Abstract:
We explicitly test if the reliability of credit ratings depends on the total number of admissible states. We analyse open access credit rating data and show that the effect of the number of states in the dynamical properties of ratings change with time, thus giving supportive evidence that the ideal number of admissible states changes with time. We use matrix estimation methods that explicitly assume the hypothesis needed for the process to be a valid rating process. By comparing with the likelihood maximization method of matrix estimation, we quantify the "likelihood-loss" of assuming that the process is a well grounded rating process.

Abstract:
We present a novel model to simulate real social networks of complex interactions, based in a granular system of colliding particles (agents). The network is build by keeping track of the collisions and evolves in time with correlations which emerge due to the mobility of the agents. Therefore, statistical features are a consequence only of local collisions among its individual agents. Agent dynamics is realized by an event-driven algorithm of collisions where energy is gained as opposed to granular systems which have dissipation. The model reproduces empirical data from networks of sexual interactions, not previously obtained with other approaches.

Abstract:
We propose a model of mobile agents to construct social networks, based on a system of moving particles by keeping track of the collisions during their permanence in the system. We reproduce not only the degree distribution, clustering coefficient and shortest path length of a large data base of empirical friendship networks recently collected, but also some features related with their community structure. The model is completely characterized by the collision rate and above a critical collision rate we find the emergence of a giant cluster in the universality class of two-dimensional percolation. Moreover, we propose possible schemes to reproduce other networks of particular social contacts, namely sexual contacts.

Abstract:
We introduce a simple model for addressing the controversy in the study of financial systems, sometimes taken as brownian-like processes and other as critical systems with fluctuations of arbitrary magnitude. The model considers a collection of economical agents which establish trade connections among them according to basic economical principles properly translated into physical properties and interaction. With our model we are able to reproduce the evolution of macroscopic quantities (indices) and to correctly retrieve the common exponent value characterizing several indices in financial markets, relating it to the underlying topology of connections.

Abstract:
Many stochastic time series can be described by a Langevin equation composed of a deterministic and a stochastic dynamical part. Such a stochastic process can be reconstructed by means of a recently introduced nonparametric method, thus increasing the predictability, i.e. knowledge of the macroscopic drift and the microscopic diffusion functions. If the measurement of a stochastic process is affected by additional strong measurement noise, the reconstruction process cannot be applied. Here, we present a method for the reconstruction of stochastic processes in the presence of strong measurement noise, based on a suitably parametrized ansatz. At the core of the process is the minimization of the functional distance between terms containing the conditional moments taken from measurement data, and the corresponding ansatz functions. It is shown that a minimization of the distance by means of a simulated annealing procedure yields better results than a previously used Levenberg-Marquardt algorithm, which permits a rapid and reliable reconstruction of the stochastic process.

Abstract:
The study of heavy-tailed distributions in economic and financial systems has been widely addressed since financial time series has become a research subject.After the eighties, several "highly improbable" market drops were observed (e.g. the 1987 stock market drop known as "Black Monday" and on even more recent ones, already in the 21st century) that produce heavy losses that were unexplainable in a GN environment. The losses incurred in these large market drop events did not change significantly the market practices or the way regulation is done but drove some attention back to the study of heavy-tails and their underlying mechanisms. Some recent findings in these context is the scope of this manuscript.

Abstract:
We address the problem of banking system resilience by applying off-equilibrium statistical physics to a system of particles, representing the economic agents, modelled according to the theoretical foundation of the current banking regulation, the so called Merton-Vasicek model. Economic agents are attracted to each other to exchange `economic energy', forming a network of trades. When the capital level of one economic agent drops below a minimum, the economic agent becomes insolvent. The insolvency of one single economic agent affects the economic energy of all its neighbours which thus become susceptible to insolvency, being able to trigger a chain of insolvencies (avalanche). We show that the distribution of avalanche sizes follows a power-law whose exponent depends on the minimum capital level. Furthermore, we present evidence that under an increase in the minimum capital level, large crashes will be avoided only if one assumes that agents will accept a drop in business levels, while keeping their trading attitudes and policies unchanged. The alternative assumption, that agents will try to restore their business levels, may lead to the unexpected consequence that large crises occur with higher probability.

Abstract:
We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an agent model, presented in the context of economic networks of trades, which shows the emergence of critical behavior. Starting from a brief discussion about the main features of the evolving network of trades, we show that the logarithmic return distributions have bounded heavy-tails, and the corresponding bounding exponent values can be derived. Finally, we discuss these findings in the context of model risk.

Abstract:
Barchans are isolated mobile dunes often organized in large dune fields. Dune fields seem to present a characteristic dune size and spacing, which suggests a cooperative behavior based on dune interaction. In Duran et al. (2009), we propose that the redistribution of sand by collisions between dunes is a key element for the stability and size selection of barchan dune fields. This approach was based on a mean-field model ignoring the spatial distribution of dune fields. Here, we present a simplified dune field model that includes the spatial evolution of individual dunes as well as their interaction through sand exchange and binary collisions. As a result, the dune field evolves towards a steady state that depends on the boundary conditions. Comparing our results with measurements of Moroccan dune fields, we find that the simulated fields have the same dune size distribution as in real fields but fail to reproduce their homogeneity along the wind direction.