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We analyze the macroscale behavior of random lower (and therefore upper) triangular matrices with entries drawn iid from a distribution with nonzero mean and finite variance. We show that such a matrix behaves like a probabilistic version…
We study a subclass of the May-Leonard stochastic model with an arbitrary, even number of species, leading to the arising of two competing partnerships where individuals are indistinguishable. By carrying out a series of accurate numerical…
We present a general algorithm which permits to construct solutions in string cosmology for heterotic and type-IIB superstrings in four dimensions. Using a chain of transformations applied in sequence: conformal, T-duality and SL(2,R)…
For an infinity of number rings we express stable motivic invariants in terms of topological data determined by the complex numbers, the real numbers, and finite fields. We use this to extend Morel's identification of the endomorphism ring…
Stochastic automata over monoids as input sets are studied. The well-definedness of these automata requires an extension postulate that replaces the inherent universal property of free monoids. As a generalization of Turakainen's result, it…
Adaptive networks model social, physical, technical, or biological systems as attributed graphs evolving at the level of both their topology and data. They are naturally described by graph transformation, but the majority of authors take an…
In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…
The transfer operator (TO) formalism of the dynamical systems (DS) theory is reformulated here in terms of the recently proposed supersymetric theory of stochastic differential equations (SDE). It turns out that the stochastically…
Trotterization is a technique that allows one to approximate a time evolution of a Hamiltonian by repeatedly evolving the individual terms of the Hamiltonian one-at-a-time for small time durations. Bounds on the error of this approximation…
Random matrix models provide a phenomenological description of a vast variety of physical phenomena. Prominent examples include the eigenvalue statistics of quantum (chaotic) systems, which are conveniently characterized using the spectral…
We consider the creeping flow of a Newtonian fluid in a hemispherical region. In a domain with spherical, or nearly spherical, geometry, the solution of Stokes equation can be expressed as a series of spherical harmonics. However, the…
This is the first in a series of papers devoted to foundations of topological stacks. We begin developing a homotopy theory for topological stacks along the lines of classical homotopy theory of topological spaces. In this paper we go as…
We propose a simple model for the phenomenon of Eulerian spontaneous stochasticity in turbulence. This model is solved rigorously, proving that infinitesimal small-scale noise in otherwise a deterministic multi-scale system yields a…
We describe the spectral theory of the adjacency operator of a graph which is isomorphic to homogeneous trees at infinity. Using some combinatorics, we reduce the problem to a scattering problem for a finite rank perturbation of the…
We consider holomorphic twists of arbitrary supersymmetric theories in four dimensions. Working in the BV formalism, we rederive classical results characterizing the holomorphic twist of chiral and vector supermultiplets, computing the…
Starting with a combinatorial partition theorem for words over an infinite alphabet dominated by a fixed sequence, established recently by the authors, we prove recurrence results for topological dynamical systems indexed by such words. In…
In "Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data" (arxiv:1209.2045) we described all smooth solutions of the two-function tt*-Toda equations in terms of asymptotic data, holomorphic data, and monodromy data.…
We develop techniques that lay out a basis for generalizations of the famous Thurston's Topological Characterization of Rational Functions for an infinite set of marked points and branched coverings of infinite degree. Analogously to the…
We prove the conjectural relation between the Stokes matrix for the quantum cohomology and an exceptional collection generating the derived category of coherent sheaves in the case of smooth cubic surfaces. The proof is based on a toric…
We define several topological spaces whose points are quivers with a given infinite vertex set $X$. In the special case when $X$ is countably infinite, we show that two of the spaces of interest are homeomorphic to the Baire space…