Noise Processes in Discrete Communication Systems

This chapter focuses on noise processes in discrete communication systems. The problem with white Gaussian noise process discretization is that a strict definition implies that the noise has theoretically infinite power. Thus, it would be impossible to generate discrete noise, because the sampling theorem requires that the sampled signal must be physically realizable, that is, the sampled noise needs to have a finite power. To overcome this problem, noise entropy is defined as an additional measure of noise properties, and a truncated Gaussian probability density function is used. Adding entropy and truncated density to the definition of the noise autocorrelation and power spectral density functions allows mathematical modelling of the discrete noise source for both baseband and bandpass noise generators and regenerators. Noise theory and noise generators are essential for a theoretical explanation of the operation of digital and discrete communications systems and their design, simulation, emulation, and testing.

The integrals and integral transformations connected with the joint vector Gaussian distribution

In many applications it is desirable to consider not one random vector but a number of random vectors with the joint distribution. This paper is devoted to the integral and integral transformations connected with the joint vector Gaussian probability density function. Such integral and transformations arise in the statistical decision theory, particularly, in the dual control theory based on the statistical decision theory. One of the results represented in the paper is the integral of the joint Gaussian probability density function. The other results are the total probability formula and Bayes formula formulated in terms of the joint vector Gaussian probability density function. As an example the Bayesian estimations of the coefficients of the multiple regression function are obtained. The proposed integrals can be used as table integrals in various fields of research.

Evaluation of a Flexible Single Ice Microphysics and a Gaussian Probability-Density-Function Macrophysics Scheme in a Single Column Model

Scale-aware parameterizations of subgrid scale physics are essentials for multiscale atmospheric modeling. A single-ice (SI) microphysics scheme and Gaussian probability-density-function (Gauss-PDF) macrophysics scheme were implemented in the single-column Global-to-Regional Integrated forecast System model (SGRIST) and they were tested using the Tropical Warm Pool-International Cloud Experiment (TWP-ICE) and the Atmospheric Radiation Measurement Southern Great Plains Experiment in 1997 (ARM97). Their performance was evaluated against observations and other reference schemes. The new schemes simulated reasonable precipitation with proper fluctuations and peaks, ice, and liquid water contents, especially in lower levels below 650 hPa during the wet period in the TWP-ICE. The root mean square error (RMSE) of the simulated cloud fraction was below 200 hPa was 0.10/0.08 in the wet/dry period, which showed an obvious improvement when compared to that, i.e., 0.11/0.11 of original scheme. Accumulated ice water content below the melting level decreased by 21.57% in the SI. The well-matched average liquid water content displayed between the new scheme and observations, which was two times larger than those with the referencing scheme. In the ARM97 simulations, the SI scheme produced considerable ice water content, especially when convection was active. Low-level cloud fraction and precipitation extremes were improved using the Gauss-PDF scheme, which displayed the RMSE of cloud fraction of 0.02, being only half of the original schemes. The study indicates that the SI and Gauss-PDF schemes are promising approaches to simplify the microphysics process and improve the low-level cloud modeling.

Non-extensive value-at-risk estimation during times of crisis

Value-at-risk (VaR) is a crucial subject that researchers and practitioners extensively use to measure and manage uncertainty in financial markets. Although VaR is a standard risk control instrument, there are criticisms about its performance. One of these cases, which has been studied in this research, is the VaR underestimation during times of crisis. In these periods, the non-Gaussian behavior of markets intensifies, and the estimated VaRs by typical models are lower than the real values. A potential approach that can be used to describe the non-Gaussian behavior of return series is the Tsallis entropy framework and nonextensive statistical methods. This paper has used the nonextensive models for analyzing financial markets’ behavior during crisis times. By applying the q-Gaussian probability density function for emerging and mature markets over 20 years, we can see a better VaR estimation than the regular models, especially during crisis times. We have shown that the q-Gaussian models composed of VaR and Expected Shortfall (ES) estimate risk better than the standard models. By comparing the ES, VaR, [Formula: see text]-VaR and [Formula: see text]-ES for emerging and mature markets, we see in confidence levels more than 0.98, the outputs of q models are more real, and the [Formula: see text]-ES model has lower errors than the other ones. Also, it is evident that in the mature markets, the difference of VaR between normal condition and nonextensive approach increases more than one standard deviation during times of crisis. Still, in the emerging markets, we cannot see a specific pattern. The findings of this paper are useful for analyzing the risk of financial crises in different markets.

Comparative Evolution and Transcription Activity of Transposable Elements in Indica and Japonica Rice

BackgroundTransposable elements (TEs) are able to diversify plant gene expression and function, sequentially promote plant variety and evolution. However, there is lack of efficient approach to investigate the evolution behavior and transcription activity of TEs in plants. Here we developed a pipeline Matrix-TE to comprehensively evaluate the super-families, differentiation and transcription activity of LTR/TEs in Indica and Japonica rice, the two considerable important and closely related monocots.ResultsSix LTR/TE super-families were identified by Matrix-TE in both Indica and Japonica rice genomes, in which the OS-type1 and OS-type2 super-families were unclassified. Indica rice specific TE peak P-Gypsy and Japonica rice specific TE peak P-Copia were observed separately. Then the two peaks were analyzed by Gaussian Probability Density Function (GPDF) fit. Significant TE transcription activities were observed in Indica and Japonica rice plants after stress treatments. Particularly, hot, cold and salt stresses induced the high expression level of LTR/TEs in rice plants.ConclusionsWe developed the approach Matrix-TE on the basis of BLASTN and GPDF algorithms, and applied it to comprehensively and quantitatively investigate LTR/TE types and contents in the close subspecies Indica and Japonica rice genomes. The individual TE burst events P-Copia and P-Gypsy were observed in Japonica and Indica rice, separately. RNA-seq and RT-PCR methods indicated that LTR/TE transcripts were induced by hot, cold and high salt stress conditions. The optimized Matrix-TE approach and procedures probably could be used in other plant species with big genomes like wheat and maize.

A Phenomenological Epidemic Model Based On the Spatio-Temporal Evolution of a Gaussian Probability Density Function

A novel phenomenological epidemic model is proposed to characterize the state of infectious diseases and predict their behaviors. This model is given by a new stochastic partial differential equation that is derived from foundations of statistical physics. The analytical solution of this equation describes the spatio-temporal evolution of a Gaussian probability density function. Our proposal can be applied to several epidemic variables such as infected, deaths, or admitted-to-the-Intensive Care Unit (ICU). To measure model performance, we quantify the error of the model fit to real time-series datasets and generate forecasts for all the phases of the COVID-19, Ebola, and Zika epidemics. All parameters and model uncertainties are numerically quantified. The new model is compared with other phenomenological models such as Logistic Grow, Original, and Generalized Richards Growth models. When the models are used to describe epidemic trajectories that register infected individuals, this comparison shows that the median RMSE error and standard deviation of the residuals of the new model fit to the data are lower than the best of these growing models by, on average, 19.6% and 35.7%, respectively. Using three forecasting experiments for the COVID-19 outbreak, the median RMSE error and standard deviation of residuals are improved by the performance of our model, on average by 31.0% and 27.9%, respectively, concerning the best performance of the growth models.

A Novel Perspective of the Kalman Filter from the Rényi Entropy

Rényi entropy as a generalization of the Shannon entropy allows for different averaging of probabilities of a control parameter α. This paper gives a new perspective of the Kalman filter from the Rényi entropy. Firstly, the Rényi entropy is employed to measure the uncertainty of the multivariate Gaussian probability density function. Then, we calculate the temporal derivative of the Rényi entropy of the Kalman filter’s mean square error matrix, which will be minimized to obtain the Kalman filter’s gain. Moreover, the continuous Kalman filter approaches a steady state when the temporal derivative of the Rényi entropy is equal to zero, which means that the Rényi entropy will keep stable. As the temporal derivative of the Rényi entropy is independent of parameter α and is the same as the temporal derivative of the Shannon entropy, the result is the same as for Shannon entropy. Finally, an example of an experiment of falling body tracking by radar using an unscented Kalman filter (UKF) in noisy conditions and a loosely coupled navigation experiment are performed to demonstrate the effectiveness of the conclusion.

Mapping sea-ice types from Sentinel-1 considering the surface-type dependent effect of incidence angle

Automated classification of sea-ice types in Synthetic Aperture Radar (SAR) imagery is complicated by the class-dependent decrease of backscatter intensity with Incidence Angle (IA). In the log-domain, this decrease is approximately linear over the typical range of space-borne SAR instruments. A global correction does not consider that different surface types show different rates of decrease in backscatter intensity. Here, we introduce a supervised classification algorithm that directly incorporates the surface-type dependent effect of IA. We replace the constant mean vector of a Gaussian probability density function in a Bayesian classifier with a linearly variable mean. During training, the classifier first retrieves the slope and intercept of the linear function describing the mean value and then calculates the covariance matrix as the mean squared deviation relative to this function. The IA dependence is no longer treated as an image property but as a class property. Based on training and validation data selected from overlapping SAR and optical images, we evaluate the proposed method in several case studies and compare to other classification algorithms for which a global IA correction is applied during pre-processing. Our results show that the inclusion of the per-class IA sensitivity can significantly improve the performance of the classifier.

Efficiency and Multifractality Analysis of the Chinese Stock Market: Evidence from Stock Indices before and after the 2015 Stock Market Crash

This paper examines the daily return series of four main indices, including Shanghai Stock Exchange Composite Index (SSE), Shenzhen Stock Exchange Component Index (SZSE), Shanghai Shenzhen 300 Index (SHSE-SZSE300), and CSI Smallcap 500 index (CSI500) in Chinese stock market from 2000 to 2018 by multifractal detrended fluctuation analysis (MF-DFA). The series of the daily return of the indices exhibit significant multifractal properties on the whole time scale and SZSE has the highest multifractal properties among the four indices, indicating the lowest market efficiency. The multifractal properties of four indices are due to long-range correlation and fat-tail characteristics of the non-Gaussian probability density function, and these two factors have different effects on the multifractality of four indices. This paper aims to compare the multifractility degrees of the four indices in three sub-samples divided by the 2015 stock market crash and to discuss its effects on efficiency of the Shanghai and Shenzhen stock market in each sub-sample. Meanwhile, we study the effect of the 2015 stock market crash on market efficiency from the statistical and fractal perspectives, which has theoretical and practical significance in the application of Effective Market Hypothesis (EMH) in China’s stock market, and it thereby affects the healthy and sustainability of the market. The results also provide important implications for further study on the dynamic mechanism and efficiency in stock market and they are relevant to portfolio managers and policy makers in a number of ways to maintain the sustainable development of China’s capital market and economy.