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Computational complexity and approximation algorithms are reported for a problem of stabbing a set of straight line segments with the least cardinality set of disks of fixed radii $r>0$ where the set of segments forms a straight line…
Channel estimation poses significant challenges in millimeter-wave massive multiple-input multiple-output systems, especially when the base station has fewer radio-frequency chains than antennas. To address this challenge, one promising…
This paper uses mathematics to analyze the challenges of geometrically noisy environments on triangulation. Given widely accepted algorithmic triangulation methods, such as O (n ln n) or a simpler O (n^3) method, we can mathematically prove…
Automated three-dimensional (3D) object reconstruction is the task of building a geometric representation of a physical object by means of sensing its surface. Even though new single view reconstruction techniques can predict the surface,…
In this paper, we introduce a definition of discrete conformality for triangulated surfaces with flat cone metrics and describe an algorithm for solving the problem of prescribing curvature, that is to deform the metric discrete conformally…
In this letter a new method based on modified self-organizing maps is presented for the reconstruction of deep ocean current velocities from surface information provided by satellites. This method takes advantage of local correlations in…
We study the space complexity of solving the bias-regularized SVM problem in the streaming model. This is a classic supervised learning problem that has drawn lots of attention, including for developing fast algorithms for solving the…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Tensor networks provide compact and scalable representations of high-dimensional data, enabling efficient computation in fields such as quantum physics, numerical partial differential equations (PDEs), and machine learning. This paper…
Let $P$ be a set of $n$ points in the plane. We compute the value of $\theta\in [0,2\pi)$ for which the rectilinear convex hull of $P$, denoted by $\mathcal{RH}_\theta(P)$, has minimum (or maximum) area in optimal $O(n\log n)$ time and…
We consider the Minimum Steiner Cut problem on undirected planar graphs with non-negative edge weights. This problem involves finding the minimum cut of the graph that separates a specified subset $X$ of vertices (terminals) into two parts.…
The optimal transport (OT) map offers the most economical way to transfer one probability measure distribution to another. Classical OT theory does not involve a discussion of preserving topological connections and orientations in…
Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none…
In this paper, we study the following problem of reconstructing a simple polygon: Given a cyclically ordered vertex sequence of an unknown simple polygon P of n vertices and, for each vertex v of P, the sequence of angles defined by all the…
This work considers a new task in geometric deep learning: generating a triangulation among a set of points in 3D space. We present PointTriNet, a differentiable and scalable approach enabling point set triangulation as a layer in 3D…
Accurate short-term predictions of phase-resolved water wave conditions are crucial for decision-making in ocean engineering. However, the initialization of remote-sensing-based wave prediction models first requires a reconstruction of wave…
Deep neural networks (DNNs) have shown great success in many machine learning tasks. Their training is challenging since the loss surface of the network architecture is generally non-convex, or even non-smooth. How and under what…
Point discretization of curved surfaces is required in many applications ranging from object rendering to the solution of surface partial differential equations (PDEs). These applications often impose that surfaces are sampled with local…
In this paper we present a scalable approach for robustly computing a 3D surface mesh from multi-scale multi-view stereo point clouds that can handle extreme jumps of point density (in our experiments three orders of magnitude). The…
This paper presents a theoretical and numerical investigation of object detection in a fluid governed by the three-dimensional evolutionary Navier--Stokes equations. To solve this inverse problem, we assume that interior velocity…