相关论文: Danzer's Problem, Effective Constructions of Dense…
The Euclidean Steiner problem is the problem of finding a set $St$, with the shortest length, such that $St \cup A$ is connected, where $A$ is a given set in a Euclidean space. The solutions $St$ to the Steiner problem will be called…
Dense Convolutional Network has been continuously refined to adopt a highly efficient and compact architecture, owing to its lightweight and efficient structure. However, the current Dense-like architectures are mainly designed manually, it…
We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of…
The classical multi-set split feasibility problem seeks a point in the intersection of finitely many closed convex domain constraints, whose image under a linear mapping also lies in the intersection of finitely many closed convex range…
A set of points $S$ in Euclidean space $\mathbb{R}^d$ is called \textit{Ramsey} if any finite partition of $\mathbb{R}^{\infty}$ yields a monochromatic copy of $S$. While characterization of Ramsey set remains a major open problem in the…
A finite set of unlabelled points in Euclidean space is the simplest representation of many real objects from mineral rocks to sculptures. Since most solid objects are rigid, their natural equivalence is rigid motion or isometry maintaining…
Tree perception is an essential building block toward autonomous forestry operations. Current developments generally consider input data from lidar sensors to solve forest navigation, tree detection and diameter estimation problems. Whereas…
We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that…
Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science.…
While faces of a polytope form a well structured lattice, in which faces of each possible dimension are present, this is not true for general compact convex sets. We address the question of what dimensional patterns are possible for the…
We are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas with large initial data of spherical symmetry. One of the main…
In this paper we introduce a technique to produce tighter cutting planes for mixed-integer non-linear programs. Usually, a cutting plane is generated to cut off a specific infeasible point. The underlying idea is to use the infeasible point…
We address the problem of reconstructing a set of points on a line or a loop from their unassigned noisy pairwise distances. When the points lie on a line, the problem is known as the turnpike; when they are on a loop, it is known as the…
We introduce the theory of div point sets, which aims to provide a framework to study the combinatoric nature of any set of points in general position on an Euclidean plane. We then show that proving the unsatisfiability of some first-order…
We present algorithms for length-constrained maximum sum segment and maximum density segment problems, in particular, and the problem of finding length-constrained heaviest segments, in general, for a sequence of real numbers. Given a…
Decision tree algorithms have been among the most popular algorithms for interpretable (transparent) machine learning since the early 1980's. The problem that has plagued decision tree algorithms since their inception is their lack of…
The wealth of data being gathered about humans and their surroundings drives new machine learning applications in various fields. Consequently, more and more often, classifiers are trained using not only numerical data but also complex data…
The implicit convex feasibility problem attempts to find a point in the intersection of a finite family of convex sets, some of which are not explicitly determined but may vary. We develop simultaneous and sequential projection methods…
We improve by an exponential factor the best known asymptotic upper bound for the density of sets avoiding 1 in Euclidean space. This result is obtained by a combination of an analytic bound that is an analogue of Lovasz theta number and of…
This paper settles the existence question for a rather general class of convex optimal design problems with a volume constraint. In low dimensions, we prove the existence of an optimal configuration for general convex minimization problems…