相关论文: Potts Model On Random Trees

Given a graph $G=(V,E)$, a $\beta$-ruling set is a subset $S\subseteq V$ that is i) independent, and ii) every node $v\in V$ has a node of $S$ within distance $\beta$. In this paper we present almost optimal distributed algorithms for…

We introduce and study a class of exchangeable random graph ensembles. They can be used as statistical null models for empirical networks, and as a tool for theoretical investigations. We provide general theorems that carachterize the…

We propose a simple adaptive-network model describing recent swarming experiments. Exploiting an analogy with human decision making, we capture the dynamics of the model by a low-dimensional system of equations permitting analytical…

A non-local model describing the growth of a tree-like transportation network with given allocation rules is proposed. In this model we focus on tree like networks, and the network transports the very resource it needs to build itself. Some…

Measuring the complexity of tree structures can be beneficial in areas that use tree data structures for storage, communication, and processing purposes. This complexity can then be used to compress tree data structures to their…

In this note we make some specific observations on the distribution of the degree of a given vertex in certain model of randomly growing networks. The rule for network growth is the following. Starting with an initial graph of minimum…

We propose a generalized model for uniform recursive tree (URT) by introducing an imperfect growth process, which may generate disconnected components (clusters). The model undergoes an interesting phase transition from a singly connected…

The dynamics of diffusion in complex networks are widely studied to understand how entities, such as information, diseases, or behaviors, spread in an interconnected environment. Complex networks often present community structure, and tools…

The analysis of stability of community structure is an important problem for scientists from many fields. Here, we propose a new framework to reveal hidden properties of community structure by quantitatively analyzing the dynamics of Potts…

We study the fundamental question of how likely it is that two randomly chosen trees are isomorphic to each other for different models of random trees. We show that the probability decays exponentially for rooted labeled trees as well as…

We introduce a general class of algorithms and supply a number of general results useful for analysing these algorithms when applied to regular graphs of large girth. As a result, we can transfer a number of results proved for random…

In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…

The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…

Various important and useful quantities or measures that characterize the topological network structure are usually investigated for a network, then they are averaged over the samples. In this paper, we propose an explicit representation by…

Regression models for supervised learning problems with a continuous target are commonly understood as models for the conditional mean of the target given predictors. This notion is simple and therefore appealing for interpretation and…

Despite the common misconception of nearly static organisms, plants do interact continuously with the environment and with each other. It is fair to assume that during their evolution they developed particular features to overcome problems…

We report on an exceptionally accurate spin-glass-type Potts model for community detection. With a simple algorithm, we find that our approach is at least as accurate as the best currently available algorithms and robust to the effects of…

The spread of infectious disease in a human community or the proliferation of fake news on social media can be modeled as a randomly growing tree-shaped graph. The history of the random growth process is often unobserved but contains…

We apply a replica inference based Potts model method to unsupervised image segmentation on multiple scales. This approach was inspired by the statistical mechanics problem of "community detection" and its phase diagram. Specifically, the…

We introduce a family of one-dimensional geometric growth models, constructed iteratively by locally optimizing the tradeoffs between two competing metrics, and show that this family is equivalent to a family of preferential attachment…