The dynamics of the 3D radial NLS with the combined terms

In this paper, we show the scattering and blow-up result of the radial solution with the energy below the threshold for the nonlinear Schr\"{o}dinger equation (NLS) with the combined terms iu_t + \Delta u = -|u|^4u + |u|^2u \tag{CNLS} in the energy space $H^1(\R^3)$. The threshold is given by the ground state $W$ for the energy-critical NLS: $iu_t + \Delta u = -|u|^4u$. This problem was proposed by Tao, Visan and Zhang in \cite{TaoVZ:NLS:combined}. The main difficulty is the lack of the scaling invariance. Illuminated by \cite{IbrMN:f:NLKG}, we need give the new radial profile decomposition with the scaling parameter, then apply it into the scattering theory. Our result shows that the defocusing, $\dot H^1$-subcritical perturbation $|u|^2u$ does not affect the determination of the threshold of the scattering solution of (CNLS) in the energy space.Comment: 46page

Semiclassical approximations for Hamiltonians with operator-valued symbols

We consider the semiclassical limit of quantum systems with a Hamiltonian given by the Weyl quantization of an operator valued symbol. Systems composed of slow and fast degrees of freedom are of this form. Typically a small dimensionless parameter $\varepsilon\ll 1$ controls the separation of time scales and the limit $\varepsilon\to 0$ corresponds to an adiabatic limit, in which the slow and fast degrees of freedom decouple. At the same time $\varepsilon\to 0$ is the semiclassical limit for the slow degrees of freedom. In this paper we show that the $\varepsilon$-dependent classical flow for the slow degrees of freedom first discovered by Littlejohn and Flynn, coming from an \epsi-dependent classical Hamilton function and an $\varepsilon$-dependent symplectic form, has a concrete mathematical and physical meaning: Based on this flow we prove a formula for equilibrium expectations, an Egorov theorem and transport of Wigner functions, thereby approximating properties of the quantum system up to errors of order $\varepsilon^2$. In the context of Bloch electrons formal use of this classical system has triggered considerable progress in solid state physics. Hence we discuss in some detail the application of the general results to the Hofstadter model, which describes a two-dimensional gas of non-interacting electrons in a constant magnetic field in the tight-binding approximation.Comment: Final version to appear in Commun. Math. Phys. Results have been strengthened with only minor changes to the proofs. A section on the Hofstadter model as an application of the general theory was added and the previous section on other applications was remove

Global dynamics above the ground state for the nonlinear Klein-Gordon equation without a radial assumption

We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground state.Comment: 40 page

Protective effects of angiopoietin-like 4 on cerebrovascular and functional damages in ischaemic stroke

AIMS: Given the impact of vascular injuries and oedema on brain damage caused during stroke, vascular protection represents a major medical need. We hypothesized that angiopoietin-like 4 (ANGPTL4), a regulator of endothelial barrier integrity, might exert a protective effect during ischaemic stroke. METHODS AND RESULTS: Using a murine transient ischaemic stroke model, treatment with recombinant ANGPTL4 led to significantly decreased infarct size and improved behaviour. Quantitative characteristics of the vascular network (density and branchpoints) were preserved in ANGPTL4-treated mice. Integrity of tight and adherens junctions was also quantified and ANGPTL4-treated mice displayed increased VE-cadherin and claudin-5-positive areas. Brain oedema was thus significantly decreased in ANGPTL4-treated mice. In accordance, vascular damage and infarct severity were increased in angptl4-deficient mice thus providing genetic evidence that ANGPTL4 preserves brain tissue from ischaemia-induced alterations. Altogether, these data show that ANGPTL4 protects not only the global vascular network, but also interendothelial junctions and controls both deleterious inflammatory response and oedema. Mechanistically, ANGPTL4 counteracted VEGF signalling and thereby diminished Src-signalling downstream from VEGFR2. This led to decreased VEGFR2-VE-cadherin complex disruption, increased stability of junctions and thus increased endothelial cell barrier integrity of the cerebral microcirculation. In addition, ANGPTL4 prevented neuronal loss in the ischaemic area. CONCLUSION: These results, therefore, show ANGPTL4 counteracts the loss of vascular integrity in ischaemic stroke, by restricting Src kinase signalling downstream from VEGFR2. ANGPTL4 treatment thus reduces oedema, infarct size, neuronal loss, and improves mice behaviour. These results suggest that ANGPTL4 constitutes a relevant target for vasculoprotection and cerebral protection during stroke

Modifications of the endosomal compartment in peripheral blood mononuclear cells and fibroblasts from Alzheimer’s disease patients

International audienceIdentification of blood-based biomarkers of Alzheimer’s disease (AD) remains a challenge. Neuropathological studies have identified enlarged endosomes in post-mortem brains as the earliest cellular change associated to AD. Here the presence of enlarged endosomes was investigated in peripheral blood mononuclear cells from 48 biologically defined AD patients (25 with mild cognitive impairment and 23 with dementia (AD-D)), and 23 age-matched healthy controls using immunocytochemistry and confocal microscopy. The volume and number of endosomes were not significantly different between AD and controls. However, the percentage of cells containing enlarged endosomes was significantly higher in the AD-D group as compared with controls. Furthermore, endosomal volumes significantly correlated to [C11]PiB cortical index measured by positron emission tomography in the AD group, independently of the APOE genotype, but not to the levels of amyloid-beta, tau and phosphorylated tau measured in the cerebrospinal fluid. Importantly, we confirmed the presence of enlarged endosomes in fibroblasts from six unrelated AD-D patients as compared with five cognitively normal controls. This study is the first, to our knowledge, to report morphological alterations of the endosomal compartment in peripheral cells from AD patients correlated to amyloid load that will now be evaluated as a possible biomarker

Laminar degeneration of frontal and temporal cortex in Parkinson disease dementia

To investigate cortical laminar degeneration in Parkinson’s disease (PD) with dementia (PDD). Changes in density of α-synuclein-immunoreactive Lewy bodies (LB), Lewy neurites (LN), and Lewy grains (LG) together with surviving neurons, abnormally enlarged neurons (EN), vacuoles, and glial cell nuclei were measured across cortical laminae of frontal and temporal cortex in fifteen cases of PDD using quantitative methods and polynomial curve-fitting. Most frequently, LB and LN were distributed across all laminae, while LG were distributed in upper cortical laminae. Low densities of EN were present in most cases distributed across all cortical laminae. Densities of vacuoles and glia were greatest in upper and lower cortical laminae, respectively. In most gyri, there were no spatial correlations between the densities of LB, LN, and LG. Cortical degeneration of frontal and temporal lobes in PDD affects all cortical laminae. Laminar distributions may result from the spread of α-synuclein pathology from subcortical regions and subsequent spread via the cortico-cortical pathways. This spread may be a major factor in the development of dementia in PD

Resample-smoothing of Voronoi intensity estimators

Voronoi estimators are non-parametric and adaptive estimators of the intensity of a point process. The intensity estimate at a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing that location. Their major drawback is that they tend to paradoxically under-smooth the data in regions where the point density of the observed point pattern is high, and over-smooth where the point density is low. To remedy this behaviour, we propose to apply an additional smoothing operation to the Voronoi estimator, based on resampling the point pattern by independent random thinning. Through a simulation study we show that our resample-smoothing technique improves the estimation substantially. In addition, we study statistical properties such as unbiasedness and variance, and propose a rule-of-thumb and a data-driven cross-validation approach to choose the amount of smoothing to apply. Finally we apply our proposed intensity estimation scheme to two datasets: locations of pine saplings (planar point pattern) and motor vehicle traffic accidents (linear network point pattern)

Potential human transmission of amyloid β pathology: surveillance and risks

Studies in experimental animals show transmissibility of amyloidogenic proteins associated with prion diseases, Alzheimer's disease, Parkinson's disease, and other neurodegenerative diseases. Although these data raise potential concerns for public health, convincing evidence for human iatrogenic transmission only exists for prions and amyloid β after systemic injections of contaminated growth hormone extracts or dura mater grafts derived from cadavers. Even though these procedures are now obsolete, some reports raise the possibility of iatrogenic transmission of amyloid β through putatively contaminated neurosurgical equipment. Iatrogenic transmission of amyloid β might lead to amyloid deposition in the brain parenchyma and blood vessel walls, potentially resulting in cerebral amyloid angiopathy after several decades. Cerebral amyloid angiopathy can cause life-threatening brain haemorrhages; yet, there is no proof that the transmission of amyloid β can also lead to Alzheimer's dementia. Large, long-term epidemiological studies and sensitive, cost-efficient tools to detect amyloid are needed to better understand any potential routes of amyloid β transmission and to clarify whether other similar proteopathic seeds, such as tau or α-synuclein, can also be transferred iatrogenically