Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Entropy Analysis of Industrial Accident Data Series

Complex industrial plants exhibit multiple interactions among smaller parts and with human operators. Failure in one part can propagate across subsystem boundaries causing a serious disaster. This paper analyzes the industrial accident data series in the perspective of dynamical systems. First, we process real world data and show that the statistics of the number of fatalities reveal features that are well described by power law (PL) distributions. For early years, the data reveal double PL behavior, while, for more recent time periods, a single PL fits better into the experimental data. Second, we analyze the entropy of the data series statistics over time. Third, we use the Kullback–Leibler divergence to compare the empirical data and multidimensional scaling (MDS) techniques for data analysis and visualization. Entropy-based analysis is adopted to assess complexity, having the advantage of yielding a single parameter to express relationships between the data. The classical and the generalized (fractional) entropy and Kullback–Leibler divergence are used. The generalized measures allow a clear identification of patterns embedded in the data.

The impact of SFAS 123R on CEO equity compensation

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

Consumption and emotional compensation in economic crisis

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Management from the NOVA – School of Business and Economics

Rényi entropy and the thermodynamic stability of black holes

Thermodynamic stability of black holes, described by the Rényi formula as equilibrium compatible entropy function, is investigated. It is shown that within this approach, asymptotically flat, Schwarzschild black holes can be in stable equilibrium with thermal radiation at a fixed temperature. This implies that the canonical ensemble exists just like in anti-de Sitter space, and nonextensive effects can stabilize the black holes in a very similar way as it is done by the gravitational potential of an anti-de Sitter space. Furthermore, it is also shown that a Hawking–Page-like black hole phase transition occurs at a critical temperature which depends on the q-parameter of the Rényi formula.

Exercise and heart failure. Relation of the severity of the disease to the anaerobic threshold and the respiratory compensation point

OBJECTIVE - To identify, the anaerobic threshold and respiratory compensation point in patients with heart failure. METHODS - The study comprised 42 Men,divided according to the functional class (FC) as follows: group I (GI) - 15 patients in FC I; group II (GII) - 15 patients in FC II; and group III (GIII) - 12 patients in FC III. Patients underwent a treadmill cardiopulmonary exercise test, where the expired gases were analyzed. RESULTS - The values for the heart rate (in bpm) at the anaerobic threshold were the following: GI, 122±27; GII, 117±17; GIII, 114±22. At the respiratory compensation point, the heart rates (in bpm) were as follows: GI, 145±33; GII, 133±14; GIII 123±22. The values for the heart rates at the respiratory compensation point in GI and GIII showed statistical difference. The values of oxygen consumption (VO2) at the anaerobic threshold were the following (in ml/kg/min): GI, 13.6±3.25; GII, 10.77±1.89; GIII, 8.7±1.44 and, at the respiratory compensation point, they were as follows: GI, 19.1±2.2; GII, 14.22±2.63; GIII, 10.27±1.85. CONCLUSION - Patients with stable functional class I, II, and III heart failure reached the anaerobic threshold and the respiratory compensation point at different levels of oxygen consumption and heart rate. The role played by these thresholds in physical activity for this group of patients needs to be better clarified.

Relative information entropy in cosmology: The problem of information entanglement

The necessary information to distinguish a local inhomogeneous mass density field from its spatial average on a compact domain of the universe can be measured by relative information entropy. The Kullback-Leibler (KL) formula arises very naturally in this context, however, it provides a very complicated way to compute the mutual information between spatially separated but causally connected regions of the universe in a realistic, inhomogeneous model. To circumvent this issue, by considering a parametric extension of the KL measure, we develop a simple model to describe the mutual information which is entangled via the gravitational field equations. We show that the Tsallis relative entropy can be a good approximation in the case of small inhomogeneities, and for measuring the independent relative information inside the domain, we propose the R\'enyi relative entropy formula.

kinetic analysis of ester hydrolysis reactions considering volume and enthalpy changes due to mixing

Magdeburg, Univ., Fak. für Verfahrens- und Systemtechnik, Diss., 2012

Computer-assisted motion compensation and analysis of perfusion ultrasound data

Magdeburg, Univ., Fak. für Informatik, Diss., 2014

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

"Vegeu el resum a l'inici del document del fitxer adjunt."

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.