Related papers: CAD Adjacency Computation Using Validated Numerics
We advertise the use of tetrahedral grids constructed via the longest edge bisection algorithm for rendering volumetric data with path tracing. The key benefits of such grids is two-fold. First, they provide a highly adaptive…
We introduce a new distributed algorithm for aligning graphs or finding substructures within a given graph. It is based on the cavity method and is used to study the maximum-clique and the graph-alignment problems in random graphs. The…
Approximate Bayesian Computation (ABC for short) is a family of computational techniques which offer an almost automated solution in situations where evaluation of the posterior likelihood is computationally prohibitive, or whenever…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We present a fast algorithm for computing discrete cubical homology of graphs over finite fields with an appropriate characteristic. This algorithm improves on several computational steps compared to constructions in the existing…
We describe the computing tasks involved in autonomous driving, examine existing autonomous driving computing platform implementations. To enable autonomous driving, the computing stack needs to simultaneously provide high performance, low…
We present a new cellular data processing scheme, a hybrid of existing cellular automata (CA) and gate array architectures, which is optimized for realization at the quantum scale. For conventional computing, the CA-like external clocking…
A coupled cell network describes interacting (coupled) individual systems (cells). As in networks from real applications, coupled cell networks can represent inhomogeneous networks where different types of cells interact with each other in…
Over the past few decades, a significant rise of camera-based applications for traffic monitoring has occurred. Governments and local administrations are increasingly relying on the data collected from these cameras to enhance road safety…
In this paper, we analyze the algebraic structure of some null boundary as well as some periodic boundary 2-D Cellular Automata (CA) rules by introducing a new matrix multiplication operation using only AND, OR instead of most commonly used…
As a new type of series expansion, the so-called one-dimensional adaptive Fourier decomposition (AFD) and its variations (1D-AFDs) have effective applications in signal analysis and system identification. The 1D-AFDs have considerable…
Cell counting in microscopy images is vital in medicine and biology but extremely tedious and time-consuming to perform manually. While automated methods have advanced in recent years, state-of-the-art approaches tend to increasingly…
We discuss existing and new computational analysis techniques to classify local atomic arrangements in large-scale atomistic computer simulations of crystalline solids. This article includes a performance comparison of typical analysis…
We use algebraic geometry to study matrix rigidity, and more generally, the complexity of computing a matrix-vector product, continuing a study initiated by Kumar, et. al. We (i) exhibit many non-obvious equations testing for (border)…
We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates…
Methods based on class activation maps (CAM) provide a simple mechanism to interpret predictions of convolutional neural networks by using linear combinations of feature maps as saliency maps. By contrast, masking-based methods optimize a…
We compute numerically the homology of several graph complexes in low loop orders, extending previous results.
We give in this paper a convergence result concerning parallel asynchronous algorithm with bounded delays to solve a nonlinear fixed point problems. This result is applied to calculate the solution of a strongly monotone operator. Special…
The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…
We show how, given a sufficiently large point cloud sampled from an embedded 2-manifold in $\mathbb{R}^n$, we may obtain a global representation as a cell complex with vertices given by a representative subset of the point cloud. The vertex…