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Efficient Computation of Collatz Sequence Stopping Times: A Novel Algorithmic Approach

IEEE ACCESS 2025年 13卷 41210-41220页

作者： Getachew, Eyob Solomon Assefa, Beakal Gizachew Addis Ababa Inst Technol Sch Informat Technol & Engn Addis Ababa 1000 Ethiopia

The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research focuses on designing an efficient algorithm to compute the stopping time of numbers in the Collatz sequence, achieving significant computational improvements. By leveraging structural patterns in the Collatz tree, the proposed algorithm minimizes redundant operations and optimizes computational steps. Unlike prior methods, it efficiently handles extremely large numbers without requiring advanced techniques such as memoization or parallelization. Experimental evaluations confirm computational efficiency improvements of approximately 28% over state-of-the-art methods. These findings underscore the algorithm's scalability and robustness, providing a foundation for future large-scale verification of the conjecture and potential applications in computational mathematics.

关键词： Computational efficiency Encryption Approximation algorithms Visualization Probabilistic logic Optimization Complexity theory Watermarking Time complexity Testing Algorithm optimization bitwise operations Collatz conjecture Collatz tree computational mathematics high-performance algorithms logarithmic complexity memoization parallel computing stopping time computational complexity sequence analysis and large-scale verification

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high-performance DSP platform for digital hearing aid SoC with flexible noise estimation

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IET CIRCUITS DEVICES & SYSTEMS 2019年第5期13卷 717-722页

作者： Kim, Sang-Won Kim, Min-Joon Kim, Jae-Seok Yonsei Univ Sch Elect & Elect Engn Seoul South Korea

Flexibility and programmability of hearing aids are important because the algorithms applied to hearing aids should be changeable based on different types of hearing impairment and the ambient environment of the user. This paper proposes a high-performance digital signal processing (DSP) platform for a digital hearing aid system on a chip (SoC) with flexible noise estimation. The proposed DSP platform comprises several dedicated accelerators and an application-specific instruction-set processor (ASIP) to achieve flexibility. To handle complex hearing aid algorithms in real time, the main algorithms of hearing aids are executed by hardware accelerators and only environment-sensitive parts of the applied algorithms are implemented as the ASIP. Simulation results show that the proposed DSP platform can handle complex and high-performance algorithms in real time, and that it provides better quality in terms of noise handling by adapting the noise estimation algorithms suitable for the noise environment. The chip area of authors' DSP design is 2.71 mm(2), and it consumes 1.3 mW at 1 V operation, 8 MHz clock frequency with a 65 nm high threshold voltage (HVT) standard cell library.

关键词： instruction sets system-on-chip hearing aids digital signal processing chips low-power electronics integrated circuit noise flexible electronics integrated circuit design flexible noise estimation complex hearing aid algorithms high-performance algorithms noise handling noise estimation algorithms noise environment high-performance DSP platform digital hearing aid SoC hearing impairment high-performance digital signal processing platform digital hearing aid system application-specific instruction-set processor ASIP hardware accelerators power 1 3 mW voltage 1 0 V frequency 8 0 MHz size 65 0 nm

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Fast and memory efficient mining of frequent closed itemsets

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2006年第1期18卷 21-36页

作者： Lucchese, C Orlando, S Perego, R Univ Ca Foscari Venezia Dipartimento Informat I-30172 Venice Italy CNR ISTI High Performance Comp Lab Area Ric Pisa I-56126 Pisa PI Italy

This paper presents a new scalable algorithm for discovering closed frequent itemsets, a lossless and condensed representation of all the frequent itemsets that can be mined from a transactional database. Our algorithm exploits a divide-and-conquer approach and a bitwise vertical representation of the database and adopts a particular visit and partitioning strategy of the search space based on an original theoretical framework, which formalizes the problem of closed itemsets mining in detail. The algorithm adopts several optimizations aimed to save both space and time in computing itemset closures and their supports. In particular, since one of the main problems in this type of algorithms is the multiple generation of the same closed itemset, we propose a new effective and memory-efficient pruning technique, which, unlike other previous proposals, does not require the whole set of closed patterns mined so far to be kept in the main memory. This technique also permits each visited partition of the search space to be mined independently in any order and, thus, also in parallel. The tests conducted on many publicly available data sets show that our algorithm is scalable and outperforms other state-of-the-art algorithms like CLOSET+ and FP-CLOSE, in some cases by more than one order of magnitude. More importantly, the performance improvements become more and more significant as the support threshold is decreased.

关键词： data mining association rules frequent itemsets condensed representations closed itemsets high-performance algorithms

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A SOFTWARE ENVIRONMENT FOR PARALLEL COMPUTER VISION

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COMPUTER 1992年第2期25卷 73-77页

作者： JAMIESON, LH DELP, EJ WANG, CC LI, J WEIL, FJ IBM CORP SAN JOSECA 95193 MOTOROLA INC CTR SOFTWARE TECHNOLSOFTWARE ENGN RES LABSCHAUMBURGIL 60196

A software environment tailored to computer vision and image processing (CVIP) that focuses on how information about the CVIP problem domain can make the high-performance algorithms and the sophisticated algorithm techniques being designed by algorithm experts more readily available to CVIP researchers is presented. The environment consists of three principle components: DISC, Cloner, and Graph Matcher. DISC (dynamic intelligent scheduling and control) supports experimentation at the CVIP task level by creating a dynamic schedule from a user's specification of the algorithms that constitute a complex task. Cloner is aimed at the algorithm development process and is an interactive system that helps a user design new parallel algorithms by building on and modifying existing library algorithms. Graph Matcher performs the critical step of mapping new algorithms onto the target parallel architecture. Initial implementations of DISC and Graph Matcher have been completed, and work on Cloner is in progress

关键词： CVIP problem domain Cloner DISC Graph Matcher algorithm development process algorithm techniques computer vision computerised picture processing dynamic intelligent scheduling dynamic schedule high-performance algorithms image processing interactive system library algorithms parallel algorithms parallel algorithms parallel architectures parallel computer vision parallel programming programming environments software environment target parallel architecture

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Computational Approach for Securing Radiology-Diagnostic Data in Connected Health Network using high-performance GPU-Accelerated AES

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INTERDISCIPLINARY SCIENCES-COMPUTATIONAL LIFE SCIENCES 2017年第1期9卷 140-152页

作者： Adeshina, A. M. Hashim, R. Univ Tun Hussein Onn Malaysia Fac Comp Sci & Informat Technol Batu Pahat 86400 Johor Malaysia

Diagnostic radiology is a core and integral part of modern medicine, paving ways for the primary care physicians in the disease diagnoses, treatments and therapy managements. Obviously, all recent standard healthcare procedures have immensely benefitted from the contemporary information technology revolutions, apparently revolutionizing those approaches to acquiring, storing and sharing of diagnostic data for efficient and timely diagnosis of diseases. Connected health network was introduced as an alternative to the ageing traditional concept in healthcare system, improving hospital-physician connectivity and clinical collaborations. Undoubtedly, the modern medicinal approach has drastically improved healthcare but at the expense of high computational cost and possible breach of diagnosis privacy. Consequently, a number of cryptographical techniques are recently being applied to clinical applications, but the challenges of not being able to successfully encrypt both the image and the textual data persist. Furthermore, processing time of encryption-decryption of medical datasets, within a considerable lower computational cost without jeopardizing the required security strength of the encryption algorithm, still remains as an outstanding issue. This study proposes a secured radiology-diagnostic data framework for connected health network using high-performance GPU-accelerated Advanced Encryption Standard. The study was evaluated with radiology image datasets consisting of brain MR and CT datasets obtained from the department of Surgery, University of North Carolina, USA, and the Swedish National Infrastructure for Computing. Sample patients' notes from the University of North Carolina, School of medicine at Chapel Hill were also used to evaluate the framework for its strength in encrypting-decrypting textual data in the form of medical report. Significantly, the framework is not only able to accurately encrypt and decrypt medical image datasets, but it also successful

关键词： Radiology data Diagnosis privacy Encryption algorithms high-performance algorithms Medical visualization

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OCT Image Processing System For Numerical Simulation of Fundus Temperature Distribution

OCT Image Processing System For Numerical Simulation of Fund...

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18th International Scientific and Technical Conference on Optical Technologies for Communications

作者： Shirokanev, Alexander S. Ilyasova, Nataly Yu Andriyanov, Nikita A. Demin, Nikita S. Samara Natl Res Univ Moskovskoye Shosse 34 Samara 443086 Russia IPSI RAS Branch FSRC Crystallog & Photon RAS Molodogvardeyskaya 151 Samara 443001 Russia Financial Univ Govt Russian Federat Leningradskiy Av 49 Moscow 125167 Russia

ISBN: (数字)9781510644250

ISBN: (纸本)9781510644250

The safety of laser coagulation in the treatment of diabetic retinopathy depends on the correct selection of laser exposure parameters. In this paper, it was proposed to use technology for numerical modeling of the temperature distribution in the fundus based on its structure formed from optical coherence tomography (OCT) images. For such a formation, it is required to process each image and then interpolate the three-dimensional surfaces. Further, the formed structure is used for numerical simulation. This approach will potentially allow automating the extremely time-consuming procedure for choosing a coagulate placement plan. The paper considers algorithms that improve performance when solving the problem of mathematical modeling using the maximum load of CPU and GPU devices, i.e. parallel and high-performance algorithms.

关键词： mathematical modeling image processing digital signal processing laser coagulation retinopathy high-performance algorithms

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Improving the spatial resolution of digital images and video sequences using subpixel scanning

Improving the spatial resolution of digital images and video...

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2021 All-Russian Conference with International Participation "Spatial Data Processing for Monitoring of Natural and Anthropogenic Processes", SDM 2021

作者： Reznik, Aleksandr L. Soloviev, Aleksandr A. Torgov, Andrey V. Institute of Automation and Electrometry of the Siberian Branch of the Russian Academy of Sciences Novosibirsk Russia

high-performance method for improving the resolution of digital images and video sequences based on minimum-variance signal reconstruction are considered. A distinctive feature of the developed algorithms is that they allow (with the availability of modern computing power) to obtain improved images and video in "real time". © 2021 Copyright for this paper by its authors.

关键词： high-performance algorithms Image reconstruction

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The Barzilai-Borwein Method for distributed optimization over unbalanced directed networks

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ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE 2021年 99卷 104151-104151页

作者： Hu, Jinhui Chen, Xin Zheng, Lifeng Zhang, Ling Li, Huaqing Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligen Coll Elect & Informat Engn Chongqing 400715 Peoples R China Chongqing Univ Sch Big Data & Software Engn Chongqing 401331 Peoples R China

This paper studies optimization problems over multi-agent systems, in which all agents cooperatively minimize a global objective function expressed as a sum of local cost functions. Each agent in the systems uses only local computation and communication in the overall process without leaking their private information. Based on the Barzilai-Borwein (BB) method and multi-consensus inner loops, a distributed algorithm with the availability of larger step-sizes and accelerated convergence, named as ADBB, is proposed. Moreover, owing to the employment of only row-stochastic weight matrices, ADBB can resolve the optimization problems over unbalanced directed networks without requiring the knowledge of neighbors' out-degree for each agent. Via establishing contraction relationships between the consensus error, the optimality gap, and the gradient tracking error, ADBB is theoretically proved to converge linearly to the global optimal solution. A real-world data set is used in simulations to validate the correctness of the theoretical analysis.

关键词： Multi-agent systems Distributed optimization Barzilai-Borwein methods high-performance algorithms Global optimization

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