Study of smart grid cyber-security, examining architectures, communication networks, cyber-attacks, countermeasure techniques, and challenges.

Smart Grid (SG) technology utilizes advanced network communication and monitoring technologies to manage and regulate electricity generation and transport. However, this increased reliance on technology and connectivity also introduces new vulnerabilities, making SG communication networks susceptible to large-scale attacks. While previous surveys have mainly provided high-level overviews of SG architecture, our analysis goes further by presenting a comprehensive architectural diagram encompassing key SG components and communication links. This holistic view enhances understanding of potential cyber threats and enables systematic cyber risk assessment for SGs. Additionally, we propose a taxonomy of various cyberattack types based on their targets and methods, offering detailed insights into vulnerabilities. Unlike other reviews focused narrowly on protection and detection, our proposed categorization covers all five functions of the National Institute of Standards and Technology cybersecurity framework. This delivers a broad perspective to help organizations implement balanced and robust security. Consequently, we have identified critical research gaps, especially regarding response and recovery mechanisms. This underscores the need for further investigation to bolster SG cybersecurity. These research needs, among others, are highlighted as open issues in our concluding section.

Expansion of error thresholds for the Moran model.

We study a finite population of individuals evolving through mutation and selection. We generalize the Eigen quasispecies model to a finite population with the Moran model. This model also presents an asymptotic phase transition, and a proper definition of the critical parameter is discussed. We retrieve the same expression for the error threshold appearing in the Eigen model along with a correction term due to the finiteness of the population. To achieve this, we estimate the average lifetime of master sequences and find it grows like an exponential in the size of the population. Our technique consists in bounding from above and below the number of master sequences in the Moran model by two simpler birth and death chains. The expectation of this lifetime is then computed with the help of explicit formulas which are in turn expanded with Laplace method.