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This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…
This paper presents a novel feedback method on the motion planning for unicycle robots in environments with static obstacles, along with an extension to the distributed planning and coordination in multi-robot systems. The method employs a…
The focus of this article is the approximation of functions which are analytic on a compact interval except at the endpoints. Typical numerical methods for approximating such functions depend upon the use of particular conformal maps from…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
Uniform Manifold Approximation and Projection (UMAP) is a widely used manifold learning technique for dimensionality reduction. This paper studies UMAP, supervised UMAP, and several competing dimensionality reduction methods, including…
We propose a parallel version of the cross interpolation algorithm and apply it to calculate high-dimensional integrals motivated by Ising model in quantum physics. In contrast to mainstream approaches, such as Monte Carlo and quasi Monte…
We present a few ways of using conformal maps in the reconstruction of two-dimensional conductivities in electrical impedance tomography. First, by utilizing the Riemann mapping theorem, we can transform any simply connected domain of…
In this paper we analyze a continuous version of the maximal covering location problem, in which the facilities are required to be interconnected by means of a graph structure in which two facilities are allowed to be linked if a given…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
Standard gradient descent methods yield point estimates with no measure of confidence. This limitation is acute in overparameterized and low-data regimes, where models have many parameters relative to available data and can easily overfit.…
Efficient and high-fidelity prior sampling and inversion for complex geological media is still a largely unsolved challenge. Here, we use a deep neural network of the variational autoencoder type to construct a parametric low-dimensional…
In the classical context of robotic mapping and localization, map matching is typically defined as the task of finding a rigid transformation (i.e., 3DOF rotation/translation on the 2D moving plane) that aligns the query and reference maps…
Bi-clustering refers to the task of finding sub-matrices (indexed by a group of columns and a group of rows) within a matrix of data such that the elements of each sub-matrix (data and features) are related in a particular way, for…
The aim of this study is to analyze the properties of harmonic fields in the vicinity of rough boundaries where either a constant potential or a zero flux is imposed, while a constant field is prescribed at an infinite distance from this…
Downsampling and path planning are essential in robotics and autonomous systems, as they enhance computational efficiency and enable effective navigation in complex environments. However, current downsampling methods often fail to preserve…
In this paper, we investigate cooperative vehicle coordination for connected and automated vehicles (CAVs) at unsignalized intersections. To support high traffic throughput while reducing computational complexity, we present a novel…
We study half-BPS line defects in $\mathcal{N}=2$ superconformal theories using the bootstrap approach. We concentrate on local excitations constrained to the defect, which means the system is a $1d$ defect CFT with $\mathfrak{osp}(4^*|2)$…
Alternating projections and their variants are classical tools for computing points in intersections of sets. Existing analyses for smooth manifolds mainly focus on local convergence rates under transversality or related regularity…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
Constructing valid and informative conformal prediction regions for multi-dimensional outputs remains a fundamental challenge. While conformal prediction provides finite-sample, distribution-free coverage guarantees, its practical…