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Computing adjoint mismatch of linear maps

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arXiv 2025年

作者： Bresch, Jonas Lorenz, Dirk A. Schneppe, Felix Winkler, Maximilian Institute of Mathematics Technical University Berlin Straße des 17. Juni 136 Berlin10623 Germany Center for Industrial Mathematics Fachbereich 3 University of Bremen Postfach 33 04 40 Bremen28334 Germany

This paper considers the problem of detecting adjoint mismatch for two linear maps. To clarify, this means that we aim to calculate the operator norm for the difference of two linear maps, where for one we only have a black-box implementation for the evaluation of the map, and for the other we only have a black-box for the evaluation of the adjoint map. We give two stochastic algorithms for which we prove the almost sure convergence to the operator norm. The algorithm is a random search method for a generalization of the Rayleigh quotient and uses optimal step sizes. Additionally, a convergence analysis is done for the corresponding singular vector and the respective eigenvalue *** Codes 65F35, 15A60, 68W20 Copyright © 2025, The Authors. All rights reserved.

关键词： consensus algorithm

Channel Resolvability Using Multiplicative Weight Update algorithm

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arXiv 2025年

作者： Takahashi, Koki Watanabe, Shun Department of Computer and Information Sciences Tokyo University of Agriculture and Technology Japan

We study the channel resolvability problem, which is used to prove strong converse of identification via channel. Channel resolvability has been solved by only random coding in the literature. We prove channel resolvability using the multiplicative weight update algorithm. This is the first approach to channel resolvability using non-random coding. © 2025, CC BY.

关键词： consensus algorithm

Solving Non-Monotone Inclusions Using Monotonicity of Pairs of Operators

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arXiv 2025年

作者： Le, Ba Khiet Dao, Minh N. Théra, Michel Optimization Research Group Faculty of Mathematics and Statistics Ton Duc Thang University Ho Chi Minh City Viet Nam School of Science RMIT University MelbourneVIC3000 Australia Mathematics and Computer Science Department University of Limoges 123 Avenue Albert Thomas Limoges87060 Cedex France

In this paper, under the monotonicity of pairs of operators, we propose some Generalized Proximal Point algorithms to solve non-monotone inclusions using warped resolvents and transformed resolvents. The weak, strong,... 详细信息

关键词： consensus algorithm

Development of an Advanced Blockchains’ Classification

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Development of an Advanced Blockchains’ Classification

Human-Computer Interaction, Optimization and Robotic Applications (HORA), International Congress on

作者： Illia Bukatych Iryna Aksonova Tetiana Milevska Anton Smirnov Dmytro Balagura Mykhailo Zhyhalov Cybersecurity Department Kharkiv Polytechnic Institute National Technical University Kharkiv Ukraine Department of Information Technology Security Kharkiv National University of Radio Electronics Kharkiv Ukraine

ISBN: (数字)9798331510886

ISBN: (纸本)9798331510893

The current state of blockchain technology development, its key concepts and impact on various branches of economics and science are analyzed. The main stages of the development of blockchain technologies are analyzed both in general and in terms of their security. Particular attention is paid to existing methods of classifying blockchains, their division into public, private and hybrid networks. The most common consensus algorithms, their features and examples of real blockchain projects in which they are used are considered. Based on the research, a generalized classification of blockchains is proposed, which takes into account such key characteristics as the type of access and architecture, the evolution of development, scalability and level of decentralization, and consensus methods. Potential threats to blockchain-based systems are highlighted, including various types of attacks, and their systematization in a graphical form is proposed. The results of the study may be useful for researchers, developers, and analysts working in the field of blockchain technologies, as well as for organizations planning to integrate blockchain into their business processes.

关键词： Industries Technological innovation Supply chain management Scalability consensus algorithm Medical services Blockchains Planning Robots Optimization

On the Locality of the Lovász Local Lemma

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arXiv 2025年

作者： Davies-Peck, Peter Durham University United Kingdom

The Lovász Local Lemma is a versatile result in probability theory, characterizing circumstances in which a collection of n ‘bad events’, each occurring with probability at most p and dependent on a set of underlying random variables, can be avoided. It is a central tool of the probabilistic method, since it can be used to show that combinatorial objects satisfying some desirable properties must exist. While the original proof was existential, subsequent work has shown algorithms for the Lovász Local Lemma: that is, in circumstances in which the lemma proves the existence of some object, these algorithms can constructively find such an object. One main strand of these algorithms, which began with Moser and Tardos’s well-known result (JACM 2010), involves iteratively resampling the dependent variables of satisfied bad events until none remain satisfied. In this paper, we present a novel analysis that can be applied to resampling-style Lovász Local Lemma algorithms. This analysis shows that an output assignment for the dependent variables of most events can be determined only from O(log log1/p n)-radius local neighborhoods, and that the events whose variables may still require resampling can be identified from these neighborhoods. This allows us to improve randomized complexities for the constructive Lovász Local Lemma (with polynomial criterion) in several parallel and distributed models. In particular, we obtain: • A LOCAL algorithm with O(log log1/p n) node-averaged complexity (while matching the O(log1/p n) worst-case complexity of Chung, Pettie, and Su). • An algorithm for the LCA and VOLUME models requiring dO(log log1/p n) probes per query. • An O(log log log1/p n)-round algorithm for CONGESTED CLIQUE, linear space MPC, and Heterogenous MPC. © 2025, CC BY.

关键词： consensus algorithm

A fast algorithm for the Frobenius problem in three variables

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arXiv 2025年

作者： Rosin, Daniel

Given the function Γ(X) = a1x1 + a2x2 + a3x3, where the set {a1, a2, a3}, denoted A, consists of positive integers and the set {x1, x2, x3}, denoted X, consists of non-negative integers, the Frobenius problem in three variables is to find the greatest integer, which is not in the codomain of Γ. The fastest known algorithm for solving the three variable case of the Frobenius problem was invented by H. Greenberg in 1988 whose worst case time complexity is a logarithmic function of A. In 2017 A. Tripathi presented another algorithm for solving the same problem. This article presents an algorithm whose foundation is the same as Tripathi’s. However, this algorithm is significantly different from Tripathi’s and we show that its worst case time complexity is also a logarithmic function of *** Codes 11D07 © 2025, CC BY.

关键词： consensus algorithm

Improved Space Bounds for Subset Sum

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arXiv 2024年

作者： Belova, Tatiana Chukhin, Nikolai Kulikov, Alexander S. Mihajlin, Ivan St. Petersburg Department of Steklov Mathematical Institute Russian Academy of Sciences Russia Neapolis University Pafos JetBrains Research Cyprus JetBrains Research Czech Republic

More than 40 years ago, Schroeppel and Shamir presented an algorithm that solves the Subset Sum problem for n integers in time O∗(20.5n) and space O∗(20.25n). The time upper bound remains unbeaten, but the space upper bound has been improved to O∗(20.249999n) in a recent breakthrough paper by Nederlof and Węgrzycki (STOC 2021). Their algorithm is a clever combination of a number of previously known techniques with a new reduction and a new algorithm for the Orthogonal Vectors problem. In this paper, we give two new algorithms for Subset Sum. We start by presenting an Arthur-Merlin algorithm: upon receiving the verifier's randomness, the prover sends an n/4-bit long proof to the verifier who checks it in (deterministic) time and space O∗(2n/4). An interesting consequence of this result is the following fine-grained lower bound: assuming that 4-SUM cannot be solved in time O(n2−Ε) for all Ε > 0, Circuit SAT cannot be solved in time O(g2(1-Ε)n), for all Ε > 0 (where n and g denote the number of inputs and the number of gates, respectively). Then, we improve the space bound by Nederlof and Węgrzycki to O∗(20.246n) and also simplify their algorithm and its analysis. We achieve this space bound by further filtering sets of subsets using a random prime number. This allows us to reduce an instance of Subset Sum to a larger number of instances of smaller size. © 2024, CC BY.

关键词： consensus algorithm

Pareto Set Identification With Posterior Sampling

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arXiv 2024年

作者： Kone, Cyrille Jourdan, Marc Kaufmann, Emilie Univ. Lille CNRS Inria Centrale Lille UMR 9189-CRIStAL LilleF-59000 France EPFL Lausanne Switzerland

The problem of identifying the best answer among a collection of items having real-valued distribution is well-understood. Despite its practical relevance for many applications, fewer works have studied its extension when multiple and potentially conflicting metrics are available to assess an item’s quality. Pareto set identification (PSI) aims to identify the set of answers whose means are not uniformly worse than another. This paper studies PSI in the transductive linear setting with potentially correlated objectives. Building on posterior sampling in both the stopping and the sampling rules, we propose the PSIPS algorithm that deals simultaneously with structure and correlation without paying the computational cost of existing oracle-based algorithms. Both from a frequentist and Bayesian perspective, PSIPS is asymptotically optimal. We demonstrate its good empirical performance in real-world and synthetic instances. © 2024, CC BY.

关键词： consensus algorithm

Advanced Veterinary Clinic Management Predictive Analytics and Blockchain Innovation

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Advanced Veterinary Clinic Management Predictive Analytics a...

Applied Artificial Intelligence and Computing (ICAAIC), International Conference on

作者： R. Vijay Sai B. G. Geetha A Hariharan A Haripriya K Kameshwaran Computer Science and Engineering K S Rangasamy College of Technology Tamil Nadu India

ISBN: (数字)9798350375190

ISBN: (纸本)9798350375206

Enhancing the security, effectiveness, and transparency of healthcare data, distributed ledger technology like blockchain holds the potential to completely transform the healthcare sector. Sensitive patient information is more difficult for bad actors to bre ach thanks to the SHA-256 algorithm, which improves data security. Standardized data formats and smart contracts make it easier for disparate healthcare systems to communicate with one another. Block chain deployment in the healthcare sector is not without its challenges, though, including user uptake, scalability, and regulatory compliance. By highlighting the potential benefits and difficulties of incorporating block chain technology in healthcare management systems, this study provides significant insights into the evolving landscape of healthcare data management.

关键词： Technological innovation Scalability Smart contracts Medical services consensus algorithm Transforms Proof of Work