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A SEMG-Force Estimation Framework Based on a Fast Orthogonal Search Method Coupled with factorization algorithms

SENSORS 2018年第7期18卷 2238-2238页

作者： Chen, Xiang Yuan, Yuan Cao, Shuai Zhang, Xu Chen, Xun Univ Sci & Technol China Dept Elect Sci & Technol Hefei 230027 Anhui Peoples R China

A novel framework based on the fast orthogonal search (FOS) method coupled with factorization algorithms was proposed and implemented to realize high-accuracy muscle force estimation via surface electromyogram (SEMG). During static isometric elbow flexion, high-density SEMG (HD-SEMG) signals were recorded from upper arm muscles, and the generated elbow force was measured at the wrist. HD-SEMG signals were decomposed into time-invariant activation patterns and time-varying activation curves using three typical factorization algorithms including principal component analysis (PCA), independent component analysis (ICA), and nonnegative matrix factorization (NMF). The activation signal of the target muscle was obtained by summing the activation curves, and the FOS algorithm was used to create basis functions with activation signals and establish the force estimation model. Static isometric elbow flexion experiments at three target levels were performed on seven male subjects, and the force estimation performances were compared among three typical factorization algorithms as well as a conventional method for extracting the average signal envelope of all HD-SEMG channels (AVG-ENVLP method). The overall root mean square difference (RMSD) values between the measured forces and the estimated forces obtained by different methods were 11.79 +/- 4.29% for AVG-ENVLP, 9.74 +/- 3.77% for PCA, 9.59 +/- 3.81% for ICA, and 9.51 +/- 4.82% for NMF. The results demonstrated that, compared to the conventional AVG-ENVLP method, factorization algorithms could substantially improve the performance of force estimation. The FOS method coupled with factorization algorithms provides an effective way to estimate the combined force of multiple muscles and has potential value in the fields of sports biomechanics, gait analysis, prosthesis control strategy, and exoskeleton devices for assisted rehabilitation.

关键词： high-density SEMG factorization algorithms fast orthogonal search muscle force estimation

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Development of Large Numbers factorization Algorithm 10

Development of Large Numbers Factorization Algorithm

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10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems - Technology and Applications (IDAACS)

作者： Illiashenko, Oleg Pevnev, Vladimir Natl Aerosp Univ Kharkiv Aviat Inst 17 Chkalov Str UA-61070 Kharkiv Ukraine

ISBN: (纸本)9781728140681

The paper analyzes existing factorization algorithms and classifies them. The elaboration of the factorization algorithm which allows working with both small and large numbers is presented. Whereas the replacement of operations of addition and multiplication by the operation of addition, in comparison with the existing algorithms, a large gain of time is achieved. The initiation of operation of inequality solution allows cutting up to N-1/4 of possible candidates for a single calculation step. The evaluation of the time of the algorithm was conducted. It is comparable to the best known.

关键词： factorization algorithms numerical methods primes algorithm complexity organization of calculations

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A modification of the Dewilde-van der Veen method for inversion of finite structured matrices

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LINEAR ALGEBRA AND ITS APPLICATIONS 2002年 343卷 419-450页

作者： Eidelman, Y Gohberg, I Tel Aviv Univ Raymond & Beverly Sackler Fac Exact Sci Sch Math Sci IL-69978 Tel Aviv Israel

We study a class of block structured matrices R = {R-ij}(i,j=1)(N) with a property that the solution of the corresponding system Rx = y of linear algebraic equations may be performed for O(N) arithmetic operations. In this paper for finite invertible matrices we analyze in detail factorization and inversion algorithms. These algorithms are related to those suggested by P.M. Dewilde and A.J. van der Veen (Time-varying Systems and Computations, Kluwer Academic Publishers, New York, 1998) for a class of finite and infinite matrices with a small Hankel rank. The algorithms presented here are more transparent and are a modification of the algorithms from the above reference, The approach and the proofs are essentially different from those in the above-mentioned reference. The paper contains also analysis of complexity and results of numerical experiments. (C) 2002 Elsevier Science Inc. All rights reserved.

关键词： structured matrices linear complexity algorithms inversion algorithms factorization algorithms solution of linear equations

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Combining modules for movement

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BRAIN RESEARCH REVIEWS 2008年第1期57卷 125-133页

作者： Bizzi, E. Cheung, V. C. K. d'Avella, A. Saltiel, P. Tresch, M. MIT 46 6189 Dept Brain & Cognit Sci Cambridge MA 02139 USA MIT 43 6189 McGovern Inst Brain Res Cambridge MA 02139 USA MIT Cambridge MA 02139 USA Harvard Univ Sch Med Div Hlth Sci & Technol Cambridge MA 02138 USA Fdn Santa Lucia Inst Ricovero & Cura Carattere Sci Dept Neuromotor Physiol Rome Italy Northwestern Univ Dept Biomed Engn Evanston IL 60208 USA Rehabil Inst Chicago Chicago IL 60611 USA

We review experiments supporting the hypothesis that the vertebrate motor system produces movements by combining a small number of units of motor output. Using a variety of approaches such as microstimulation of the spinal cord, NMDA iontophoresis, and an examination of natural behaviors in intact and deafferented animals we have provided evidence for a modular organization of the spinal cord. A module is a functional unit in the spinal cord that generates a specific motor output by imposing a specific pattern of muscle activation. Such an organization might help to simplify the production of movements by reducing the degrees of freedom that need to be specified. (c) 2007 Elsevier B.V. All rights reserved.

关键词： modular organization spinal cord muscle synergies factorization algorithms

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GENERATION OF OPTIMAL CODE FOR EXPRESSIONS VIA factorization

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COMMUNICATIONS OF THE ACM 1969年第6期12卷 333-&页

作者： BREUER, MA Univ. of Southern California Los Angeles CA

Given a set of expressions which are to be compiled, methods are presented for increasing the efficiency of the object code produced by first factoring the expressions, i.e. finding a set of subexpressions each of which occurs in two or more other expressions or subexpressions. Once all the factors have been ascertained, a sequencing procedure is applied which orders the factors and expressions such that all information is computed in the correct sequence and factors need be retained in memory a minimal amount of time. An assignment algorithm is then executed in order to minimize the total number of temporary storage cells required to hold the results of evaluating the factors. In order to make these techniques computationally feasible, heuristic procedures are applied, and hence global optimal results are not necessarily generated. The factorization algorithms are also applicable to the problem of factoring Boolean switching expressions and of factoring polynomials encountered in symbol manipulating systems.

关键词： code optimization detection of common subexpressions factorization algorithms factorization of Boolean expressions sequencing of operations

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Symbolic Computation Applied to the Study of the Kernel of Special Classes of Paired Singular Integral Operators

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MATHEMATICS IN COMPUTER SCIENCE 2021年第1期15卷 63-90页

作者： Conceicao, Ana C. Univ Algarve Dept Matemat Ctr Funct Anal Linear Struct & Applicat CEAFEL P-8005139 Faro Portugal

Operator theory has many applications in several main scientific research areas (structural mechanics, aeronautics, quantum mechanics, ecology, probability theory, electrical engineering, among others) and the importance of its study is globally acknowledged. On the study of the operator's kernel some progress has been achieved for some specific classes of singular integral operators whose properties allow the use of particular strategies. However, the existing algorithms allow, in general, to study the dimension of the kernel of some classes of singular integral operators but are not designed to be implemented on a computer. The main goal of this paper is to show how the symbolic and numeric capabilities of a computer algebra system can be used to study the kernel of special classes of paired singular integral operators with essentially bounded coefficients defined on the unit circle. It is described how some factorization algorithms can be used to compute the dimension of the kernel of special classes of singular integral operators. The analytical algorithms [ADimKerPaired-Scalar], [AKerPaired-Scalar], and [ADimKerPaired-Matrix] are presented. The design of these new algorithms was focused on the possibility of implementing on a computer all the extensive symbolic and numeric calculations present in the algorithms. For the essentially bounded hermitian coefficients case, there exist some relations with Hankel operators. The paper contains some interesting and nontrivial examples obtained with the use of a computer algebra system.

关键词： Symbolic computation Kernel of paired singular integral operators factorization algorithms Essentially bounded matrix functions Wolfram Mathematica

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Computing LZ78-Derivates with Suffix Trees

Computing LZ78-Derivates with Suffix Trees

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Data Compression Conference (DCC)

作者： Koppl, Dominik Univ Yamanashi Kofu Yamanashi Japan

ISBN: (纸本)9798350385885;9798350385878

We propose algorithms computing the semi-greedy Lempel-Ziv 78 (LZ78), the Lempel-Ziv Double (LZD), and the Lempel-Ziv-Miller-Wegman (LZMW) factorizations in linear time for integer alphabets. For LZD and LZMW, we additionally propose data structures that can be constructed in linear time, which can solve the substring compression problems for these factorizations in time linear in the output size.

关键词： lossless data compression factorization algorithms substring compression

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Symbolic Computation Applied to the Study of the Kernel of a Singular Integral Operator with Non-Carleman Shift and Conjugation

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MATHEMATICS IN COMPUTER SCIENCE 2016年第3期10卷 365-386页

作者： Conceicao, Ana C. Marreiros, Rui C. Pereira, Jose C. Univ Algarve Dept Matemat Fac Ciencias & Tecnol Ctr Funct Anal Linear Struct & Applicat CEAFEL P-8005139 Faro Portugal Univ Algarve Fac Ciencias & Tecnol Dept Engn Elect & Informat Ctr Environm & Sustainabil Res CENSE P-8005139 Faro Portugal

On the Hilbert space the singular integral operator with non-Carleman shift and conjugation is considered, where are the Cauchy projectors, , , , are continuous functions on the unit circle , U is the shift operator and C is the operator of complex conjugation. We show how the symbolic computation capabilities of the computer algebra system Mathematica can be used to explore the dimension of the kernel of the operator K. The analytical algorithm [ADimKer-NonCarleman] is presented;several nontrivial examples are given.

关键词： Singular integral operators Non-Carleman shift Conjugation Kernel dimension factorization algorithms Symbolic computation Wolfram Mathematica

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Computing Lexicographic Parsings

Computing Lexicographic Parsings

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Data Compression Conference (DCC)

作者： Koppl, Dominik Tokyo Med & Dent Univ M&D Data Sci Ctr Tokyo Japan

We give memory-friendly algorithms computing the compression schemes plcpcomp or lex-parse in linear or near-linear time, and give upper and lower bounds on the space requirements of our algorithm computing plcpcomp.

ISBN: (纸本)9781665478939

关键词： lossless data compression factorization algorithms memory-efficiency

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Exploring the Spectra of Some Classes of Singular Integral Operators with Symbolic Computation

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MATHEMATICS IN COMPUTER SCIENCE 2016年第2期10卷 291-309页

作者： Conceicao, Ana C. Pereira, Jose C. Univ Algarve Ctr Funct Anal Linear Struct & Applicat CEAFEL Fac Ciencias & Tecnol Dept Matemat P-8005139 Faro Portugal Univ Algarve Ctr Funct Anal Linear Struct & Applicat CEAFEL Ctr Environm & Sustainabil Res CENSE Dept Engn Elect & InformatFac Ciencias & Tecnol P-8005139 Faro Portugal

Spectral theory has many applications in several main scientific research areas (structural mechanics, aeronautics, quantum mechanics, ecology, probability theory, electrical engineering, among others) and the importance of its study is globally acknowledged. In recent years, several software applications were made available to the general public with extensive capabilities of symbolic computation. These applications, known as computer algebra systems (CAS), allow to delegate to a computer all, or a significant part, of the symbolic calculations present in many mathematical algorithms. In our work we use the CAS Mathematica to implement for the first time on a computer analytical algorithms developed by us and others within the Operator Theory. The main goal of this paper is to show how the symbolic computation capabilities of Mathematica allow us to explore the spectra of several classes of singular integral operators. For the one-dimensional case, nontrivial rational examples, computed with the automated process called [ASpecPaired-Scalar], are presented. For the matrix case, nontrivial essentially bounded and rational examples, computed with the analytical algorithms [AFact], [SInt], and [ASpecPaired-Matrix], are presented. In both cases, it is possible to check, for each considered paired singular integral operator, if a complex number (chosen arbitrarily) belongs to its spectrum.

关键词： Spectral algorithms factorization algorithms Paired singular integral operators Essentially bounded matrix functions Rational matrix functions Wolfram Mathematica

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