相关论文: Borromean Hypergraph Formation in Dense Random Rec…

Collapse of the polymer chain upon the sharp decrease of solvent quality is studied. During collapse, any pair of polymer units appearing in a sufficiently close vicinity in space has the possibility with a certain probability to form an…

We analyze the quantum entanglement properties of bosonic particles hopping over graph structures.Mode-entanglement of a graph vertex with respect the rest of the graph is generated, starting from a product state, by turning on for a finite…

Bootstrap percolation has been used effectively to model phenomena as diverse as emergence of magnetism in materials, spread of infection, diffusion of software viruses in computer networks, adoption of new technologies, and emergence of…

We describe a model of random links based on random 4-valent maps, which can be sampled due to the work of Schaeffer. We will look at the relationship between the combinatorial information in the diagram and the hyperbolic volume.…

Given a weighted graph, we introduce a partition of its vertex set such that the distance between any two clusters is bounded from below by a power of the minimum weight of both clusters. This partition is obtained by recursively merging…

We compute the Hausdorff, upper box and packing dimensions for certain inhomogeneous Moran set constructions. These constructions are beyond the classical theory of iterated function systems, as different nonlinear contraction…

Let $c$ be a positive constant. Suppose that $r=o(n^{5/12})$ and the members of $\binom{[n]}{r}$ are chosen sequentially at random to form an intersecting hypergraph $\mathcal{H}$. We show that whp $\mathcal{H}$ consists of a simple…

We study percolation on self-dual hypergraphs that contain hyperedges with four bounding vertices, or "four-edges", using three different generators, each containing bonds or sites with three distinct probabilities $p$, $r$, and $t$…

Analytical results are derived for the bond percolation threshold and the size of the giant connected component in a class of random networks with non-zero clustering. The network's degree distribution and clustering spectrum may be…

While there has been much interest in adapting conventional clustering procedures---and in higher dimensions, persistent homology methods---to directed networks, little is known about the convergence of such methods. In order to even…

Hypergraphs have emerged as a powerful modeling framework to represent systems with multiway interactions, that is systems where interactions may involve an arbitrary number of agents. Here we explore the properties of real-world…

We consider the $r$-neighbor bootstrap percolation process on the graph with vertex set $V=\{0,1\}^n$ and edges connecting the pairs at Hamming distance $1,2,\dots,k$, where $k\ge 2$. We find asymptotics of the critical probability of…

Many organisms exhibit branching morphologies that twist around each other and become entangled. Entanglement occurs when different objects interlock, creating complex and often irreversible configurations. This physical phenomenon is…

Motivated by applications in social and biological network analysis, we introduce a new form of agnostic clustering termed~\emph{motif correlation clustering}, which aims to minimize the cost of clustering errors associated with both edges…

We consider how beads can diffuse along a chain that wraps them, without becoming displaced from the chain; our proposed mechanism is analogous to the reptation of "stored length" in more familiar situations of polymer dynamics. The problem…

Bootstrap percolation in (random) graphs is a contagion dynamics among a set of vertices with certain threshold levels. The process is started by a set of initially infected vertices, and an initially uninfected vertex with threshold $k$…

In this work, we propose a comprehensive theoretical framework combining percolation theory with nonlinear dynamics in order to study hypergraphs with a time-varying giant component. We consider in particular hypergraphs with higher-order…

Entanglement percolation aims at generating maximal entanglement between any two nodes of a quantum network by utilizing strategies based solely on local operations and classical communication between the nodes. As it happens in classical…

Blends of polymers of different topologies, such as ring and supercoiled, naturally occur in biology and often exhibit emergent viscoelastic properties coveted in industry. However, due to their complexity, along with the difficulty of…

In this paper we examine the percolation properties of higher-order networks that have non-trivial clustering and subgraph-based assortative mixing (the tendency of vertices to connect to other vertices based on subgraph joint degree). Our…