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
In this paper we examine the large deviations principle (LDP) for sequences of classic Cramér-Lundberg risk processes under suitable time and scale modifications, and also for a wide class of claim distributions ...In this paper we examine the large deviations principle (LDP) for sequences of classic Cramér-Lundberg risk processes under suitable time and scale modifications, and also for a wide class of claim distributions including (the non-super- exponential) exponential claims. We prove two large deviations principles: first, we obtain the LDP for risk processes on D∈[0,1] with the Skorohod topology. In this case, we provide an explicit form for the rate function, in which the safety loading condition appears naturally. The second theorem allows us to obtain the LDP for Aggregate Claims processes on D∈[0,∞) with a different time-scale modification. As an application of the first result we estimate the ruin probability, and for the second result we work explicit calculations for the case of exponential claims.展开更多
Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and c...Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and can predict the risk for exacerbation in asthma. However, it is uncertain why this PDF plays a major role in predicting the dynamic conditions of the respiratory system. This paper introduces a stochastic optimal control model for noisy spontaneous breathing, and obtains a Shrödinger’s wave equation as the motion equation that can produce a PDF as a solution. Based on the lobules-bronchial tree model of the lung system, the tidal volume variable was expressed by a polar coordinate, by use of which the Shrödinger’s wave equation of inter-breath intervals (IBIs) was obtained. Through the wave equation of IBIs, the respiratory rhythm generator was characterized by the potential function including the PDF and the parameter concerning the topographical distribution of regional pulmonary ventilations. The stochastic model in this study was assumed to have a common variance parameter in the state variables, which would originate from the variability in metabolic energy at the cell level. As a conclusion, the PDF of IBIs would become a marker of neuroplasticity in the respiratory rhythm generator through Shr?dinger’s wave equation for IBIs.展开更多
The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder expon...The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder exponent of a function is calculated by developing an algorithm for the numerical evaluation of HSlder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.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In this paper we examine the large deviations principle (LDP) for sequences of classic Cramér-Lundberg risk processes under suitable time and scale modifications, and also for a wide class of claim distributions including (the non-super- exponential) exponential claims. We prove two large deviations principles: first, we obtain the LDP for risk processes on D∈[0,1] with the Skorohod topology. In this case, we provide an explicit form for the rate function, in which the safety loading condition appears naturally. The second theorem allows us to obtain the LDP for Aggregate Claims processes on D∈[0,∞) with a different time-scale modification. As an application of the first result we estimate the ruin probability, and for the second result we work explicit calculations for the case of exponential claims.
文摘Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and can predict the risk for exacerbation in asthma. However, it is uncertain why this PDF plays a major role in predicting the dynamic conditions of the respiratory system. This paper introduces a stochastic optimal control model for noisy spontaneous breathing, and obtains a Shrödinger’s wave equation as the motion equation that can produce a PDF as a solution. Based on the lobules-bronchial tree model of the lung system, the tidal volume variable was expressed by a polar coordinate, by use of which the Shrödinger’s wave equation of inter-breath intervals (IBIs) was obtained. Through the wave equation of IBIs, the respiratory rhythm generator was characterized by the potential function including the PDF and the parameter concerning the topographical distribution of regional pulmonary ventilations. The stochastic model in this study was assumed to have a common variance parameter in the state variables, which would originate from the variability in metabolic energy at the cell level. As a conclusion, the PDF of IBIs would become a marker of neuroplasticity in the respiratory rhythm generator through Shr?dinger’s wave equation for IBIs.
文摘The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwisc Hǒlder exponent of a function is calculated by developing an algorithm for the numerical evaluation of HSlder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.
