Roseli S. Wedemann

Creativity and delusions: the dopaminergic modulation of cortical maps

Since little is still known about fundamental brain mechanisms associated to thought, its different manifestations are usually classified in an oversimplified way into normal and abnormal, like delusional and disorganized thought or creative thinking. Considering dopaminergic signal-to-noise neuronal modulation in the central nervous system, and the existence of semantic maps in the human brain, we developed a self-organizing neural network model to unify different thought processes into a single neurocomputational substrate. We performed simulations varying dopaminergic modulation and observed the total patterns that emerged at the resulting semantic map, assuming that these correspond to thought. The model thus shows how normal and abnormal thinking are generated, and that there are no clear borders between their different manifestations. Actually, a continuum of different qualitative reasoning, ranging from delusion to disorganized thought, and passing through normal and creative thinking, seems to be more plausible.

Generalized memory associativity in a network model for the neuroses

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 Freuds 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.

Memory Functioning in Psychopathology

The mental pathology known as neurosis, its aetiology, and the development of symptoms are described in terms of their relation to memory function. We propose, based on a neural network model, that neurotic behavior may be understood as an associative memory process in the brain, and that the linguistic, symbolic associative process involved in psychoanalytic working-through can be mapped onto a corresponding process of reconfiguration of the neural network. The model is illustrated through a computer simulation implementation. We relate the sensitivity to temperature and the adaptive capabilities of our model, with the sensitivity of cortical map modulation to the catecholamines (norepinephrine and dopamine). The signal-to-noise ratio regulated by these substances influence thought associativity, suggesting a continuum from psychotic functioning through to normal and neurotic behavior and creativity.

Curl forces and the nonlinear Fokker-Planck equation

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, time-dependent 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.

Modeling the electric potential across neuronal membranes: the effect of fixed charges on spinal ganglion neurons and neuroblastoma cells.

We present a model for the electric potential profile across the membranes of neuronal cells. We considered the resting and action potential states, and analyzed the influence of fixed charges of the membrane on its electric potential, based on experimental values of membrane properties of the spinal ganglion neuron and the neuroblastoma cell. The spinal ganglion neuron represents a healthy neuron, and the neuroblastoma cell, which is tumorous, represents a pathological neuron. We numerically solved the non-linear Poisson-Boltzmann equation for the regions of the membrane model we have adopted, by considering the densities of charges dissolved in an electrolytic solution and fixed on both glycocalyx and cytoplasmic proteins. Our model predicts that there is a difference in the behavior of the electric potential profiles of the two types of cells, in response to changes in charge concentrations in the membrane. Our results also describe an insensitivity of the neuroblastoma cell membrane, as observed in some biological experiments. This electrical property may be responsible for the low pharmacological response of the neuroblastoma to certain chemotherapeutic treatments.

A complex neural network model for memory functioning in psychopathology

In an earlier paper [1], we described the mental pathology known as neurosis in terms of its relation to memory function. We proposed a mechanism whereby neurotic behavior may be understood as an associative memory process in the brain, and the symbolic associative process involved in psychoanalytic working-through can be mapped onto a process of reconfiguration of the neuronal network. Memory was modeled by a Boltzmann machine represented by a complete graph. However, it is known that brain neuronal topology is selectively structured. Here, we further develop the memory model, by including known mechanisms that control synaptic properties, showing that the network self organizes to a hierarchical, clustered structure. Two modules corresponding to sensorial and declarative memory interact, producing sensorial and symbolic activity, representing unconscious and conscious mental processes. This extension of the model allows an evaluation of the idea of working-through in a hierarchical network structure.

Some things psychopathologies can tell us about consciousness

We review the contributions of some known models to the discussion of what the underlying neuronal mechanisms of consciousness creation should be. In particular, we note how different aspects of human mental behavior, such as in psychopathologies and dreams, may contribute to the understanding of these basic components. The interplay of conscious and unconscious mental functioning in the description of the psychoneuroses is analyzed. Aspects such as attentional capabilities, memory functioning, sequentiality and the capacity to create metarepresentations are discussed.

Avalanches and generalized memory associativity in a network model for conscious and unconscious mental functioning

We explore statistical characteristics of avalanches associated with the dynamics of a complex-network model, where two modules corresponding to sensorial and symbolic memories interact, representing unconscious and conscious mental processes. The model illustrates Freud’s ideas regarding the neuroses and that consciousness is related with symbolic and linguistic memory activity in the brain. It incorporates the Stariolo–Tsallis generalization of the Boltzmann Machine in order to model memory retrieval and associativity. In the present work, we define and measure avalanche size distributions during memory retrieval, in order to gain insight regarding basic aspects of the functioning of these complex networks. The avalanche sizes defined for our model should be related to the time consumed and also to the size of the neuronal region which is activated, during memory retrieval. This allows the qualitative comparison of the behaviour of the distribution of cluster sizes, obtained during fMRI measurements of the propagation of signals in the brain, with the distribution of avalanche sizes obtained in our simulation experiments. This comparison corroborates the indication that the Nonextensive Statistical Mechanics formalism may indeed be more well suited to model the complex networks which constitute brain and mental structure.

Nonlinear Wave Equations Related to Nonextensive Thermostatistics

We advance two nonlinear wave equations related to the nonextensive thermostatistical formalism based upon the power-law nonadditive S q entropies. Our present contribution is in line with recent developments, where nonlinear extensions inspired on the q-thermostatistical formalism have been proposed for the Schroedinger, Klein–Gordon, and Dirac wave equations. These previously introduced equations share the interesting feature of admitting q-plane wave solutions. In contrast with these recent developments, one of the nonlinear wave equations that we propose exhibits real q-Gaussian solutions, and the other one admits exponential plane wave solutions modulated by a q-Gaussian. These q-Gaussians are q-exponentials whose arguments are quadratic functions of the space and time variables. The q-Gaussians are at the heart of nonextensive thermostatistics. The wave equations that we analyze in this work illustrate new possible dynamical scenarios leading to time-dependent q-Gaussians. One of the nonlinear wave equations considered here is a wave equation endowed with a nonlinear potential term, and can be regarded as a nonlinear Klein–Gordon equation. The other equation we study is a nonlinear Schroedinger-like equation.

Asymmetries in Synaptic Connections and the Nonlinear Fokker-Planck Formalism

In previous work we have developed illustrative, neurocomputational models to describe mechanisms associated with mental processes. In these efforts, we have considered mental processes in phenomena such as neurosis, creativity, consciousness/unconsciousness, and some characteristics of the psychoses. Memory associativity is a key feature in the theoretical description of these phenomena, and much of our work has focused on modeling this mechanism. In traditional neural network models of memory, the symmetry of synaptic connections is a necessary condition for reaching stationary states. The assumption of symmetric weights seems however to be biologically unrealistic. Efforts to model stationary network states with asymmetric weights are mathematically complex and are usually applied to restricted situations. This has motivated us to explore the possibility of a new approach to the synaptic symmetry problem, based on its analogies with some features of the nonlinear Fokker-Planck formalism.