Physical-Layer Encryption Using Digital Chaos for Secure OFDM Transmission

Due to the broadcasting nature of passive optical network (PON), data security is challenging. For the transmission of orthogonal frequency division multiplexing (OFDM) signals, the high peak-to-average power ratio (PAPR) is considered as one of the major drawbacks. This chapter reviews the digital chaos-based secure OFDM data encryption schemes, where the transmission performance is improved via PAPR reduction. The digital chaos is incorporated into the signal scrambling approaches: selective mapping (SLM), partial transmit sequence (PTS); and precoding approaches: discrete Fourier transform (DFT) and Walsh-Hadamard transform (WHT) for PAPR reduction. Multi-fold data encryption is achieved with a huge key space provided by digital chaos, to enhance the physical-layer security for OFDM-PON, while the pseudo-random properties of digital chaos are applied for PAPR reduction, which consequently improves the transmission performance. The evidences of these encryption approaches are presented in terms of theories, simulations, as well as experimental demonstrations. The chaotic data encryption schemes could be promising candidates for next-generation OFDM-PON

On a question of Drinfeld on the Weil representation I: the finite field case

Let F be a finite field of odd cardinality, and let G= GL2(F). The group G \times G \times G acts on F^2 \otimes F^2 \otimes F^2 via symplectic similitudes, and has a natural Weil representation. Answering a question rasised by V. Drinfeld, we decompose that representation into irreducibles. We also decompose the analogous representation of GL2(A), where A is a cubic algebra over F.Comment: 29 pages. Comments welcom

Understanding the power-law nature of participation in community sports organizations

The improvement of living standards and awareness of chronic diseases have increased the importance of community sports organizations in promoting the physical activity levels of the public. However, limited understanding of human behavior in this context often leads to suboptimal resource utilization. In this study, we analyzed the participation behavior of 2,956 members with a time span of 6 years in a community sports organization. Our study reveals that, at the population level, the participation frequency in activities adheres to a power-law distribution. To understand the underlying mechanisms driving crowd participation, we introduce a novel behavioral model called HFBI (Habit-Formation and Behavioral Inertia), demonstrating a robust fit to the observed power-law distribution. The habit formation mechanism indicates that individuals who are more engaged are more likely to maintain participation, while the behavioral inertia mechanism suggests that individuals' willingness to participate in activities diminishes with their absences from activities. At the individual level, our analysis reveals a burst-quiet participation pattern, with bursts often commencing with incentive activities. We also find a power-law distribution in the intervals between individual participations. Our research offers valuable insights into the complex dynamics of human participation in community sports activity and provides a theoretical foundation to inform intervention design. Furthermore, the flexibility of our model enables its application to other data exhibiting power-law properties, broadening its potential impact beyond the realm of community sports