相关论文: A generalized chordal metric making strong stabili…

We develop a model-theoretic framework for the study of distal factors of strongly ergodic, measure-preserving dynamical systems of countable groups. Our main result is that all such factors are contained in the (existential) algebraic…

Differential sensitivity techniques originally developed to study the robustness of energy landscape controllers are generalized to the important case of closed quantum systems subject to continuously varying controls. Vanishing sensitivity…

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential…

Conformal prediction provides finite-sample, distribution-free coverage under exchangeability, but standard constructions may lack robustness in the presence of outliers or heavy tails. We propose a robust conformal method based on a…

Autonomous systems increasingly rely on machine learning techniques to transform high-dimensional raw inputs into predictions that are then used for decision-making and control. However, it is often easy to maliciously manipulate such…

The problem of robustly, asymptotically stabilizing a point (or a set) with two output-feedback hybrid controllers is considered. These control laws may have different objectives, e.g., the closed-loop systems resulting with each controller…

Robustness of neural networks has recently attracted a great amount of interest. The many investigations in this area lack a precise common foundation of robustness concepts. Therefore, in this paper, we propose a rigorous and flexible…

The notion of a (metric) modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by the author [V. V. Chistyakov, Metric modulars and their application, Dokl.…

The robust disturbance rejection controller has been the subject of intensive research due to its undeniable importance for automation. Modern control theory tends to use model-based approaches versus model-free approaches, especially when…

The robustness of classifiers has become a question of paramount importance in the past few years. Indeed, it has been shown that state-of-the-art deep learning architectures can easily be fooled with imperceptible changes to their inputs.…

The paper deals with local robust feedback synthesis for systems with multidimensional control and unknown bounded perturbations. Using V.~I.~Korobov's controllability function method, we construct a bounded control which steers an…

This paper explores the properties of adaptive systems with closed-loop reference models. Using additional design freedom available in closed-loop reference models, we design new adaptive controllers that are (a) stable, and (b) have…

Conformal prediction is a popular, modern technique for providing valid predictive inference for arbitrary machine learning models. Its validity relies on the assumptions of exchangeability of the data, and symmetry of the given model…

By definition, transverse intersections are stable under infinitesimal perturbations. Using persistent homology, we extend this notion to a measure. Given a space of perturbations, we assign to each homology class of the intersection its…

This paper presents a new approach to distributed controller design that exploits a partial-structure representation of linear time invariant systems to characterize the structure of a system. This partial-structure representation, called…

The conformal method in general relativity aims to successfully parametrise the set of all initial data associated with globally hyperbolic spacetimes. One such mapping was suggested by David Maxwell. I verify that the solutions of the…

A branch of generalizations of the Banach Fixed Point Theorem replaces contractivity by a weaker but still effective property. The aim of the present note is to extend the contraction principle in this spirit for such complete semimetric…

Answering an open question affirmatively it is shown that every ergodic invariant measure of a mean equicontinuous (i.e. mean-L-stable) system has discrete spectrum. Dichotomy results related to mean equicontinuity and mean sensitivity are…

Starting with the relative entropy for two close statistical states we define the metric and calculate the scalar curvature $R$ for systems with classical, boson and fermion fractal distribution functions with moment order parameter $q$. In…

An improved version of quasiinvariance property of the quasihyperbolic metric under M\"obius transformations of the unit ball in ${\mathbb R}^n, n \ge 2,$ is given. Next, a quasiinvariance property, sharp in a local sense, of the…