We review concepts introduced in earlier work, where a neural network mechanism describes some mental processes in neurotic pathology and psychoanalytic working-through, as associative memory functioning, according to the findings of Freud. We developed a complex network model, where modules corresponding to sensorial and symbolic memories interact, representing unconscious and conscious mental processes. The model illustrates Freud's idea that consciousness is related to symbolic and linguistic memory activity in the brain. We have introduced a generalization of the Boltzmann machine to model memory associativity. Model behavior is illustrated with simulations and some of its properties are analyzed with methods from statistical mechanics.

En este artı́culo abordamos el tema de la generación automática de frases literarias, que es una parte importante de los estudios relacionados al área de la Creatividad Computacional (CC). Proponemos tres modelos de generación textual guiados por un contexto, basados principalmente en algoritmos estadı́sticos y análisis sintáctico superficial. Los textos generados fueron evaluados por siete personas a partir de 4 criterios: gramaticalidad, coherencia, relación con el contexto y una adaptación del test de Turing, en donde se pidio a los evaluadores clasificar los textos en: textos generados automáticamente y textos generados por humanos. Los resultados obtenidos son bastante alentadores.

Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated.The conditions under which these evolution equations admit stationary solutions, which are q-exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an H-theorem in terms of a free-energy like quantity involving the S q entropy. A particular two dimensional model admitting analytical, timedependent, q-Gaussian solutions is discussed in detail. This model describes a system of particles with short-range interactions, performing overdamped motion under drag effects due to a rotating resisting medium. It is related to models that have been recently applied to the study of type-II superconductors. The relevance of the present developments to the study of complex systems in physics, astronomy, and biology, is discussed.

Diverse processes in statistical physics are usually analyzed on the assumption that the drag force acting on a test particle moving in a resisting medium is linear on the velocity of the particle. However, nonlinear drag forces do appear in relevant situations that are currently the focus of experimental and theoretical work. Motivated by these developments, we explore the consequences of nonlinear drag forces for the thermostatistics of systems of interacting particles performing overdamped motion. We derive a family of nonlinear Fokker-Planck equations for these systems, taking into account the effects of nonlinear drag forces. We investigate the main properties of these evolution equations, including an H-theorem, and obtain exact solutions of the stretched q-exponential form.

Nonlinear Fokker–Planck equations (NLFPEs) constitute useful effective descriptions of some interacting many-body systems. Important instances of these nonlinear evolution equations are closely related to the thermostatistics based on the S q power-law entropic functionals. Most applications of the connection between the NLFPE and the S q entropies have focused on systems interacting through short-range forces. In the present contribution we re-visit the NLFPE approach to interacting systems in order to clarify the role played by the range of the interactions, and to explore the possibility of developing similar treatments for systems with long-range interactions, such as those corresponding to Newtonian gravitation. In particular, we consider a system of particles interacting via forces following the inverse square law and performing overdamped motion, that is described by a density obeying an integro-differential evolution equation that admits exact time-dependent solutions of the q-Gaussian form. These q-Gaussian solutions, which constitute a signature of S q -thermostatistics, evolve in a similar but not identical way to the solutions of an appropriate nonlinear, power-law Fokker–Planck equation.