# Eikonal Blog

## Concepts

Graph theory:

• nodes and edges
• degree = number of edges for a given node
• isolated nodes
• connected nodes
• hub = well connected node
• Scale-free networks = average number of nodes stays constant
• preferential attachment:
• the fraction of nodes with k edges: $p(k) \sim k^{-\gamma}$
• a long tail distribution
• Degree of distribution

## Papers

• “Power laws, Pareto distributions and Zipf’s law” by M.E.J. Newman (arXiv) – http://arxiv.org/abs/cond-mat/0412004
• When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distributions of the sizes of cities, earthquakes, solar flares, moon craters, wars and people’s personal fortunes all appear to follow power laws. The origin of power-law behaviour has been a topic of debate in the scientific community for more than a century. Here we review some of the empirical evidence for the existence of power-law forms and the theories proposed to explain them.
• more papers by M.E.J. Newman at arXiv – arxiv.org/find/cond-mat/1/au:+Newman_M/0/1/0/all/0/1

## 2010.11.24

### Fluid dynamics

Filed under: complexity, fluid dynamics, physics — Tags: — sandokan65 @ 11:49

## 2010.09.11

### Gossip

• “Gossip or “Viruses in the Body Politic” by Rod Graham (2010.08.07) – http://grahamsoc.wordpress.com/2010/08/07/gossip-or-viruses-in-the-body-politic/
• “The effect of gossip on social networks” by Allison K. Shaw, Milena Tsvetkova and Roozbeh Daneshvar (Complexity; 2010.08.17; DOI: 10.1002/cplx.20334) – http://onlinelibrary.wiley.com/doi/10.1002/cplx.20334/abstract
Abstract: In this article, we develop a simple model for the effect of gossip spread on social network structure. We define gossip as information passed between two individuals A and B about a third individual C which affects the strengths of all three relationships: it strengthens A-B and weakens both B-C and A-C. We find, in both an analytic derivation and model simulations, that if gossip does not spread beyond simple triads, it destroys them but if gossip propagates through large dense clusters, it strengthens them. Additionally, our simulations show that the effect of gossip on network metrics (clustering coefficient, average-path-length, and sum-of-strengths) varies with network structure and average-node-degree.

## 2010.07.12

### Book: “Alternate Realities: Mathematical Models of Nature and Man”

Filed under: books, complexity, mathematics — sandokan65 @ 15:17

“Alternate Realities: Mathematical Models of Nature and Man” by John L. Casti

Recently I have re-read this book 15 years after the first reading. It covers various topics from definition of complexity (as a measure of surprise/difference between the anticipated and real outputs of the system), building mathematical model generating predetermined series of outputs, introduction to theory of catastrophes, cellular automata, etc.

## 2010.01.08

### Buterfly curves

Filed under: fractals — Tags: , — sandokan65 @ 15:14

$r = e^{\cos(a\theta)} - A\cdot\cos(b\theta) + \sin(\theta/c)^B$

Source:

## 2010.01.06

### How to halt spread of an infectious disease with limited amount of vaccine

Filed under: complexity, health, small worlds — Tags: , — sandokan65 @ 10:38

The ArXiv blog has a new article (http://www.technologyreview.com/blog/arxiv/24623/) on the more sophisticated controls for the epidemics via targeted and timed applications of smaller doses of vaccines. The original research paper is at the arXiv: arXiv:1001.0170 “Speeding up disease extinction with a limited amount of vaccine” (by M. Khasin, M.I. Dykman, B. Meerson; 2009.12.31)http://arxiv.org/abs/1001.0170