An algebra of deformation quantization for star-exponentials on complex symplectic manifolds

The cotangent bundle $T^*X$ to a complex manifold $X$ is classically endowed with the sheaf of \cor-algebras \W[T^*X] of deformation quantization, where \cor\eqdot \W[\rmptt] is a subfield of \C[[\hbar,\opb{\hbar}]. Here, we construct a new sheaf of \cor-algebras \TW[T^*X] which contains \W[T^*X] as a subalgebra and an extra central parameter $t$. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If $P$ is any section of order zero of \W[T^*X], we show that \exp(t\opb{\hbar} P) is well defined in \TW[T^*X].Comment: Latex file, 24 page

A proposal for a comprehensive grading of Parkinson's disease severity combining motor and non-motor assessments: meeting an unmet need.

Non-motor symptoms are present in Parkinson's disease (PD) and a key determinant of quality of life. The Non-motor Symptoms Scale (NMSS) is a validated scale that allows quantifying frequency and severity (burden) of NMS. We report a proposal for using NMSS scores to determine levels of NMS burden (NMSB) and to complete PD patient classification

The PINK1-Parkin mitophagy signalling pathway is not functional in peripheral blood mononuclear cells

Mutations in the PINK1 and PRKN genes are the most common cause of early-onset familial Parkinson disease. These genes code for the PINK1 and Parkin proteins, respectively, which are involved in the degradation of dysfunctional mitochondria through mitophagy. An early step in PINK1 -Parkin mediated mitophagy is the ubiquitination of the mitofusin proteins MFN1 and -2. The ubiquitination of MFN1 and -2 in patient samples may therefore serve as a biomarker to determine the functional effects of PINK1 and PRKN mutations, and to screen idiopathic patients for potential mitophagy defects. We aimed to characterise the expression of the PINK1 -Parkin mitophagy machinery in peripheral blood mononuclear cells (PBMCs) and assess if these cells could serve as a platform to evaluate mitophagy via analysis of MFN1 and -2 ubiquitination. Mitophagy was induced through mitochondrial depolarisation by treatment with the protonophore CCCP and ubiquitinated MFN proteins were analysed by western blotting. In addition, PINK1 and PRKN mRNA and protein expression levels were characterised with reverse transcriptase quantitative PCR and western blotting, respectively. Whilst CCCP treatment led to MFN ubiquitination in primary fibroblasts, SH-SY5Y neuroblastoma cells and Jurkat leukaemic cells, treatment of PBMCs did not induce ubiquitination of MFN. PRKN mRNA and protein was readily detectable in PBMCs at comparable levels to those observed in Jurkat and fibroblast cells. In contrast, PINK1 protein was undetectable and PINK1 mRNA levels were remarkably low in control PBMCs. Our findings suggest that the PINK1 -Parkin mitophagy signalling pathway is not functional in PBMCs. Therefore, PBMCs are not a suitable biosample for analysis of mitophagy function in Parkinson disease patients

Euler-Bessel and Euler-Fourier Transforms

We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible \zed-valued functions to continuous $\real$-valued functions over a vector space. Core contributions include: the definition of the topological Bessel transform; a relationship in terms of the logarithmic blowup of the topological Fourier transform; and a novel Morse index formula for the transforms. We then apply the theory to problems of target reconstruction from enumerative sensor data, including localization and shape discrimination. This last application utilizes an extension of spatially variant apodization (SVA) to mitigate sidelobe phenomena