Related papers: Wild ramification determines the characteristic cy…
Mutualistic interactions, which are beneficial for both interacting species, are recurrently present in ecosystems. Observations of natural systems showed that, if we draw mutualistic relationships as binary links between species, the…
Phenological timing -- i.e. the course of annually recurring development stages in nature -- is of particular interest since it can be understood as a proxy for the climate at a specific region; moreover changes in the so called…
A finite separable extension of a field is called primitive if there are no intermediate extensions. The most interesting primitive extensions of a local field with finite residue field are the wildly ramified ones, and our aim here is to…
We discuss how to characterize the behavior of a chaotic dynamical system depending on a parameter that varies periodically in time. In particular, we study the predictability time, the correlations and the mean responses, by defining a…
Models in evolutionary game theory traditionally assume symmetric interactions in homogeneous environments. Here, we consider populations evolving in a heterogeneous environment, which consists of patches of different qualities that are…
This paper builds fundamental perfect fields of positive characteristic and shows the structure of perfect fields that a field of positive characteristic is a perfect field if and only if it is an algebraic extension of a fundamental…
In this paper we consider wildly ramified power series, \emph{i.e.}, power series defined over a field of positive characteristic, fixing the origin, where it is tangent to the identity. In this setting we introduce a new invariant under…
Complementarity among species with different traits is one of the basic processes affecting biodiversity, defined as the number of species in the ecosystem. We present here a soluble model ecosystem in which the species are characterized by…
Ecology studies biodiversity in its variety and complexity. It describes how species distribute and perform in response to environmental changes. Ecological processes and structures are highly complex and adaptive. In order to quantify…
Biological systems are generally complicated and/or complex. In the former approach, one sets up a model with a large number of parameters to describe the system in detail. The latter approach focuses on understanding the universal aspects…
Let $K$ be a complete discrete valuation field with residue class field $k$, where both are of positive characteristic $p$. Then the group of wild automorphisms of $K$ can be identified with the group under composition of formal power…
Ecosystems are formed by networks of species and their interactions. Traditional models of such interactions assume a constant interaction strength between a given pair of species. However, there is often significant trait variation among…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…
Trait variation and similarity among coexisting species can provide a window into the mechanisms that maintain their coexistence. Recent theoretical explorations suggest that competitive interactions will lead to groups, or clusters, of…
Self-assembly processes are widespread in nature, and lie at the heart of many biological and physical phenomena. The characteristics of self-assembly building blocks determine the structures that they form. Two crucial properties are the…
Formal orbifolds are defined in higher dimension. Their \'etale fundamental groups are also defined. It is shown that the fundamental groups of formal orbifolds have certain finiteness property and it is also shown that they can be used to…
Elementary arguments show that a tree or forest is determined (up to isomorphism) by binary matroids defined using the adjacency matrix.
Diversification models describe the random growth of evolutionary trees, modeling the historical relationships of species through speciation and extinction events. One class of such models allows for independently changing traits, or types,…
The maintenance of diversity, the `commonness of rarity', and compositional turnover are ubiquitous features of species-rich communities. Through a minimal model, we consider how these features reflect the interplay between environmental…
Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the…