Speaker
Ulrich Parlitz

Description Prediction and analysis of complex dynamics requires a suitable representation of the underlying dynamical structure in terms of a mathematical model (ODE, PDE, ..) and methods for estimating relevant model parameters and the current state of the system. Whether this task can be solved depends on the observability of the required quantities given the available (time series) data and the efficacy of the estimation algorithm chosen. We shall present methods to address the observability problem and algorithms for parameter and state estimation employing nonlinear optimization and synchronization.

Speaker
Oleguer Sagarra

Description THIS SEMINAR HAS BEEN CANCELLED! In this talk I will justify the need for big (analytical) models in the era of big data. Using a particular example on human mobility records, I will introduce some basic concepts about the use of maximum entropy models as null proxies to assess relevant features observed in big datasets susceptible to be represented as complex networks. In particular, a quick review over the theory of ensembles applied to networks covering the three fundamental collectivities (micro-canonical, canonical and grand-canonical) will be performed. Hence, I will try to introduce from a "modern" viewpoint the tools laid by Gibbs in the XIXth century and show that they can be very useful to address XXIth century problems.

Speaker
Albert Diaz-Guilera

Description La complexitat s'estén a través de múltiples escales, que van des de l’àtom a les galàxies, i que formen geometries intricades. El comportament complex emergent pot tenir diferents orígens, però avui dia és clar que més enllà de les interaccions no lineals entre unitats, la topologia de les interaccions exerceix un paper fonamental a totes les escales. D'altra banda, les xarxes a diferents nivells estan interactuant. En aquesta xerrada revisarem els diferents nivells de descripció dels sistemes vius en què ens trobem amb xarxes complexes i mostrarem com sorgeixen en diferents escales i com interactuen. Això va des de l'escala cel·lular mitjançant xarxes metabòliques o xarxes de regulació gènica a les xarxes dels individus a nivell mundial, com Facebook o Twitter, en la societat de les tecnologies de la informació i la comunicació, o les xarxes d'interacció d'espècies en ecosistemes complexos.

Speaker
Mario Chavez

Speaker
Toni Guillamon

Description The phase of an oscillator such as a spiking neuron is one of the main indicators of the effects of external stimuli on the (membrane potential) dynamics, and a key information to study synchrony in biological oscillators. Experimentally, the phase advancement is mostly computed through phase response curves (PRCs) obtained from recordings of the time variations in reaching the next peak of the membrane potential; successful methods have been used to predict it by means of theoretical PRCs evaluated on the attractor (limit cycle). However, stimulation in transient states may induce phase advancements that differ from the predictions given in the asymptotic state. By computing the isochrons (curves of constant phase) in a vicinity of the limit cycle, we are able to accurately generalize the PRCs to the transient states and, as well, to provide a methodology to compute the phase advancement under any type of stimulus (weak or strong, instantaneous or long-lasting). We use this methodology to illustrate how classical (non-transient) PRCs do not reflect important differences among cells such as bistability. We will also present theoretical examples to illustrate the goodness of the generalized PRCs, especially in cases of "weak" attractors or high-frequency stimuli. Finally, we will remark how the knowledge of second-order PRCs, together with a geometrical interpretation of the isochrons, can help to use the contribution of successive return times to refine experimentally computed PRCs.