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An implicit difference scheme and algorithm implementation for the one-dimensional time-fractional Burgers equations

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MATHEMATICS AND COMPUTERS IN SIMULATION 2019年 166卷 298-314页

作者： Qiu, Wenlin Chen, Hongbin Zheng, Xuan Hunan Normal Univ Sch Math & Stat Key Lab Comp & Stochast Math Minist Educ Changsha 410081 Hunan Peoples R China Cent South Univ Forestry & Technol Coll Sci Inst Math & Phys Changsha 410004 Hunan Peoples R China Changsha Univ Sci & Technol Sch Math & Stat Changsha 410114 Hunan Peoples R China

An implicit difference scheme with the truncation of order 2 - alpha(0 < alpha < 1) for time and order 2 for space is considered for the one-dimensional time-fractional Burgers equations. The L-1-discretization formula of the fractional derivative in the Caputo sense is employed. The second-order spatial derivative is approximated by means of the three-point centered formula and the nonlinear convection term is discretized by the Galerkin method based on piecewise linear test functions. The stability and convergence in the L-infinity norm are proved by the energy method. Meanwhile, a novel iterative algorithm is proposed and implemented to solve the nonlinear systems. Numerical experiment shows that the results are consistent with our theoretical analysis, and the comparison between the proposed iterative algorithm and the existing methods shows the efficiency of our method. (C) 2019 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： One-dimensional time-fractional Burgers equations Implicit difference scheme L-1-discretization formula Stability and convergence algorithm implementation

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Rapid design and algorithm implementation for knitted sweater pattern

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JOURNAL OF THE TEXTILE INSTITUTE 2020年第4期112卷 636-645页

作者： Lu, Lisha Jiang, Gaoming Cong, Honglian Xia, Fenglin Peng, Jiajia Jiang Nan Univ Minist Educ Engn Res Ctr Knitting Technol 1800 Lihu Ave Wuxi Jiangsu Peoples R China

Sweater pattern design plays a crucial role in practical production, determining whether the finished products can meet the requirements of customers. In addition, pattern-designing is also a vital link in the production of sweaters, affecting the development cycle and final quality of products. For this reason, this work proposed two different kinds of algorithms for sweater pattern design: synchronous filling algorithm and asynchronous filling algorithm, so as to realise the rapid design of sweater pattern in Computer-Aided Design (CAD) system by reducing the complex technique calculation. Firstly, the data structures of specifications and styles were established respectively based on the technological characteristics of sweaters, and then the algorithms for sweater pattern-generating were implemented by using C+ + programming technology. At last, the running time of each algorithm was tested to analyse the performances of the algorithms under the same filling scales and different filling scales, respectively. The results showed that the execution efficiency and stability of synchronous filling algorithm are better than that of asynchronous filling algorithm.

关键词： Rapid design sweater pattern algorithm implementation

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A derivative-free root-finding algorithm using exponential method and its implementation

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BMC RESEARCH NOTES 2023年第1期16卷 1-7页

作者： Thota, Srinivasarao Awad, Mohamed M. Shanmugasundaram, P. Rathour, Laxmi Amrita Vishwa Vidyapeetham Amrita Sch Phys Sci Dept Math Amaravati 522503 Andhra Pradesh India Mansoura Univ Fac Engn Mech Power Engn Dept Mansoura 35516 Egypt Mizan Tepi Univ Coll Nat & Computat Sci Dept Math Mizan Teferi Ethiopia Natl Inst Technol Dept Math Aizawl 796012 Mizoram India

Objective In this paper, we develop a new root-finding algorithm to solve the given non-linear equations. The proposed root-finding algorithm is based on the exponential method. This algorithm is derivative-free and converges *** Several numerical examples are presented to illustrate and validation of the proposed methods. Microsoft Excel and Maple implementation of the proposed algorithm is presented with sample computations.

关键词： Iterative algorithms Nonlinear equations Exponential method algorithm implementation Root-finding algorithms 65Hxx

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implementation and Experiments with an algorithm for Parallel Scheduling of Complex Dags under Uncertainty

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8th Workshop on algorithm Engineering and Experiments/3rd Workshop on Analytic algorithms and Combinatorics

作者： Malewicz, Grzegorz Google Inc Mountain View CA 94043 USA

ISBN: (纸本)9780898716108

Our earlier paper introduced a parallel scheduling problem where a directed acyclic graph modeling t tasks and their dependencies needs to be executed on n unreliable workers. Worker i executes task j correctly with probability p(i,j). The goal is to find a regimen Sigma, that dictates how workers get assigned to tasks (possibly in parallel and redundantly) throughout execution, to minimize the expected completion time. The paper provided a polynomial time algorithm for the problem restricted to the case when dag width and the number of workers are at most a constant, and showed necessity of these restrictions, unless P=NP. The current paper describes algorithm engineering approaches used to produce an efficient implementation of the algorithm, and experiments demonstrating how the algorithm scales.

关键词： Parallel scheduling combinatorial optimization algorithm implementation application of perfect hashing grid computing project management

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A comparative study of antenna array algorithm implementations using FPGA and DSP for cdma2000

A comparative study of antenna array algorithm implementatio...

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3rd International Symposium on Wireless Communication Systems (ISWCS 2006)

作者： Sahin, Suhap Dikmese, Sener Kucuk, Kerem Kavak, Adnan Kocaeli Univ Comp Engn Kocaeli Turkey Kocaeli Univ Elect Comp Ed Kocaeli Turkey

ISBN: (纸本)9781424403974

This paper demonstrates implementation of some CDMA system compatible antenna array algorithms namely LMS and space code correlator (SCC) on an FPGA. A comparative study of FPGA and DSP implementation issues such as architecture complexity and weight vector computation time is also given. The implementations of the algorithms are performed on Xilinx Virtex 11 Pro FPGA and Texas Instruments (TI) TMS320C67x floating-point DSP platforms. For the signal modeling, cdma2000 reverse link signal model is considered for uniform linear array topology and varying multipath propagation conditions. Results show that the both algorithms, which were implemented on Xilinx XC2VP4 and TMS320C6713 DSP, provides weight vector computation time smaller than 10 ms period.

关键词： algorithm implementation cdma2000 digital signal processor (DSP) FPGA smart antenna systems (SAS) 3G systems

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Mathematical Foundation of a Functional implementation of the CNF algorithm

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algorithmS 2023年第10期16卷

作者： Garcia-Olmedo, Francisco Miguel Garcia-Miranda, Jesus Gonzalez-Rodelas, Pedro Univ Granada Dept Algebra E-18071 Granada Spain Univ Granada Dept Matemat Aplicada E-18071 Granada Spain

The conjunctive normal form (CNF) algorithm is one of the best known and most widely used algorithms in classical logic and its applications. In its algebraic approach, it makes use in a loop of a certain well-defined operation related to the "distributivity" of logical disjunction versus conjunction. For those types of implementations, the loop iteration runs a comparison between formulas to decide when to stop. In this article, we explain how to pre-calculate the exact number of loop iterations, thus avoiding the work involved in the above-mentioned comparison. After that, it is possible to concatenate another loop focused now on the "associativity" of conjunction and disjunction. Also for that loop, we explain how to calculate the optimal number of rounds, so that the decisional comparison phase for stopping can be also avoided.

关键词： CNF SAT problem classical logic Boolean algebra Horn clauses reverse engineering automatic theorems proving algorithm implementation functional programming Haskell

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Maximum Likelihood Estimation and Non-Linear Least Squares Fitting implementation in FPGA Devices for High Resolution Hodoscopy

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 2013年第5期60卷 3578-3584页

作者： Blasco, Jose M. Sanchis, Enrique Gonzalez, Vicente Martin, Jose D. Egea, Francisco J. Barrientos, Diego Granero, Domingo Sanchis-Sanchez, Enrique Univ Valencia Dept Fisioterapia Valencia Spain Univ Valencia Dept Engn Elect Escola Tecn Super Engn Valencia Spain Eresa Grp Med Valencia Spain

This work compares two possible solutions to achieve a high resolution in a hodoscope based on Plastic Scintillating Fibers (PSF) by obtaining the point of maximum interaction of the radioactive beam with the detector. The two fitting algorithms are the Maximum Likelihood Estimation and a non-linear least-squares fitting with the Levenberg-Marquardt algorithm. Both approaches have been tested, compared and implemented in Field Programmable Gate Array (FPGA) devices.

关键词： algorithm implementation beam calibration FPGA high-resolution hodoscopy maximum interaction

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Real-Time Prediction of Acute Kidney Injury in Hospitalized Adults: implementation and Proof of Concept

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AMERICAN JOURNAL OF KIDNEY DISEASES 2020年第6期76卷 806-+页

作者： Ugwuowo, Ugochukwu Yamamoto, Yu Arora, Tanima Saran, Ishan Partridge, Caitlin Biswas, Aditya Martin, Melissa Moledina, Dennis G. Greenberg, Jason H. Simonov, Michael Mansour, Sherry G. Testani, Jeffrey M. Rao, Veena Rentfro, Keith Obeid, Wassim Parikh, Chirag R. Wilson, F. Perry Yale Univ Sch Med Dept Med Sect Nephrol New Haven CT 06510 USA Yale Univ Sch Med Clin & Translat Res Accelerator New Haven CT USA Emory Univ Dept Phys Atlanta GA 30322 USA Yale Univ Sch Med Joint Data Analyt Team New Haven CT USA Yale Univ Sch Med Dept Pediat New Haven CT 06510 USA Univ Texas El Paso Dept Mech Engn El Paso TX 79968 USA Yale Univ Sch Med Dept Internal Med Sect Cardiol New Haven CT 06510 USA Johns Hopkins Univ Sch Med Baltimore MD USA Johns Hopkins Med Dept Med Div Nephrol Baltimore MD USA

Rationale & Objective: Acute kidney injury (AKI) is diagnosed based on changes in serum creatinine concentration, a late marker of this syndrome. algorithms that predict elevated risk for AKI are of great interest, but no studies have incorporated such an algorithm into the electronic health record to assist with clinical care. We describe the experience of implementing such an algorithm. Study Design: Prospective observational cohort study. Setting & Participants: 2,856 hospitalized adults in a single urban tertiary-care hospital with an algorithm-predicted risk for AKI in the next 24 hours >15%. Alerts were also used to target a convenience sample of 100 patients for measurement of 16 urine and 6 blood biomarkers. Exposure: Clinical characteristics at the time of pre-AK I alert. Outcome: AKI within 24 hours of pre-AK I alert (AKI(24)). Analytical Approach: Descriptive statistics and univariable associations. Results: At enrollment, mean predicted probability of AKI(24) was 19.1%;18.9% of patients went on to develop AKI(24). Outcomes were generally poor among this population, with 29% inpatient mortality among those who developed AKI(24) and 14% among those who did not (P < 0.001). Systolic blood pressure 100 mm Hg (28% of patients with AKI(24) vs 18% without), heart rate 100 beats/min (32% of patients with AKI(24) vs 24% without), and oxygen saturation < 92% (15% of patients with AKI(24) vs 6% without) were all more common among those who developed AKI(24). Of all biomarkers measured, only hyaline casts on urine microscopy (72% of patients with AKI(24) vs 25% without) and fractional excretion of urea nitrogen (20% [IQR, 12%-36%] among patients with AKI(24) vs 34% [IQR, 25%-44%] without) differed between those who did and did not develop AKI(24). Limitations: Single-center study, reliance on serum creatinine level for AKI diagnosis, small number of patients undergoing biomarker evaluation. Conclusions: A real-time AKI risk model was successfully integrated into the

关键词： Acute kidney injury (AKI) prediction prospective biomarker assessment algorithm implementation AKI risk hospitalized patients electronic health record (EHR) prognostic model serum creatinine (Scr) inpatient mortality renal function trajectory kidney injury marker [TIMP-2] × [IGFBP-7] NGAL KIM-1 IL-18 MCP-1

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Fast parallel sorting under LogP: Experience with the CM-5

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 1996年第8期7卷 791-805页

作者： Dusseau, AC Culler, DE Schauser, KE Martin, RP Computer Science Division University of California Berkeley CA USA University of California Santa Barbara USA

In this paper, we analyze four parallel sorting algorithms (bitonic, column, radix, and sample sort) with the LogP model. LogP characterizes the performance of modern parallel machines with a small set of parameters: the communication latency (L), overhead (o), bandwidth (g), and the number of processors (P). We develop implementations of these algorithms in Split-C, a parallel extension to C, and compare the performance predicted by LogP to actual performance on a CM-5 of 32 to 512 processors for a range of problem sizes. We evaluate the robustness of the algorithms by varying the distribution and ordering of the key values. We also briefly examine the sensitivity of the algorithms to the communication parameters. We show that the LogP model is a valuable guide in the development of parallel algorithms and a good predictor of implementation performance. The model encourages the use of data layouts which minimize communication and balanced communication schedules which avoid contention. With an empirical model of local processor performance, LogP predictions closely match observed execution times on uniformly distributed keys across a broad range of problem and machine sizes. We find that communication performance is oblivious to the distribution of the key values, whereas the local processor performance is not;some communication phases are sensitive to the ordering of keys due to contention. Finally, our analysis shows that overhead is the most critical communication parameter in the sorting algorithms.

关键词： massively parallel processing models of parallel computation sorting algorithm implementation communication performance communication schedules performance prediction performance analysis data layout

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Precision control for generalized pattern search algorithms with adaptive precision function evaluations

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SIAM JOURNAL ON OPTIMIZATION 2006年第3期16卷 650-669页

作者： Polak, E Wetter, M Univ Calif Berkeley Dept Elect Engn Berkeley CA 94720 USA United Technol Res Ctr E Hartford CT 06108 USA

In the literature on generalized pattern search algorithms, convergence to a stationary point of a once continuously differentiable cost function is established under the assumption that the cost function can be evaluated exactly. However, there is a large class of engineering problems where the numerical evaluation of the cost function involves the solution of systems of differential algebraic equations. Since the termination criteria of the numerical solvers often depend on the design parameters, computer code for solving these systems usually defines a numerical approximation to the cost function that is discontinuous with respect to the design parameters. Standard generalized pattern search algorithms have been applied heuristically to such problems, but no convergence properties have been stated. In this paper we extend a class of generalized pattern search algorithms to include a subprocedure that adaptively controls the precision of the approximating cost functions. The numerical approximations to the cost function need not de. ne a continuous function. Our algorithms can be used for solving linearly constrained problems with cost functions that are at least locally Lipschitz continuous. Assuming that the cost function is smooth, we prove that our algorithms converge to a stationary point. Under the weaker assumption that the cost function is only locally Lipschitz continuous, we show that our algorithms converge to points at which the Clarke generalized directional derivatives are nonnegative in predefined directions. An important feature of our adaptive precision scheme is the use of coarse approximations in the early iterations, with the approximation precision controlled by a test. We show by numerical experiments that such an approach leads to substantial time savings in minimizing computationally expensive functions.

关键词： algorithm implementation approximations generalized pattern search Hooke Jeeves Clarke's generalized directional derivative nonsmooth optimization

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