相关论文: Vapnik-Chervonenkis Dimension of Axis-Parallel Cut…

This paper presents an optimized and scalable semi-Lagrangian solver for the Vlasov-Poisson system in six-dimensional phase space. Grid-based solvers of the Vlasov equation are known to give accurate results. At the same time, these solvers…

VVC is the next generation video coding standard, offering coding capability beyond HEVC standard. The high computational complexity of the latest video coding standards requires high-level parallelism techniques, in order to achieve…

The rate-distortion dimension (RDD) of an analog stationary process is studied as a measure of complexity that captures the amount of information contained in the process. It is shown that the RDD of a process, defined as two times the…

Since its introduction by Vapnik and Chervonenkis in the 1960s, the VC dimension and its variants have played a central role in numerous fields. In this paper, we investigate several variants of the VC dimension and their applications to…

Let $G=(V,E)$ be a connected graph. The distance between two vertices $u,v\in V$, denoted by $d(u, v)$, is the length of a shortest $u-v$ path in $G$. The distance between a vertex $v\in V$ and a subset $P\subset V$ is defined as $min\{d(v,…

Information about size and shape of particles produced in various manufacturing processes is very important for process and product development because design of downstream processes as well as final product properties strongly depend on…

Voronoi constellations (VCs) are finite sets of vectors of a coding lattice enclosed by the translated Voronoi region of a shaping lattice, which is a sublattice of the coding lattice. In conventional VCs, the shaping lattice is a scaled-up…

This paper demonstrates that parallel vector curves are piecewise cubic rational curves in 3D piecewise linear vector fields. Parallel vector curves -- loci of points where two vector fields are parallel -- have been widely used to extract…

Motivated by the problem of testing planarity and related properties, we study the problem of designing efficient {\em partition oracles}. A {\em partition oracle} is a procedure that, given access to the incidence lists representation of a…

We present a rectangle-based segmentation algorithm that sets up a graph and performs a graph cut to separate an object from the background. However, graph-based algorithms distribute the graph's nodes uniformly and equidistantly on the…

Recovering the spatial layout of the cameras and the geometry of the scene from extreme-view images is a longstanding challenge in computer vision. Prevailing 3D reconstruction algorithms often adopt the image matching paradigm and presume…

We study the generalization capabilities of Group Convolutional Neural Networks (GCNNs) with ReLU activation function by deriving upper and lower bounds for their Vapnik-Chervonenkis (VC) dimension. Specifically, we analyze how factors such…

Non-separable $D-$dimensional partial differential Schr\"{o}dinger equations are considered at $D=2$ and $D=3$, with the even-parity local potentials $V(x,y,\ldots)$ which are polynomials of degree four (cusp catastrophe resembling case)…

We describe and analyze a simple algorithm for principal component analysis and singular value decomposition, VR-PCA, which uses computationally cheap stochastic iterations, yet converges exponentially fast to the optimal solution. In…

We construct fractional Sobolev spaces on arbitrary time scales, both in one dimension and on product time scales. In 1D, we define $W^{\alpha(\cdot),p}_{\mathrm{rd}}(\mathcal I)$ through a variable-order Gagliardo-type seminorm and prove…

We propose a simple yet very predictive form, based on a Poisson's equation, for the functional dependence of the cost from the density of points in the Euclidean bipartite matching problem. This leads, for quadratic costs, to the analytic…

We study the Convex Set Disjointness (CSD) problem, where two players have input sets taken from an arbitrary fixed domain~$U\subseteq \mathbb{R}^d$ of size $\lvert U\rvert = n$. Their mutual goal is to decide using minimum communication…

The VVC codec is applied to the task of multispectral image (MSI) compression using adaptive and scalable coding structures. In a 'plain' VVC approach, concepts from picture-to-picture temporal prediction are employed for decorrelation…

In this paper a vectorized algorithm for simultaneously computing up to eight singular value decompositions (SVDs, each of the form $A=U\Sigma V^{\ast}$) of real or complex matrices of order two is proposed. The algorithm extends to a batch…

We present a detailed calculation of next-to-leading order QCD corrections to the $tW$ associated production using the one cutoff phase space slicing method. Such QCD corrections have been calculated independently by two groups already,…