The Insula of Reil Revisited: Multiarchitectonic Organization in Macaque Monkeys

The insula of Reil represents a large cortical territory buried in the depth of the lateral sulcus and subdivided into 3 major cytoarchitectonic domains: agranular, dysgranular, and granular. The present study aimed at reinvestigating the architectonic organization of the monkey's insula using multiple immunohistochemical stainings (parvalbumin, PV; nonphosphorylated neurofilament protein, with SMI-32; acetylcholinesterase, AChE) in addition to Nissl and myelin. According to changes in density and laminar distributions of the neurochemical markers, several zones were defined and related to 8 cytoarchitectonic subdivisions (Ia1-Ia2/Id1-Id3/Ig1-Ig2/G). Comparison of the different patterns of staining on unfolded maps of the insula revealed: 1) parallel ventral to dorsal gradients of increasing myelin, PV- and AChE-containing fibers in middle layers, and of SMI-32 pyramidal neurons in supragranular layers, with merging of dorsal and ventral high-density bands in posterior insula, 2) definition of an insula "proper” restricted to two-thirds of the "morphological” insula (as bounded by the limiting sulcus) and characterized most notably by lower PV, and 3) the insula proper is bordered along its dorsal, posterodorsal, and posteroventral margin by a strip of cortex extending beyond the limits of the morphological insula and continuous architectonically with frontoparietal and temporal opercular areas related to gustatory, somatosensory, and auditory modalitie

Interaction of vortices in viscous planar flows

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter \nu, and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex system is well-posed on the interval [0,T]. Under these assumptions, we prove that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a superposition of Lamb-Oseen vortices whose centers evolve according to a viscous regularization of the point vortex system. Convergence holds uniformly in time, in a strong topology which allows to give an accurate description of the asymptotic profile of each individual vortex. In particular, we compute to leading order the deformations of the vortices due to mutual interactions. This allows to estimate the self-interactions, which play an important role in the convergence proof.Comment: 39 pages, 1 figur

The Camassa-Holm equation as the long-wave limit of the improved Boussinesq equation and of a class of nonlocal wave equations

In the present study we prove rigorously that in the long-wave limit, the unidirectional solutions of a class of nonlocal wave equations to which the improved Boussinesq equation belongs are well approximated by the solutions of the Camassa-Holm equation over a long time scale. This general class of nonlocal wave equations model bidirectional wave propagation in a nonlocally and nonlinearly elastic medium whose constitutive equation is given by a convolution integral. To justify the Camassa-Holm approximation we show that approximation errors remain small over a long time interval. To be more precise, we obtain error estimates in terms of two independent, small, positive parameters $\epsilon$ and $\delta$ measuring the effect of nonlinearity and dispersion, respectively. We further show that similar conclusions are also valid for the lower order approximations: the Benjamin-Bona-Mahony approximation and the Korteweg-de Vries approximation.Comment: 24 pages, to appear in Discrete and Continuous Dynamical System

Risk Factors for Mortality after COVID-19 in Patients with Preexisting Interstitial Lung Disease.

International audienc

Large time existence for 3D water-waves and asymptotics

We rigorously justify in 3D the main asymptotic models used in coastal oceanography, including: shallow-water equations, Boussinesq systems, Kadomtsev-Petviashvili (KP) approximation, Green-Naghdi equations, Serre approximation and full-dispersion model. We first introduce a ``variable'' nondimensionalized version of the water-waves equations which vary from shallow to deep water, and which involves four dimensionless parameters. Using a nonlocal energy adapted to the equations, we can prove a well-posedness theorem, uniformly with respect to all the parameters. Its validity ranges therefore from shallow to deep-water, from small to large surface and bottom variations, and from fully to weakly transverse waves. The physical regimes corresponding to the aforementioned models can therefore be studied as particular cases; it turns out that the existence time and the energy bounds given by the theorem are always those needed to justify the asymptotic models. We can therefore derive and justify them in a systematic way.Comment: Revised version of arXiv:math.AP/0702015 (notations simplified and remarks added) To appear in Inventione

Lipopolysaccharide (LPS)-binding protein in human serum determines the tumor necrosis factor response of monocytes to LPS

Lipopolysaccharide (LPS)-binding protein (LBP) and CD14 represent key elements in monocyte activation by LPS. The mean concentration of LBP was 18.1 microgram/mL in normal serum and 40-60 micrograms/mL in serum of patients with septic shock, independent of the fact that patients had gram-negative or other infections. Ten percent normal serum presented large concentrations of LPS (in the microgram range) to monocytes. Only when diluted 1:100 was LBP in plasma a limiting factor for monocyte activation, as measured by tumor necrosis factor (TNF) release. When LBP was depleted from serum with anti-LBP antibodies, the resulting serum did not support TNF release of monocytes upon LPS challenge. In conclusion, monocyte activation resulting in TNF secretion was related to LBP, which is abundantly present in normal serum, and elevated two to three times in patients with septic shock

Coherent vortex structures and 3D enstrophy cascade

Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physical scales. The goal of this paper is to show that the same geometric condition preventing the formation of singularities - 1/2-H\"older coherence of the vorticity direction - coupled with a suitable condition on a modified Kraichnan scale, and under a certain modulation assumption on evolution of the vorticity, leads to existence of 3D enstrophy cascade in physical scales of the flow.Comment: 15 pp; final version -- to appear in CM

Modulational Instability in Equations of KdV Type

It is a matter of experience that nonlinear waves in dispersive media, propagating primarily in one direction, may appear periodic in small space and time scales, but their characteristics --- amplitude, phase, wave number, etc. --- slowly vary in large space and time scales. In the 1970's, Whitham developed an asymptotic (WKB) method to study the effects of small "modulations" on nonlinear periodic wave trains. Since then, there has been a great deal of work aiming at rigorously justifying the predictions from Whitham's formal theory. We discuss recent advances in the mathematical understanding of the dynamics, in particular, the instability of slowly modulated wave trains for nonlinear dispersive equations of KdV type.Comment: 40 pages. To appear in upcoming title in Lecture Notes in Physic