There is no closed form analytical equation or quick method to calculate probabilities based only on the entropy of a signal or process. Except in the cases where there are constraints on the state probabilities, one must typically derive the underly
ing probabilities through search algorithms. These become more computationally expensive as entropies of higher orders are investigated. In this paper, a method to calculate a joint probability matrix based on the entropy for any order is elaborated. With this method, only first order entropies need to be successfully calculated while the others are derived via multiplicative cascades.
The development and evolution of malware including computer viruses, worms, and trojan horses, is shown to be closely analogous to the process of community succession long recognized in ecology. In particular, both changes in the overall environment
by external disturbances, as well as, feedback effects from malware competition and antivirus coevolution have driven community succession and the development of different types of malware with varying modes of transmission and adaptability.
In this paper, new techniques that allow conditional entropy to estimate the combinatorics of symbols are applied to animal communication studies to estimate the communications repertoire size. By using the conditional entropy estimates at multiple o
rders, the paper estimates the total repertoire sizes for animal communication across bottlenose dolphins, humpback whales, and several species of birds for N-grams length one to three. In addition to discussing the impact of this method on studies of animal communication complexity, the reliability of these estimates is compared to other methods through simulation. While entropy does undercount the total repertoire size due to rare N-grams, it gives a more accurate picture of the most frequently used repertoire than just repertoire size alone.
The relationship between period doubling bifurcations and Feigenbaums constants has been studied for nearly 40 years and this relationship has helped uncover many fundamental aspects of universal scaling across multiple nonlinear dynamical systems. T
his paper will combine information entropy with symbolic dynamics to demonstrate how period doubling can be defined using these tools alone. In addition, the technique allows us to uncover some unexpected, simple estimates for Feigenbaums constants which relate them to log 2 and the golden ratio, phi, as well as to each other.
The distribution of frequency counts of distinct words by length in a languages vocabulary will be analyzed using two methods. The first, will look at the empirical distributions of several languages and derive a distribution that reasonably explains
the number of distinct words as a function of length. We will be able to derive the frequency count, mean word length, and variance of word length based on the marginal probability of letters and spaces. The second, based on information theory, will demonstrate that the conditional entropies can also be used to estimate the frequency of distinct words of a given length in a language. In addition, it will be shown how these techniques can also be applied to estimate higher order entropies using vocabulary word length.
In this paper we analyze Greshams Law, in particular, how the rate of inflow or outflow of currencies is affected by the demand elasticity of arbitrage and the difference in face value ratios inside and outside of a country under a bimetallic system.
We find that these equations are very similar to those used to describe drift in systems of free charged particles. In addition, we look at how Greshams Law would play out with multiple currencies and multiple countries under a variety of connecting topologies.
Ecological and economic networks have many similarities and are often compared. However, the comparison is often more apt as metaphor than a direct equivalence. In this paper, five key differences are explained which should inform any analysis which compares the two.
A general theory of top-down cascades in complex networks is described which explains two similar types of perturbation amplifications in the complex networks of business supply chains (the `bullwhip effect) and ecological food webs (trophic cascades
). The dependence of the strength of the effects on the interaction strength and covariance in the dynamics as well as the graph structure allows both explanation and prediction of widely recognized effects in each type of system.
The key findings of classical population genetics are derived using a framework based on information theory using the entropies of the allele frequency distribution as a basis. The common results for drift, mutation, selection, and gene flow will be
rewritten both in terms of information theoretic measurements and used to draw the classic conclusions for balance conditions and common features of one locus dynamics. Linkage disequilibrium will also be discussed including the relationship between mutual information and r^2 and a simple model of hitchhiking.
The Internet is the most complex system ever created in human history. Therefore, its dynamics and traffic unsurprisingly take on a rich variety of complex dynamics, self-organization, and other phenomena that have been researched for years. This pap
er is a review of the complex dynamics of Internet traffic. Departing from normal treatises, we will take a view from both the network engineering and physics perspectives showing the strengths and weaknesses as well as insights of both. In addition, many less covered phenomena such as traffic oscillations, large-scale effects of worm traffic, and comparisons of the Internet and biological models will be covered.
