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arXiv 2024年

作者： Boscheri, Walter Busto, Saray Dumbser, Michael Laboratoire de Mathématiques UMR 5127 CNRS Université Savoie Mont Blanc Le Bourget du Lac73376 France Department of Mathematics and Computer Science University of Ferrara Ferrara44121 Italy Department of Applied Mathematics Universidade de Santiago de Compostela Santiago de Compostela15782 Spain Galician Center for Mathematical Research and Technology CITMAga Santiago de Compostela15782 Spain Department of Civil Environmental and Mechanical Engineering University of Trento Trento38123 Italy

We present a novel high order semi-implicit hybrid finite volume/virtual element numerical scheme for the solution of compressible flows on Voronoi tessellations. The method relies on the flux splitting of the compressible Navier-Stokes equations into three sub-systems: a convective sub-system solved explicitly using a finite volume (FV) scheme, and the viscous and pressure sub-systems which are discretized implicitly at the aid of a virtual element method (VEM). Consequently, the time step restriction of the overall algorithm depends only on the mean flow velocity and not on the fast pressure waves nor on the viscous eigenvalues. As such, the proposed methodology is well suited for the solution of low Mach number flows at all Reynolds numbers. Moreover, the scheme is proven to be globally energy conserving so that shock capturing properties are retrieved in high Mach number flows. To reach high order of accuracy in time and space, an IMEX Runge-Kutta time stepping strategy is employed together with high order spatial reconstructions in terms of CWENO polynomials and virtual element space basis functions. The chosen discretization techniques allow the use of general polygonal grids, a useful tool when dealing with complex domain configurations. The new scheme is carefully validated in both the incompressible limit and the high Mach number regime through a large set of classical benchmarks for fluid dynamics, assessing robustness and *** Codes 65M08, 65M60, 76N06 © 2024, CC BY-NC-ND.

关键词： Mach number

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Graph Fourier MMD for Signals on Graphs

Graph Fourier MMD for Signals on Graphs

引用

International Conference on Sampling Theory and Applications (SampTA)

作者： Samuel Leone Aarthi Venkat Guillaume Huguet Alexander Tong Guy Wolf Smita Krishnaswamy Applied Math Program New Haven Connecticut Computational Biology & Bioinformatics Program Yale University New Haven Connecticut Dept. of Math. & Stat Mila - Quebec AI Institute Université de Montréal Montreal Canada Dept. of Comp. Sci. & Oper. Res. Mila-Quebec AI Institute Université de Montréal Montreal Canada Department of Computer Science Department of Genetics Yale University New Haven Connecticut

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes the difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization.

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EVALUATION OF THE PRONUNCIATION OF TAJWEED RULES BASED ON DNN AS A STEP TOWARDS INTERACTIVE RECITATION LEARNING

arXiv

引用

arXiv 2025年

作者： Shaiakhmetov, Dim Gimaletdinova, Gulnaz Cankurt, Selcuk Momunov, Kadyrmamat Department of Computer Science Ala-Too International University Bishkek Kyrgyzstan Department of Applied Math Ala-Too International University Bishkek Kyrgyzstan Department of Computer Engineering Vistula University Warsaw Poland Department of Engineering and Natural Sciences Suleyman Demirel University Almaty Kazakhstan

Proper recitation of the Quran, adhering to the rules of Tajweed, is crucial for preventing mistakes during recitation and requires significant effort to master. Traditional methods of teaching these rules are limited by the availability of qualified instructors and time constraints. Automatic evaluation of recitation can address these challenges by providing prompt feedback and supporting independent practice. This study focuses on developing a deep learning model to classify three Tajweed rules—separate stretching (Al Mad), tight noon (Ghunnah), and hide (Ikhfaa)—using the publicly available QDAT dataset, which contains over 1,500 audio recordings. The input data consisted of audio recordings from this dataset, transformed into normalized mel-spectrograms. For classification, the EfficientNet-B0 architecture was used, enhanced with a Squeeze-and-Excitation attention mechanism. The developed model achieved accuracy rates of 95.35%, 99.34%, and 97.01% for the respective rules. An analysis of the learning curves confirmed the model’s robustness and absence of overfitting. The proposed approach demonstrates high efficiency and paves the way for developing interactive educational systems for Tajweed study. Copyright © 2025, The Authors. All rights reserved.

关键词： Transfer learning

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INVERSE PROBLEMS FOR QUANTUM GRAPH ASSOCIATED WITH SQUARE AND HEXAGONAL LATTICES

arXiv

引用

arXiv 2024年

作者： Ando, K. Blåsten, E. Exner, P. Isozaki, H. Korotyaev, E. Lassas, M. Lu, J. Morioka, H. Department of Electrical and Electronic Engineering and Computer Science Ehime University Matsuyama790-8577 Japan School of Engineering Science LUT University Lahti Campus Lahti15210 Finland Department of Math. Analysis Saint-Petersburg State University Universitetskaya Nab. 7/9 St. Petersburg199034 Russia National Research University Higher School of Economics St. Petersburg Russia Doppler Institute for Mathematical Physics and Applied Mathematics Czech Technical University in Prague Břehová 7 Prague115 19 Czech Republic Nuclear Physics Institute Czech Academy of Science Rež 250 68 Czech Republic Graduate School of Pure and Applied Sciences University of Tsukuba Tsukuba305-8571 Japan Department of Mathematics and Statistics University of Helsinki HelsinkiFI-00014 Finland

We solve inverse problems from the D-N map for the quantum graph on a finite domain in a square lattice and that on a hexagonal lattice, as well as inverse scattering problems from the S-matrix for a locally perturbed... 详细信息

关键词： Inverse problems

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Calcination Temperature-Dependent Structural and Photoluminescence Properties of Hydroxyapatite Derived from Labeo Rohita Fish Scales

引用

Journal of The Institution of Engineers (India): Series D 2020年第2期101卷 223-232页

作者： Sinha, Arijit Pal, Anindya Santra, A. Murmu, S. Ghorai, U.K. Chowdhury, Amit Roy Banerjee, D. Dr. M.N. Dastur School of Materials Science Engineering Indian Institute of Engineering Science and Technology Botanic Garden Shibpur Howrah711103 India Ramakrishna Mission Vidyamandira Department of Industrial Chemistry & Applied Chemistry Swami Vivekananada Research Centre Belur Math Howrah711202 India Aerospace Engineering and Applied Mechanics Indian Institute of Engineering Science and Technology Botanic Garden Shibpur Howrah711103 India Faculty of Engineering and Computer Science Teerthanker Mahaveer University MoradabadUP244001 India

The nanocrystalline hydroxyapatite was synthesized from Labeo Rohita fish scales by calcination of raw scales at temperatures ranges from 400 to 1000 °C. The synthesized powders were characterized using, X-ray diffraction (XRD), thermogravimetric/differential thermal analyzer (TG–DTA), Fourier transform infrared spectroscopy, scanning and high-resolution transmission electron microscope and energy-dispersive X-ray analysis, respectively. Crystallite size, crystallinity and lattice parameters of HAp were evaluated from XRD, and it is shown that the average crystallite sizes were significantly enhanced with the calcination temperature attending its maximum value at ~ 40 nm. TG–DTA analysis predicts the thermal stability of the samples, and it has been observed that the thermal stability increases with the calcination temperature. Moreover, a detailed photoluminescence study of the as-synthesized samples has been carried out for the first time and an appropriate excitation energy gives rise to several distinct peaks in the emission spectra which has not been reported previously. © 2020, The Institution of Engineers (India).

关键词： Optical properties

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Electrical Detection of Magnetization Switching in Single-Molecule Magnets

arXiv

引用

arXiv 2024年

作者： Alqahtani, Amjad Henry, DaVonne Havlíček, Lubomír Marie, Luke St. Hrubý, Jakub Sojka, Antonín Hale, Morgan Felsenfeld, Samuel El Fatimy, Abdelouahad Myers-Ward, Rachael L. Kurt Gaskill, D. Nemec, Ivan Neugebauer, Petr Liu, Amy Y. Barbara, Paola Department of Physics Georgetown University WashingtonDC20057 United States Central European Institute of Technology CEITECBUT Purkyňova 656/123 Brno61200 Czech Republic Department of Math Computer Science and Physics Roanoke College RoanokeVA24153 United States Department of Physics University of Maryland College ParkMD20742 United States Institute of Applied Physics Mohammed VI Polytechnic University Lot 660 Hay Moulay Rachid Ben Guerir43150 Morocco U.S. Naval Research Laboratory WashingtonDC20375 United States Institute for Research in Electronics and Applied Physics University of Maryland College ParkMD20742 United States Department of Inorganic Chemistry Faculty of Science Palacký University Olomouc Olomouc77146 Czech Republic

Single-molecule magnets (SMMs) with chemically tailorable properties are potential building blocks for quantum computing, high-density magnetic memory, and spintronics.1 2 3,4 These applications require isolated or few molecules on substrates, but studies of SMMs have mainly focused on bulk crystals. Moreover, fabrication of SMM-based devices and electrical detection of the SMM magnetic state are still coveted milestones that have so far been achieved mainly for double-decker rare-earth phthalocyanines at temperatures below 1 K.5-8 Here we demonstrate electrical detection of magnetization switching for a modification of the archetypal SMM Mn12, up to 70 K, based on the supramolecular spin valve effect5 with graphene quantum dots9. Notably, the exchange interaction between the molecules and the graphene, as well as the dot-mediated intermolecular interaction, can be directly extracted from the electrical response, opening the way to an effective characterization of the quantum properties of different types of SMMs in a wide temperature range. Copyright © 2024, The Authors. All rights reserved.

关键词： Nanocrystals

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The Manifold Scattering Transform for High-Dimensional Point Cloud Data

arXiv

引用

arXiv 2022年

作者： Chew, Joyce Steach, Holly R. Viswanath, Siddharth Wu, Hau-Tieng Hirn, Matthew Needell, Deanna Krishnaswamy, Smita Perlmutter, Michael UCLA Department of Mathematics Los AngelesCA United States Yale University Department of Genetics New HavenCT United States UC Irvine Department of Computer Science IrvineCA United States Duke University Department of Mathematics DurhamNC United States Duke University Department of Statistical Science DurhamNC United States Michigan State University Department of Mathematics East Lansing United States Michigan State University Department of CMSE East Lansing United States Yale University Department of Computer Science New HavenCT United States Yale University Applied Math Program New HavenCT United States

The manifold scattering transform is a deep feature extractor for data defined on a Riemannian manifold. It is one of the first examples of extending convolutional neural network-like operators to general manifolds. The initial work on this model focused primarily on its theoretical stability and invariance properties but did not provide methods for its numerical implementation except in the case of two-dimensional surfaces with predefined meshes. In this work, we present practical schemes, based on the theory of diffusion maps, for implementing the manifold scattering transform to datasets arising in naturalistic systems, such as single cell genetics, where the data is a high-dimensional point cloud modeled as lying on a low-dimensional manifold. We show that our methods are effective for signal classification and manifold classification *** Codes 68T07 Copyright © 2022, The Authors. All rights reserved.

关键词： Numerical methods

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A Stochastic Covariance Shrinkage Approach in Ensemble Transform Kalman Filtering

arXiv

引用

arXiv 2020年

作者： Popov, Andrey A. Sandu, Adrian Nino-Ruiz, Elias D. Evensen, Geir Computational Science Laboratory Department of Computer Science Virginia Tech United States Applied Math and Computer Science Lab Universidad del Norte Colombia Norway

The Ensemble Kalman Filters (EnKF) employ a Monte-Carlo approach to represent covariance information, and are affected by sampling errors in operational settings where the number of model realizations is much smaller than the model state dimension. To alleviate the effects of these errors EnKF relies on model-specific heuristics such as covariance localization, which takes advantage of the spatial locality of correlations among the model variables. This work proposes an approach to alleviate sampling errors that utilizes a locally averaged-in-time dynamics of the model, described in terms of a climatological covariance of the dynamical system. We use this covariance as the target matrix in covariance shrinkage methods, and develop a stochastic covariance shrinkage approach where synthetic ensemble members are drawn to enrich both the ensemble subspace and the ensemble transformation. We additionally provide for a way in which this methodology can be localized similar to the state-of-the-art LETKF method, and that for a certain model setup, our methodology significantly outperforms it. Copyright © 2020, The Authors. All rights reserved.

关键词： Dynamical systems

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Graph Fourier MMD for Signals on Graphs

arXiv

引用

arXiv 2023年

作者： Leone, Samuel Venkat, Aarthi Huguet, Guillaume Tong, Alexander Wolf, Guy Krishnaswamy, Smita Applied Math Program New HavenCT United States Computational Biology & Bioinformatics Program Yale University New HavenCT United States Dept. of Math. & Stat Université de Montréal Mila - Quebec AI Institute MontrealQC Canada Dept. of Comp. Sci. & Oper. Res. Université de Montréal Mila - Quebec AI Institute MontrealQC Canada Department of Computer Science Department of Genetics Yale University New HavenCT United States

While numerous methods have been proposed for computing distances between probability distributions in Euclidean space, relatively little attention has been given to computing such distances for distributions on graphs. However, there has been a marked increase in data that either lies on graph (such as protein interaction networks) or can be modeled as a graph (single cell data), particularly in the biomedical sciences. Thus, it becomes important to find ways to compare signals defined on such graphs. Here, we propose Graph Fourier MMD (GFMMD), a novel distance between distributions and signals on graphs. GFMMD is defined via an optimal witness function that is both smooth on the graph and maximizes difference in expectation between the pair of distributions on the graph. We find an analytical solution to this optimization problem as well as an embedding of distributions that results from this method. We also prove several properties of this method including scale invariance and applicability to disconnected graphs. We showcase it on graph benchmark datasets as well on single cell RNA-sequencing data analysis. In the latter, we use the GFMMD-based gene embeddings to find meaningful gene clusters. We also propose a novel type of score for gene selection called gene localization score which helps select genes for cellular state space characterization. Copyright © 2023, The Authors. All rights reserved.

关键词： Genes

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Qudit Dynamical Decoupling on a Superconducting Quantum Processor

arXiv

引用

arXiv 2024年

作者： Tripathi, Vinay Goss, Noah Vezvaee, Arian Nguyen, Long B. Siddiqi, Irfan Lidar, Daniel A. Department of Physics & Astronomy University of Southern California Los AngelesCA90089 United States Center for Quantum Information Science & Technology University of Southern California Los AngelesCA90089 United States Quantum Nanoelectronics Laboratory Department of Physics University of California at Berkeley BerkeleyCA94720 United States Applied Math and Computational Research Division Lawrence Berkeley National Lab BerkeleyCA94720 United States Department of Electrical & Computer Engineering University of Southern California Los AngelesCA90089 United States Department of Chemistry University of Southern California Los AngelesCA90089 United States

Multi-level qudit systems are increasingly being explored as alternatives to traditional qubit systems due to their denser information storage and processing potential. However, qudits are more susceptible to decoherence than qubits due to increased loss channels, noise sensitivity, and crosstalk. To address these challenges, we develop protocols for dynamical decoupling (DD) of qudit systems based on the Heisenberg-Weyl group. We implement and experimentally verify these DD protocols on a superconducting transmon processor that supports qudit operation based on qutrits (d = 3) and ququarts (d = 4). Specifically, we demonstrate single-qudit DD sequences to decouple qutrits and ququarts from system-bath-induced decoherence. We also introduce two-qudit DD sequences designed to suppress the detrimental cross-Kerr couplings between coupled qudits. This allows us to demonstrate a significant improvement in the fidelity of time-evolved qutrit Bell states. Our results highlight the utility of leveraging DD to enable scalable qudit-based quantum computing. © 2024, CC BY.

关键词： Qubits

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