CONICET | Buscador de Institutos y Recursos Humanos

Much of the experimental data obtained in complex systems, is in the form of simultaneous recordings of the activity of units interacting in potentially unknown ways. With the aim to provide a qualitative analysis tool for electrophysiological data obtained in simultaneous multi recording experiments [1], we analyse the behaviour of a density based clustering algorithms for highly dimensional time series which combines the exploitation of recurrences [2] with the idea of an underlying effective energy landscape with associated attractors [3]. In this way the complex dynamics of the system is reduced to a compact description in terms of effective basins of attractions.When tested in Hopfield (spins) systems [4], the algorithm finds many (local) minima of the Hamiltonian, even when the time series was generated in the disordered phase.Once the local minima of the effective attractor landscape are estimated, a dimensional reduction can be performed by introducing effective interactions between them. This allows for an easier search of spatio-temporal patterns. The optimal weights of these interactions are found by means of a Minimum Probability Flow analysis [5].To get closer to empirical data, the algorithm is applied to multi-modular networks of Integrate and Fire neurons with and without Spike Frequency Adaptation, in which some memories have been stored. This allows for the construction of a quantitative dictionary between a microscopic description in terms of spiking neurons and a mesoscopic description in terms of interacting bistable modules. [1] I. H. Stevenson, K. P. Kording, {\it Nat. Neurosci.} {\bf 14} 139 (2011) [2] R. V. Donner {\it et al,} {\it Int J Bifurcation Chaos} {\bf 21} 1019 (2011) [3] J. Braun, M. Mattia, {\it Neuroimage} {\bf 52} 740 (2010) [4] J. J. Hopfield, {\it PNAS} {\bf 79} 2554 (1982) [5] J. Sohl-Dickstein {\it et al,} {\it Phys. Rev. Lett.} {\bf 107} 220601 (2011)