Related papers: Smooth Parametrizations in Dynamics, Analysis, Dio…
We demonstrate that the concept of strict proto-differentiability of subgradient mappings can play a similar role as smoothness of the gradient mapping of a function in the study of subgradient mappings of prox-regular functions. We then…
In the last years many results in the area of semidefinite programming were obtained for invariant (finite dimensional, or infinite dimensional) semidefinite programs - SDPs which have symmetry. This was done for a variety of problems and…
We introduce the class of "smooth rough paths" and study their main properties. Working in a smooth setting allows us to discard sewing arguments and focus on algebraic and geometric aspects. Specifically, a Maurer-Cartan perspective is the…
The aim of this work is to study the geometry underlying mechanics and its application to describe autonomous and nonautonomous conservative dynamical systems of different types; as well as dissipative dynamical systems. We use different…
The advancements in neural rendering have increased the need for techniques that enable intuitive editing of 3D objects represented as neural implicit surfaces. This paper introduces a novel neural algorithm for parameterizing neural…
The goal of this paper is twofold. First, we present a unified way of formulating numerical integration problems from both approximation theory and discrepancy theory. Second, we show how techniques, developed in approximation theory, work…
We analyze actual methods that generate smooth frame fields both in 2D and in 3D. We formalize the 2D problem by representing frames as functions (as it was done in 3D), and show that the derived optimization problem is the one that…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
In this paper, we introduce soft continuous mappings which are defined over an initial universe set with a fixed set of parameters. Later we study soft open and soft closed mappings, soft homeomorphism and investigate some properties of…
We present the results from a two-day study in which we discussed various implementations of Smooth Particle Hydrodynamics (SPH), one of the leading methods used across a variety of areas of large-scale astrophysical simulations. In…
The purpose of this paper is to show that functions that derivate the two-variable product function and one of the exponential, trigonometric or hyperbolic functions are also standard derivations. The more general problem considered is to…
In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A function that has a prescribed value on the domain in which a differential…
The present paper mainly presents, for example, explicit classifications of compact smooth manifolds having non-empty boundaries and simple structures where the dimensions are general. Studies of this type is fundamental and important. They…
We present a static analysis for discovering differentiable or more generally smooth parts of a given probabilistic program, and show how the analysis can be used to improve the pathwise gradient estimator, one of the most popular methods…
This survey contains a selection of topics unified by the concept of positive semi-definiteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or…
This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both…
State-space smoothing has found many applications in science and engineering. Under linear and Gaussian assumptions, smoothed estimates can be obtained using efficient recursions, for example Rauch-Tung-Striebel and Mayne-Fraser algorithms.…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds…
Andrews plots provide aesthetically pleasant visualizations of high-dimensional datasets. This work proves that Andrews plots (when defined in terms of the principal component scores of a dataset) are optimally ``smooth'' on average, and…