Search Results

Perturbation of renewal processes

Description: Renewal theory began development in the early 1940s, as the need for it in the industrial engineering sub-discipline operations research had risen. In time, the theory found applications in many stochastic processes. In this thesis I investigated the effect of seasonal effects on Poisson and non-Poisson renewal processes in the form of perturbations. It was determined that the statistical analysis methods developed at UNT Center for Nonlinear Science can be used to detect the effects of seasonality on the data obtained from Poisson/non-Poisson renewal systems. It is proved that a perturbed Poisson process can serve as a paradigmatic model for a case where seasonality is correlated to the noise and that diffusion entropy method can be utilized in revealing this relation. A renewal model making a connection with the stochastic resonance phenomena is used to analyze a previous neurological experiment, and it was shown that under the effect of a nonlinear perturbation, a non-Poisson system statistics may make a transition and end up in the of Poisson basin of statistics. I determine that nonlinear perturbation of the power index for a complex system will lead to a change in the complexity characteristics of the system, i.e., the system will reach a new form of complexity.
Date: May 2008
Creator: Akin, Osman Caglar
Partner: UNT Libraries

A Dynamic and Thermodynamic Approach to Complexity.

Description: The problem of establishing the correct approach to complexity is a very hot and crucial issue to which this dissertation gives some contributions. This dissertation considers two main possibilities, one, advocated by Tsallis and co-workers, setting the foundation of complexity on a generalized, non-extensive , form of thermodynamics, and another, proposed by the UNT Center for Nonlinear Science, on complexity as a new condition that, for physical systems, would be equivalent to a state of matter intermediate between dynamics and thermodynamics. In the first part of this dissertation, the concept of Kolmogorov-Sinai entropy is introduced. The Pesin theorem is generalized in the formalism of Tsallis non-extensive thermodynamics. This generalized form of Pesin theorem is used in the study of two major classes of problems, whose prototypes are given by the Manneville and the logistic map respectively. The results of these studies convince us that the approach to complexity must be made along lines different from those of the non-extensive thermodynamics. We have been convinced that the Lévy walk can be used as a prototype model of complexity, as a condition of balance between order and randomness that yields new phenomena such as aging, and multifractality. We reach the conclusions that these properties must be studied within a dynamic rather than thermodynamic perspective. The second part focuses on the study of the heart beating problem using a dynamic model, the so-called memory beyond memory, based on the Lévy walker model. It is proved that the memory beyond memory effect is more obvious in the healthy heart beating sequence. The concepts of fractal, multifractal, wavelet transformation and wavelet transform maximum modulus (WTMM) method are introduced. Artificial time sequences are generated by the memory beyond memory model to mimic the heart beating sequence. Using WTMM method, the multifratal singular spectrums of the sequences ...
Date: August 2003
Creator: Yang, Jin
Partner: UNT Libraries

Reply to the Comment "Intercluster correlation in Seismicity" by Helmstetter and Sornette

Description: This paper is a reply to the comment by Helmstetter and Sornette titled "Intercluster correlation in Seismicity" which addresses an important point in a paper written by the authors that needs to be clarified.
Date: September 15, 2003
Creator: Mega, Mirko S.; Allegrini, Paolo; Grigolini, Paolo; Latora, Vito; Palatella, Luigi; Rapisarda, Andrea et al.
Item Type: Paper
Partner: UNT College of Arts and Sciences

Modeling femtosecond pulse propagation in optical fibers.

Description: Femtosecond pulse propagation in optical fibers requires consideration of higher-order nonlinear effects when implementing the non-linear Schroedinger equation. We show excellent agreement of our model with experimental results both for the temporal and phase features of the pulses. Ultrafast pulse propagation in optical fibers presents a number of challenges given the effect of nonlinearities which become important on such a short time scale. The modeling of femtosecond pulse propagation becomes, consequently, a harder task which has to account for all these effects. In this work, we have included higher order corrections in the non-linear Schroedinger equation and compared the numerical simulation results with experimental data. Our work, besides taking into account the temporal evolution of the pulse, keeps into account also the phase behavior of the electric field, which we compare with experimental results obtained with Frequency Resolved Optical Gating [l]. We also account for self-frequency shift of the pulse and obtain excellent agreement with the experimental results on the Raman shift.
Date: January 1, 2001
Creator: Chung, Y. J. (Yeo-Jin); Schaefer, T. B. (Tobias B.); Gabitov, I. R. (Ildar R.); Omenetto, F. G. (Fiorenzo G.) & Taylor, Antoinette J.,
Item Type: Article
Partner: UNT Libraries Government Documents Department

Mega et al. Reply

Description: This article is a reply to a comment by A. Helmstetter and D. Sornette about the article 'Power-Law Time Distribution of Large Earthquakes' from 2003.
Date: March 26, 2004
Creator: Mega, Mirko S.; Allegrini, Paolo; Grigolini, Paolo; Latora, Vito; Palatella, Luigi; Rapisarda, Andrea et al.
Item Type: Article
Partner: UNT College of Arts and Sciences

Scaling Breakdown: A Signature of Aging

Description: In this article, the authors prove that the Lévy walk is characterized by bilinear scaling. This effect mirrors the existence of a form of aging that does not require the adoption of nonstationary conditions.
Date: July 12, 2002
Creator: Allegrini, Paolo; Bellazzini, Jacopo; Bramanti, G.; Ignaccolo, Massimiliano; Grigolini, Paolo & Yang, J.
Item Type: Article
Partner: UNT College of Arts and Sciences

Real event detection and the treatment of congestive heart failure: an efficient technique to help cardiologists to make crucial decisions

Description: Paper discussing the treatment of congestive heart failure. Abstract: Using a method of entropic analysis of time series we establish the correlation between heartbeat long-range memory and mortality risk in patients with congestive heart failure.
Date: September 2002
Creator: Allegrini, Paolo; Balocchi, Rita; Chillemi, Santi; Grigolini, Paolo; Hamilton, P.; Maestri, Roberto et al.
Item Type: Paper
Partner: UNT College of Arts and Sciences

Scaling in Non-stationary Time Series 2: Teen Birth Phenomenon

Description: This paper is devoted to the problem of statistical mechanics raised by the analysis of an issue of sociological interest: the teen birth phenomenon.
Date: February 2, 2008
Creator: Ignaccolo, Massimiliano; Allegrini, Paolo; Grigolini, Paolo; Hamilton, P. & West, Bruce J.
Item Type: Paper
Partner: UNT College of Arts and Sciences

Stromatolites: why do we care?

Description: Article discussing stromatolites. The authors apply the method of Diffusion Entropy (DE) to the study of stromatolites by means of a two-dimensional procedure that makes it possible for us to compare the DE analysis to the results of a compression method.
Date: April 2004
Creator: Ignaccolo, Massimiliano; Schwettmann, Arne; Failla, Roberto; Storrie-Lombardi, Michael C. & Grigolini, Paolo
Item Type: Article
Partner: UNT College of Arts and Sciences

Fingering Instabilities, Collapse, Avalanches and Self-Organized Criticality in Liquid Foams

Description: Foam is solid-like under low stress and liquid-like under high stress. It can sustain a small load elastically but a large one causes it to flow indefinitely. When shear stress is present, a pair of adjacent bubbles can be squeezed apart by another pair, leading to a T1 switching event. This local but abrupt topological change results in bubble-complexes rearranging from one metastable configuration to another. The resulting macroscopic dynamics is highly nonlinear and complex, involving large local motion that depends on correlations between nearby bubbles. The main goal of this study was to find the connection between the behavior of individual membranes and the whole network and to relate local rearrangements to global rheological properties of flowing foams.
Date: November 29, 2002
Creator: Glazier, J. A.
Item Type: Report
Partner: UNT Libraries Government Documents Department

Towards the timely detection of toxicants

Description: Article discussing the problem of enhancing the sensitivity of biosensors to the influence of toxicants, with an entropy method of analysis, denoted as CASSANDRA, for the specific purpose of studying non-stationary time series.
Date: April 2004
Creator: Ignaccolo, Massimiliano; Grigolini, Paolo & Gross, Guenter W.
Item Type: Article
Partner: UNT College of Arts and Sciences

Power-Law Time Distribution of Large Earthquakes

Description: Article discussing power-law time distribution of large earthquakes and a study of the statistical properties of time distribution of seismicity in California by means of diffusion entropy.
Date: May 2003
Creator: Mega, Mirko S.; Allegrini, Paolo; Grigolini, Paolo; Latora, Vito; Palatella, Luigi; Rapisarda, Andrea et al.
Item Type: Article
Partner: UNT College of Arts and Sciences