Related papers: GridPyM: a Python module to handle grid diagrams
For 20 years the beautiful structure in the grid cell code has presented an attractive puzzle: what computation do these representations subserve, and why does it manifest so curiously in neurons. The first question quickly attracted an…
Geometric graphs are a special kind of graph with geometric features, which are vital to model many scientific problems. Unlike generic graphs, geometric graphs often exhibit physical symmetries of translations, rotations, and reflections,…
Knowledge Graphs (KG) constitute a flexible representation of complex relationships between entities particularly useful for biomedical data. These KG, however, are very sparse with many missing edges (facts) and the visualisation of the…
We present SymPix, a special-purpose spherical grid optimized for efficient sampling of rotationally invariant linear operators. This grid is conceptually similar to the Gauss-Legendre (GL) grid, aligning sample points with iso-latitude…
This paper presents a new Graph Neural Network (GNN) type using feature-wise linear modulation (FiLM). Many standard GNN variants propagate information along the edges of a graph by computing "messages" based only on the representation of…
Deciding whether a graph can be embedded in a grid using only unit-length edges is NP-complete, even when restricted to binary trees. However, it is not difficult to devise a number of graph classes for which the problem is polynomial, even…
Computational physics problems often have a common set of aspects to them that any particular numerical code will have to address. Because these aspects are common to many problems, having a framework already designed and ready to use will…
Directed graphs are widely used in modelling of nonsymmetric relations in various sciences and engineering disciplines. We discuss invariants of strongly connected directed graphs - minimal number of vertices or edges necessary to remove to…
We describe a novel, interdisciplinary, computational methods course that uses Python and associated numerical and visualization libraries to enable students to implement simulations for a number of different course modules. Problems in…
The multigrid algorithm is a multilevel approach to accelerate the numerical solution of discretized differential equations in physical problems involving long-range interactions. Multiresolution analysis of wavelet theory provides an…
Expressivity plays a fundamental role in evaluating deep neural networks, and it is closely related to understanding the limit of performance improvement. In this paper, we propose a three-pipeline training framework based on critical…
Graphs face challenges when dealing with massive datasets. They are essential tools for modeling interconnected data and often become computationally expensive. Graph embedding techniques, on the other hand, provide an efficient approach.…
Recently, the deep learning community has given growing attention to neural architectures engineered to learn problems in relational domains. Convolutional Neural Networks employ parameter sharing over the image domain, tying the weights of…
Despite the recent success of reconciling spike-based coding with the error backpropagation algorithm, spiking neural networks are still mostly applied to tasks stemming from sensory processing, operating on traditional data structures like…
Computational grids that couple geographically distributed resources are becoming the de-facto computing platform for solving large-scale problems in science, engineering, and commerce. Software to enable grid computing has been primarily…
Graph mining applications, such as subgraph pattern matching and mining, are widely used in real-world domains such as bioinformatics, social network analysis, and computer vision. Such applications are considered a new class of…
This work introduces a new software package `Sesame' for the numerical computation of classical semiconductor equations. It supports 1 and 2-dimensional systems and provides tools to easily implement extended defects such as grain…
In this paper we introduce and describe an implementation of curved (surface) geometries within the Dune framework for grid-based discretizations. Therefore, we employ the abstraction of geometries as local-functions bound to a grid…
RNA 3D architectures are stabilized by sophisticated networks of (non-canonical) base pair interactions, which can be conveniently encoded as multi-relational graphs and efficiently exploited by graph theoretical approaches and recent…
We present evidence that multigrid works for wave equations in disordered systems, e.g. in the presence of gauge fields, no matter how strong the disorder, but one needs to introduce a "neural computations" point of view into large scale…