DYNAMICAL AND TOPOLOGICAL INVARIANTS OF NONLINEAR DYNAMICS OF THE CHAOTIC LASER DIODES WITH AN ADDITIONAL OPTICAL INJECTION

Nonlinear chaotic dynamics of the of the chaotic laser diodes with an additional optical injection is computed within rate equations model, based on the a set of rate equations for the slave laser electric complex amplitude and carrier density. To calculate the system dynamics in a chaotic regime the known chaos theory and non-linear analysis methods such as a correlation integral algorithm, the Lyapunov’s exponents and Kolmogorov entropy analysis are used. There are listed the data of computing dynamical and topological invariants such as the correlation, embedding and Kaplan-Yorke dimensions, Lyapunov’s exponents, Kolmogorov entropy etc. New data on topological and dynamical invariants are computed and firstly presented.

On Rényi Permutation Entropy

Among various modifications of the permutation entropy defined as the Shannon entropy of the ordinal pattern distribution underlying a system, a variant based on Rényi entropies was considered in a few papers. This paper discusses the relatively new concept of Rényi permutation entropies in dependence of non-negative real number q parameterizing the family of Rényi entropies and providing the Shannon entropy for q=1. Its relationship to Kolmogorov–Sinai entropy and, for q=2, to the recently introduced symbolic correlation integral are touched.

A Hybrid MPI-OpenMP Parallel Algorithm for the Assessment of the Multifractal Spectrum of River Networks

The possibility to create a flood wave in a river network depends on the geometric properties of the river basin. Among the models that try to forecast the Instantaneous Unit Hydrograph (IUH) of rainfall precipitation, the so-called Multifractal Instantaneous Unit Hydrograph (MIUH) by De Bartolo et al. (2003) rather successfully connects the multifractal properties of the river basin to the observed IUH. Such properties can be assessed through different types of analysis (fixed-size algorithm, correlation integral, fixed-mass algorithm, sandbox algorithm, and so on). The fixed-mass algorithm is the one that produces the most precise estimate of the properties of the multifractal spectrum that are relevant for the MIUH model. However, a disadvantage of this method is that it requires very long computational times to produce the best possible results. In a previous work, we proposed a parallel version of the fixed-mass algorithm, which drastically reduced the computational times almost proportionally to the number of Central Processing Unit (CPU) cores available on the computational machine by using the Message Passing Interface (MPI), which is a standard for distributed memory clusters. In the present work, we further improved the code in order to include the use of the Open Multi-Processing (OpenMP) paradigm to facilitate the execution and improve the computational speed-up on single processor, multi-core workstations, which are much more common than multi-node clusters. Moreover, the assessment of the multifractal spectrum has also been improved through a direct computation method. Currently, to the best of our knowledge, this code represents the state-of-the-art for a fast evaluation of the multifractal properties of a river basin, and it opens up a new scenario for an effective flood forecast in reasonable computational times.

Information Theory and Symbolic Analysis: Theory and Applications

Symbolic analysis has been developed and used successfully in very diverse fields. In recent literature, the contributions of symbolic analysis to the study of complex dynamics and network structures are easy to find, especially those based on symbolic entropy measures (such as permutation entropy) and the symbolic correlation integral (connected with Renyi and Tsallis entropies)[...]

Constraining the Moho Depth Below Bhutan With Global-Phase Seismic Interferometry

We use a novel technique named global-phase seismic interferometry (GloPSI) to image the lithospheric structure, and in particular the Moho, below two parallel north-south transects belonging to the GANSSER network (2013–2014). The profiles cross the Himalayan orogenic wedge in Bhutan, a tectonically important area within the largest continent-continent collision zone on Earth that is still undergoing crustal thickening and represents a challenging imaging target for the GloPSI approach. GloPSI makes use of direct waves from distant earthquakes and receiver-side reverberations with near vertical incidence. Reflections are isolated from earthquake recordings by solving a correlation integral and are turned into a reflectivity image of the lithosphere below the arrays. Our results compare favorably with first-order features observed from a previous receiver function (RF) study. We show that a combined interpretation of GloPSI and RF results allows for a more in-depth understanding of the lithospheric structure across the orogenic wedge in Bhutan.

Reducing the prior identification uncertainty of the bearing of active interference sources

Problem statement. In measuring the spatial coordinates of sources of active interference, one of the main tasks is to identify their bearings. This problem belongs to the class of multi-alternative problems of statistical choice of hypotheses, the solution of which becomes much more complicated with an increase in the number of sources of active interference.Objective. Reduce the prior uncertainty in identifying bearings of active interference sources due to the use of differences in their energy characteristics at the stage of primary processing of interference signals, recalculated to the points of intersection of bearings.Results. The article discusses the processing features of bearing information in a two-position radar system. It is shown that in these systems, due to the absence of redundant information, the identification of bearings is a multi-alternative problem of statistical choice of hypotheses. The analysis of the matrix of coordinates of intersections of azimuthal bearings is carried out, a rule for identifying possible hypotheses of identification is formulated. It is proposed to use the energy differences of interference signals to reduce the prior uncertainty in identifying bearings. It is shown that a measure of this difference can be the value of the correlation integral, calculated at the stage of primary processing of interference signals.Practical implications. The principle of bearing identification considered in the article can be used to implement the identification of bearings from sources of active interference and other various radio emission objects, including space ones, when upgrading the mathematical and software systems for information processing.

MEOD: Memory-Efficient Outlier Detection on Streaming Data

In this paper, a memory-efficient outlier detection (MEOD) approach for streaming data is proposed. The approach uses a local correlation integral (LOCI) algorithm for outlier detection, finding the outlier based on the density of neighboring points defined by a given radius. The radius value detection problem is converted into an optimization problem. The radius value is determined using a particle swarm optimization (PSO)-based approach. The results of the MEOD technique application are compared with existing approaches in terms of memory, time, and accuracy, such as the memory-efficient incremental local outlier factor (MiLOF) detection technique. The MEOD technique finds outlier points similar to MiLOF with nearly equal accuracy but requires less memory for processing.

Selection of Embedding Dimension and Delay Time in Phase Space Reconstruction via Symbolic Dynamics

The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay τ∗ and embedding dimension p for phase space reconstruction. The value of τ∗ can be estimated from the Mutual Information, but this method is rather cumbersome computationally. Additionally, some researchers have recommended that τ∗ should be chosen to be dependent on the embedding dimension p by means of an appropriate value for the time delay τw=(p−1)τ∗, which is the optimal time delay for independence of the time series. The C-C method, based on Correlation Integral, is a method simpler than Mutual Information and has been proposed to select optimally τw and τ∗. In this paper, we suggest a simple method for estimating τ∗ and τw based on symbolic analysis and symbolic entropy. As in the C-C method, τ∗ is estimated as the first local optimal time delay and τw as the time delay for independence of the time series. The method is applied to several chaotic time series that are the base of comparison for several techniques. The numerical simulations for these systems verify that the proposed symbolic-based method is useful for practitioners and, according to the studied models, has a better performance than the C-C method for the choice of the time delay and embedding dimension. In addition, the method is applied to EEG data in order to study and compare some dynamic characteristics of brain activity under epileptic episodes

Space-time processing for «range – azimuth – elevation» measurements in non-cooperative systems of radars with phased array antennas

The methods of measuring the three coordinates of an aircraft in the takeoff and landing mode on the runway of airfields based on the use of non - cooperative two-and three-position systems of radars with phased array antennas are considered. For these variants, general analytical expressions are obtained for the complex generalized correlation integral of space – time processing in the function of spatial coordinates, taking into account the individual directional pattern of phased array antennas. On the basis of two – dimensional profiles of the correlation integral modules «range – elevation» and «azimuth – elevation», examples of comparing particular variants of two-position and three-position systems of radars with their location on one straight line parallel runway are given. In conditions of large signal-to-noise ratios, power-law nonlinear transformations of the correlation integral correlation integral module are applied to reduce the level of side lobes in the two – dimensional sections «range – elevation» and «azimuth – elevation». The following results are obtained using examples. Two-dimensional diagrams of the correlation integral module «range – elevation» do not depend on the azimuth of the aircraft in the range of azimuth values β=0…10 ̊ and correctly display the angle of elevation and the range of the aircraft when 2…3 radars of a non-cooperative system are located on the straight line parallel runway. The two-dimensional diagrams of the correlation integral module «azimuth – elevation angle» have an interference structure, and the number and level of their side lobes increase with increasing azimuth of the aircraft. With azimuth β≥10 ̊, this can lead to ambiguity in the measurement of the azimuth and uncertainty in the elevation angle . One of the measures to reduce the side level of the diagrams of the correlation integral module can be the use of a power-law transformation of normalized diagrams exponentiation of degree 3...4. An increase in the number of radars from two to three when they are located on one straight line parallel to the runway led to a decrease in the side lobes level of the «range – elevation angle» and «azimuth – elevation angle» diagrams. In this case, it may be advisable to solve the problem of optimal choice of the position of the intermediate radar on the same straight line. Calculations were also carried out for an additional example of the location of the intermediate radar of a 3-position system with its removal from the base line. At the same time, there was an increase of the side lobes level in the «azimuth – elevation angle» sections, which in the future may require additional research in terms of optimizing the placement of the radars in horizontal plane for such a radar systems.