Related papers: GridPyM: a Python module to handle grid diagrams

We explore the use of graph neural networks (GNNs) to model spatial processes in which there is no a priori graphical structure. Similar to finite element analysis, we assign nodes of a GNN to spatial locations and use a computational…

Designing spectral convolutional networks is a formidable task in graph learning. In traditional spectral graph neural networks (GNNs), polynomial-based methods are commonly used to design filters via the Laplacian matrix. In practical…

The Python package pylimer-tools is a comprehensive toolkit for computational studies of polymer networks, particularly bead-spring networks. The package provides functionality to generate polymer networks using Monte Carlo (MC) procedures…

Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective…

We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the…

We develop improved physics-informed neural networks (PINNs) for high-order and high-dimensional power system models described by nonlinear ordinary differential equations. We propose some novel enhancements to improve PINN training and…

Large networks are becoming a widely used abstraction for studying complex systems in a broad set of disciplines, ranging from social network analysis to molecular biology and neuroscience. Despite an increasing need to analyze and…

Data analysis encompasses a spectrum of tasks, from high-level conceptual reasoning to lower-level execution. While AI-powered tools increasingly support execution tasks, there remains a need for intelligent assistance in conceptual tasks.…

The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…

We present theoretical rudiments of Petri nets over ontological graphs as well as the designed and implemented Python toolkit for dealing with such nets. In Petri nets over ontological graphs, the domain knowledge is enclosed in a form of…

Social network analysis is the process of investigating social structures through the use of networks and graph theory. It combines a variety of techniques for analyzing the structure of social networks as well as theories that aim at…

We present pygiftgenerator, a python module for systematically preparing a large number of numerical and multiple-choice questions for Moodle-based quizzes oriented to students' formative evaluation. The use of the module is illustrated by…

Background: The study of genome-scale metabolic models and their underlying networks is one of the most important fields in systems biology. The complexity of these models and their description makes the use of computational tools an…

This book collects the lectures about graph theory and its applications which were given to students of mathematical departments of Moscow State University and Peking University. Graph theory is a very wide field with a lot of applications…

deepstruct connects deep learning models and graph theory such that different graph structures can be imposed on neural networks or graph structures can be extracted from trained neural network models. For this, deepstruct provides deep…

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems like the power grid, social, and neural networks, and they form the…

Hypergraphs, or generalization of graphs such that edges can contain more than two nodes, have become increasingly prominent in understanding complex network analysis. Unlike graphs, hypergraphs have relatively few supporting platforms, and…

As a consequence to the hype of Grid computing, such systems have seldom been designed using formal techniques. The complexity and rapidly growing demand around Grid technologies has favour the use of classical development techniques,…

Mechanics-related problems often present unique challenges in achieving accurate geometric and physical representations, particularly for non-uniform structures. Graph neural networks (GNNs) have emerged as a promising tool to tackle these…

A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph with edge types. KGs are an important primitive in modern machine learning and artificial intelligence.…