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Some Results on Ricci-Yamabe Soliton and Its Cosmological Models

IAENG International Journal of applied mathematics 2025年第4期55卷 979-983页

作者： Pandey, Pankaj Yadav, Santosh Kumar Sharma, Kamakshi Chaturvedi, Braj Bhushan Department of Mathematics School of Chemical Engineering and Physical Sciences Lovely Professional University Punjab Phagwara144411 India Department of Mathematics School of Computer Science & Artificial Intelligence SR University Telangana Warangal506371 India Department of Pure & Applied Mathematics Guru Ghasidas Vishwavidyalaya Chhattisgarh Bilaspur495009 India

This article aims to investigate the characteristics of Ricci-Yamabe Soliton (briefly: (RYS)n). We study the cosmological models on (RYS)4 under Lorentzian para Sasakian (LPS)4 spacetime. Parallel Ricci tensor, Poisson structure and gradient property also reveal on (RYS)n. Example of (RYS)4 constructed to verify the results. © (2025), (International Association of Engineers). All rights reserved.

关键词： Solitons

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Convergence analysis of a Legendre spectral collocation method for nonlinear Fredholm integral equations in multidimensions

Convergence analysis of a Legendre spectral collocation meth...

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作者： Zaky, Mahmoud A. Hendy, Ahmed S. Department of Applied Mathematics National Research Centre Cairo Egypt Department of Mathematics Faculty of Science Benha University Benha Egypt Department of Computational Mathematics and Computer Science Institute of Natural Sciences and Mathematics Ural Federal University Yekaterinburg Russia

It is a very challenging task to solve a nonlinear integral equation in multidimensions. The main purpose of this paper is to develop and analyze a spectral collocation method for a class of nonlinear Fredholm integral equations of the second kind in multidimensions. The proposed spectral collocation method is based on a multivariate Legendre approximation in the frequency space. It is shown by both theory and numerics that the proposed spectral collocation scheme not only significantly reduces the number of degrees of freedom but also produces very accurate approximations. © 2020 John Wiley & Sons, Ltd.

关键词： Fredholm integral equations

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On the Effectiveness of ViT Features as Local Semantic Descriptors 17th

On the Effectiveness of ViT Features as Local Semantic De...

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17th European Conference on computer Vision, ECCV 2022

作者： Amir, Shir Gandelsman, Yossi Bagon, Shai Dekel, Tali Department of Computer Science and Applied Mathematics The Weizmann Institute of Science Rehovot Israel Berkeley United States

ISBN: (纸本)9783031250682

We study the use of deep features extracted from a pre-trained Vision Transformer (ViT) as dense visual descriptors. We observe and empirically demonstrate that such features, when extracted from a self-supervised ViT model (DINO-ViT), exhibit several striking properties, including: (i) the features encode powerful, well-localized semantic information, at high spatial granularity, such as object parts;(ii) the encoded semantic information is shared across related, yet different object categories, and (iii) positional bias changes gradually throughout the layers. These properties allow us to design simple methods for a variety of applications, including co-segmentation, part co-segmentation and semantic correspondences. To distill the power of ViT features from convoluted design choices, we restrict ourselves to lightweight zero-shot methodologies (e.g., binning and clustering) applied directly to the features. Since our methods require no additional training nor data, they are readily applicable across a variety of domains. We show by extensive qualitative and quantitative evaluation that our simple methodologies achieve competitive results with recent state-of-the-art supervised methods, and outperform previous unsupervised methods by a large margin. Code is available in https://***/. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Zero-shot learning

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Depth Separation in Norm-Bounded Infinite-Width Neural Networks 37

Depth Separation in Norm-Bounded Infinite-Width Neural Netwo...

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37th Annual Conference on Learning Theory, COLT 2024

作者： Parkinson, Suzanna Ongie, Greg Willett, Rebecca Shamir, Ohad Srebro, Nathan Committee on Computational and Applied Mathematics University of Chicago United States Department of Mathematical and Statistical Sciences Marquette University United States Department of Statistics Department of Computer Science University of Chicago United States Department of Computer Science and Applied Mathematics Weizmann Institute of Science Israel Toyota Technological Institute Chicago United States

We study depth separation in infinite-width neural networks, where complexity is controlled by the overall squared 2-norm of the weights (sum of squares of all weights in the network). Whereas previous depth separation results focused on separation in terms of width, such results do not give insight into whether depth determines if it is possible to learn a network that generalizes well even when the network width is unbounded. Here, we study separation in terms of the sample complexity required for learnability. Specifically, we show that there are functions that are learnable with sample complexity polynomial in the input dimension by norm-controlled depth-3 ReLU networks, yet are not learnable with sub-exponential sample complexity by norm-controlled depth-2 ReLU networks (with any value for the norm). We also show that a similar statement in the reverse direction is not possible: any function learnable with polynomial sample complexity by a norm-controlled depth-2 ReLU network with infinite width is also learnable with polynomial sample complexity by a norm-controlled depth-3 ReLU network. © 2024 S. Parkinson, G. Ongie, R. Willett, O. Shamir & N. Srebro.

关键词： Source separation

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Fully-Scalable MPC Algorithms for Clustering in High Dimension 51

Fully-Scalable MPC Algorithms for Clustering in High Dimensi...

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51st International Colloquium on Automata, Languages, and programming, ICALP 2024

作者： Czumaj, Artur Gao, Guichen Jiang, Shaofeng H.-C. Krauthgamer, Robert Veselý, Pavel Department of Computer Science University of Warwick Coventry United Kingdom School of Computer Science Peking University Beijing China Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel Computer Science Institute of Charles University Prague Czech Republic

ISBN: (纸本)9783959773225

We design new parallel algorithms for clustering in high-dimensional Euclidean spaces. These algorithms run in the Massively Parallel Computation (MPC) model, and are fully scalable, meaning that the local memory in each machine may be nσ for arbitrarily small fixed σ > 0. Importantly, the local memory may be substantially smaller than the number of clusters k, yet all our algorithms are fast, i.e., run in O(1) rounds. We first devise a fast MPC algorithm for O(1)-approximation of uniform Facility Location. This is the first fully-scalable MPC algorithm that achieves O(1)-approximation for any clustering problem in general geometric setting;previous algorithms only provide poly(log n)-approximation or apply to restricted inputs, like low dimension or small number of clusters k;e.g. [Bhaskara and Wijewardena, ICML’18;Cohen-Addad et al., NeurIPS’21;Cohen-Addad et al., ICML’22]. We then build on this Facility Location result and devise a fast MPC algorithm that achieves O(1)-bicriteria approximation for k-Median and for k-Means, namely, it computes (1 + Ε)k clusters of cost within O(1/Ε2)-factor of the optimum for k clusters. A primary technical tool that we introduce, and may be of independent interest, is a new MPC primitive for geometric aggregation, namely, computing for every data point a statistic of its approximate neighborhood, for statistics like range counting and nearest-neighbor search. Our implementation of this primitive works in high dimension, and is based on consistent hashing (aka sparse partition), a technique that was recently used for streaming algorithms [Czumaj et al., FOCS’22]. © Artur Czumaj, Guichen Gao, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý.

关键词： Nearest neighbor search

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Curl Constraint-Preserving Reconstruction and the Guidance it Gives for Mimetic Scheme Design

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Communications on applied mathematics and Computation 2023年第1期5卷 235-294页

作者： Dinshaw S.Balsara Roger Käppeli Walter Boscheri Michael Dumbser Physics and ACMS Departments University of Notre DameNotre DameINUSA Seminar for Applied Mathematics(SAM) Department of MathematicsETH ZürichCH-8092 ZurichSwitzerland Department of Mathematics and Computer Science University of FerraraFerraraItaly Laboratory of Applied Mathematics Department of CivilEnvironmental and Mechanical EngineeringUniversity of TrentoTrentoItaly

Several important PDE systems,like magnetohydrodynamics and computational electrodynamics,are known to support involutions where the divergence of a vector field evolves in divergence-free or divergence constraint-preserving ***,new classes of PDE systems have emerged for hyperelasticity,compressible multiphase flows,so-called firstorder reductions of the Einstein field equations,or a novel first-order hyperbolic reformulation of Schrödinger’s equation,to name a few,where the involution in the PDE supports curl-free or curl constraint-preserving evolution of a vector *** study the problem of curl constraint-preserving reconstruction as it pertains to the design of mimetic finite volume(FV)WENO-like schemes for PDEs that support a curl-preserving involution.(Some insights into discontinuous Galerkin(DG)schemes are also drawn,though that is not the prime focus of this paper.)This is done for two-and three-dimensional structured mesh problems where we deliver closed form expressions for the *** importance of multidimensional Riemann solvers in facilitating the design of such schemes is also *** two dimensions,a von Neumann analysis of structure-preserving WENOlike schemes that mimetically satisfy the curl constraints,is also *** shows the tremendous value of higher order WENO-like schemes in minimizing dissipation and dispersion for this class of *** results are also presented to show that the edge-centered curl-preserving(ECCP)schemes meet their design *** paper is the first paper that invents non-linearly hybridized curl-preserving reconstruction and integrates it with higher order Godunov *** its very design,this paper is,therefore,intended to be forward-looking and to set the stage for future work on curl involution-constrained PDEs.

关键词： PDEs Numerical schemes Mimetic

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On Error-Based Step Size Control for Discontinuous Galerkin Methods for Compressible Fluid Dynamics

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应用数学与计算数学学报 2025年第1期7卷 3-39页

作者： Hendrik Ranocha Andrew R.Winters Hugo Guillermo Castro Lisandro Dalcin Michael Schlottke-Lakemper Gregor J.Gassner Matteo Parsani Applied Mathematics University of HamburgBundesstr.5520146 HamburgGermany Department of Mathematics Applied Mathematics Linköping UniversityLinköpingSweden Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Applied and Computational Mathematics RWTH Aachen UniversityAachenGermany High-Performance Computing Center Stuttgart University of StuttgartStuttgartGermany Department of Mathematics and Computer Science University of CologneCologneGermany Center for Data and Simulation Science University of CologneCologneGermany Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Physical Science and Engineering Division(PSE) King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia

We study a temporal step size control of explicit Runge-Kutta(RK)methods for com-pressible computational fluid dynamics(CFD),including the Navier-Stokes equations and hyperbolic systems of conservation laws such as the Euler *** demonstrate that error-based approaches are convenient in a wide range of applications and compare them to more classical step size control based on a Courant-Friedrichs-Lewy(CFL)*** numerical examples show that the error-based step size control is easy to use,robust,and efficient,e.g.,for(initial)transient periods,complex geometries,nonlinear shock captur-ing approaches,and schemes that use nonlinear entropy *** demonstrate these properties for problems ranging from well-understood academic test cases to industrially relevant large-scale computations with two disjoint code bases,the open source Julia pack-ages *** with *** and the C/Fortran code SSDC based on PETSc.

关键词： Explicit Runge-Kutta(RK)methods Step size control Compressible fluid dynamics Adaptivity in space and time Shock capturing

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BEESO:Multi-strategy Boosted Snake-Inspired Optimizer for Engineering Applications

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Journal of Bionic Engineering 2023年第4期20卷 1791-1827页

作者： Gang Hu Rui Yang Muhammad Abbas Guo Wei Department of Applied Mathematics Xi’an University of TechnologyXi’an710054China School of Computer Science and Engineering Xi’an University of TechnologyXi’an710048China Department of Mathematics University of SargodhaSargodha40100Pakistan University of North Carolina at Pembroke PembrokeNC28372USA

This paper presents an efficient enhanced snake optimizer termed BEESO for global optimization and engineering *** a newly mooted meta-heuristic algorithm,snake optimizer(SO)mathematically models the mating characteristics of snakes to find the optimal *** has a simple structure and offers a delicate balance between exploitation and ***,it also has some shortcomings to be *** proposed BEESO consequently aims to lighten the issues of lack of population diversity,convergence slowness,and the tendency to be stuck in local optima in *** presentation of Bi-Directional Search(BDS)is to approach the global optimal value along the direction guided by the best and the worst individuals,which makes the convergence speed *** increase in population diversity in BEESO benefits from Modified Evolutionary Population Dynamics(MEPD),and the replacement of poorer quality individuals improves population *** Elite Opposition-Based Learning(EOBL)provides improved local exploitation ability of BEESO by utilizing solid solutions with good *** performance of BEESO is illustrated by comparing its experimental results with several algorithms on benchmark functions and engineering ***,the results of the experiment are analyzed again from a statistical point of view using the Friedman and Wilcoxon rank sum *** findings show that these introduced strategies provide some improvements in the performance of SO,and the accuracy and stability of the optimization results provided by the proposed BEESO are competitive among all *** conclude,the proposed BEESO offers a good alternative to solving optimization issues.

关键词： Snake optimizer Bi-Directional Search Evolutionary Population Dynamics Elite Opposition-Based Learning Strategy Mechanical optimization design

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GeoBeeDashboard: An Intelligent Geospatial Platform for Enhancing Waste Management in Tangerang City 13

GeoBeeDashboard: An Intelligent Geospatial Platform for Enha...

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13th IEEE International Conference on Communication, Networks and Satellite, COMNETSAT 2024

作者： Muljana, Richie Deffansyah, Syauqi Akmal Andrew, Hari Gunawan, Alexander Agung Santoso Irwansyah, Edy Pramudya, Fabian Surya Ario, Muhamad Keenan Syahputra, Muhammad Edo Achmad, Said School of Computer Science Bina Nusantara University Data Science Program Computer Science Department Jakarta11480 Indonesia Bina Nusantara University School of Computer Science Computer Science Department Jakarta11480 Indonesia Bina Nusantara University School of Computer Science Mathematics Department Jakarta11480 Indonesia

ISBN: (纸本)9798350368086

In this study, we created an Intelligent Geospatial Platform called GeoBeeDashboard. The GeoBeeDashboard combines advanced geospatial technologies and artificial intelligence (AI), allowing real-time data visualization and optimized decision-making across multiple sectors. The system architecture consists of a ***-based front end, a FastAPI-driven back end, and PostGIS for geospatial data management. One of the GeoBeeDashboard's primary use cases is addressing waste management issues in Tangerang City, Indonesia. As rapid urbanization increases waste generation, effective management becomes critical. The dashboard identifies critical trends and inefficiencies in Tangerang's districts by K-Means clustering waste management data from 2020 to 2023. Our findings identify distinct clusters, highlighting areas with effective waste management and those that require targeted interventions. The benefits that local government can get from GeoBeeDashboard by utilising insights based on clustering analysis of data per each district in Tangerang to optimise waste collection, allocate resources efficiently, and improve the policy-making process for each district in Tangerang. The GeoBeeDashboard improves local government capabilities by providing a scalable model for other cities facing similar urban challenges. In conclusion, GeoBeeDashboard provides local governments with a powerful tool for addressing waste management inefficiencies and fostering sustainable urban development. © 2024 IEEE.

关键词： Urban planning

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Numerical Analysis of Bacterial Meningitis Stochastic Delayed Epidemic Model through Computational Methods

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computer Modeling in Engineering & sciences 2024年第10期141卷 311-329页

作者： Umar Shafique Mohamed Mahyoub Al-Shamiri Ali Raza Emad Fadhal Muhammad Rafiq Nauman Ahmed Department of Mathematics National College of Business Administration and EconomicsLahore54660Pakistan Department of Mathematics Applied CollegeMahayl AssirKing Khalid UniversityAbha62529Saudi Arabia Department of Physical Sciences The University of ChenabGujrat50700Pakistan Department of Mathematics&Statistics College of ScienceKing Faisal UniversityP.O.Box 400Al-Ahsa31982Saudi Arabia Department of Computer Science and Mathematics Lebanese American UniversityBeirut1102-2801Lebanon Department of Mathematics Faculty of Science and TechnologyUniversity of Central PunjabLahore54000Pakistan Department of Mathematics and Statistics University of LahoreLahore54000Pakistan

Based on theWorld Health Organization(WHO),Meningitis is a severe infection of the meninges,the membranes covering the brain and spinal *** is a devastating disease and remains a significant public health *** study investigates a bacterial meningitis model through deterministic and stochastic ***-compartment population dynamics explain the concept,particularly the susceptible population,carrier,infected,and *** model predicts the nonnegative equilibrium points and reproduction number,i.e.,the Meningitis-Free Equilibrium(MFE),and Meningitis-Existing Equilibrium(MEE).For the stochastic version of the existing deterministicmodel,the twomethodologies studied are transition probabilities and non-parametric ***,positivity,boundedness,extinction,and disease persistence are studiedrigorouslywiththe helpofwell-known *** and nonstandard techniques such as EulerMaruyama,stochastic Euler,stochastic Runge Kutta,and stochastic nonstandard finite difference in the sense of delay have been presented for computational analysis of the stochastic ***,standard methods fail to restore the biological properties of the model,so the stochastic nonstandard finite difference approximation is offered as an efficient,low-cost,and independent of time step *** addition,the convergence,local,and global stability around the equilibria of the nonstandard computational method is studied by assuming the perturbation effect is *** simulations and comparison of the methods are presented to support the theoretical results and for the best visualization of results.

关键词： Bacterial Meningitis disease stochastic delayed model stability analysis extinction and persistence computational methods

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