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Topic: Lyapunov test

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	Aleksandr Lyapunov: Dictionary definition and more
		Lyapunov had already begun to study this stability in his previous two-years attempts at solving the task.
		Lyapunov had lectured already from 1880 at the faculty for mechanics and this had taken him a lot of time.
		Lyapunov lectured at the university on themes from theoretical mechanics, integrals of differential equations and the theory of probability.
	www.encyclopedian.com /al/Aleksandr-Lyapunov.html (1628 words)

	Encyclopedia: Lyapunov (Site not responding. Last check: 2007-11-07)
		Aleksandr Mikhailovich Lyapunov (Александр Михайлович Ляпунов) (June 6, 1857 - November 3, 1918, all new style) was a Russian mathematician, mechanician and physicist.
		Lyapunov wrote his first independent scientific works under the guidance of professor of mechanics, D. Bobylev.
		Lyapunov had lectured already from 1880 at the Department of Mechanics and this had taken him a lot of time.
	www.nationmaster.com /encyclopedia/Lyapunov (1670 words)

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		A scraping, brushing, or smear, is taken from the surface of the vagina or cervix and is prepared on a slide and stained for microscopic examination and cytological analysis.
		Turing test Turing test, a procedure to test whether a computer is capable of humanlike thought.
		Marsh test Marsh test, method for the detection of arsenic, so sensitive that it can be used to detect minute amounts of arsenic in foods (the residue of fruit spray) or in stomach contents.
	www.encyclopedia.com /searchpool.asp?target=Lyapunov+test (338 words)

	Aleksandr Lyapunov -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Lyapunov was born in (Click link for more info and facts about Yaroslavl) Yaroslavl, (Click link for more info and facts about Imperial Russia) Imperial Russia.
		Lyapunov had already begun to study this (The quality or attribute of being firm and steadfast) stability in his previous two-years attempts at solving the task.
		Lyapunov lectured at the university on themes from theoretical mechanics, (The result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x)) integrals of (An equation containing differentials of a function) differential equations and the (Click link for more info and facts about theory of probability) theory of probability.
	www.absoluteastronomy.com /encyclopedia/A/Al/Aleksandr_Lyapunov.htm (1992 words)

	Encyclopedia: Lyapunov test (Site not responding. Last check: 2007-11-07)
		The Lyapunov exponent or Lyapunov characteristic exponent of a dynamical system is a measure that determines for each point of phase space, how quickly trajectories that begin in this point diverge over time.
		Actually, the number of Lyapunov exponents is equal to the number of dimensions of the embedding phase space, but it is common to just refer to the largest one, because it determines the predictability of a dynamical system.
		The Lyapunov test, also known as the Lyapunov exponent, the methods of approximation by Aleksandr Lyapunov which provide ways of determining the stability of sets of ordinary differential equations (determining the prediction horizon).
	www.nationmaster.com /encyclopedia/Lyapunov-test (391 words)

	NONLINEARITY TEST FOR ISTANBUL STOCK EXCHANGE (Site not responding. Last check: 2007-11-07)
		BDS test is the most widely used nonlinearity test may be because of no distributional assumption, or easily applied to time series, or theory behind it.
		NEGM is a procedure for testing for chaos by estimating the dominant Lyapunov exponent.
		Test statistics is given in the table 4 shows that null hypothesis of linearity cannot be rejected.
	idari.cu.edu.tr /sempozyum/bil3.htm (3267 words)

	MOTOTSUGU SHINTANI
		Such a test is useful in the identification of permanent and temporary shocks within the framework of the exogenous model.
		An earlier test proposed by Johansen (1991) involves parametric estimation of a vector autoregressive (VAR) model, and it is known that the performance of this test is sensitive to the misspecification.
		With an appropriate standardization, the test statistic is shown to have a nuisance parameter free limiting distribution and to be consistent under reasonable conditions.
	www.econ.yale.edu /graduate/placement/1999-00/shintani.htm (980 words)

	Dictionary of Meaning www.mauspfeil.net
		The '''Lyapunov exponent''' or '''Lyapunov characteristic exponent''' of a dynamical system is a measure (mathematics) measure that characterizes rate of separation of infinitesimally close trajectory trajectories.
		Lyapunov spectrum can be used as a tool in analysis of a system.
		The inverse of the largest Lyapunov exponent is sometimes referred in literature as ''Lyapunov time'', and defines the characteristic e-folding time.
	www.mauspfeil.net /Lyapunov_exponent.html (516 words)

	Papers (Site not responding. Last check: 2007-11-07)
		In particular, we develop the asymptotic theory of the inf-t test for the null hypothesis of a unit root in a wide class of nonlinear autoregressive models having parameters that are identified only under the alternative of stationarity.
		The critical values of the test are provided for some of the commonly used models under the conventional specification of the parameter space.
		The results are applied to an average derivative based test for martingale hypothsis, nonlinear half-life measure of mean reversion and a Lyapunov exponent based test for chaos and random walk.
	www.vanderbilt.edu /econ/faculty/Shintani/paper.html (1284 words)

	README for NETLE 2.1
		Neural networks are estimated by the method of nonlinear least squares (NLS) (Kuan and Liu (1995)); Lyapunov exponents are calculated from the derivative matrices of estimated network models (Gencay and Dechert (1992)).
		Note that a positive Lyapunov exponent indicates that the underlying series is chaotic.
		Hiddens 1: MSE =.226113 SIC = -1.35426 Lyapunov Exponents: lambda(1) = -1.451576 lambda(2) = -4.839406 Hiddens 2: MSE =.744204E-08 SIC = -18.4777 Lyapunov Exponents: lambda(1) =.4331328 lambda(2) = -1.636965 The values of lambda's are the estimated Lyapunov exponents.
	web.bsu.edu /tliu/research/readme2.html (1492 words)

	0-1 test (Site not responding. Last check: 2007-11-07)
		We describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic.
		In contrast to the usual method of computing the maximal Lyapunov exponent, our method is applied directly to the time series data and does not require phase space reconstruction.
		The test is universally applicable to any deterministic dynamical system, in particular to ordinary and partial differential equations, and to maps.
	www.maths.surrey.ac.uk /personal/st/I.Melbourne/papers/01chaos.html (161 words)

	Smoothing Marmousi model
		The Lyapunov exponent is averaged over the angles with a uniform weight, in accordance with the isotropic Sobolev scalar products used for smoothing.
		Although the Lyapunov exponent is little bit better than we formerly required, it is not as small as to decrease the smoothness of the model without testing ray tracing and the widths of Gaussian beams in the model.
		Unlike all previous tests, the standard halfwidths of Gaussian beams indicate that the model is at the edge of applicability of Gaussian beams and Gaussian packets, because of too small frequencies for the high-frequency asymptotic methods.
	seis.karlov.mff.cuni.cz /software/sw3dcd7/data/mar/mar-inv.htm (1420 words)

	Global Dynamics Section’s Annual Scientific Report (FY97) (Site not responding. Last check: 2007-11-07)
		Within GDS the purpose of diagnostic analyses is twofold, diagnosis is used to test theoretical ideas concerning the mechanisms responsible for climate variations and their relative import and also test (i.e., validate) the behavior of comprehensive climate models like the CCM against that of the observed climate system.
		This was a very strict test to pass, because the magnitudes of the perturbations grew by factors of ten or more.
		Tests using the adjoint version of MAMS to estimate perturbed precipitation accumulations from significantly large, initial condition perturbations revealed high accuracy in regions of strong cyclogenesis where precipitation was strong.
	www.cgd.ucar.edu /asr97/gds.html (4406 words)

	[No title]
		Roughly speaking, a test body is in resonance with the perturber if the ratio of the orbital periods of the test body and the perturber is rational, or \be %$ {a\over a'}\approx\left({k\over k+q}\right)^{2/3}, \ee %$ where $k$ and $q$ are integers.
		This arises because of the near certainty that a test particle on a chaotic orbit that crosses the orbit of the perturbing body will be removed from the system by a near encounter or collision with the perturber.
		The Lyapunov times of the orbits in the $7:4$ resonance are longer than those of particles in the $5:3$ resonance, yet the removal time for objects in the $5:3$ resonance are nearly an order of magnitude longer than those found for objects in the $7:4$ resonance.
	www.cita.utoronto.ca /~murray/Work/Asteroids/Diffusion/ms.tex (5234 words)

	NEA-1551: ZZ BWRSB-FORSMARKS, Stability Benchmark Data from BWR FORSMARKS 1 and 2 (Site not responding. Last check: 2007-11-07)
		Typically, the main stability parameters are assumed to be the decay ratio (DR) and the frequency of the oscillation.
		In fact, the Lyapunov exponents are also a measure of the stability of the neutronic time series.
		The data given in this benchmark were obtained during several stability tests performed at the Swedish BWR reactors Forsmarks 1 and 2, in the period 1989 to 1997.
	www.nea.fr /abs/html/nea-1551.html (1140 words)

	[No title]
		"Testing for Stochastic Dominance Efficiency" (with Thierry Post and Yoon-Jae Whang) We propose a new test of the stochastic dominance efficiency of a given asset over a class of portfolios.
		A nonparametric test using consistent standard errors "(with M. Shintani) A positive Lyapunov exponent is one practical definition of chaos.
		We develop a formal test for chaos in a noisy system based on estimates of the sign of the Lyapunov exponent.
	econ.lse.ac.uk /staff/olinton/research (3430 words)

	Manchester Applied Mathematics and Numerical Analysis Seminars (Site not responding. Last check: 2007-11-07)
		A new test for chaos in deterministic nonlinear dynamical systems Abstract: Recently, Georg Gottwald (Sydney) and I developed a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic.
		Moreover, the test is applied directly to the time series data, so the underlying equations need not be known.
		In this talk, I will describe (i) How the test is implemented, and comparison with the Lyapunov exponent method; (ii) Why the test works (rigorous ergodic-theoretical results of Ashwin, Field, Nicol, Torok and myself).
	www.ma.man.ac.uk /~hewitt/DeptWeb/Abstracts/Melbourne.html (150 words)

	0-1 test (Site not responding. Last check: 2007-11-07)
		Recently, we introduced a new test for distinguishing regular from chaotic dynamics in deterministic dynamical systems and argued that the test had certain advantages over the traditional test for chaos using the maximal Lyapunov exponent.
		In this paper, we investigate the capability of the test to cope with moderate amounts of noisy data.
		Comparisons are made between an improved version of our test and both the ``tangent space'' and ``direct method'' for computing the maximal Lyapunov exponent.
	www.maths.surrey.ac.uk /personal/st/I.Melbourne/papers/noise.html (126 words)

	Nonlinear Science FAQ (Site not responding. Last check: 2007-11-07)
		Lyapunov was born in Russia in 6 June 1857.
		Lyapunov was interested in showing how to discover if a solution to a dynamical system is stable or not for all times.
		Thus given a time series that we are testing for determinism we (1) pick a test state (2) search the time series for a similar or 'nearby' state and (3) compare their respective time evolution.
	www.faqs.org /faqs/sci/nonlinear-faq (11547 words)

	A New Test for Chaotic Dynamics Using Lyapunov Exponents (Site not responding. Last check: 2007-11-07)
		We propose a new test to detect chaotic dynamics, based on the stability of the largest Lyapunov exponent from different sample sizes.
		This test is applied to the data used in the single-blind controlled competition tests for nonlinearity and chaos that were generated by Barnett et al.
		The test size is one for large samples, although for small sample sizes it diminishes below the nominal size for two out of the three chaotic processes considered, what is not a surprise given some well-known properties of such processes.
	www.uv.es /bibsoc/GM/data/Papers/fdafdaddt2003-09.html (163 words)

	FORTRAN source code and manual for NEGM's (Nychka, Ellner, Gallant, and McCaffrey) LENNS ("Lyapunov Exponent of Noisy ... (Site not responding. Last check: 2007-11-07)
		This is the FORTRAN source code and manual for the NEGM LENNS test for noisy chaos.
		This test was among those entered into the single blind controlled competition run by Barnett et al.
		The competition was among tests for nonlinearity and tests for chaos.
	econwpa.wustl.edu /eprints/prog/papers/9603/9603002.abs (524 words)

	Planetary Systems (Site not responding. Last check: 2007-11-07)
		They considered the planets to be test particles moving in the field of an eccentric binary system, and studied a range of values of the binary eccentricity and mass ratio.
		The theory predicts the location and extent in (a,e) space of the chaotic motion, the Lyapunov time, and the removal time of bodies on chaotic orbits.
		The latter is given by the time for test bodies with small initial eccentricities to diffuse to the eccentricity at which they cross the orbit of the perturbing body.
	www.cita.utoronto.ca /webpages/CITA/annrep96/node34.html (1434 words)

	Testing Chaotic Dynamics via Lyapunov Exponents... (Site not responding. Last check: 2007-11-07)
		In this paper, we propose a new test, based on the stability of the largest Lyapunov exponent from different sample sizes, to detect chaotic dynamics in economic and financial time series.
		We apply this new test to the simulated data used in the single-blind controlled competition among tests for for nonlinearity and chaos provided by Barnet et al.
		The results suggest that the new test has high power against different stochastic alternatives (both linear and nonlinear) and that behaves well in small samples.
	db.socionet.nw.ru /RuPEc/xml/fda/paper-fdaddt/fdafdaddt2000-07.xml (96 words)

	Titration of chaos with added noise -- Poon and Barahona 98 (13): 7107 -- Proceedings of the National Academy of ...
		Chaos is indicated by a positive Lyapunov exponent LE (blue, right scale), as derived analytically from the noiseless map.
		The noise limit NL (red, left scale) is the minimum amount of added white noise that prevents the detection of nonlinearity in the data.
		test of chaos but also a measure of its relative intensity.
	www.pnas.org /cgi/content/full/98/13/7107 (4668 words)

	EconPapers: Random Walk or Chaos: A Formal Test on the Lyapunov Exponent (Site not responding. Last check: 2007-11-07)
		The test is based on the Nadaraya-Watson kernel estimate of the Lyapunov exponent.
		We show that the estimator is consistent: The estimated Lyapunov exponent converges to zero under the random walk hypothesis, while it converges to a positive constant for the chaotic system.
		It is shown that the null distribution of the test statistic is given by the range of standard Brownian motion on the unit interval.
	netec.wustl.edu /WoPEc/data/Papers/snuioerwpno9.html (343 words)

	[No title]
		All points between (and including) the ; lower and upper limits are considered in the ; "linear part" for each shell.
		Each element ; is the value of the scale-dependent Lyapunov ; exponent for a shell interval (see Shell_Bounds).
		To ; test these derivatives, we take the absolute value of the derivatives ; and normalize them by their maximum values and then test against ; zerotest and nonzerotest.
	www.johnny-lin.com /idl_code/scale_lyapunov.pro (1636 words)

	Notes 31 -
		We test the developed model on a step lane change maneuver and propose a model-reference based controller for remote control of a vehicle.
		Closed loop tests enable us to analyse the interaction between the control system and the actions of the drivers.
		The presented tests clearly show the increase of primary safety caused by slip control systems in passenger cars, as well as the danger that is to be seen in systems which do not operate properly.
	www.eng.warwick.ac.uk /~esrql/notes031.htm (3701 words)

	Research Interests (Site not responding. Last check: 2007-11-07)
		Recently, Georg Gottwald and I have developed a new 0-1 test for chaos.
		This test appears to have many advantages over the standard test of computing the maximal Lyapunov exponent.
		Here is an improved version of the 0-1 test that works well with moderately noisy data (and which seems to compare favourably with the maximal Lyapunov exponent).
	www.math.uh.edu /~ism (302 words)

	File Name
		The Hansen test of Overidentifying Restrictions is used in an instrumental variables context.
		This tests for homoscedasticity of the residuals in eq1 based on the auxiliary regression of the squared residuals against the explanatory variables listed in vlist.
		The Lagrange Multiplier test is a general test for testing the restrictions imposed on a model, when the model estimated is the restricted model.
	www.econotron.com /gaussx/readme2.htm (14228 words)

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