Related papers: Phylogenetic Ornstein-Uhlenbeck regression curves
We investigate stochastic parabolic evolution equations with time-dependent random generators and locally Lipschitz continuous drift terms. Using pathwise mild solutions, we construct an infinite-dimensional stationary Ornstein-Uhlenbeck…
We give a overview of stochastic models of evolution that have found applications in genetics, ecology and linguistics for an audience of nonspecialists, especially statistical physicists. In particular, we focus mostly on neutral models in…
We study the statistics of ecosystems with a variable number of co-evolving species. The species interact in two ways: by prey-predator relationships and by direct competition with similar kinds. The interaction coefficients change slowly…
Continuous random processes and fields are regularly applied to model temporal or spatial phenomena in many different fields of science, and model fitting is usually done with the help of data obtained by observing the given process at…
The small noise cut-off phenomenon in continuous time and space has been studied in the recent literature for the linear and non-linear stable Langevin dynamics with additive L\'evy drivers - understood as abrupt thermalization of the…
Although many phenotypic traits are determined by a large number of genetic variants, how a polygenic trait adapts in response to the changes in the environment is still poorly understood. Here we study the adaptation dynamics of a…
Molecular phenotypes are important links between genomic information and organismic functions, fitness, and evolution. Complex phenotypes, which are also called quantitative traits, often depend on multiple genomic loci. Their evolution…
We develop a time-optimal $O(mn^2)$-time algorithm to construct the subtree prune-regraft (SPR) graph on a collection of m phylogenetic trees with n leaves. This improves on the previous bound of $O(mn^3)$. Such graphs are used to better…
Phylogenetic analyses of gene expression have great potential for addressing a wide range of questions. These analyses will, for example, identify genes that have evolutionary shifts in expression that are correlated with evolutionary…
Time-series forecasting is one of the most active research topics in artificial intelligence. Applications in real-world time series should consider two factors for achieving reliable predictions: modeling dynamic dependencies among…
We consider a transformed Ornstein-Uhlenbeck process model that can be a good candidate for modelling real-life processes characterized by a combination of time-reverting behaviour with heavy distribution tails. We begin with presenting the…
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…
The ancestral sequence reconstruction problem is the inference, back in time, of the properties of common sequence ancestors from measured properties of contemporary populations. Standard algorithms for this problem assume independent…
Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel…
A pruning-aware adaptive gradient method is proposed which classifies the variables in two sets before updating them using different strategies. This technique extends the ``relevant/irrelevant" approach of Ding (2019) and Zimmer et al.…
We propose a novel approach for learning the evolution that employs differentiable neural networks to approximate the full GENERIC structure. Instead of manually choosing the fitted parameters, we learn the whole model together with the…
Although regression trees were originally designed for large datasets, they can profitably be used on small datasets as well, including those from replicated or unreplicated complete factorial experiments. We show that in the latter…
Dynamic graphs are rife with higher-order interactions, such as co-authorship relationships and protein-protein interactions in biological networks, that naturally arise between more than two nodes at once. In spite of the ubiquitous…
In this paper, we consider the problem of statistical inference for generalized Ornstein-Uhlenbeck processes of the type \[ X_{t} = e^{-\xi_{t}} \left( X_{0} + \int_{0}^{t} e^{\xi_{u-}} d u \right), \] where \(\xi_s\) is a L{\'e}vy process.…
We consider a biological population evolving under the joint action of selection, mutation and random genetic drift. The evolutionary dynamics are described by a one-dimensional Fokker-Planck equation whose eigenfunctions obey a confluent…