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EUCLIDEAN algorithmS ARE GAUSSIAN OVER IMAGINARY QUADRATIC FIELDS

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arXiv 2024年

作者： Kim, Dohyeong Lee, Jungwon Lim, Seonhee Department of Mathematical Sciences Research Institute of Mathematics Seoul National University Gwanakro 1 Gwanak-ku Seoul08826 Korea Republic of Mathematics Institute University of Warwick CoventryCV4 7AL United Kingdom

The distributional analysis of Euclidean algorithms was carried out by Baladi and Vallée. They showed the asymptotic normality of the number of division steps and associated costs in the Euclidean algorithm as a random variable on the set of rational numbers with bounded denominator based on the transfer operator methods. We extend their result to the Euclidean algorithm over appropriate imaginary quadratic fields by studying dynamics of the nearest integer complex continued fraction map, which is piecewise analytic and expanding but not a full branch map. By observing a finite Markov partition with a regular CW-structure, which enables us to associate the transfer operator acting on a direct sum of spaces of C1-functions, we obtain the limit Gaussian distribution as well as residual equidistribution. Copyright © 2024, The Authors. All rights reserved.

关键词： consensus algorithm

Laminar Matroid Secretary: Greedy Strikes Back

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arXiv 2023年

作者： Huang, Zhiyi Parsaeian, Zahra Zhu, Zixuan Department of Computer Science The University of Hong Kong Hong Kong University of Freiburg Germany

We show that a simple greedy algorithm is 4.75-competitive for the Laminar Matroid Secretary Problem, improving the 3√3 ≈ 5.196-competitive algorithm based on the forbidden sets technique (Soto, Turkieltaub, and Ver... 详细信息

关键词： consensus algorithm

A Comparative Analysis of Bitcoin and Ethereum Blockchain

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A Comparative Analysis of Bitcoin and Ethereum Blockchain

Artificial Intelligence, Networking and Information Technology (AINIT), International Seminar on

作者： Keyao Huang Jingyu Ma Xinyuan Wang Xi’an Jiaotong Liverpool University Suzhou China Pre-Engineering Div General Studies Admin University of Illinois at Urbana-Champaign Champaign US Hebei Agricultural University Langfang China

ISBN: (纸本)9781665412971

With the development of blockchain, various blockchain-based applications emerged. Of which Bitcoin and Ethereum are the most representative and popular blockchain applications. Therefore, it is important to compare Bitcoin with Ethereum and infer their developing trends. In the paper, we compare Bitcoin and Ethereum from different perspectives, including consensus algorithm, transaction cost, extension, and security. Comparative results demonstrate that Ethereum is better than Bitcoin on extension and transaction mechanism. Also, based on the results, we discuss about the essential development trend about blockchain applications. In the future, blockchain applications will be a platform which can provide more functions than digital currencies.

关键词： Seminars Costs Limiting Online banking Smart contracts Bitcoin consensus algorithm

Support Vector Machine Based Dynamic Obstacle Avoidance Strategy for First-Order Consistent Formation Control

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Support Vector Machine Based Dynamic Obstacle Avoidance Stra...

Chinese Automation Congress (CAC)

作者： Zhipeng Luo Li Fan Zheming Yan Jinhu Niu Bo Yu Aimin An School of Electrical and Information Engineering Lanzhou University of Technology LanZhou China Gansu Guokai New Energy Equipment Co. LTD Lanzhou University of Technology Baiyin China

ISBN: (数字)9798350368604

ISBN: (纸本)9798350368611

This paper addresses the challenge of dynamic obstacle avoidance in wheeled mobile robots by developing a classifier grounded in multi-agent consensus theory, leveraging support vector machines to enhance obstacle avoidance efficiency. Firstly, the current main methods of dynamic obstacle avoidance were introduced. Based on the existing consensus algorithm, support vector machine was selected as the dynamic obstacle avoidance method. Subsequently, specific attackers are designated to target both the leader and the follower, followed by simulations of the formation system to derive significant conclusions. That is, support vector machine can have good performance in multi-agent obstacle avoidance, which proves the feasibility and effectiveness of support vector machine in multi-agent dynamic obstacle avoidance. The simulation results show that in the limit case, that is, when the dynamic obstacle avoidance target continuously attacks the formation, the consensus formation system can still maintain the formation and recover to the original formation.

关键词： Support vector machines Automation Heuristic algorithms Simulation consensus algorithm Formation control Mobile robots Collision avoidance

Harmonizing vs Polarizing Platform Influence Functions

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arXiv 2024年

作者： AlMahmoud, Hind Mallmann-Trenn, Frederik King’s College London United Kingdom

We investigate the dynamics of opinion formation on social networking platforms, focusing on how individual opinions, influenced by both social connections and platform algorithms, evolve. We model this process using a differential equation, accounting for both peer influence and the platform’s content curation based on user preferences. Our primary aim is to analyze how these factors contribute to opinion polarization and identify potential strategies for its mitigation. We explore the conditions under which opinions converge to a consensus or remain polarized, emphasizing the role of the platform’s influence function. Our findings in two-agent, complete graphs, and stochastic block model provide insights into the impact of social media algorithms on public discourse and offer a framework for understanding how polarization can be avoided. © 2024, CC BY.

关键词： consensus algorithm

Towards Scalable and Practical Batch-Dynamic Connectivity

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arXiv 2024年

作者： De Man, Quinten Lącki, Jakub Dhulipala, Laxman Shun, Julian Karczmarz, Adam Wang, Zhongqi University of Maryland United States Google Research United States MIT CSAIL United States University of Warsaw IDEAS NCBR Poland

We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem which is work-efficient, supports batches of updates, runs in polylogarithmic depth, and uses only linear total space. The existing algorithms for the problem either use super-linear space, do not come with strong theoretical bounds, or are not parallel. On the empirical side, we provide the first implementation of the cluster forest algorithm, the first linear-space and poly-logarithmic update time algorithm for dynamic connectivity. Experimentally, we find that our algorithm uses up to 19.7× less space and is up to 6.2× faster than the level-set algorithm of HDT, arguably the most widely-implemented dynamic connectivity algorithm with strong theoretical guarantees. © 2024, CC BY.

关键词： consensus algorithm

FORWARD PRIMAL-DUAL HALF-FORWARD algorithm FOR SPLITTING FOUR OPERATORS

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arXiv 2023年

作者： Roldán, Fernando Departamento de Ingeniería Matemática Universidad de Concepción Concepción Chile

In this article, we propose a splitting algorithm to find zeros of the sum of four maximally monotone operators in real Hilbert spaces. In particular, we consider a Lipschitzian operator, a cocoercive operator, and a linear composite term. In the case when the Lipschitzian operator is absent, our method reduces to the Condat-Vũ algorithm. On the other hand, when the linear composite term is absent, the algorithm reduces to the Forward-Backward-Half-Forward algorithm (FBHF). Additionally, in each case, the set of step-sizes that guarantee the weak convergence of those methods are recovered. Therefore, our algorithm can be seen as a generalization of Condat-Vũ and FBHF. Moreover, we propose extensions and applications of our method in multivariate monotone inclusions and saddle point problems. Finally, we present a numerical experiment in image deblurring *** Codes 47H05, 65K05, 65K15, 90C25 Copyright © 2023, The Authors. All rights reserved.

关键词： consensus algorithm

Blockchain based smart marketplace for secure internet bandwidth trading

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Blockchain based smart marketplace for secure internet bandw...

Multidisciplinary Engineering and Applied Science (ICMEAS), International Conference on

作者： Bello Musa Yakubu Muhammad Mahmoud Ahmad Abdullahi Binta Sulaiman Ahamed Sani Kazaure Majid Iqbal Khan Nadeem Javaid COMSATS University Islamabad Islamabad Pakistan Kano University of Science and Technology Wudil Kano-Nigeria Islamic University of Technology Gazipur Bangladesh Federal University Dutse Jigawa state Nigeria

ISBN: (纸本)9781665434942

Internet broadband usage is increasing dramatically as the number of Internet of Things (IoT) devices in smart homes that rely on Internet connectivity for effective communication between them grows. As a result, many network and Internet communication issues arise, including network traffic congestion, insecurity, high connection rates, and excess bandwidth waste. This work aims to create a secure and decentralized smart marketplace (SMP) for a fair, transparent, robust, and less expensive way of trading excess or idle traffic from a smart home by directly paying the owner of the bandwidth. The internet bandwidths may initially come from a direct Tel-com product or from other users (smart homeowners) who decide to sell their excess Internet bandwidth. The research was carried out by integrating a given smart marketplace scenario with blockchain technology using proof-of-authority (PoA) consensus mechanism. The simulation results show that the model is more reliable and appears to be an efficient solution to dealing with excess bandwidth waste and offering safe excess bandwidth trading within a smart city. Besides, the excess bandwidth wastage is controlled at least by 75% by making it available in the SMP for buyers.

关键词： Smart cities Simulation Switched mode power supplies Bandwidth Smart homes Telecommunication traffic consensus algorithm

ON SEQUENTIAL GREEDY-TYPE BASES

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arXiv 2023年

作者： Berasategui, Miguel Berná, Pablo M. Chu, Hung Viet IMAS - UBA - CONICET - PAB I FACULTAD DE CIENCIAS EXACTAS Y NATURALES UNIVERSIDAD DE BUENOS AIRES 1428 Buenos Aires Argentina DEPARTAMENTO DE MATEMÁTICAS CUNEF UNIVERSIDAD Madrid28040 Spain DEPARTMENT OF MATHEMATICS TEXAS A&M UNIVERSITY TX77843 United States

It is known that a basis is almost greedy if and only if the thresholding greedy algorithm gives essentially the smallest error term compared to errors from projections onto intervals or in other words, consecutive terms of N. In this paper, we fix a sequence (an)∞n=1 and compare the TGA against projections onto consecutive terms of the sequence and its shifts. We call the corresponding greedy-type condition the F(an)-almost greedy property. Our first result shows that the F(an)-almost greedy property is equivalent to the classical almost greedy property if and only if (an)∞n=1 is bounded. Then we establish an analog of the result for the strong partially greedy property. Finally, we show that under a certain projection rule and conditions on the sequence (an)∞n=1, we obtain a greedy-type condition that lies strictly between the almost greedy and strong partially greedy *** Codes 41A65, 46B15 Copyright © 2023, The Authors. All rights reserved.

关键词： consensus algorithm