Related papers: A simple algorithm for uniform sampling on the sur…
Scanning devices often produce point clouds exhibiting highly uneven distributions of point samples across the surfaces being captured. Different point cloud subsampling techniques have been proposed to generate more evenly distributed…
Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning. We present SURF, an algorithm for approximating distributions by piecewise polynomials. SURF is: simple, replacing…
This paper presents a novel algorithm solving the classic problem of generating a random sample of size s from population of size n with non-uniform probabilities. The sampling is done with replacement. The algorithm requires constant…
An algorithm for sampling exactly from the normal distribution is given. The algorithm reads some number of uniformly distributed random digits in a given base and generates an initial portion of the representation of a normal deviate in…
We develop a geometric version of the circle method and use it to compute the compactly supported cohomology of the space of rational curves through a point on a smooth affine hypersurface of sufficiently low degree.
We introduce a new algorithm for computing the periods of a smooth complex projective hypersurface. The algorithm intertwine with a new method for computing an explicit basis of the singular homology of the hypersurface. It is based on…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
We develop and test high-order methods for integration on surface point clouds. The task of integrating a function on a surface arises in a range of applications in engineering and the sciences, particularly those involving various integral…
We give efficient algorithms for volume sampling, i.e., for picking $k$-subsets of the rows of any given matrix with probabilities proportional to the squared volumes of the simplices defined by them and the origin (or the squared volumes…
Graph Sampling provides an efficient yet inexpensive solution for analyzing large graphs. While extracting small representative subgraphs from large graphs, the challenge is to capture the properties of the original graph. Several sampling…
The recent advances in 3D sensing technology have made possible the capture of point clouds in significantly high resolution. However, increased detail usually comes at the expense of high storage, as well as computational costs in terms of…
Representing complex shapes with simple primitives in high accuracy is important for a variety of applications in computer graphics and geometry processing. Existing solutions may produce suboptimal samples or are complex to implement. We…
We consider the problem of sampling an edge almost uniformly from an unknown graph, $G = (V, E)$. Access to the graph is provided via queries of the following types: (1) uniform vertex queries, (2) degree queries, and (3) neighbor queries.…
We propose a new, very efficient algorithm for sampling of random surfaces in the Monte Carlo simulations, based on so-called baby universe surgery, i.e. cutting and pasting of baby universes. It drastically reduces slowing down as compared…
Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable…
We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed…
We present a simple sublinear-time algorithm for sampling an arbitrary subgraph $H$ \emph{exactly uniformly} from a graph $G$ with $m$ edges, to which the algorithm has access by performing the following types of queries: (1) degree…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
There has been significant progress in the study of sampling discretization of integral norms for both a designated finite-dimensional function space and a finite collection of such function spaces (universal discretization). Sampling…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…