En plus des photorécepteurs canoniques traditionnels (bâtonnets etcônes), des cellules ganglionnaires contenant le photopigment mélanopsineont récemment été découverts. Une étude récente de notrelaboratoire a suggéré que, dans la rétine humaine, ce nouveau photopigmentexprime des propriétés bistables similaires à celles notéeschez les invertébrés tant in vitro qu’in vivo. Dans les systèmes dephotopigments bistables, la lumière déclenche une réponse photosensoriellemais permet aussi la régénération du chromophore pourrétablir la réactivité lumineuse du photopigment. Cette dernière étudea montré qu’une exposition lumineuse antérieure peut moduler l’amplitudedes réponses lumineuses de la mélanopsine.L’objectif de ma thèse est d’étudier (1) la bistabilité présumée de lamélanopsine chez l’Homme en utilisant comme outil le réflexe photomoteurpupillaire. Ma thèse comporte aussi 2) le développementd’une technique d’évaluation quantitative des effets du brunissementdu cristallin oculaire sur la photoréception impliquant la mélanopsine;3) le développement d’un modèle mathématique portant sur lefonctionnement des photopigments bistables et du système photiquenon visuel.L’exploitation des propriétés bistables de la mélanopsine et l’utilisationappropriée des effets photorégénérateurs des longueurs d’ondeslumineuses longues pourraient servir dans l’optimisation de la compositionspectrale des applications photothérapeutiques (expérimentales,industrielles, domestiques et cliniques). / In addition to the canonical photoreceptors, rods and cones, a novelmelanopsin-expressing retinal ganglion cell (mRGC) was recently discovered.The novel photopigment melanopsin in the human retinahas been shown to express invertebrate-like bistable properties bothin vitro and in vivo. In bistable photopigment systems, light elicitsphotosensory responses and drives photoregeneration of the chromophoreto restore photic responsiveness. These studies have shownthat prior light exposure can modulate the amplitude of subsequentphotic responses of melanopsin.In this thesis, the putative bistability of melanopin in humans isexamined. The bistability was studied using 1) pupillary light reflex(PLR) as a tool, 2) developing a method for quantifying the effectsof lens density for melanopsin-mediated photoreception, and 3) providinga quantitative mathematical framework for modeling bistablepigment systems and non-image forming (NIF) visual system.Exploiting the bistable properties of melanopsin could allow foroptimization of spectral light distribution in experimental, industrial,domestic and clinical phototherapy applications by appropriate useof the photoregenerative effects of long wavelength light. / Perinteisten fotoreseptorien, sauvasolujen ja tappisolujen, lisäksi verkkokalvoltaon löydetty melanopsiinia sisältäviä gangliosoluja. Fotopigmenttimelanopsiinin on huomattu käyttäytyvän ihmisen verkkokalvollaselkärangattomien eläimien bistabiilin näköjärjestelmän tavoinsekä in vivo- ja in vitro- olosuhteissa. Bistabiileissa fotopigmenttijärjestelmissävalo aiheuttaa sensoristen vasteiden lisäksi kromoforin fogeneraationvastevalmiisen tilaan. Nämä aiemmat tutki-mukset ovatosoittaneet, että aiempi valoaltistus voi moduloida siitä seuraaviamelanopsiinivasteita.Tässä väitöskirjassa melanopsiinin oletettua bistabiiliutta tutkittiinkäyttäen 1) Pupillireaktiota työkaluna, 2) kehittämällä kvantitaviinenmenetelmä mykiöntiheyden vaikutuksiin melanopsiini-fotoreseptiossa,ja 3) kehittäen kvantitatiivisen matemaattisen kehyksen bistabiilien pigmenttijärjestelmien ja ei-visuaalisen näköjärjestelmän mallintamiseen.Melanopsiinin bistabiileita ominaisuuksia on mahdollista optimoidavalon spektrikoostumusta niin tieteellisissä, teollisissa, kotitalouksellisissaja kliinisissä valoterapia sovelluksissa hyväksikäyttämälläpunaisen aallonpituusalueen fotoregeneroivia vaikutuksia.

L’optique non linéaire traite les modifications des propriétés optiques d'un matériau induites par la propagation de la lumière. Depuis ses débuts, il y a cinquante ans, des nombreuses applications ont été démontrées dans presque tous les domaines de la science. Dans le domaine de la micro et nano-photonique, les phénomènes non linéaires sont à la fois au cœur d’une physique fondamentale fascinante et des applications intéressantes: ils permettent d'adapter et de contrôler le flux de lumière à une échelle spatiale inferieure à la longueur d'onde. En effet, les effets non linéaires peuvent être amplifiés dans des systèmes qui confinent la lumière dans des espaces restreints et avec de faibles pertes optiques. Des bons candidats pour ce confinement sont les nanocavités à cristaux photoniques (CPs), qui ont été largement étudiées ces dernières années. Parmi la grande diversité des processus non linéaires en optique, les phénomènes dynamiques tels que la bistabilité et l'excitabilité font l’objet de nombreuses études. La bistabilité est bien connue pour ces applications potentielles pour les mémoires et les commutateurs optiques et pour les portes logiques. Une réponse excitable typique est celle subjacente dans le déclanchement du potentiel d'action dans les neurones. En optique, l'excitabilité a été observée il y a une quinzaine d’années. Dans ce travail, nous avons étudié les régimes bistables, auto-oscillants et excitables dans des nanocavités semiconductrices III-V à CP. Afin de coupler efficacement la lumière dans les nanocavités, nous avons développé une technique de couplage par onde évanescente en utilisant une microfibre optique étirée. Grâce à cette technique, nous avons démontré pour la première fois l’excitabilité dans une nanocavité à CP. En parallèle, nous avons accompli la première étape vers la dynamique non linéaire dans un réseau de cavités couplées en démontrant le couplage optique linéaire entre nanocavitités adjacentes. Ceci a été réalisé en utilisant de mesures de photoluminescence en champ lointain. Un ensemble de résonateurs non linéaires couplés ouvre la voie à une famille de phénomènes dynamiques non linéaires très riches, basés sur la rupture spontanée de symétrie. Nous avons démontré théoriquement ce phénomène dans deux cavités couplées par onde évanescente. Les premières études expérimentales de ce régime ont été menées, établissant ainsi les bases pour une future démonstration de la rupture spontanée de symétrie dans un réseau de nanocavités non linéaires couplées. / Nonlinear optics concerns the modifications of the optical properties of a material induced by the propagation of light. Since its beginnings, fifty years ago, it has already found applications in almost any field of science. In micro and nano-photonics, nonlinear phenomena are at the heart of both fascinating fundamental physics and interesting potential applications: they give a handle to tailor and control the flow of light within a sub-wavelength spatial scale. Indeed, the nonlinear effects can be enhanced in systems allowing tight light confinement and low optical loses. Good candidates for this are the Photonic Crystal (PhC) nanocavities, which have been extensively studied in recent years. Among the great diversity of nonlinear processes in optics, nonlinear dynamical phenomena such as bistability and excitability have recently received considerable attention. While bistability is well known as a building block for all-optical memories, switching and logic gates, excitability has been demonstrated in optics about fifteen years ago: coming from neuroscience, it is the mechanism underlying action potential firing in neurons. In this work, we have studied bistable, self-pulsing and excitable regimes in InP-based PhC nanocavities. In order to achieve efficient light coupling into the nanocavities, we have developed an evanescent coupling technique using tapered optical microfibers. As a result, we have demonstrated for the first time excitability in a PhC nanocavity. In addition, we have accomplished the first step towards nonlinear dynamics in arrays of coupled cavities by demonstrating optical linear coupling between adjacent nanocavitites. This was achieved using far field measurements of photoluminescence. A set of coupled nonlinear resonators opens the door to a rich family of nonlinear dynamical phenomena based on spontaneous symmetry breaking. We have theoretically demonstrated this phenomenon in two evanescently coupled cavities. The first experimental studies on this regime were carried out, which establish a basis for a future demonstration of spontaneous symmetry breaking in arrays of nonlinear coupled PhC nanocavities.

Modelos matemáticos de motoneurônios têm sido desenvolvidos para auxiliar na compreensão dos fenômenos que envolvem o sistema neuromuscular. Entretanto, a maioria dos modelos já desenvolvidos baseou-se na premissa de que a árvore dendrítica tem um comportamento passivo, o que ocorre em animais anestesiados, mas pode não ocorrer durante o comportamento motor normal de um animal intacto. Experimentos com animais descerebrados, em que as vias monoaminérgicas encontravam-se ativas, mostraram que os motoneurônios podem apresentar comportamentos mais complexos decorrentes da presença de condutâncias iônicas voltagem-dependentes que se situam nos dendritos e são responsáveis pela gênese de uma corrente de entrada persistente. Nesse sentido, um primeiro objetivo deste trabalho foi o de desenvolver novos modelos matemáticos de motoneurônios de diferentes tipos (i.e. dos tipos S, FR e FF), computacionalmente eficientes e contendo em seus compartimentos dendríticos uma condutância de cálcio do tipo L, de forma que os fenômenos de biestabilidade, potencial platô e amplificação da corrente sináptica efetiva possam ser gerados. Um segundo objetivo foi o de verificar como a presença da condutância iônica ativa no dendrito influencia o comportamento motoneuronal quando o mesmo está sujeito a entradas sinápticas de diferentes tipos. Os novos modelos foram parametrizados baseando-se em dados da literatura experimental para motoneurônios de gatos descerebrados e validados segundo os protocolos experimentais básicos que permitem caracterizar cada tipo de modelo como sendo totalmente ou parcialmente biestável. As entradas sinápticas foram simuladas por processos pontuais de Poisson e os trens de potenciais de ação dos motoneurônios foram analisados. Uma modulação senoidal da intensidade do processo pontual foi usada para estimar as respostas em frequência de cada modelo. Observou-se que, funcionalmente, a presença da condutância iônica dendrítica pode favorecer a ação do motoneurônio durante tarefas posturais, pois, uma vez ativada, a corrente de entrada persistente eleva a excitabilidade motoneuronal tornando os disparos mais regulares, além de prover uma alta sensibilidade dos modelos a entradas sinápticas de baixa frequência, correspondentes às oscilações observadas durante a manutenção da postura ereta quieta. / Mathematical models of motoneurons have been developed as an aid to the understanding of phenomena involving the neuromuscular system, but most of these models have been based on the hypothesis of a passive dendritic tree. This holds for anesthetized animals but not necessarily during normal motor behavior of the intact animal. Experiments with decerebrate animals in which the monoaminergic tracts were maintained intact have shown that more complex behaviors may emerge in motoneurons due to dendritic voltage-gated ionic conductances, which are responsible for a persistent inward current. Therefore, the first aim of this work was to develop computationally-efficient new motoneuron models of different types (i.e. type S, FR and FF) that include a dendritic L-type calcium conductance so that bistability, plateau potential and enhancement of effective synaptic current may be generated. The second aim of this research was to evaluate the effects of the active dendritic ionic conductance on the input-output mapping of presynaptic to postsynaptic spike trains. The new models were parameterized based on data reported in experimental literature on the decerebrate cat preparation, and they were validated using appropriate protocols for either fully or partially bistable dynamics. The synaptic inputs were simulated by Poisson point processes and the output spike trains were analyzed. Sinusoidal modulation of the point process intensity was used for the estimation of each models frequency response. The results suggested that an active dendritic ionic conductance in motoneurons has a functional role during postural tasks, because, when activated, the persistent inward current enhances the motoneuronal excitability, reducing the variability of interspike intervals, and focusing the sensitivity of the models to low frequency inputs that correspond to the low-frequency oscillations that typically occur during quiet standing posture.

La gestion et transmission d’information au sein d’organismes vivants implique la production et le trafic de molécules via des voies de signalisation sutructurées en réseaux de réactions chimiques. Ces derniers varient selon leur forme, taille ainsi que la nature des molécules mises en jeu. Parmi eux, les réseaux de régulation génétiques nous ont servi de modèle pour le développement et la mise en place d’un système de programmation moléculaire in vitro. En effet, l’expression d’un gène est majoritairement dominé par des facteurs de transcription, autres protéines ou acides nucléiques, eux-mêmes exprimés par d’autres gènes. L’ensemble forme l’interactome de la cellule, carte globale des interactions entre gènes et sous-produits, où la fonction du réseau est relié à sa topologie. L’observation des noeuds et sous-architectures dénote trois mécanismes récurrents : premièrement, la nature des interactions est de type activation ou inhibition, ce qui implique que tout comportement non trivial est obtenu par une combinaison de noeuds plutôt que le développement de nouvelles interactions. Ensuite, la longévité du réseau est assurée par la stabilité chimique de l’ADN couplée à la chimiosélectivié des réactions enzymatiques. Enfin, l’aspect dynamique est maintenu par le constant anabolisme/catabolisme des intermédiaires et donc l’utilisation de combustible/énergie. C’est suivant ces observations que nous avons développé un ensemble de trois réactions enzymatiques élémentaires : la «PEN-DNA toolbox». L’architecture du réseau, à savoir les connections entre les noeuds est médiée par la séquence de brins d’ADN synthétiques (appelés matrice), et trois enzymes (polymérase, nickase, et exonucléase) assurent la catalyse des réactions chimiques. La production et dégradation des intermédiaires consomme des désoxyribonucléotides triphosphates et rejette des désoxyribonucléotides monophosphate, dissipant ainsi le potentiel chimique. Les réactions sont suivies grâce au greffage d’un fluorophore sur le brin matriciel et au «nucleobase quenching» qui intervient lorsqu’une base d’un intermédiaire se rapproche du fluorophore après hybdridation sur le brin matriciel. L’activation correspond alors à la synthèse d’un brin output en réponse à un brin input, alors que l’inhibition survient lorsqu’un brin output s’hybride sur un brin matriciel, empêchant ainsi à l’input correspondant de s’y fixer. Oscillations, bistabilité et mémoire sont des exemples de comportements implémentés en PEN-DNA toolbox, faisant appel à des architectures de plus en plus complexes. Pour cela, un réglage fin des concentrations en effecteurs (ADN et enzymes) est nécessaire, ce qui sous-tend l’existence de plusieurs comportements pour un même circuit, dépendant des conditions paramétriques. L’établissement d’une carte de chaque combinaison de paramètres avec le comportement global associé permettrait de comprendre le fonctionnement du réseau dans son ensemble, et donnerait accès à tous les comportements disponibles. Dans le cas d’un système dynamique non linéaire, une telle carte est un diagramme de bifurcation du système. Pour explorer de manière exhaustive les possibilités d’un réseau dans un cadre expérimental raisonable, nous avons développé une plateforme microfluidique capable de générer des goutelettes d’eau dans l’huile à partir de quatres canaux aqueux différents. Ce dispositif nous donne accès, grâce à un contrôle fin des contributions de chaque canal aqueux, à des goutelettes monodisperses (volume de l’ordre du picolitre) dont le contenu est différent pour chaque goutelette. Nous avons adapté notre dispositif aux contraintes matérielles (design microfluidique, génération de goutelettes à contenu différents et controllés, observation et stabilité à long terme) et techniques (tracabilité des goutelettes et stabilité/compatibilité chimique). (...) / Information processing within and in between living organisms involves the production and exchange of molecules through signaling pathways organized in chemical reactions networks. They are various by their shape, size, and by the nature of the molecules embroiled. Among them, gene regulatory networks were our inspiration to develop and implement a new framework for in-vitro molecular programming. Indeed, the expression of a gene is mostly controlled by transcription factors or regulatory proteins and/or nucleic acids that are themselves triggered by other genes. The whole assembly draws a web of cross-interacting genes and their subproducts, in which the well controlled topology relates to a precise function. With a closer look at the links between nodes in such architectures, we identify three key points in the inner operating system. First, the interactions either activate or inhibit the production of the later node, meaning that non trivial behaviors are obtained by a combination of nodes rather than a specific new interaction. Second, the chemical stability of DNA, together with the precise reactivity of enzymes ensures the longevity of the network. Finally, the dynamics are sustained by the constant anabolism/catabolism of the effectors, and the subsequent use of fuel/energy. All together, these observations led us to develop an original set of 3 elementary enzymatic reactions: the PEN-DNA toolbox. The architecture of the assembly, i.e. the connectivity between nodes relies on the sequence of synthetic DNA strands (called DNA templates), and 3 enzymes (a polymerase, a nickase and an exonuclease) are taking care of catalysis. The production and degradation of intermediates consume deoxyribonucleoside triphosphates (dNTP) and produce deoxynucleotide monophosphates leading to the dissipation of chemical potential. Reactions are monitored thanks to a backbone modification of a template with a fluorophore and the nucleobase quenching effect consecutive to an input strand binding the template. The activation mechanism is then the production of an output following the triggering of an input strand, and the inhibition comes from the production of an output strand that binds the activator-producing sequence. Various behaviors such as oscillation, bistability, or switchable memory have been implemented, requiring more and more complex topologies. For that, each circuit requires a fine tuning in the amount of chemical parameters, such as templates and enzymes. This underlies the fact that a given network may lead to different demeanors depending on the set of parameters. Mapping the output of each combination in the parameter space to find out the panel of behaviors leads to the bifurcation diagram of the system. In order to explore exhaustively the possibilities of one circuit with a reasonable experimental cost, we developped a microfluidic tool generating picoliter-sized water-in-oil droplets with different contents. We overcame the technical challenges in hardware (microfluidic design, droplet generation and long-term observation) and wetware (tracability of the droplet and emulsion compatibility/stability). So far, bifurcation diagrams were calculated from mathematical models based on the enzymes kinetics and the thermodynamic properties of each reaction. The model was then fitted with experimental data taken in distant points in the parameter space. Here, millions of droplets are created, and each one encloses a given amount of parameters, becoming one point in the diagram. The parameter coordinates are barcoded in the droplet, and the output fluorescence signal is recorded by time lapse microscopy. We first applied this technique to a well-known network, and obtained the first experimental two-dimensional bifurcation diagram of the bistable system. The diagram enlightens features that were not described by the previous mathematical model. (...)

Si les diagrammes de phase des alliages binaires massifs sont désormais bien connus, il en va tout autrement de ceux des nanoalliages, particules constituées de quelques centaines à quelques milliers d’atomes. Le développement des nanotechnologies est un puissant moteur pour développer la connaissance des diagrammes de phase des nanoparticules. Dans ce but, nous avons étudié le polyèdre de Wulff de 405 atomes (PW405) dans le système Cu-Ag caractérisé par une forte différence de rayons atomiques entre les constituants et une tendance à la démixtion, du moins dans sa forme massive. L’étude est réalisée par simulations Monte Carlo utilisant un potentiel interatomique à N-corps, en tirant parti de la richesse de deux ensembles thermodynamiques, à savoir les ensembles pseudo-grand canonique, i.e. à différence de potentiel chimique fixée, et canonique, i.e. à concentration nominale fixée. Nous montrons tout d’abord qu’un diagramme de phase de nanoalliage est constitué d’un ensemble de diagrammes de phase attachés à des classes de sites de surface ou des couches internes. Ainsi, pour le PW405, nous distinguons trois diagrammes de phase : ceux des facettes (100) et (111) et celui des couches de cœur. Chacun de ces trois diagrammes est attaché à des phénomènes physiques très différents. Ainsi, le diagramme de phase des facettes (100) est relatif à une transition structuro-chimique, alors que celui des facettes (111) caractérise une transition démixtion – désordre sans évolution structurale. Dans l’ensemble p-GC, cela se traduit par une bistabilité collective pour les facettes (100) et individuelle pour les facettes (111). Une conséquence de ce dernier point est la possibilité d’observer des facettes (111) pures en cuivre et d’autres pures en argent au sein d’un même agrégat !L’utilisation de la méthode de Widom pour déterminer dans l’ensemble canonique s’est révélée déterminante pour pouvoir séparer les régimes monophasés de ségrégation superficielle ou sub-superficielle des régimes biphasés. La différence de rayons atomiques joue un rôle important, tant dans la stabilisation dans l’état biphasé de la configuration Janus dissimulée par une coquille d’argent, que dans l’abaissement de la température critique par un facteur d’environ 2 par rapport au diagramme de phase massif.Une analyse des simulations Monte Carlo par une approche en champ moyen sur réseau effectif s’est révélée d’une richesse insoupçonnée pour déterminer les fores motrices de chaque type de transition, tant à la surface que dans les couches de cœur. Cela nous a permis de plus de montrer que les arêtes jouent le rôle d’une véritable nano-armature pour l’agrégat. Ce travail s’achève par ce qui constitue, à notre connaissance, la proposition du premier diagramme de phase de nanoalliage. / If bulk phase diagrams of binary alloys are now well known, it is not the case for nanoalloys, which are particles consisting in a few hundred to a few thousand of atoms. The development of nanotechnologies is a powerful driving force to develop the interest in the phase diagrams of nanoparticles. For this purpose, we have studied the Wulff polyhedron of 405 atoms (PW405) in the Cu-Ag system characterized by a large difference in atomic radii between the components and a tendency to phase separation, at least in the bulk. The study is carried out by Monte Carlo simulations using N-body interatomic potentials, taking advantage of the complementarity of two thermodynamic ensembles, namely the semigrand canonical ensemble (sGC), i.e. at fixed difference in chemical potentials and the canonical ensemble, i.e. at fixed nominal concentration.We first show that a phase diagram of nanoalloy consists in a set of phase diagrams related to the various classes of surface sites or to the internal layers. Thus, for the PW405, we distinguish three phase diagrams: the (100) facets diagram, the (111) facets diagram and the phase diagram for the layers of the core. Each of these diagrams is linked to very different physical phenomena. Thus, the phase diagram of the (100) facets is related to a structural and chemical transition, while the one of the (111) facets characterizes a transition between phase separation and disorder, without structural evolution. In the sGC ensemble, this results in a collective bistability for the (100) facets and an individual bistability for the (111) facets. A consequence of this last point is the possibility to observe some (111) facets pure in copper and other (111) facets pure in silver within the same nanoparticle !The use of the Widom method to determine in the canonical ensemble is decisive in order to discriminate between a single-phase regime (with surface or subsurface segregation) and a two-phase regime. Furthermore, the difference of atomic radii between Cu and Ag plays an important role, both for stabilizing the Janus configuration (with an Ag shell) in the two-phase state, and for lowering the critical temperature of the core layers by a factor of about 2 with respect to the bulk phase diagram.An analysis of the Monte Carlo simulations within an effective lattice formalism and a mean-field approximation is very powerful to determine the driving forces at the origin of each type of transition, both for the different facets of the surface layers and for the core. Moreover, this allowed us to show that the edges act as a nano-armature for the nanoparticles. This work ends with the establishment of what should be considered as the first phase diagram of nanoalloys, to the best of our knowledge.

Snap-through is a striking instability in which an elastic object rapidly jumps from one state to another. It is seen in the leaves of the Venus flytrap plant and umbrellas flipping on a windy day among many other examples. Similar structures that snap-through are used to generate fast motions in soft robotics, switches in micro-scale electronics and artificial heart valves. Despite the ubiquity of snap-through in nature and engineering, its dynamics is usually only understood qualitatively. In this thesis we develop analytical understanding of this dynamics, focussing on how the mathematical structure underlying the snap-through transition controls the timescale of instability. We begin by considering the dynamics of 'pull-in' instabilities in microelectromechanical systems (MEMS) - a type of snap-through caused by electrostatic forces in which the motions are dominated by fluid damping. Using a lumped-parameter model, we show that the observed time delay near the pull-in transition is a type of critical slowing down - a so-called 'bottleneck' due to the 'ghost' of a saddle-node bifurcation. We obtain a scaling law describing this slowing down, and, in the process, unify a large range of experiments and simulations that exhibit delay phenomena during pull-in. We also investigate the pull-in dynamics of MEMS microbeams, extending the lumped-parameter approach to incorporate the details of the beam geometry. This provides a model system in which to understand snap-through of a continuous elastic structure due to external loading. We develop a perturbation method that systematically exploits the proximity to pull-in to reduce the governing equations to a simpler evolution equation, with a structure that highlights the saddle-node bifurcation. This allows us to analyse the bottleneck dynamics in detail, which we compare with previous experimental and numerical data. The remainder of the thesis is concerned with the dynamics of snap-through in macroscopic systems. In particular, we explore the extent to which dissipation is required to explain anomalously slow snap-through. Considering an elastic arch as an archetype of a snapping system, we use the perturbation method developed earlier to show that two bottleneck regimes are possible, depending delicately on the relative importance of external damping. In particular, we show that critical slowing down occurs even in the absence of damping, leading to a new scaling law for the snap-through time that is confirmed by elastica simulations and experiments. In many real systems material viscoelasticity is present to some degree. Finally, we examine how this influences the snap-through dynamics of a simple truss-like structure. We present a regime diagram that characterises when the timescale of snap-through is controlled by viscous, elastic or viscoelastic effects.

coordenadoria de aperfeiÃoamento de pessoal de ensino superior / Estudamos por meio de simulaÃÃes de Monte Carlo e anÃlises de escala de tamanho finito as transiÃÃes de fase que os modelos do votante majoritÃrio e do processo de contato descrevem em redes de Kleinberg. Tais estruturas sÃo construÃdas a partir de uma rede regular onde conexÃes de longo alcance sÃo adicionadas aleatoriamente seguindo a probabilidade Pij ~ r&#945;, sendo rij a distÃncia Manhattan entre dois nÃs i e j e o expoente &#945; um parÃmetro de controle [J. M. Kleinberg, Nature 406, 845 (2000)]. Nossos resultados mostram que o comportamento coletivo desses sistemas exibe uma transiÃÃo de fase contÃnua, do tipo ordem-desordem para o votante majoritÃrio e ativo absorvente para o processo de contato, no parÃmetro crÃtico correspondente. Tal parÃmetro à monotÃnico com o expoente &#945;, sendo crescente para o votante majoritÃrio e decrescente para o processo de contato. O comportamento crÃtico dos modelos apresenta uma dependÃncia nÃo trivial com o expoente &#945;. Precisamente, considerando as funÃÃes de escala e os expoentes crÃticos, concluÃmos que os sistemas passam pelo fenÃmeno de crossover entre duas classes de universalidade. Para &#945; &#8804; 3, o comportamento crÃtico à descrito pelos expoentes de campo mÃdio enquanto que para &#945; &#8805; 4 os expoentes pertencem à classe de universalidade de Ising 2D, para o modelo do votante majoritÃrio, e à classe da percolaÃÃo direcionada no caso do processode contato. Finalmente, na regiÃo 3< &#945; <4 os expoentes crÃticos variam continuamente com o parÃmetro &#945;. Revisamos o processo de contato simbiÃtico aplicando um mÃtodo alternativo para gerarmos estados quase estacionÃrios. Desta forma, realizamos simulaÃÃes de Monte Carlo em grafos completos, aleatÃrios, redes espacialmente incorporadas e em redes regulares. Observamos que os resultados para o grafo completo e redes aleatÃrias concordam com as soluÃÃes das equaÃÃes de campo mÃdio, com a presenÃa de ciclos de histerese e biestabilidade entre as fases ativa e absorvente. Para redes regulares, comprovamos a ausÃncia de biestabilidade e comportamento histerÃtico, implicando em uma transiÃÃo de fase contÃnua para qualquer valor do parÃmetro que controla a interaÃÃo simbiÃtica. E por fim, conjecturamos que a transiÃÃo de fase descrita pelo processo de contato simbiÃtico serà contÃnua ou descontÃnua se a topologia de interesse estiver abaixo ou acima da dimensÃo crÃtica superior, respectivamente. / We study through Monte Carlo simulations and finite-size scaling analysis the nonequilibrium phase transitions of the majority-vote model and the contact process taking place on spatially embedded networks. These structures are built from an underlying regular lattice over which long-range connections are randomly added according to the probability, Pij ~ r&#945; , where rij is the Manhattan distance between nodes i and j, and the exponent &#945; is a controlling parameter [J. M. Kleinberg, Nature 406, 845 (2000)]. Our results show that the collective behavior of those systems exhibits a continuous phase transition, order-disorder for the majority-vote model and active-absorbing for the contact process, at a critical parameter, which is a monotonous function of the exponent &#945;. The critical behavior of the models has a non-trivial dependence on the exponent &#945;. Precisely, considering the scaling functions and the critical exponents calculated, we conclude that the systems undergoes a crossover between distinct universality classes. For &#945; &#8804; 3 the critical behavior in both systems is described by mean-field exponents, while for &#945; &#8805; 4 it belongs to the 2D Ising universality class for majority-vote model and to Directed Percolation universality class for contact process. Finally, in the region where the crossover occurs, 3< &#945; <4, the critical exponents vary continuously with the exponent &#945;. We revisit the symbiotic contact process considering a proper method to generate the quasistatiorary state. We perform Monte Carlo simulations on complete and random graphs that are in accordance with the mean-field solutions. Moreover, it is observed hysteresis cycles between the absorbing and active phases with the presence of bistable regions. For regular square lattice, we show that bistability and hysteretic behavior are absence, implying that model undergone a continuous phase transition for any value of the parameter that controlled the symbiotic interaction. Finally, we conjecture that the phase transition undergone by the symbiotic contact process will be continuous or discontinuous if the topology considered is below or above of the upper critical dimension, respectively.

Modelos matemáticos de motoneurônios têm sido desenvolvidos para auxiliar na compreensão dos fenômenos que envolvem o sistema neuromuscular. Entretanto, a maioria dos modelos já desenvolvidos baseou-se na premissa de que a árvore dendrítica tem um comportamento passivo, o que ocorre em animais anestesiados, mas pode não ocorrer durante o comportamento motor normal de um animal intacto. Experimentos com animais descerebrados, em que as vias monoaminérgicas encontravam-se ativas, mostraram que os motoneurônios podem apresentar comportamentos mais complexos decorrentes da presença de condutâncias iônicas voltagem-dependentes que se situam nos dendritos e são responsáveis pela gênese de uma corrente de entrada persistente. Nesse sentido, um primeiro objetivo deste trabalho foi o de desenvolver novos modelos matemáticos de motoneurônios de diferentes tipos (i.e. dos tipos S, FR e FF), computacionalmente eficientes e contendo em seus compartimentos dendríticos uma condutância de cálcio do tipo L, de forma que os fenômenos de biestabilidade, potencial platô e amplificação da corrente sináptica efetiva possam ser gerados. Um segundo objetivo foi o de verificar como a presença da condutância iônica ativa no dendrito influencia o comportamento motoneuronal quando o mesmo está sujeito a entradas sinápticas de diferentes tipos. Os novos modelos foram parametrizados baseando-se em dados da literatura experimental para motoneurônios de gatos descerebrados e validados segundo os protocolos experimentais básicos que permitem caracterizar cada tipo de modelo como sendo totalmente ou parcialmente biestável. As entradas sinápticas foram simuladas por processos pontuais de Poisson e os trens de potenciais de ação dos motoneurônios foram analisados. Uma modulação senoidal da intensidade do processo pontual foi usada para estimar as respostas em frequência de cada modelo. Observou-se que, funcionalmente, a presença da condutância iônica dendrítica pode favorecer a ação do motoneurônio durante tarefas posturais, pois, uma vez ativada, a corrente de entrada persistente eleva a excitabilidade motoneuronal tornando os disparos mais regulares, além de prover uma alta sensibilidade dos modelos a entradas sinápticas de baixa frequência, correspondentes às oscilações observadas durante a manutenção da postura ereta quieta. / Mathematical models of motoneurons have been developed as an aid to the understanding of phenomena involving the neuromuscular system, but most of these models have been based on the hypothesis of a passive dendritic tree. This holds for anesthetized animals but not necessarily during normal motor behavior of the intact animal. Experiments with decerebrate animals in which the monoaminergic tracts were maintained intact have shown that more complex behaviors may emerge in motoneurons due to dendritic voltage-gated ionic conductances, which are responsible for a persistent inward current. Therefore, the first aim of this work was to develop computationally-efficient new motoneuron models of different types (i.e. type S, FR and FF) that include a dendritic L-type calcium conductance so that bistability, plateau potential and enhancement of effective synaptic current may be generated. The second aim of this research was to evaluate the effects of the active dendritic ionic conductance on the input-output mapping of presynaptic to postsynaptic spike trains. The new models were parameterized based on data reported in experimental literature on the decerebrate cat preparation, and they were validated using appropriate protocols for either fully or partially bistable dynamics. The synaptic inputs were simulated by Poisson point processes and the output spike trains were analyzed. Sinusoidal modulation of the point process intensity was used for the estimation of each models frequency response. The results suggested that an active dendritic ionic conductance in motoneurons has a functional role during postural tasks, because, when activated, the persistent inward current enhances the motoneuronal excitability, reducing the variability of interspike intervals, and focusing the sensitivity of the models to low frequency inputs that correspond to the low-frequency oscillations that typically occur during quiet standing posture.

Notre stratégie de stockage d’électrons repose sur la formation et la rupture de liaisons chimiques fonctionnant comme des réservoirs d’électrons. Le processus de formation réversible de liaisons est rendu possible grâce à la pré-organisation de groupements électroactifs – des pyridiniums – autour de plateformes aromatiques rigides et semi-rigides. Le relargage des électrons stockés au sein des réservoirs d’électrons par rupture de liaison suggère de manipuler des liaisons de nature affaiblie, c’est-à-dire allongées et contraintes stériquement, comme celles résultantes d’interactions hors-du-plan des groupements électrophoriques. Les contraintes stériques permettent ainsi la formation et la rupture de ces liaisons dans une gamme d’énergie raisonnable. Les pyridiniums sont des unités électrophoriques de choix dû à la versatilité de leurs propriétés de réduction. Les assemblages obtenus sont des systèmes bistables qui montrent des propriétés électrochimiques hystérétiques remarquables. En général, ce comportement repose sur la proche proximité des groupements électrophoriques qui permettent la formation d’une (ou plusieurs) orbitale(s) supramoléculaire(s) vacante(s) et liante(s) (SupLUMOs). Lors de la réduction, cette orbitale accueille deux électrons créant ainsi la liaison d’intérêt. Une famille de composés modèles a ainsi été conçue et synthétisée impliquant la formation réversible de liaisons homonucléaires (Csp3‒Csp3). Ces liaisons sont de nature localisée dans des systèmes à deux pyridiniums (bi-électroniques) et délocalisée dans des systèmes de plus de deux pyridiniums. / Our strategy to store electrons is based on chemical bond formation/cleavage being used as electron reservoirs. Reversible bond formation results from the preorganization of electrophoric moieties – pyridiniums – around aromatic rigid and semi-rigid scaffold. Using lower energy bonds is required to release stored electrons from the reservoirs. Such bonds can be obtained from sterically hindered out-of-plan bond formation between two electrophorical subunits. The resulting elongated bond can be cleaved in an available level of energy. Pyridiniums are prime candidates to achieve such properties based on their noteworthy redox behavior. The resulting molecular devices are bistable systems that display remarkable hysteretic electrochemical properties, based on close proximity of electrophoric subunits allowing one (or more) unoccupied supramolecular bonding orbital(s) (SupLUMOs). Upon reduction, two electrons are injected in this orbital resulting in the bond of interest. An entire family of compounds has been designed and synthesized to highlight reversible homonuclear bond formation (Csp3‒Csp3). Those bonds are localized in the case of a two-pyridiniums system, and delocalized when more pyridiniums are involved.

Die Tiefenkonvektion ist ein wesentlicher Bestandteil der Zirkulation im Nordatlantik. Sie beeinflusst den nordwärtigen Wärmetransport der thermohalinen Zirkulation. Ein Verständnis ihrer Stabilität und Variabilität ist daher nötig, um Klimaveränderungen im Bereich des Nordatlantiks einschätzen zu können. <br /> <br /> Diese Arbeit hat zum Ziel, das konzeptionelle Verständnis der Stabilität und der Variabilität der Tiefenkonvektion zu verbessern. Beobachtungsdaten aus der Labradorsee zeigen Phasen mit und ohne Tiefenkonvektion. Ein einfaches Modell mit zwei Boxen wird an diese Daten angepasst. Das Ergebnis legt nahe, dass die Labradorsee zwei koexistierende stabile Zustände hat, einen mit regelmäßiger Tiefenkonvektion und einen ohne Tiefenkonvektion. Diese Bistabilität ergibt sich aus einer positiven Salzgehalts-Rückkopplung, deren Ursache ein Netto-Süßwassereintrag in die Deckschicht ist. Der konvektive Zustand kann schnell instabil werden, wenn der mittlere Antrieb sich hin zu wärmeren oder weniger salzhaltigen Bedingungen ändert. <br /> <br /> Die wetterbedingte Variabilität des externen Antriebs wird durch die Addition eines stochastischen Antriebsterms in das Modell eingebaut. Es zeigt sich, dass dann die Tiefenkonvektion häufig an- und wieder ausgeschaltet wird. Die mittlere Aufenthaltszeit in beiden Zuständen ist ein Maß ihrer stochastischen Stabilität. Die stochastische Stabilität hängt in glatter Weise von den Parametern des Antriebs ab, im Gegensatz zu der deterministischen (nichtstochastischen) Stabilität, die sich abrupt ändern kann. Sowohl das Mittel als auch die Varianz des stochastischen Antriebs beeinflussen die Häufigkeit von Tiefenkonvektion. Eine Abnahme der Konvektionshäufigkeit, als Reaktion auf eine Abnahme des Salzgehalts an der Oberfläche, kann zum Beispiel durch eine Zunahme der Variabilität in den Wärmeflüssen kompensiert werden. <br /> <br /> Mit einem weiter vereinfachten Box-Modell werden einige Eigenschaften der stochastischen Stabilität analytisch untersucht. Es wird ein neuer Effekt beschrieben, die wandernde Monostabilität: Auch wenn die Tiefenkonvektion aufgrund geänderter Parameter des Antriebs kein stabiler Zustand mehr ist, kann der stochastische Antrieb immer noch häufig Konvektionsereignisse auslösen. Die analytischen Gleichungen zeigen explizit, wie die wandernde Monostabilität sowie andere Effekte von den Modellparametern abhängen. Diese Abhängigkeit ist für die mittleren Aufenthaltszeiten immer exponentiell, für die Wahrscheinlichkeit langer nichtkonvektiver Phasen dagegen nur dann, wenn diese Wahrscheinlichkeit gering ist. Es ist zu erwarten, dass wandernde Monostabilität auch in anderen Teilen des Klimasystems eine Rolle spielt. <br /> <br /> Insgesamt zeigen die Ergebnisse, dass die Stabilität der Tiefenkonvektion in der Labradorsee sehr empfindlich auf den Antrieb reagiert. Die Rolle der Variabilität ist entscheidend für ein Verständnis dieser Empfindlichkeit. Kleine Änderungen im Antrieb können bereits die Häufigkeit von Tiefenkonvektionsereignissen deutlich mindern, was sich vermutlich stark auf das regionale Klima auswirkt. / Deep convection is an essential part of the circulation in the North Atlantic Ocean. It influences the northward heat transport achieved by the thermohaline circulation. Understanding its stability and variability is therefore necessary for assessing climatic changes in the area of the North Atlantic. <br /> <br /> This thesis aims at improving the conceptual understanding of the stability and variability of deep convection. Observational data from the Labrador Sea show phases with and without deep convection. A simple two-box model is fitted to these data. The results suggest that the Labrador Sea has two coexisting stable states, one with regular deep convection and one without deep convection. This bistability arises from a positive salinity feedback that is due to the net freshwater input into the surface layer. The convecting state can easily become unstable if the mean forcing shifts to warmer or less saline conditions. <br /> <br /> The weather-induced variability of the external forcing is included into the box model by adding a stochastic forcing term. It turns out that deep convection is then switched &quot;on&quot; and &quot;off&quot; frequently. The mean residence time in either state is a measure of its stochastic stability. The stochastic stability depends smoothly on the forcing parameters, in contrast to the deterministic (non-stochastic) stability which may change abruptly. The mean and the variance of the stochastic forcing both have an impact on the frequency of deep convection. For instance, a decline in convection frequency due to a surface freshening may be compensated for by an increased heat flux variability. <br /> <br /> With a further simplified box model some stochastic stability features are studied analytically. A new effect is described, called wandering monostability: even if deep convection is not a stable state due to changed forcing parameters, the stochastic forcing can still trigger convection events frequently. The analytical expressions explicitly show how wandering monostability and other effects depend on the model parameters. This dependence is always exponential for the mean residence times, but for the probability of long nonconvecting phases it is exponential only if this probability is small. It is to be expected that wandering monostability is relevant in other parts of the climate system as well. <br /> <br /> All in all, the results demonstrate that the stability of deep convection in the Labrador Sea reacts very sensitively to the forcing. The presence of variability is crucial for understanding this sensitivity. Small changes in the forcing can already significantly lower the frequency of deep convection events, which presumably strongly affects the regional climate. <br><br>----<br>Anmerkung:<br> Der Autor ist Träger des durch die Physikalische Gesellschaft zu Berlin vergebenen Carl-Ramsauer-Preises 2003 für die jeweils beste Dissertation der vier Universitäten Freie Universität Berlin, Humboldt-Universität zu Berlin, Technische Universität Berlin und Universität Potsdam.