Related papers: Neighborhood growth dynamics on the Hamming plane
Non-equilibrium dynamics of many-body quantum systems under the effect of measurement protocols is attracting an increasing amount of attention. It has been recently revealed that measurements may induce an abrupt change in the scaling-law…
We consider exploration algorithms of the random sequential adsorption type both for homogeneous random graphs and random geometric graphs based on spatial Poisson processes. At each step, a vertex of the graph becomes active and its…
For two-loop two-point diagrams with arbitrary masses, an algorithm to derive the asymptotic expansion at large external momentum squared is constructed. By using a general theorem on asymptotic expansions of Feynman diagrams, the…
Bootstrap percolation on a graph is a deterministic process that iteratively enlarges a set of occupied sites by adjoining points with at least $\theta$ occupied neighbors. The initially occupied set is random, given by a uniform product…
We present a proof of the monotonic entropy growth for a nonlinear discrete-time model of a random market. This model, based on binary collisions, also may be viewed as a particular case of Ulam's redistribution of energy problem. We…
We investigate the dynamics of the entanglement Hamiltonian in a system of one-dimensional free fermions, following a local joining quench of two initially disconnected half-chains in their ground states. Applying techniques of conformal…
The problem of designing policies for in-network function computation with minimum energy consumption subject to a latency constraint is considered. The scaling behavior of the energy consumption under the latency constraint is analyzed for…
An algorithm is constructed to derive a small momentum expansion for two-loop two-point diagrams in all cases where, due to the presence of physical thresholds, there are singularities at zero external momentum. The coefficients of this…
We map the dynamics of entanglement in random unitary circuits, with finite on-site Hilbert space dimension $q$, to an effective classical statistical mechanics, and develop general diagrammatic tools for calculations in random unitary…
For many random graph models, the analysis of a related birth process suggests local sampling algorithms for the size of, e.g., the giant connected component, the $k$-core, the size and probability of an epidemic outbreak, etc. In this…
We investigate the complexity of local search based on steepest ascent. We show that even when all variables have domains of size two and the underlying constraint graph of variable interactions has bounded treewidth (in our construction,…
We found that models of evolving random networks exhibit dynamic scaling similar to scaling of growing surfaces. It is demonstrated by numerical simulations of two variants of the model in which nodes are added as well as removed [Phys.…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
A bidimensional parameter space of unitary area is introduced to study phenomenologically the dynamic and thermodynamic behavior of inflationary models driven by a scalar field coupled to a thermal component. In this enlarged context the…
We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, $1- \varepsilon > 0$ or $ - (1 + \varepsilon) < 0$. We study the specific case where the…
In this paper we consider a population process evolving on a dynamic random graph. The dynamic random graph is an Erd\H{o}s--R\'enyi graph that is resampled every time unit, independently of the previous ones, with `edge existence…
The behaviour of two-loop two-point diagrams at non-zero thresholds corresponding to two-particle cuts is analyzed. The masses involved in a cut and the external momentum are assumed to be small as compared to some of the other masses of…
Networks in nature are often formed within a spatial domain in a dynamical manner, gaining links and nodes as they develop over time. We propose a class of spatially-based growing network models and investigate the relationship between the…
The dynamics of a population expanding into unoccupied habitat has been primarily studied for situations in which growth and dispersal parameters are uniform in space or vary in one dimension. Here we study the influence of finite-sized…
We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…