Related papers: A short proof that sweeping is always possible for…
Smoothing is omnipresent in astronomy, because almost always measurements performed at discrete positions in the sky need to be interpolated into a smooth map for subsequent analysis. Still, the statistical properties of different…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
In this paper we consider a scalar transport equation with constant coefficients on domains with discrete space and continuous, discrete or general time. We show that on all these underlying domains solutions of the transport equation can…
We have found provably optimal algorithms for full-domain discrete-ordinate transport sweeps on a class of grids in 2D and 3D Cartesian geometry that are regular at a coarse level but arbitrary within the coarse blocks. We describe these…
The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…
Discretization of the uniform norm of functions from a given finite dimensional subspace of continuous functions is studied. We pay special attention to the case of trigonometric polynomials with frequencies from an arbitrary finite set…
We propose an image processing scheme based on reordering of its patches. For a given corrupted image, we extract all patches with overlaps, refer to these as coordinates in high-dimensional space, and order them such that they are chained…
Comparison principles for Volterra equations play a role analogous to maximum principles in PDEs: they provide positivity and stability information on the solution and allow one to control the output of bounded inputs. In the continuous…
We present a generalized formulation of sweeping process where the behaviour of the solution is prescribed at the jump points of the driving moving set. An existence and uniqueness theorem for such formulation is proved. As a consequence we…
This paper extends a recently proposed robust computational framework for constructing the boundary representation (brep) of the volume swept by a given smooth solid moving along a one parameter family $h$ of rigid motions. Our extension…
The aim of this paper is to study a wide class of non-convex sweeping processes with moving constraint whose translation and deformation are represented by regulated functions, i.e., functions of not necessarily bounded variation admitting…
Many computer vision challenges require continuous outputs, but tend to be solved by discrete classification. The reason is classification's natural containment within a probability $n$-simplex, as defined by the popular softmax activation…
Given an $N$-dimensional subspace $X$ of $L_p([0,1])$, we consider the problem of choosing $M$-sampling points which may be used to discretely approximate the $L_p$ norm on the subspace. We are particularly interested in knowing when the…
We study the task of smoothing a circuit, i.e., ensuring that all children of a plus-gate mention the same variables. Circuits serve as the building blocks of state-of-the-art inference algorithms on discrete probabilistic graphical models…
We consider entropically regularized, semi-discrete versions of variational problems on the set of probability measures involving optimal transport as well as other terms. We prove that the solutions can be characterized by well-posed…
We consider sweeping domain decomposition preconditioners to solve the Helmholtz equation in the case of stripwise domain decomposition with or without overlaps. We unify their derivation and convergence studies by expressing them as…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
The recently developed dynamic discretization discovery (DDD) is a powerful method that allows many time-dependent problems to become more tractable. While DDD has been applied to a variety of problems, one particular challenge has been to…
In this paper we generalize and improve a recently developed domain decomposition preconditioner for the iterative solution of discretized Helmholtz equations. We introduce an improved method for transmission at the internal boundaries…
We study the relation between sweeping processes with the cone of limiting normals and projection processes. We prove the existence of solution of a perturbed sweeping process with the cone of limiting normals and of nonstationary…