There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

[1] The complex system of the Earth's magnetosphere corresponds to an open spatially extended nonequilibrium (input-output) dynamical system. The nonextensive Tsallis entropy has been recently introduced as an appropriate information measure to investigate dynamical complexity in the magnetosphere. The method has been employed for analyzing Dst time series and gave promising results, detecting the complexity dissimilarity among different physiological and pathological magnetospheric states (i.e., prestorm activity and intense magnetic storms, respectively). This paper explores the applicability and effectiveness of a variety of computable entropy measures (e.g., block entropy, Kolmogorov entropy, T complexity, and approximate entropy) to the investigation of dynamical complexity in the magnetosphere. We show that as the magnetic storm approaches there is clear evidence of significant lower complexity in the magnetosphere. The observed higher degree of organization of the system agrees with that inferred previously, from an independent linear fractal spectral analysis based on wavelet transforms. This convergence between nonlinear and linear analyses provides a more reliable detection of the transition from the quiet time to the storm time magnetosphere, thus showing evidence that the occurrence of an intense magnetic storm is imminent. More precisely, we claim that our results suggest an important principle: significant complexity decrease and accession of persistency in Dst time series can be confirmed as the magnetic storm approaches, which can be used as diagnostic tools for the magnetospheric injury (global instability). Overall, approximate entropy and Tsallis entropy yield superior results for detecting dynamical complexity changes in the magnetosphere in comparison to the other entropy measures presented herein. Ultimately, the analysis tools developed in the course of this study for the treatment of Dst index can provide convenience for space weather applications.

Investigating dynamical complexity in the magnetosphere using various entropy measures

In this paper, Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) is introduced. It is an extension of Multidimensional Recurrence Quantification Analysis (MdRQA), which allows to quantify the (auto-)recurrence properties of a single multidimensional time-series. MdCRQA extends MdRQA to bi-variate cases to allow for the quantification of the co-evolution of two multidimensional time-series. Moreover, it is shown how a Diagonal Cross-Recurrence Profile (DCRP) can be computed from the MdCRQA output that allows to capture time-lagged coupling between two multidimensional time-series. The core concepts of these analyses are described, as well as practical aspects of their application. In the supplementary materials to this paper, implementations of MdCRQA and the DCRP as MatLab- and R-functions are provided.

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Multidimensional Cross-Recurrence Quantification Analysis (MdCRQA) – A Method for Quantifying Correlation between Multivariate Time-Series

A lot of effort and time is utilized in the planning and building of the cellular wireless networks to use minimum infrastructural components to provide the best network coverage as well as delivery of quality of service Generally, path loss models are used for the prediction of wireless network coverage Therefore, detailed knowledge of the appropriate path loss model suitable for the proposed geographical area is needed to determine the coverage quality of any wireless network design However, to the best of our knowledge, despite the importance of path loss models, as used for the prediction of wireless network coverage, there doesn't exist any comprehensive survey in this field Therefore, the purpose of this paper is to survey the existing techniques and mechanisms which can be addressed in this domain Briefly, the contributions of this paper are: (1) providing a comprehensive and up to date survey of the various network coverage prediction techniques, indicating the different frequency ranges the models were developed, (2) the different suitable terrains for each of the model and the best suit mobile generation were presented, and lastly, (3) providing comparative analysis to aid the planning and implementation of the cellular networks

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Cellular Communications Coverage Prediction Techniques: A Survey and Comparison

Characterization of precipitation is important for proper interpretation of rain information from remotely sensed data. Rain attenuation and radar reflectivity (Z) depend directly on the drop size distribution (DSD). The relation between radar reflectivity/rain attenuation and rain rate (R) varies widely depending upon the origin, topography, and drop evolution mechanism and needs further understanding of the precipitation characteristics. The present work utilizes 2 years of concurrent measurements of DSD using a ground-based disdrometer at five diverse climatic conditions in Indian subcontinent and explores the possibility of rain classification based on microphysical characteristics of precipitation. It is observed that both gamma and lognormal distributions are performing almost similar for Indian region with a marginally better performance by one model than other depending upon the locations. It has also been found that shape-slope relationship of gamma distribution can be a good indicator of rain type. The Z-R relation, Z = ARb, is found to vary widely for different precipitation systems, with convective rain that has higher values of A than the stratiform rain for two locations, whereas the reverse is observed for the rest of the three locations. Further, the results indicate that the majority of rainfall (>50%) in Indian region is due to the convective rain although the occurrence time of convective rain is low (<10%).

Characterization of tropical precipitation using drop size distribution and rain rate-radar reflectivity relation

Rain attenuation is a major source of impairment to signal propagation at microwave and millimeter wave bands. The procedures for the estimation of rain attenuation values as regard to microwave signals however rely mainly on 1-minute rain rate statistics, particularly those obtained locally from experimental measurement campaigns over a given location. In this paper, we present recent results on 1-minute rain rate statistics required for satellite and terrestrial link designs, as obtained from a 2-year measurement over Akure, Nigeria. The performance of the selected rain rate models; Rice- Holmberg (RH) model, the Kitami model, Moupfouma model and the global ITU rain rate model were tested based on four metrics namely: Prediction error, Root Mean Square Error (RMSE), Spread- Corrected Root Mean Square Error (SC-RMSE) and the Spearman's rank correlation. Results indicate that no single model completely outperforms all others. Interestingly, the RH model is particularly best behaved over the distribution, while the Moupfouma model performs suitably well. Others seem to vary largely from the measured rain rate distribution. Results for the rain rate exceeded for 0.01% of the time agrees with earlier estimates for the cumulative rain rate distribution derived from higher integration-time statistics over this tropical site.

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Performance Analysis of Rain Rate Models for Microwave Propagation Designs Over Tropical Climate

Observation of bright-band height data from TRMM-PR for satellite communication in South Africa

This paper presents the comparison of existing rain rate models with three years one minute average rain rate obtained using a vertically looking micro rain radar. The improved Moupfouma model showed good agreement with the measured rain rate. Rain attenuation for selected broadcast satellites with varying look angles was also estimated. The satellite with the lowest antenna elevation accounts for the highest rain induced attenuation. Finally, recent experimental efforts on beacon signal measurement for extensive rain attenuation modeling for satellite-earth link are also presented.

Rain rate and rain attenuation prediction with experimental rain attenuation efforts in south-western Nigeria

As technology advances and more demands are on satellite services, rain-induced attenuation still creates one of the most damaging effects of the atmosphere on the quality of radio communication signals, especially those operating above 10 GHz. System designers therefore require statistical information on rain-induced attenuation over the coverage area in order to determine the appropriate transmitter and receiver characteristics to be adopted. This paper presents results on the time-varying rain characterization and diurnal variation of slant path rain attenuation in the Ka-band frequency simulated with synthetic storm techniques over a subtropical location in South Africa using 10-year rain rate time-series data. The analysis is based on the CDF of one-minute rain rate; time-series seasonal variation of rain rate observed over four time intervals: 00:00–06:00, 06:00–12:00, 12:00–18:00, and 18:00–24:00; diurnal fades margin; and diurnal variation of rain attenuation. Comparison was also made between the synthesized values and measured attenuation data. The predicted statistics are in good agreement with those obtained from the propagation beacon measurement in the area. The overall results will be needed for an acceptable planning that can effectively reduce the fade margin to a very low value for an optimum data communication over this area.

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Application of Synthetic Storm Technique for Diurnal and Seasonal Variation of Slant Path Ka-Band Rain Attenuation Time Series over a Subtropical Location in South Africa

J. S. Ojo

Papers

Performance Analysis of Rain Rate Models for Microwave Propagation Designs Over Tropical Climate

Observation of bright-band height data from TRMM-PR for satellite communication in South Africa

Rain rate and rain attenuation prediction with experimental rain attenuation efforts in south-western Nigeria

Application of Synthetic Storm Technique for Diurnal and Seasonal Variation of Slant Path Ka-Band Rain Attenuation Time Series over a Subtropical Location in South Africa

Comparative study on Radio Refractivity Gradient in the troposphere using Chaotic Quantifiers