680 research outputs found
Analysis and visualization of seismic data using mutual information
Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis,
visualization maps are generated, providing an intuitive and useful representation of the
complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes
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
Expand-and-Cluster: Exact Parameter Recovery of Neural Networks
Can we recover the hidden parameters of an Artificial Neural Network (ANN) by
probing its input-output mapping? We propose a systematic method, called
`Expand-and-Cluster' that needs only the number of hidden layers and the
activation function of the probed ANN to identify all network parameters. In
the expansion phase, we train a series of networks of increasing size using the
probed data of the ANN as a teacher. Expansion stops when a minimal loss is
consistently reached in networks of a given size. In the clustering phase,
weight vectors of the expanded students are clustered, which allows structured
pruning of superfluous neurons in a principled way. We find that an
overparameterization of a factor four is sufficient to reliably identify the
minimal number of neurons and to retrieve the original network parameters in
of tasks across a family of 150 toy problems of variable difficulty.
Furthermore, shallow and deep teacher networks trained on MNIST data can be
identified with less than overhead in the neuron number. Thus, while
direct training of a student network with a size identical to that of the
teacher is practically impossible because of the highly non-convex loss
function, training with mild overparameterization followed by clustering and
structured pruning correctly identifies the target network.Comment: Preprint: 14 pages, 6 figures. Appendix: 8 pages, 7 figure
Gravitational Lensing
Gravitational lensing has developed into one of the most powerful tools for
the analysis of the dark universe. This review summarises the theory of
gravitational lensing, its main current applications and representative results
achieved so far. It has two parts. In the first, starting from the equation of
geodesic deviation, the equations of thin and extended gravitational lensing
are derived. In the second, gravitational lensing by stars and planets,
galaxies, galaxy clusters and large-scale structures is discussed and
summarised.Comment: Invited review article to appear in Classical and Quantum Gravity, 85
pages, 15 figure
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