A fractal analysis of skin pigmented lesions using the novel tool of the variogram technique

The incidence of the cutaneous malignant melanoma is increasing rapidly in the world [Ferlay J, Bray F, Pisani P, et al. GLOBOCAN 2000: Cancer incidence, mortality and prevalence worldwide, Version 1.0 IARC Cancer Base no. 5. Lyon: IARC Press, 2001]. The therapeutic address requires a method having high sensitivity and capability to diagnose such disease at an early stage. We introduce a new diagnostic method based on non-linear methodologies. In detail we suggest that fractal as well as noise and chaos dynamics are the most important components responsible for genetic instability of melanocytes. As consequence we introduce the new technique of the variogram and of fractal analysis extended to the whole regions of interest of skin in order to obtain parameters able to identify the malignant lesion. In a preliminary analysis, satisfactory results are reached.     

Laminar recurrences, maxline, unstable singularities and biological dynamics

Recurrence quantification analysis can reveal subtle aspects of dynamics not easily appreciated by other methods such as the Fourier transform. Laminarity and maxline are two RQA variables that can demonstrate the presence of unstable singularities which are often found in biological dynamics. Examples are presented and their implications are discussed relative to deterministic dynamics and stochastic processes.     

Application of trilinear SLICING to analyse a single relaxation curve

Determining the time constants and amplitudes of exponential decays from relaxation data is a common task in LF-NMR. In this communication, we present an application of the SLICING algorithm to evaluate its possibilities for solving this problem. The method, originally introduced to compare different samples, is applied here to analyse a single relaxation curve, using the embedding technique. To test this procedure, we acquired data sets from samples of liquids properly separated, and characterized by different relaxation times. The results show a good estimation of parameters, comparable with those obtained applying Marquardt's algorithm, when the components have sufficiently different relaxation times.     

Statistical approaches for investigating silk properties

Amino acid repeats or motifs have engendered interest because of their significance for protein physical characteristics as well as folding properties. Spider dragline silk proteins are unique because they are composed of long repetitive sections and relatively short non-repetitive sections that are known to interact to generate the very peculiar mechanical and solubility properties of silk. Computational analysis compared with in vitro measurements suggest that the silks achieve their unique pattern of extreme solubility inside the spider glands/complete insolubility outside by correlating their repetitive hydrophobic regions through a type of stochastic resonance, generated by the addition of the non-repetitive sequences to a basically periodic hydrophobicity pattern. PACS 87.14.Ee; 87.15.Cc; 87.15.He; 02.50.Ey; 05.40.Ca     

Fractal fluctuations and quantum-like chaos in the brain by analysis of variability of brain waves: A new method based on a fractal variance function and random matrix theory: A link with El Naschie fractal Cantorian space–time and V. Weiss and H. Weiss golden ratio in brain

We develop a new method for analysis of fundamental brain waves as recorded by the EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given. We also discuss the link of such formulation with H. Weiss and V. Weiss golden ratio found in the brain, and with El Naschie fractal Cantorian space–time theory.     

The Wiener-Khinchin theorem and recurrence quantification

The Wiener-Khinchin theorem states that the power spectrum is the Fourier transform of the autocovariance function. One form of the autocovariance function can be obtained through recurrence quantification. We show that the advantage of defining the autocorrelation function with recurrences can demonstrate higher dimensional dynamics.