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The MS¯ -scheme αs5 QCD contributions to the Adler function and Bjorken polarized sum rule in the Crewther-type two-fold {β}-expanded representation

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Journal of High Energy physics 2022年第5期2022卷 1-34页

作者： Goriachuk, I.O. Kataev, A.L. Molokoedov, V.S. Department of Theoretical Physics Faculty of Physics Moscow State University Moscow 119991 Russian Federation Institute for Nuclear Research of the Russian Academy of Science Moscow 117312 Russian Federation Research Computing Center Moscow State University Moscow 119991 Russian Federation Moscow Center for Fundamental and Applied Mathematics Moscow 119992 Russian Federation Moscow Institute of Physics and Technology Moscow Region Dolgoprudny 141700 Russian Federation

We consider the two-fold expansion in powers of the conformal anomaly and of the strong coupling αs for the non-singlet contributions to Adler D-function and Bjorken polarized sum rule calculated previously in the MS... 详细信息

We consider the two-fold expansion in powers of the conformal anomaly and of the strong coupling α_s for the non-singlet contributions to Adler D-function and Bjorken polarized sum rule calculated previously in the MS¯ -scheme at the four-loop level. This representation provides relations between definite terms of different loop orders appearing within the {β}-expansion of these quantities. Supposing the validity of this two-fold representation at the five-loop order and using these relations, we obtain some O(αs5) corrections to the D-function, to the R-ratio of e⁺e⁻-annihilation into hadrons and to Bjorken polarized sum rule. These corrections are presented both analytically in the case of the generic simple gauge group and numerically for the SU(3) color group. The arguments in the favor of validity of the two-fold representation are given at least at the four-loop level. Within the {β}-expansion procedure the analytical Riemann ζ₄-contributions to the five-loop expressions for the Adler function and Bjorken polarized sum rule are also fixed for the case of the generic simple gauge group. © 2022, The Author(s).

关键词： Conformal and W Symmetry Perturbative QCD Renormalization Group

Semantic data Representation for Explainable Windows Malware Detection Models

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arXiv 2024年

作者： Švec, Peter Balogh, Štefan Homola, Martin Kľuka, Ján Bisták, Tomáš Institute of Computer Science and Mathematics Faculty of Electrical Engineering and Information Technology Slovak University of Technology Ilkovičova 3 Bratislava Slovakia Department of Applied Informatics Faculty of Mathematics Physics and Informatics Comenius University in Bratislava Mlynská dolina Bratislava Slovakia

Ontologies are a standard tool for creating semantic schemata in many knowledge intensive domains of human interest. They are becoming increasingly important also in the areas that have been until very recently dominated by subsymbolic knowledge representation and machine-learning (ML) based data processing. One such area is information security, and specifically, malware detection. We thus propose PE Malware Ontology that offers a reusable semantic schema for Portable Executable (PE – the Windows binary format) malware files. This ontology is inspired by the structure of the EMBER dataset, which focuses on the static malware analysis of PE files. With this proposal, we hope to provide a unified semantic representation for the existing and future PE-malware datasets and facilitate the application of symbolic, neuro-symbolic, or otherwise explainable approaches in the PE-malware-detection domain, which may produce interpretable results described by the terms defined in our ontology. In addition, we also publish semantically treated EMBER data, including fractional datasets, to support the reproducibility of experiments on EMBER. We supplement our work with a preliminary case study, conducted using concept learning, to show the general feasibility of our approach. While we were not able to match the precision of the state-of-the-art ML tools, the learned malware discriminators were interesting and highly interpretable. Copyright © 2024, The Authors. All rights reserved.

关键词： Ontology

An intermediate case of exponential multivalued forbidden matrix configuration

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arXiv 2023年

作者： Peaslee, Wallace Sali, Attila Yan, Jun University of Cambridge Department of Applied Mathematics and Theoretical Physics Cambridge United Kingdom HUN-REN Alfréd Rényi Institute of Mathematics Department of Computer Science BUTE Budapest Hungary University of Warwick Mathematics Institute Coventry United Kingdom

The forbidden number forb(m, F), which denotes the maximum number of distinct columns in an m-rowed (0, 1)-matrix with no submatrix that is a row and column permutation of F, has been widely studied in extremal set theory. Recently, this function was extended to r-matrices, whose entries lie in {0, 1, · · ·, r − 1}. forb(m, r, F) is the maximum number of distinct columns in an r-matrix with no submatrix that is a row and column permutation of F. While forb(m, F) is polynomial in m, forb(m, r, F) is exponential for r ≥ 3. Recently, forb(m, r, F) was studied for some small (0, 1)-matrices F, and exact values were determined in some cases. In this paper we study forb(m, r, M) for (Equation presented), which is the smallest matrix for which this forbidden number is unknown. Interestingly, it turns out that this problem is closely linked with the following optimisation problem. For each triangle in the complete graph Km, pick one of its edges. Let me denote the number of times edge e is picked. For each α ∈ R, what is (Equation presented) ? We establish a relationship between forb(m, r, M) and H (m, (r − 1)/(r − 2)), find upper and lower bounds for H (m, α), and use them to significantly improve known bounds for forb(m, r, M).MSC Codes 05D05 © 2023, CC BY.

关键词： Matrix algebra

Free-space quantum information platform on a chip

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arXiv 2024年

作者： Gurses, Volkan Davis, Samantha I. Sinclair, Neil Spiropulu, Maria Hajimiri, Ali Division of Engineering and Applied Science California Institute of Technology PasadenaCA United States Division of Physics Mathematics and Astronomy Caltech PasadenaCA United States California Institute of Technology PasadenaCA United States John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA United States

Emerging technologies that employ quantum physics offer fundamental enhancements in information processing tasks, including sensing, communications, and computing [1–3]. Here, we introduce the quantum phased array, which generalizes the operating principles of phased arrays [4] and wavefront engineering [5] to quantum fields, and report the first quantum phased array technology demonstration. An integrated photonic-electronic system is used to manipulate free-space quantum information to establish reconfigurable wireless quantum links in a standalone, compact form factor. Such a robust, scalable, and integrated quantum platform can enable broad deployment of quantum technologies with high connectivity, potentially expanding their use cases to real-world applications. We report the first, to our knowledge, free-space-to-chip interface for quantum links, enabled by 32 metamaterial antennas with more than 500,000 sub-wavelength engineered nanophotonic elements over a 550 × 550 µm2 physical aperture. We implement a 32-channel array of quantum coherent receivers with 30.3 dB shot noise clearance and 90.2 dB common-mode rejection ratio that downconverts the quantum optical information via homodyne detection and processes it coherently in the radio-frequency domain. With our platform, we demonstrate 32-pixel imaging of squeezed light for quantum sensing, reconfigurable free-space links for quantum communications, and proof-of-concept entanglement generation for measurement-based quantum computing. This approach offers targeted, real-time, dynamically-adjustable free-space capabilities to integrated quantum systems that can enable wireless quantum technologies. © 2024, CC BY.

关键词： Quantum optics

Resource-Efficient Invariant Networks: Exponential Gains by Unrolled Optimization

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arXiv 2022年

作者： Buchanan, Sam Yan, Jingkai Haber, Ellie Wright, John Department of Electrical Engineering Columbia University United States Data Science Institute Columbia University United States NYU Tandon School of Engineering United States Department of Applied Physics and Applied Mathematics Columbia University United States

Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of transformations, making them unable to cope with natural variabilities in visual data such as changes in pose and perspective. We identify a common limitation of these approaches—they rely on sampling to traverse the high-dimensional space of transformations—and propose a new computational primitive for building invariant networks based instead on optimization, which in many scenarios provides a provably more efficient method for high-dimensional exploration than sampling. We provide empirical and theoretical corroboration of the efficiency gains and soundness of our proposed method, and demonstrate its utility in constructing an efficient invariant network for a simple hierarchical object detection task when combined with unrolled optimization. Code for our networks and experiments is available at https://***/sdbuch/refine. Copyright © 2022, The Authors. All rights reserved.

关键词： Object detection

ARGUABLY @ AI Debater-NLPCC 2021 Task 3: Argument Pair Extraction from Peer Review and Rebuttals 10th

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ARGUABLY @ AI Debater-NLPCC 2021 Task 3: Argument Pair Extra...

10th CCF Conference on Natural Language Processing and Chinese Computing, NLPCC 2021

作者： Kohli, Guneet Singh Kaur, Prabsimran Singh, Muskaan Ghosal, Tirthankar Rana, Prashant Singh Department of Computer Science and Engineering Thapar Institute of Engineering and Technology Patiala India Institute of Formal and Applied Linguistics Faculty of Mathematics and Physics Charles University Prague Czech Republic

ISBN: (纸本)9783030884826

This paper describes our participating system run to the argumentative text understanding shared task for AI Debater at NLPCC 2021 (http://***/sharedtask/AIDebater21/*** ). The tasks are motivated towards developing an autonomous debating system. We make an initial attempt with Track-3, namely, argument pair extraction from peer review and rebuttal where we extract arguments from peer reviews and their corresponding rebuttals from author responses. Compared to the multi-task baseline by the organizers, we introduce two significant changes: (i) we use ERNIE 2.0 token embedding, which can better capture lexical, syntactic, and semantic aspects of information in the training data, (ii) we perform double attention learning to capture long-term dependencies. Our proposed model achieves the state-of-the-art results with a relative improvement of 8.81% in terms of F1 score over the baseline model. We make our code available publicly at https://***/guneetsk99/ArgumentMining_SharedTask. Our team ARGUABLY is one of the third prize-winning teams in Track 3 of the shared task. © 2021, Springer Nature Switzerland AG.

关键词： Extraction

LINEARIZED OPTIMAL TRANSPORT PYLOT LIBRARY: A TOOLKIT FOR MACHINE LEARNING ON POINT CLOUDS

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arXiv 2025年

作者： Linwu, Jun Khurana, Varun Karris, Nicholas Cloninger, Alexander Halıcıoğlu Data Science Institute University of California La Jolla San DiegoCA92093 United States Department of Applied Mathematics Brown University ProvidenceRI02912 United States Department of Mathematics University of California La Jolla San DiegoCA92093 United States Department of Mathematics Halıcıoğlu Data Science Institute University of California La Jolla San DiegoCA92093 United States

The pyLOT library offers a Python implementation of linearized optimal transport (LOT) techniques and methods to use in downstream tasks. The pipeline embeds probability distributions into a Hilbert space via the Optimal Transport maps from a fixed reference distribution, and this linearization allows downstream tasks to be completed using off the shelf (linear) machine learning algorithms. We provide a case study of performing ML on 3D scans of lemur teeth, where the original questions of classification, clustering, dimension reduction, and data generation reduce to simple linear operations performed on the LOT embedded representations. Copyright © 2025, The Authors. All rights reserved.

关键词： Linearization

On the Connectivity and the Diameter of Betweenness-Uniform Graphs 7th

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On the Connectivity and the Diameter of Betweenness-Uniform ...

7th International Conference on Algorithms and Discrete applied mathematics, CALDAM 2021

作者： Hartman, David Pokorná, Aneta Valtr, Pavel Computer Science Institute of Charles University Faculty of Mathematics and Physics Charles University Prague118 00 Czech Republic The Institute of Computer Science of the Czech Academy of Sciences Prague Czech Republic Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Prague118 00 Czech Republic

ISBN: (纸本)9783030678982

Betweenness centrality is a centrality measure based on the overall amount of shortest paths passing through a given vertex. A graph is betweenness-uniform if all its vertices have the same betweenness centrality. We study the properties of betweenness-uniform graphs. In particular, we show that every connected betweenness-uniform graph is either a cycle or a 3-connected graph. Also, we show that betweenness uniform graphs of high maximal degree have small diameter. © 2021, Springer Nature Switzerland AG.

关键词： Graph theory

Coherent enhancement of a frequency comb modulated by a terahertz laser field in high-order harmonic generation

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Physical Review A 2023年第4期108卷 043101-043101页

作者： Yuan-Yuan Wu Chang-Tong Liang Bao-Guang Zhao Peng-Cheng Li Research Center for Advanced Optics and Photoelectronics Department of Physics College of Science Shantou University Shantou Guangdong 515063 China Key Laboratory of Intelligent Manufacturing Technology of MOE Shantou University Shantou Guangdong 515063 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

We present the coherent enhancement of the frequency comb via high-order harmonic generation (HHG) in a train of infrared laser pulses combined with terahertz (THz) laser fields. The HHG spectra are obtained by solving the three-dimensional time-dependent Schrödinger equation by means of the time-dependent generalized pseudospectral method. We find that the structure of the frequency comb via HHG becomes much smoother and more regular, and the yield of the comb is increased by nearly two orders of magnitude. By analyzing the phase coherence of HHG spectra, we demonstrate that the THz laser fields are responsible for the optimization of the structure and yield of the frequency comb since the constructive phase coherence of the HHG spectra is modulated by the THz field. The physical origin of the constructive phase coherence is thanks to the uniform ionization efficiency induced by the THz laser field for each laser pulse, which greatly improves the synchronization of the harmonic emission. Our finding provides a promising method for the enhancement of the frequency comb via HHG.

关键词： Atomic & molecular processes in external fields High-order harmonic generation Light-matter interaction Ultrafast phenomena