Patterns in random walks and Brownian motion

We ask if it is possible to find some particular continuous paths of unit length in linear Brownian motion. Beginning with a discrete version of the problem, we derive the asymptotics of the expected waiting time for several interesting patterns. These suggest corresponding results on the existence/non-existence of continuous paths embedded in Brownian motion. With further effort we are able to prove some of these existence and non-existence results by various stochastic analysis arguments. A list of open problems is presented.Comment: 31 pages, 4 figures. This paper is published at http://link.springer.com/chapter/10.1007/978-3-319-18585-9_

Brain Cortical Mapping by Simultaneous Recording of Functional Near Infrared Spectroscopy and Electroencephalograms from the Whole Brain During Right Median Nerve Stimulation

To investigate relationships between hemodynamic responses and neural activities in the somatosensory cortices, hemodynamic responses by near infrared spectroscopy (NIRS) and electroencephalograms (EEGs) were recorded simultaneously while subjects received electrical stimulation in the right median nerve. The statistical significance of the hemodynamic responses was evaluated by a general linear model (GLM) with the boxcar design matrix convoluted with Gaussian function. The resulting NIRS and EEGs data were stereotaxically superimposed on the reconstructed brain of each subject. The NIRS data indicated that changes in oxy-hemoglobin concentration increased at the contralateral primary somatosensory (SI) area; responses then spread to the more posterior and ipsilateral somatosensory areas. The EEG data indicated that positive somatosensory evoked potentials peaking at 22 ms latency (P22) were recorded from the contralateral SI area. Comparison of these two sets of data indicated that the distance between the dipoles of P22 and NIRS channels with maximum hemodynamic responses was less than 10 mm, and that the two topographical maps of hemodynamic responses and current source density of P22 were significantly correlated. Furthermore, when onset of the boxcar function was delayed 5–15 s (onset delay), hemodynamic responses in the bilateral parietal association cortices posterior to the SI were more strongly correlated to electrical stimulation. This suggests that GLM analysis with onset delay could reveal the temporal ordering of neural activation in the hierarchical somatosensory pathway, consistent with the neurophysiological data. The present results suggest that simultaneous NIRS and EEG recording is useful for correlating hemodynamic responses to neural activity

Optical imaging in vivo with a focus on paediatric disease: technical progress, current preclinical and clinical applications and future perspectives

To obtain information on the occurrence and location of molecular events as well as to track target-specific probes such as antibodies or peptides, drugs or even cells non-invasively over time, optical imaging (OI) technologies are increasingly applied. Although OI strongly contributes to the advances made in preclinical research, it is so far, with the exception of optical coherence tomography (OCT), only very sparingly applied in clinical settings. Nevertheless, as OI technologies evolve and improve continuously and represent relatively inexpensive and harmful methods, their implementation as clinical tools for the assessment of children disease is increasing. This review focuses on the current preclinical and clinical applications as well as on the future potential of OI in the clinical routine. Herein, we summarize the development of different fluorescence and bioluminescence imaging techniques for microscopic and macroscopic visualization of microstructures and biological processes. In addition, we discuss advantages and limitations of optical probes with distinct mechanisms of target-detection as well as of different bioluminescent reporter systems. Particular attention has been given to the use of near-infrared (NIR) fluorescent probes enabling observation of molecular events in deeper tissue

Phenolic composition of Vitis vinifera C.V. gamay N

*INRA Centre de Montpellier (FRA) Diffusion du document : INRA Centre de Montpellier (FRA)International audienc

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Localized layers of turbulence in vertically-stratified plane Poiseuille flow

This article presents a numerical analysis of the instability developing in horizontal plane Poiseuille flow, when stratification extends along the direction orthogonal to the plane of shear. Our study builds up on the previous work that originally detected the linear instability of such configuration, by means of experiments, theoretical analysis and numerical simulations (Le Gal et al. 2021). We extend hereafter this former investigation beyond linear theory, investigating nonlinear regimes with direct numerical simulations. We notice a tendency for the flow to lose its vertical homogeneity through a point of secondary bifurcation, due to harmonic resonances, and further describe this symmetrybreaking mechanism in the vicinity of the instability threshold. When departing away from this limit, we observe a series of bursting events that break down the flow into disordered motions driven by localized shear instabilities. This intermittent dynamics leads to the coexistence of localized layers of stratified turbulence surrounded by quiescent regions of meandering waves

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Localized layers of turbulence in vertically-stratified plane Poiseuille flow

This article presents a numerical analysis of the instability developing in horizontal plane Poiseuille flow, when stratification extends along the direction orthogonal to the plane of shear. Our study builds up on the previous work that originally detected the linear instability of such configuration, by means of experiments, theoretical analysis and numerical simulations (Le Gal et al. 2021). We extend hereafter this former investigation beyond linear theory, investigating nonlinear regimes with direct numerical simulations. We notice a tendency for the flow to lose its vertical homogeneity through a point of secondary bifurcation, due to harmonic resonances, and further describe this symmetrybreaking mechanism in the vicinity of the instability threshold. When departing away from this limit, we observe a series of bursting events that break down the flow into disordered motions driven by localized shear instabilities. This intermittent dynamics leads to the coexistence of localized layers of stratified turbulence surrounded by quiescent regions of meandering waves