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FIXED POINT RESULTS AND THE EKELAND VARIATIONAL PRINCIPLE IN VECTOR B-METRIC SPACES

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arXiv 2025年

作者： Precup, Radu Stan, Andrei Faculty of Mathematics and Computer Science Institute of Advanced Studies in Science and Technology Babeş-Bolyai University Cluj-Napoca400084 Romania Tiberiu Popoviciu Institute of Numerical Analysis Romanian Academy P.O. Box 68-1 Cluj-Napoca400110 Romania Department of Mathematics Babeş-Bolyai University Cluj-Napoca400084 Romania

In this paper, we extend the concept of b-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the b-metric setting: fixed-point theorems, stability results, and a variant of Ekeland’s variational principle. As a consequence, we also derive a variant of Caristi’s fixed-point theorem. © 2025, CC BY.

关键词： Vector spaces

Splitting criteria for ordinal decision trees: an experimental study

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arXiv 2024年

作者： Ayllón-Gavilán, Rafael Martínez-Estudillo, Francisco José Guijo-Rubio, David Hervás-Martínez, César Gutiérrez, Pedro Antonio Department of Computer Science and Numerical Analysis Universidad de Córdoba Campus de Rabanales Ctra. N-IVa Km. 396 Córdoba14071 Spain Department of Quantitative Methods Universidad Loyola Andalucía C. Escritor Castilla Aguayo 4 Córdoba14004 Spain

Ordinal Classification (OC) is a machine learning field that addresses classification tasks where the labels exhibit a natural order. Unlike nominal classification, which treats all classes as equally distinct, OC takes the ordinal relationship into account, producing more accurate and relevant results. This is particularly critical in applications where the magnitude of classification errors has implications. Despite this, OC problems are often tackled using nominal methods, leading to suboptimal solutions. Although decision trees are one of the most popular classification approaches, ordinal tree-based approaches have received less attention when compared to other classifiers. This work conducts an experimental study of tree-based methodologies specifically designed to capture ordinal relationships. A comprehensive survey of ordinal splitting criteria is provided, standardising the notations used in the literature for clarity. Three ordinal splitting criteria, Ordinal Gini (OGini), Weighted Information Gain (WIG), and Ranking Impurity (RI), are compared to the nominal counterparts of the first two (Gini and information gain), by incorporating them into a decision tree classifier. An extensive repository considering 45 publicly available OC datasets is presented, supporting © 2024, CC BY-NC-ND.

关键词： Adversarial machine learning

Continuous Wavelet Transform Based Variable Projection Networks

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Continuous Wavelet Transform Based Variable Projection Netwo...

European Signal Processing Conference (EUSIPCO)

作者： Attila Miklós Ámon Kristian Fenech Péter Kovács Tamás Dózsa Department of Numerical Analysis Eötvös Loránd University Budapest Department of Artificial Intelligence Eötvös Loránd University Budapest Széchenyi Itsván University and HUN-REN Institute for Computer Science and Control Vehicle Industry Research Center Budapest Systems and Control Laboratory Budapest

ISBN: (数字)9789464593617

ISBN: (纸本)9798331519773

A novel feature extraction layer using the continuous wavelet transform is developed for use with neural networks. The learned parameters (scales and shifts in time) of the proposed wavelet layer can be interpreted by humans. In addition, using the concept of adaptive orthogonal projections to approximate wavelet coefficients, a sparse representation of the input is achieved. The proposed method is applicable with any analytic mother wavelet. As a case study, the application of bearing fault detection is considered to demonstrate the efficiency of the method, using a benchmark dataset. The results clearly show that the proposed model can be used to solve fault detection problems achieving near perfect classification accuracy. Qualitative and quantitative comparisons are made to a previous wavelet based neural network architecture. It is shown that the proposed method matches or outperforms previous approaches while using significantly less parameters. This sparsity improves model performance from the point of view of interpretability as well as model complexity.

关键词： Adaptation models Continuous wavelet transforms Sparse approximation Fault detection Neural networks Europe Wavelet analysis Feature extraction numerical models Wavelet coefficients

A Sensitivity analysis of Cellular Automata and Heterogeneous Topology Networks: Partially-Local Cellular Automata and Homogeneous Homogeneous Random Boolean Networks

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arXiv 2024年

作者： Glover, Tom Eivind Jahren, Ruben Martinuzzi, Francesco Lind, Pedro Gonçalves Nichele, Stefano Department of Computer Science OsloMet - Oslo Metropolitan University Oslo Norway Department of Computer Science and Communication Østfold University College Halden Norway Simula Research Laboratory Numerical Analysis and Scientific Computing Oslo0164 Norway Center for Scalable Data Analytics and Artificial Intelligence Leipzig University Leipzig Germany Institute for Earth System Science & Remote Sensing Leipzig University Leipzig Germany Remote Sensing Centre for Earth System Research Leipzig University Leipzig Germany

Elementary Cellular Automata (ECA) are a well-studied computational universe that is, despite its simple configurations, capable of impressive computational variety. Harvesting this computation in a useful way has historically shown itself to be difficult, but if combined with reservoir computing (RC), this becomes much more feasible. Furthermore, RC and ECA enable energy-efficient AI, making the combination a promising concept for Edge AI. In this work, we contrast ECA to substrates of Partially-Local CA (PLCA) and Homogeneous Homogeneous Random Boolean Networks (HHRBN). They are, in comparison, the topological heterogeneous counterparts of ECA. This represents a step from ECA towards more biological-plausible substrates. We analyse these substrates by testing on an RC benchmark (5-bit memory), using Temporal Derrida plots to estimate the sensitivity and assess the defect collapse rate. We find that, counterintuitively, disordered topology does not necessarily mean disordered computation. There are countering computational"forces" of topology imperfections leading to a higher collapse rate (order) and yet, if accounted for, an increased sensitivity to the initial condition. These observations together suggest a shrinking critical range. © 2024, CC BY.

关键词： Sensitivity analysis

ON EQUILIBRIUM IN CONTROL PROBLEMS WITH APPLICATIONS TO EVOLUTION SYSTEMS

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arXiv 2024年

In this paper we examine a mutual control problem for systems of two abstract evolution equations subject to a proportionality final condition. Related observability and semi-observability problems are discussed. The analysis employs a vector fixed-point approach, using matrices rather than constants, and applies the technique of Bielecki equivalent norms. © 2024, CC BY.

关键词： Choquet integral

A MUTUAL CONTROL PROBLEM FOR SEMILINEAR SYSTEMS VIA FIXED POINT APPROACH

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arXiv 2024年

In this paper, we introduce and discuss the concept of a mutual control problem. Our analysis relies on a vector fixed-point approach based on the fixed-point theorems of Perov, Schauder, and Avramescu. In our analysi...

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Global and Diverse Ensemble model for regression

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Neurocomputing 2025年 647卷

作者： Antonio M. Durán-Rosal Thomas Ashley Javier Pérez-Rodríguez Francisco Fernández-Navarro Department of Quantitative Methods Universidad Loyola Andalucía Spain Department of Computer Science and Numerical Analysis University of Córdoba Spain Department of Computer Languages and Computer Science University of Málaga Spain

Diversity is a fundamental component in ensemble methods, crucial for enhancing the overall performance and robustness of predictive models. In bagging and boosting, diversity is implicitly generated through the data sampling process. In stacking, diversity is introduced by incorporating heterogeneous machine learning models as base learners, and an error function is created to focus on minimizing the meta-learner’s overall errors. Some models promote diversity directly within the error function; however, they often prioritize generating competitive and diverse individual learners, neglecting the necessity of creating an ensemble that is collectively accurate, as seen in stacking, whilst ensuring diversity among its members. Motivated by this point, two ensemble models are proposed in this manuscript, named Global and Diverse Ensemble Methods. These models incorporate implicit diversity through data, diversity in the heterogeneity of base learners, and an error function designed to produce a competitive overall ensemble with diverse individuals. The two diversity proposals included in the models are negative correlation and squared Pearson correlation. In both cases, the error function incorporates the minimization of the ensemble’s overall error (global error measure) in addition to promoting diversity. The proposed methods have been rigorously tested on 45 publicly available regression datasets using shallow base learners, as well as on 7 additional datasets using deep base learners, yielding very promising results. These findings underscore the importance of integrating these diversity-promoting elements and minimizing the global errors of the ensemble, rather than focusing solely on the errors of individual base learners, in the design of ensemble methods.

关键词： Ensemble learning Bagging Stacking Diversity

Global random walk for one-dimensional one-phase Stefan-type moving-boundary problems: Simulation results

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arXiv 2024年

作者： Suciu, Nicolae Nepal, Surendra Wondmagegne, Yosief Ögren, Magnus Muntean, Adrian Tiberiu Popoviciu Institute of Numerical Analysis Romanian Academy Fântânele str. no. 57 Cluj-Napoca Romania Department of Mathematics and Computer Science Karlstad University Universitetsgatan 2 Karlstad65188 Sweden School of Science and Technology Örebro University ÖrebroSE-70182 Sweden HMU Research Center Institute of Emerging Technologies HeraklionGR-71004 Greece

MSC Codes 35R37, 65M75, 65M60This work presents global random walk approximations of solutions to one-dimensional Stefan-type moving-boundary problems. We are particularly interested in the case when the moving boundary is driven by an explicit representation of its speed. This situation is usually referred to in the literature as moving-boundary problem with kinetic condition. As a direct application, we propose a numerical scheme to forecast the penetration of small diffusants into a rubber-based material. To check the quality of our results, we compare the numerical results obtained by global random walks either using the analytical solution to selected benchmark cases or relying on finite element approximations with a priori known convergence rates. It turns out that the global random walk concept can be used to produce good quality approximations of the weak solutions to the target class of problems. © 2024, CC BY.

关键词： Random processes

A MULTISCALE MODEL FOR WEAKLY NONLINEAR SHALLOW WATER WAVES OVER PERIODIC BATHYMETRY

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arXiv 2023年

作者： Ketcheson, David I. Lóczi, Lajos Russo, Giovanni Thuwal23955-6900 Saudi Arabia Department of Numerical Analysis ELTE Eötvös Loránd University Pázmány P. s. 1/C BudapestH-1117 Hungary Department of Analysis and Operations Research BME Budapest University of Technology and Economics Hungary Department of Mathematics and Computer Science University of Catania Viale A. Doria 6 Catania95125 Italy

We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical experiments suggest a different behavior in the presence of periodic bathymetry. Starting from the first-order variable-coefficient hyperbolic system, we apply a multiple-scale perturbation approach in order to derive a system of constant-coefficient high-order partial differential equations whose solution approximates that of the original system. The high-order system turns out to be dispersive and exhibits solitary-wave formation, in close agreement with direct numerical simulations of the original system. We show that the constant-coefficient homogenized system can be used to study the properties of solitary waves and to conduct efficient numerical simulations. Copyright © 2023, The Authors. All rights reserved.

关键词： Bathymetry