Related papers: Reflect-Push Methods Part I: Two Dimensional Techn…
In the first part of this paper we give a solution for the one-dimensional reflected backward stochastic differential equation (BSDE for short) when the noise is driven by a Brownian motion and an independent Poisson point process. The…
Cheeger's fundamental inequality states that any edge-weighted graph has a vertex subset $S$ such that its expansion (a.k.a. conductance) is bounded as follows: \[ \phi(S) \defeq \frac{w(S,\bar{S})}{\min \set{w(S), w(\bar{S})}} \leq…
Neural-network-based compressors have proven to be remarkably effective at compressing sources, such as images, that are nominally high-dimensional but presumed to be concentrated on a low-dimensional manifold. We consider a continuous-time…
This paper studies the problem of matching two complete graphs with edge weights correlated through latent geometries, extending a recent line of research on random graph matching with independent edge weights to geometric models.…
A general fusion method to find solutions to the reflection equation in higher spin representations starting from the fundamental one is shown. The method is illustrated by applying it to obtaining the $K$ diagonal boundary matrices in an…
We study approximations of reflected It\^o diffusions on convex subsets $D$ of $\Rd$ by solutions of stochastic differential equations with penalization terms. We assume that the diffusion coefficients are merely measurable (possibly…
Holographic duality implies that the geometric properties of the gravitational bulk theory should be encoded in the dual field theory. These naturally include the metric on dimensions that become compact near the conformal boundary, as is…
We study a correlated Brownian motion in two dimensions, which is reflected, stopped or killed in a wedge represented as the intersection of two half spaces. First, we provide explicit density formulas, hinted by the method of images. These…
Recent advances in 3D vision have demonstrated the strengths of photometric bundle adjustment. By directly minimizing reprojected pixel errors, instead of geometric reprojection errors, such methods can achieve sub-pixel alignment accuracy…
We consider three variants of the problem of finding a maximum weight restricted $2$-matching in a subcubic graph $G$. (A $2$-matching is any subset of the edges such that each vertex is incident to at most two of its edges.) Depending on…
A convergence result for a discontinuous Galerkin multiscale method for a second order elliptic problem is presented. We consider a heterogeneous and highly varying diffusion coefficient in $L^\infty(\Omega,\mathbb{R}^{d\times d}_{sym})$…
Solutions to inverse problems that are ill-conditioned or ill-posed may have significant intrinsic uncertainty. Unfortunately, analysing and quantifying this uncertainty is very challenging, particularly in high-dimensional problems. As a…
We describe a simple, black-box compression format for tensors with a multiscale structure. By representing the tensor as a sum of compressed tensors defined on increasingly coarse grids, we capture low-rank structures on each grid-scale,…
Light reflection plays a crucial role in a number of modern technologies. In this paper, analytical expressions for maximal reflected power in any direction and for any polarization are given for generic planar structures made of a single…
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…
The isodiametric inequality states that the Euclidean ball maximizes the volume among all convex bodies of a given diameter. We are motivated by a conjecture of Makai Jr.~on the reverse question: Every convex body has a linear image whose…
Imaging systems are inherently prone to aberrations. We present an optimization method to design two-dimensional freeform reflectors that minimize aberrations for various parallel ray beams incident on the optical system. We iteratively…
We prove a generalization of Reifenberg's isoperimetric inequality. The main result of this paper is used to establish existence of a minimizer for an anisotropically-weighted area functional among a collection of surfaces which satisfies a…
Angular deviations and lateral displacements are optical effects widely investigated in literature. In this paper, by using the Taylor expansion of the Fresnel coefficients, we obtain an analytic expression for the beam reflected by and…
We consider chance-constrained binary knapsack problems, where the weights of items are independent random variables with the means and standard deviations known. The chance constraint can be reformulated as a second-order cone constraint…