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We develop a geometrically intrinsic formulation of the arbitrary-order Virtual Element Method (VEM) on polygonal cells for the numerical solution of elliptic surface partial differential equations (PDEs). The PDE is first written in…
We propose a 2-d computational model-system comprising a mixture of spheres and the objects of some other shapes, interacting via the Lennard-Jones potential. We propose a reliable and efficient numerical algorithm to obtain void…
In this work we propose a model that can manipulate individual visual attributes of objects in a real scene using examples of how respective attribute manipulations affect the output of a simulation. As an example, we train our model to…
A classification theorem for linear differential equations in two variables (one real and one Grassmann) having polynomial solutions(the generalized Bochner problem) is given. The main result is based on the consideration of the eigenvalue…
The recent development of multidimensional ultrafast spectroscopy techniques calls for the introduction of computational schemes that allow for the simulation of such experiments and the interpretation of the corresponding results from a…
The 3D city metaphor in software visualization is a well-explored rendering method. Numerous tools use their custom variation to visualize offline-analyzed data. Heat map overlays are one of these variants. They introduce a separate…
We propose definitions of SVD, spectral decomposition (for self-adjoint matrices) and Jordan decomposition which make sense for all rings. For many rings, these decompositions can be shown to exist. For some specific rings, these…
Recent work has demonstrated that volumetric scene representations combined with differentiable volume rendering can enable photo-realistic rendering for challenging scenes that mesh reconstruction fails on. However, these methods entangle…
In this paper, the problem of decentralized eigenvalue decomposition of a general symmetric matrix that is important, e.g., in Principal Component Analysis, is studied, and a decentralized online learning algorithm is proposed. Instead of…
We present a system for applying sim2real approaches to "in the wild" scenes with realistic visuals, and to policies which rely on active perception using RGB cameras. Given a short video of a static scene collected using a generic phone,…
Recent advances in machine learning allow us to analyze and describe the content of high-dimensional data like text, audio, images or other signals. In order to visualize that data in 2D or 3D, usually Dimensionality Reduction (DR)…
The value proposition of a dataset often resides in the implicit interconnections or explicit relationships (patterns) among individual entities, and is often modeled as a graph. Effective visualization of such graphs can lead to key…
Self-driving vehicles rely on urban street maps for autonomous navigation. In this paper, we introduce Pix2Map, a method for inferring urban street map topology directly from ego-view images, as needed to continually update and expand…
We study a general class of recurrence relations that appear in the application of a matrix diagonalization procedure. We find general closed formula and determine analytical properties of the solutions. We finally apply these findings in…
The Intelligent Fault Diagnosis of rotating machinery currently proposes some captivating challenges. Although results achieved by artificial intelligence and deep learning constantly improve, this field is characterized by several open…
Data visualizations typically show retrospective views of an existing dataset with little or no focus on repeatability. However, consumers of these tools often use insights gleaned from retrospective visualizations as the basis for…
We introduce a continuous domain framework for the recovery of a planar curve from a few samples. We model the curve as the zero level set of a trigonometric polynomial. We show that the exponential feature maps of the points on the curve…
Recently, the theory of diffusion maps was extended to a large class of local kernels with exponential decay which were shown to represent various Riemannian geometries on a data set sampled from a manifold embedded in Euclidean space.…
An important part of many machine learning workflows on graphs is vertex representation learning, i.e., learning a low-dimensional vector representation for each vertex in the graph. Recently, several powerful techniques for unsupervised…
Many complex systems have natural representations as multi-layer networks. While these formulations retain more information than standard single-layer network models, there is not yet a fully developed theory for computing network metrics…