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Computational scheme for the numerical solution of fractional order pantograph delay-integro-differential equations via the Bernstein approach

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Partial Differential Equations in applied mathematics 2025年 14卷

作者： Aourir, E. Dastjerdi, H. Laeli Shah, Kamal Abdeljawad, Thabet Laboratory of Mathematical Engineering and Computer Science Faculty of Science Ibn Zohr University Morocco Department of Mathematics Education Farhangian University P.O. Box 14665-889 Tehran Iran Department of Mathematics and Sciences Prince Sultan University Riyadh 11586 Saudi Arabia Department of Mathematics Saveetha School of Engineering Saveetha Institute of Medical and Technical Sciences Saveetha University Tamil Nadu Chennai 602105 India Department of Mathematics and Applied Mathematics School of Science and Technology Sefako Makgatho Health Sciences University Ga-Rankuwa South Africa Center for Applied Mathematics and Bioinformatics (CAMB) Gulf University for Science and Technology Hawally 32093 Kuwait

The main objective of this research is to provide an efficient computational algorithm for solving a class of fractional order pantograph delay-integro-differential equations. The Bernstein approximation technique is employed for approximating the solutions of such equations by taking into account the properties of Bernstein polynomials, which transform the original problem into a simplified linear system of algebraic equations. The formulation of the suggested scheme is carefully described, and its convergence performance is examined. Both existence and uniqueness theorems are provided to establish the theoretical reliability of the methodology. Additionally, an estimation of the error bounds is reported to evaluate the precision of the approximation. The reliability, stability and computational effectiveness of the algorithm developed are confirmed by a series of numerical experiments. A comparative analysis with other available methodologies and analytical solutions further highlights the practicality and robustness of the new technique, offering reduced computational and memory costs. © 2025 The Authors

关键词： Bernstein approximation Caputo derivative Error analysis Fractional pantograph delay integro-differential equations

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A Natural Gas Consumption Forecasting System for Continual Learning Scenarios based on Hoeffding Trees with Change Point Detection Mechanism

arXiv

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arXiv 2023年

作者： Svoboda, Radek Basterrech, Sebastián Kozal, Jędrzej Platoš, Jan Woźniak, Michal Faculty of Electrical Engineering and Computer Science VŠB-Technical University of Ostrava 17. listopadu 2172/15 Ostrava70833 Czech Republic Department of Applied Mathematics and Computer Science Technical University of Denmark Kongens Lyngby Denmark Department of Systems and Computer Networks University of Science and Technology Wroclaw Poland

Forecasting natural gas consumption, considering seasonality and trends, is crucial in planning its supply and consumption and optimizing the cost of obtaining it, mainly by industrial entities. However, in times of threats to its supply, it is also a critical element that guarantees the supply of this raw material to meet individual consumers' needs, ensuring society's energy security. This article introduces a novel multistep forecasting of natural gas consumption with change point detection integration for model collection selection with continual learning capabilities using data stream processing. The performance of the forecasting models based on the proposed approach is evaluated in a complex real-world use case of natural gas consumption forecasting. Furthermore, the methodology generability was verified in an electricity load forecasting task. We employed Hoeffding tree predictors as forecasting models and the Pruned Exact Linear Time (PELT) algorithm for the change point detection procedure. The change point detection integration enables the selection of a different model collection for successive time frames. Thus, three model collection selection procedures are defined and evaluated for forecasting scenarios with various densities of detected change points. These models were compared with change point agnostic baseline approaches and deep learning models. Our experiments show that the proposed approach provides superior results to deep learning models for both datasets and that fewer change points result in a lower forecasting error regardless of the model collection selection procedure employed. © 2023, CC BY.

关键词： Contrastive Learning

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A Vision Transformer Model for Violence Detection from Real-Time Videos 5

A Vision Transformer Model for Violence Detection from Real-...

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5th International Conference on Future Networks and Distributed Systems: The Premier Conference on Smart Next Generation Networking Technologies, ICFNDS 2021

作者： Shagufta, Arfin Hesham, Mohammad Tarique Masood, Sarfaraz Abd El-Latif, Ahmed Department of Applied Sc. and Humanities Jamia Millia Islamia New Delhi India Department of Computer Engineering Jamia Millia Islamia New Delhi India Department of Mathematics and Computer Science Faculty of Science Menoufia University Menoufia Egypt

ISBN: (纸本)9781450387347

Based on the rising incidences of crime and violence, it has become a matter of general importance that technology may be developed to automatically detect the presence of violence in the surveillance footage. For law enforcement, the detection of violent incidents can play an important role in urban safety. The efficiency of event detectors is usually measured in terms of detection speed, precision, and generality over many types of video inputs in a distinct format. However, various recent studies in this area have either focused on the correctness of the model, its response speed, or both, but have missed on considering the multiple data sources for effective model analysis. The main objective of the work is to propose a real-time violence event identifier based on state-of-the-art deep learning methods. Primarily the proposed model is based on the ViT (Vision Transformer) architecture, while other models like ConvLSTM and VGG16 with LSTM were also explored in this work. Two benchmark datasets viz. the RLVS (Real Life Violence Situations) and the Hockey fight datasets were used in this work for robust training and test analysis of the proposed model. For evaluating the model's performance various metrics including accuracy, f1-score, precision, and recall were evaluated. The results show that the Vision Transformer-based model outperformed all the explored models with an overall accuracy of 98% and 97% on the RLVS dataset and the Hockey datasets respectively, which are also significantly higher than the recent solutions proposed on these datasets. © 2021 ACM.

关键词： Long short-term memory

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THE EFFECT OF LIMITED MOBILITY ON THE EXPERIENCED SEGREGATION OF FOREIGN-BORN MINORITIES

arXiv

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arXiv 2024年

作者： Liao, Yuan Gil, Jorge Yeh, Sonia Pereira, Rafael H.M. Alessandretti, Laura Department of Space Earth and Environment Chalmers University of Technology Gothenburg Sweden Department of Architecture and Civil Engineering Chalmers University of Technology Gothenburg Sweden - Brazil Data Science Division Brazil Department of Applied Mathematics and Computer Science Technical University of Denmark Lyngby Denmark

Segregation is a key challenge in promoting more diverse and inclusive cities. Research based on large-scale mobility data indicates that segregation between majority and minority groups persists in daily activities beyond residential areas, like visiting shops and restaurants. Aspects including lifestyle differences, homophily, and mobility constraints have been proposed as drivers of this phenomenon, but their contributions remain poorly quantified. Here, we elucidate how different mechanisms influence segregation outside home, looking at the distinctive segregation experienced by native and foreign-born individuals. Our study is based on the movement of ∼320,000 individual smartphone devices collected in Sweden, where immigration creates profound divides. We find that while day-to-day activities lead to mixing for native-born individuals, foreign-born individuals remain segregated in their out-of-home activities. Using counterfactual simulations, we show that this heterogeneous effect of mobility on experienced segregation results mainly from two mechanisms: homophily and limited travel, i.e. foreign-born individuals (i) tend to visit destinations visited by similar individuals, and (ii) have limited mobility ranges. We show that homophily, as represented by destination preference, plays a minor role, while limited mobility, associated with reduced transport access, limits opportunities for foreign-born minorities to diversify their encounters. Our findings suggest that enhancing transport accessibility in foreign-born concentrated areas could reduce social segregation. © 2024, CC BY-SA.

关键词： Smartphones

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Thermal-Aware Channel with Multiple Wires

Thermal-Aware Channel with Multiple Wires

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IEEE International Symposium on Information Theory

作者： Yeow Meng Chee Tuvi Etzion Kees A. Schouhamer Immink Tuan Thanh Nguyen Van Khu Vu Jos H. Weber Eitan Yaakobi Department of Industrial Systems Engineering and Management National University of Singapore Singapore Department of Computer Science Technion-Israel Institute of Technology Haifa Israel Turing Machines Inc Rotterdam The Netherlands Science Mathematics and Technology Cluster Singapore University of Technology and Design Singapore Department of Applied Mathematics Delft University of Technology Delft The Netherlands

ISBN: (数字)9798350382846

ISBN: (纸本)9798350382853

The thermal-aware channel has been studied recently to control the temperature of some electronic devices for better performance and longer lifetime. In this work, we consider a thermal-aware channel model where multiple wires are available to the user. The user can use one wire or several wires to write an information word. Particularly, we study the two extreme cases. In the first case, only one wire is permitted for writing the information. The other extreme case is that we are allowed to write information on all the wires in parallel. In the first case, when we send a message through a wire that reaches the highest allowed temperature, we switch to another available wire. We determine the minimum number of wires required to send any arbitrary message. Given the number of wires, our second task is to determine the constrained codewords that can be sent through these wires. We compute the maximum information rate achieved and provide some constructions of codes satisfying these constraints. In the second case when all the wires are available for writing many, interesting questions arise and we briefly describe one of them and its solutions.

关键词： Performance evaluation Codes Wires Switches Writing Temperature control Channel models

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An adaptive solution strategy for Richards' equation

arXiv

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arXiv 2023年

作者： Stokke, Jakob S. Mitra, Koondanibha Storvik, Erlend Both, Jakub W. Radu, Florin A. Center for Modeling of Coupled Subsurface Dynamics Department of Mathematics University of Bergen Norway Computational Mathematics Group Hasselt University Belgium Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Norway

Flow in variably saturated porous media is typically modelled by the Richards equation, a nonlinear elliptic-parabolic equation which is notoriously challenging to solve numerically. In this paper, we propose a robust and fast iterative solver for Richards’ equation. The solver relies on an adaptive switching algorithm, based on rigorously derived a posteriori indicators, between two linearization methods: L-scheme and Newton. Although a combined L-scheme/Newton strategy was introduced previously in [1], here, for the first time we propose a reliable and robust criteria for switching between these schemes. The performance of the solver, which can be in principle applied to any spatial discretization and linearization methods, is illustrated through several numerical *** Codes 65M12, 65J08, 65M50, 76Sxx © 2023, CC BY.

关键词： Nonlinear equations

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Deep Learning for Diabetic Retinopathy in Fundus Images

Deep Learning for Diabetic Retinopathy in Fundus Images

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International Symposium on Computational Intelligence and Informatics

作者： Keyvan Rahimi Rituraj Rituraj Diana Ecker Computer Engineering Faculty of Art and Engineering Islamic Azad University Science and Research Branch Tehran Iran Doctoral School of Applied Informatics and Applied Mathematics Obuda University Budapest Hungary

Clinically, using fundus pictures for predicting and detecting blind illnesses such as diabetic retinopathy (DR) is crucial. Deep learning (DL) is becoming a more common and promising technique in the different applications of DR, such as prediction, detection, classification, and disease diagnosis. Developing a review paper to analyze the DL techniques and their performance in the field is essential. We prepared a standard systematic review database including 341 publications. Accordingly, the main aim of the present review work is to present a systematic state-of-the-art by relying on PRISMA guidelines for the performance analysis of the DL in DR applications. The study has been shown in three main steps. The first step is to collect the database, the second step is to analyze the databases, and the last step is to conclude the study’s main findings. According to the results, most studies employed accuracy as the most reliable and general evaluation metric for analyzing the DL techniques in different DR applications. Also, CNN has the most share of applications compared to other DL techniques. On the other hand, the best performance is related to the ensemble and advanced DL techniques. We’ll also publish and regularly update the most recent discoveries in future studies to stay up with the quick technological improvements.

关键词： computer science Systematics Databases Retinopathy Retina Diabetes Reliability

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Relativistic Digital Twin: Bringing the IoT to the Future

arXiv

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arXiv 2023年

作者： Sciullo, Luca De Marchi, Alberto Trotta, Angelo Montori, Federico Bononi, Luciano Felice, Marco Di Department of Computer Science and Engineering University of Bologna Italy Advanced Research Center on Electronic Systems University of Bologna Italy Institute of Applied Mathematics and Scientific Computing Department of Aerospace Engineering University of the Bundeswehr Munich Germany

Complex IoT ecosystems often require the usage of Digital Twins (DTs) of their physical assets in order to perform predictive analytics and simulate what-if scenarios. DTs are able to replicate IoT devices and adapt over time to their behavioral changes. However, DTs in IoT are typically tailored to a specific use case, without the possibility to seamlessly adapt to different scenarios. Further, the fragmentation of IoT poses additional challenges on how to deploy DTs in heterogeneous scenarios characterized by the usage of multiple data formats and IoT network protocols. In this paper, we propose the Relativistic Digital Twin (RDT) framework, through which we automatically generate general-purpose DTs of IoT entities and tune their behavioral models over time by constantly observing their real counterparts. The framework relies on the object representation via the Web of Things (WoT), to offer a standardized interface to each of the IoT devices as well as to their DTs. To this purpose, we extended the W3C WoT standard in order to encompass the concept of behavioral model and define it in the Thing Description (TD) through a new vocabulary. Finally, we evaluated the RDT framework over two disjoint use cases to assess its correctness and learning performance, i.e., the DT of a simulated smart home scenario with the capability of forecasting the indoor temperature, and the DT of a real-world drone with the capability of forecasting its trajectory in an outdoor scenario. Experiments show that the generated DT can estimate the behavior of its real counterpart after an observation stage, regardless of the considered scenario. © 2023, CC BY.

关键词： Internet of things

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Blocking Sparse Matrices to Leverage Dense-Specific Multiplication

Blocking Sparse Matrices to Leverage Dense-Specific Multipli...

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Workshop on Irregular Applications: Architecture and Algorithms (IA3)

作者： Paolo Sylos Labini Massimo Bernaschi Werner Nutt Francesco Silvestri Flavio Vella Dept. of Computer Science Free University of Bozen Italy Institute for applied mathematics National Research Council Italy Dept. of Engineering and Computer Science University of Padova Italy Dept. of Engineering and Computer Science University of Trento Italy

ISBN: (纸本)9781665475075

Research to accelerate matrix multiplication, pushed by the growing computational demands of deep learning, has sprouted many efficient architectural solutions, such as NVIDIA's Tensor Cores. These accelerators are designed to process efficiently a high volume of small dense matrix products in parallel. However, it is not obvious how to leverage these accelerators for sparse matrix multiplication. A natural way to adapt the accelerators to this problem is to divide the matrix into small blocks, and then multiply only the nonzero blocks. In this paper, we investigate ways to reorder the rows of a sparse matrix to reduce the number of nonzero blocks and cluster the nonzero elements into a few dense blocks. While this pre-processing can be computationally expensive, we show that the high speed-up provided by the accelerators can easily repay the cost, especially when several multiplications follow one reordering.

关键词： Deep learning Tensors Costs Conferences Focusing computer architecture Software

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Modeling of Measurement Error in Financial Returns Data

arXiv

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arXiv 2024年

作者： Jasra, Ajay Maama, Mohamed Mijatović, Aleksandar School of Data Science The Chinese University of Hong Kong Shenzhen China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistics University of Warwick United Kingdom

In this paper we consider the modeling of measurement error for fund returns data. In particular, given access to a time-series of discretely observed log-returns and the associated maximum over the observation period, we develop a stochastic model which models the true log-returns and maximum via a Lévy process and the data as a measurement error there-of. The main technical difficulty of trying to infer this model, for instance Bayesian parameter estimation, is that the joint transition density of the return and maximum is seldom known, nor can it be simulated exactly. Based upon the novel stick breaking representation of [12] we provide an approximation of the model. We develop a Markov chain Monte Carlo (MCMC) algorithm to sample from the Bayesian posterior of the approximated posterior and then extend this to a multilevel MCMC method which can reduce the computational cost to approximate posterior expectations, relative to ordinary MCMC. We implement our methodology on several applications including for real data. Copyright © 2024, The Authors. All rights reserved.

关键词： Markov chains

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