Related papers: Continuous and Tractable models for the Variation …
In this paper, we wish to investigate the dynamics of information transfer in evolutionary dynamics. We use information theoretic tools to track how much information an evolving population has obtained and managed to retain about different…
We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum…
Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…
In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…
Ridge regression with random coefficients provides an important alternative to fixed coefficients regression in high dimensional setting when the effects are expected to be small but not zeros. This paper considers estimation and prediction…
We study a discrete Susceptible-Infected-Recovered (SIR) model for the spread of infectious disease on a homogeneous tree and the limit behavior of the model in the case when the tree vertex degree tends to infinity. We obtain the…
This article presents a new model to predict the evolution of infective diseases under uncertainty or low-quality information, just as it has happened in the initial scenario during the CoVid-19 spread in China and Europe. The model has…
We introduce a Markov model for the evolution of a gene family along a phylogeny. The model includes parameters for the rates of horizontal gene transfer, gene duplication, and gene loss, in addition to branch lengths in the phylogeny. The…
Estimation of molecular evolutionary divergence times requires models of rate change. These vary with regard to the assumption of what quantity is penalized. The possibilities considered are the rate of evolution, the log of the rate of…
We present a continuous-time maximum likelihood estimation methodology for credit rating transition probabilities, taking into account the presence of censored data. We perform rolling estimates of the transition matrices with exponential…
We presents the closed form formulae for the likelihood Hessian matrix of a family of multivariate continuous-trait Gaussian Markov trait evolution model along a given phylogeny, in which the trait vector's mean is an affine function of…
We study a general setting of neutral evolution in which the population is of finite, constant size and can have spatial structure. Mutation leads to different genetic types ("traits"), which can be discrete or continuous. Under minimal…
This paper introduces a novel stochastic model for credit spreads. The stochastic approach leverages the diffusion of default intensities via a CIR++ model and is formulated within a risk-neutral probability space. Our research primarily…
Pattern formation in biological tissues plays an important role in the development of living organisms. Since the classical work of Alan Turing, a pre-eminent way of modelling has been through reaction-diffusion mechanisms. More recently,…
The inheritance of characteristics induced by the environment has often been opposed to the theory of evolution by natural selection. Yet, while evolution by natural selection requires new heritable traits to be produced and transmitted, it…
We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…
The tree-based ensembles are known for their outstanding performance in classification and regression problems characterized by feature vectors represented by mixed-type variables from various ranges and domains. However, considering…
We propose a new, flexible approach for dynamically maintaining successful mutation rates in evolutionary algorithms using $k$-bit flip mutations. The algorithm adds successful mutation rates to an archive of promising rates that are…
We introduce perhaps the simplest models of graph evolution with choice that demonstrate discontinuous percolation transitions and can be analyzed via mathematical evolution equations. These models are local, in the sense that at each step…
Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…