Tsallis Entropy

The availability of historical textual corpora has led to the study of words’ volume (i.e. frequency) along the historical time line, as representing the public’s focus of attention over time. However, study of the dynamics of words’ meaning is still in its infancy. In this paper, we first propose that the meaning of a word may be studied through the entropy of its embedding. Using two historical case studies, we show that this entropy measure is correlated with how much a word is used (i.e. its volume). More importantly, we show that using Tsallis entropy with a superadditive entropy index may provide a better estimation of a word’s volume than using Shannon entropy. We explain this finding as resulting from an increasing redundancy between the words that comprise the semantic field of the target word and develop a new measure of redundancy between words. Using this measure, which relies on the Tsallis version of the Kullback–Leibler divergence, we show that the evolving meaning of a word involves the dynamics of increasing redundancy between components of its semantic field. The proposed methodology may enrich the toolkit of researchers who study the dynamics of word senses in textual historical corpora.

Keywords: complex social systems, Tsallis entropy, word dynamics, historical corpora, multidisciplinary science

* This paper has been submitted for publication

In addition to the well-known Shannon entropy, generalized entropies, such as the Renyi and Tsallis entropies, are increasingly used in many applications. Entropies are computed by means of nonparametric kernel methods that are commonly used to estimate the density function of empirical data. Generalized entropy estimation techniques for one-dimensional data using sample spacings are proposed. By means of computational experiments, it is shown that these techniques are robust and accurate, compare favorably to the popular Parzen window method for estimating entropies, and, in many cases, require fewer computations than Parzen methods.

Knowledge of the electronic structures of atomic and molecular systems deepens our understanding of the desired system. In particular, several information-theoretic quantities, such as Shannon entropy, have been applied to quantify the extent of electron delocalization for the ground state of various systems. To explore excited states, we calculated Shannon entropy and two of its one-parameter generalizations, Rényi entropy of order α and Tsallis entropy of order α, and Onicescu Information Energy of order α for four low-lying singly excited states (1s2s 1 S e , 1s2s 3 S e , 1s3s 1 S e , and 1s3s 3 S e states) of helium. This paper compares the behavior of these three quantities of order 0.5 to 9 for the ground and four excited states. We found that, generally, a higher excited state had a larger Rényi entropy, larger Tsallis entropy, and smaller Onicescu information energy. However, this trend was not definite and the singlet-triplet reversal occurred for Rényi entropy, Tsallis entropy and Onicescu information energy at a certain range of order α.

In this work, we analyze two important stochastic processes, the fractional Brownian motion and fractional Gaussian noise, within the framework of the Tsallis permutation entropy. This entropic measure, evaluated after using the Bandt & Pompe method to extract the associated probability distribution, is shown to be a powerful tool to characterize fractal stochastic processes. It allows for a better discrimination of the processes than the Shannon counterpart for appropriate ranges of values of the entropic index. Moreover, we find the optimum value of this entropic index for the stochastic processes under study.

In this article, we present a new algorithm to deal with foregroundbackground separation in very degraded documents. In particular, our work is applied to patrimonial document images which suffer from several types of degradation as aging effects, noise, back-to-front ink interference, etc. Our main objective is to correctly classify ink and paper to allow an efficient segmentation of the image creating high quality monochromatic images. This makes easier the broadcast of these images through the Internet. The new algorithm is based on the classical Shannon definition of entropy and a generalization defined as Tsallis Entropy and it is compared to 19 well-known classical algorithms, including DjVu algorithm. It achieved the best results by analyzing precision, recall, accuracy, specificity, PSNR and MSE.

Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar power-law distributions. In this paper, we address the question whether the Renyi entropy is equally suitable to describe those systems with power-law behaviour, where the use of the Tsallis entropy is relevant. We discuss a specific class of dynamical systems, namely, one dimensional dissipative maps at chaos threshold and make our study from two aspects: i) power-law sensitivity to the initial conditions and the rate of entropy increase, ii) generalized bit cumulants. We present evidence that the Tsallis entropy is the more appropriate entropic form for such studies as opposed to Renyi form.

In this paper we apply shape-from-shading to face images to extract fields of surface normals and make estimates of surface curvature attributes. The attributes studied include minimum and maximum curvature, mean and Gaussian curvature, and, curvedness and shape-index. The curvature attributes are encoded as histograms and are used to perform recognition using a number of distance and similarity measures including the Euclidean distance, the Shannon entropy, the Renyi entropy and the Tsallis entropy. We compare the results obtained using the different curvature attributes and the different entropy measures. Using precisionrecall curves, we find that the best performance is delivered when the Shannon entropy is applied to histograms of shape index and curvedness.

This paper describes a comparative study of the use of Shannon, Rényi and Tsallis entropies for designing Decision Tree, with goal to find more efficient alternatives applied to Intrusion Tolerant Systems. Decision Tree has been used in classification model problems related to intrusion detection in networks, presenting good results. A very used decision tree is the C4.5 one that applies the Shannon entropy in order to choose the attributes that better divide data into classes. However, other ways to measure entropy, e.g., Tsallis and Rényi entropy, may be applied aiming at guaranteeing better generalization related to split criteria. Experimental results demonstrate that Tsallis and Rényi entropy can be used to construct more compact and efficient decision trees compared with Shannon entropy and these models can to provide more accurate intrusion tolerante systems.

In this paper we present a study of anomalous diffusion using a Fokker-Planck description with fractional velocity derivatives. The distribution functions are found using numerical means for varying degree of fractionality of the stable Lévy distribution.

This paper presents a fuzzy partition and Tsallis entropy based thresholding approach for multi-level image segmentation. Image segmentation is considered as one of the most critical tasks in image processing and pattern recognition area. However, discriminating many objects present in an image automatically is the most challenging one. As a result, multilevel thresholding based methods gain importance in recent times, because of its ability to split the image into more than one segments. Efficiency of these algorithms still remains a matter of concern. Over the years, fuzzy partition of 1-D histogram has been employed successfully in bi-level image segmentation to improve the separation between object and the background. Here a fuzzy based technique is adopted in multi-level image segmentation scenario using Tsallis entropy based thresholding. Differential Evolution, a widely used meta-heuristic in recent times, is used for lesser computation time of the proposed algorithm. Both visual and statistical comparison of outcomes between Tsallis and Fuzzy - Tsallis entropy based methods are given in this paper to establish the superiority of the technique.

The thresholding process based on the optimization of one criterion only does not work well for a lot of images. In many cases, even when equipped with the optimal value of the threshold of its single criterion, the thresholding program does not produce a satisfactory result. In this paper, we propose to use the multiobjective optimization approach to find the optimal thresholds of three criteria: the within-class criterion, the entropy and the overall probability of error criterion. In addition we develop a new variant of simulated annealing adapted to continuous problems to solve the Gaussian curve-fitting problem. Some examples of test images are presented to compare our segmentation method, based on the multiobjective optimization approach, with that of four competing methods: Otsu method, Gaussian curve fitting-based method, valleyemphasis-based method and two-dimensional Tsallis entropy-based method. From the viewpoints of visualization, object size and image contrast, our experimental results show that the thresholding method based on multiobjective optimization performs better than the competing methods.

Intrusion Detection Systems of computer network perform their detection capabilit ies by monitoring a set of attributes from network traffic. Since some attributes may be irrelevant, redundant or even noisy, their usage can decrease the intrusion detection efficiency as well as increase the set of attributes. In this context, selecting optimal attributes is a difficult task considering that the set of all attributes can assume a huge variety of data formats (for examp le: symbol set, e.g. binary, alphanumeric, real number, etc., types, length, among others). In this work, it is presented an empirical investigation of attribute selection techniques based on Shannon, Rényi and Tsallis entropies in order to obtain optimal attribute subsets that increase the detection capability of classifying network traffic as either normal or suspicious. Simu lation experiments have been carried out and the obtained results show that when Rényi or Tsallis entropy is applied the number of attributes and the processing time are reduced and, in addition, the classificat ion efficiency is increased.

The stationary states of the half-line Coulomb potential are described by quantum-mechanical wavefunctions which are controlled by the Laguerre polynomials $L_n^{(1)}(x$). Here we first calculate the $q$th-order frequency or entropic moments of this quantum system, which is controlled by some entropic functionals of the Laguerre polynomials. These functionals are shown to be equal to a Lauricella function $F_A^{(2q+1)}(\frac{1}{q},...,\frac{1}{q},1)$ by use

One of the major issues studied in finance that has always intrigued, both scholars and practitioners, and to which no unified theory has yet been discovered, is the reason why prices move over time. Since there are several well-known traditional techniques in the literature to measure stock market volatility, a central point in this debate that constitutes the actual scope of this paper is to compare this common approach in which we discuss such popular techniques as the standard deviation and an innovative methodology based on Econophysics. In our study, we use the concept of Tsallis entropy to capture the nature of volatility. More precisely, what we want to find out is if Tsallis entropy is able to detect volatility in stock market indexes and to compare its values with the ones obtained from the standard deviation. Also, we shall mention that one of the advantages of this new methodology is its ability to capture nonlinear dynamics. For our purpose, we shall basically focus on the behaviour of stock market indexes and consider the CAC 40, MIB 30, NIKKEI 225, PSI 20, IBEX 35, FTSE 100 and SP 500 for a comparative analysis between the approaches mentioned above.

We consider the Shannon-Khinchin axiomatic systems for the characterization of generalized entropies such as Sharma-Mital and Frank-Daffertshofer entropy. We provide the generalization of Shannon-Khinchin axioms and give the corresponding uniqueness theorem. The previous attempts at such axiomatizations are also discussed.

We review from the point of view of nonextensive statistics the ubiquitous presence in elementary and heavy-ion collisions of power-law distributions. Special emphasis is placed on the conjecture that this is just a reflection of some intrinsic fluctuations existing in the hadronic systems considered. These systems summarily described by a single parameter q playing the role of a nonextensivity measure in the nonextensive statistical models based on Tsallis entropy.

Examples of joint probability distributions are studied in terms of Tsallis' nonextensive statistics both for correlated and uncorrelated variables, in particular it is explicitely shown how correlations in the system can make Tsallis entropy additive and that the effective nonextensivity parameter q N decreases towards unity when the number of variables N increases. We demonstrate that Tsallis distribution of energies of particles in a system leads in natural way to the Negative Binomial multiplicity distribution in this system.

The definitions of the temperature in the nonextensive statistical thermodynamics based on Tsallis entropy are analyzed. A definition of pressure is proposed for nonadditive systems by using a nonadditive effective volume. The thermodynamics of nonadditive photon gas is discussed on this basis. We show that the Stefan-Boltzmann law can be preserved within nonextensive thermodynamics.

We further study the connection between Algorithmic Entropy and Shannon and Rényi Entropies. It is given an example for which the difference between the expected value of algorithmic entropy and Shannon Entropy meets the known upperbound and, for Rényi Entropy, proving that all other values of the parameter (α), the same difference can be big. We also prove that for a particular type of distributions Shannon Entropy is able to capture the notion of computationally accessible information by relating it to time-bounded algorithmic entropy. In order to better study this unexpected relation it is investigated the behavior of the different entropies (Shannon, Rényi and Tsallis) under the distribution based on the time-bounded algorithmic entropy.

Our recent analysis on nonlinear nonextensive dust-acoustic waves (DA) [Amour and Tribeche in Phys. Plasmas 17:063702, 2010] is extended to include self-consistent nonadiabatic grain charge fluctuation. The appropriate nonextensive electron charging current is rederived based on the orbit-limited motion theory. Our results reveal that the amplitude, strength and nature of the nonlinear DA waves (solitons and shocks) are extremely sensitive to the degree of ion nonextensivity. Stronger is the electron correlation, more important is the charge variation induced nonlinear wave damping. The anomalous dissipation effects may prevail over that dispersion as the electrons evolve far away from their Maxwellian equilibrium. Our investigation may be of wide relevance to astronomers and space scientists working on interstellar dusty plasmas where nonthermal distributions are turning out to be a very common and characteristic feature.

We introduce a labeled point set registration algorithm based on a family of novel information-theoretic measures derived as a generalization of the well-known Shannon entropy. This generalization, known as the Havrda-Charvat-Tsallis entropy, permits a fine-tuning between solution types of varying degrees of robustness of the divergence measure between multiple point sets. A variant of the traditional free-form deformation approach, known as directly manipulated free-form deformation, is used to model the transformation of the registration solution. We provide an overview of its open source implementation based on the Insight Toolkit of the National Institutes of Health. Characterization of the proposed framework includes comparison with other state of the art kernel-based methods and demonstration of its utility for lung registration via labeled point set representation of lung anatomy.

1] The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing D st time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in D st time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of D st index can provide convenience for space weather applications.

Entanglement is the fundamental quantum property behind the now popular field of quantum transport of information. This quantum property is incompatible with the separation of a single system into two uncorrelated subsystems. Consequently, it does not require the use of an additive form of entropy. We discuss the problem of the choice of the most convenient entropy indicator, focusing our attention on a system of 2 qubits, and on a special set, denoted by ℑ. This set contains both the maximally and the partially entangled states that are described by density matrices diagonal in the Bell basis set. We select this set for the main purpose of making more straightforward our work of analysis. As a matter of fact, we find that in general the conventional von Neumann entropy is not a monotonic function of the entanglement strength. This means that the von Neumann entropy is not a reliable indicator of the departure from the condition of maximum entanglement. We study the behavior of a form of non-additive entropy, made popular by the 1988 work by Tsallis. We show that in the set ℑ, implying the key condition of non-vanishing entanglement, this non-additive entropy indicator turns out

Non-extensive statistical mechanics appears as a powerful way to describe complex systems. Tsallis entropy, the main core of this theory has been remained as an unproven assumption. Many people have tried to derive the Tsallis entropy axiomatically. Here we follow the work of Wang (EPJB, 2002) and use the incomplete information theory to retrieve the Tsallis entropy. We change the incomplete information axioms to consider the escort probability and obtain a correct form of Tsallis entropy in comparison with Wang's work.

For a dynamical system far from equilibrium, one has to deal with empirical probabilities defined through time-averages, and the main problem is then how to formulate an appropriate statistical thermodynamics. The common answer is that the standard functional expression of Boltzmann-Gibbs for the entropy should be used, the empirical probabilities being substituted for the Gibbs measure. Other functional expressions have been suggested, but apparently with no clear mechanical foundation. Here it is shown how a natural extension of the original procedure employed by Gibbs and Khinchin in defining entropy, with the only proviso of using the empirical probabilities, leads for the entropy to a functional expression which is in general different from that of Boltzmann-Gibbs. In particular, the Gibbs entropy is recovered for empirical probabilities of Poisson type, while the Tsallis entropies are recovered for a deformation of the Poisson distribution.

We consider several low-dimensional chaotic maps started in far-from-equilibrium initial conditions and we study the process of relaxation to equilibrium. In the case of conservative maps the Boltzmann–Gibbs entropy S(t) increases linearly in time with a slope equal to the Kolmogorov–Sinai entropy rate. The same result is obtained also for a simple case of dissipative system, the logistic map, when considered in the chaotic regime. A very interesting results is found at the chaos threshold. In this case, the usual Boltzmann–Gibbs is not appropriate and in order to have a linear increase, as for the chaotic case, we need to use the generalized q-dependent Tsallis entropy Sq(t) with a particular value of a q different from 1 (when q=1 the generalized entropy reduces to the Boltzmann–Gibbs). The entropic index q appears to be characteristic of the dynamical system.

The q-Gaussians are discussed from the point of view of variance mixtures of normals and exchangeability. For each q< 3, there is a q-Gaussian distribution that maximizes the Tsallis entropy under suitable constraints. This paper shows that q-Gaussian random variables can be represented as variance mixtures of normals. These variance mixtures of normals are the attractors in central limit theorems for sequences of exchangeable random variables; thereby, providing a possible model that has been extensively studied in probability theory. The formulation provided has the additional advantage of yielding process versions which are naturally q-Brownian motions. Explicit mixing distributions for q-Gaussians should facilitate applications to areas such as option pricing. The model might provide insight into the study of superstatistics.

Based on the Tsallis entropy, the nonextensive thermodynamic properties are studied as a qdeformation of classical statistical results using only probabilistic methods and straightforward calculations. It is shown that the constant in the Tsallis entropy depends on the deformation parameter and must be redefined to recover the usual thermodynamic relations. The notions of variance and covariance are generalised. A partial derivative formula of the entropy is established. It verifies important relations from which most of the nonextensive thermodynamics relations can be recovered. This leads to a new proof of a highly nontrivial conclusion that thermodynamic relations and Maxwell relations in non extensive thermodynamic have the same forms as those in ordinary nonextensive statistical mechanics. Theoretical results are applied to ideal gas. The case of fermions and bosons systems with fractal distributions is also considered.

We investigate a two-parameter entropy introduced by Schwämmle and Tsallis and obtain its probability distribution in the canonical ensemble. The probability distribution is given in terms of the Lambert W-function which has been used in many branches of physics, especially in fractal structures. Also, extensivity of S q,q ′ is discussed and a relationship is found to exist between the probabilities of a composite system and its subsystems so that the two-parameter entropy, S q,q ′ , is extensive. * The above equation shows that W -function can be used to express self-similarity in some fractal structures. This has been recently shown in a number of studies. Banwell and Jayakumar showed that W -function describes the relation between voltage, current and resistance in a diode, Packel and Yuen [25] applied the W -function to a ballistic projectile in the presence of air resistance.

Monte Carlo based methods such as path tracing are the only to do the physically correct simulations of global illumination. Due to its high capability to exploit acceleration structures and SIMD parallelism of modern processors, path tracing is becoming potential in the sense of real time. Basically path tracing generates images with heavy noise. Adaptive sampling is an interesting way

In this paper, we introduce Nonadditive Information Theory through the axiomatic formulation of Tsallis entropy. We show that systems with transitions from high dimensionality to few degrees of freedom are better described by nonadditive formalism. Such a biological system is the brain and brain rhythms is its macroscopic dynamic trace. We will show with simulations that Tsallis entropy is a powerful information measure, and we present results of brain dynamics analyzed using EEG recordings from a brain injury model.

Although several in silico promoter prediction methods have been developed to date, they are still limited in predictive performance. The limitations are due to the challenge of selecting appropriate features of promoters that distinguish them from non-promoters and the generalization or predictive ability of the machine-learning algorithms. In this paper we attempt to define a novel approach by using unique descriptors and machine-learning methods for the recognition of eukaryotic polymerase II promoters. In this study, non-linear time series descriptors along with non-linear machine-learning algorithms, such as support vector machine (SVM), are used to discriminate between promoter and non-promoter regions. The basic idea here is to use descriptors that do not depend on the primary DNA sequence and provide a clear distinction between promoter and non-promoter regions. The classification model built on a set of 1000 promoter and 1500 non-promoter sequences, showed a 10-fold cross-v...

We review some approaches to the understanding of fluctuations in some models used to describe socio and economic systems. Our approach builds on the development of a simple Langevin equation that characterises stochastic processes. This provides a unifying approach that allows first a straightforward description of the early approaches of Bachelier. We generalise the approach to stochastic equations that model interacting agents. Using a simple change of variable, we show that the peer pressure model of Marsilli and the wealth dynamics model of Solomon are closely related. The methods are further shown to be consistent with a global free energy functional that invokes an entropy term based on the Boltzmann formula. A more recent approach by Michael and Johnson maximised a Tsallis entropy function subject to simple constraints. We show how this approach can be developed from an agent model where the simple Langevin process is now conditioned by local rather than global noise. The approach yields a BBGKY type hierarchy of equations for the system correlation functions. Of especial interest is that the results can be obtained from a new free energy functional similar to that mentioned above except that a Tsallis like entropy term replaces the Boltzmann entropy term. A mean field approximation yields the results of Michael and Johnson. We show how personal income data for Brazil, the US, Germany and the UK, analysed recently by Borgas can be qualitatively understood by this approach. Agent models We consider a simple type of agent model consisting of a set {i) of agents, each of which can have an intrinsic attribute, x i. This could be a measure of attractiveness or repulsiveness. It could be proportional to the financial health or wealth of the agent. Now assume that this gives rise to some kind

Fault population statistics play a key role in the understanding of any statistical seismicity approach. In the present work a non-extensive statistical physics approach is formulated and tested for the local fault length distribution. The approach is composed of the following parts: (i) Tsallis entropy, S q , (ii) maximization of the Tsallis entropy under appropriate constrains, and (iii) derivation of the cumulative distribution function (CDF) of the fault length population. This model is tested using fault length data from the Central Crete graben in front of the Hellenic arc and estimated a thermodynamic q parameter equal to 1.16, which supports the conclusion that the fault system in Central Crete graben is a sub-extensive one.

The main objective of analyzing functional magnetic resonance imaging (fMRI) data sets is to screen the physiologically induced signals from noise or artifacts resulting either from involuntary patient motion or MRI detection techniques. One problem, that is not yet solved, is related to the dependency of the results in regard to the threshold applied within each analysis. Recently, an alternative fMRI time series analysis method has been proposed to decrease the dependency of the results with the applied threshold. This method is based on the calculation of the generalized mutual information (GMI) between the blood oxygenation level dependence time series and the paradigm slope. Since the analysis relies heavily on the Tsallis q parameter, a broad spectrum of results can be produced. So simulated data analysis was performed in order to construct the receiver operating characteristic curves. The parameters that evaluate the quality of the curves were determined thus allowing for an optimization of the q values. Results for simulated and real fMRI data were compared for both GMI and classical deterministic analysis.

The superposition of medical images, technically known as co-registration, can take a major role in determining the topographic and morphological changes in functional diagnostic and therapeutic purposes. This paper describes a study focused on to find an alternative cost function method for medical images co-registration through the study of performance and robustness of the TSallis Entropy in Statistical Parametric Mapping package (SPM). Images of Magnetic Resonance (MR) and Single Photon Emission Computed Tomography (SPECT) of 3 patients morphologically normal were used for the construction of anatomic phantoms containing predetermined geometric variations. The simulated images were co-registered with the original images using traditional techniques and the proposed method. The comparative analysis of the Root Mean Square (RMS) error showed that the Tsallis Entropy was more efficient in the intramodality alignment, while the Shannon Entropy in the intermodality one; revealing therefore the importance of the implementation of the Tsallis Entropy in SPM for applications in neurology and neuropsychiatric evaluation. H. T. Amaral Silva is with the

Maximum entropy principle does not seem to distinguish between the use of Tsallis and Renyi entropies as either of them may be used to derive similar kind of q-exponential distributions. In this paper, we address the question whether the Renyi entropy is equally suitable to describe those systems with q-exponential behaviour, where the use of the Tsallis entropy is relevant. We discuss a speciÿc class of dynamical systems, namely, one-dimensional dissipative maps at chaos threshold and make our study from two aspects: (i) power-law sensitivity to the initial conditions and the rate of entropy increase, (ii) generalized bit cumulants. We present evidence that the Tsallis entropy is more appropriate entropic form for such studies as compared to Renyi form.

Image analysis usually refers to processing of images with the goal of finding objects presented in the image. Image segmentation is one of the most critical tasks in automatic image analysis. The nonextensive entropy is a recent development in statistical mechanics and it is a new formalism in which a real quantity q was introduced as parameter for physical systems that present long range interactions, long time memories and fractal-type structures. In image processing, one of the most efficient techniques for image segmentation is entropy-based thresholding. This approach uses the Shannon entropy originated from the information theory considering the gray level image histogram as a probability distribution. In this paper, Tsallis entropy is applied as a general entropy formalism for information theory. For the first time image thresholding by nonextensive entropy is proposed regarding the presence of nonadditive information content in some image classes. Some typical results are p...

We present the results for the study and classification of urine sediments and coproparasitoscopic specimens using neural networks. This method has the additional advantage of taking into account the internal geometry of certain structures and to classify them according to certain parameters such as fractal dimension and entropies. In this case we use Renyi and Tsallis entropies with order q. These results are introduced as information for a hierarchical neuronal network, and allows increasing the precision of the urine sediment and parasite microscopic determination..

In this article, Shannon, Rényi and Tsallis entropies are considered for a system of events characterized by an arbitrary probability distribution P that can be incomplete, complete or overcomplete. After a suitable transformation that leads to the escort probabilities of P, these can be written as the canonical probability distribution for a set of pseudo-energies (Hartley information, E n = − ln P n) and a dimensionless parameter q that plays the role of thermodynamics β. Several relations between the entropies are presented, including the analysis of compound systems. The method is illustrated with an example.

We have conducted experiments on an asymmetrically forced quasi-two-dimensional turbulent flow in a rapidly rotating annulus. Assuming conservation of potential enstrophy and energy, we maximize a nonextensive entropy function to obtain the azimuthally averaged vorticity as a function of radial position. The predicted vorticity profile is in good accord with the observations. A nonextensive formalism is appropriate because long-range correlations between small-scale vortices give rise to large coherent structures in the turbulence. We also derive probability distribution functions for the vorticity from both extensive and nonextensive entropies, and we find that the prediction from nonextensive theory is in better accord with experiment, especially in the tails of the distribution function. The nonextensive parameter q has the value 1.9 ± 0.2.