相关论文: Coarse Graining for Synchronization in Directed Ne…

Coarse graining (CG) is an important task for efficient modeling and simulation of complex multi-scale systems, such as the conformational dynamics of biomolecules. This work presents a projection-based coarse-graining formalism for general…

Graph topology inference of network processes with co-evolving and interacting time-series is crucial for network studies. Vector autoregressive models (VAR) are popular approaches for topology inference of directed graphs; however, in…

Using an information theoretic point of view, we investigate how a dynamics acting on a network can be coarse grained through the use of graph partitions. Specifically, we are interested in how aggregating the state space of a Markov…

We propose an adaptive graph coarsening method to jointly learn graph neural network (GNN) parameters and merge nodes via K-means clustering during training. As real-world graphs grow larger, processing them directly becomes increasingly…

We consider a Graph Neural Network (GNN) non-Markovian modeling framework to identify coarse-grained dynamical systems on graphs. Our main idea is to systematically determine the GNN architecture by inspecting how the leading term of the…

We propose and illustrate an approach to coarse-graining the dynamics of evolving networks (networks whose connectivity changes dynamically). The approach is based on the equation-free framework: short bursts of detailed network evolution…

Coarse-graining has become an area of tremendous importance within many different research fields. For molecular simulation, coarse-graining bears the promise of finding simplified models such that long-time simulations of large-scale…

A communication network can be modeled as a directed connected graph with edge weights that characterize performance metrics such as loss and delay. Network tomography aims to infer these edge weights from their pathwise versions measured…

Network analysis is rapidly becoming a standard tool for studying functional magnetic resonance imaging (fMRI) data. In this framework, different brain areas are mapped to the nodes of a network, whose links depict functional dependencies…

We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…

Many real-world networks display a natural bipartite structure, while analyzing or visualizing large bipartite networks is one of the most challenges. As a result, it is necessary to reduce the complexity of large bipartite systems and…

Very recently, a kind of spatial network constructed with power-law distance distribution and total energy constriction is proposed. Moreover, it has been pointed out that such spatial networks have the optimal exponents $\delta$ in the…

Coarse-graining is a powerful tool for extending the reach of dynamic models of proteins and other biological macromolecules. Topological coarse-graining, in which biomolecules or sets thereof are represented via graph structures, is a…

We perform the renormalization-group-like numerical analysis of geographically embedded complex networks on the two-dimensional square lattice. At each step of coarsegraining procedure, the four vertices on each $2 \times 2$ square box are…

We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of the adjacency…

Many real-world systems of coupled agents exhibit directed interactions, meaning that the influence of an agent on another is not reciprocal. Furthermore, interactions usually do not have identical amplitude and/or sign. To describe…

Finding accurate reduced descriptions for large, complex, dynamically evolving networks is a crucial enabler to their simulation, analysis, and, ultimately, design. Here we propose and illustrate a systematic and powerful approach to…

Tensor network techniques have proved to be powerful tools that can be employed to explore the large scale dynamics of lattice systems. Nonetheless, the redundancy of degrees of freedom in lattice gauge theories (and related models) poses a…

We propose, and illustrate via a neural network example, two different approaches to coarse-graining large heterogeneous networks. Both approaches are inspired from, and use tools developed in, methods for uncertainty quantification in…

Most real systems are growing. In order to model the evolution of real systems, many growing network models have been proposed to reproduce some specific topology properties. As the structure strongly influences the network function,…