Related papers: A Relaxed Drift Diffusion Model for Phylogenetic T…
We study interacting systems of linear Brownian motions whose drift vector at every time point is determined by the relative ranks of the coordinate processes at that time. Our main objective has been to study the long range behavior of the…
Generative modeling can be formulated as learning a mapping f such that its pushforward distribution matches the data distribution. The pushforward behavior can be carried out iteratively at inference time, for example in diffusion and…
In this paper, we consider a mathematical model for the evolution of neutral genetic diversity in a spatial continuum including mutations, genetic drift and either short range or long range dispersal. The model we consider is the spatial $…
Complex networks have established themselves along the last years as being particularly suitable and flexible for representing and modeling several complex natural and human-made systems. At the same time in which the structural intricacies…
Co-localization of networks of genes in the nucleus is thought to play an important role in determining gene expression patterns. Based upon experimental data, we built a dynamical model to test whether pure diffusion could account for the…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit…
We implement Bayesian model selection and parameter estimation for the case of fractional Brownian motion with measurement noise and a constant drift. The approach is tested on artificial trajectories and shown to make estimates that match…
Motivated as a null model for comparison with data, we study the following model for a phylogenetic tree on $n$ extant species. The origin of the clade is a random time in the past, whose (improper) distribution is uniform on $(0,\infty)$.…
While Neutral Theory famously describes the number of discrete genetic differences in populations, we consider the number of genetic backgrounds under which such differences are observed - setting limits to the generalizability of their…
Infectious disease dynamics operate across multiple biological scales, with within-host viral dynamics being a key driver of between-host transmission. However, while models that explicitly link these scales exist, none have been developed…
Clinical trials are complex and usually involve multiple objectives such as controlling type I error rate, increasing power to detect treatment difference, assigning more patients to better treatment, and more. In literature, both…
Stretched-exponential relaxation is a widely observed phenomenon found in ordered ferromagnets as well as glassy systems. One modeling approach connects this behavior to a droplet dynamics described by an effective Langevin equation for the…
$N$-Brownian bees is a branching-selection particle system in $\mathbb{R}^d$ in which $N$ particles behave as independent binary branching Brownian motions, and where at each branching event, we remove the particle furthest from the origin.…
Consider a graph where the sites are distributed in space according to a Poisson point process on $\mathbb R^n$. We study a population evolving on this network, with individuals jumping between sites with a rate which decreases…
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…
Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) which converges back to a Brownian motion with reduced diffusion coefficient at long times, after the anomalous…
To model discrete sequences such as DNA, proteins, and language using diffusion, practitioners must choose between three major methods: diffusion in discrete space, Gaussian diffusion in Euclidean space, or diffusion on the simplex. Despite…
For refracted skew Brownian motion (skew Brownian motion with two-valued drift), adopting a perturbation approach we find expressions of its potential densities. As applications, we recover its transition density and study its long-time…
In this paper, we extend the transfer learning classification framework from regression function-based methods to decision rules. We propose a novel methodology for modeling posterior drift through Bayes decision rules. By exploiting the…