相关论文: Laplacian networks: growth, local symmetry and sha…

We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible.…

We consider the motion by curvature of a network of smooth curves with multiple junctions in the plane, that is, the geometric gradient flow associated to the length functional. Such a flow represents the evolution of a two--dimensional…

This paper presents a statistically sound method for measuring the accuracy with which a probabilistic model reflects the growth of a network, and a method for optimising parameters in such a model. The technique is data-driven, and can be…

Modeling the spontaneous evolution of morphology in natural systems and its preservation by proportionate growth remains a major scientific challenge. Yet, it is conceivable that if the basic mechanisms of growth and the coupled kinetic…

This work applies Generative Flow Networks (GFlowNets) to three graph optimization problems: the Traveling Salesperson Problem, Minimum Spanning Tree, and Shortest Path. GFlowNets are generative models that learn to sample solutions…

We generalize the poissonian evolving random graph model of Bauer and Bernard to deal with arbitrary degree distributions. The motivation comes from biological networks, which are well-known to exhibit non poissonian degree distribution. A…

Two important aspects of the Internet, namely the properties of its topology and the characteristics of its data traffic, have attracted growing attention of the physics community. My thesis has considered problems of both aspects. First I…

The effects of link rewiring are considered for the class of directed networks where each node has the same fixed out-degree. We model a network generated by three mechanisms that are present in various networked systems; growth, global…

Several problems in machine learning are naturally expressed as the design and analysis of time-evolving probability distributions. This includes sampling via diffusion methods, optimizing the weights of neural networks, and analyzing the…

Graph Laplacians and related nonlinear mappings into low dimensional spaces have been shown to be powerful tools for organizing high dimensional data. Here we consider a data set X in which the graph associated with it changes depending on…

In the interdisciplinary field of network science, a complex-valued network, with edges assigned complex weights, provides a more nuanced representation of relationships by capturing both the magnitude and phase of interactions.…

The recently introduced hierarchical regular networks HN3 and HN4 are analyzed in detail. We use renormalization group arguments to show that HN3, a 3-regular planar graph, has a diameter growing as \sqrt{N} with the system size, and random…

We study here a standard next-nearest-neighbor (NNN) model of ballistic growth on one- and two-dimensional substrates focusing our analysis on the probability distribution function $P(M,L)$ of the number $M$ of maximal points (i.e., local…

We consider the logistic metapopulation model over a stream network and use the metapopulation growth rate and the total biomass (of the positive equilibrium) as metrics for different aspects of population persistence. Our objective is to…

We consider transport networks with nodes scattered at random in a large domain. At certain local rates, the nodes generate traffic flowing according to some navigation scheme in a given direction. In the thermodynamic limit of a growing…

We represent transport between different regions of a fluid domain by flow networks, constructed from the discrete representation of the Perron-Frobenius or transfer operator associated to the fluid advection dynamics. The procedure is…

Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…

We propose a probabilistic growth model for transport networks which employs a balance between popularity of nodes and the physical distance between nodes. By comparing the degree of each node in the model network and the WAN, we observe…

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…

We prove several geometric theorems using tools from the theory of convex optimization. In the Riemannian setting, we prove the max flow-min cut theorem for boundary regions, applied recently to develop a "bit-thread" interpretation of…