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Nous avons étudié l’impact de la structure temporelle de l'activité neuronale sur la dynamique de réseaux recevant cette activité et impliqués dans la cognition. Nous avons caractérisé le code qui permet de lire l'information dans des signaux du cortex cingulaire antérieur dorsal (CCAd) simien, qui intervient dans les processus d'adaptation comportementale. Nos analyses suggèrent que la variabilité importante du nombre de potentiels d'action émis par les neurones, ainsi que la fiabilité temporelle conséquente de ces signaux, favorisent un décodage par des réseaux sensibles à la structure temporelle. De plus, quand nous avons séparé les données entre un groupe avec un grand nombre de potentiels d'action, et un groupe avec un faible nombre de potentiels d'action, nous n'avons pas trouvé pas de différence robuste du comportement du singe entre ces deux groupes. Par contre, lorsque l'activité d'un neurone devenait moins semblable à la réponse typique de ce neurone, le singe semblent répondait plus lentement pendant la tâche comportementale. L'activité d'un neurone semblait pouvoir se différencier de sa réponse typique par une augmentation ou une diminution du nombre de potentiels d'actions, ou par des imprécisions sur le temps d'émission des potentiels d'action. Nos résultats suggèrent que les réseaux neuronaux qui décodent les signaux du CCAd détectent des motifs spatiotemporels. Enfin, nous avons ensuite analysé mathématiquement des modèles de réseaux de neurones récurrents dans le but mieux comprendre l’impact des signaux du CCAd sur le décodeur. Le modèle de neurone utilisé peut reproduire la réponse dynamique de neurones biologique par l’inclusion d’une adaptation neurale. / We investigated the putative function of the fine temporal dynamics of neuronal networks for implementing cognitive processes. First, we characterized the coding properties of spike trains recorded from the dorsal Anterior Cingulate Cortex (dACC) of monkeys. dACC is thought to trigger behavioral adaptation. We found evidence for (i) high spike count variability and (ii) temporal reliability (favored by temporal correlations) which respectively hindered and favored information transmission when monkeys were cued to switch the behavioral strategy. Also, we investigated the nature of the neuronal variability that was predictive of behavioral variability. High vs. low firing rates were not robustly associated with different behavioral responses, while deviations from a neuron-specific prototypical spike train predicted slower responses of the monkeys. These deviations could be due to increased or decreased spike count, as well as to jitters in spike times. Our results support the hypothesis of a complex spatiotemporal coding of behavioral adaptation by dACC, and suggest that dACC signals are unlikely to be decoded by a neural integrator. Second, we further investigated the impact of dACC temporal signals on the downstream decoder by developing mean-field equations to analyze network dynamics. We used an adapting single neuron model that mimics the response of cortical neurons to realistic dynamic synaptic-like currents. We approximated the time-dependent population rate for recurrent networks in an asynchronous irregular state. This constitutes an important step towards a theoretical study of the effect of temporal drives on networks which could mediate cognitive functions.

[résumé trop long] / The important relationship between structure and function has always been a fundamental question in neuroscience research. In particular in the case of movement, brain controls large groups of muscles and combines it with sensory informations from the environment to execute purposeful motor behavior. Mapping dynamics encoded in a high dimensional neural space onto low-dimensional behavioral space has always been a difficult challenge as far as theory is concerned. Here, we develope a framework to study spike/burst dynamics having low dimensional phase description, which can readily be extended under certain biological constraints on the coupling to low dimensional functional descriptions. In general, phase models are amongst the simplest of neuron models reproducing spike-burst behavior, excitability and bifurcations towards periodic firing. However, the coupling among neurons has only been considered using generic arguments valid close to the bifurcation point, and the distinction between electric and synaptic coupling remains an open question. In this thesis we aim to address this question and derive a mathematical formulation for the various forms of biologically realistic coupling. We begin by constructing a mathematical model based on a planar simplification of the Morris-Lecar model. Using geometric arguments we then derive a phase description of a network of neurons with biologically realistic electric coupling and subsequently with chemical coupling under the fast synapse approximation. We then demonstrate that electric and synaptic coupling are expressed differently on the level of the network’s phase description, exhibiting qualitatively different dynamics. Our numerical investigations confirm these findings and show excellent correspondence between the dynamics of the full network and the network’s phase description. Following the success of the phase description of the spiking neural network, we extend this approach in order to propose a generating mechanism for parabolic bursting captured by only a single phase variable. This is the first model in the literature which captures bursting dynamics in one dimension. In order to study the emergent behavior we extend this to a network of bursters with global coupling and analytically reduce a high dimensional system to only two dimensions. Further, we investigate the bifurcation properties numerically as well as analytically. One of the key conclusion is that the stability states remain invariant to the increasing number of spikes per burst. Finally we investigate a spikeburst neuron network coupled via mean field type of fast synapses developed in this thesis and systematically carry out a detailed bifurcation analysis of the model, for a tractable special case. Numerical simulations investigate this mean field model beyond special case and clearly reveals qualitative correspondence with the full network model. Moreover, these network displays rich collective dynamics as a function of two parameters, mainly the synaptic coupling strength and the width of the distribution in applied stimulus. Besides incoherence, frequency locking, and oscillator death (a total cessation of firing caused by excessively strong coupling), there exist multistable solutions in the full and the phase network of neurons.

Graphs are a great tool for representing complex physical and social systems, where the interactions among many units, from tens of animal species in a food-web, to millions of users in a social network, give rise to emergent, complex system behaviours. In the field of network science this representation, which is usually called a complex network, can be complicated at will to better represent the real system under study. For instance, interactions may be directed or may differ in their strength or cost, leading to directed weighted networks, but they may also depend on time, like in temporal networks, or nodes (i.e. the units of the system) may interact in different ways, in which case edge-coloured multi-graphs and multi-layer networks represent better the system. Besides this rich repertoire of network structures, we cannot forgot that edges represent interactions and that this interactions are not static, but are, instead, purposely established to reach some function of the system, as for instance, routing people and goods through a transportation network or cognition, through the exchange of neuro-physiological signals in the brain. Building on the foundations of spectral graph theory, of non-linear dimensionality reduction and diffusion maps, and of the recently introduced diffusion distance [Phys. Rev. Lett. 118, 168301 (2017)] we use the simple yet powerful tool of continuous-time Markov chains on networks to model their process-driven geometry and characterise their functional shape. The main results are: (i) the generalisation of the diffusion geometry framework to different types of interconnected systems (from edge-coloured multigraphs to multi-layer networks) and of random walk dynamics [Phys. Rev. E 103, 042301 (2021)] and (ii) the introduction of new descriptors based on the diffusion geometry to quantify and describe the micro- (through the network depth [J. Complex Netw. 8, 4 (2020)]), meso- (functional rich-club) and macro-scale (using statistics of the pairwise distances between the network's nodes [Comm. Phys. 4, 125 (2021)]) of complex networks.

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Complexity lies halfway between stochasticity and determinism, suggesting that brain activity is neither fully random nor fully predictable but lives by the rules of nonlinear high- and low-complexity dynamics. One important aspect of brain function is noise-like activity (NLA), defined as background, electrical potential fluctuations in the nervous system distinct from spiking rhythms in the foreground. The objective of this thesis was to investigate the neurodynamical complexity of NLA recorded at the cellular and local network scales in in vitro preparations of mouse and human hippocampal tissue, under healthy and epileptiform conditions. In particular, it was found that neuronal NLA arises out of the physiological contributions of gap junctions and chemical synaptic channels and is characterized by a spectrum of complexity, ranging from high- to low-complexity, that was measured using methods from nonlinear dynamical systems theory. Importantly, the complexity of background, neuronal NLA was shown to depend on the degree of cellular interconnectivity to the surrounding local network. In addition, the complexity and multifractality of NLA was further studied at the cellular and local network scales in epileptiform transitions to seizure-like events, identifying emergent low-complexity and reduced multifractality (bordering on monofractal-type dynamics) in the pathological ictal state. Finally, dual intracellular recordings of hippocampal epileptiform activity were analyzed to measure NLA synchronicity, showing evidence for increased same- and cross-frequency correlations and increased phase synchronization in the pathological ictal state. Convergence towards increased phase synchrony manifested in lower frequency regions including theta (4-10 Hz) and beta (12-30 Hz), but also in higher frequency bands (gamma, 30-80 Hz). In summary, there is evidence to suggest that background NLA captures important neurodynamical information pertinent to the classification and identification of brain state transitions in healthy and epileptiform hippocampal dynamics, using sophisticated neuroengineering analyses of these physiological signals.

Knowledge diffusion networks consist of individuals who exchange knowledge and knowledge flows connecting the individuals. By studying knowledge diffusion in a network perspective, it helps us understand how the connections between individuals affect the knowledge diffusion processes. Existing research on knowledge diffusion networks mostly adopts a uni-dimensional perspective, where all the individuals in the networks are assumed to be of the same type. It also assumes that there is only one type of knowledge flow in the network. This dissertation proposes a multi-dimensional perspective of knowledge diffusion networks and examines the patterns of knowledge diffusion with Exponential Random Graph Model (ERGM) based approaches. The objective of this dissertation is to propose a framework that effectively addresses the multi-dimensionality of knowledge diffusion networks, to enable researchers and practitioners to conceptualize the multi-dimensional knowledge diffusion networks in various domains, and to provide implications on how to stimulate and control the knowledge diffusion process. The dissertation consists of three essays, all of which examine the multi-dimensional knowledge diffusion networks in a specific context, but each focuses on a different aspect of knowledge diffusion. Chapter 2 focuses on how structural properties of networks affect various types of knowledge diffusion processes in the domain of commercial technology. The study uses ERGM to simultaneously model multiple types of knowledge flows and examine their interactions. The objective is to understand the impacts of network structures on knowledge diffusion processes. Chapter 3 focuses on examining the impact of individual attributes and the attributes of knowledge on knowledge diffusion in the context of scientific innovation. Based on social capital theory, the study also utilizes ERGM to examine how knowledge transfer and knowledge co-creation can be affected by the attributes of individual researchers and the attributes of scientific knowledge. Chapter 4 considers the dynamic aspect of knowledge diffusion and proposes a novel network model extending ERGM to identify dynamic patterns of knowledge diffusion in social media. In the proposed model, dynamic patterns in social media networks are modeled based on the nodal attributes of individuals and the temporal information of network ties.

Complexity lies halfway between stochasticity and determinism, suggesting that brain activity is neither fully random nor fully predictable but lives by the rules of nonlinear high- and low-complexity dynamics. One important aspect of brain function is noise-like activity (NLA), defined as background, electrical potential fluctuations in the nervous system distinct from spiking rhythms in the foreground. The objective of this thesis was to investigate the neurodynamical complexity of NLA recorded at the cellular and local network scales in in vitro preparations of mouse and human hippocampal tissue, under healthy and epileptiform conditions. In particular, it was found that neuronal NLA arises out of the physiological contributions of gap junctions and chemical synaptic channels and is characterized by a spectrum of complexity, ranging from high- to low-complexity, that was measured using methods from nonlinear dynamical systems theory. Importantly, the complexity of background, neuronal NLA was shown to depend on the degree of cellular interconnectivity to the surrounding local network. In addition, the complexity and multifractality of NLA was further studied at the cellular and local network scales in epileptiform transitions to seizure-like events, identifying emergent low-complexity and reduced multifractality (bordering on monofractal-type dynamics) in the pathological ictal state. Finally, dual intracellular recordings of hippocampal epileptiform activity were analyzed to measure NLA synchronicity, showing evidence for increased same- and cross-frequency correlations and increased phase synchronization in the pathological ictal state. Convergence towards increased phase synchrony manifested in lower frequency regions including theta (4-10 Hz) and beta (12-30 Hz), but also in higher frequency bands (gamma, 30-80 Hz). In summary, there is evidence to suggest that background NLA captures important neurodynamical information pertinent to the classification and identification of brain state transitions in healthy and epileptiform hippocampal dynamics, using sophisticated neuroengineering analyses of these physiological signals.

Orientador: Marcus Aloizio Martinez de Aguiar / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Fisica Gleb Wataghin / Made available in DSpace on 2018-08-10T18:23:05Z (GMT). No. of bitstreams: 1 Chinellato_DavidDobrigkeit_M.pdf: 15300810 bytes, checksum: 36fdea424f1c7f83a5f50742e82465f8 (MD5) Previous issue date: 2007 / Resumo: Nesta tese, estudamos as propriedades estatísticas de processos dinâmicos de influência em redes complexas sujeitas a perturbações externas. Consideramos redes cujos nós admitem dois estados internos, digamos 0 e 1. Os estados internos se alteram de acordo com os estados dos nós vizinhos. Supomos que há N1 nós com estado interno fixo em 1, N0 elementos com estado interno fixo em 0 e outros N elementos com estado interno livre. Os nós com estado interno ½xo podem ser interpretados como perturbações externas à subrede de N elementos livres. Este sistema é uma generalização do modelo do eleitor [25] e pode descrever diversas situações interessantes, indo de sistemas sociais [26] para a física e a genética. Neste trabalho, calcularemos analiticamente a evolução de um sistema de rede totalmente conectada, obtendo expressões para as distribuições de equilíbrio de uma rede qualquer e também de todas as probabilidades de transição. Em seguida, generalizamos os resultados para o caso em que N0 e N1 são menores do que 1, representando um acoplamento fraco do sistema com um reservatório externo. Mostramos que os resultados exatos são excelentes aproximações para várias outras redes, incluindo redes aleatórias, reticuladas, livres de escala, estrela e mundo pequeno, e estudamos a dinâmica destas outras redes numericamente. Finalmente, demonstramos que, se os dois parâmetros da solução para redes totalmente conectadas, N0 e N1, forem alterados para valores efetivos para cada tipo de rede específico, o nosso resultado analítico explica satisfatoriamente todas as dinâmicas e estados assintóticos de outras topologias. O nosso modelo é portanto bastante geral, se aplicado cuidadosamente / Abstract: We study the statistical properties of in²uence networks subjected to external perturbations. We consider networks whose nodes have internal states that can assume the values 0 or 1. The internal states can change depending on the state of the neighboring nodes. We let N1 nodes be frozen in the state 1, N0 be frozen in the state 0 and the remaining N nodes be free to change their internal state. The frozen nodes are interpreted as external perturbations to the sub-network of N free nodes. The system is a generalization of the voter model [25] and can describe a variety of interesting situations, from social systems [26] to physics and genetics. In this thesis, we calculate analytically the equilibrium distribution and the transition probabilities between any two states for arbitrary values of N, N1 and N0 for the case of fully connected networks. Next we generalize the results for the case where N0 and N1 are smaller than 1, representing the weak coupling of the network to an external reservoir. We show that our exact results are excellent approximations for several other topologies, including random, regular lattices, scale-free, star and small world networks, and study the dynamics of these other networks numerically. We then proceed to show that, by appropriately tuning the two parameters from the solution from fully connected networks, N0and N1, to eÿective values when dealing with other, more sophisticated network types, we can easily explain their asymptotic network behaviour. Our model is therefore quite general in applicability, if used consciously / Mestrado / Física Estatistica e Termodinamica / Mestre em Física

Le concept de réseau offre un modèle de représentation pour une grande variété d'objets et de systèmes, aussi bien naturels que sociaux, dans lesquels un ensemble d'entités homogènes ou hétérogènes interagissent entre elles. Il est aujourd'hui employé couramment pour désigner divers types de structures relationnelles. Pourtant, si chacun a une idée plus ou moins précise de ce qu'est un réseau, nous ignorons encore souvent les implications qu'ont ces structures dans de nombreux phénomènes du monde qui nous entoure. C'est par exemple le cas de processus tels que la diffusion d'une rumeur, la transmission d'une maladie, ou même l'émergence de sujets d'intérêt commun à un groupe d'individus, dans lesquels les relations que maintiennent les individus entre eux et leur nature s'avèrent souvent être les principaux facteurs déterminants l'évolution du phénomène. C'est ainsi que l'étude des réseaux est devenue l'un des domaines émergents du 21e siècle appelé la "Science des réseaux". Dans ce mémoire, nous abordons trois problèmes de la science des réseaux: le problème de la diffusion dans les réseaux sociaux, où nous nous sommes intéressés plus particulièrement à l'impact de la dynamique du réseau sur le processus de diffusion, le problème de l'analyse des réseaux sociaux, dans lequel nous avons proposé une solution pour tirer parti de l'ensemble des informations disponibles en combinant les informations sur la structure du réseau et les attributs des noeuds et le problème central de la collecte de données sociales, où nous nous sommes intéressés au cas particulier de la collecte de données en milieux sauvages / The concept of network provides a model for representing a wide variety of objects and systems, both natural and social, in which a set of homogeneous or heterogeneous entities interact. It is now widely used to describe various kinds of relational structures. However, if everyone has an idea of the concept of network, we often ignore the implications that these structures have in real world phenomena. This is for example the case of processes such as the spread of a rumor, the disease transmission, or even the emergence of subjects of common interest for a group of individuals, in which the relations maintained between individuals, and their nature, often prove to be the main factors determining the evolution of the phenomenon. This is the reason why the study of networks has become one of the emerging areas in the 21st century called the "Science of networks." ln this thesis, we address three issues of the domain of the science of networks: the problem of diffusion in social networks, where we have addressed more particularly the impact of the network dynamics on the diffusion process, the problem of the analysis of social networks, in which we have proposed a solution to take full advantage of all information available on the network by combining information on both structure and node attributes and the central problem of the social data collection, for which we have focused on the particular case of the data collection in a wild environment.