相关论文: A characterization of maximal homogeneous-quadrati…

Semispaces of a convexity space $(X,C)$ are maximal convex sets missing a point. The separation axiom $S_3$ asserts that any point $x_0\in X$ and any convex set $A$ not containing $x_0$ can be separated by complementary halfspaces (convex…

We present a new framework for the analysis and design of randomized algorithms for solving various types of linear systems, including consistent or inconsistent, full rank or rank-deficient. Our method is formulated with four randomized…

A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $\gamma -$law…

A standard objective in computer experiments is to approximate the behaviour of an unknown function on a compact domain from a few evaluations inside the domain. When little is known about the function, space-filling design is advisable:…

Consider the Maximum Weight Independent Set problem for rectangles: given a family of weighted axis-parallel rectangles in the plane, find a maximum-weight subset of non-overlapping rectangles. The problem is notoriously hard both in the…

We consider a primitive distance-regular graph $\Gamma$ with diameter at least $3$. We use the intersection numbers of $\Gamma$ to find a positive semidefinite matrix $G$ with integer entries. We show that $G$ has determinant zero if and…

We address the Multi-Robot Motion Planning (MRMP) problem of computing collision-free trajectories for multiple robots in shared continuous environments. While existing frameworks effectively decompose MRMP into single-robot subproblems,…

Establishing dense correspondence across 3D shapes is crucial for fundamental downstream tasks, including texture transfer, shape interpolation, and robotic manipulation. However, learning these mappings without manual supervision remains a…

Classical existence theorems and solution methods for quadratic programming traditionally rely on the analytical properties of real numbers, specifically compactness and completeness. These tools are unavailable in general linearly ordered…

Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

Let $\mathcal{T}$ be a set of $n$ flat (planar) semi-algebraic regions in $\mathbb{R}^3$ of constant complexity (e.g., triangles, disks), which we call plates. We wish to preprocess $\mathcal{T}$ into a data structure so that for a query…

Squaregraphs were originally defined as finite plane graphs in which all inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e., the vertices not incident with the outer face) have degrees larger than three. The planar…

A strong $s$-blocking set in a projective space is a set of points that intersects each codimension-$s$ subspace in a spanning set of the subspace. We present an explicit construction of such sets in a $(k - 1)$-dimensional projective space…

Given a 0-dimensional affine K-algebra R=K[x_1,...,x_n]/I, where I is an ideal in a polynomial ring K[x_1,...,x_n] over a field K, or, equivalently, given a 0-dimensional affine scheme, we construct effective algorithms for checking whether…

A unified structural framework is presented for model-based fault diagnosis that explicitly incorporates both fault locations and constraints imposed by the residual generation methodology. Building on the concepts of proper and minimal…

Finding a maximum independent set (MIS) of a given fam- ily of axis-parallel rectangles is a basic problem in computational geom- etry and combinatorics. This problem has attracted significant atten- tion since the sixties, when Wegner…

Semidefinite programs (SDPs) are a framework for exact or approximate optimization that have widespread application in quantum information theory. We introduce a new method for using reductions to construct integrality gaps for SDPs. These…

Many machine learning applications such as in vision, biology and social networking deal with data in high dimensions. Feature selection is typically employed to select a subset of features which im- proves generalization accuracy as well…

This paper presents an algorithmic framework for the minimization of strictly convex quadratic functions. The framework is flexible and generic. At every iteration the search direction is a linear combination of the negative gradient, as…