In addition, environmental conflict analysis (ECA) also is used to prevent conflicts during planning and implementation of projects or programs, as evidenced by the studies on conflicts related to ecological tourism [13], or water management [14], [15]. ECA has been mostly conducted using qualitative methods, as showed by the study on environmental conflict from an infrastructure project [1], which was based on the capability perspective. In this study, we apply a quantitative method for ECA, the **entropy**-weight method, which is based on the **Shannon** **entropy** theory. **Shannon** proposed the concept of **entropy** as a measure of uncertainty in information, formulated in terms of probability theory [16]. The concept of **entropy** is well suited to identify the contrast criteria for decision-making [17]. Subsequent, research on **Shannon** **entropy** has contributed to the resolution of problems on different topics such as pollution [18], water quality [19], management [20], or fault detection [21].

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Then, in order to analyze violence against women in Peru, a computational model based on the **entropy** weight method, which is an approach from the **Shannon** **entropy** theory, was used. This method was applied to calculate the objective weights of the criteria; as if there was a big difference between the alternatives, the criterion will give decision-makers a great amount of information and the criterion can be considered as an important factor, as evidenced by the study to solve a problem of prioritization of strategies [8], to evaluate an environmental conflict [9], or social topics [10]. Therefore, the specific objective in this study is to determine a ranking of the departments of Peru, on violence against women, applying the **entropy**-weigh method.

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Several authors have studied the problem of retinal diseases using different types of medical images and statistical model- ing. For example, in [7] a study for tumor classification using a probabilistic framework is presented. In [10] a method for vessel segmentation using active contours is introduced. In [4] a work focused on retinoblastoma detection is presented and several processing techniques are reviewed, all of them based on different types of medical image processing. In [8], the authors contribute to retinoblastoma understanding by study- ing drug penetration and chemotherapy response in order to optimize patient treatment. However, in these previous studies, the level of penetration could not be quantified nor statistically evaluated. In addition, to the extent of our knowledge, the evaluation of topotecan penetration into retinoblastoma cells has never been performed using automatic image interpretation techniques. One of the ways to measure the penetration of topotecan within the tumorsphere is to measure the homogene- ity of gray levels of the pixels within it. There are numerous techniques to perform this measurement. In this work we use **Shannon** **entropy** and the coefficient of variation.

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The current study proposes the use of CNT Raman spectra as the main molecular information. Raman spectroscopy is a technique that provides the chemical fingerprint of molecules as vibrational, rotational, and other low-frequency modes. Thus, it is used for the study of biomolecular systems and nanoscale structure such as DNA, 41 proteins, 42 antibodies, 43 and carbon nanotubes (CNTs). 44 The Raman spectra can be transformed into **Shannon** entropies of the star graph, similar to a Fourier spectra transform. The use of star graphs as a graphical method to encode molecular/signal information has been proven for protein prediction 45-47 and nucleic acid 48 function, as well as cancer prediction using blood protein mass spectra 49 and epileptic seizure prediction using electroencephalogram (EEG) signals. 50 The end point (mitochondrial respiration or E3) used in the QSPR/QSAR analyses is a predictive function of the mitochondrial oxygen consumption (E3 pred ), which is the mitochondrial respiration under carbon nanotubes exposure

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Abstract: In this contribution, a comparison between different permutation entropies as classifiers of electroencephalogram (EEG) records corresponding to normal and pre-ictal states is made. A discrete probability distribution function derived from symbolization techniques applied to the EEG signal is used to calculate the Tsallis **entropy**, **Shannon** **Entropy**, Renyi **Entropy**, and Min **Entropy**, and they are used separately as the only independent variable in a logistic regression model in order to evaluate its capacity as a classification variable in a inferential manner. The area under the Receiver Operating Characteristic (ROC) curve, along with the accuracy, sensitivity, and specificity are used to compare the models. All the permutation entropies are excellent classifiers, with an accuracy greater than 94.5% in every case, and a sensitivity greater than 97%. Accounting for the amplitude in the symbolization technique retains more information of the signal than its counterparts, and it could be a good candidate for automatic classification of EEG signals.

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The six signals displayed in Fig. 4 were analyzed using the Information Theory based quantifiers: normalized **Shannon** **entropy**, statistical complexity and Fisher information measure, all the three quantifiers evaluated with Bandt–Pompe PDF. In particular, the study of interest is the behavioral transition between the different dynamics, from balanced to non- balanced. In order to do that, the above quantifiers are evaluated in overlapping sliding time windows of length N = 512 data and overlap δ = 1 data. For the Bandt and Pompe PDF evaluation a pattern length (embedding dimension) of D = 4 and embedding time τ = 1 are considered. The three quantifiers time evolution, normalized **Shannon** **entropy**, statistical complexity and Fisher information are given in Figs. 5 to 7 respectively. Each point represents the quantifier value in the corresponding time window. From these figures, one can see three different distinguishable behavioral zones. The first one which can be associated with a balance behavior (pure signal Type 0), which corresponds to time window 1–512, a transitional behavioral zone between windows 513–1024, and a third zone, corresponding to non-balance behavior (pure signal Type 1–6) between windows 1025–1537.

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A key aspect to explore in NILM applications is the adequate characterization of electrical energy consumption of domestic appliances. To tackle this issue we present a characterization of the behavior of electrical devices by using quantifiers stemming from Information Theory. The characterization is performed in two stages. Firstly, the original time series of the electrical consumption is transformed into a histogram with a nonparametric transformation that retains time causal information: the Bandt–Pompe methodology [4]. Secondly, this histogram is mapped onto the Causality Complexity–**Entropy** Plane (CCEP) [5], and its location is shown to serve as a characterization of a number of typical regimes. This plane is a compact manifold spanning values of the normalized **Shannon** **entropy** H and the statistical complexity C .

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We study the notion of approximate **entropy** within the framework of network theory. Approximate **entropy** is an uncertainty measure originally proposed in the context of dynamical systems and time series. We first define a purely structural **entropy** obtained by computing the approximate **entropy** of the so-called slide sequence. This is a surrogate of the degree sequence and it is suggested by the frequency partition of a graph. We examine this quantity for standard scale-free and Erd¨os-R´enyi networks. By using classical results of Pincus, we show that our **entropy** measure often converges with network size to a certain binary **Shannon** **entropy**. As a second step, with specific attention to networks generated by dynamical processes, we investigate approximate **entropy** of horizontal visibility graphs. Visibility graphs allow us to naturally associate with a network the notion of temporal correlations, therefore providing the measure a dynamical garment. We show that approximate **entropy** distinguishes visibility graphs generated by processes with different complexity. The result probes to a greater extent these networks for the study of dynamical systems. Applications to certain biological data arising in cancer genomics are finally considered in the light of both approaches.

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A mathematical framework has been proposed for analyzing Random Network Models (RNMs) and for characterizing their complexity. Such framework allows the study of several network properties or features (link density, clustering coefficient, degree distribution, connectivity), and their relationship with the RNM complexity. For doing so, different **entropy** measures have been evaluated and their relationship has been assessed. The sample degree distribution **entropy** has shown to be correlated with the RNM **entropy**, providing a practical measurable indicator of complexity in real networks. Acknowledgments: This work has been partially supported by project MTM2015-67396-P of Ministerio de Economía y Competitividad, Spain.

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At this stage we are in a position to draw an important consequence. In general, deformed (or Tsallis’) entropies are quite different objects as compared with Shannon’s one, save for q close to unity. This is not the case for q-Wehrl entropies! q-deformation becomes in this case a smooth shape-deformation. At the semiclassical level the difference between Tsallis and **Shannon** entropies becomes weaker than either at the quantal or the classical levels.

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Open systems are in constant interaction with their environment and demonstrate a remarkable degree of self-regulation. They are capable of preserving or restoring homeostasis and thus can resist the disorganiza- tion predicted by the second law; therefore, they may temporarily escape, or delay, the rapid increase in **entropy** defined for closed systems. In addition to self-regulation, they maintain order against constantly grow- ing **entropy** by performing work. The higher the **entropy**, the greater amount of work is required to restore the system to its initial state. The processes of nourishment, elimination, and repair result in a continuous exchange of the original material of the cell for new material derived from the environment.

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AbstrAct: The classical approach to estimate spatial models lays on the choice of a spatial weights matrix that reflects the interactions among locations. The rule used to define this matrix is supposed to be the most similar to the «true» spatial relationships, but for the researcher is difficult to elucidate when the choice of this matrix is right and when is wrong. This key step in the process of estimating spa- tial models is a somewhat arbitrary choice, as Anselin (2002) pointed out, and it can be seen as one of their main methodological problems. This note proposes not imposing the elements of the spatial matrix but estimating them by cross **entropy** (CE) econometrics. Since the spatial weight matrices are often row-standardized, each one of their rows can be approached as probability distributions. **Entropy** Econometrics (EE) techniques are a useful tool for recovering unknown probabi- lity distributions and its application allows the estimation of the elements of the spatial weights matrix instead of the imposition by researcher. Hence, the spatial lag matrix is not a matter of choice for researcher but of empirical estimation by CE. We compare classical with CE estimators by means of Monte Carlo simula- tions in several scenarios on the true spatial effect. The results show that Cross **Entropy** estimates outperform the classical estimates, especially when the specifi- cation of the weights matrix is not similar to the true one. This result points to CE as a helpful technique to reduce the degree of arbitrariness imposed in the estima- tion of spatial models.

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Tropical ecosystems are a very important part of the world’s richness, abundance and diversity of species. It is one of the most. The work present was carried out with the objective of comparing the floristic composition, the diversity of species, and the horizontal and vertical structure of the two subperennifolia forests in the small town of Haro, Escárcega, Campeche. 11 rectangular permanent sites of 1000 m2 were established under systematic sampling with a random point. In each site the variables heights and diameters of each individual were evaluated, species diversity indexes were determined, with the **Shannon** index, Simpson index and Pielou index; in the analysis of the structures, the importance value index and the Pretzsch A index were determined. The richness of species shows that in the La Corriente property is where the richest species were found with 51 species in 26 families, including the Euphorbiaceae family. In the Los Nances site, 38 species were recorded in 28 families, including the Faboideae family. The values of **Shannon**- Wiener index, Simpson dominance index and Pielou index show that in the La Corriente estate, the highest results were found, however, both properties show low values in species diversity. The species with the highest importance value index was Lysiloma latisiliquum (L.) Benth in the Los Nances property and the La Corriente property was the Sabal Mexican Martius species. In the vertical structure for the Pretzsch A index, the values between the two properties are similar as a result of a greater number of young individuals in the strata. However, significant differences were found for horizontal structure with the basal areas of both properties and in the **Shannon**-Wiener index of both properties with the frequency variable, no significant differences were found in the comparison of vertical structure with the pretzsch index of both properties.

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Abstract. The variational method with constraints recently developed by Verkley and Gerkema to describe maximum- **entropy** atmospheric profiles is generalized to ideal gases but with temperature-dependent specific heats. In so doing, an extended and non standard potential temperature is intro- duced that is well suited for tackling the problem under con- sideration. This new formalism is successfully applied to the atmosphere of Venus. Three well defined regions emerge in this atmosphere up to a height of 100 km from the surface: the lowest one up to about 35 km is adiabatic, a transition layer located at the height of the cloud deck and finally a third region which is practically isothermal.

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separated in three main groups corresponding to the three re- gions defined above. In particular, Region I is characterized by a low **entropy** value for E-W channel and an intermedi- ate value for N-S. In contrast, Region II is described by a high **entropy** value for E-W channel and a low **entropy** for N-S. According to Fig. 5a, Region III shows a strong corre- lation in **entropy** values of E-W and N-S channels, that is, the high **entropy** in both channels resembles white noise behav- ior. Furthermore, as shown in Fig. 5a the high **entropy** values of shuffled data in both channels confirm a high variability which resembles white noise. For Coyuca station (Fig. 6a), we observe a clear correlation between **entropy** values for scale 1, indicating that S E values are positively related. We

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del río Sendamal (Cajamarca), en el que se registró para las épocas seca y húmeda del año 2012, 62 especies repartidas en 14 Familias, correspondientes a 9 órdenes, tales como Melosirales, Tabelariales, Fragilariales, Achnanthales, Thalassiophysales, Naviculales, Cymbellales, Bacillaria/es y Surirellales; de los cuales los órdenes Naviculales y Cymbellales fueron los más abundantes, y tras el análisis del índice de diversidad se **Shannon** & Wiener H' para especies de diatomeas, se determinó que el agua presenta una Contaminación "Imperceptible" y "Leve", con valores que varían de 2.423 y 3.300 bits cel -1.

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as´ı como el propio art´ıculo de **Shannon** Scientific Aspects of Juggling se introducir´ a la notaci´ on “SITESWAP” como modelo matem´ atico para definir los lanzamientos de diferentes alturas, a partir de las funciones y secuencias o matrices malabares respectivamente para los casos de malabar simple (una persona, dos manos) o m´ ultiples manos. Posteriormente, se enunciar´ an y demostrar´ an resultados principales como el Teorema de la Media para el n´ umero de bolas o el Test de Permutaci´ on para comprobar si una secuencia de n´ umeros es o no malabar. Para la demostraci´ on de estos resultados nos hemos servido del art´ıculo Juggling drops and descents escrito por Joe Buhler, David Eisenbud, Ron Graham y Colin Wright

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The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block **entropy** functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

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The definition of **entropy** and its interpretation in terms of the evolution to equilibrium of isolated systems was a crucial step in understanding the link between mechanical and thermal features in classical mechanics [1]. The notion of probability applies, both in classical phase-space as well as in quantum mechanics, and from this the connection between **entropy** and the number of degrees of freedom of a system has been established [2]. The main difference between classical and quantum mechanical counting of states is, of course, the existence of the exclusion principle (for fermions) and other symmetry restrictions (both for fermions and bosons) imposed to quantum states. In both cases, fermions and bosons, the definition of the probability assigned to a state remains valid. This is not the case for states with complex energies, where the time evolution is non-oscillatory. States with complex energy, such as the Gamow states [3], are well described in the theory of scattering [4] and found as solutions of the analytical continuation of quantum relativistic and non-relativistic equations [5]. Several problems arise in dealing with these states, particularly their non-normalizability [6,7]. Most of these difficulties are removed with the use of amplitudes, which are the solutions of the equations and/or with the corresponding propagators, instead of working with their modulus. A suitable tool to work with Gamow states, in order to extract their thermodynamical information, is the path integration. In performing the path-integration we shall be dealing with amplitudes instead of probabilities, a concept which cannot be applied to states with complex energy.

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La Sierra Zapalinamé se localiza en el sureste del estado de Coahuila, es un área natural protegida decretada en 1996 por el gobierno estatal como zona de conservación ecológica. El Matorral Xerófilo y bosque de Pino Piñonero son los principales tipos de vegetación. La presente investigación se realizó con el objetivo de comparar los efectos de un incendio en la composición y estructura de la vegetación de Matorral Submontano de Rosáceas. Se evaluaron 10 sitios de muestreo de forma selectiva, siendo 5 sitios dentro del área afectada por el incendio y 5 sitios fuera del área afectada; con parcelas de 100 m 2 para medir el estrato arbustivo y cuadros de 1 m 2 para el estrato herbáceo. Se calcularon los atributos de la vegetación (Densidad, Frecuencia, Dominancia y Altura), para estimar Valor de Importancia Relativa (VIR), Índice de diversidad **Shannon**-Weaver, Índice de Riqueza de Margalef, Índice de Similitud y Coeficiente de Complementariedad. Se utilizó la prueba t student modificada por Magurran para evaluar si existen diferencias significativas entre las dos áreas. Se registraron 104 especies distribuidas en 32 familias; 42 especies del estrato arbustivo y 62 especies para el estrato herbáceo. Los resultados indican que existe una mayor diversidad de especies en los sitios no afectados por el incendio (H =herbáceo 3.64 nats/3.53 nats; H =Arbustivo 3.36 nats/3.26 nats). En el estrato arbustivo la riqueza de especies fue mayor en sitios no afectados (D mg = 4.72 nats); similar que el arbustivo, en el estrato herbáceo (D mg =

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