Related papers: The trouble with deautonomising higher order maps
We study sublevel set and superlevel set persistent homology on discrete functions through the perspective of finite ordered sets of both linearly ordered and cyclically ordered domains. Finite ordered sets also serve as the codomain of our…
When neural networks are used to model dynamics, properties such as stability of the dynamics are generally not guaranteed. In contrast, there is a recent method for learning the dynamics of autonomous systems that guarantees global…
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we derive conditions for arbitrarily high order. We derive…
We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R^m into a pseudo-Riemannian manifold which is two times…
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 article, we establish some new second main theorems for meromorphic mappings of $\mathbb C^m$ into $\mathbb P^n(\mathbb C)$ and moving hypersurfaces with truncated counting functions. A uniqueness theorem for these mappings sharing…
Decoupling multivariate polynomials is useful for obtaining an insight into the workings of a nonlinear mapping, performing parameter reduction, or approximating nonlinear functions. Several different tensor-based approaches have been…
We present a Lohner-type algorithm for rigorous integration of systems of Delay Differential Equations (DDEs) with multiple delays and its application in computation of Poincar\'e maps to study the dynamics of some bounded, eternal…
Across many disciplines from neuroscience and genomics to machine learning, atmospheric science and finance, the problems of denoising large data matrices to recover signals obscured by noise, and of estimating the structure of these…
The ability to differentiate through optimization problems has unlocked numerous applications, from optimization-based layers in machine learning models to complex design problems formulated as bilevel programs. It has been shown that…
Deep functional maps have emerged in recent years as a prominent learning-based framework for non-rigid shape matching problems. While early methods in this domain only focused on learning in the functional domain, the latest techniques…
Differentially-private histograms have emerged as a key tool for location privacy. While past mechanisms have included theoretical & experimental analysis, it has recently been observed that much of the existing literature does not fully…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
In this work, we prove global existence of solutions for second order differential problems in a general framework. More precisely, we consider second order differential inclusions involving proximal normal cone to a set-valued map. This…
Non-holonomic constraints, both in the Lagragian and Hamiltonian formalism, are discussed from the geometrical viewpoint of implicit differential equations. A precise statement of both problems is presented remarking the similarities and…
It is known that automorphisms of quasi-circular domains fixing the origin are polynomial mappings. By introducing the so-called resonance order and quasi-resonance order, we provide a uniform upper bound for the degree of such polynomial…
This paper presents four novel domain decomposition algorithms integrated with nonlinear mapping techniques to address collocation-based solutions of eigenvalue problems involving sharp interfaces or steep gradients. The proposed methods…
In this paper we explore the general conditions in order that a 2-dimensional natural Hamiltonian system possess a second invariant which is a polynomial in the momenta and is therefore Liouville integrable. We examine the possibility that…
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…
This paper presents and explores a theory of \emph{multiholomorphic maps}. This group of ideas generalizes the theory of pseudoholomorphic curves in a direction suggested by consideration of the kinds of compatible geometric structures that…