula.
基金Project supported by the National Natural Science Foundation,China (Grant No.10904033)the Natural Science Foundation of Hubei Province,China (Grant No.2009CDA145)+1 种基金the Science Foundation of the Educational Commission of Hubei Province,China (Grant No.D20092204)the Postgraduate Programme of Hubei Normal University of China (Grant No.2007D20)
文摘In this paper,we investigate the dynamical behaviour of entanglement in terms of concurrence in a bipartite system subjected to an external magnetic field under the action of dissipative environments in the extended Werner-like initial state.The interesting phenomenon of entanglement sudden death as well as sudden birth appears during the evolution process.We analyse in detail the effect of the purity of the initial entangled state of two qubits via Heisenberg XY interaction on the apparition time of entanglement sudden death and entanglement sudden birth.Furthermore,the conditions on the conversion of entanglement sudden death and entanglement sudden birth can be generalized when the initial entangled state is not pure.In particular,a critical purity of the initial mixed entangled state exists,above which entanglement sudden birth vanishes while entanglement sudden death appears.It is also noticed that stable entanglement,which is independent of different initial states of the qubits (pure or mixed state),occurs even in the presence of decoherence.These results arising from the combination of the extended Werner-like initial state and dissipative environments suggest an approach to control and enhance the entanglement even after purity induced sudden birth,death and revival.
文摘In recent years some interrelationships between time of birth and longevity were published. Concomitant publications appeared demonstrating links between Space Weather and the timing of medical events;in part of both these studies it was shown that Space Weather indices are stronger connected with the time of conception as with the birth time. The aim of these study was to consider birth and conception month of patients suffering from a number of “big killer” pathologies, affecting human longevity and comparing with published data on centenarians—100 - 112 years old persons in the USA. Patients and Methods: We included monthly births distribution of our four papers including patients with Acute Myocardial Infarction undergoing Percutaneous Coronary Intervention (PCI)—n-3765, and admitted in another tertiary medical facility for AMI—n-22,047, and, also patients suffering Rapid—n-1239 and Sudden Cardiac Death—n-327 and, also, patients with oncologic malignancies—n-44587. At all in this group 71,965 patients were included. Their birth and conception months were compared with analogical data of 1574 people of 100 - 112 years old using data of L.A. and N.S. Gavrilov for USA centenarians. Results: The birth months of the cardiovascular and oncology patients were maximal in January, March and April (above 10% at each of these months);their conception was maximal in April, June and July. The monthly distribution of conception and birth of the studied population is presented in Tables 1-3. The maximal birth months of the centenarians were November, September, and October;the maximal conception months were December, January, and February. Conclusion: People suffering Myocardial Infarction, Sudden Cardiac Death and Oncologic Malignancies are in higher numbers born in the first four months of the year and conception in April, June and July. The maximal birth months of the very old people were November, September and October and conception were December, January and February.
文摘We further study the kinetic behavior of the exchange-driven growth with birth and death for the case of birth rate kernel being less than that of death based on the mean-field theory. The symmetric exchange rate kernel is K(k,j) = K'(k,j) = Ikjv, and the birth and death rates are proportional to the aggregate's size. The long time asymptotic behavior of the aggregate size distribution ak(t) is found to obey a much unusual scaling law with an exponentially growing scaling function φ(x) = exp(x).
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 α 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.
