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A proof-theoretic metatheorem for tracial von Neumann algebras

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arXiv 2022年

作者： Păunescu, Liviu Sipoş, Andrei Department of Computer Science Faculty of Mathematics and Computer Science University of Bucharest Academiei 14 Bucharest010014 Romania Simion Stoilow Institute of Mathematics The Romanian Academy Calea Griviţei 21 Bucharest010702 Romania Institute for Logic and Data Science Popa Tatu 18 Bucharest010805 Romania

We adapt a continuous logic axiomatization of tracial von Neumann algebras due to Farah, Hart and Sherman in order to prove a metatheorem for this class of structures in the style of proof mining, a research program that aims to obtain the hidden computational content of ordinary mathematical proofs using tools from proof *** Codes 03F10, 46E30, 46L10 Copyright © 2022, The Authors. All rights reserved.

关键词： Algebra

Communication and Control Co-Design in 6G: Sequential Decision-Making with LLMs

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IEEE Network 2024年

作者： Chen, Xianfu Wu, Celimuge Shen, Yi Ji, Yusheng Yoshinaga, Tsutomu Ni, Qiang Zarakovitis, Charilaos C. Zhang, Honggang Shenzhen CyberAray Network Technology Co. Ltd China Chinese Academy of Sciences Shanghai Advanced Research Institute China Meta-Networking Research Center China The University of Electro-Communications Graduate School of Informatics and Engineering Tokyo Japan National Institute of Informatics Information Systems Architecture Research Division Tokyo Japan Lancaster University School of Computing and Communications Ukraine AXON Logic Greece City University of Macau Faculty of Data Science Macau China China

This article investigates a control system within the context of sixth-generation wireless networks. The remote control performance optimization confronts the technical challenges that arise from the intricate interactions between communication and control sub-systems, asking for a co-design. Considering the system dynamics, we formulate the sequential co-design decision-makings of communication and control over a discrete time horizon as a Markov decision process, for which a practical offline learning framework is proposed. Our proposed framework integrates large language models into the elements of reinforcement learning. We present a case study on the age of semantics-aware communication and control co-design to showcase the potential of our proposed learning framework. Furthermore, we discuss the open issues remaining to make our offline learning framework feasible for real-world implementations and highlight the research directions for future explorations. © 1986-2012 IEEE.

关键词： Markov processes

When accurate prediction models yield harmful self-fulfilling prophecies

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arXiv 2023年

作者： van Amsterdam, Wouter A.C. van Geloven, Nan Krijthe, Jesse H. Ranganath, Rajesh Cinà, Giovanni Department of Data Science and Biostatistics Julius Center of Health Sciences Primary Care University Medical Center Utrecht Heidelberglaan 100 Utrecht3584 CX Netherlands University of Utrecht Heidelberglaan 100 Utrecht3584 CX Netherlands Department of Biomedical Data Sciences Leiden University Medical Center Leiden Netherlands Pattern Recognition & Bioinformatics Delft University of Technology Delft Netherlands Courant Institute of Mathematical Science Department of Computer Science Center for Data Science New York University New York City United States Department of Medical Informatics Amsterdam University Medical Center Amsterdam Netherlands Institute for Logic Language and Computation University of Amsterdam Amsterdam Netherlands Pacmed Amsterdam Netherlands

Prediction models are popular in medical research and practice. By predicting an outcome of interest for specific patients, these models may help inform difficult treatment decisions, and are often hailed as the poster children for personalized, data-driven healthcare. We show however, that using prediction models for decision making can lead to harmful decisions, even when the predictions exhibit good discrimination after deployment. These models are harmful self-fulfilling prophecies: their deployment harms a group of patients but the worse outcome of these patients does not invalidate the predictive power of the model. Our main result is a formal characterization of a set of such prediction models. Next we show that models that are well calibrated before and after deployment are useless for decision making as they made no change in the data distribution. These results point to the need to revise standard practices for validation, deployment and evaluation of prediction models that are used in medical decisions. © 2023, CC BY.

关键词： Prediction models

Mathematical Capabilities of ChatGPT

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arXiv 2023年

作者： Frieder, Simon Pinchetti, Luca Chevalier, Alexis Griffiths, Ryan-Rhys Salvatori, Tommaso Lukasiewicz, Thomas Petersen, Philipp Christian Berner, Julius Department of Computer Science University of Oxford Oxford United Kingdom Institute of Logic and Computation Vienna University of Technology Vienna Austria School of Mathematics Institute for Advanced Study Princeton United States Department of Physics University of Cambridge Cambridge United Kingdom Faculty of Mathematics University of Vienna Vienna Austria Research Network Data Science University of Vienna Vienna Austria VERSES Research Lab Los AngelesCA90016 United States

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In contrast to formal mathematics, where large databases of formal proofs are available (e.g., the Lean Mathematical Library), current datasets of natural-language mathematics, used to benchmark language models, either cover only elementary mathematics or are very small. We address this by publicly releasing two new datasets: GHOSTS and miniGHOSTS. These are the first natural-language datasets curated by working researchers in mathematics that (1) aim to cover graduate-level mathematics, (2) provide a holistic overview of the mathematical capabilities of language models, and (3) distinguish multiple dimensions of mathematical reasoning. These datasets also test whether ChatGPT and GPT-4 can be helpful assistants to professional mathematicians by emulating use cases that arise in the daily professional activities of mathematicians. We benchmark the models on a range of fine-grained performance metrics. For advanced mathematics, this is the most detailed evaluation effort to date. We find that ChatGPT can be used most successfully as a mathematical assistant for querying facts, acting as a mathematical search engine and knowledge base interface. GPT-4 can additionally be used for undergraduate-level mathematics but fails on graduate-level difficulty. Contrary to many positive reports in the media about GPT-4 and ChatGPT’s exam-solving abilities (a potential case of selection bias), their overall mathematical performance is well below the level of a graduate student. Hence, if your goal is to use ChatGPT to pass a graduate-level math exam, you would be better off copying from your average peer! Copyright © 2023, The Authors. All rights reserved.

关键词： Benchmarking

Large Physics Models: Towards a collaborative approach with Large Language Models and Foundation Models

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arXiv 2025年

作者： Barman, Kristian G. Caron, Sascha Sullivan, Emily de Regt, Henk W. de Austri, Roberto Ruiz Boon, Mieke Färber, Michael Fröse, Stefan Hasibi, Faegheh Ipp, Andreas Kapoor, Rukshak Kasieczka, Gregor Kostić, Daniel Krämer, Michael Golling, Tobias Lopez, Luis G. Marco, Jesus Otten, Sydney Pawlowski, Pawel Vischia, Pietro Weber, Erik Weniger, Christoph CLPS - Centre for Logic and Philosophy of Science UGent Belgium IMAPP Radboud University and Nikhef NL Netherlands Utrecht University Netherlands Institute for Science in Society Radboud University Netherlands CSIC-UV Spain University of Twente Netherlands TU Dresden & ScaDS.AI Germany ErUM-Data-Hub & TU Dortmund University Germany Computing and Information Science Radboud University Netherlands TU Wien Austria Patiala India Universität Hamburg Germany Institute of Philosophy University of Leiden Netherlands RWTH Aachen University Germany University of Geneva Switzerland Munich Center for Mathematical Philosophy LMU Munich Germany CSIC-UC Spain Radboud University Netherlands Ippen Digital Germany Universidad de Oviedo ICTEA Spain GRAPPA Institute of Physics University of Amsterdam Netherlands

This paper explores ideas and provides a potential roadmap for the development and evaluation of physics-specific large-scale AI models, which we refer to as Large Physics Models (LPMs). These models, based on foundation models such as Large Language Models (LLMs) - trained on broad data - are tailored to address the unique demands of physics research. LPMs can function independently or as part of an integrated framework. This framework can incorporate specialized tools, including symbolic reasoning modules for mathematical manipulations, frameworks to analyse specific experimental and simulated data, and mechanisms for synthesizing insights from physical theories and scientific literature. We begin by examining whether the physics community should actively develop and refine dedicated models, rather than relying solely on commercial LLMs. We then outline how LPMs can be realized through interdisciplinary collaboration among experts in physics, computer science, and philosophy of science. To integrate these models effectively, we identify three key pillars: Development, Evaluation, and Philosophical Reflection. Development focuses on constructing models capable of processing physics texts, mathematical formulations, and diverse physical data. Evaluation assesses accuracy and reliability through testing and benchmarking. Finally, Philosophical Reflection encompasses the analysis of broader implications of LLMs in physics, including their potential to generate new scientific understanding and what novel collaboration dynamics might arise in research. Inspired by the organizational structure of experimental collaborations in particle physics, we propose a similarly interdisciplinary and collaborative approach to building and refining Large Physics Models. This roadmap provides specific objectives, defines pathways to achieve them, and identifies challenges that must be addressed to realise physics-specific large scale AI models. © 2025, CC BY.

关键词： Benchmarking

Nodal Hydraulic Head Estimation through Unscented Kalman Filter for data-driven Leak Localization in Water Networks

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arXiv 2023年

作者： Romero-Ben, Luis Irofti, Paul Stoican, Florin Puig, Vicenç Institut de Robòtica i Informàtica Industrial CSIC-UPC Llorens i Artigas 4-6 Barcelona08028 Spain LOS-CS-FMI University of Bucharest Romania Institute for Logic and Data Science Bucharest Romania Department of Automation Control and Systems Engineering Politehnica University of Bucharest Romania UPC Campus de Terrassa Terrassa Barcelona08222 Spain

In this paper, we present a nodal hydraulic head estimation methodology for water distribution networks (WDN) based on an Unscented Kalman Filter (UKF) scheme with application to leak localization. The UKF refines an initial estimation of the hydraulic state by considering the prediction model, as well as available pressure and demand measurements. To this end, it provides customized prediction and data assimilation steps. Additionally, the method is enhanced by dynamically updating the prediction function weight matrices. Performance testing on the Modena benchmark under realistic conditions demonstrates the method’s effectiveness in enhancing state estimation and data-driven leak localization. © 2023, CC BY-NC-ND.

关键词： data fusion

Wikipedia Citations: A comprehensive dataset of citations with identifiers extracted from English Wikipedia

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arXiv 2020年

作者： Singh, Harshdeep West, Robert Colavizza, Giovanni Data Science Laboratory EPFL Institute for Logic Language and Computation University of Amsterdam Netherlands

Wikipedia’s contents are based on reliable and published sources. To this date, little is known about what sources Wikipedia relies on, in part because extracting citations and identifying cited sources is challenging. To close this gap, we release Wikipedia Citations, a comprehensive dataset of citations extracted from Wikipedia. A total of 29.3M citations were extracted from 6.1M English Wikipedia articles as of May 2020, and classified as being to books, journal articles or Web contents. We were thus able to extract 4.0M citations to scholarly publications with known identifiers — including DOI, PMC, PMID, and ISBN — and further labeled an extra 261K citations with DOIs from Crossref. As a result, we find that 6.7% of Wikipedia articles cite at least one journal article with an associated DOI. Scientific articles cited from Wikipedia correspond to 3.5% of all articles with a DOI currently indexed in the Web of science. We release all our code to allow the community to extend upon our work and update the dataset in the future. Copyright © 2020, The Authors. All rights reserved.

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Learning Dictionaries from Physical-Based Interpolation for Water Network Leak Localization

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arXiv 2023年

作者： Irofti, Paul Romero-Ben, Luis Stoican, Florin Puig, Vicenç Department of Computer Science Faculty of Mathematics and Computer Science University of Bucharest 010014 Romania The Institute for Logic and Data Science Popa Tatu 18 Bucharest010805 Romania The Institut de Robòtica i Informàtica Industrial CSIC-UPC Llorens i Artigas 4-6 Barcelona08028 Spain The Universitat Politècnica de Catalunya Campus de Terrassa Gaia Building Rambla Sant Nebridi 22 Terrassa Barcelona08222 Spain The Deptartment of Automation Control and Systems Engineering Politehnica University of Bucharest 060042 Romania

This article presents a leak localization methodology based on state estimation and learning. The first is handled by an interpolation scheme, whereas dictionary learning is considered for the second stage. The novel proposed interpolation technique exploits the physics of the interconnections between hydraulic heads of neighboring nodes in water distribution networks. Additionally, residuals are directly interpolated instead of hydraulic head values. The results of applying the proposed method to a well-known case study (Modena) demonstrated the improvements of the new interpolation method with respect to a state-of-the-art approach, both in terms of interpolation error (considering state and residual estimation) and posterior localization. Copyright © 2023, The Authors. All rights reserved.

关键词： Interpolation

Extending a conjecture of Graham and Lovász on the distance characteristic polynomial

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arXiv 2022年

作者： Abiad, Aida Brimkov, Boris Hayat, Sakander Khramova, Antonina P. Koolen, Jack H. Department of Mathematics and Computer Science Eindhoven University of Technology Netherlands Department of Mathematics: Analysis Logic and Discrete Mathematics Ghent University Belgium Department of Mathematics and Data Science Vrije Universiteit Brussel Belgium Department of Mathematics and Statistics Slippery Rock University United States Faculty of Engineering Sciences GIK Institute of Engineering Sciences and Technology Topi Swabi Pakistan School of Mathematical Sciences University of Science and Technology of China China

Graham and Lovász conjectured in 1978 that the sequence of normalized coefficients of the distance characteristic polynomial of a tree of order n is unimodal with the maximum value occurring at ⌊ n2 ⌋. In this paper we investigate this problem for block graphs. In particular, we prove the unimodality part and we establish the peak for several extremal cases of uniform block graphs with small diameter. © 2022, CC BY.

关键词： Polynomials