Related papers: Multi-type Galton-Watson processes with affinity-d…
We observe the Galton-Watson Branching Processes. Limit properties of transition functions and their convergence to invariant measures are investigated.
Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be…
Reinforced Galton--Watson processes describe the dynamics of a population where reproduction events are reinforced, in the sense that offspring numbers of forebears can be repeated randomly by descendants. More specifically, the evolution…
Conditioning a multitype Galton-Watson process to stay alive into the indefinite future leads to what is known as its associated $Q$-process. We show that the same holds true if the process is conditioned to reach a positive threshold or a…
Multi-model inference covers a wide range of modern statistical applications such as variable selection, model confidence set, model averaging and variable importance. The performance of multi-model inference depends on the availability of…
We consider a (sub) critical Galton-Watson process with neutral mutations (infinite alleles model), and decompose the entire population into clusters of individuals carrying the same allele. We specify the law of this allelic partition in…
We consider the bifurcating Markov chain model introduced by Guyon to detect cellular aging from cell lineage. To take into account the possibility for a cell to die, we use an underlying Galton-Watson process to describe the evolution of…
Multi-type inhomogeneous Galton--Watson process with immigration is investigated, where the offspring mean matrix slowly converges to a critical mean matrix. Under general conditions we obtain limit distribution for the process, where the…
Cells are known to exert forces to sense their physical surroundings for guidance of motion and fate decisions. Here, we propose that cells might do mechanical work to drive their own evolution, taking inspiration from the adaptive immune…
We study an extension of the so-called defective Galton-Watson processes obtained by allowing the offspring distribution to change over the generations. Thus, in these processes, the individuals reproduce independently of the others and in…
We study a model of a branching process subject to selection, modeled by giving each family an individual fitness acting as a branching rate, and mutation, modeled by resampling the fitness of a proportion of offspring in each generation.…
This paper is concerned with an extended Galton-Watson process so as to allow individuals to live and reproduce for more than one unit time. We assume that each individual can live $k$ seasons (time-units) with probability $h_k$, and…
We are frequently faced with a large collection of antibodies, and want to select those with highest affinity for their cognate antigen. When developing a first-line therapeutic for a novel pathogen, for instance, we might look for such…
The clonal selection principle explains the basic features of an adaptive immune response to a antigenic stimulus. It established the idea that only those cells that recognize the antigens are selected to proliferate and differentiate. This…
In this work we adopt a statistical mechanics approach to investigate basic, systemic features exhibited by adaptive immune systems. The lymphocyte network made by B-cells and T-cells is modeled by a bipartite spin-glass, where, following…
In response to pathogens, the adaptive immune system generates specific antibodies that bind and neutralize foreign antigens. Understanding the composition of an individual's immune repertoire can provide insights into this process and…
One of the problems in applying Genetic Algorithm is that there is some situation where the evolutionary process converges too fast to a solution which causes it to be trapped in local optima. To overcome this problem, a proper diversity in…
We are interested in modeling theoretical immunology within a statistical mechanics flavor: focusing on the antigen-independent maturation process of B-cells, in this paper we try to revise the problem of self vs non-self discrimination by…
A properly scaled critical Galton-Watson process converges to a continuous state critical branching process $\xi(\cdot)$ as the number of initial individuals tends to infinity. We extend this classical result by allowing for overlapping…
The persistence of life requires populations to adapt at a rate commensurate with the dynamics of their environment. Successful populations that inhabit highly variable environments have evolved mechanisms to increase the likelihood of…