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arXiv 2024年

作者： Awadelkarim, Elsiddig Jasra, Ajay 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 School of Data Science The Chinese University of Hong Kong Shenzhen China

In this paper we consider the filtering problem associated to partially observed McKean-Vlasov stochastic differential equations (SDEs). The model consists of data that are observed at regular and discrete times and the objective is to compute the conditional expectation of (functionals) of the solutions of the SDE at the current time. This problem, even the ordinary SDE case is challenging and requires numerical approximations. Based upon the ideas in [3, 12] we develop a new particle filter (PF) and multilevel particle filter (MLPF) to approximate the afore-mentioned expectations. We prove under assumptions that, for ϵ > 0, to obtain a mean square error of O(ϵ2) the PF has a cost per-observation time of O(ϵ−5) and the MLPF costs O(ϵ−4) (best case) or O(ϵ−4 log(ϵ)2) (worst case). Our theoretical results are supported by numerical experiments. © 2024, CC BY.

关键词： Mean square error

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Secrecy Outage Probability of Full-Duplex Relaying Vehicular Networks 10

Secrecy Outage Probability of Full-Duplex Relaying Vehicular...

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10th International Japan-Africa Conference on Electronics, Communications, and Computations, JAC-ECC 2022

作者： Abd El Ghafour, Mohamed G. Abd El-Malek, Ahmed H. Hassan, Ola E. Abo-Zahhad, Mohammed Alexandria University Faculty of Engineering Department of Engineering Mathematics and Physics Alexandria21544 Egypt Egypt-Japan University of Science & Technology School of Electronics Communications & Computer Engineering Alexandria21934 Egypt Arab Academy for Science Technology & Maritime Transport Basic and Applied Science Department Smart Village Campus Giza12577 Egypt Assiut University Faculty of Engineering Electrical Engineering Department Assiut71515 Egypt

ISBN: (纸本)9781665464635

This paper investigates the secrecy performance of full-duplex cooperative vehicular relaying networks under passive eavesdropping attacks in the presence of co-channel interference. In the considered system model, a static source communicates with a static destination through a mobile full-duplex relay in the presence of a mobile passive eavesdropper and a static co-channel interferer. A closed-form expression for the exact secrecy outage probability of the system is derived for the Nakagami-m fading environment. Hence, the asymptotic secrecy outage probability is obtained at high signal-to-noise values. Numerical and Simulation results are obtained to validate the derived analytical expressions. © 2022 IEEE.

关键词： Signal to noise ratio

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Correction: Non‑linear Cointegration Test, Based on Record Counting Statistic

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Computational Economics 2024年第4期64卷 2231-2232页

作者： Atil, Lynda Fellag, Hocine Sipols, Ana E. Santos-Martín, M. T. de Blas, Clara Simón Laboratory of Pure and Applied Mathematics Mouloud Mammeri University of Tizi Ouzou Tizi Ouzou Algeria Department of Applied Mathematics Materials Science and Engineering and Electronic Technology Rey Juan Carlos University Madrid Spain Department of Statistics University of Salamanca Salamanca Spain Department of Computer Sciences and Statistics Rey Juan Carlos University Madrid Spain

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Convergence of the Two Point Flux Approximation Method and the Fitted Two Point Flux Approximation Method for Options Pricing with Local Volatility Function

SSRN

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SSRN 2024年

作者： Koffi, Rock S. Tambue, Antoine 6-8 Melrose Road Muizenberg7945 South Africa Department of Mathematics and Applied Mathematics University of Cape Town Rondebosch7701 South Africa Department of Computer science Electrical engineering and Mathematical sciences Western Norway University of Applied Sciences Inndalsveien 28 Bergen5063 Norway

In this paper, we deal with numerical approximations for solving the Black-Scholes Partial Differential Equation(PDE) for European and American options pricing with local volatility. This PDE is well-known to be degenerated. Local volatility model is a model where the volatility depends locally for both stock price and time. In contrast to constant volatility or time-dependent volatility models for which analytical representations of the exact solution is known for European Call options, there is no analytical solution for local volatility. The space discretization is performed using the classical finite volume method with Two-Point Flux Approximation (TPFA) and a novel scheme called Fitted Two-Point Flux Approximation (FTPFA). The Fitted Two-Point Flux Approximation (FTPFA) combines the fitted finite volume method and the standard TPFA method. More precisely the fitted finite volume method is used when the stock price approaches zero with the goal to handle the degeneracy of the PDE while the TPFA method is used on the rest of space domain. This combination yields our fitted TPFA scheme. The Euler method is used for the time discretization. We provide the rigorous convergence proofs of the two fully discretized schemes. Numerical experiments to support theoretical results are provided. © 2024, The Authors. All rights reserved.

关键词： Finite volume method

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Analytical Approximation for ATTR with Respect to Node Removals

Analytical Approximation for ATTR with Respect to Node Remov...

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International Workshop on Design of Reliable Communication Networks (DRCN)

作者： Fenghua Wang Jinyi Zou Robert E. Kooij Faculty of Electrical Engineering Mathematics and Computer Science Delft University of Technology Delft The Netherlands Unit ICT Strategy and Policy Netherlands Organisation for Applied Scientific Research (TNO) Den Haag The Netherlands

ISBN: (数字)9798350348972

ISBN: (纸本)9798350348989

We propose an analytical approach to approximate the average two-terminal reliability (ATT R) for graphs where a fraction of the nodes is removed. The approximation is based on the generating function of the network's degree distribution under random node removals and stochastic degree-based node removals. Through validation on synthetic graphs, including Erdos Renyi random graphs and Barabasi-Albert graphs, as well as four real-world networks from the Internet Topology Zoo, we observe that the analytical method effectively approximates the average two-terminal reliability under random node removals for synthetic graphs. In the case of real-world graphs under random and stochastic degree-based node removals or synthetic graphs under stochastic degree-based node removals, the analytical ap-proximation yields reasonably accurate results when the fraction of removed nodes is small, specifically less than 10%, provided that the initial analytical approximation closely aligns with the real ATT R values.

关键词： Reliability engineering Communication networks Internet topology

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Improved bounds on the size of permutation codes under Kendall τ-metric

arXiv

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arXiv 2024年

作者： Parvaresh, Farzad Sobhani, Reza Abdollahi, Alireza Bagherian, Javad Jafari, Fatemeh Khatami, Maryam Department of Electrical Engineering University of Isfahan Isfahan Iran Department of Applied Mathematics and Computer Science Faculty of Mathematics and Statistics University of Isfahan Isfahan81746-73441 Iran Department of Pure Mathematics Faculty of Mathematics and Statistics University of Isfahan Isfahan81746-73441 Iran Tehran19395-5746 Iran

In order to overcome the challenges caused by flash memories and also to protect against errors related to reading information stored in DNA molecules in the shotgun sequencing method, the rank modulation is proposed. In the rank modulation framework, codewords are permutations. In this paper, we study the largest size P (n, d) of permutation codes of length n, i.e., subsets of the set Sn of all permutations on {1, ..., n} with the minimum distance at least d ∈ {1, . . ., (n2 )} under the Kendall τ -metric. By presenting an algorithm and some theorems, we managed to improve the known lower and upper bounds for P (n, d). In particular, we show that P (n, d) = 4 for all n ≥ 6 and 3/5(n2) n2). Additionally, we prove that for any prime number n and integer r ≤ n/6 , P (n, 3) ≤ (n − 1)! − n − 6r / √n2 − 8rn + 20r2 √ (n − 1)! / n(n − r)! . This result greatly improves the upper bound of P (n, 3) for all primes n ≥ 37. © 2024, CC BY-NC-SA.

关键词： Flash memory

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Insight into the Hamilton and Crosser model for ternary hybrid nanofluid flow over a Riga wedge with heterogeneous catalytic reaction

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The European Physical Journal Special Topics 2024年 1-22页

作者： Obalalu, A. M. Shah, S. H. A. M. Darvesh, Adil Khan, Umair Ishak, Anuar Adegbite, Peter Ojewola, O. B. Muhammad, Taseer Galal, Ahmed M. Department of Mathematics and Statistics Kwara State University Malete Nigeria Department of Mathematics and Social Sciences Sukkur IBA University Sukkur Pakistan Department of Mathematics and Statistics Hazara University Mansehra Pakistan Department of Mathematical Sciences Faculty of Science and Technology Universiti Kebangsaan Malaysia Bangi Malaysia Department of Mathematics Faculty of Science Sakarya University Serdivan/Sakarya Turkey Department of Computer Science and Mathematics Lebanese American University Byblos Lebanon Department of Pure and Applied Mathematics LAUTECH Ogbomosho Nigeria Department of Mathematics College of Science King Khalid University Abha Saudi Arabia Department of Mechanical Engineering College of Engineering in Wadi Alddawasir Prince Sattam bin Abdulaziz University Wadi Alddawasir Saudi Arabia Production Engineering and Mechanical Design Department Faculty of Engineering Mansoura University Mansoura Egypt

The present article is designed to study the Hamilton and Crosser model applied to the flow of ternary hybrid nanofluids over a Riga wedge, incorporating the effects of heterogeneous catalytic reactions. The complex interactions within the ternary hybrid nanofluids, comprising three distinct nanoparticles suspended in a base fluid, present significant challenges in accurately predicting flow and thermal characteristics. The Hamilton and Crosser model, known for its efficacy in determining the thermal conductivity of composite materials, is employed to analyze this intricate system. The analysis reveals the model's potential in offering a comprehensive understanding of the thermal and fluid dynamics involved, highlighting its suitability for predicting the behavior of ternary hybrid nanofluids in the presence of catalytic reactions. The governing model equations and boundary conditions are non-dimensionalized by introducing suitable similarity transformations. Thereafter, the computational Chebyshev collocation spectral technique implemented in the MATHEMATICA 11.3 software is used to calculate the numerical solution. The study reveals that the Casson parameter has a negative influence on the velocity distribution, causing it to reduce as the Casson parameter rises. This research contributes to the advancement of modeling techniques for complex fluid systems, with implications for enhanced design and optimization in various industrial and engineering applications.

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Unbiased Parameter Estimation for Bayesian Inverse Problems

arXiv

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arXiv 2025年

作者： Chada, Neil K. Jasra, Ajay Maama, Mohamed Tempone, Raul Department of Mathematics City University of Hong Kong China School of Data Science The Chinese University of Hong Kong Shenzhen CN 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

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a solution of a differential equation and, even if exact solutions are available, an analytical intractability of the marginal likelihood and its associated gradient, which is used for parameter estimation. The focus of this article is to deliver unbiased estimates of the unknown parameters, that is, stochastic estimators that, in expectation, are equal to the maximizer of the marginal likelihood, and possess no numerical approximation error. Based upon the ideas of [4] we develop a new approach for unbiased parameter estimation for Bayesian inverse problems. We prove unbiasedness and establish numerically that the associated estimation procedure is faster than the current state-of-the-art methodology for this problem. We demonstrate the performance of our methodology on a range of problems which include a PDE and ODE. Copyright © 2025, The Authors. All rights reserved.

关键词： Markov processes

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A PSO-Based Sanitization Process with Multi-thresholds Model 25th

A PSO-Based Sanitization Process with Multi-thresholds Model

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25th International Conference on Pattern Recognition Workshops, ICPR 2020

作者： Wu, Jimmy Ming-Tai Srivastava, Gautam Tayeb, Shahab Lin, Jerry Chun-Wei College of Computer Science and Engineering Sandong University of Science and Technology Qingdao Sandong China Department of Mathematics and Computer Science Brandon University Brandon Canada Department of Electrical and Computer Engineering California State University Fresno United States Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Bergen Norway

ISBN: (纸本)9783030687984

Earlier, many PPDM algorithms have been proposed to conceal sensitive items in a database in order to disclose sensitive itemsets. All prior techniques, however, ignored a crucial problem in setting minimum support thresholds. Thus, a new concept of minimal support for solving this issue is proposed in this paper. In compliance with a given threshold function, the proposed approach would set a tighter threshold for an object containing several items. Experimental results are then evaluated to show the performance of the traditional Greedy PPDM approach, GA-based PPDM approaches, and the proposed PSO-based algorithm with the new flexible and minimal support function. © 2021, Springer Nature Switzerland AG.

关键词： Data mining

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Deep Reinforcement Learning for Robotic Hand Manipulation

Deep Reinforcement Learning for Robotic Hand Manipulation

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2020 International Conference on computer, Control, Electrical, and Electronics engineering, ICCCEEE 2020

作者： Saeed, Muhammed Nagdi, Mohammed Rosman, Benjamin Ali, Hiba H. S. M. University of Khartoum Electronic and Electrical Engineering Department Omdurman Sudan University of the Witwatersrand School of Computer Science and Applied Mathematics Johannesburg South Africa

ISBN: (纸本)9781728191119

Researchers have made a lot of progress in combining the advances in Deep Learning and the generalization and applicability of Reinforcement learning to the sequential decision-making process and introduce Deep Reinforcement Learning, which allows using Reinforcement Learning in high dimensional input space environments. Deep Reinforcement Learning achieved notable results in Atari-Games, continuous control tasks such as Robotics. In this project we benchmark the performance of three different deep reinforcement Learning techniques Deep Deterministic Policy Gradient 'DDPG' [1], Deep Deterministic Policy Gradient with Hindsight Experience Replay 'DDPG + HER' [2] and state-of-Art policy gradient method Proximal Policy optimization 'PPO' [3], on multi-goal continuous control environments Fetch task and HandManipulate tasks, we benchmarked the three algorithms on six different environments using sparse and dense reward settings. Deep Deterministic Policy Gradient with Hindsight Experience Replay [2] achieves the best success-rate overall the environments when applied with sparse rewards, while both Proximal Policy Optimization [3] and Deep Deterministic Policy Gradient [1] were able to converge only on FetchReach environment. © 2021 IEEE.

关键词： Reinforcement learning

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