Current neuroanatomical knowledge about the structure of brain networks is still so fragmentary that it renders corresponding models for brain function notoriously underdetermined. In order to improve our understanding of the impact of structural features of cortical networks, we considered several types of networks with biologically motivated synaptic connectivities. Stochastic graph theory was used to characterize structural properties of these networks. One specifically useful trait was the mean path length between any two nodes. The aim of this project is to characterize large networks by suitable parameters that can be interpreted neuroanatomically.

Analytic relations between the structure of neural networks and their activity dynamics are hardly known so far. We explored several new concepts for local cortical networks comprising some 10⁵ excitatory and inhibitory neurons. The dynamics of spontaneous activity in such ensembles was studied using the spectral theory of random graphs combined with the theory of stochastic dynamical systems. In some cases we could explicitly show how particular structural parameters of the network influence its activity dynamics.

We also employed techniques such as "machine learning"' and "data mining" to relate the structure and dynamics of neuronal networks to one another. We developed an algorithm which can extract meaningful features from the network graph, which are then related to its activity as it is observed in numerical simulations. In this manner we were able to successfully predict population activity and firing rates of output neurons in random networks.

Following up on recent results by Kuhn et al. for individual neurons, we investigated the dynamics of large random networks of spiking neurons with conductance-based, nonlinear synapses. In systems with sparse, inhibition-dominated and massively recurrent connectivity structure, small external inputs induce asynchronous irregular (AI) firing at low rates, similar to what is seen in the brain of behaving animals. In contrast to the classical model with current-based, linear synapses the fluctuation statistics of membrane potentials of individual neurons also agrees with corresponding in vivo recordings. Moreover, the AI activity of conductance-based networks persists even if external inputs or cortical pacemakers are absent. Simulations of very large networks with about 10⁵ neurons demonstrate that the lifetime of this persistent activity increases rapidly as a function of increasing network size.

An important issue in the analysis of simultaneously recorded neuronal spike data is the identification of neuronal ensembles, whose activity expresses itself by the synchronous firing of action potentials. However, suitable tools for the analysis of such massively parallel spike trains are not available so far. We follow an approach in which mathematical models of parallel spike trains are constructed on the basis of different kinds of correlations. Our goal is to employ this framework to extract statistical observables that help to identify models which concisely characterize complex data of unknown origin.

In current approaches, the characterization of mental states with respect to neural states is often proposed in terms of their "multiple realization" by neuronal ensembles. That is, a particular neural realization is regarded as sufficient but not necessary for a particular mental state. As a complementing alternative, we worked out an approach referring to necessary but not sufficient conditions for the emergence of mental states. This approach is essentially based on a partitioning of the neuronal state space, such that equivalence classes of neural states arise that can be interpreted as mental states.

This procedure leads to meaningfully defined mental states only if generating partitions are utilized. Applications of this condition to neural data at mesoscopic and macroscopic levels are possible and will be carried out. If arbitrary partitions are employed, this leads in general (i) to ill-defined mental states whose properties (ii) belong to incompatible psychological models. This consequence is, for instance, important for the discussion of a unified theoretical framework for psychology or cognitive science, respectively.

In the 1970s, Freeman and Nicolis proposed to model cognitive processes using central concepts of nonlinear dynamics. The key idea is to model mental representations or categories as attractors of dynamical systems with particular stability properties. Such an approach provides, for instance, a new access to our understanding of a variety of psychopathological symptoms.

The approach worked out so far was extended to phenomenological descriptions of extraordinary states of consciousness (meditation, flow, etc.). Many observed cases indicate that such "acategorial" states of consciousness are closely related to mental instabilities. Applications referring to creative processes in the solution of problems requiring insight were initiated. More generally, the concept of acategoriality is expected to acquire great significance for transrational modes of knowledge.

A concrete application of the recently developed framework of a generalized quantum theory is the description of the bistable perception of ambiguous stimuli with the so-called Necker-Zeno model. Using this model we derived a formal relation among three time scales (of the order of 10, 100, and 1000 msec) that are of central significance for cognitive processes. This relation is at variance with earlier proposals and could be empirically confirmed. Our approach provides interesting conjectures from novel results by Pettigrew, who observed switching rates lowered by a factor of 1000 in meditating subjects.

We extended the Necker-Zeno model such as to be able to include an initially decreased switching rate. Moreover, the model was adapted to various experimental conditions (in particular randomized presentations) with computer simulations.

The neuronal activity in the cortex of behaving animals exhibits strong fluctuations on different time scales. This variability does not necessarily reflect variable behavior but can also be due to behavior-independent ongoing network activity. Indeed, a statistical analysis of recorded neuronal spike trains can only be consistently interpreted under the assumption of additional slow ( ≥ 1 second) fluctuations of the firing rate which is not time-locked to behavior. This hypothesis could be verified by a comparison of in vitro and in vivo data.

In addition to the intensity of individual cells in the intact brain, the temporal structure of their synaptic activity can strongly affect their integrative properties. As an experimental approach to this issue, we developed the method of dynamic photo stimulation, allowing us to study the integrative properties of cells with physiologically realistic input. Data obtained with this technique suggest that not only the neuronal spike generator but also synaptic transmission and dendritic integration in neocortical pyramid cells can be highly reliable.

Continuing earlier observations that slow components of local field potentials (LFP) in the motor cortex contain information about goal-directed arm movements, we investigated how different LFP components in the time and frequency domain are modulated during arm movements. The results suggest that the high-frequency components of the signal must be divided into at least two functionally different regimes at around 30Hz and beyond 60Hz. Furthermore, we succeeded in decoding the movement direction with high precision from the amplitude spectrum.