Ion kinetic transport in TJ-II

The ion Drift Kinetic Equation (DKE) which describes the ion coUisional transport is solved for the TJ-II device plasmas. This non-linear equation is computed by peribrming a mean field iterative calculation. In each step of the calculation, a Fokker-Planck equation is solved by means of the Langevin approach: one million particles are followed in a realistic TJ-II magnetic configuration, taking into account collisions and electric field. This allows to avoid the assumptions made in the usual neoclassical approach, namely considering radially narrow particle trajectories, diffusive transport, energy conservation and infinite parallel transport. As a consequence, global features of transport, not present in the customary neoclassical models, appear: non-diffusive transport and asymmetries on the magnetic surfaces.

A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as 6 and a increase, and reaches 7% of the linear solution. (C) 2003 Elsevier Ltd. All rights reserved.

Recursive self-organizing map as a contractive iterative function system

Recently, there has been a considerable research activity in extending topographic maps of vectorial data to more general data structures, such as sequences or trees. However, the representational capabilities and internal representations of the models are not well understood. We rigorously analyze a generalization of the Self-Organizing Map (SOM) for processing sequential data, Recursive SOM (RecSOM [1]), as a non-autonomous dynamical system consisting off a set of fixed input maps. We show that contractive fixed input maps are likely to produce Markovian organizations of receptive fields o the RecSOM map. We derive bounds on parameter $\beta$ (weighting the importance of importing past information when processing sequences) under which contractiveness of the fixed input maps is guaranteed.

A pragmatic Bayesian approach to wind field retrieval

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

Transgenic Expression of Endothelin Receptor-B Rescues the Aganglionosis Phenotype of Piebald Lethal Mice

Neural crest cells (NCC) are a unique population of cells in vertebrates that arise between the presumptive epidermis and the dorsal most region of the neural tube. During neurulation, NCC migrate to many regions of the body to give rise to a wide variety of cell types. NCC that originate from the neural tube at the levels of somite 1-7 colonize the gut and give rise to the enteric ganglia. The endothelin signaling pathway has been shown to be crucial for proper development of some neural crest derivatives. Mice and humans with mutations in the Endothelin receptor b (Ednrb) gene exhibit similar phenotypes characterized by hypopigmentation, hearing loss, and megacolon. Thesephenotypes are due to lack of melanocytes in the skin, inner ear and enteric ganglia in the distal portion of the colon, respectively. It is well established that Ednrb is required early during the embryonic development for normal innervation of the gut. However, it is not clear if Ednrb acts on enteric neuron precursor cells or in pre-committed NC precursors. Additionally, it is controversial whether the action of Ednrb is cell autonomous or non- autonomous. We generated transgenic mice that express Ednrb under the control of the Nestin second intron enhancer (Nes) which drives expression to pre-migrating NCC. These mice were crosses to the spontaneous mouse mutant piebald lethal, which carriers a null mutation in Ednrb and exhibits enteric aganglionosis. The Nes-Ednrb was capable of rescuing the aganglianosis phenotype of piebald lethal mutants demonstrating that expression of Ednrb in pre-committed precursors is sufficient for normal enteric ganglia development. This study provides insight in early embryonic development of NCC and could eventually have potential use in cellular therapies for Hirschsprung's disease.

Ordering induced by chemical, thermal and mechanical constraints at solid interfaces

We know that classical thermodynamics even out of equilibrium always leads to stable situation which means degradation and consequently d sorder. Many experimental evidences in different fields show that gradation and order (symmetry breaking) during time and space evolution may appear when maintaining the system far from equilibrium. Order through fluctuations, stochastic processes which occur around critical points and dissipative structures are the fundamental background of the Prigogine-Glansdorff and Nicolis theory. The thermodynamics of macroscopic fluctuations to stochastic approach as well as the kinetic deterministic laws allow a better understanding of the peculiar fascinating behavior of organized matter. The reason for the occurence of this situation is directly related to intrinsic non linearities of the different mechanisms responsible for the evolution of the system. Moreover, when dealing with interfaces separating two immiscible phases (liquid - gas, liquid -liquid, liquid - solid, solid - solid), the situation is rather more complicated. Indeed coupling terms playing the major role in the conditions of instability arise from the peculiar singular static and dynamic properties of the surface and of its vicinity. In other words, the non linearities are not only intrinsic to classical steps involving feedbacks, but they may be imbedded with the non-autonomous character of the surface properties. In order to illustrate our goal we discuss three examples of ordering in far from equilibrium conditions: i) formation of chemical structures during the oxidation of metals and alloys; ii) formation of mechanical structures during the oxidation of metals iii) formation of patterns at a solid-liquid moving interface due to supercooling condition in a melt of alloy. © 1984, Walter de Gruyter. All rights reserved.

Dissecting signaling pathways that control glia migration in the developing Drosophila retina

The function of a complex nervous system relies on an intricate interaction between neurons and glial cells. However, as glial cells are generally born distant from the place where they settle, molecular cues are important to direct their migration. Glial cell migration is important in both normal development and disease, thus current research in the laboratory has been focused on dissecting regulatory events underlying that crucial process. With this purpose, the Drosophila eye imaginal disc has been used as a model. In response to neuronal photoreceptor differentiation, glial cells migrate from the CNS into the eye disc where they act to correctly wrap axons. To ensure proper development, attractive and repulsive signals must coordinate glial cell migration. Importantly, one of these signals is Bnl, a Fibroblast Growth Factor (FGF) ligand expressed by retinal progenitor cells that was suggested to act as a non-autonomous negative regulator of excessive glial cell migration (overmigration) by binding and activating the Btl receptor expressed by glial cells. Through the experimental results described in chapter 3 we gained a detailed insight into the function of bnl in eye disc growth, photoreceptor development, and glia migration. Interestingly, we did not find a direct correlation between the defects on the ongoing photoreceptors and the glia overmigration phenotype; however, bnl knockdown caused apoptosis of eye progenitor cells what was strongly correlated with glia migration defects. Glia overmigration due to Bnl down-regulation in eye progenitor cells was rescued by inhibiting the pro-apoptotic genes or caspases activity, as well as, by depleting JNK or Dp53 function in retinal progenitor cells. Thus, we suggest a cross-talk between those developmental signals in the control of glia migration at a distance. Importantly, these results suggest that Bnl does not control glial migration in the eye disc exclusively through its ability to bind and activate its receptor Btl in glial cells. We also discuss possible biological roles for the glia overmigration in the bnl knockdown background. Previous results in the lab showed an interaction between dMyc, a master regulator of tissue growth, and Dpp, a Transforming Growth Factor-β important for retinal patterning and for accurate glia migration into the eye disc. Thus, we became interested in understanding putative relationships between Bnl and dMyc. In chapter 4, we show that they positively cooperate in order to ensure proper development of the eye disc. This work highlights the importance of the FGF signaling in eye disc development and reveals a signaling network where a range of extra- and intra-cellular signals cooperate to non-autonomously control glial cell migration. Therefore, such inter-relations could be important in other Drosophila cellular contexts, as well as in vertebrate tissue development.

Non-diagonal solutions of the reflection equation for the trigonometric A((1)) (n-1) vertex model

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric A(n-1)((1)) vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a discrete (positive integer) parameter l, 1 less than or equal to l less than or equal to n, the solution contains n + 2 continuous boundary parameters.

Non-cell autonomous neuroprotective effect of carbon monoxide : microglia-to-neuron communication

RESUMO: A isquémia cerebral é uma das doenças mais predominantes a nivel mundial, sendo uma das principais causas de mortalidade e invalidez. Parte da propagação de dano no cérebro é causado por inflamação descontrolada, causada principalmente por disfunção da microglia. Desta forma, existe a necessidade de tentar desenvolver estratégias para melhor compreender e modular as acções destas células. O monóxido de carbono (CO), é uma molécula endógena com provas dadas como anti-neuroinflamatório em vários modelos. Assim, o principal objectivo do trabalho foi o estudo do CO como um modulador da acção da microglia, com principal foco dado à comunicação entre estas células e neurónios, tentando entender se existe um efeito neuroprotector por inibição da inflamação. Um protocolo de meio condicionado foi estabelecido usando as linhas celulares BV2 e SH-SY5Y, de microglia e neurónio. A molécula CORM-A1, que liberta expontaniamente CO, foi usada como método de entrega da molécula às celulas. Demonstrámos que o pre-tratamento de células BV2 com CORM-A1 gera neuroprotecção já que reduz a morte celular de neurónios SH-SY5Y quando são incubados com meio condicionado de microglia activada em conjunto com o pró-oxidante t-BHP (tert-butil hidroperóxido). Assim, considerámos que o CO promove neuroprotecção ao inibir as acções inflamatórias da microglia. O papel anti-inflamatório da molécula CORM-A1 foi confirmado quando se verificou que pré-tratamento desta molécula em microglia BV2 limita a secreção de TNF-α mas estimula a secreção de IL-10. Por último, a CORM-A1 induziu a expressão do receptor da microglia CD200R1, molécula que participa na comunicação neurónio-microglia e fundamental para a modulação das acções inflamatórias destas últimas. Em suma, o nosso trabalho reforçou as propriedades anti-neuroinflamatórias do CO e uma capacidade de modular viabilidade neuronal através do seu efeito a nível de comunicação célula-célula. ---------------------------- ABSTRACT: Brain ischemia is a widespread disease worldwide, being one of the main causes of mortality and permanent disability. A portion of the damage that ensues following the ischemic event is caused by unrestrained inflammation, which is mainly orchestrated by exacerbated microglial activity. Hence, developing strategies for modulating microglial inflammation is a major concern nowadays. The endogenous molecule carbon monoxide (CO) has been shown to possess anti-neuroinflammatory properties using in vitro and in vivo approaches. Thus, our objective was to study CO as modulator of microglial activity, in particular in what concerns their communication with neurons, by promoting neuronal viability and limiting inflammatory output of activated microglia. A conditioned media strategy was established with BV2 microglia and SH-SY5Y neurons as cell models. CO-releasing molecule A1 (CORM-A1), a compound that releases CO spontaneously, was used as method of CO delivery to cells. We found that CORM-A1 pre-treatment in BV2 cells yields neuroprotective results, as it limits cell death when SH-SY5Y neurons are challenged with conditioned media from LPS-activated microglia and the pro-oxidant t-BHP (tert-butyl-hydroperoxide). Thus, we assumed carbon monoxide promotes neuroprotection via inhibition of microglial inflammation, displaying a non-cell autonomous role. CORM-A1 pre-treatment limited inflammation by inhibiting BV2 secretion of TNF-α and stimulating IL-10 production. These results reinforce that CO’s anti-inflammatory role confers neuroprotection, as the alterations in these cytokines occur concurrently with the increase in SH-SY5Y viability. Finally, we showed for the first time that carbon monoxide promotes the expression of CD200R1, a microglial receptor involved in neuron-glia communication and modulation of microglia inflammation. Further studies are necessary to clarify this role. Altogether, other than just highlighting CO as an anti-inflammatory and neuroprotective molecule, this work set the foundation for disclosing its involvement in cell-to-cell communication.

Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Effective Electrodiffusion equation for non uniform nanochannels

We derive a one dimensional formulation of the Planck-Nernst-Poisson equation to describe the dynamics of of a symmetric binary electrolyte in channels whose section is of nanometric section and varies along the axial direction. The approach is in the spirit of the Fick-Jacobs di fusion equation and leads to a system of coupled equations for the partial densities which depends on the charge sitting at the walls in a non trivial fashion. We consider two kinds of non uniformities, those due to the spatial variation of charge distribution and those due to the shape variation of the pore and report one and three-dimensional solutions of the electrokinetic equations.