Related papers: Asymptotic Transfer in Critical Recursive Composit…
The problem of finding graph structure of functions commuting with a given function in terms of their functional graphs is considered. Structure of functional graphs of commuting functions is described. The problem is reduced to describing…
We study measures on $\mathbb{R}^d$ which are induced by a class of infinite and recursive iterations in symbolic dynamics. Beginning with a finite set of data, we analyze prescribed recursive iteration systems, each involving subdivisions.…
Let G be a totally disconnected, locally compact group admitting a contractive automorphism f. We prove a Jordan-Holder theorem for series of f-stable closed subgroups of G, classify all possible composition factors and deduce consequences…
Functional decomposition is the process of breaking down a function $f$ into a composition $f=g(f_1,\dots,f_k)$ of simpler functions $f_1,\dots,f_k$ belonging to some class $\mathcal{F}$. This fundamental notion can be used to model…
Every Model of High-Level Computation (MHC) has an underlying composition mechanism for combining simple computing devices into more complex ones. Composition can be done by (explicitly or implicitly) defining control flow, data flow or any…
As countless examples show, it can be fruitful to study a sequence of complicated objects all at once via the formalism of generating functions. We apply this point of view to the homology and combinatorics of orbit configuration spaces:…
The purpose of this paper is to study the limiting distribution of special {\it additive functionals} on random planar maps, namely the number of occurrences of a given {\it pattern}. The main result is a central limit theorem for these…
If F is a master function corresponding to a hyperplane arrangement A and a collection of weights y, we investigate the relationship between the critical set of F, the variety defined by the vanishing of the one-form w = d log F, and the…
In the last years the attention towards topological dynamical properties of highly discontinuous maps has increased significantly. In [D.Corona, A. Della Corte. The critical exponent functions. Comptes Rendus Math\'ematique, 360(G4),…
Atomistic simulations provide the most detailed picture of grain boundary (GB) migration currently available. Nevertheless, extracting unit mechanisms from atomistic simulation data is difficult because of the zoo of competing,…
We present the results of an experimental study of patterned segregation in a horizontally shaken shallow layer of a binary mixture of dry particles. An order parameter for the segregated structures is defined and the effect of the…
Let G be a possibly disconnected reductive group over a finite field with Frobenius map F. The main result of this paper is that the characteristic functions af "admissible complexes" A on G such that F^*A is isomorphic to A form a basis of…
We present a categorical theory of the composition methods in finite model theory -- a key technique enabling modular reasoning about complex structures by building them out of simpler components. The crucial results required by the…
This paper studies the distribution of the component spectrum of combinatorial structures such as uniform random forests, in which the classical generating function for the numbers of (irreducible) elements of the different sizes converges…
This paper establishes that generic linear quantum stochastic systems have a pure cascade realization of their transfer function, generalizing an earlier result established only for the special class of completely passive linear quantum…
Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables) and computing the outcome in other…
We deal with the random combinatorial structures called assemblies. By weakening the logarithmic condition which assures regularity of the number of components of a given order, we extend the notion of logarithmic assemblies. Using the…
We prove two main results on Denjoy-Carleman classes: (1) a composite function theorem which asserts that a function f(x) in a quasianalytic Denjoy-Carleman class Q, which is formally composite with a generically submersive mapping y=h(x)…
We establish a number of "concatenation theorems" that assert, roughly speaking, that if a function exhibits "polynomial" (or "Gowers anti-uniform", "uniformly almost periodic", or "nilsequence") behaviour in two different directions…
We present an extensive treatment of the generalized mode-coupling theory (GMCT) of the glass transition, which seeks to describe the dynamics of glass-forming liquids using only static structural information as input. This theory amounts…