Power-law relationships, relating events with magnitudes to their frequency, are common in natural disasters and violent conflict. Compared to many statistical distributions, power laws drop off more gradually, i.e. they have “fat tails”. Existing studies on natural disaster power laws are mostly confined to physical measurements, e.g., the Richter scale, and seldom cover casualty distributions...

The three Power-Laws proposed by Faloutsos et al. (1999) are important discoveries among many recent works on finding hidden rules in the seemingly chaotic Internet topology. In this note, we want to point out that the first two laws discovered by Faloutsos et al. (1999, hereafter, Faloutsos’ Power Laws) are in fact equivalent. That is, as long as any one of them is true, the other can be deriv...

Power laws arise through many natural processes. Zipf showed that the frequencies of words, as they appear in Shakespeare’s Hamlet, follow a power law distribution. Mandelbrot explained this effect as a result of an underlying information-theoretic optimization problem. Miller invoked doubt by showing that a very simple mechanism could also explain the presence of power laws: A monkey typing wo...

The three Power-Laws proposed by Faloutsos et al. (1999) are important discoveries among many recent works on finding hidden rules in the seemingly chaotic Internet topology. In this note, we want to point out that the first two laws discovered by Faloutsos et al. (1999, hereafter, Faloutsos’ Power Laws) are in fact equivalent. That is, as long as any one of them is true, the other can be deriv...

Power laws are ubiquitous in social media [2], but they exhibit great variety and do not appear for the same, or even agreed upon, reasons. For instance, individual behaviors that give rise to power-laws in social information streams can be explained via either random [6] or correlated behaviors [1]. And the well known “80/20” rule (80% of the work is done by 20% of the users) is often only a r...

Highly optimized tolerance (HOT) is a mechanism that relates evolving structure to power laws in interconnected systems. HOT systems arise where design and evolution create complex systems sharing common features, including (1) high efficiency, performance, and robustness to designed-for uncertainties, (2) hypersensitivity to design flaws and unanticipated perturbations, (3) nongeneric, special...

This paper deals with analytical and simulation approach for choice of activation functions and instead of a number of nodes for a class of neural network controllers for frequency control of thermal power systems. Neural network update laws are derived via Lyapunov like stability analysis. When number of nodes is fixed, then simulation analysis is conducted to find the best performer activatio...

Earthquake sources represent dynamic rupture within rocky materials at depth and often can be modeled as propagating shear slip controlled by friction laws. These laws provide boundary conditions on fault planes embedded in elastic media. Recent developments in observation networks, laboratory experiments, and methods of data analysis have expanded our knowledge of the physics of earthquakes. N...

Stabilization in multimachine (synchronous generators) power systems is dealt with through a class of decentralized and nonlinear state feedback laws that can be separately designed in a generator-wise fashion, based on what we call the improved swing equations. Stability of the closed-loop power systems is robust with regard to perturbations in electric torques happening in the synchronous gen...