Related papers: Retractions on closed sets
We describe the supports of a class of real-valued maps on $C*(X)$ introduced by Radul. Using this description, a characterization of compact-valued retracts of a given space in terms of functional extenders is obtained. For example, if…
In this paper, we compare the performance of different numerical schemes in approximating Pontryagin's Maximum Principle's necessary conditions for the optimal control of nonholonomic systems. Retraction maps are used as a seed to construct…
In this paper, we extend the control contraction metrics (CCM) approach, which was originally proposed for the universal tracking control of nonlinear systems, to those that evolves on Lie groups. Our idea is to view the manifold as a…
Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
This paper proposes an intrinsic pseudospectral convexification framework for optimal control problems with manifold constraints. While successive pseudospectral convexification combines spectral collocation with successive convexification,…
A novel spherical convolution is defined through the sifting property of the Dirac delta on the sphere. The so-called sifting convolution is defined by the inner product of one function with a translated version of another, but with the…
Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that…
An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…
The purpose of this paper is twofold. First, we introduce the notion of a $\Gamma$-martingale on a Euclidean manifold with a boundary (i.e., the closure of an open connected domain in R d ), we provide its equivalent characterization…
In this paper, we introduce a set of tools for providing user-friendly explanations in an explanation-based constraint programming system. The idea is to represent the constraints of a problem as an hierarchy (a tree). Users are then…
Alternating projections and their variants are classical tools for computing points in intersections of sets. Existing analyses for smooth manifolds mainly focus on local convergence rates under transversality or related regularity…
Twin reduction defines an equivalence relation on the vertex set of a graph. I give a characterisation of this equivalence relation. A consequence is a structure theorem for the automorphism group of the graph.
We consider the fundamental task of optimising a real-valued function defined in a potentially high-dimensional Euclidean space, such as the loss function in many machine-learning tasks or the logarithm of the probability distribution in…
A matrix approach to continuous iteration is proposed for general formal series. It leads, in particular, to an order{to{order iteration of the exponential function, and consequently to an algorithmic approach to tetration. Lower{order…
We consider two disjoint sets of points. If at least one of the sets can be embedded into an Euclidean space, then we provide sufficient conditions for the two sets to be jointly embedded in one Euclidean space. In this joint Euclidean…
We describe the additive subgroups of fields which are closed with respect to taking inverses. In particular, in characteristic different from two any such subgroup is either a subfield or the kernel of the trace map of a quadratic…
Abstract convexity generalises classical convexity by considering the suprema of functions taken from an arbitrarily defined set of functions. These are called the abstract linear (abstract affine) functions. The purpose of this paper is to…
Entanglement is a digraph complexity measure that origins in fixed-point theory. Its purpose is to count the nested depth of cycles in digraphs. In this paper we prove that the class of undirected graphs of entanglement at most $k$, for…
A `discrete differential manifold' we call a countable set together with an algebraic differential calculus on it. This structure has already been explored in previous work and provides us with a convenient framework for the formulation of…