An interesting example for spectral invariants

In "Illinois J. of Math. {\bf 38} (1994) 653--678", the heat operator of a Bismut superconnection for a family of generalized Dirac operators is defined along the leaves of a foliation with Hausdorff groupoid. The Novikov-Shubin invariants of the Dirac operators were assumed greater than three times the codimension of the foliation. It was then showed that the associated heat operator converges to the Chern character of the index bundle of the operator. In "J. K-Theory {\bf 1} (2008) 305--356", we improved this result by reducing the requirement on the Novikov-Shubin invariants to one half of the codimension. In this paper, we construct examples which show that this is the best possible result.Comment: Third author added. Some typos corrected and some material added. Appeared in Journal of K Theory, Volume 13, in 2014, pages 305 to 31

Exosomes and their Cargo as a New Avenue for Brain and Treatment of CNSRelated Diseases

Extracellular Vesicles (EVs), which belong to nanoscale vesicles, including microvesicles (MVs) and exosomes, are now considered a new important tool for intercellular neuronal communication in the Central Nervous System (CNS) under physiological and pathological conditions. EVs are shed into blood, peripheral body fluids and cerebrospinal fluid (CSF) by a large variety of cells. EVs can act locally on neighboring and distant cells. EVs represent the fingerprints of the originating cells and can carry a variety of molecular constituents of their cell of origin, including protein, lipids, DNA and microRNAs (miRNAs). The most studied EVs are the exosomes because they are ubiquitous and have the capacity to transfer cell-derived components and bioactive molecules to target cells. In this minireview, we focused on cell-cell communication in CNS mediated by exosomes and their important cargo as an innovative way to treat or follow up with CNS diseases. © 2022 Benameur et al

Extracellular vesicles miRNA cargo for microglia polarization in traumatic brain injury

Traumatic brain injury (TBI) is one of the major causes of death and disability worldwide, and despite its high dissemination, effective pharmacotherapies are lacking. TBI can be divided into two phases: the instantaneous primary mechanical injury, which occurs at the moment of insult, and the delayed secondary injury, which involves a cascade of biological processes that lead to neuroinflammation. Neuroinflammation is a hallmark of both acute and chronic TBI, and it is considered to be one of the major determinants of the outcome and progression of disease. In TBI one of the emerging mechanisms for cell–cell communication involved in the immune response regulation is represented by Extracellular Vesicles (EVs). These latter are produced by all cell types and are considered a fingerprint of their generating cells. Exosomes are the most studied nanosized vesicles and can carry a variety of molecular constituents of their cell of origin, including microRNAs (miRNAs). Several miRNAs have been shown to target key neuropathophysiological pathways involved in TBI. The focus of this review is to analyze exosomes and their miRNA cargo to modulate TBI neuroinflammation providing new strategies for prevent long‐term progression of disease

Gap-labelling conjecture with nonzero magnetic field

Given a constant magnetic field on Euclidean space Rpdetermined by a skew-symmetric (p x p)matrix Theta, and a Zp-invariant probability measure mu on the disorder set Sigma which is by hypothesis a Cantor set, where the action is assumed to be minimal, the corresponding Integrated Density of States of any self-adjoint operator affiliated to the twisted crossed product algebra C(Sigma) ⋊ sigma Zp, where sigma is the multiplier on Zp associated to Theta, takes on values on spectral gaps in the magnetic gap-labelling group. The magnetic frequency groupis defined as an explicit countable subgroup of Rinvolving Pfaffians of Theta and its sub-matrices. We conjecture that the magnetic gap labelling group is a subgroup of the magnetic frequency group. We give evidence for the validity of our conjecture in 2D, 3D, the Jordan block diagonal case and the periodic case in all dimensionsMoulay Tahar Benameur, Varghese Matha

Kyste synovial intraosseux du scaphoïde carpien bilatéral révélé par une fracture pathologique: à propos d’un cas et revu de la littérature

Nous rapportons l'observation d'un jeune patient qui présente un kyste synovial intraosseux (KSIO) du scaphoïde révélé par une fracture pathologique. Le kyste synovial intraosseux du scaphoïde constitue une étiologie très rare des douleurs du poignet encore plus des fractures et la forme bilatérale associe à une fracture demeure une entité exceptionnelle, non décrite dans la littérature

Image Restoration Using Functional and Anatomical Information Fusion with Application to SPECT-MRI Images

Image restoration is usually viewed as an ill-posed problem in image processing, since there is no unique solution associated with it. The quality of restored image closely depends on the constraints imposed of the characteristics of the solution. In this paper, we propose an original extension of the NAS-RIF restoration technique by using information fusion as prior information with application in SPECT medical imaging. That extension allows the restoration process to be constrained by efficiently incorporating, within the NAS-RIF method, a regularization term which stabilizes the inverse solution. Our restoration method is constrained by anatomical information extracted from a high resolution anatomical procedure such as magnetic resonance imaging (MRI). This structural anatomy-based regularization term uses the result of an unsupervised Markovian segmentation obtained after a preliminary registration step between the MRI and SPECT data volumes from each patient. This method was successfully tested on 30 pairs of brain MRI and SPECT acquisitions from different subjects and on Hoffman and Jaszczak SPECT phantoms. The experiments demonstrated that the method performs better, in terms of signal-to-noise ratio, than a classical supervised restoration approach using a Metz filter

Visibility of dichalcogenide nanolayers

Dichalcogenides with the common formula MX2 are layered materials with electrical properties that range from semiconducting to superconducting. Here, we describe optimal imaging conditions for optical detection of ultrathin, two-dimensional dichalcogenide nanocrystals containing single, double and triple layers of MoS2, WSe2 and NbSe2. A simple optical model is used to calculate the contrast for nanolayers deposited on wafers with varying thickness of SiO2. The model is extended for imaging using the green channel of a video camera. Using AFM and optical imaging we confirm that single layers of MoS2, WSe2 and NbSe2 can be detected on 90nm and 270 nm SiO2 using optical means. By measuring contrast under broad-band green illumination we are also able to distinguish between nanostructures containing single, mono and triple layers of MoS2, WSe2 and NbSe2

L^2 rho form for normal coverings of fibre bundles

We define the secondary invariants L^2- eta and -rho forms for families of generalized Dirac operators on normal coverings of fibre bundles. On the covering family we assume transversally smooth spectral projections, and Novikov--Shubin invariants bigger than 3(dim B+1) to treat the large time asymptotic for general operators. In the particular case of a bundle of spin manifolds, we study the L^2- rho class in relation to the space of positive scalar curvature vertical metrics.Comment: 21 pages, revised versio