Efficient simulation of large-scale mammalian brain models provides a crucial computational means for understanding complex brain functions and neuronal dynamics. However, such tasks are hindered by significant computational complexities. In this work, we attempt to address the significant computational challenge in simulating large-scale neural networks based on the most biophysically accurate Hodgkin-Huxley (HH) neuron models. Unlike simpler phenomenological spiking models, the use of HH models allows one to directly associate the observed network dynamics with the underlying biological and physiological causes, but at a significantly higher computational cost. We exploit recent commodity massively parallel graphics processors (GPUs) to alleviate the significant computational cost in HH model based neural network simulation. We develop look-up table based HH model evaluation and efficient parallel implementation strategies geared towards higher arithmetic intensity and minimum thread divergence. Furthermore, we adopt and develop advanced multi-level numerical integration techniques well suited for intricate dynamical and stability characteristics of HH models. On a commodity CPU card with 240 streaming processors, for a neural network with one million neurons and 200 million synaptic connections, the presented GPU neural network simulator is about 600X faster than a basic serial CPU based simulator, 28X faster than the CPU implementation of the proposed techniques, and only two to three times slower than the GPU based simulation using simpler spiking models.

O estudo de redes complexas tem despertado muita atenção nos últimos anos, principalmente pela sua capacidade de permitir a análise dos mais diversificados sistemas através de um mesmo conjunto de ferramentas matemáticas e computacionais. Até pouco tempo a ênfase nessa área era sobre o estudo das propriedades estruturas e sua influência em característica globais da dinâmica ocorrendo sobre o sistema. Recentemente foi-se percebendo a riqueza de comportamentos que podemos estudar ao olharmos para grupos de vértices e as interações que ocorrem entre esses grupos, de forma que cada vez mais se torna necessária a criação de uma forma sistemática de quantificar, a nível de nó, como uma dinâmica é influenciada (ou diferenciada) pela estrutura do sistema. Apresentamos nesse trabalho um primeiro passo nessa direção, no qual definimos uma medida que, baseada em características dinâmicas obtidas em diversas condições iniciais, busca comparar o comportamento dos nós presentes no sistema. Através dessa medida encontramos a alta capacidade de modelos de rede geográficas de produzir, por simples flutuações estatísticas, grupos de nós de dinâmica muito distinta em relação ao demais, um fato que não ocorre para uma rede definida de forma semelhante mas não geográfica. Nessas redes conseguimos verificar também se um nó de topologia local distinta dos demais consegue possuir uma dinâmica diferenciada, o que encontramos foi que mesmo em regiões da rede extremamente regulares existe a formação de grupos dinâmicos devido ao efeito da borda dessa região. Saindo de modelos de redes para apresentar aplicações práticas do método, encontramos na rede neuronal do verme Caenorhabditis elegans um conjunto de nós de alta diferenciação dinâmica, que representam os interneurônios do cordão ventral do verme. Adicionalmente encontramos na rede cortical do macaco da família Cercopithecidae uma divisão em relação a regularidade dos sinais dinâmicos, o que indica a presença de comunidades funcionais nessa rede. Além da metodologia de diferenciação desenvolvemos ainda uma ferramenta que busca encontrar de forma totalmente automatizada as características dinâmicas mais relevantes do sistema em estudo, que foi capaz de representar medidas dinâmicas tradicionalmente utilizadas na área. Todos esses resultados abrem caminho para diversas vertentes de estudo, em especial citamos a influência de uma borda irregular no interior de uma região regular, o estudo da rede Caenorhabditis elegans com dinâmicas neuronais mais precisas e a aplicação sistemática de dinâmicas para encontrar a divisão funcional de comunidades em redes direcionadas, um tema que apresenta resultados promissores. / The study of complex networks has drawn much attention over the last years, mainly by virtue of its potential to characterize the most diverse systems through the same mathematical and computational tools. Not long ago the emphasis on this field mostly focused on the effects of the structural properties on the global behavior of a dynamical process taking place in the system. Recently, some studies started to unveil the richness of interactions that occur between groups of nodes when we look at the small scale of interactions occurring in the network. Such findings call for a new systematic methodology to quantify, at node level, how a dynamics is being influenced (or differentiated) by the structure of the underlying system. Here we present a first step towards this direction, in which we define a new measurement that, based on dynamical characteristics obtained for a series of initial conditions, compares the dynamical behavior of the nodes present in the system. Through this measurement we find the high capacity of networks generated by geographical models to exhibit, by means of statistical fluctuations, groups of nodes with very distinct dynamics compared to the rest of the network, a behavior that does not occur for a similar non-geographical network. We also verify if a large topological differentiation of a node necessarily reflects on its dynamics. We find that even in very regular regions of the network the nodes tend to form dynamical groups influenced by the border effects. In addition to the network models used, we present practical applications of the methodology by using the neuronal network of the nematode Caenorhabditis elegans, where we show that the interneurons of the ventral cord presents a very large dynamical differentiation when compared to the rest of the network. We also analyze the cortical network of the Cercopithecidae monkey by means of signal communication complexity, finding that it contains two well-defined functional communities. Besides the differentiation measurement, we also presents an useful mechanism for automatically obtaining the relevant dynamical characteristics of the nodes, which showed promising results by obtaining traditional measurements of the area with little effort. All these results pave the way to a range of different studies, of which we highlight the influence of an irregular border on the dynamics taking place inside a regular network region, the study of the neurons of Caenorhabditis elegans using more robust neuronal dynamics and the systematic application of different dynamics in order to find the functional community division of directed networks.

No description available.

O estudo de redes complexas tem despertado muita atenção nos últimos anos, principalmente pela sua capacidade de permitir a análise dos mais diversificados sistemas através de um mesmo conjunto de ferramentas matemáticas e computacionais. Até pouco tempo a ênfase nessa área era sobre o estudo das propriedades estruturas e sua influência em característica globais da dinâmica ocorrendo sobre o sistema. Recentemente foi-se percebendo a riqueza de comportamentos que podemos estudar ao olharmos para grupos de vértices e as interações que ocorrem entre esses grupos, de forma que cada vez mais se torna necessária a criação de uma forma sistemática de quantificar, a nível de nó, como uma dinâmica é influenciada (ou diferenciada) pela estrutura do sistema. Apresentamos nesse trabalho um primeiro passo nessa direção, no qual definimos uma medida que, baseada em características dinâmicas obtidas em diversas condições iniciais, busca comparar o comportamento dos nós presentes no sistema. Através dessa medida encontramos a alta capacidade de modelos de rede geográficas de produzir, por simples flutuações estatísticas, grupos de nós de dinâmica muito distinta em relação ao demais, um fato que não ocorre para uma rede definida de forma semelhante mas não geográfica. Nessas redes conseguimos verificar também se um nó de topologia local distinta dos demais consegue possuir uma dinâmica diferenciada, o que encontramos foi que mesmo em regiões da rede extremamente regulares existe a formação de grupos dinâmicos devido ao efeito da borda dessa região. Saindo de modelos de redes para apresentar aplicações práticas do método, encontramos na rede neuronal do verme Caenorhabditis elegans um conjunto de nós de alta diferenciação dinâmica, que representam os interneurônios do cordão ventral do verme. Adicionalmente encontramos na rede cortical do macaco da família Cercopithecidae uma divisão em relação a regularidade dos sinais dinâmicos, o que indica a presença de comunidades funcionais nessa rede. Além da metodologia de diferenciação desenvolvemos ainda uma ferramenta que busca encontrar de forma totalmente automatizada as características dinâmicas mais relevantes do sistema em estudo, que foi capaz de representar medidas dinâmicas tradicionalmente utilizadas na área. Todos esses resultados abrem caminho para diversas vertentes de estudo, em especial citamos a influência de uma borda irregular no interior de uma região regular, o estudo da rede Caenorhabditis elegans com dinâmicas neuronais mais precisas e a aplicação sistemática de dinâmicas para encontrar a divisão funcional de comunidades em redes direcionadas, um tema que apresenta resultados promissores. / The study of complex networks has drawn much attention over the last years, mainly by virtue of its potential to characterize the most diverse systems through the same mathematical and computational tools. Not long ago the emphasis on this field mostly focused on the effects of the structural properties on the global behavior of a dynamical process taking place in the system. Recently, some studies started to unveil the richness of interactions that occur between groups of nodes when we look at the small scale of interactions occurring in the network. Such findings call for a new systematic methodology to quantify, at node level, how a dynamics is being influenced (or differentiated) by the structure of the underlying system. Here we present a first step towards this direction, in which we define a new measurement that, based on dynamical characteristics obtained for a series of initial conditions, compares the dynamical behavior of the nodes present in the system. Through this measurement we find the high capacity of networks generated by geographical models to exhibit, by means of statistical fluctuations, groups of nodes with very distinct dynamics compared to the rest of the network, a behavior that does not occur for a similar non-geographical network. We also verify if a large topological differentiation of a node necessarily reflects on its dynamics. We find that even in very regular regions of the network the nodes tend to form dynamical groups influenced by the border effects. In addition to the network models used, we present practical applications of the methodology by using the neuronal network of the nematode Caenorhabditis elegans, where we show that the interneurons of the ventral cord presents a very large dynamical differentiation when compared to the rest of the network. We also analyze the cortical network of the Cercopithecidae monkey by means of signal communication complexity, finding that it contains two well-defined functional communities. Besides the differentiation measurement, we also presents an useful mechanism for automatically obtaining the relevant dynamical characteristics of the nodes, which showed promising results by obtaining traditional measurements of the area with little effort. All these results pave the way to a range of different studies, of which we highlight the influence of an irregular border on the dynamics taking place inside a regular network region, the study of the neurons of Caenorhabditis elegans using more robust neuronal dynamics and the systematic application of different dynamics in order to find the functional community division of directed networks.

Neuroprosthetics is at the intersection of neuroscience, biomedical engineering, and physics. A biocompatible neuroprosthesis contains artificial neurons exhibiting biophysically plausible dynamics. Hybrid systems analysis could be used to prototype such artificial neurons. Biohybrid systems are composed of artificial and living neurons coupled via real-time computing and dynamic clamp. Model neurons must be thoroughly tested before coupled with a living cell. We use bifurcation theory to identify hazardous regimes of activity that may compromise biocompatibility and to identify control strategies for regimes of activity desirable for functional behavior. We construct real-time artificial neurons for the analysis of hybrid systems and demonstrate a mechanism through which an artificial neuron could maintain duty cycle independent of variations in period.

We can affirm to apprehend a system in its totality only when we know how it behaves under its natural operating conditions. However, in the face of the complexity of the world, science can only evolve by simplifications, which paradoxically hide a good deal of the very mechanisms we are interested in. On the other hand, scientific enterprise is very tightly related to the advances in technology and the latter inevitably influences the manner in which the scientific experiments are conducted. Due to this factor, experimental conditions which would have been impossible to bring into laboratory not more than 20 years ago, are today within our reach. This thesis investigates neuronal integrative processes by using a variety of theoretical and experimental techniques wherein the approximation of ecologically relevant conditions within the laboratory is the common denominator. The working hypothesis of this thesis is that neurons and neuronal systems, in the sensory and higher cortices, are specifically adapted, as a result of evolutionary processes, to the sensory signals most likely to be received under ecologically relevant conditions. In order to conduct the present study along this line, we first recorded movies with the help of two microcameras carried by cats exploring a natural environment. This resulted in a database of binocular natural movies that was used in our theoretical and experimental studies. In a theoretical study, we aimed to understand the principles of binocular disparity encoding in terms of spatio-temporal statistical properties of natural movies in conjunction with simple mathematical expressions governing the activity levels of simulated neurons. In an unsupervised learning scheme, we used the binocular movies as input to a neuronal network and obtained receptive fields that represent these movies optimally with respect to the temporal stability criterion. Many distinctive aspects of the binocular coding in complex cells, such as the phase and position encoding of disparity and the existence of unbalanced ocular contributions, were seen to emerge as the result of this optimization process. Therefore we conclude that the encoding of binocular disparity by complex cells can be understood in terms of an optimization process that regulates activities of neurons receiving ecologically relevant information. Next we aimed to physiologically characterize the responses of the visual cortex to ecologically relevant stimuli in its full complexity and compare these to the responses evoked by artificial, conventional laboratory stimuli. To achieve this, a state-of-the-art recording method, voltage-sensitive dye imaging was used. This method captures the spatio-temporal activity patterns within the millisecond range across large cortical portions spanning over many pinwheels and orientation columns. It is therefore very well suited to provide a faithful picture of the cortical state in its full complexity. Drifting bar stimuli evoked two major sets of components, one coding for the position and the other for the orientation of the grating. Responses to natural stimuli involved more complex dynamics, which were locked to the motion present in the natural movies. In response to drifting gratings, the cortical state was initially dominated by a strong excitatory wave. This initial spatially widespread hyper-excitatory state had a detrimental effect on feature selectivity. In contrast, natural movies only rarely induced such high activity levels and the onset of inhibition cut short a further increase in activation level. An increase of 30% of the movie contrast was estimated to be necessary in order to produce activity levels comparable to gratings. These results show that the operating regime within which the natural movies are processed differs remarkably. Moreover, it remains to be established to what extent the cortical state under artificial conditions represents a valid state to make inferences concerning operationally more relevant input. The primary visual cortex contains a dense web of neuronal connections linking distant neurons. However the flow of information within this local network is to a large extent unknown under natural stimulation conditions. To functionally characterize these long-range intra-areal interactions, we presented natural movies also locally through either one or two apertures and analyzed the effects of the distant visual stimulation on the local activity levels. The distant patch had a net facilitatory effect on the local activity levels. Furthermore, the degree of the facilitation was dependent on the congruency between the two simultaneously presented movie patches. Taken together, our results indicate that the ecologically relevant stimuli are processed within a distinct operating regime characterized by moderate levels of excitation and/or high levels of inhibition, where facilitatory cooperative interactions form the basis of integrative processes. To gather better insights into the motion locking phenomenon and test the generalizability of the local cooperative processes toward larger scale interactions, we resorted to the unequalized temporal resolution of EEG and conducted a multimodal study. Inspired from the temporal properties of our natural movies, we designed a dynamic multimodal stimulus that was either congruent or incongruent across visual and auditory modalities. In the visual areas, the dynamic stimulation unfolded neuronal oscillations with frequencies well above the frequency spectrum content of the stimuli and the strength of these oscillations was coupled to the stimuli's motion profile. Furthermore, the coupling was found to be stronger in the case where the auditory and visual streams were congruent. These results show that the motion locking, which was so far observed in cats, is a phenomenon that also exists in humans. Moreover, the presence of long-range multimodal interactions indicates that, in addition to local intra-areal mechanisms ensuring the integration of local information, the central nervous system embodies an architecture that enables also the integration of information on much larger scales spread across different modalities. Any characterization of integrative phenomena at the neuronal level needs to be supplemented by its effects at the behavioral level. We therefore tested whether we could find any evidence of integration of different sources of information at the behavioral level using natural stimuli. To this end, we presented to human subjects images of natural scenes and evaluated the effect of simultaneously played localized natural sounds on their eye movements. The behavior during multimodal conditions was well approximated by a linear combination of the behavior under unimodal conditions. This is a strong indication that both streams of information are integrated in a joint multimodal saliency map before the final motor command is produced. The results presented here validate the possibility and the utility of using natural stimuli in experimental settings. It is clear that the ecological relevance of the experimental conditions are crucial in order to elucidate complex neuronal mechanisms resulting from evolutionary processes. In the future, having better insights on the nervous system can only be possible when the complexity of our experiments will match to the complexity of the mechanisms we are interested in.

Signalverarbeitung im Nervensystem hängt sowohl von der Netzwerkstruktur, als auch den zellulären Eigenschaften der Nervenzellen ab. In dieser Abhandlung werden zwei zelluläre Eigenschaften im Hinblick auf ihre funktionellen Anpassungsmöglichkeiten untersucht: Es wird gezeigt, dass neuronale Morphologie die Signalweiterleitung unter Berücksichtigung energetischer Beschränkungen verstärken kann, und dass selbst kleine Änderungen in biophysikalischen Parametern die Aktivierungsbifurkation in Nervenzellen, und damit deren Informationskodierung, wechseln können. Im ersten Teil dieser Abhandlung wird, unter Verwendung von mathematischen Modellen und Daten, die Hypothese aufgestellt, dass Energie-effiziente Signalweiterleitung als starker Evolutionsdruck für unterschiedliche Zellkörperlagen bei Nervenzellen wirkt. Um Energie zu sparen, kann die Signalweiterleitung vom Dendrit zum Axon verstärkt werden, indem relativ kleine Zellkörper zwischen Dendrit und Axon eingebaut werden, während relativ große Zellkörper besser ausgelagert werden. Im zweiten Teil wird gezeigt, dass biophysikalische Parameter, wie Temperatur, Membranwiderstand oder Kapazität, den Feuermechanismus des Neurons ändern, und damit gleichfalls Aktionspotential-basierte Informationsverarbeitung. Diese Arbeit identifiziert die sogenannte "saddle-node-loop" (Sattel-Knoten-Schlaufe) Bifurkation als den Übergang, der besonders drastische funktionale Auswirkungen hat. Neben der Änderung neuronaler Filtereigenschaften sowie der Ankopplung an Stimuli, führt die "saddle-node-loop" Bifurkation zu einer Erhöhung der Netzwerk-Synchronisation, was möglicherweise für das Auslösen von Anfällen durch Temperatur, wie bei Fieberkrämpfen, interessant sein könnte. / Signal processing in nervous systems is shaped by the connectome as well as the cellular properties of nerve cells. In this thesis, two cellular properties are investigated with respect to the functional adaptations they provide: It is shown that neuronal morphology can improve signal transmission under energetic constraints, and that even small changes in biophysical parameters can switch spike generation, and thus information encoding. In the first project of the thesis, mathematical modeling and data are deployed to suggest energy-efficient signaling as a major evolutionary pressure behind morphological adaptations of cell body location: In order to save energy, the electrical signal transmission from dendrite to axon can be enhanced if a relatively small cell body is located between dendrite and axon, while a relatively large cell body should be externalized. In the second project, it is shown that biophysical parameters, such as temperature, membrane leak or capacitance, can transform neuronal excitability (i.e., the spike onset bifurcation) and, with that, spike-based information processing. This thesis identifies the so-called saddle-node-loop bifurcation as the transition with particularly drastic functional implications. Besides altering neuronal filters and stimulus locking, the saddle-node-loop bifurcation leads to an increase in network synchronization, which may potentially be relevant for the initiation of seizures in response to increased temperature, such as during fever cramps.