Search Results (11)

Mexico is a well-known seismically active country, which is primarily affected by several tectonic plate interactions along the southern Pacific coastline and by active structures in the Gulf of California. In this paper, we investigate this seismicity using the classical Gutenberg–Richter (GR) law and a non-extensive statistical approach based on Tsallis entropy. The analysis is performed using data from the corrected Mexican seismic catalog provided by the National Seismic Service, spanning the period from January 2000 to October 2023, and unlike previous work, it includes six different regions along the entire west coastline of Mexico. The Gutenberg–Richter law fitting to the earthquake sub-catalogs for all six regions studied indicates magnitudes of completeness between 3.30 and 3.76, implying that the majority of seismic movements occur for magnitudes less than 4. The cumulative distribution of earthquakes as derived from the Tsallis entropy was fitted to the corrected catalog data to estimate the q-entropic index for all six regions, which for values greater than one is a measure of the non-extensivity (i.e., non-equilibrium) of the system. All regions display values of the entropic index in the range $1.52\lesssim q\lesssim 1.61$, slightly lower than previously estimated ( $1.54\lesssim q\lesssim 1.70$) using catalog data from 1988 to 2010. The reason for this difference is related to the use of modern recording devices, which are sensitive to the detection of a larger number of low-magnitude events compared to older instrumentation. Full article

Recent evidence supports that air is the main transmission pathway of the recently identified SARS-CoV-2 coronavirus that causes COVID-19 disease. Estimating the infection risk associated with an indoor space remains an open problem due to insufficient data concerning COVID-19 outbreaks, as well as, methodological challenges arising from cases where environmental (i.e., out-of-host) and immunological (i.e., within-host) heterogeneities cannot be neglected. This work addresses these issues by introducing a generalization of the elementary Wells-Riley infection probability model. To this end, we adopted a superstatistical approach where the exposure rate parameter is gamma-distributed across subvolumes of the indoor space. This enabled us to construct a susceptible (S)–exposed (E)–infected (I) dynamics model where the Tsallis entropic index q quantifies the degree of departure from a well-mixed (i.e., homogeneous) indoor-air-environment state. A cumulative-dose mechanism is employed to describe infection activation in relation to a host’s immunological profile. We corroborate that the six-foot rule cannot guarantee the biosafety of susceptible occupants, even for exposure times as short as 15 min. Overall, our work seeks to provide a minimal (in terms of the size of the parameter space) framework for more realistic indoor $SEI$ dynamics explorations while highlighting their Tsallisian entropic origin and the crucial yet elusive role that the innate immune system can play in shaping them. This may be useful for scientists and decision makers interested in probing different indoor biosafety protocols more thoroughly and comprehensively, thus motivating the use of nonadditive entropies in the emerging field of indoor space epidemiology. Full article

In recent years, there has been an exponential growth in sequencing projects due to accelerated technological advances, leading to a significant increase in the amount of data and resulting in new challenges for biological sequence analysis. Consequently, the use of techniques capable of analyzing large amounts of data has been explored, such as machine learning (ML) algorithms. ML algorithms are being used to analyze and classify biological sequences, despite the intrinsic difficulty in extracting and finding representative biological sequence methods suitable for them. Thereby, extracting numerical features to represent sequences makes it statistically feasible to use universal concepts from Information Theory, such as Tsallis and Shannon entropy. In this study, we propose a novel Tsallis entropy-based feature extractor to provide useful information to classify biological sequences. To assess its relevance, we prepared five case studies: (1) an analysis of the entropic index q; (2) performance testing of the best entropic indices on new datasets; (3) a comparison made with Shannon entropy and (4) generalized entropies; (5) an investigation of the Tsallis entropy in the context of dimensionality reduction. As a result, our proposal proved to be effective, being superior to Shannon entropy and robust in terms of generalization, and also potentially representative for collecting information in fewer dimensions compared with methods such as Singular Value Decomposition and Uniform Manifold Approximation and Projection. Full article

Non-extensive statistical mechanics (NESM), introduced by Tsallis based on the principle of non-additive entropy, is a generalisation of the Boltzmann–Gibbs statistics. NESM has been shown to provide the necessary theoretical and analytical implementation for studying complex systems such as the fracture mechanisms and crack evolution processes that occur in mechanically loaded specimens of brittle materials. In the current work, acoustic emission (AE) data recorded when marble and cement mortar specimens were subjected to three distinct loading protocols until fracture, are discussed in the context of NESM. The NESM analysis showed that the cumulative distribution functions of the AE interevent times (i.e., the time interval between successive AE hits) follow a q-exponential function. For each examined specimen, the corresponding Tsallis entropic q-indices and the parameters β_q and ${\tau }_q$ were calculated. The entropic index $q$ shows a systematic behaviour strongly related to the various stages of the implemented loading protocols for all the examined specimens. Results seem to support the idea of using the entropic index $q$ as a potential pre-failure indicator for the impending catastrophic fracture of the mechanically loaded specimens. Full article

Events occurring with a frequency described by power laws, within a certain range of validity, are very common in natural systems. In many of them, it is possible to associate an energy spectrum and one can show that these types of phenomena are intimately related to Tsallis entropy $S_q$ . The relevant parameters become: (i) The entropic index q, which is directly related to the power of the corresponding distribution; (ii) The ground-state energy ${\epsilon }_0$ , in terms of which all energies are rescaled. One verifies that the corresponding processes take place at a temperature $T_q$ with $k{T}_q\propto {\epsilon }_0$ (i.e., isothermal processes, for a given q), in analogy with those in the class of self-organized criticality, which are known to occur at fixed temperatures. Typical examples are analyzed, like earthquakes, avalanches, and forest fires, and in some of them, the entropic index q and value of $T_q$ are estimated. The knowledge of the associated entropic form opens the possibility for a deeper understanding of such phenomena, particularly by using information theory and optimization procedures. Full article

The observed earthquake scaling laws indicate the existence of phenomena closely associated with the proximity of the system to a critical point. Taking this view that earthquakes are critical phenomena (dynamic phase transitions), here we investigate whether in this case the Lifshitz–Slyozov–Wagner (LSW) theory for phase transitions showing that the characteristic size of the minority phase droplets grows with time as $t^{1/3}$ is applicable. To achieve this goal, we analyzed the Japanese seismic data in a new time domain termed natural time and find that an LSW behavior is actually obeyed by a precursory change of seismicity and in particular by the fluctuations of the entropy change of seismicity under time reversal before the Tohoku earthquake of magnitude 9.0 that occurred on 11 March 2011 in Japan. Furthermore, the Tsallis entropic index q is found to exhibit a precursory increase. Full article

Lane detection for traffic surveillance in intelligent transportation systems is a challenge for vision-based systems. In this paper, a novel pixel-entropy based algorithm for the automatic detection of the number of lanes and their centers, as well as the formation of their division lines is proposed. Using as input a video from a static camera, each pixel behavior in the gray color space is modeled by a time series; then, for a time period $\tau$ , its histogram followed by its entropy are calculated. Three different types of theoretical pixel-entropy behaviors can be distinguished: (1) the pixel-entropy at the lane center shows a high value; (2) the pixel-entropy at the lane division line shows a low value; and (3) a pixel not belonging to the road has an entropy value close to zero. From the road video, several small rectangle areas are captured, each with only a few full rows of pixels. For each pixel of these areas, the entropy is calculated, then for each area or row an entropy curve is produced, which, when smoothed, has as many local maxima as lanes and one more local minima than lane division lines. For the purpose of testing, several real traffic scenarios under different weather conditions with other moving objects were used. However, these background objects, which are out of road, were filtered out. Our algorithm, compared to others based on trajectories of vehicles, shows the following advantages: (1) the lowest computational time for lane detection (only 32 s with a traffic flow of one vehicle/s per-lane); and (2) better results under high traffic flow with congestion and vehicle occlusion. Instead of detecting road markings, it forms lane-dividing lines. Here, the entropies of Shannon and Tsallis were used, but the entropy of Tsallis for a selected q of a finite set achieved the best results. Full article

We analyse seismicity during the 6-year period 2012–2017 in the new time domain termed natural time in the Chiapas region where the M8.2 earthquake occurred, Mexico’s largest earthquake in more than a century, in order to study the complexity measures associated with fluctuations of entropy as well as with entropy change under time reversal. We find that almost three months before the M8.2 earthquake, i.e., on 14 June 2017, the complexity measure associated with the fluctuations of entropy change under time reversal shows an abrupt increase, which, however, does not hold for the complexity measure associated with the fluctuations of entropy in forward time. On the same date, the entropy change under time reversal has been previously found to exhibit a minimum [Physica A 506, 625–634 (2018)]; we thus find here that this minimum is also accompanied by increased fluctuations of the entropy change under time reversal. In addition, we find a simultaneous increase of the Tsallis entropic index q. Full article

The Boltzmann–Gibbs and Tsallis entropies are essential concepts in statistical physics, which have found multiple applications in many engineering and science areas. In particular, we focus our interest on their applications to image processing through information theory. We present in this article a novel numeric method to calculate the Tsallis entropic index q characteristic to a given image, considering the image as a non-extensive system. The entropic index q is calculated through q-redundancy maximization, which is a methodology that comes from information theory. We find better results in the image processing in the grayscale by using the Tsallis entropy and thresholding q instead of the Shannon entropy. Full article

Boltzmann introduced in the 1870s a logarithmic measure for the connection between the thermodynamical entropy and the probabilities of the microscopic configurations of the system. His celebrated entropic functional for classical systems was then extended by Gibbs to the entire phase space of a many-body system and by von Neumann in order to cover quantum systems, as well. Finally, it was used by Shannon within the theory of information. The simplest expression of this functional corresponds to a discrete set of W microscopic possibilities and is given by $S_{BG}=-k{\sum }_{i=1}^W{p}_{i}ln{p}_i$ (k is a positive universal constant; BG stands for Boltzmann–Gibbs). This relation enables the construction of BGstatistical mechanics, which, together with the Maxwell equations and classical, quantum and relativistic mechanics, constitutes one of the pillars of contemporary physics. The BG theory has provided uncountable important applications in physics, chemistry, computational sciences, economics, biology, networks and others. As argued in the textbooks, its application in physical systems is legitimate whenever the hypothesis of ergodicity is satisfied, i.e., when ensemble and time averages coincide. However, what can we do when ergodicity and similar simple hypotheses are violated, which indeed happens in very many natural, artificial and social complex systems. The possibility of generalizing BG statistical mechanics through a family of non-additive entropies was advanced in 1988, namely $S_q=k\frac{1-{\sum }_{i=1}^W{p}_i^q}{q-1}$ , which recovers the additive $S_{BG}$ entropy in the q→ 1 limit. The index q is to be determined from mechanical first principles, corresponding to complexity universality classes. Along three decades, this idea intensively evolved world-wide (see the Bibliography in http://tsallis.cat.cbpf.br/biblio.htm) and led to a plethora of predictions, verifications and applications in physical systems and elsewhere. As expected, whenever a paradigm shift is explored, some controversy naturally emerged, as well, in the community. The present status of the general picture is here described, starting from its dynamical and thermodynamical foundations and ending with its most recent physical applications. Full article

One of the crucial properties of the Boltzmann-Gibbs entropy in the context of classical thermodynamics is extensivity, namely proportionality with the number of elements of the system. The Boltzmann-Gibbs entropy satisfies this prescription if the subsystems are statistically (quasi-) independent, or typically if the correlations within the system are essentially local. In such cases the energy of the system is typically extensive and the entropy is additive. In general, however, the situation is not of this type and correlations may be far from negligible at all scales. Tsallis in 1988 introduced an entropic expression characterized by an index q which leads to a non-extensive statistics. Tsallis entropy, Sq, is the basis of the so called non-extensive statistical mechanics, which generalizes the Boltzmann-Gibbs theory. Tsallis statistics have found applications in a wide range of phenomena in diverse disciplines such as physics, chemistry, biology, medicine, economics, geophysics, etc. The focus of this special issue of Entropy was to solicit contributions that apply Tsallis entropy in various scientific fields. [...] Full article