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.

Concentration of human pollution tracers with ionic liquids

The main objective of the present thesis consists on the development of an analytical preconcentration technology for the concomitant extraction and concentration of human pollution tracers from wastewater streams. Due to the outstanding tunable properties of ionic liquids (ILs), aqueous biphasic systems (ABS) composed of ILs can provide higher and more selective extraction efficiencies for a wide range of compounds, being thus a promising alternative to the volatile and hazardous organic solvents (VOCs) typically used. For that purpose, IL-based ABS were employed and adequately characterized as an one-step extraction and concentration technique. The applicability of IL-based ABS was verified by their potential to completely extract and concentrate two representative pharmaceutical pollution tracers, namely caffeine (CAF) and carbamazepine (CBZ), from wastewaters. The low concentration of these persistent pollutants (usually found in μg·dm-3 and ng·dm-3 levels, respectively) by conventional analytical equipment does not permit a proper detection and quantification without a previous concentration step. Preconcentration methods commonly applied are costly, timeconsuming, with irregular recoveries and make use of VOCs. In this work, the ABS composed of the IL tetrabutylammonium chloride ([N4444]Cl) and the salt potassium citrate (K3[C6H5O7]) was investigated while demonstrating to be able to completely extract and concentrate CAF and CBZ, in a single-step, overcoming thus the detection limit of the applied analytical equipment. Finally, the hydrotropic effect responsible for the ability of IL-based ABS to extract and concentrate a wide variety of compounds was also investigated. It was shown that the IL rules the hydrotropic mechanism in the solubility of CAF in aqueous solutions, with an increase in solubility up to 4-fold. Moreover, the proper selection of the IL enables the design of the system that leads to a more enhanced solubility of a given solute in the IL-rich phase, while allowing a better extraction and concentration. IL-based ABS are a promising and more versatile technique, and are straightforwardly envisaged as selective extraction and concentration routes of target micropollutants from wastewater matrices.