Related papers: Asymptotic Transfer in Critical Recursive Composit…
Let $\mathcal G$ denote the space of finitely generated marked groups. For any finitely generated group $G$, we construct a continuous, injective map $f$ from the space of subgroups $Sub(G)$ to $\mathcal G$ that sends conjugate subgroups to…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence an epidemic state within a population. "Explosive" first-order transitions have…
In the vicinity of a phase transition, the order parameter starts fluctuating before vanishing at the critical point. The fluctuation regime, i.e. the way the ordered phase disappears, is a characteristics of a transition, and determines…
For a fixed graph H, the function #IndSub(H,*) maps graphs G to the count of induced H-copies in G; this function obviously "counts something" in that it has a combinatorial interpretation. Linear combinations of such functions are called…
We assess the probability of resonances between sufficiently distant states in a combinatorial graph serving as the configuration space of an N-particle disordered quantum system. This includes the cases where the transition "shuffles" the…
Recent feed-forward neural methods of arbitrary image style transfer mainly utilized encoded feature map upto its second-order statistics, i.e., linearly transformed the encoded feature map of a content image to have the same mean and…
Monadically stable and monadically NIP classes of structures were initially studied in the context of model theory and defined in logical terms. They have recently attracted attention in the area of structural graph theory, as they…
Scanning probes reveal complex, inhomogeneous patterns on the surface of many condensed matter systems. In some cases, the patterns form self-similar, fractal geometric clusters. In this paper, we advance the theory of criticality as it…
Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…
The critical behavior of a dimer model with an interaction favoring parallel dimers in each plaquette of the square lattice is studied numerically by means of the Corner Transfer Matrix Renormalization Group algorithm. The critical…
A two parameter percolation model with nucleation and growth of finite clusters is developed taking the initial seed concentration \rho and a growth parameter g as two tunable parameters. Percolation transition is determined by the final…
The mechanisms of comprehension during language processing remains an open question. Classically, building the meaning of a linguistic utterance is said to be incremental, step-by-step, based on a compositional process. However, many…
We study the full-counting statistics of charges transmitted through a single-level quantum dot weakly coupled to a local Einstein phonon which causes fluctuations in the dot energy. An analytic expression for the cumulant generating…
A structural analysis of construction schemes is developed. That analysis is used to give simple and new constructions of combinatorial objects which have been of interest to set theorists and topologists. We then continue the study of…
We employ techniques from optimal transport in order to prove decay of transfer operators associated to iterated functions systems and expanding maps, giving rise to a new proof without requiring a Doeblin-Fortet (or Lasota-Yorke)…
We present models where $\gamma_+$ and $\gamma_-$, the exponents of the susceptibility in the high and low temperature phases, are generically different. In these models, continuous symmetries are explicitly broken down by discrete…
We prove connections between Zeckendorf decompositions and Benford's law. Recall that if we define the Fibonacci numbers by $F_1 = 1, F_2 = 2$ and $F_{n+1} = F_n + F_{n-1}$, every positive integer can be written uniquely as a sum of…
We develop a model that establishes a quantitative link between the physical properties of molecular aggregates and their constituent building blocks. The relation is built on the coherent potential approximation, calibrated against exact…
We show that continuous filling or wedge-wetting transitions are possible in 3D wedge-geometries made from (angled) substrates exhibiting first-order wetting transitions and develop a comprehensive fluctuation theory yielding a complete…