Basic circuits, which form the building blocks of the brain, have been identiffied in recent literature. We propose to treat these basic circuits as "stochastic generators" whose instances serve to wire a portion of the mouse brain. Very much in the same manner as genes generate proteins by providing templates for their construction, we view the catalog of basic circuits as providing templates for wiring up the neurons of the brain. This thesis work involves a) deffining a framework for the stochastic generation of brain networks, b) generation of sample networks from the basic circuits, and c) visualization of the generated networks.

The recent discovery of an intricate and nontrivial interaction topology among the elements of a wide range of natural systems has altered the manner we understand complexity. For example, the axonal fibres transmitting electrical information between cortical regions form a network which is neither regular nor completely random. Their structure seems to follow functional principles to balance between segregation (functional specialisation) and integration. Cortical regions are clustered into modules specialised in processing different kinds of information, e.g. visual or auditory. However, in order to generate a global perception of the real world, the brain needs to integrate the distinct types of information. Where this integration happens, nobody knows. We have performed an extensive and detailed graph theoretical analysis of the cortico-cortical organisation in the brain of cats, trying to relate the individual and collective topological properties of the cortical areas to their function. We conclude that the cortex possesses a very rich communication structure, composed of a mixture of parallel and serial processing paths capable of accommodating dynamical processes with a wide variety of time scales. The communication paths between the sensory systems are not random, but largely mediated by a small set of areas. Far from acting as mere transmitters of information, these central areas are densely connected to each other, strongly indicating their functional role as integrators of the multisensory information. In the quest of uncovering the structure-function relationship of cortical networks, the peculiarities of this network have led us to continuously reconsider the stablished graph measures. For example, a normalised formalism to identify the “functional roles” of vertices in networks with community structure is proposed. The tools developed for this purpose open the door to novel community detection techniques which may also characterise the overlap between modules. The concept of integration has been revisited and adapted to the necessities of the network under study. Additionally, analytical and numerical methods have been introduced to facilitate understanding of the complicated statistical interrelations between the distinct network measures. These methods are helpful to construct new significance tests which may help to discriminate the relevant properties of real networks from side-effects of the evolutionary-growth processes. / Die jüngste Entdeckung einer komplexen und nicht-trivialen Interaktionstopologie zwischen den Elementen einer großen Anzahl natürlicher Systeme hat die Art und Weise verändert, wie wir Komplexität verstehen. So bilden zum Beispiel die Nervenfasern, welche Informationen zwischen Regionen des Kortex übermitteln, ein Netzwerk, das weder vollkommen regelmäßig noch völlig zufallig ist. Die Struktur dieser Netzwerke scheint Funktionsprinzipien zu folgen, die ein Gleichgewicht zwischen Segregation (funktionale Spezialisierung) und Integration (Verarbeitung von Informationen) halten. Die Regionen des Kortex sind in Module gegliedert, welche auf die Verarbeitung unterschiedlicher Arten von Informationen, wie beispielsweise Visuelle oder Auditive, spezialisiert sind. Um eine umfassende Vorstellung von der Realität zu erzeugen, muss das Gehirn verschiedene Informationsarten kombinieren (integrieren). Wo diese Integration jedoch geschieht, ist noch ungeklärt. In dieser Dissertation wurde eine weitreichende und detaillierte graphen- theoretische Analyse der kortiko-kortikalen Organisation des Katzengehirns durchgeführt. Dabei wurde der Versuch unternommen, individuelle sowie kollektive topologische Eigenschaften der Kortexareale zu ihrer Funktion in Beziehung zu setzen. Aus der Untersuchung wird geschlussfolgert, dass der Kortex eine äußerst reichhaltige Kommunikationsstruktur aufweist, die aus einer Mischung von parallelen und seriellen übertragungsbahnen besteht, die es ermöglichen dynamische Prozesse auf vielen verschiedenen Zeitskalen zu tragen. Die Kommunikationsbahnen zwischen den sensorischen Systemen sind nicht zufällig verteilt, sondern verlaufen fast alle durch eine geringe Anzahl von Arealen. Diese zentralen Areale agieren nicht allein als übermittler von Informationen. Sie sind dicht untereinander verbunden, was auf ihre Funktion als Integrator hinweist. Bei der Analyse der Struktur-Funktions-Beziehungen kortikaler Netzwerke wurden unter Berucksichtigung der Besonderheiten des untersuchten Netzwerkes die bisher verwandten Graphenmaße überdacht und zum Teil überarbeitet. So wurde beispielsweise ein normalisierter Formalismus vorgeschlagen, um die funktionalen Rollen der Knoten in Netzwerken mit einer Community-Struktur zu identifizieren. Die für diesen Zweck entwickelten Werkzeuge ermöglichen neue Methoden zur Erkennung dieser Strukturen, die möglicherweise auch die überlappung von Modulen beschreiben. Das Konzept der Integration wurde revidiert und den Bedürfnissen des untersuchten Netzwerkes angepasst. Außerdem wurden analytische und numerische Methoden eingeführt, um das Verständnis des komplizierten statistischen Zusammenhangs zwischen den verschiedenen Netzwerkmaßen zu erleichtern. Diese Methoden sind hilfreich für die Konstruktion neuer Signifikanztests, die relevante Eigenschaften realer Netzwerke von Nebeneffekten ihrer evolutionären Wachstumsprozesse unterscheiden können.

A teoria de redes complexas se consolidou nos últimos anos, graças ao seu potencial como ferramenta versátil no estudo de diversos sistemas discretos. É possível enumerar aplicações em áreas tão distintas como engenharia, sociologia, computação, linguística e biologia. Tem merecido atenção, por exemplo, o estudo da organização estrutural do cérebro, tanto em nível microscópico (em nível de neurônios) como regional (regiões corticais). Acredita-se que tal organização visa otimizar a dinâmica, favorecendo processos como sincronização e processamento paralelo. Estrutura e funcionamento, portanto, estão relacionados. Tal relação é abordada pela teoria de redes complexas nos mais diversos sistemas, sendo possivelmente seu principal objeto de estudo. Neste trabalho exploramos as relações entre aspectos estruturais de redes neuronais e corticais e a atividade nas mesmas. Especificamente, estudamos como a interconectividade entre o córtex e o tálamo pode interferir em estados de ativação do último, considerando-se o sistema tálamo-cortical do gato bem como alguns modelos para geração de rede encontrados na literatura. Também abordamos a relação entre a morfologia individual de neurônios e a conectividade em redes neuronais, e consequentemente o impacto da forma neuronal em dinâmicas atuando sobre tais redes e a eficiência das mesmas no transporte de informação. Como tal eficiência pode ter como consequência a facilitação de processos maléficos às redes, como por exemplo, ataques causados por vírus neurotrópicos, também exploramos possíveis correlações entre características individuais dos elementos que formam as redes complexas e danos causados por processos infecciosos iniciados nos mesmos. / Complex network theory has been consolidated along the last years, owing to its potential as a versatile framework for the study of diverse discrete systems. It is possible to enumerate applications in fields as distinct as Engineering, Sociology, Computing, Linguistics and Biology, to name a few. For instance, the study of the structural organization of the brain at the microscopic level (neurons), as well as at regional level (cortical areas), has deserved attention. It is believed that such organization aims at optimizing the dynamics, supporting processes like synchronization and parallel processing. Structure and functioning are thus interrelated. Such relation has been addressed by complex network theory in diverse systems, possibly being its main subject. In this thesis we explore the relations between structural aspects and the activity in cortical and neuronal networks. Specifically, we study how the interconnectivity between the cortex and thalamus can interfere in activation states of the latter, taking into consideration the thalamocortical system of the cat, along with networks generated through models found in literature. We also address the relation between the individual morphology of the neurons and the connectivity in neuronal networks, and consequently the effect of the neuronal shape on dynamic processes actuating over such networks and on their efficiency on information transport. As such efficiency can consequently facilitate prejudicial processes on the networks, e.g. attacks promoted by neurotropic viruses, we also explore possible correlations between individual characteristics of the elements forming such systems and the damage caused by infectious processes started at these elements.

A teoria de redes complexas se consolidou nos últimos anos, graças ao seu potencial como ferramenta versátil no estudo de diversos sistemas discretos. É possível enumerar aplicações em áreas tão distintas como engenharia, sociologia, computação, linguística e biologia. Tem merecido atenção, por exemplo, o estudo da organização estrutural do cérebro, tanto em nível microscópico (em nível de neurônios) como regional (regiões corticais). Acredita-se que tal organização visa otimizar a dinâmica, favorecendo processos como sincronização e processamento paralelo. Estrutura e funcionamento, portanto, estão relacionados. Tal relação é abordada pela teoria de redes complexas nos mais diversos sistemas, sendo possivelmente seu principal objeto de estudo. Neste trabalho exploramos as relações entre aspectos estruturais de redes neuronais e corticais e a atividade nas mesmas. Especificamente, estudamos como a interconectividade entre o córtex e o tálamo pode interferir em estados de ativação do último, considerando-se o sistema tálamo-cortical do gato bem como alguns modelos para geração de rede encontrados na literatura. Também abordamos a relação entre a morfologia individual de neurônios e a conectividade em redes neuronais, e consequentemente o impacto da forma neuronal em dinâmicas atuando sobre tais redes e a eficiência das mesmas no transporte de informação. Como tal eficiência pode ter como consequência a facilitação de processos maléficos às redes, como por exemplo, ataques causados por vírus neurotrópicos, também exploramos possíveis correlações entre características individuais dos elementos que formam as redes complexas e danos causados por processos infecciosos iniciados nos mesmos. / Complex network theory has been consolidated along the last years, owing to its potential as a versatile framework for the study of diverse discrete systems. It is possible to enumerate applications in fields as distinct as Engineering, Sociology, Computing, Linguistics and Biology, to name a few. For instance, the study of the structural organization of the brain at the microscopic level (neurons), as well as at regional level (cortical areas), has deserved attention. It is believed that such organization aims at optimizing the dynamics, supporting processes like synchronization and parallel processing. Structure and functioning are thus interrelated. Such relation has been addressed by complex network theory in diverse systems, possibly being its main subject. In this thesis we explore the relations between structural aspects and the activity in cortical and neuronal networks. Specifically, we study how the interconnectivity between the cortex and thalamus can interfere in activation states of the latter, taking into consideration the thalamocortical system of the cat, along with networks generated through models found in literature. We also address the relation between the individual morphology of the neurons and the connectivity in neuronal networks, and consequently the effect of the neuronal shape on dynamic processes actuating over such networks and on their efficiency on information transport. As such efficiency can consequently facilitate prejudicial processes on the networks, e.g. attacks promoted by neurotropic viruses, we also explore possible correlations between individual characteristics of the elements forming such systems and the damage caused by infectious processes started at these elements.

Diese Arbeit ist ein erster Versuch, mit Modellbildung und mathematischer Analyse die Experimente zu verstehen, die zeigten, dass die Stimulation eines einzelnen Neurons im Cortex eine Verhaltensreaktion auslösen kann. Dieser Befund stellt die verbreitete Ansicht infrage, dass viele Neurone nötig sind, um Information zuverlässig kodieren zu können. Der Ausgangspunkt der vorliegenden Untersuchung ist die Stimulation einer zufällig ausgewählten Zelle in einem Zufallsnetzwerk exzitatorischer und inhibitorischer Neuronmodelle. Es wird dann nach einem plausiblen Ausleseverfahren gesucht, das die Einzelzellstimulation mit einer mit den Experimenten vergleichbaren Zuverlässigkeit detektieren kann. Das erste Ausleseschema reagiert auf Abweichungen vom spontanen Zustand in der Aktivität einer Auslesepopulation. Die Stimulation wird detektiert, wenn bei der Auswahl der Auslesepopulation denjenigen Neuronen ein Vorzug gegeben wird, die eine direkte Verbindung von der stimulierten Zelle bekommen. Im zweiten Teil der Arbeit wird das Ausleseschema erweitert, indem ein zweites Netzwerk als Ausleseschaltkreis dient. Interessanterweise erweist sich dieses Ausleseschema nicht nur als plausibler, sondern auch als effektiver. Diese Resultate basieren sowohl auf Simulationen als auch auf analytischen Rechnungen. Weitere Experimente zeigten, dass eine konstante Strominjektion einen Effekt auslöst, der kaum von Dauer und Intensität der Stimulation abhängt, der aber bei unregelmäßiger Stimulation zunimmt. Der letzte Teil der Arbeit befasst sich mit einer theoretischen Erklärung für diese Ergebnisse. Hierzu werden die biologischen Eigenschaften des Systems im Modell detaillierter beschrieben. Weiterhin wird die Funktionsweise des Ausleseschemas so modifiziert, dass es auf Veränderungen reagiert, anstatt den Input zu integrieren. Dieser Differenzierdetektor liefert Ergebnisse, die mit den Experimenten übereinstimmen, und könnte bei nichtstationärem Input vorteilhaft sein. / This thesis is a first attempt at developing a theoretical model of the experiments which show that the stimulation of a single cell in the cortex can trigger a behavioral reaction and that challenge the common belief that many neurons are needed to reliably encode information. As a starting point of the present work, one neuron selected at random within a random network of excitatory and inhibitory integrate-and-fire neurons is stimulated. One important goal of this thesis is to seek a readout scheme that can detect the single-cell stimulation in a plausible way with a reliability compatible with the experiments. The first readout scheme reacts to deviations from the spontaneous state in the activity of a readout population. When the choice of readout neurons is sufficiently biased towards those receiving direct links from the stimulated cell, the stimulation can be detected. In the second part of the thesis, the readout scheme is extended by employing a second network as a readout circuit. Interestingly, this new readout scheme is not only more plausible, but also more effective. These results are based both on numerical simulations of the network and on analytical approximations. Further experiments showed that the probability of the behavioral reaction is substantially independent of the length and intensity of the stimulation, but it increases when an irregular current is used. The last part of this thesis seeks a theoretical explanation for these findings. To this end, a recurrent network including more biological details of the system is considered. Furthermore, the functioning principle of the readout is modified to react to changes in the activity of the local network (a differentiator readout), instead of integrating the input. This differentiator readout yields results in accordance with the experiments and could be advantageous in the presence of nonstationarities.

Establishing and maintaining successful communication stands as a critical prerequisite for achieving the goals of inducing and studying advanced computation in small-scale living neuronal networks. The following work establishes a novel and effective method for communicating arbitrary "sensory" input information to cultures of living neurons, living neuronal networks (LNNs), consisting of approximately 20 000 rat cortical neurons plated on microelectrode arrays (MEAs) containing 60 electrodes. The sensory coding algorithm determines a set of effective codes (symbols), comprised of different spatio-temporal patterns of electrical stimulation, to which the LNN consistently produces unique responses to each individual symbol. The algorithm evaluates random sequences of candidate electrical stimulation patterns for evoked-response separability and reliability via a support vector machine (SVM)-based method, and employing the separability results as a fitness metric, a genetic algorithm subsequently constructs subsets of highly separable symbols (input patterns). Sustainable input/output (I/O) bit rates of 16-20 bits per second with a 10% symbol error rate resulted for time periods of approximately ten minutes to over ten hours. To further evaluate the resulting code sets' performance, I used the system to encode approximately ten hours of sinusoidal input into stimulation patterns that the algorithm selected and was able to recover the original signal with a normalized root-mean-square error of 20-30% using only the recorded LNN responses and trained SVM classifiers. Response variations over the course of several hours observed in the results of the sine wave I/O experiment suggest that the LNNs may retain some short-term memory of the previous input sample and undergo neuroplastic changes in the context of repeated stimulation with sensory coding patterns identified by the algorithm.