Related papers: Wild ramification determines the characteristic cy…
Genetic information and environmental factors determine the path of an individuals life and therefore, the evolution of its entire species. We have succeeded in proposing and studying a model that captures this idea. In our model, a…
Ecological systems comprise an astonishing diversity of species that cooperate or compete with each other forming complex mutual dependencies. The minimum requirements to maintain a large species diversity on long time scales are in general…
Let $K$ be a complete discrete valued field of characteristic $p$ with residue $k$ which is not necessarily perfect. We prove the Conjecture in \cite{cs} that a $p$-algebra over $K$ contains a totally ramified cyclic maximal subfield if it…
Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is…
For a wildly ramified extension $K/k$ of complete discrete valuation fields we study collections of elements of $k[G]$ (where $G=Gal(K/k)$) that fit well for constructing bases of various associated Galois modules and orders. In the case…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Species trees represent the historical divergences of populations or species, while gene trees trace the ancestry of individual gene copies sampled within those populations. In cases involving rapid speciation, gene trees with topologies…
Each Gr\"obner stratum of a tropical variety is a connected set of points, all of which induce the same initial subscheme. The Gr\"obner stratification is a coarsening of the decomposition into Gr\"obner polyhedra, and has the advantage…
The known bijections on Dyck paths are either involutions or have notoriously intractable cycle structure. Here we present a size-preserving bijection on Dyck paths whose cycle structure is amenable to complete analysis. In particular, each…
If one isolated species is supposed to evolve following the logistic mapping, then we are tempted to think that the dynamics of two species can be expressed by a coupled system of two discrete logistic equations. As three basic…
We investigate relations between the pseudo-orbit-tracing property, topological stability and openness for tree-shifts. We prove that a tree-shift is of finite type if and only if it has the pseudo-orbit-tracing property which implies that…
We define generalizations of classical invariants of wild ramification for coverings on a variety of arbitrary dimension over a local field. For an l-adic sheaf, we define its Swan class as a 0-cycle class supported on the wild ramification…
We explore to what extent the properties of a Gauss diagram are affected by the choice of its Hamiltonian cycle. We present an example of a realizable Gauss diagram and an unrealizable Gauss diagram that differ only by a choice of the…
Complexity in biology is often described using a multi-map architecture, where the genotype, representing the encoded information, is mapped to the functional level, known as the phenotype, which is then connected to a latent phenotype we…
Mutualistic interactions, where individuals from different species can benefit from each other, are widespread across ecosystems. This study develops a general deterministic model of mutualism involving two populations, assuming that…
Protein structures in nature often exhibit a high degree of regularity (secondary structures, tertiary symmetries, etc.) absent in random compact conformations. We demonstrate in a simple lattice model of protein folding that structural…
We give an intrinsic parametrisation of the set of tamely ramified extensions of a local field with finite residue field and bring to the fore the role played by group cohomology. We show that two natural definitions of the cohomology class…
Given a self-equivalence of a global function field, its wild set is the set of points where the self-equivalence fails to preserve parity of valuation. In this paper we describe structure of finite wild sets.
Mutualisms are key for structuring ecological communities, but they are sensitive to environmental change and fluctuations in population size. Consequently, how mutualisms achieve stability remains an open question in ecological theory.…
Disordered systems theory provides powerful tools to analyze the generic behaviors of highdimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality…