Multiresolution Diffusion Entropy Analysis of time series: an application to births to teenagers in Texas

The multiresolution diffusion entropy analysis is used to evaluate the stochastic information left in a time series after systematic removal of certain non-stationarities. This method allows us to establish whether the identified patterns are sufficient to capture all relevant information contained in a time series. If they do not, the method suggests the need for further interpretation to explain the residual memory in the signal. We apply the multiresolution diffusion entropy analysis to the daily count of births to teens in Texas from 1964 through 2000 because it is a typical example of a non-stationary time series, having an anomalous trend, an annual variation, as well as short time fluctuations. The analysis is repeated for the three main racial/ethnic groups in Texas (White, Hispanic and African American), as well as, to married and unmarried teens during the years from 1994 to 2000 and we study the differences that emerge among the groups.Comment: 14 pages, 3 figures, 1 table. In press on 'Chaos, Solitons & Fractals

Linear Response and Fluctuation Dissipation Theorem for non-Poissonian Renewal Processes

The Continuous Time Random Walk (CTRW) formalism is used to model the non-Poisson relaxation of a system response to perturbation. Two mechanisms to perturb the system are analyzed: a first in which the perturbation, seen as a potential gradient, simply introduces a bias in the hopping probability of the walker from on site to the other but leaves unchanged the occurrence times of the attempted jumps ("events") and a second in which the occurrence times of the events are perturbed. The system response is calculated analytically in both cases in a non-ergodic condition, i.e. for a diverging first moment in time. Two different Fluctuation-Dissipation Theorems (FDTs), one for each kind of mechanism, are derived and discussed

An out-of-equilibrium model of the distributions of wealth

The distribution of wealth among the members of a society is herein assumed to result from two fundamental mechanisms, trade and investment. An empirical distribution of wealth shows an abrupt change between the low-medium range, that may be fitted by a non-monotonic function with an exponential-like tail such as a Gamma distribution, and the high wealth range, that is well fitted by a Pareto or inverse power-law function. We demonstrate that an appropriate trade-investment model, depending on three adjustable parameters associated with the total wealth of a society, a social differentiation among agents, and economic volatility referred to as investment can successfully reproduce the distribution of empirical wealth data in the low, medium and high ranges. Finally, we provide an economic interpretation of the mechanisms in the model and, in particular, we discuss the difference between Classical and Neoclassical theories regarding the concepts of {\it value} and {\it price}. We consider the importance that out-of-equilibrium trade transactions, where the prices differ from values, have in real economic societies.Comment: 11 pages + 7 figures. in press on Quantitavive Financ

Role of Committed Minorities in Times of Crisis

We use a Cooperative Decision Making (CDM) model to study the effect of committed minorities on group behavior in time of crisis. The CDM model has been shown to generate consensus through a phase-transition process that at criticality establishes long-range correlations among the individuals within a model society. In a condition of high consensus, the correlation function vanishes, thereby making the network recover the ordinary locality condition. However, this state is not permanent and times of crisis occur when there is an ambiguity concerning a given social issue. The correlation function within the cooperative system becomes similarly extended as it is observed at criticality. This combination of independence (free will) and long-range correlation makes it possible for very small but committed minorities to produce substantial changes in social consensus

Fractional calculus ties the microscopic and macroscopic scales of complex network dynamics

A two-state master equation based decision making model has been shown to generate phase transitions, to be topologically complex and to manifest temporal complexity through an inverse power-law probability distribution function in the switching times between the two critical states of consensus. These properties are entailed by the fundamental assumption that the network elements in the decision making model imperfectly imitate one another. The process of subordination establishes that a single network element can be described by a fractional master equation whose analytic solution yields the observed inverse power-law probability distribution obtained by numerical integration of the two-state master equation to a high degree of accuracy