Related papers: The Laplace Motion in Phylogenetic Comparative Met…
This is a guide to the mathematical theory of Brownian motion and related stochastic processes, with indications of how this theory is related to other branches of mathematics, most notably the classical theory of partial differential…
This manuscript contains nothing new, but synthesizes known results: For the theoretical population geneticist with a probabilistic background, we provide a summary of some key results on stochastic differential equations. For the…
We study a stochastic spatial model of biological competition in which two species have the same birth and death rates, but different diffusion constants. In the absence of this difference, the model can be considered as an off-lattice…
Evolving morphologies and controllers of robots simultaneously leads to a problem: Even if the parents have well-matching bodies and brains, the stochastic recombination can break this match and cause a body-brain mismatch in their…
There have been many studies to examine whether one trait is correlated with another trait across a group of present-day species (for example, do species with larger brains tend to have longer gestation times. Since the introduction of the…
Lanchester's model of combat has certain deficiencies in its standard form arising from the neglect of the influence of random fluctuations. Several approaches to rectify this have been proposed and various results are scattered throughout…
Molecular motion through pores plays a crucial role in various natural and industrial processes. One of the most fascinating features of biological channel-facilitated transport is a stochastic gating process, when the channels dynamically…
Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections…
Due to recent advances in synthetic biology and artificial life, the origin of life is currently a hot topic of research. We review the literature and argue that the two traditionally competing "replicator-first" and "metabolism-first"…
Biological data objects often have both of the following features: (i) they are functions rather than single numbers or vectors, and (ii) they are correlated due to phylogenetic relationships. In this paper we give a flexible statistical…
This paper investigates the motion of falling leaves through modeling using papers and the corresponding data collected from more than four thousands experiments. Two series of experiments were designed in order to study the relationship…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described…
Diffusion processes are a class of stochastic differential equations (SDEs) providing a rich family of expressive models that arise naturally in dynamic modelling tasks. Probabilistic inference and learning under generative models with…
We present a novel extension of multi-output Gaussian processes for handling heterogeneous outputs. We assume that each output has its own likelihood function and use a vector-valued Gaussian process prior to jointly model the parameters in…
Emerging data analysis involves the ingestion and exploration of new data sets, application of complex functions, and frequent query revisions based on observing prior query answers. We call this new type of analysis evolutionary analytics…
Estimating the phylogeny of the genus Homo is entering a new phase of vastly improved data and methodology. There is increasing evidence of 6 to 10 competing species/lineages at any point in the last half million years, making the…
In the classical (non-quantum) relativity theory the course of the moving clock is dilated as compared to the course of the clock at rest (the Einstein dilation). Any unstable system may be regarded as a clock. The time evolution (e.g., the…
In this article we propose a novel method to estimate the frequency distribution of linguistic variables while controlling for statistical non-independence due to shared ancestry. Unlike previous approaches, our technique uses all available…
Current phylogenetic comparative methods generally employ the Ornstein-Uhlenbeck(OU) process for modeling trait evolution. Being able of tracking the optimum of a trait within a group of related species, the OU process provides information…