相关论文: Self-Assembly as Graph Grammar as Distributed Syst…

Graphical models use graphs to represent conditional independence structure in the distribution of a random vector. In stochastic processes, graphs may represent so-called local independence or conditional Granger causality. Under some…

Modularity was introduced by Newman and Girvan in 2004 and is used as a measure of community structure of networks represented by graphs. In our work we study modularity of the random intersection graph model first considered by Karo\'nski,…

The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means of linear subspaces, contained in the graphs of two (primal and dual) generalized derivatives. This class of mappings includes the…

A paradigm that was successfully applied in the study of both pure and algorithmic problems in graph theory can be colloquially summarized as stating that "any graph is close to being the disjoint union of expanders". Our goal in this paper…

Recent advances in Large Language Models (LLMs) have demonstrated the emergence of capabilities (learned skills) when the number of system parameters and the size of training data surpass certain thresholds. The exact mechanisms behind such…

The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. Its simplest formulation is in two steps: (1) We cut every edge of G into two halves, thus obtaining a…

Graph theory provides a language for studying the structure of relations, and it is often used to study interactions over time too. However, it poorly captures the both temporal and structural nature of interactions, that calls for a…

In this short survey article, we present an elementary, yet quite powerful, method of enumerating independent sets in graphs. This method was first employed more than three decades ago by Kleitman and Winston and has subsequently been used…

Discrete Lagrangian Systems on graphs are considered. Vector-valued closed differential 2-form on the space of solutions is constructed. This form takes values in the first homology group of the graph. This construction generalizes the…

Distributional learning provides a framework for studying the learnability of structured languages from positive data. In this paper, we extend this framework to graph languages generated by fixed-interface clause systems. We formulate…

We introduce an unsupervised graph embedding that trades off local node similarity and connectivity, and global structure. The embedding is based on a generalized graph Laplacian, whose eigenvectors compactly capture both network structure…

Dynamical systems consisting of a set of autonomous agents face the challenge of having to accomplish a global task, relying only on local information. While centralized controllers are readily available, they face limitations in terms of…

An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have…

State-of-the-art text-to-image models produce visually impressive results but often struggle with precise alignment to text prompts, leading to missing critical elements or unintended blending of distinct concepts. We propose a novel…

This paper introduces some tools from graph theory and distributed consensus algorithms to construct an optimal, yet robust, hierarchical information sharing structure for large-scale decision making and control problems. The proposed…

The paper addresses large-scale, convex optimization problems that need to be solved in a distributed way by agents communicating according to a random time-varying graph. Specifically, the goal of the network is to minimize the sum of…

We consider a family of problems that are concerned about making predictions for the majority of unlabeled, graph-structured data samples based on a small proportion of labeled samples. Relational information among the data samples, often…

Graphcodes were recently introduced as a technique to employ two-parameter persistence modules in machine learning tasks (Kerber and Russold, NeurIPS 2024). We show in this work that a compressed version of graphcodes yields a description…

Assembly theory has received considerable attention in the recent past. Here we analyze the formal framework of this model and show that assembly pathways coincide with certain minimal hyperpaths in B-hypergraphs. This makes it possible to…

Stationary graph process models are commonly used in the analysis and inference of data sets collected on irregular network topologies. While most of the existing methods represent graph signals with a single stationary process model that…