Related papers: A Geometry-Grounded Data Perimeter in Azure
Unmanned aerial vehicle (UAV) assisted communication is a revolutionary technology that has been recently presented as a potential candidate for beyond fifth-generation millimeter wave (mmWave) communications. Although mmWaves can offer a…
Optical metrology has progressed beyond the Abbe-Rayleigh limit, unlocking (sub)atomic precision by leveraging nonlinear phenomena, statistical accumulation, and AI estimators trained on measurand variations. Here, we show that Fisher…
Matrix factorization-based recommender system is in effect an angle preserving dimensionality reduction technique. Since the frequency of items follows power-law distribution, most vectors in the original dimension of user feature vectors…
We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…
Addressing the challenge of automated geometry math problem-solving in artificial intelligence (AI) involves understanding multi-modal information and mathematics. Current methods struggle with accurately interpreting geometry diagrams,…
The Covering Salesman Problem (CSP) is a generalization of the Traveling Salesman Problem in which the tour is not required to visit all vertices, as long as all vertices are covered by the tour. The objective of CSP is to find a minimum…
We begin with pervasive ultrametricity due to high dimensionality and/or spatial sparsity. How extent or degree of ultrametricity can be quantified leads us to the discussion of varied practical cases when ultrametricity can be partially or…
The anticipated widespread use of unmanned aerial vehicles (UAVs) raises significant safety and security concerns, including trespassing in restricted areas, colliding with other UAVs, and disrupting high-traffic airspaces. To mitigate…
Cyber Physical Systems (CPS) are becoming ubiquitous and affect the physical world, yet security is seldom at the forefront of their design. This is especially true of robotic control algorithms which seldom consider the effect of a cyber…
Given a graph whose arc traversal times vary over time, the Time-Dependent Travelling Salesman Problem consists in finding a Hamiltonian tour of least total duration covering the vertices of the graph. The main goal of this work is to…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
Geometry problem solving (GPS) represents a critical frontier in artificial intelligence, with profound applications in education, computer-aided design, and computational graphics. Despite its significance, automating GPS remains…
We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…
We establish that many fundamental concepts and techniques in quantum field theory and collider physics can be naturally understood and unified through a simple new geometric language. The idea is to equip the space of collider events with…
Computational modeling of aerodynamics is a key problem in aerospace engineering, often involving flows interacting with solid objects such as airfoils. Deep surrogate models have emerged as purely data-driven approaches that learn direct…
The travelling salesperson problem (TSP) is a classic resource allocation problem used to find an optimal order of doing a set of tasks while minimizing (or maximizing) an associated objective function. It is widely used in robotics for…
Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a query point and receives a noisy version of its distance to the target. This problem arises naturally in…
We consider a perimeter surveillance problem introduced by Kingston, Beard, and Holt in 2008 and studied by Davis, Humphrey, and Kingston in 2019. In this problem, $n$ drones surveil a finite interval, moving at uniform speed and exchanging…
We consider a perimeter defense problem in which a single vehicle seeks to defend a compact region from intruders in a one-dimensional environment parameterized by the perimeter size and the intruder-to-vehicle speed ratio. The intruders…
Delineating the lesion area is an important task in image-based diagnosis. Pixel-wise classification is a popular approach to segmenting the region of interest. However, at fuzzy boundaries such methods usually result in glitches,…