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36 results on '"Maletzky, Alexander"'

2. Comparing the Machine Readability of Traffic Sign Pictograms in Austria and Germany

Author

Maletzky, Alexander, Thumfart, Stefan, and Wruß, Christoph

Subjects
Computer Science - Computer Vision and Pattern Recognition, Computer Science - Machine Learning
Abstract

We compare the machine readability of pictograms found on Austrian and German traffic signs. To that end, we train classification models on synthetic data sets and evaluate their classification accuracy in a controlled setting. In particular, we focus on differences between currently deployed pictograms in the two countries, and a set of new pictograms designed to increase human readability. Besides other results, we find that machine-learning models generalize poorly to data sets with pictogram designs they have not been trained on. We conclude that manufacturers of advanced driver-assistance systems (ADAS) must take special care to properly address small visual differences between current and newly designed traffic sign pictograms, as well as between pictograms from different countries.

Published
2021

3. CaTabRa: Efficient Analysis and Predictive Modeling of Tabular Data

Author

Maletzky, Alexander, Kaltenleithner, Sophie, Moser, Philipp, Giretzlehner, Michael, Rannenberg, Kai, Editor-in-Chief, Soares Barbosa, Luís, Editorial Board Member, Goedicke, Michael, Editorial Board Member, Tatnall, Arthur, Editorial Board Member, Neuhold, Erich J., Editorial Board Member, Stiller, Burkhard, Editorial Board Member, Stettner, Lukasz, Editorial Board Member, Pries-Heje, Jan, Editorial Board Member, Kreps, David, Editorial Board Member, Rettberg, Achim, Editorial Board Member, Furnell, Steven, Editorial Board Member, Mercier-Laurent, Eunika, Editorial Board Member, Winckler, Marco, Editorial Board Member, Malaka, Rainer, Editorial Board Member, Maglogiannis, Ilias, editor, Iliadis, Lazaros, editor, MacIntyre, John, editor, and Dominguez, Manuel, editor

Published
2023
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4. A Generic and Executable Formalization of Signature-Based Gr\'obner Basis Algorithms

Author

Maletzky, Alexander

Subjects
Computer Science - Symbolic Computation
Abstract

We present a generic and executable formalization of signature-based algorithms (such as Faug\`ere's $F_5$) for computing Gr\"obner bases, as well as their mathematical background, in the Isabelle/HOL proof assistant. Said algorithms are currently the best known algorithms for computing Gr\"obner bases in terms of computational efficiency. The formal development attempts to be as generic as possible, generalizing most known variants of signature-based algorithms, but at the same time the implemented functions are effectively executable on concrete input for efficiently computing mechanically verified Gr\"obner bases. Besides correctness the formalization also proves that under certain conditions the algorithms a-priori detect and avoid all useless reductions to zero, and return minimal signature Gr\"obner bases. To the best of our knowledge, the formalization presented here is the only formalization of signature-based Gr\"obner basis algorithms in existence so far.

Published
2020
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7. Gr\'obner Bases of Modules and Faug\`ere's $F_4$ Algorithm in Isabelle/HOL

Author

Maletzky, Alexander and Immler, Fabian

Subjects
Computer Science - Logic in Computer Science, Computer Science - Symbolic Computation
Abstract

We present an elegant, generic and extensive formalization of Gr\"obner bases in Isabelle/HOL. The formalization covers all of the essentials of the theory (polynomial reduction, S-polynomials, Buchberger's algorithm, Buchberger's criteria for avoiding useless pairs), but also includes more advanced features like reduced Gr\"obner bases. Particular highlights are the first-time formalization of Faug\`ere's matrix-based $F_4$ algorithm and the fact that the entire theory is formulated for modules and submodules rather than rings and ideals. All formalized algorithms can be translated into executable code operating on concrete data structures, enabling the certified computation of (reduced) Gr\"obner bases and syzygy modules., Comment: extended version of paper submitted to CICM2018

Published
2018

8. Verifying Buchberger's Algorithm in Reduction Rings

Author

Maletzky, Alexander

Subjects
Computer Science - Symbolic Computation, Computer Science - Logic in Computer Science, Mathematics - Commutative Algebra, 13P10, F.4.1, I.2.3
Abstract

In this paper we present the formal, computer-supported verification of a functional implementation of Buchberger's critical-pair/completion algorithm for computing Gr\"obner bases in reduction rings. We describe how the algorithm can be implemented and verified within one single software system, which in our case is the Theorema system. In contrast to existing formal correctness proofs of Buchberger's algorithm in other systems, e. g. Coq and ACL2, our work is not confined to the classical setting of polynomial rings over fields, but considers the much more general setting of reduction rings; this, naturally, makes the algorithm more complicated and the verification more difficult. The correctness proof is essentially based on some non-trivial results from the theory of reduction rings, which we formalized and formally proved as well. This formalization already consists of more than 800 interactively proved lemmas and theorems, making the elaboration an extensive example of higher-order theory exploration in Theorema., Comment: 8 pages; appeared in the proceedings of PAS'2015 (Program Verification, Automated Debugging, and Symbolic Computation, Beijing, China, October 21--23, 2015)

Published
2016

9. Mathematical Theory Exploration in Theorema: Reduction Rings

Author

Maletzky, Alexander

Subjects
Computer Science - Symbolic Computation, Computer Science - Logic in Computer Science, Mathematics - Commutative Algebra, 13P10, F.4.1, I.2.3
Abstract

In this paper we present the first-ever computer formalization of the theory of Gr\"obner bases in reduction rings, which is an important theory in computational commutative algebra, in Theorema. Not only the formalization, but also the formal verification of all results has already been fully completed by now; this, in particular, includes the generic implementation and correctness proof of Buchberger's algorithm in reduction rings. Thanks to the seamless integration of proving and computing in Theorema, this implementation can now be used to compute Gr\"obner bases in various different domains directly within the system. Moreover, a substantial part of our formalization is made up solely by "elementary theories" such as sets, numbers and tuples that are themselves independent of reduction rings and may therefore be used as the foundations of future theory explorations in Theorema. In addition, we also report on two general-purpose Theorema tools we developed for an efficient and convenient exploration of mathematical theories: an interactive proving strategy and a "theory analyzer" that already proved extremely useful when creating large structured knowledge bases., Comment: submitted to CICM 2015 (Conference on Intelligent Computer Mathematics)

Published
2016
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11. Formalization of Dubé’s Degree Bounds for Gröbner Bases in Isabelle/HOL

Author

Maletzky, Alexander, Hutchison, David, Editorial Board Member, Kanade, Takeo, Editorial Board Member, Kittler, Josef, Editorial Board Member, Kleinberg, Jon M., Editorial Board Member, Mattern, Friedemann, Editorial Board Member, Mitchell, John C., Editorial Board Member, Naor, Moni, Editorial Board Member, Pandu Rangan, C., Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Terzopoulos, Demetri, Editorial Board Member, Tygar, Doug, Editorial Board Member, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Kaliszyk, Cezary, editor, Brady, Edwin, editor, Kohlhase, Andrea, editor, and Sacerdoti Coen, Claudio, editor

Published
2019
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13. Gröbner Bases of Modules and Faugère’s Algorithm in Isabelle/HOL

Author

Maletzky, Alexander, Immler, Fabian, Hutchison, David, Series Editor, Kanade, Takeo, Series Editor, Kittler, Josef, Series Editor, Kleinberg, Jon M., Series Editor, Mattern, Friedemann, Series Editor, Mitchell, John C., Series Editor, Naor, Moni, Series Editor, Pandu Rangan, C., Series Editor, Steffen, Bernhard, Series Editor, Terzopoulos, Demetri, Series Editor, Tygar, Doug, Series Editor, Weikum, Gerhard, Series Editor, Rabe, Florian, editor, Farmer, William M., editor, Passmore, Grant O., editor, and Youssef, Abdou, editor

Published
2018
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14. The Formalization of Vickrey Auctions: A Comparison of Two Approaches in Isabelle and Theorema

Author

Maletzky, Alexander, Windsteiger, Wolfgang, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Geuvers, Herman, editor, England, Matthew, editor, Hasan, Osman, editor, Rabe, Florian, editor, and Teschke, Olaf, editor

Published
2017
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16. Interactive Proving, Higher-Order Rewriting, and Theory Analysis in Theorema 2.0

Author

Maletzky, Alexander, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Greuel, Gert-Martin, editor, Koch, Thorsten, editor, Paule, Peter, editor, and Sommese, Andrew, editor

Published
2016
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17. Two-Point Boundary Problems with One Mild Singularity and an Application to Graded Kirchhoff Plates

Author

Rosenkranz, Markus, Liu, Jane, Maletzky, Alexander, Buchberger, Bruno, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Gerdt, Vladimir P., editor, Koepf, Wolfram, editor, Seiler, Werner M., editor, and Vorozhtsov, Evgenii V., editor

Published
2015
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18. Automated Reasoning in Reduction Rings Using the Theorema System

Author

Maletzky, Alexander, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Gerdt, Vladimir P., editor, Koepf, Wolfram, editor, Seiler, Werner M., editor, and Vorozhtsov, Evgenii V., editor

Published
2015
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19. Complexity Analysis of the Bivariate Buchberger Algorithm in Theorema

Author

Maletzky, Alexander, Buchberger, Bruno, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Hong, Hoon, editor, and Yap, Chee, editor

Published
2014
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20. Groebner Bases in Theorema

Author

Buchberger, Bruno, Maletzky, Alexander, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Kobsa, Alfred, Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Nierstrasz, Oscar, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Hong, Hoon, editor, and Yap, Chee, editor

Published
2014
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27. Journal of Medical Systems volume / Domain Shifts in Machine Learning Based Covid-19 Diagnosis From Blood Tests

Author

Roland, Theresa, Böck, Carl, Tschoellitsch, Thomas, Maletzky, Alexander, Hochreiter, Sepp, Meier, Jens, and Klambauer, Günter

Subjects
Machine learning, Domain shift, COVID-19, Blood test
Abstract

Many previous studies claim to have developed machine learning models that diagnose COVID-19 from blood tests. However, we hypothesize that changes in the underlying distribution of the data, so called domain shifts, affect the predictive performance and reliability and are a reason for the failure of such machine learning models in clinical application. Domain shifts can be caused, e.g., by changes in the disease prevalence (spreading or tested population), by refined RT-PCR testing procedures (way of taking samples, laboratory procedures), or by virus mutations. Therefore, machine learning models for diagnosing COVID-19 or other diseases may not be reliable and degrade in performance over time. We investigate whether domain shifts are present in COVID-19 datasets and how they affect machine learning methods. We further set out to estimate the mortality risk based on routinely acquired blood tests in a hospital setting throughout pandemics and under domain shifts. We reveal domain shifts by evaluating the models on a large-scale dataset with different assessment strategies, such as temporal validation. We present the novel finding that domain shifts strongly affect machine learning models for COVID-19 diagnosis and deteriorate their predictive performance and credibility. Therefore, frequent re-training and re-assessment are indispensable for robust models enabling clinical utility. Version of record

Published
2022
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34. Computer-assisted exploration of Gröbner bases theory in Theorema

Author

Maletzky, Alexander

Subjects
Automatisches Beweisverfahren, Theorema, Reduktionsringe, Gröbner Basen, Gröbner bases, Exploration, Gröbner-Basis, automatisches Beweisen, reduction rings, Computer-unterstützte Theorieexploration, automated reasoning, Computerunterstütztes Verfahren, computer-assisted theory exploration
Abstract

eingereicht von DI Alexander Maletzky Zusammenfassung in deutscher Sprache Universität Linz, Univ., Dissertation, 2016 OeBB

Published
2016

35. Theorema 2.0: Computer-Assisted Natural-Style Mathematics

Author

Buchberger, Bruno, Jebelean, Tudor, Kutsia, Temur, Maletzky, Alexander, Windsteiger, Wolfgang, Buchberger, Bruno, Jebelean, Tudor, Kutsia, Temur, Maletzky, Alexander, and Windsteiger, Wolfgang

Abstract

The Theorema project aims at the development of a computer assistant for the working mathematician. Support should be given throughout all phases of mathematical activity, from introducing new mathematical concepts by definitions or axioms, through first (computational) experiments, the formulation of theorems, their justification by an exact proof, the application of a theorem as an algorithm, until to the dissemination of the results in form of a mathematical publication, the build up of bigger libraries of certified mathematical content and the like. This ambitious project is exactly along the lines of the QED manifesto issued in 1994 (see e.g. http://www.cs.ru.nl/~freek/qed/qed.html) and it was initiated in the mid-1990s by Bruno Buchberger. The Theorema system is a computer implementation of the ideas behind the Theorema project. One focus lies on the natural style of system input (in form of definitions, theorems, algorithms, etc.), system output (mainly in form of mathematical proofs) and user interaction. Another focus is theory exploration, i.e. the development of large consistent mathematical theories in a formal frame, in contrast to just proving single isolated theorems. When using the Theorema system, a user should not have to follow a certain style of mathematics enforced by the system (e.g. basing all of mathematics on set theory or certain variants of type theory), rather should the system support the user in her preferred flavour of doing math. The new implementation of the system, which we refer to as Theorema 2.0, is open-source and available through GitHub.

Published
2016

36. Two-Point Boundary Problems with One Mild Singularity and an Application to Graded Kirchhoff Plates

Author

Gerdt, Vladimir P., Koepf, Wolfram, Seiler, Werner, Vorozhtsov, Evgenii V., Rosenkranz, Markus, Liu, Jane, Maletzky, Alexander, Buchberger, Bruno, Gerdt, Vladimir P., Koepf, Wolfram, Seiler, Werner, Vorozhtsov, Evgenii V., Rosenkranz, Markus, Liu, Jane, Maletzky, Alexander, and Buchberger, Bruno

Abstract

We develop a new theory for treating boundary problems for linear ordinary differential equations whose fundamental system may have a singularity at one of the two endpoints of the given interval. Our treatment follows an algebraic approach, with (partial) implementation in the Theorema software system (which is based on Mathematica). We study an application to graded Kirchhoff plates for illustrating a typical case of such boundary problems.

Published
2015

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