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Interdependent networks are more fragile under random attacks than simplex networks, because interlayer dependencies lead to cascading failures and finally to a sudden collapse. This is a hybrid phase transition (HPT), meaning that at the…
We describe a phase transition in continuum limits of interacting particle systems that exhibits a vertical bifurcation diagram. The transition is mediated by a competition short-range repulsion and long-range attraction. As a consequence…
We study the active to absorbing phase transition (AAPT) in a simple two-component model system for a species and its mutant. We uncover the nontrivial critical scaling behavior and weak dynamic scaling near the AAPT that shows the…
Growing network models with both heterogeneity of the nodes and topological constraints can give rise to a rich phase structure. We present a simple model based on preferential attachment with rewiring of the links. Rewiring probabilities…
We introduce the vacillating voter model in which each voter consults two neighbors to decide its state, and changes opinion if it disagrees with either neighbor. This irresolution leads to a global bias toward zero magnetization. In…
We investigate a quadratic dynamical system known as nonlinear recombinations. This system models the evolution of a probability measure over the Boolean cube, converging to the stationary state obtained as the product of the initial…
Phase separation and coarsening is a phenomenon commonly seen in binary physical and chemical systems that occur in nature. Often times, thermal fluctuations, modeled as stochastic noise, are present in the system and the phase segregation…
We present a novel framework exploiting the cascade of phase transitions occurring during a simulated annealing of the Expectation-Maximisation algorithm to cluster datasets with multi-scale structures. Using the weighted local covariance,…
Dynamic graph-level embedding aims to capture structural evolution in networks, which is essential for modeling real-world scenarios. However, existing methods face two critical yet under-explored issues: Structural Visit Bias, where random…
We consider the two-opinion voter model on a regular random graph with n vertices and degree $d \geq 3$. It is known that consensus is reached on time scale n and that on this time scale the volume of the set of vertices with one opinion…
Latent variable models for network data extract a summary of the relational structure underlying an observed network. The simplest possible models subdivide nodes of the network into clusters; the probability of a link between any two nodes…
Our general subject is the emergence of phases, and phase transitions, in large networks subjected to a few variable constraints. Our main result is the analysis, in the model using edge and triangle subdensities for constraints, of a sharp…
A simple two dimensional model of a phase growing on a substrate is introduced. The model is characterized by an adsorption rate q, and a desorption rate p. It exhibits a wetting transition which may be viewed as an unbinding transition of…
The constrained voter model describes the dynamics of opinions in a population of individuals located on a connected graph. Each agent is characterized by her opinion, where the set of opinions is represented by a finite sequence of…
Fluid mixtures, such as the cellular cytoplasm and synthetic DNA nanostars, can spontaneously compartmentalize into many coexisting phases through liquid-liquid phase separation. Despite the diversity of fluid structures that emerge from…
This paper focuses on the problem of growing multiplex networks. Currently, the results on the joint degree distribution of growing multiplex networks present in the literature pertain to the case of two layers, and are confined to the…
Transition out of a topological phase is typically characterized by discontinuous changes in topological invariants along with bulk gap closings. However, as a clean system is geometrically punctured, it is natural to ask the fate of an…
We propose a dual system for unsupervised object segmentation in video, which brings together two modules with complementary properties: a space-time graph that discovers objects in videos and a deep network that learns powerful object…
Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we…
We analyze Axelrod's model of social interactions on coevolving complex networks. We introduce four extensions with different mechanisms of edge rewiring. The models are intended to catch two kinds of interactions - preferential attachment,…