Short-term electrical load series forecast plays an essential role in energy demand management, however power consumption data are non-stationary, nonlinear and multi-dimensional series, leaving prediction a difficult task. Recently, fractional- order partial differential equations are attracting attention as they have been successfully utilized to describe power consumption behaviors in complex electrical systems and power grids. In this paper, a clustering fractional order predictive model called C-FGM is introduced for short-term electrical load forecast missions. The novelty of the C-FGM is that it initiates a parameter α to describe the accumulative weather trends of multiple clustering sub-series, and this parameter is also assigned to a fractional-order partial differential equation to depict the previous power series. Hyper parameters of these equations are then sent to a global optimization algorithm to reduce predictive errors. Simulation results on two electricity datasets demonstrated that our algorithm can learn from datasets hyper parameters inside equations and produce forecast values efficiently. Com- pared with contemporary models such as LSTM and the Transformer, C-FGM clearly achieved a higher accuracy (MAPE from 1.97 to 4.67%, outperforms LSTM whose average MAPE is 4.34% and Transformer whose average MAPE is 5.42%). This satisfactory performance suggests that our data-driven model can be used as an effective tool for real time forecasting missions.

Optimal coding over the additive white Gaussian noise channel under the peak energy constraint is studied when there is noisy feedback over an orthogonal additive white Gaussian noise channel. Previously, Shepp, Wolf, Wyner, and Ziv, and Pinsker showed that under the peak energy constraint the best error exponent for transmission of two messages is achieved by antipodal signaling, regardless of the presence of feedback. This negative result might lead to an impression that under the peak energy constraint, even noise-free feedback does not improve the reliability of communication. Pinsker proved the contrary by showing that the best error exponent for sending M messages does not depend on M, and hence can be strictly larger than the best error exponent without feedback. This paper further extends this and shows that if the noise level in the feedback link is sufficiently small, then the best error exponent for transmission of three messages can be strictly larger than the one without feedback. This result is motivated by a series of recent papers of Burnashev and Yamamoto who considered a similar problem over binary symmetric channels.

Since December 2019, a novel coronavirus (COVID-19) has spread all over the world, causing unpredictable economic losses and public fear. Although vaccines against this virus have been developed and administered for months, many countries still suffer from secondary COVID-19 infections, including the United Kingdom, France, and Malaysia. Observations of COVID-19 infections in the United Kingdom and France and their governance measures showed a certain number of similarities. A further investigation of these countries COVID-19 transmission patterns suggested that when a turning point appeared, the values of their stringency indices per population density (PSI) were nearly proportional to their absolute infection rate (AIR). To justify our assumptions, we developed a mathematical model named VSHR to predict the COVID-19 turning point for Malaysia. VSHR was first trained on 30-day infection records prior to the United Kingdom, Germany, France, and Belgiums known turning points. It was then transferred to Malaysian COVID-19 data to predict this nations turning point. Given the estimated AIR parameter values in 5 days, we were now able to locate the turning points appearance on June 2^nd, 2021. VSHR offered two improvements: (1) gathered countries into groups based on their SI patterns and (2) generated a model to identify the turning point for a target country within 5 days with 90 CI. Our research on COVID-19s turning point for a country is beneficial for governments and clinical systems against future COVID-19 infections.

Based on the wavelet domain scale edge detection algorithm, a simple and effective multi-scale edge detection method was proposed. By multiplying the wavelet coefficients on the adjacent scale product, one-dimensional adjacent scale product coefficients and two-dimensional adjacent scale product coefficients are defined. At the same time of noise suppression, the causality of edge in different scales is implied, and the edge point is considered to be the local modulus maximum point of scale product coefficient after threshold. Finally, through the performance analysis, it is found that the scale product can not only improve the detection performance, but also reduce the interaction between adjacent edges.