Mathematical methods to analyze and interpret calcium signals of astrocytes

Astrocytes are the most numerous glial cell type in the mammalian brain and permeate the entire CNS interacting with neurons, vasculature, and other glial cells. Astrocytes display intracellular calcium signals that encode information about local synaptic function, distributed network activity, and high-level cognitive functions. Several studies have investigated the calcium dynamics of astrocytes in sensory areas and have shown that these cells can encode sensory stimuli. Nevertheless, only recently the neuro-scientific community has focused its attention on the role and functions of astrocytes in associative areas such as the hippocampus. In our first study, we used the information theory formalism to show that astrocytes in the CA1 area of the hippocampus recorded with 2-photon fluorescence microscopy during spatial navigation encode spatial information that is complementary and synergistic to information encoded by nearby "place cell" neurons. In our second study, we investigated various computational aspects of applying the information theory formalism to astrocytic calcium data. For this reason, we generated realistic simulations of calcium signals in astrocytes to determine optimal hyperparameters and procedures of information measures and applied them to real astrocytic calcium imaging data. Calcium signals of astrocytes are characterized by complex spatiotemporal dynamics occurring in subcellular parcels of the astrocytic domain which makes studying these cells in 2-photon calcium imaging recordings difficult. However, current analytical tools which identify the astrocytic subcellular regions are time consuming and extensively rely on user-defined parameters. Here, we present Rapid Astrocytic calcium Spatio-Temporal Analysis (RASTA), a novel machine learning algorithm for spatiotemporal semantic segmentation of 2-photon calcium imaging recordings of astrocytes which operates without human intervention. We found that RASTA provided fast and accurate identification of astrocytic cell somata, processes, and cellular domains, extracting calcium signals from identified regions of interest across individual cells and populations of hundreds of astrocytes recorded in awake mice.

Monitoring time-dependent deformation patterns through geodetic techniques

In this thesis we focus on the analysis and interpretation of time dependent deformations recorded through different geodetic methods. Firstly, we apply a variational Bayesian Independent Component Analysis (vbICA) technique to GPS daily displacement solutions, to separate the postseismic deformation that followed the mainshocks of the 2016-2017 Central Italy seismic sequence from the other, hydrological, deformation sources. By interpreting the signal associated with the postseismic relaxation, we model an afterslip distribution on the faults involved by the mainshocks consistent with the co-seismic models available in literature. We find evidences of aseismic slip on the Paganica fault, responsible for the Mw 6.1 2009 L’Aquila earthquake, highlighting the importance of aseismic slip and static stress transfer to properly model the recurrence of earthquakes on nearby fault segments. We infer a possible viscoelastic relaxation of the lower crust as a contributing mechanism to the postseismic displacements. We highlight the importance of a proper separation of the hydrological signals for an accurate assessment of the tectonic processes, especially in cases of mm-scale deformations. Contextually, we provide a physical explanation to the ICs associated with the observed hydrological processes. In the second part of the thesis, we focus on strain data from Gladwin Tensor Strainmeters, working on the instruments deployed in Taiwan. We develop a novel approach, completely data driven, to calibrate these strainmeters. We carry out a joint analysis of geodetic (strainmeters, GPS and GRACE products) and hydrological (rain gauges and piezometers) data sets, to characterize the hydrological signals in Southern Taiwan. Lastly, we apply the calibration approach here proposed to the strainmeters recently installed in Central Italy. We provide, as an example, the detection of a storm that hit the Umbria-Marche regions (Italy), demonstrating the potential of strainmeters in following the dynamics of deformation processes with limited spatio-temporal signature

Idee, Natur, Geist. Schellings allgemeine Ontologie des Wirklichen nach der "Darstellung des Naturprocesses" von 1843/44

Ziel dieser Dissertation ist es, die grundlegenden philosophisch-theoretischen Implikationen von Schellings letzter systematischer Darlegung seiner Naturphilosophie nach dem Berliner Textfragment von 1843/44, der “Darstellung des Naturprocesses”, zu untersuchen. Angesichts der sich zwischen den 1830 und den 1860 Jahren in Berlin abzeichnenden neuen intellektuellen Tendenzen und der Entwicklungen in den Naturwissenschaften legt Schelling hier die Grundlagen für eine allgemeine Ontologie des Wirklichen in kritischer Auseinandersetzung mit Kants transzendentalem Idealismus. Innerhalb des systematischen Horizonts der "apriorischen Vernunftwissenschaft" oder "negativen Philosophie" stellt er im ersten Teil seines Werkes die Prinzipien fest, die die „Idee des Existierenden“ ausmachen, und beschreibt die rationale Operation, die durchgeführt werden muss, um zum Gedanken einer „Welt außer der Idee“ zu gelangen. Die philosophisch-systematischen Annahmen, die mit dem Übergang von der bloßen Idee des Existierenden zum Gedanken der außeridealen Welt verbunden sind, werden im ersten Kapitel dieser Dissertation untersucht. Im zweiten Teil seines Werkes definiert Schelling durch eine detaillierte Analyse von Kants Transzendentalen Ästhetik den Raum als diejenige Form, in der uns die Existenzen als voneinander getrennt vorstellen lassen. Obwohl der Zeitbegriff von Schelling nur am Rande behandelt wird, trägt er zusammen mit dem Raum dazu bei, die erste ontologische Grundstruktur der außeridealen Welt zu definieren. Die Analyse von Schellings Konzeption der raumzeitlichen Grundstruktur der außeridealen Welt stellt das Thema des zweiten Kapitels dieser Dissertation dar. Schließlich bestimmt Schelling im dritten Teil seines Werkes die Finalität als diejenige Kausalitätsform, die es ermöglicht, die außerideale Welt als einen werdenden Kontext zu verstehen, dessen Entwicklungsstufen die siderische Welt, die unorganische Welt und die organische Welt sind. Die Schelling‘sche Definition der Teleologie der Natur als zweite ontologische Grundstruktur der außeridealen Welt ist das Thema des dritten Kapitels dieser Dissertation.