Abstract: A network captures how components in a system interact. Take humans as an example. Humans are complex dynamic systems, whose emotions, cognitions, and behaviors constantly fluctuate and interact over time. Networks in this case represent, for example, the interaction or dynamics between emotions over time. However, in time the dynamics of a process are themselves prone to change. Consider, for example, external factors like stress, which can lower the self-predictability and interaction of emotions and thus change the dynamics. In this case, there should not be a single network or static figure of the emotion dynamics, but a network movie representing the evolution of the network over time. We have developed a new data-driven model that can explicitly model the change in temporal dependency within an individual without pre-existing knowledge of the nature of the change: the semi-parametric time-varying vector autoregressive method (TV-VAR). The TV-VAR proposed here is based on the easy applicable and well-studied generalized additive modeling techniques (GAM), available in the software R. Using the semi-parametric TV-VAR one can detect and model changing dynamics or network movies for a single individual or system.

Abstract: Background: Mental disorders are influenced by such a complex interplay of factors that it is extremely difficult to develop accurate predictive models. Complex dynamical system theory may provide a new route to assessment of personalized risk for transitions in depression. In complex systems early warning signals (EWS), signaling critical slowing down of the system, are found to precede critical transitions. Experience Sampling Methodology (ESM) may help to empirically test whether principals of complex dynamical systems also apply to mental disorders. Method: ESM techniques were employed to examine whether EWS can be detected in intra-individual change patterns of affect. Previously reported EWS are rising autocorrelation, variance and strength of associations between elements in the system. Results: Empirical findings support the idea that higher levels of autocorrelation, variance and connection strength may indeed function as EWS for mood transitions. Results will be visualized in network models during the presentation. Conclusion: Empirical findings, as obtained with ESM, suggest that transitions in mental disorders may behave according to principles of complex dynamical system theory. This may change our view upon mental disorders and yield novel possibilities for personalized assessment or risk for transition.

Abstract: Graphical models have become a popular way to abstract complex systems and gain insights into relational patterns among observed variables. For temporally evolving systems, time-varying graphical models offer additional insights as they provide information about organizational processes, information diffusion, vulnerabilities and the potential impact of interventions. In many of these situations the variables of interest do not follow the same type of distribution, for instance, one might be interested in the relations between physiological and psychological measures (continuous) and the type of drug (categorical) in a medical context. We present a novel method based on generalized covariance matrices and kernel smoothed neighborhood regression to estimate time-varying mixed graphical models in a high-dimensional setting. In addition to our theory, we present a freely available software implementation, performance benchmarks in realistic situations and an illustration of our method using a dataset from the field of psychopathology.

Abstract: We describe the dynamics of networks using one-dimensional discrete time dynamical systems theory obtained from a mean field approach to (elementary) probabilistic cellular automata (PCA). Often the mean field approach is used on a regular graph (a grid or torus) where each node has the same number of edges and the same probability of becoming active. We consider finite elementary PCA where each node has two states (two-letter alphabet): ?active? or ?inactive? (0/1). We then use the mean field approach to describe the dynamics of the PCA on a random, and a small world graph. We verified the accuracy of the mean field by means of a simulation study. Results showed that the mean field accurately estimates the percentage of active nodes (density) across various simulation conditions, and thus performs well when non-regular network structures are under consideration. The application we have in mind is that of psychopathology. The mean field approach then allows possible explanations of ?jumping? behaviour in depression, for instance. We show with an extensive time-series dataset how the mean field is applied and how the risk for phase transitions can be assessed.

Abstract: The Cinematic Theory of Cognition (CTC) postulates that cognition is a dynamical process manifested in the sequence of complex metastable patterns. Each consecutive pattern can be viewed as a frame in a movie, while the transition from one frame to the other acts as the movie shutter. Experimental evidence indicates that each pattern is maintained for about 100-200 ms (theta rate), while the transition from one pattern to the other is rapid (10-20 ms). This talk will address the following issues: 1. Experimental evidence of the CTC. Experiments involve intracranial ECoG of animals and human patients in preparation to epilepsy surgery, as well as noninvasive scalp EEG of human volunteers. 2. Dynamical systems theory of cognition and neurodynamics. Accordingly, the brain is viewed as a complex system with a trajectory exploring a high-dimensional attractor landscape. Experimentally observed, metastable patterns represent brain states corresponding to the meaning of the environmental inputs, while the transitions signify the ?aha? moment of deep insights and decision. 3. Modeling of the sequence of metastable patterns as phase transitions in the brain networks and a large-scale graph. Synchronization-desynchronization transitions with singular dynamics are described in the brain graph as a dissipative system. The hypothesis is made that the observed long-range correlations are neural correlates of cognition (NCC).