1,721,011 research outputs found
Relaxation to the asymptotic distribution of global errors due to round off
No full textWe propose an analysis of the effects introduced by finite accuracy and round-off
arithmetic on discrete dynamical systems. We investigate, from a statistical viewpoint and using
the tool of the decay of fidelity, the error of the numerical orbit with respect to the exact one. As a
model we consider a random perturbation of the exact orbit with an additive noise, for which exact
results can be obtained for some prototype maps. For regular anysocrounous maps the fidelity has
a power law decay, whereas the decay is exponential if a random perturbation is introduced. For
chaotic maps the decay is superexponential after an initial plateau and our method is suitable to
identify the reliability threshold of numerical results, i.e. a number of iterations below which global
errors can be ignored. The same behaviour is observed if a random perturbation is introduced
Asymptotic distribution of global errors in the numerical computations of dynamical systems
Full text linkWe propose an analysis of the effects introduced by finite-accuracy and round-off arithmetic on numerical computations of discrete dynamical systems. Our method, which uses
the statistical tool of the decay of fidelity, computes the error by directly comparing the
numerical orbit with the exact one (or, more precisely, with another numerical orbit computed with a much higher accuracy). Furthermore, as a model of the effects of round-off
arithmetic on the map, we also consider a random perturbation of the exact orbit with
an additive noise, for which exact results can be obtained for some prototype maps. We
investigate the decay laws of fidelity and their relationship with the error probability distribution for regular and chaotic maps, for both additive and numerical noise. In particular,
for regular maps we find an exponential decay for additive noise, and a power-law decay
for numerical noise. For chaotic maps, numerical noise is equivalent to additive noise, and
our method is suitable for identifying a threshold for the reliability of numerical results, i.e.,
the number of iterations below which global errors can be ignored. This threshold grows
linearly with the number of bits used to represent real numbers
Analysis of Bank Leverage via Dynamical Systems and Deep Neural Networks
Full text linkWe consider a model of a simple financial system consisting of a leveraged investor that invests in a risky asset and manages risk by using value-at-risk (VaR). The VaR is estimated by using past data via an adaptive expectation scheme. We show that the leverage dynamics can be described by a dynamical system of slow-fast type associated with a unimodal map on [0,1] with an addi-tive heteroscedastic noise whose variance is related to the portfolio rebalancing frequency to target leverage. In absence of noise the model is purely deterministic and the parameter space splits into two regions: (i) a region with a globally attracting fixed point or a 2-cycle; (ii) a dynamical core region, where the map could exhibit chaotic behavior. Whenever the model is randomly perturbed, we prove the existence of a unique stationary density with bounded variation, the stochastic stability of the process, and the almost certain existence and continuity of the Lyapunov exponent for the stationary measure. We then use deep neural networks to estimate map parameters from a short time series. Using this method, we estimate the model in a large dataset of US commercial banks over the period 2001--2014. We find that the parameters of a substantial fraction of banks lie in the dynamical core, and their leverage time series are consistent with a chaotic behavior. We also present evidence that the time series of the leverage of large banks tend to exhibit chaoticity more frequently than those of small banks
DYNAMIC INTEGRAL TRANSFORM ON FRACTAL SETS AND THE COMPUTATION OF ENTROPY
No full textWe introduce an integral transform of wavelet type, which we call
Dynamical Integral Transform, and we show that it can be used to compute
the second Renyi entropy for a large class of invariant measures. The
method is then generalized to the whole spectrum of the Renyi entropies
and establishes a correspondence between thermodynamic formalism and the
Dynamical Integral Transform of expanding strange sets. Numerical
examples are presented
Error distribution in randomly perturbed orbits
Full text linkGiven an observable f defined on the phase space of some dynamical system generated by the map
T, we consider the error between the value of the function f(T^n x0) computed at time n along the
orbit with initial condition x0 , and the value f(T^n_omega x0) of the same observable computed by replacing the map T n with the composition of maps T_omegai , where each T_omega is chosen randomly, by varying omega, in a neighborhood of size epsilon of T. We show that the random variable Delta^epsilon_n=f(T^n x0)-f(T_omega^n x0), depending on the initial condition x0 and on the choice of the realization omega , will converge in distribution when n → infinity to what we call the asymptotic error. We study in detail the density of the distribution function of the asymptotic error for a wide class of dynamical systems perturbed with additive noise: for a few of them we give rigorous results, for the others we provide a numerical investigation. Our study is intended as a model for the effects of numerical noise due to roundoff on dynamical systems
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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