Abstract: Hodge theory provides a unifying view of the various line, surface, and volume integrals that appear in physics and engineering applications. Hodge theory on graphs develops discrete ...

Graphic design software has forever changed the way designers and fine artists work, with artificial intelligence (AI) further accelerating developments. PCMag has been evaluating graphic design ...

In pursuing advancements in digital computing, mainly aimed at addressing the complexities of AI and large-scale optimization problems, the inherent limitations of the traditional von Neumann ...

RLzoo is a collection of the most practical reinforcement learning algorithms, frameworks and applications. It is implemented with Tensorflow 2.0 and API of neural network layers in TensorLayer2.0+, ...

Abstract: Chaotic time series widely exists in nature and society (e.g., meteorology, physics, economics, etc.), which usually exhibits seemingly unpredictable features due to its inherent ...

There are numerous algorithms and architectures that have emerged for the modeling of complex dynamic systems using deep learning (12). Indeed, many deep learning algorithms have shown ...

Over the past 30 years, physical optics has been enriched by the appearance of singular optics as a new branch approved in scientific classifiers. This review briefly outlines the main concepts of the ...

Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that ...

There will be homeworks, followed by the final project. Everyone needs to present their work and submit a project report. 1-page Final Project proposal due : just before Spring Break Final Project ...

Rotation is antisymmetric and therefore is not a coherent element of the classical elastic theory, which is characterized by symmetry. A new theory of linear elasticity is developed from the concept ...

We introduce topological vector edge solitons in a Floquet insulator, consisting of two honeycomb arrays of helical waveguides with opposite directions of rotation in a focusing nonlinear optical ...