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FPGA-based implementation of recursive algorithms

MICROPROCESSORS AND MICROSYSTEMS 2004年第5-6期28卷 197-211页

作者： Sklyarov, V Univ Aveiro IEETA Dept Elect & Telecommun P-3810193 Aveiro Portugal

The paper suggests a novel method for implementing recursive algorithms in hardware. The required support for recursion has been provided through a modular and a hierarchical specification of it control unit that can be translated to an implementation of the respective hardware circuit on the basis of a recursive hierarchical finite state machine and through a mechanism that permits the contents of an execution unit to be stored/restored between hierarchical calls/retums. The paper describes all the details that are required to implement recursive algorithms in hardware. It begins with software (C++) models and finishes with synthesizable VHDL codes. Two practical applications of recursive algorithms in the data sorting and compression area have been studied in detail. (C) 2004 Elsevier B.V. All rights reserved.

关键词： recursive algorithms hierarchical finite state machines sorting binary tree data compression

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WEAK-CONVERGENCE AND LOCAL STABILITY PROPERTIES OF FIXED STEP-SIZE recursive algorithms

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IEEE TRANSACTIONS ON INFORMATION THEORY 1993年第3期39卷 966-978页

作者： BUCKLEW, JA KURTZ, TG SETHARES, WA UNIV WISCONSIN DEPT MATHMADISONWI 53706

A recursive equation which subsumes several common adaptive filtering algorithms is analyzed for general stochastic inputs and disturbances by relating the motion of the parameter estimate errors to the behavior of an unforced deterministic ordinary differential equation (ODE). Local stability of the ODE implies long term stability of the algorithm while instability of the differential equation implies nonconvergence of the parameter estimates. The analysis does not require continuity of the update equation, and the asymptotic distribution of the parameter trajectories for all stable cases (under some mild conditions) is shown to be an Ornstein-Uhlenbeck process. The ODE's describing the motion of several common adaptive filters are examined in some simple settings, including the least mean square (LMS) algorithm and all three of its signed variants (the signed regressor, the signed error, and the sign-sign algorithms). Stability and instability results are presented in terms of the eigenvalues of a correlation-like matrix. This generalizes known results for LMS, signed regressor and signed error LMS, and gives new stability criteria for the sign-sign algorithm. The ability of the algorithms to track moving parameterizations can be analyzed in a similar manner, by relating the time varying system to a forced ODE. The asymptotic distribution about the forced ODE is again (under similar conditions) an Ornstein-Uhlenbeck process, whose properties can be described in a straightforward manner.

关键词： WEAK CONVERGENCE ADAPTIVE FILTERS recursive algorithms

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The contraction method for recursive algorithms

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ALGORITHMICA 2001年第1-2期29卷 3-33页

作者： Rösler, U Rüschendorf, L Univ Kiel D-24118 Kiel Germany Univ Freiburg D-79104 Freiburg Germany

In this paper we give an introduction to the analysis of algorithms by the contraction method. By means of this method several interesting classes of recursions can be analyzed as particular cases of our general framework. We introduce the main steps of this technique which is based on contraction properties of the algorithm with respect to suitable probability metrics. Typically the limiting distribution is characterized as a fixed point of a limiting operator on the class of probability distributions. We explain this method in the context of several "divide and conquer" algorithms. In the second part of the paper we introduce a new quite general model for branching dynamical systems and explain that the contraction method can be applied in this model. This model includes many classical examples of random trees and gives a general frame for further applications.

关键词： recursive algorithms contraction method branching dynamical systems random trees branching process

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Emergence of Self-Reproducing Metabolisms as recursive algorithms in an Artificial Chemistry

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ARTIFICIAL LIFE 2022年第3-4期27卷 277-299页

作者： Kruszewski, German Mikolov, Tomas Naver Labs Europe Meylan France Czech Inst Informat Robot & Cybernet Prague Czech Republic Czech Tech Univ Prague Czech Republic

One of the main goals of Artificial Life is to research the conditions for the emergence of life, not necessarily as it is, but as it could be. Artificial chemistries are one of the most important tools for this purpose because they provide us with a basic framework to investigate under which conditions metabolisms capable of reproducing themselves, and ultimately, of evolving, can emerge. While there have been successful attempts at producing examples of emergent self-reproducing metabolisms, the set of rules involved remain too complex to shed much light on the underlying principles at work. In this article, we hypothesize that the key property needed for self-reproducing metabolisms to emerge is the existence of an autocatalyzed subset of Turing-complete reactions. We validate this hypothesis with a minimalistic artificial chemistry with conservation laws, which is based on a Turing-complete rewriting system called combinatory logic. Our experiments show that a single run of this chemistry, starting from a tabula rasa state, discovers-with no external intervention-a wide range of emergent structures including ones that self-reproduce in each cycle. All of these structures take the form of recursive algorithms that acquire basic constituents from the environment and decompose them in a process that is remarkably similar to biological metabolisms.

关键词： Artificial chemistry emergence self-reproduction metabolisms recursive algorithms

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Acoustic multiple scattering using recursive algorithms

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JOURNAL OF COMPUTATIONAL PHYSICS 2015年 299卷 787-803页

作者： Amirkulova, Feruza A. Norris, Andrew N. Rutgers State Univ Mech & Aerosp Engn Piscataway NJ 08854 USA

Acoustic multiple scattering by a cluster of cylinders in an acoustic medium is considered. A fast recursive technique is described which takes advantage of the multilevel Block Toeplitz structure of the linear system. A parallelization technique is described that enables efficient application of the proposed recursive algorithm for solving multilevel Block Toeplitz systems on high performance computer clusters. Numerical comparisons of CPU time and total elapsed time taken to solve the linear system using the direct LAPACK and TOEPLITZ libraries on Intel FORTRAN, show the advantage of the TOEPLITZ solver. Computations are optimized by multi-threading which displays improved efficiency of the TOEPLITZ solver with the increase of the number of scatterers and frequency. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Acoustics Multiple scattering Wave propagation recursive algorithms Computation methods Parallel computation OpenMP

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Laguerre based predictors in discrete-time recursive algorithms: A solution for open-loop identification under oversampling

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IFAC-PapersOnLine 2017年第1期50卷 12911-12918页

作者： Vau, Bernard Bourlès, Henri SATIE Ecole normale supérieure de Cachan Cachan94230 France

In this paper we propose a novel formulation of the predictor used in open-loop recursive identification algorithms. The predicted output is expressed by means of an orthogonal Laguerre transfer functions basis. This predictor representation presents many advantages: It makes it possible to identify robustly oversampled systems without any bias in low frequency, and to obtain relevant reduced order models. The Laguerre pole plays the role of a tuning parameter enabling the selection of the best approximation frequency area. The proposed schemes address both output error and ARMAX systems. Simulation and experimental results show all the practical benefits provided by these algorithms. © 2017

关键词： Transfer functions Orthogonal functions Adaptive Control ARMAX model Identification algorithms Laguerre Output error models recursive algorithms recursive estimation

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Using recursive algorithms for the efficient identification of smoothing spline ANOVA models

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ASTA-ADVANCES IN STATISTICAL ANALYSIS 2010年第4期94卷 367-388页

作者： Ratto, Marco Pagano, Andrea Commiss European Communities Joint Res Ctr I-21027 Ispra VA Italy

In this paper we present a unified discussion of different approaches to the identification of smoothing spline analysis of variance (ANOVA) models: (i) the "classical" approach (in the line of Wahba in Spline Models for Observational Data, 1990;Gu in Smoothing Spline ANOVA Models, 2002;Storlie et al. in Stat. Sin., 2011) and (ii) the State-Dependent Regression (SDR) approach of Young in Nonlinear Dynamics and Statistics (2001). The latter is a nonparametric approach which is very similar to smoothing splines and kernel regression methods, but based on recursive filtering and smoothing estimation (the Kalman filter combined with fixed interval smoothing). We will show that SDR can be effectively combined with the "classical" approach to obtain a more accurate and efficient estimation of smoothing spline ANOVA models to be applied for emulation purposes. We will also show that such an approach can compare favorably with kriging.

关键词： Smoothing spline ANOVA models recursive algorithms Backfitting Sensitivity analysis

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A general limit theorem for recursive algorithms and combinatorial structures

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ANNALS OF APPLIED PROBABILITY 2004年第1期14卷 378-418页

作者： Neininger, R Rüschendorf, L McGill Univ Sch Comp Sci Montreal PQ H3A 2K6 Canada Univ Freiburg Inst Math Stochast D-79104 Freiburg Germany

Limit laws are proven by the contraction method for random vectors of a recursive nature as they arise as parameters of combinatorial structures such as random trees or recursive algorithms, where we use the Zolotarev metric. In comparison to previous applications of this method, a general transfer theorem is derived which allows us to establish a limit law on the basis of the recursive structure and the asymptotics of the first and second moments of the sequence. In particular, a general asymptotic normality result is obtained by this theorem which typically cannot be handled by the more common l(2) metrics. As applications we derive quite automatically many asymptotic limit results ranging from the size of tries or m-ary search trees and path lengths in digital structures to mergesort and parameters of random recursive trees, which were previously shown by different methods one by one. We also obtain a related local density approximation result as well as a global approximation result. For the proofs of these results we establish that a smoothed density distance as well as a smoothed total variation distance can be estimated from above by the Zolotarev metric, which is the main tool in this article.

关键词： contraction method multivariate limit law asymptotic normality random trees recursive algorithms divide-and-conquer algorithm random recursive structures Zolotarev metric

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LARGE DEVIATIONS ANALYSIS OF SOME recursive algorithms WITH STATE DEPENDENT NOISE

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ANNALS OF PROBABILITY 1988年第4期16卷 1509-1536页

作者： DUPUIS, P BOSTON UNIV BOSTONMA 02215 UNIV MINNESOTA IMAMINNEAPOLISMN 55455

Consider the recursive, stochastic algorithm Xn+1ε=Xnε+εb(Xnε,ξn), where {ξn} is a random process and Xnε lives in Rd. algorithms of this type arise frequently in applications in control and communications, as well as elsewhere. In the study of the important long term behavior of such recursive algorithms the "large deviations" behavior of the system, which describes the asymptotics of the order 1 deviations of the system from its "mean" trajectory as ε tends to 0, plays a central role. Typical systems arising in communication theory and control often use complicated forcing terms involving correlated and state dependent noises and forcing terms with discontinuities. This paper presents a general approach for proving large deviations type theorems for such systems. The problem of proving such a theorem is considered first for the general case of a stochastic process with Lipschitz continuous sample paths. The assumptions are stated in terms of the conditional distribution of time increments of the process. After giving the proof in this general framework, we give several examples (in both continuous and discrete time) of driving terms that satisfy the hypotheses. The results are subsequently extended to a "projected" version of the discrete time model. The paper concludes with an application of the results to an automatic routing mechanism.

关键词： 60F10 62L20 asymptotic analysis large deviations recursive algorithms state dependent noises

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Applying Online Multiplayer Educational Games based on Generic Shells to Enhance Learning of recursive algorithms: Students' Preliminary Results 2

Applying Online Multiplayer Educational Games based on Gener...

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2nd European Conference on Games-Based Learning

作者： Rossiou, Eleni Papadakis, Spyros Univ Macedonia Thessaloniki Greece Hellen Open Univ Patras Greece

ISBN: (纸本)9781906638184

This paper provides a methodology for the implementation of an online multiplayer educational game during a virtual classroom. We investigate the students' preliminary results of applying a multiplayer Educational Game to enhance learning of recursive algorithms. The game was provided during synchronous tele-educational service complementary to f2f lecturing in the compulsory (first semester) course "algorithms with C" of the Department of Applied Informatics at the University of Macedonia, Greece. The Recursion game was embedded in one of a series of synchronous virtual classrooms, the Tutoring Tele-Meetings (TTMs) for complementing face-to-face classroom instruction in conventional higher education with methods and tools of Open and Distance Education. Virtual Classrooms were implemented on CENTRA Symposium platform, through the server of the Hellenic Open University. Educational games were created on the Online Educational Games Central (EGC) of TELUQ University of Quebec, Canada. Savie's online EGC was designed as a virtual meeting-place for those interested in using games for educational purposes. Teachers can choose between either using pre-defined available games. Teachers need to add the content based on pre-determined objectives to generate a new educational game adapted to their audience. Our goal using a synchronous educational game was to provide our students with the opportunity to our students to work together, to review, to ascertain misunderstandings and to integrate what they have learned about recursive algorithms. Thirty three (33) undergraduates of first semester "played" the web-based educational game "recursive algorithms", which was created based on the "Snakes and Ladders" shell. The usability of integrating an educational game based on EGC platform in virtual classrooms, the students' motivation and their perceptions and attitudes were investigated. In details, the way how students faced up the "game" educational approach and their results i

关键词： Educational game multiplayer recursive algorithms virtual classroom

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