相关论文: On the Inverse Problem for a Size-Structured Popul…

Starting from the dynamical system model capturing the splitting-differentiation process of populations, we extend this notion to show how the speciation mechanism from a single species leads to the consideration of several well known…

We examine the problem of family size statistics (the number of individuals carrying the same surname, or the same DNA sequence) in a given size subsample of an exponentially growing population. We approach the problem from two directions.…

The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most…

A ubiquitous feature of living cells is their growth over time followed by division into daughter cells. How isogenic cell populations maintain size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental…

Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…

We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a…

In this paper, we establish a new law of large numbers with the rate of convergence for special partial sums in a probability space. The proof relies on nonlinear expectation theory, as the uncertainty of random variables in the special…

We present an explicit solution to a classic model of cell-population growth introduced by Luria and Delbrueck 70 years ago to study the emergence of mutations in bacterial populations. In this model a wild-type population is assumed to…

Regular variation of distributional tails is known to be preserved by various linear transformations of some random structures. An inverse problem for regular variation aims at understanding whether the regular variation of a transformed…

This paper investigates a nonlinear logistic model for age-structured population dynamics. The model incorporates interdependent fertility and mortality functions within a logistic framework, offering insights into stationary solutions and…

Solving the inverse problem is the key step in evaluating the capacity of a physical model to describe real phenomena. In medical image computing, it aligns with the classical theme of image-based model personalization. Traditionally, a…

We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…

We model the growth of a cell population using a piecewise deterministic Markov branching tree. In this model, each cell splits into two offspring at a division rate $B(x)$, which depends on its size $x$. The size of each cell increases…

In this work, an inverse problem in the fractional diffusion equation with random source is considered. Statistical moments are used of the realizations of single point observation $u(x_0,t,\omega).$ We build the representation of the…

How can one change a system, in order to change its statistical properties in a prescribed way? In this note we consider a control problem related to the theory of linear response. Given an expanding map of the unit circle with an…

The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…

Population stratification is a problem encountered in several areas of biology and public health. We tackle this problem by mapping a population and its elements attributes into a hypergraph, a natural extension of the concept of graph or…

In this paper, we study the inverse problem for a class of abstract ultraparabolic equations which is well-known to be ill-posed. We employ some elementary results of semi-group theory to present the formula of solution, then show the…

This is a truncation of the second year group project at Imperial college london. In this paper, we consider a semilinear reaction diffusion system of SIR model which involves the birth rate and the death rate. We first prove the…

We consider the general character of the spatial distribution of a population that grows through reproduction and subsequent local resettlement of new population members. We present several simple one and two-dimensional point placement…