Phase transitions and nonlinear phenomena in neuronal network models

Communication and cooperation between billions of neurons underlie the power of the brain. How do complex functions of the brain arise from its cellular constituents? How do groups of neurons self-organize into patterns of activity? These are crucial questions in neuroscience. In order to answer them, it is necessary to have solid theoretical understanding of how single neurons communicate at the microscopic level, and how cooperative activity emerges. In this thesis we aim to understand how complex collective phenomena can arise in a simple model of neuronal networks. We use a model with balanced excitation and inhibition and complex network architecture, and we develop analytical and numerical methods for describing its neuronal dynamics. We study how interaction between neurons generates various collective phenomena, such as spontaneous appearance of network oscillations and seizures, and early warnings of these transitions in neuronal networks. Within our model, we show that phase transitions separate various dynamical regimes, and we investigate the corresponding bifurcations and critical phenomena. It permits us to suggest a qualitative explanation of the Berger effect, and to investigate phenomena such as avalanches, band-pass filter, and stochastic resonance. The role of modular structure in the detection of weak signals is also discussed. Moreover, we find nonlinear excitations that can describe paroxysmal spikes observed in electroencephalograms from epileptic brains. It allows us to propose a method to predict epileptic seizures. Memory and learning are key functions of the brain. There are evidences that these processes result from dynamical changes in the structure of the brain. At the microscopic level, synaptic connections are plastic and are modified according to the dynamics of neurons. Thus, we generalize our cortical model to take into account synaptic plasticity and we show that the repertoire of dynamical regimes becomes richer. In particular, we find mixed-mode oscillations and a chaotic regime in neuronal network dynamics.

The influence of photon excitation and proton irradiation on the luminescence properties of yttria stabilized zirconia doped with praseodymium ions

Lanthanide doped zirconia based materials are promising phosphors for lighting applications. Transparent yttria stabilized zirconia fibres, in situ doped with Pr3+ ions, were grown by the laser floating zone method. The single crystalline doped fibres were found to be homogeneous in composition and provide an intense red luminescence at room temperature. The stability of this luminescence due to transitions between the 1D2 → 3H4 multiplets of the Pr3+ ions (intra-4f2 configuration) was studied by photo- and iono-luminescence. The evolution of the red integrated photoluminescence intensity with temperature indicates that the overall luminescence decreases to ca. 40% of the initial intensity at 14 K when heated to room temperature (RT). RT analysis of the iono-luminescence dependence on irradiation fluence reveals a decrease of the intensity (to slightly more than ∼60% of the initial intensity after 25 min of proton irradiation exposure). Nevertheless the luminescence intensity saturates at non-zero values for higher irradiation fluences revealing good potential for the use of this material in radiation environments.

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.