Related papers: Approximate derivations of order $n$

We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations…

Many real-world phenomena are naturally modeled by graphs and networks. However, classical graph models are often limited to pairwise interactions and may not adequately capture the richer structures that arise in practice. Higher-order…

Ext-int.\ one affine functions are functions affine in the direction of one-divisible exterior forms, with respect to exterior product in one variable and with respect to interior product in the other. The purpose of this article is to…

We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…

The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…

We define triangulated factorization systems on triangulated categories, and prove that a suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to $t$-structures on the same category. This result is…

The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay…

We develop a comprehensive theory of the stable representation categories of several sequences of groups, including the classical and symmetric groups, and their relation to the unstable categories. An important component of this theory is…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…

A brief introduction to the theory of ordered sets and lattice theory is given. To illustrate proof techniques in the theory of ordered sets, a generalization of a conjecture of Daykin and Daykin, concerning the structure of posets that can…

These notes derive a number of technical results on nonlinear contraction theory, a comparatively recent tool for system stability analysis. In particular, they provide new results on the preservation of contraction through system…

We consider the following property of a first order theory T with a distinguished unary predicate P: every model of the theory of P occurs as the P-part of some model of T. We call this property the Gaifman property. Gaifman conjectured…

This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…

This paper deals with the convergence time analysis of a class of fixed-time stable systems with the aim to provide a new non-conservative upper bound for its settling time. Our contribution is fourfold. First, we revisit the well-known…

We give a principled method for decomposing the predictive uncertainty of a model into aleatoric and epistemic components with explicit semantics relating them to the real-world data distribution. While many works in the literature have…

We introduce a provably stable variant of neural ordinary differential equations (neural ODEs) whose trajectories evolve on an energy functional parametrised by a neural network. Stable neural flows provide an implicit guarantee on…

We write down a series of basic laws for (strict) higher-order circuit diagrams. More precisely, we define higher-order circuit theories in terms of: (a) nesting, (b) temporal and spatial composition, and (c) equivalence between lower-order…

As the main contribution, this document provides a consistent discretization of a class of fixed-time stable systems, namely predefined-time stable systems. In the unperturbed case, the proposed approach allows obtaining not only a…

The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes…

The odds theorem and the corresponding solution algorithm (odds algorithm) are tools to solve a wide range of optimal stopping problems. Its generality and tractability have caught much attention. (Google for instance "Bruss odds" to obtain…