arXiv subjects

Leonardo Aguirre

Publications and source records attributed to Leonardo Aguirre.

4 recordsLinked to original sources

arXiv2026

Coexistence coalitions in propagule disperser quasi-communities

Many natural ecosystems harbor large numbers of coexisting species competing for far fewer distinct resources, in apparent defiance of the competitive exclusion principle. Various mechanisms have been proposed to explain this apparent paradox, often pertaining to organisms with a two-stage sessile--propagule life cycle. Here we develop a stochastic model class for such propagule disperser communities that combines competition--colonization trade-offs, spatial heterogeneity, demographic stochasticity, as well as inherited trait variation, and recover several classical models as special or limiting cases. Using bifurcation analysis, we classify equilibrium coalitions near the extinction threshold and give sufficient conditions for their realization by macroscopic equilibria away from the threshold, bypassing the costly numerical computation of the actual equilibrium states. Illustrative examples examine the resulting trait distributions and coalition patterns, demonstrating the interactive effects of different coexistence mechanisms.

q-bio.PE↗

arXiv2018

Finitary Process Evolution I: Information Geometry of Configuration Space and the Process-Replicator Dynamics

This report presents some fundamental mathematical results towards elucidating the information-geometric underpinnings of evolutionary modelling schemes for (quasi-)stationary discrete stochastic processes. The model class under consideration is that of finite causal-state processes, known from the computational mechanics programme, along with their minimal unifilar hidden Markov generators. The respective configuration space is exhibited as a collection of combinatorially related Riemannian manifolds wherein the metric tensor field is an infinitesimal version of the relative entropy rate. Furthermore, a certain evolutionary inference iteration is defined which can be executed by generator-carrying agents and generalizes the Wright-Fisher model from population genetics. The induced dynamics on configuration space is studied from the large deviation point of view and it is shown that the associated asymptotic expectation dynamics follows the Riemannian gradient flow of a given fitness potential. In fact, this flow can formally be viewed as an information-geometric generalization of the replicator dynamics from population biology.

math.PR↗

arXiv2015

Gaudin subalgebras and wonderful models

Gaudin hamiltonians form families of r-dimensional abelian Lie subalgebras of the holonomy Lie algebra of the arrangement of reflection hyperplanes of a Coxeter group of rank r. We consider the set of principal Gaudin subalgebras, which is the closure in the appropriate Grassmannian of the set of spans of Gaudin hamiltonians. We show that principal Gaudin subalgebras form a smooth projective variety isomorphic to the De Concini-Procesi compactification of the projectivized complement of the arrangement of reflection hyperplanes.

math-ph↗

arXiv2010

Gaudin subalgebras and stable rational curves

Gaudin subalgebras are abelian Lie subalgebras of maximal dimension spanned by generators of the Kohno-Drinfeld Lie algebra t_n. We show that Gaudin subalgebras form a variety isomorphic to the moduli space of stable curves of genus zero with n+1 marked points. In particular, this gives an embedding of the moduli space in a Grassmannian of (n-1)-planes in an n(n-1)/2-dimensional space. We show that the sheaf of Gaudin subalgebras over the moduli space is isomorphic to a sheaf of twisted first order differential operators. For each representation of the Kohno--Drinfeld Lie algebra with fixed central character, we obtain a sheaf of commutative algebras whose spectrum is a coisotropic subscheme of a twisted version of the logarithmic cotangent bundle of the moduli space.

math.AG↗