951 research outputs found
Ergodic Properties of Classical SU(2) Lattice Gauge Theory
We investigate the relationship between the Lyapunov exponents of periodic
trajectories, the average and fluctuations of Lyapunov exponents of ergodic
trajectories, and the ergodic autocorrelation time for the two-dimensional
hyperbola billiard. We then study the fluctuation properties of the ergodic
Lyapunov spectrum of classical SU(2) gauge theory on a lattice. Our results are
consistent with the notion that this system is globally hyperbolic. Among the
many powerful theorems applicable to such systems, we discuss one relating to
the fluctuations in the entropy growth rate.Comment: 21 pages, 7 figure
Continuous time random walk, Mittag-Leffler waiting time and fractional diffusion: mathematical aspects
We show the asymptotic long-time equivalence of a generic power law waiting
time distribution to the Mittag-Leffler waiting time distribution,
characteristic for a time fractional CTRW. This asymptotic equivalence is
effected by a combination of "rescaling" time and "respeeding" the relevant
renewal process followed by a passage to a limit for which we need a suitable
relation between the parameters of rescaling and respeeding. Turning our
attention to spatially 1-D CTRWs with a generic power law jump distribution,
"rescaling" space can be interpreted as a second kind of "respeeding" which
then, again under a proper relation between the relevant parameters leads in
the limit to the space-time fractional diffusion equation. Finally, we treat
the `time fractional drift" process as a properly scaled limit of the counting
number of a Mittag-Leffler renewal process.Comment: 36 pages, 3 figures (5 files eps). Invited lecture by R. Gorenflo at
the 373. WE-Heraeus-Seminar on Anomalous Transport: Experimental Results and
Theoretical Challenges, Physikzentrum Bad-Honnef (Germany), 12-16 July 2006;
Chairmen: R. Klages, G. Radons and I.M. Sokolo
Theoretical Interpretations and Applications of Radial Basis Function Networks
Medical applications usually used Radial Basis Function Networks just as Artificial Neural Networks. However, RBFNs are Knowledge-Based Networks that can be interpreted in several way: Artificial Neural Networks, Regularization Networks, Support Vector Machines, Wavelet Networks, Fuzzy Controllers, Kernel Estimators, Instanced-Based Learners. A survey of their interpretations and of their corresponding learning algorithms is provided as well as a brief survey on dynamic learning algorithms. RBFNs' interpretations can suggest applications that are particularly interesting in medical domains
Forecast Uncertainties in Macroeconomics Modelling: An Application to the UK Economy
This paper argues that probability forecasts convey information on the uncertainties that surround marco-economic forecasts in a manner which is straightforward and which is preferable to other alternatives, including the use of confidence intervals. Probability forecasts relating to UK output growth and inflation, obtained using a small macro-econometric model, are presented. We discuss in detail the probability that inflation will fall within the Bank of England's target range and that recession will be avoided, both as separate single events and jointly. The probability forecasts are also used to provide insights on the interrelatedness of output growth and inflation outcomes at different horizons.Probability Forecasting, Long Run Structural VARs, Macroeconometric Modelling, Forecast Evaluation, Probability Forecasts of Inflation and Output Growth
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