Sparse Randomized Shortest Paths Routing with Tsallis Divergence Regularization

This work elaborates on the important problem of (1) designing optimal randomized routing policies for reaching a target node t from a source note s on a weighted directed graph G and (2) defining distance measures between nodes interpolating between the least cost (based on optimal movements) and the commute-cost (based on a random walk on G), depending on a temperature parameter T. To this end, the randomized shortest path formalism (RSP, [2,99,124]) is rephrased in terms of Tsallis divergence regularization, instead of Kullback-Leibler divergence. The main consequence of this change is that the resulting routing policy (local transition probabilities) becomes sparser when T decreases, therefore inducing a sparse random walk on G converging to the least-cost directed acyclic graph when T tends to 0. Experimental comparisons on node clustering and semi-supervised classification tasks show that the derived dissimilarity measures based on expected routing costs provide state-of-the-art results. The sparse RSP is therefore a promising model of movements on a graph, balancing sparse exploitation and exploration in an optimal way

Wavepacket of the Universe and its spreading

Wavepackets in quantum mechanics spread and the Universe in cosmology expands. We discuss a formalism where the two effects can be unified. The basic assumption is that the Universe is determined by a unitarily evolving wavepacket defined on space-time. Space-time is static but the Universe is dynamic. Spreading analogous to expansion known from observational cosmology is obtained if one regards time evolution as a discrete process with probabilities of jumps determined by a variational principle employing Kolmogorov-Nagumo-R\'enyi averages. The choice of the R\'enyi calculus implies that the form of the Universe involves an implicit fractal structure. The formalism automatically leads to two types of "time" parameters: $\tau$, with dimension of $x^0$, and dimensionless $\varepsilon=\ln \epsilon_\tau$, related to the form of diffeomorphism that defines the dynamics. There is no preferred time foliation, but effectively the dynamics leads to asymptotic concentration of the Universe on spacelike surfaces that propagate in space-time. The analysis is performed explicitly in $1+1$ dimensions, but the unitary evolution operator is brought to a form that makes generalizations to other dimensions and other fields quite natural.Comment: v1 preliminary report, v2 includes sections on the explicit form of the evolution operator, v3 includes an explicit analysis based on Kolmogorov-Nagumo-Renyi averaging, v4 section on 1+3 generalization is corrected, v5 conflict of notation in Bernoulli and Renyi forms is fixed; v6 accepted in Int.J.Theor.Phy

A precise bare simulation approach to the minimization of some distances. Foundations

In information theory -- as well as in the adjacent fields of statistics, machine learning, artificial intelligence, signal processing and pattern recognition -- many flexibilizations of the omnipresent Kullback-Leibler information distance (relative entropy) and of the closely related Shannon entropy have become frequently used tools. To tackle corresponding constrained minimization (respectively maximization) problems by a newly developed dimension-free bare (pure) simulation method, is the main goal of this paper. Almost no assumptions (like convexity) on the set of constraints are needed, within our discrete setup of arbitrary dimension, and our method is precise (i.e., converges in the limit). As a side effect, we also derive an innovative way of constructing new useful distances/divergences. To illustrate the core of our approach, we present numerous examples. The potential for widespread applicability is indicated, too; in particular, we deliver many recent references for uses of the involved distances/divergences and entropies in various different research fields (which may also serve as an interdisciplinary interface)

Imaging time series for the classification of EMI discharge sources

In this work, we aim to classify a wider range of Electromagnetic Interference (EMI) discharge sources collected from new power plant sites across multiple assets. This engenders a more complex and challenging classification task. The study involves an investigation and development of new and improved feature extraction and data dimension reduction algorithms based on image processing techniques. The approach is to exploit the Gramian Angular Field technique to map the measured EMI time signals to an image, from which the significant information is extracted while removing redundancy. The image of each discharge type contains a unique fingerprint. Two feature reduction methods called the Local Binary Pattern (LBP) and the Local Phase Quantisation (LPQ) are then used within the mapped images. This provides feature vectors that can be implemented into a Random Forest (RF) classifier. The performance of a previous and the two new proposed methods, on the new database set, is compared in terms of classification accuracy, precision, recall, and F-measure. Results show that the new methods have a higher performance than the previous one, where LBP features achieve the best outcome

Image similarity in medical images

Recent experiments have indicated a strong influence of the substrate grain orientation on the self-ordering in anodic porous alumina. Anodic porous alumina with straight pore channels grown in a stable, self-ordered manner is formed on (001) oriented Al grain, while disordered porous pattern is formed on (101) oriented Al grain with tilted pore channels growing in an unstable manner. In this work, numerical simulation of the pore growth process is carried out to understand this phenomenon. The rate-determining step of the oxide growth is assumed to be the Cabrera-Mott barrier at the oxide/electrolyte (o/e) interface, while the substrate is assumed to determine the ratio β between the ionization and oxidation reactions at the metal/oxide (m/o) interface. By numerically solving the electric field inside a growing porous alumina during anodization, the migration rates of the ions and hence the evolution of the o/e and m/o interfaces are computed. The simulated results show that pore growth is more stable when β is higher. A higher β corresponds to more Al ionized and migrating away from the m/o interface rather than being oxidized, and hence a higher retained O:Al ratio in the oxide. Experimentally measured oxygen content in the self-ordered porous alumina on (001) Al is indeed found to be about 3% higher than that in the disordered alumina on (101) Al, in agreement with the theoretical prediction. The results, therefore, suggest that ionization on (001) Al substrate is relatively easier than on (101) Al, and this leads to the more stable growth of the pore channels on (001) Al

Temporal organization of magnetospheric fluctuations unveiled by recurrence patterns in the Dst index

This work has been financially supported by the joint Greek-German project “Transdisciplinary assessment of dynamical complexity in magnetosphere and climate: A unified description of the nonlinear dynamics across extreme events” funded by IKY and DAAD. Individual financial support of the authors has been granted by the LINC (Learning about Interacting Networks in Climate) project (project no. 289447) funded by the Marie Curie Initial Training Network (ITN) program (FP7-PEOPLE2011-ITN), the German Federal Ministry for Science and Education (BMBF) via the Young Investigator’s Group CoSy-CC2 (grant no. 01LN1306A) and the project GLUES, the Stordalen Foundation (Planetary Boundary Research Network PB.net), and the International Research Training Group IRTG 1740/TRP 2014/50151-0, jointly funded by the German Research Foundation (DFG, Deutsche Forschungsgemeinschaft) and the S˜ao Paulo Research Foundation (FAPESP, Funda¸c˜ao de Amparo `a Pesquisa do Estado de S˜ao Paulo). Numerical codes used for estimating RQA and RNA properties can be found in the software package pyunicorn70, which is available at https://github.com/pik-copan/pyunicorn. The Dst data have been obtained from the World Data Center for Geomagnetism, Kyoto (http://wdc.kugi.kyoto-u.ac.jp/index.html). We are grateful to three reviewers of an earlier version of this manuscript for their detailed comments.Peer reviewedPublisher PD