Related papers: Phase transition in the two star Exponential Rando…
Conventionally used exponential random graphs cannot directly model weighted networks as the underlying probability space consists of simple graphs only. Since many substantively important networks are weighted, this limitation is…
We consider the Ising model for two interacting groups of spins embedded in an Erd\"{o}s-R\'{e}nyi random graph. The critical properties of the system are investigated by means of extensive Monte Carlo simulations. Our results evidence the…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
The two-star random graph is the simplest exponential random graph model with nontrivial interactions between the graph edges. We propose a set of auxiliary variables that control the thermodynamic limit where the number of vertices N tends…
The unconstrained exponential family of random graphs assumes no prior knowledge of the graph before sampling, but it is natural to consider situations where partial information about the graph is known, for example the total number of…
Based on numerical simulation and local stability analysis we describe the structure of the phase space of the edge/triangle model of random graphs. We support simulation evidence with mathematical proof of continuity and discontinuity for…
Exponential Random Graph Models (ERGM) behave peculiar in large networks with thousand(s) of actors (nodes). Standard models containing two-star or triangle counts as statistics are often unstable leading to completely full or empty…
Consider a graph $G$ and an initial random configuration, where each node is black with probability $p$ and white otherwise, independently. In discrete-time rounds, each node becomes black if it has at least $r$ black neighbors and white…
This paper examines a model involving two dynamic Erd\H{o}s-R\'enyi random graphs that evolve in parallel, with edges in each graph alternating between being present and absent according to specified on- and off-time distributions. A key…
We present a new few-parameter phenomenological model of light curves of eclipsing binaries and stars with transiting planets that is able to fit the observed light curves with the accuracy better than 1\% of their amplitudes. The model can…
We show that by restricting the degrees of the vertices of a graph to an arbitrary set \( \Delta \), the threshold point $ \alpha(\Delta) $ of the phase transition for a random graph with $ n $ vertices and $ m = \alpha(\Delta) n $ edges…
Two-phase flow systems in porous media have complex dynamics. It is well established that a wide range of system parameters like viscosities and porosity as well as flow parameters such as pressure gradient and fluid saturation have strong…
We demonstrate the identification and classification of topological phase transitions from experimental data using Diffusion Maps: a nonlocal unsupervised machine learning method. We analyze experimental data from an optical system…
Consider the complete graph on \(n\) vertices where each edge is independently open with probability \(p,\) or closed otherwise. Phase transitions for such graphs for \(p = \frac{C}{n}\) have previously been studied using techniques like…
The analytical zero-temperature phase diagram of the double exchange model for classical background spins as a function of the carrier density and Hund's coupling in the entire range of these parameters is presented. By constructing a…
Monte Carlo simulations and dynamical mean-field approximations are performed to study the phase transitions in rock-scissors-paper game on different host networks. These graphs are originated from lattices by introducing quenched and…
A phase transition of gas-liquid type with an upper critical point is examined which arises in a model of charges of one sign on compensating background (OCP). The phase transition parameters are dependent on the detailed assumptions about…
We use a simplified model which is based on the same physics as inherent in most statistical models for nuclear multifragmentation. The simplified model allows exact calculations for thermodynamic properties of systems of large number of…
The observed light curves of most eclipsing binaries and stars with transiting planets can be well described and interpreted by current advanced physical models which also allow for the determination of many physical parameters of eclipsing…
We study a random graph model in continuous time. Each vertex is partially copied with the same rate, i.e.\ an existing vertex is copied and every edge leading to the copied vertex is copied with independent probability $p$. In addition,…