相关论文: Efficient sphere-covering and converse measure con…
A typical computational geometry problem begins: Consider a set P of n points in R^d. However, many applications today work with input that is not precisely known, for example when the data is sensed and has some known error model. What if…
We analyze a semi-implicit finite volume scheme for the Gray--Scott system, a model for pattern formation in chemical and biological media. We prove unconditional well-posedness of the fully discrete problem and establish qualitative…
Determining the minimum density of a covering of $\mathbb{R}^{n}$ by Euclidean unit balls as $n\to\infty$ is a major open problem, with the best known results being the lower bound of $\left(\mathrm{e}^{-3/2}+o(1)\right)n$ by Coxeter, Few…
Given a probability measure $\mu$ over ${\mathbb R}^n$, it is often useful to approximate it by the convex combination of a small number of probability measures, such that each component is close to a product measure. Recently, Ronen Eldan…
Bernardeau et al. (1997), using perturbation theory, showed that the skewness of the large-scale lensing-convergence, or projected mass density, could be used to constrain $\Omega_m$, the matter content of the universe. On the other hand,…
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…
We consider the inverse problem of reconstructing an effective model for a prototypical diffusion process in strongly heterogeneous media based on coarse measurements. The approach is motivated by quasi-local numerical effective forward…
A new locally averaged density for sphere packing in R^3 is defined by a proper combination of the local cell (Voronoi cell) and Delaunay decompositions (\S 1.2.2), using only a single layer of surrounding spheres. Local packings attaining…
Compressed sensing allows for the recovery of sparse signals from few measurements, whose number is proportional to the sparsity of the unknown signal, up to logarithmic factors. The classical theory typically considers either random linear…
Given a Riemannian metric on the 2-sphere, sweep the 2-sphere out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight by, in a continuous way, pulling each curve as tight as…
Is it possible to detect a feature in an image without ever looking at it? Images are known to have sparser representation in Wavelets and other similar transforms. Compressed Sensing is a technique which proposes simultaneous acquisition…
Let $\Gamma$ be the fundamental group of a closed orientable surface of genus at least two. Consider the composition of a uniformly random element of $\mathrm{Hom}(\Gamma,S_n)$ with the $(n-1)$-dimensional irreducible representation of…
Sample reuse techniques have significantly reduced the numerical complexity of probabilistic robustness analysis. Existing results show that for a nested collection of hyper-spheres the complexity of the problem of performing $N$ equivalent…
This paper develops a systematic and geometric theory of optimal quantization on the unit sphere $\mathbb S^2$, focusing on finite uniform probability distributions supported on the spherical surface - rather than on lower-dimensional…
The fully quantum reverse Shannon theorem establishes the optimal rate of noiseless classical communication required for simulating the action of many instances of a noisy quantum channel on an arbitrary input state, while also allowing for…
Here we show that, in principle it is possible to clone (measure) a single arbitrary unknown quantum state of a spin-$\frac{1}{2}$ particle (an electron) with arbitrary precision and with success probability tending to one, using protective…
The paper concerns the uniform polynomial approximation of a function $f$, continuous on the unit Euclidean sphere of ${\mathbb R}^3$ and known only at a finite number of points that are somehow uniformly distributed on the sphere. First we…
In this paper, we discuss some numerical realizations of Shannon's sampling theorem. First we show the poor convergence of classical Shannon sampling sums by presenting sharp upper and lower bounds of the norm of the Shannon sampling…
This paper describes a recent mathematical method called conflation for consolidating data from independent experiments that are designed to measure the same quantity, such as Planck's constant or the mass of the top quark. Conflation is…