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Leveraging real-time data analysis and multiple kernel learning for manufacturing of innovative steels

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Journal of mathematics in Industry 2025年第1期15卷 1-22页

作者： Rannetbauer, Wolfgang Hubmer, Simon Hambrock, Carina Ramlau, Ronny oestalpine Stahl GmbH Linz Austria Institute of Industrial Mathematics Johannes Kepler University Linz Linz Austria Johann Radon Institute for Computational and Applied Mathematics Linz Austria

The implementation of thermally sprayed components in steel manufacturing presents challenges for production and plant maintenance. While enhancing performance through specialized surface properties, these components may encounter difficulties in meeting modified requirements due to standardization in the refurbishment process. This article proposes updating the established coating process for thermally spray coated components for steel manufacturing (TCCSM) by integrating real-time data analytics and predictive quality management. Two essential components–the data aggregator and the quality predictor–are designed through continuous process monitoring and the application of data-driven methodologies to meet the dynamic demands of the evolving steel landscape. The quality predictor is powered by the simple and effective multiple kernel learning strategy with the goal of realizing predictive quality. The data aggregator, designed with sensors, flow meters, and intelligent data processing for the thermal spray coating process, is proposed to facilitate real-time analytics. The performance of this combination was verified using small-scale tests that enabled not only the accurate prediction of coating quality based on the collected data but also proactive notification to the operator as soon as significant deviations are identified.

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A Linear Frequency Domain Solver Workflow for Fast Simulation of Transmission Systems 6th

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A Linear Frequency Domain Solver Workflow for Fast Simulati...

6th Joint International Conference on Multibody System Dynamics and 10th Asian Conference on Multibody Systems, IMSD-ACMD 2020

作者： Bauer, K.D. Haslinger, J. Offner, G. Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences and MathConsult GmbH Altenberger Str. 69 Linz4040 Austria Advanced Simulation Technologies AVL List GmbH Hans-List-Platz 1 Graz8020 Austria

ISBN: (纸本)9789819775248

The contribution presents a complete frequency solver workflow applied to automotive transmissions modeled as multi-body systems consisting of mechanical components like rotating rigid and elastic shafts interconnected by gear contacts and supported by bearing joints. Solving the equations of motion in frequency domain based on a linearized model yields the periodic steady-state results very fast compared to transient time integration methods, where fast oscillating components may decay slowly. The frequency domain solver workflow is described in detail from getting a loaded state of the model, which is used for linearization, up to solving linear equation systems for each non-negligible frequency load component. The presented solver workflow is applied to a simple gearbox model. Resulting vibrations from the linear frequency domain solution are compared against results of a transient time domain solution, where the frequency domain solution matches well the time domain results but is obtained within a fraction of CPU time. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： Frequency domain analysis

NEW ESTIMATES FOR CHARACTER SUMS OVER SPARSE ELEMENTS OF FINITE FIELDS

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arXiv 2025年

作者： Cheng, Kaimin Winterhof, Arne School of Mathematics and Information China West Normal University Nanchong637002 China Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Science Linz4040 Austria

Let q be a prime power and r a positive integer. Let Fq be the finite field with q elements, and let Fqr be its extension field of degree r. Let χ be a nontrivial multiplicative character of Fqr. In this paper, we provide new estimates for the character sums Pg∈G χ(f(g)), where G is a given sparse subsets of Fqr and f(X) is a polynomial over Fqr of certain type. Specifically, by extending a sum over sparse subsets to subfields, rather than to general linear spaces, we obtain significant improvements of previous *** Codes 11T23 Copyright © 2025, The Authors. All rights reserved.

关键词： Finite element method

Is a single lethal electric field threshold sufficient to characterize the lesion size in computational modeling of cardiac pulsed-field ablation?

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Heart Rhythm O2

Heart Rhythm O2 2025年第5期6卷 671-677.0页

作者： Petras, Argyrios Amoros Figueras, Gerard Moreno Weidmann, Zoraida García-Sánchez, Tomás Viladés Medel, David Ivorra, Antoni Guerra, Jose M. Gerardo-Giorda, Luca RICAM–Johann Radon Institute for Computational and Applied Mathematics Linz Austria Department of Cardiology Hospital de la Santa Creu i Sant Pau Universitat Autònoma de Barcelona CIBER CV Barcelona Spain Department of Information and Communication Technologies Universitat Pompeu Fabra Barcelona Spain Institute for Mathematical Methods in Medicine and Data-Based Modelling Johannes Kepler University Linz Austria

Background: Pulsed-field ablation (PFA) is a novel cardiac ablation technology based on irreversible electroporation (IRE). PFA computational models rely on identification of a lethal electric field threshold to predict the IRE area. However, the predicted lesion anisotropy ratios (width over depth) vary extensively among recent studies, and these discrepancies remain a subject of discussion. Objective: This work aims to evaluate the predicted lesion anisotropy ratios using a PFA computational model by applying it to an open-chest in vivo porcine model geometry. Methods: Six domestic swine underwent epicardial PFA applications using a previously described waveform protocol. Animals were killed at least 3 hours after the last ablation, and lesions were assessed using triphenyltetrazolium chloride (TTC) staining. Numeric simulations were performed on a segmented and meshed porcine thoracic computed tomography (CT) scan, mimicking the open-chest experimental setup. Results: The maximum width of all simulated lesions was observed at the epicardial surface. The anisotropy ratios (AR) of the experimental lesions were smaller than the simulated ones (AR experimental vs simulated, 1.0–1.7 vs 2–2.7;Q1–Q3 quartiles). Increasing the peak voltage resulted in larger lesions;however, the computational model clearly underestimated the increase in lesion depth compared with the experimental data. Conclusion: Our computational model shows that a single lethal electric field threshold is insufficient to accurately predict both lesion depth and width in cardiac PFA. Our study suggests that for the given PFA waveforms, a threshold between 270 and 500 V/cm provides satisfactory lesion depth estimations, and a higher threshold between 790 and 1000 V/cm better captures the lesion width. © 2025 Heart Rhythm Society

关键词： Cardiac ablation Computer simulations Electric field threshold Mathematical modeling Pulsed field ablation

On the Nth 2-adic complexity of binary sequences identified with algebraic 2-adic integers

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Discrete applied mathematics 2025年 373卷 279-289页

作者： Chen, Zhixiong Winterhof, Arne Fujian Key Laboratory of Financial Information Processing Putian University Putian Fujian351100 China Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergestr. 69 LinzA-4040 Austria

We identify a binary sequence S=(sn)n=0∞ with the 2-adic integer GS(2)=∑n=0∞sn2n. In the case that GS(2) is algebraic over Q of degree d≥2, we prove that the Nth 2-adic complexity of S is at least [Formula presented], where the implied constant depends only on the minimal polynomial of GS(2). This result is an analog of the bound of Mérai and the second author on the linear complexity of automatic sequences, that is, sequences with algebraic GS(X) over the rational function field F2(X). We further discuss the most important case d=2 in both settings and explain that the intersection of the set of 2-adic algebraic sequences and the set of automatic sequences is the set of (eventually) periodic sequences. Finally, we provide some experimental results supporting the conjecture that 2-adic algebraic sequences can have also a desirable Nth linear complexity and automatic sequences a desirable Nth 2-adic complexity, respectively. © 2025 Elsevier B.V.

关键词： Rational functions

Phase retrieval in Fock space and perturbation of Liouville sets

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Revista Matematica Iberoamericana 2025年第3期41卷 969-1008页

作者： Grohs, Philipp Liehr, Lukas Rathmair, Martin Faculty of Mathematics University of Vienna Oskar-Morgenstern-Platz 1 Vienna 1090 Austria Research Network DataScience@UniVie University of Vienna Kolingasse 14-16 Vienna 1090 Austria Johann Radon Institute of Applied and Computational Mathematics Austrian Academy of Sciences Altenbergstrasse 69 Linz 4040 Austria Institut de Mathématiques de Bordeaux Université Bordeaux 351 Cours de la Libération Talence 33405 France

We study the determination of functions in Fock space from samples of their absolute value, known as the phase retrieval problem in Fock space. An important finding in this research field asserts that phaseless sampling on lattices of arbitrary density renders the problem unsolvable. The present study establishes solvability when using irregular sampling sets of the form A ∪ B ∪ C, where A, B, and C constitute perturbations of a Liouville set, i.e., a set with the property that all functions in Fock space bounded on the set are constant. The sets A, B, and C adhere to specific geometrical conditions of closeness and noncollinearity. We show that these conditions are sufficiently generic so as to allow the perturbations to be chosen also at random. By proving that Liouville sets occupy an intermediate position between sets of stable sampling and sets of uniqueness, we obtain the first construction of uniqueness sets for the phase retrieval problem in Fock space having a finite density. The established results apply to the Gabor phase retrieval problem in subspaces of L²(R), where we derive additional reductions of the size of uniqueness sets: for the class of real-valued functions, uniqueness is achieved from two perturbed lattices;for the class of even real-valued functions, a single perturbation suffices, resulting in a separated set. © 2025 Real Sociedad Matemática Española.

关键词： lattices Liouville sets perturbations phase retrieval phaseless sampling

Simplifying Formal Proof-Generating Models with ChatGPT and Basic Searching Techniques

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arXiv 2025年

作者： Han, Sangjun Hur, Taeil Hur, Youngmi Lee, Kathy Sangkyung Lee, Myungyoon Lim, Hyojae Yonsei University Seoul Korea Republic of JENTI Inc. Seoul Korea Republic of Korea Institute for Advanced Study Seoul Korea Republic of Johann Radon Institute for Computational and Applied Mathematics Linz Austria

The challenge of formal proof generation has a rich history, but with modern techniques, we may finally be at the stage of making actual progress in real-life mathematical problems. This paper explores the integration of ChatGPT and basic searching techniques to simplify generating formal proofs, with a particular focus on the miniF2F dataset. We demonstrate how combining a large language model like ChatGPT with a formal language such as Lean, which has the added advantage of being verifiable, enhances the efficiency and accessibility of formal proof generation. Despite its simplicity, our best-performing Lean-based model surpasses all known benchmarks with a 31.15% pass rate. We extend our experiments to include other datasets and employ alternative language models, showcasing our models’ comparable performance in diverse settings and allowing for a more nuanced analysis of our results. Our findings offer insights into AI-assisted formal proof generation, suggesting a promising direction for future research in formal mathematical proof. Copyright © 2025, The Authors. All rights reserved.

关键词： Formal languages

On the Nth 2-adic complexity of binary sequences identified with algebraic 2-adic integers

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arXiv 2025年

作者： Chen, Zhixiong Winterhof, Arne Fujian Key Laboratory of Financial Information Processing Putian University Fujian Putian351100 China Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergestr. 69 LinzA-4040 Austria

We identify a binary sequence S = (sn)∞n=0 with the 2-adic integer GS(2) = ∞ P sn2n. In the case that GS(2) is algebraic over Q of degree d ≥ 2, we prove n=0 that the Nth 2-adic complexity of S is at least Nd + O(1), where the implied constant depends only on the minimal polynomial of GS(2). This result is an analog of the bound of Mérai and the second author on the linear complexity of automatic sequences, that is, sequences with algebraic GS(X) over the rational function field F2(X). We further discuss the most important case d = 2 in both settings and explain that the intersection of the set of 2-adic algebraic sequences and the set of automatic sequences is the set of (eventually) periodic sequences. Finally, we provide some experimental results supporting the conjecture that 2-adic algebraic sequences can have also a desirable Nth linear complexity and automatic sequences a desirable Nth 2-adic complexity, respectively. © 2025, CC BY.

关键词： Rational functions

Probabilistic results on the 2-adic complexity

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arXiv 2025年

This work is devoted to solving some closely related open problems on the average and asymptotic behavior of the 2-adic complexity of binary sequences. First, for fixed N, we prove that the expected value EN2−adic of the 2-adic complexity over all binary sequences of length N is close to N/2 and the deviation from N2 is at most of order of magnitude log(N). More precisely, we show that N/2 − 1 ≤ EN2−adic = N/2 + O(log(N)). We also prove bounds on the expected value of the Nth rational complexity. Our second contribution is to prove for a random binary sequence S that the Nth 2-adic complexity satisfies with probability 1 λS(N) = N/2 + O(log(N)) for all N. © 2025, CC BY.

关键词： Shift registers