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Limit theorems for globally perturbed random walks

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arXiv 2025年

作者： Iksanov, Alexander Kondratenko, Oleh Faculty of Computer Science and Cybernetics Taras Shevchenko National University of Kyiv Ukraine

Let (ξ1, η1), (ξ2, η2), . . . be independent copies of an R2-valued random vector (ξ, η) with arbitrarily dependent components. Put Tn := ξ1+. . .+ξn−1+ηn for n ∈ N and define τ(t):= inf{n ≥ 1: Tn > t} the first passage time into (t, ∞), N(t):= Pn≥1 1{Tn≤t} the number of visits to (−∞, t] and ρ(t):= sup{n ≥ 1: Tn ≤ t} the associated last exit time for t ∈ R. The standing assumption of the paper is E[ξ] ∈ (0, ∞). We prove a weak law of large numbers for τ(t) and strong laws of large numbers for τ(t), N(t) and ρ(t). The strong law of large numbers for τ(t) holds if, and only if, E[η+] +] = ∞ we prove functional limit theorems in the Skorokhod space for (τ(ut))u≥0, properly normalized without centering. Also, we provide sufficient conditions under which finite dimensional distributions of (τ(ut))u≥0, (N(ut))u≥0 and (ρ(ut))u≥0, properly normalized and centered, converge weakly as t → ∞ to those of a Brownian motion. Quite unexpectedly, the centering needed for (N(ut)) takes in general a more complicated form than the centering ut/E[ξ] needed for (τ(ut)) and (ρ(ut)). Finally, we prove a functional limit theorem in the Skorokhod space for (N(ut)) under optimal moment conditions. Copyright © 2025, The Authors. All rights reserved.

关键词： Brownian movement

Anomaly-Focused Augmentation Method for Industrial Visual Inspection

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IEEE Access 2025年 13卷 89118-89139页

作者： Lara, Melvin A. Hameed, Ibrahim A. Koziorek, Jiri Faculty of Electrical Engineering and Computer Science Department of Cybernetics and Biomedical Engineering Ostrava 70800 Czech Republic Norwegian University of Life Sciences (NMBU) Department of Mechanical Engineering and Technology Management Ås 1433 Norway

In industrial inspection, the detection of surface defects—such as scratches, dents, or other defects—is crucial for ensuring product quality. However, the limited availability of annotated images of such defects poses challenges for developing reliable detection models. This paper proposes a novel image augmentation algorithm to address this limitation by generating synthetic imperfections from a small sample set. Unlike traditional approaches that augment entire images, the proposed approach isolates defects and applies spatial transformations (e.g., rotation, shear) before blending them into background images. This allows for the creation of diverse training datasets. The algorithm employs a 2D binary map to encode the spatial relationship between defect and background regions of images and then applies an AI-driven model to generate new realistic blended images. By leveraging a generator-discriminator framework, the augmentation process is iteratively refined during training to maintain the style and texture of the original imperfections. Experimental results show that the proposed method significantly enhances the performance of defect detection models compared to existing augmentation techniques while preserving the realism of the generated images. © 2013 IEEE.

关键词： Artificial Intelligence Defect Detection Image Augmentation Image Processing Neural Networks

Large-area Tomographic Tactile Skin with Air Pressure Sensing for Improved Force Estimation

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arXiv 2025年

作者： Chen, Haofeng Himmel, Bedrich Kubik, Jiri Hoffmann, Matej Lee, Hyosang Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague Czech Republic Department of Computer Science Faculty of Electrical Engineering Czech Technical University in Prague Czech Republic Eindhoven Netherlands

This paper presents a dual-channel tactile skin that integrates Electrical Impedance Tomography (EIT) with air pressure sensing to achieve accurate multi-contact force detection. The EIT layer provides spatial contact information, while the air pressure sensor delivers precise total force measurement. Our framework combines these complementary modalities through: deep learning-based EIT image reconstruction, contact area segmentation, and force allocation based on relative conductivity intensities from EIT. The experiments demonstrated 15.1% average force estimation error in single-contact scenarios and 20.1% in multi-contact scenarios without extensive calibration data requirements. This approach effectively addresses the challenge of simultaneously localizing and quantifying multiple contact forces without requiring complex external calibration setups, paving the way for practical and scalable soft robotic skin applications. © 2025, CC BY.

关键词： Image segmentation

ALMOST PERIODIC STOCHASTIC PROCESSES WITH APPLICATIONS TO ANALYTIC NUMBER THEORY

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arXiv 2025年

作者： Iksanov, Alexander Kabluchko, Zakhar Marynych, Alexander Faculty of Computer Science and Cybernetics Taras Shevchenko National University of Kyiv Kyiv01601 Ukraine Institute of Mathematical Stochastics Department of Mathematics and Computer Science University of Münster Orléans-Ring 10 MünsterD-48149 Germany

A classical fact of the theory of almost periodic functions is the existence of their asymptotic distributions. In probabilistic terms, this means that if f is a Besicovitch almost periodic function and V is a random variable uniformly distributed on [−1, 1], then the random variables f (L · V ) converge in distribution, as L → ∞, to a proper non-degenerate random variable. We prove a functional extension of this result for the random processes (f (L · V + t))t∈R in the space of Besicovitch almost periodic functions, and also in the sense of weak convergence of finite-dimensional distributions. We further investigate the properties of the limiting stationary process and demonstrate applications in analytic number theory by extending the one-dimensional results of [Limiting distributions of the classical error terms of prime number theory, Quart. J. Math. 65 (2014), 743–780] and earlier *** Codes Primary: 11N37, 60F17, secondary: 60G10, 11M26 Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

Extinguishing Real Fires by Fully Autonomous Multirotor UAVs in the MBZIRC 2020 Competition

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Field Robotics

Field Robotics 2025年 2卷 406-436页

作者： Viktor Walter Vojtěch Spurný Matěj Petrlík Tomáš Báča David Žaitlík Lyubomyr Demkiv Martin Saska Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague http://mrs.felk.cvut.cz Robotics Group of SoftServe Inc. and with the Institute of Computer Science and Information Technologies Lviv Polytechnic National University Ukraine

In this paper, we describe a system for combating real fires with sprayed liquid extinguishing agent using a team of multirotor UAVs. The system design relies on onboard sensors and operates without the need for human intervention throughout its complex mission, from its takeoff to landing. The core UAV platform can estimate its state, self-localize, navigate and locate and extinguishing fires. Thermal and RGB cameras are used, each with a specialized computer vision subsystem and are combined with planar LIDAR for 3D localization of fires on multistory building facades. The system conducts aerial firefighting with a software stack that addresses flight dynamics and sensor limitations and a liquid-spraying subsystem incorporating a rigidly-attached water nozzle. The approach presented in this paper was motivated by the Mohamed Bin Zayed International Robotics Challenge (MBZIRC 2020) firefighting scenario, which focused on coordinated multi-UAV teams that can autonomously combat high-rise building fires. The MBZIRC series places particular emphasis on fast and reliable deployment of robots in realistic conditions. These contests promote development of real-world applications that are greatly needed by society, but which still exceed State-of-the-Art in the robotics community. To our knowledge, our system was the only MBZIRC 2020 contender to extinguish a facade fire successfully in autonomous mode without using an RTK-GNSS system. Our approach contributed to victory in the overall competition and we have now adapted it into an industrial prototype for a firefighting UAV. A video attachment to this paper is available at http://***/fr2020firechallenge-facadefires.

关键词： Robots Buildings Autonomous aerial vehicles Location awareness Robot kinematics Inspection Navigation Cameras Monitoring Sensor systems

Towards New Frontiers in Mobile Manipulation: Team CTU-UPenn-NYU at MBZIRC 2020

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Field Robotics

Field Robotics 2025年 2卷 75-106页

作者： Petr Štibinger George Broughton Filip Majer Zdeněk Rozsypálek Anthony Wang Kshitij Jindal Alex Zhou Dinesh Thakur Giuseppe Loianno Tomáš Krajník Martin Saska Department of Cybernetics Faculty of Electrical Engineering Czech Technical University in Prague Department of Computer Science Faculty of Electrical Engineering Czech Technical University in Prague Department of MAE Tandon School of Engineering New York University GRASP Laboratory University of Pennsylvania Philadelphia PA USA Department of ECE and MAE Tandon School of Engineering New York University

In this paper we present an autonomous robotic system for picking, transporting, and precisely placing magnetically graspable objects. Such a system would be especially beneficial for construction tasks where human presence is not possible, e.g. due to chemical or radioactive pollution. The system comprises of two primary components — a wheeled, mobile platform and a manipulator arm. Both are interconnected through an onboard computer and utilize various onboard sensors for estimating the state of the robot and its surroundings. By using efficient processing algorithms, data from the onboard sensors can be used in a feedback loop during all critical operational sections, resulting in a robust system capable of operating on uneven terrain and in environments without access to satellite navigation. System functionality has been proven in Challenge II of the MBZIRC 2020 competition. The Challenge required a ground robot to build an L-shaped structure of colored bricks laid in a predefined pattern. Such a mission incorporates several demanding subchallenges, spanning multiple branches of computer science, cybernetics, and robotics. Moreover, all the subchallenges had to be performed flawlessly in rapid succession, in order to complete the Challenge successfully. The extreme difficulty of the task was highlighted in the MBZIRC 2020 finals, where our system was among the only two competitors (out of 32) that managed to complete the task in autonomous mode.

关键词： Robots Manipulators Robot sensing systems Reliability Autonomous aerial vehicles Service robots Multi-robot systems Assembly Valves Safety

The use of combined remote electronic monitoring and blood concentrations of antipsychotics for assessment of therapeutic adherence in patients with schizophrenia: results of a prospective study

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BMC Psychiatry 2025年第1期25卷 1-11页

作者： Šilhán, Petr Hýža, Martin Ambroš, Samuel Dostálek, Petr Schwarzová, Jana Skřont, Tomáš Perničková, Denisa Baarová, Pavla Augustynek, Martin Kacířová, Ivana Uřinovská, Romana Department of Psychiatry University Hospital Ostrava Ostrava Poruba Czech Republic Department of Clinical Neurosciences Faculty of Medicine University of Ostrava Ostrava Czech Republic Department of Cybernetics and Biomedical Engineering Faculty of Electrical Engineering and Computer Science VSB-Technical University Ostrava Ostrava Czech Republic Department of Clinical Pharmacology Institute of Laboratory Medicine University Hospital Ostrava Ostrava Czech Republic Institute of Clinical Pharmacology Faculty of Medicine University of Ostrava Ostrava Czech Republic

Schizophrenia is a serious mental illness, the pharmacological treatment of which comprises primarily the use of antipsychotics. However, non-adherence to their use and its reliable determination present a serious clinical and economic problem. This study aimed to determine therapeutic adherence in outpatients with schizophrenia spectrum disorders by combining short-term electronic monitoring of dispenser opening with the measurement of antipsychotic blood concentrations. A total of 55 patients underwent a week-long electronic monitoring of dispenser opening and measurement of blood concentrations before and after monitoring. Patients who correctly opened the dispenser at least in 80% of scheduled time points during the weekly interval and, at the same time, did not show a change in blood concentration of the antipsychotic by more than 30% in any direction, were considered adherent. 69.1% of the patients met the adherence criteria, which was less than that determined by the Drug Attitude Inventory (DAI-10), the Visual Analogue Scale (VAS), and the Clinician Rating Scale (CRS). 7.3% of the patients took less than 80% of the prescribed doses and a change in blood concentrations of the antipsychotic by more than 30% was detected in 25.4% of the patients. In 70.9% of patients, the detected concentrations were within the recommended therapeutic reference interval. The groups of adherent and non-adherent patients did not differ statistically significantly in the severity of their illness as determined by the Clinical Global Impression (CGI), the Personal and Social Performance scale (PSP), and the Positive and Negative Syndrome Scale (PANSS). The combined method of evaluating adherence in schizophrenia patients confirmed the results determined by other methods. The benefits of this approach are described in the paper.

关键词： Antipsychotics Schizophrenia Telehealth Therapeutic adherence Therapeutic drug monitoring

Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation

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arXiv 2025年

作者： Jalowy, Jonas Kabluchko, Zakhar Marynych, Alexander Paderborn University Institute of Mathematics Warburger Str. 100 Paderborn33098 Germany Institute of Mathematical Stochastics Department of Mathematics and Computer Science University of Münster Orléans-Ring 10 MünsterD-48149 Germany School of Mathematical Sciences Queen Mary University of London Mile End Road LondonE14NS United Kingdom Faculty of Computer Science and Cybernetics Taras Shevchenko National University of Kyiv Kyiv01601 Ukraine

Given a sequence of polynomials (Pn)n∈N with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting zero distribution of Pn as deg Pn → ∞. The method is based on establishing an equivalence between the existence of a limiting empirical zero distribution µ and the existence of an exponential profile g associated with the coefficients of the polynomials (Pn)n∈N. The exponential profile g, which can be roughly described by [zk]Pn(z) ≈ exp (ng(k/n)), offers a direct route to computing the Cauchy transform G of µ: the functions t → tG(t) and α → exp (− g′(α)) are mutual inverses. This relationship, in various forms, has previously appeared in the literature, most notably in the paper [Van Assche, Fano and Ortolani, SIAM J. Math. Anal., 1987]. As a first contribution, we present a self-contained probabilistic proof of this equivalence by representing the polynomials as generating functions of sums of independent Bernoulli random variables. This probabilistic framework naturally lends itself to tools from large deviation theory, such as the exponential change of measure. The resulting theorems generalize and unify a range of previously known results, which were traditionally established through analytic or combinatorial methods. Secondly, using the profile-based approach, we investigate how the exponential profile and the limiting zero distribution behave under certain operations on polynomials, including finite free convolutions, Hadamard products, and repeated differentiation. In particular, our approach yields new proofs of the convergence results ‘⊞n → ⊞’ and ‘⊠n → ⊠’, extending them to cases where the distributions are not necessarily compactly supported. This paper is the first in a series of three. In Part II, we shall explore a wide range of examples, covering many classical families of polynomials, while Part III will focus on random polynomials and establish functional limit theorems for their random pr

关键词： Polynomials

Weakening Topologies on a Countable Abelian group of Finite Exponent

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Journal of Mathematical sciences (United States) 2020年第2期248卷 188-189页

作者： Protasov, Igor Faculty of Computer Science and Cybernetics Kyiv University Kyiv Ukraine

We prove that a countable locally minimal Abelian group of finite exponent m is discrete. For prime m, this answers Question 7.35(b) from [2]. © 2020, Springer science+Business Media, LLC, part of Springer Nature.

关键词： Locally minimal group