Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations

We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process: in this framework we develop an extreme value theory for a few classes of observables and we show how to get the (usual) limiting distributions together with an extremal index depending on the strength of the noise.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1407.041

Environmental and genetic influences on neurocognitive development: the importance of multiple methodologies and time-dependent intervention

Genetic mutations and environmental factors dynamically influence gene expression and developmental trajectories at the neural, cognitive, and behavioral levels. The examples in this article cover different periods of neurocognitive development—early childhood, adolescence, and adulthood—and focus on studies in which researchers have used a variety of methodologies to illustrate the early effects of socioeconomic status and stress on brain function, as well as how allelic differences explain why some individuals respond to intervention and others do not. These studies highlight how similar behaviors can be driven by different underlying neural processes and show how a neurocomputational model of early development can account for neurodevelopmental syndromes, such as autism spectrum disorders, with novel implications for intervention. Finally, these studies illustrate the importance of the timing of environmental and genetic factors on development, consistent with our view that phenotypes are emergent, not predetermined

Regulatory Taking: A Contract Approach

This Article begins by defining the parameters of the fifth amendment\u27s taking clause. The Article then reviews the various tests used in determining whether governmental action constitutes a taking, and discusses the recent Supreme Court decisions within the framework of case law as it has evolved since the Court\u27s 1922 landmark decision, Pennsylvania Coal Co. v. Mahon. Finally, the Article suggests a formula based on well-established contract principles for analyzing the impact of land use regulation on private property interests

Transverse intrafascicular multichannel electrode (TIME) system for treatment of phantom limb pain in amputees

International audienceAIM: Phantom limb pain (PLP) develops in the lost limb in 50-80% of amputees. Today, it is not completely understood why the pain occurs, and no effective treatments are available. The favorable effect of electrical stimulation on PLP has been demonstrated. Our aim is to develop a novel system for manipulation of sensations by application of multi-channel microstimulation to the nerve stump of an amputee and explore this method as a treatment for clinched fist PLP (see figure). RESULTS: 1) Electrode design. Non-corrugated TIME electrodes with different dimensions and 8-12 active sites have been manufactued and tested in vivo and in vitro testing in the rat and pig. Methods for corrugated prototypes were developed and the first prototypes were realized. 2) Electrode selectivity modeling. A peripheral nerve model is under development to evaluate the electrode's selective stimulation properties and to optimize electrode design. Simulated currents and neural activity generated were qualitatively assessed using experimental data obtained from rat nerves. 3) Implant modeling. To optimize the implantation procedure, a theoretical peripheral nervous tissue model and a 3D FEM was implemented. Both models closely reproduce the experimental peripheral nervous tissue behaviour and simulate the insertion forces transmitted to the electrode during implantation. 4) Multi-channel stimulators and connectors. A 12-pole prototype, bench-top stimulator has been implemented and successfully tested in animal experiments. A high-count, implantable connector between stimulator and electrode has been designed. 5) Biocompatibility. Electrode materials were evaluated and did not induce immune rejection and significant inflammatory reaction after in vivo implantation in the rat. Electrode implantation will require an understanding of the fascicular characteristics of the target nerve. Morphological characteristics of the rat, pig and human nerves are currently evaluated and compared. 6) Animal testing. First TIME electrodes test were carried out in the acute rat and acute pig. Results indicated selective stimulation of different fascicles with graded recruitment. 7) Clinical evaluation: To quantify the location of artificially evoked sensations and evaluate the strength of artificially evoked sensations a psychophysical testing platform is under development. Main inclusion criteria for patient recruitment have been identified and protocols have been defined. CONCLUSION: The feasibility of the corrugated version of the TIME electrode has yet to be explored. Further work designing, optimizing and testing the TIME electrode and all technological developments will be carried out including theoretical stimulations and animal experimental work before the optimal electrode for human implant will be chosen

Wave-dominated siliciclastic and carbonate sedimentation in a Lower Cretaceous lake (Cameros basin, northern Spain)

De acuerdo con los datos estructurales, sedimentológicos y bioestratigráficos disponibles, la cuenca de rift del noreste de Cameros (norte de España) presenta el registro de unos 8000 metros de depósitos de sedimentos continentales de edad Jurásico Superior a Cretácico Inferior, con incursiones menores de origen marino. El propósito del presente trabajo es: (1) documentar la presencia en esta cuenca de las facies carbonatadas y silicicláslicas del Grupo Enciso: (2) proponer un modelo deposicional : y (3) realizar la reconstrucción paleoambiental de un gran sistema lacustre. Nuestro modelo deposicional está basado en la integración de datos cartográfícos con los procedentes del análisis de secciones estratigráficas. A partir del estudio de seis secciones estratigráficas, se han podido identificar tres asociaciones de facies diferentes, reconocidas a su vez en otros afloramientos del Grupo Enciso. Estas asociaciones de facies son: 1) asociación de facies de ambiente lacustre abierto 2) asociación de facies de ambiente lacustre marginal siliciclástico (canal distributario, barra de desembocadura pantanosas de shoreface Iake fringin ) y 3 ambiente 1acustre marginal de facies carbonatada (asociaciones de facies palustres dominadas por tormentas y lacustre abierta con desecación. A lo largo del tiempo se alternan dos tipos de margen 1acustre: uno silicicrástico, dominado por la acción del oleaje, y otro carbonatado según un modelo de rampa suavemente inclinada. Se sugiere que el establecimiento de estos dos tipos de depósitos lacustres estuvo controlada por factores climáticos

Integrate and Fire Neural Networks, Piecewise Contractive Maps and Limit Cycles

We study the global dynamics of integrate and fire neural networks composed of an arbitrary number of identical neurons interacting by inhibition and excitation. We prove that if the interactions are strong enough, then the support of the stable asymptotic dynamics consists of limit cycles. We also find sufficient conditions for the synchronization of networks containing excitatory neurons. The proofs are based on the analysis of the equivalent dynamics of a piecewise continuous Poincar\'e map associated to the system. We show that for strong interactions the Poincar\'e map is piecewise contractive. Using this contraction property, we prove that there exist a countable number of limit cycles attracting all the orbits dropping into the stable subset of the phase space. This result applies not only to the Poincar\'e map under study, but also to a wide class of general n-dimensional piecewise contractive maps.Comment: 46 pages. In this version we added many comments suggested by the referees all along the paper, we changed the introduction and the section containing the conclusions. The final version will appear in Journal of Mathematical Biology of SPRINGER and will be available at http://www.springerlink.com/content/0303-681

Atypical audiovisual speech integration in infants at risk for autism

The language difficulties often seen in individuals with autism might stem from an inability to integrate audiovisual information, a skill important for language development. We investigated whether 9-month-old siblings of older children with autism, who are at an increased risk of developing autism, are able to integrate audiovisual speech cues. We used an eye-tracker to record where infants looked when shown a screen displaying two faces of the same model, where one face is articulating/ba/and the other/ga/, with one face congruent with the syllable sound being presented simultaneously, the other face incongruent. This method was successful in showing that infants at low risk can integrate audiovisual speech: they looked for the same amount of time at the mouths in both the fusible visual/ga/− audio/ba/and the congruent visual/ba/− audio/ba/displays, indicating that the auditory and visual streams fuse into a McGurk-type of syllabic percept in the incongruent condition. It also showed that low-risk infants could perceive a mismatch between auditory and visual cues: they looked longer at the mouth in the mismatched, non-fusible visual/ba/− audio/ga/display compared with the congruent visual/ga/− audio/ga/display, demonstrating that they perceive an uncommon, and therefore interesting, speech-like percept when looking at the incongruent mouth (repeated ANOVA: displays x fusion/mismatch conditions interaction: F(1,16) = 17.153, p = 0.001). The looking behaviour of high-risk infants did not differ according to the type of display, suggesting difficulties in matching auditory and visual information (repeated ANOVA, displays x conditions interaction: F(1,25) = 0.09, p = 0.767), in contrast to low-risk infants (repeated ANOVA: displays x conditions x low/high-risk groups interaction: F(1,41) = 4.466, p = 0.041). In some cases this reduced ability might lead to the poor communication skills characteristic of autism

Decay and Continuity of Boltzmann Equation in Bounded Domains

Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: inflow, bounce-back reflection, specular reflection, and diffuse reflection. We establish exponential decay in $L^{\infty}$ norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set of the velocity at the boundary. Our contribution is based on a new $L^{2}$ decay theory and its interplay with delicate $$ decay analysis for the linearized Boltzmann equation, in the presence of many repeated interactions with the boundary.Comment: 89 pages

Functional near infrared spectroscopy (fNIRS) to assess cognitive function in infants in rural Africa

Cortical mapping of cognitive function during infancy is poorly understood in low-income countries due to the lack of transportable neuroimaging methods. We have successfully piloted functional near infrared spectroscopy (fNIRS) as a neuroimaging tool in rural Gambia. Four-to-eight month old infants watched videos of Gambian adults perform social movements, while haemodynamic responses were recorded using fNIRS. We found distinct regions of the posterior superior temporal and inferior frontal cortex that evidenced either visual-social activation or vocally selective activation (vocal > non-vocal). The patterns of selective cortical activation in Gambian infants replicated those observed within similar aged infants in the UK. These are the first reported data on the measurement of localized functional brain activity in young infants in Africa and demonstrate the potential that fNIRS offers for field-based neuroimaging research of cognitive function in resource-poor rural communities