# abstract Lucia Schiatti

**Lucia Schiatti** (Department of Data Analysis, UGent)

### Brain Connectivity during a Problem Solving Task.

Data coming from two monkeys implanted with cortical electrodes on the pre-frontal and sensorimotor cortex and related to the execution of a problem solving task were processed and analyzed to assess brain connectivity measures among couples and groups of variables in the framework of information theory.

During the task, the monkeys had to search by trial and error which of four simultaneously presented targets were associated to a reward [1]. In each trial the animal had to choose a target by fixating and then touching it. Targets switched off 600 ms after the touch. A reward (positive feedback) was delivered if the correct target was chosen. No reward was given in case of an incorrect choice (negative feedback). Each block of trials contained a search period (exploration) during which the animal was searching for the rewarded target and, after its discovery, a repetition period (exploitation) during which the correct response was repeated at least three times.

Coupling measures between couples and groups of variables (ECoG signals) during presentation of the stimulus, execution of the motion task and feedback, were inferred in terms of transfer entropy, an information-theoretic measure of time-directed information transfer between jointly dependent processes, and Granger causality, a statistical notion of causal influence based on prediction via vector autoregression. Transfer entropy was assessed computing first and second order terms of the expansion presented in [2], which put in evidence irreducible sets of variables providing information for the future state of each assigned target. First order terms coincide with the bivariate transfer entropies, while second order terms may be seen as the generalization of the interaction information; hence a positive (negative) term corresponds to a redundant (synergetic) flow of information from variables to the target.

Granger causality was computed taking in account the conditioning effect of the other variables on the causal influence of one time series to another, by achieving a partial conditioning to a limited set of variables, in the framework of information theory [3]. Conditioning on a small number of variables, chosen as the most informative for the candidate driver variable, is sufficient to remove indirect interactions for sparse connectivity patterns, and leads to better results with respect to a fully multivariate approach, which can entrain computational but even conceptual problems (e.g. underestimation of causalities in the presence of redundant variables).

[1] Coordination of high gamma activity in anterior cingulate and lateral prefrontal cortical areas during adaptation. M. Rothé, R. Quilodran, J. Sallet, E. Procyk. J. Neurosci., 31, 11110 (2011)

[2] Expanding the transfer entropy to identify information circuits in complex systems. S. Stramaglia, G. Wu, M. Pellicoro, D. Marinazzo. Physical Review E, 86, 066211 (2012)

[3] Causal information approach to partial conditioning in multivariate data sets. D. Marinazzo, M. Pellicoro, S. Stramaglia. Computational and Mathematical Methods in Medicine, 2012, ID 303601 (2012)