Related papers: Dynamics on Wild Character Varieties
Differential equations with the Painlev\'e property have been studied extensively due to their appearance in many branches of mathematics and their applicability in physics. Although a modern, differential algebraic treatment of the order…
Natural experiments are observational studies where the assignment of treatment conditions to different populations occurs by chance "in the wild". Researchers from fields such as economics, healthcare, and the social sciences leverage…
We establish a theory for multivariate extreme value analysis of dynamical systems. Namely, we provide conditions adapted to the dynamical setting which enable the study of dependence between extreme values of the components of…
The theory of Hitchin systems is something like a "global theory of Lie groups", where one works over a Riemann surface rather than just at a point. We'll describe how one can take this analogy a few steps further by attempting to make…
Graphical models are a key class of probabilistic models for studying the conditional independence structure of a set of random variables. Circular variables are special variables, characterized by periodicity, arising in several contexts…
It has been postulated that a good representation is one that disentangles the underlying explanatory factors of variation. However, it remains an open question what kind of training framework could potentially achieve that. Whereas most…
The purpose of this article is to motivate the study of invariant, and especially conformally invariant, differential pairings. Since a general theory is lacking, this work merely presents some interesting examples of these pairings,…
A key goal in studies of ecology and evolution is understanding the causes of phenotypic diversity in nature. Most traits of interest, such as those relating to morphology, life-history, immunity and behaviour are quantitative, and…
The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model (VM) dynamics)…
Let k be an algebraically closed field of odd characteristic. We describe derivations of a large class of quantizations of affine normal Poisson varieties over k.
We introduce the special issue on the Statistical Mechanics of Climate published on the Journal of Statistical Physics by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great…
The sixth Painlev\'e equation is hiding extremely rich geometric structures behind its outward appearance. This article tries to give as a total picture as possible of its dynamical natures, based on the Riemann-Hilbert approach recently…
We investigate some of the discrete Painleve equations (dPII, qPI and qPII) and the discrete KdV equation over finite fields. The first part concerns the discrete Painleve equations. We review some of the ideas introduced in our previous…
We provide an introduction to enumerating and constructing invariants of group representations via character methods. The problem is contextualised via two case studies arising from our recent work: entanglement measures, for characterising…
Simple analytic considerations are applied to recently discovered patterns in a generalized Fisher equation for population dynamics. The generalization consists of the inclusion of non-local competition interactions among individuals. We…
The current observational and experimental bounds on time variation of the constants of Nature are briefly reviewed.
We test against two different sets of data an apparently new approach to the analysis of the variance of a numerical variable which depends on qualitative characters. We suggest that this approach be used to complement other existing…
Analysis of experimental kinetic dependences and results of the computer modeling of pairwise interactions in the heterogeneous system have shown that a character of its fractal property variation in the evolution process would be different…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
Living species, ranging from bacteria to animals, exist in environmental conditions that exhibit spatial and temporal heterogeneity which requires them to adapt. Risk-spreading through spontaneous phenotypic variations is a known concept in…