Fractional Dynamics in Forest Fires

Every year forest fires consume large areas, being a major concern in many countries like Australia, United States and Mediterranean Basin European Countries (e.g., Portugal, Spain, Italy and Greece). Understanding patterns of such events, in terms of size and spatiotemporal distributions, may help to take measures beforehand in view of possible hazards and decide strategies of fire prevention, detection and suppression. Traditional statistical tools have been used to study forest fires. Nevertheless, those tools might not be able to capture the main features of fires complex dynamics and to model fire behaviour [1]. Forest fires size-frequency distributions unveil long range correlations and long memory characteristics, which are typical of fractional order systems [2]. Those complex correlations are characterized by self-similarity and absence of characteristic length-scale, meaning that forest fires exhibit power-law (PL) behaviour. Forest fires have also been proved to exhibit time-clustering phenomena, with timescales of the order of few days [3]. In this paper, we study forest fires in the perspective of dynamical systems and fractional calculus (FC). Public domain forest fires catalogues, containing data of events occurred in Portugal, in the period 1980 up to 2011, are considered. The data is analysed in an annual basis, modelling the occurrences as sequences of Dirac impulses. The frequency spectra of such signals are determined using Fourier transforms, and approximated through PL trendlines. The PL parameters are then used to unveil the fractional-order dynamics characteristics of the data. To complement the analysis, correlation indices are used to compare and find possible relationships among the data. It is shown that the used approach can be useful to expose hidden patterns not captured by traditional tools.

On the analysis of data emerging in non-linear and complex systemscomparison of two X-Ray prony spectra

New arguments proving that successive (repeated) measurements have a memory and actually remember each other are presented. The recognition of this peculiarity can change essentially the existing paradigm associated with conventional observation in behavior of different complex systems and lead towards the application of an intermediate model (IM). This IM can provide a very accurate fit of the measured data in terms of the Prony's decomposition. This decomposition, in turn, contains a small set of the fitting parameters relatively to the number of initial data points and allows comparing the measured data in cases where the “best fit” model based on some specific physical principles is absent. As an example, we consider two X-ray diffractometers (defined in paper as A- (“cheap”) and B- (“expensive”) that are used after their proper calibration for the measuring of the same substance (corundum a-Al2O3). The amplitude-frequency response (AFR) obtained in the frame of the Prony's decomposition can be used for comparison of the spectra recorded from (A) and (B) - X-ray diffractometers (XRDs) for calibration and other practical purposes. We prove also that the Fourier decomposition can be adapted to “ideal” experiment without memory while the Prony's decomposition corresponds to real measurement and can be fitted in the frame of the IM in this case. New statistical parameters describing the properties of experimental equipment (irrespective to their internal “filling”) are found. The suggested approach is rather general and can be used for calibration and comparison of different complex dynamical systems in practical purposes.

Frequency of TERT promoter mutations in human cancers

Reactivation of telomerase has been implicated in human tumorigenesis, but the underlying mechanisms remain poorly understood. Here we report the presence of recurrent somatic mutations in the TERT promoter in cancers of the central nervous system (43%), bladder (59%), thyroid (follicular cell-derived, 10%) and skin (melanoma, 29%). In thyroid cancers, the presence of TERT promoter mutations (when occurring together with BRAF mutations) is significantly associated with higher TERT mRNA expression, and in glioblastoma we find a trend for increased telomerase expression in cases harbouring TERT promoter mutations. Both in thyroid cancers and glioblastoma, TERT promoter mutations are significantly associated with older age of the patients. Our results show that TERT promoter mutations are relatively frequent in specific types of human cancers, where they lead to enhanced expression of telomerase.

Fractional derivatives: probability interpretation and frequency response of rational approximations

The theory of fractional calculus (FC) is a useful mathematical tool in many applied sciences. Nevertheless, only in the last decades researchers were motivated for the adoption of the FC concepts. There are several reasons for this state of affairs, namely the co-existence of different definitions and interpretations, and the necessity of approximation methods for the real time calculation of fractional derivatives (FDs). In a first part, this paper introduces a probabilistic interpretation of the fractional derivative based on the Grünwald-Letnikov definition. In a second part, the calculation of fractional derivatives through Padé fraction approximations is analyzed. It is observed that the probabilistic interpretation and the frequency response of fraction approximations of FDs reveal a clear correlation between both concepts.

Robotic manipulators with vibrations: short time fourier transform of fractional spectra

This paper analyzes the signals captured during impacts and vibrations of a mechanical manipulator. In order to acquire and study the signals an experimental setup is implemented. The signals are treated through signal processing tools such as the fast Fourier transform and the short time Fourier transform. The results show that the Fourier spectrum of several signals presents a non integer behavior. The experimental study provides valuable results that can assist in the design of a control system to deal with the unwanted effects of vibrations.

Low frequency of TERT promoter mutations in gastrointestinal stromal tumors (GISTs)

Somatic mutations in the promoter region of telomerase reverse transcriptase (TERT) gene, mainly at positions c.-124 and c.-146 bp, are frequent in several human cancers; yet its presence in gastrointestinal stromal tumor (GIST) has not been reported to date. Herein, we searched for the presence and clinicopathological association of TERT promoter mutations in genomic DNA from 130 bona fide GISTs. We found TERT promoter mutations in 3.8% (5/130) of GISTs. The c.-124C>T mutation was the most common event, present in 2.3% (3/130), and the c.-146C>T mutation in 1.5% (2/130) of GISTs. No significant association was observed between TERT promoter mutation and patient's clinicopathological features. The present study establishes the low frequency (4%) of TERT promoter mutations in GISTs. Further studies are required to confirm our findings and to elucidate the hypothetical biological and clinical impact of TERT promoter mutation in GIST pathogenesis.

On similarities in infrared spectra of complex drugs

A chromatographic separation of active ingredients of Combivir, Epivir, Kaletra, Norvir, Prezista, Retrovir, Trivizir, Valcyte, and Viramune is performed on thin layer chromatography. The spectra of these nine drugs were recorded using the Fourier transform infrared spectroscopy. This information is then analyzed by means of the cosine correlation. The comparison of the infrared spectra in the perspective of the adopted similarity measure is possible to visualize with present day computer tools, and the emerging clusters provide additional information about the similarities of the investigated set of complex drugs.

Dynamical Analysis and Visualization of Tornadoes Time Series

In this paper we analyze the behavior of tornado time-series in the U.S. from the perspective of dynamical systems. A tornado is a violently rotating column of air extending from a cumulonimbus cloud down to the ground. Such phenomena reveal features that are well described by power law functions and unveil characteristics found in systems with long range memory effects. Tornado time series are viewed as the output of a complex system and are interpreted as a manifestation of its dynamics. Tornadoes are modeled as sequences of Dirac impulses with amplitude proportional to the events size. First, a collection of time series involving 64 years is analyzed in the frequency domain by means of the Fourier transform. The amplitude spectra are approximated by power law functions and their parameters are read as an underlying signature of the system dynamics. Second, it is adopted the concept of circular time and the collective behavior of tornadoes analyzed. Clustering techniques are then adopted to identify and visualize the emerging patterns.