Noncommutative symmetric functions and W-polynomials

Let K,S,D be a division ring, an endomorphism and a S-derivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Vieta formula and decompositions of differential operators. W-polynomials show up naturally, their connections with P-independency, Vandermonde and Wronskian matrices are briefly studied. The different linear factorizations of W-polynomials are analysed. Connections between the existence of LLCM of monic linear polynomials with coefficients in a ring and the left duo property are established at the end of the paper

Lehmann rotation of cholesteric droplets subjected to a temperature gradient: role of the concentration of chiral molecules

International audienceWe present a systematic study of the Lehmann rotation of cholesteric droplets subjected to a temperature gradient when the concentration of chiral molecules is changed. The liquid crystal chosen is an eutectic mixture of 8CB and 8OCB doped with a small amount of the chiral molecule R811. The angular velocity of the droplets strongly depend on their size and on the concentration of chiral molecules. The Lehmann coefficient is estimated by using three different methods. Our results are consistent with a Lehmann coefficient proportional to the concentration of chiral molecules. We additionally show the existence of a critical size of the droplets below which they change texture and stop rotating

Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

Thermal and Optical Characterization of Undoped and Neodymium-Doped Y3ScAl4O12 Ceramics

Y3–3xNd3xSc1Al4O12 (x = 0, 0.01, and 0.02) ceramics were fabricated by sintering at high temperature under vacuum. Unit cell parameter refinement and chemical analysis have been performed. The morphological characterization shows micrograins with no visible defects. The thermal analysis of these ceramics is presented, by measuring the specific heat in the temperature range from 300 to 500 K. Their values at room temperature are in the range 0.81–0.90 J g1–K–1. The thermal conductivity has been determined by two methods: by the experimental measurement of the thermal diffusivity by the photopyroelectric method, and by spectroscopy, evaluating the thermal load. The thermal conductivities are in the range 9.7–6.5 W K–1 m–1 in the temperature interval from 300 to 500 K. The thermooptic coefficients were measured at 632 nm by the dark mode method using a prism coupler, and the obtained values are in the range 12.8–13.3 × 10–6 K–1. The nonlinear refractive index values at 795 nm have been evaluated to calibrate the nonlinear optical response of these materials.This work is supported by the Spanish Government under projects MAT2011-29255-C02-01-02, MAT2013-47395-C4-4-R, and the Catalan Government under project 2014SGR1358. It was also funded by the European Commission under the Seventh Framework Programme, project Cleanspace, FP7-SPACE-2010-1-GA No. 263044

An early diagnosis is not the same as a timely diagnosis of Parkinson's disease

referee-status: Indexed referee-response-35490: 10.5256/f1000research.15815.r35490, Matthew J. Farrer, Djavad Mowafhagian Centre for Brain, University of British Columbia, Vancouver, British Columbia, Canada, 18 Jul 2018, version 1, indexed referee-response-35489: 10.5256/f1000research.15815.r35489, Mayela Rodriguez-Violante, Movement Disorders Clinic, National Institute of Neurology and Neurosurgery, Mexico City, Mexico, 18 Jul 2018, version 1, indexed grant-information: This review was supported by grants from: Parkinson’s UK (G-1606), National Institute for Health Research University College Hospitals Biomedical Research Centre and Bart’s Charity (Preventative Neurology Grant). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. copyright-info: This is an open access article distributed under the terms of the Creative Commons Attribution Licence, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.This review was supported by grants from: Parkinson’s UK (G-1606), National Institute for Health Research University College Hospitals Biomedical Research Centre and Bart’s Charity (Preventative Neurology Grant)

Neonatal AAV delivery of alpha-synuclein induces pathology in the adult mouse brain

Abstract Abnormal accumulation of alpha-synuclein (αsyn) is a pathological hallmark of Lewy body related disorders such as Parkinson’s disease and Dementia with Lewy body disease. During the past two decades, a myriad of animal models have been developed to mimic pathological features of synucleinopathies by over-expressing human αsyn. Although different strategies have been used, most models have little or no reliable and predictive phenotype. Novel animal models are a valuable tool for understanding neuronal pathology and to facilitate development of new therapeutics for these diseases. Here, we report the development and characterization of a novel model in which mice rapidly express wild-type αsyn via somatic brain transgenesis mediated by adeno-associated virus (AAV). At 1, 3, and 6 months of age following intracerebroventricular (ICV) injection, mice were subjected to a battery of behavioral tests followed by pathological analyses of the brains. Remarkably, significant levels of αsyn expression are detected throughout the brain as early as 1 month old, including olfactory bulb, hippocampus, thalamic regions and midbrain. Immunostaining with a phospho-αsyn (pS129) specific antibody reveals abundant pS129 expression in specific regions. Also, pathologic αsyn is detected using the disease specific antibody 5G4. However, this model did not recapitulate behavioral phenotypes characteristic of rodent models of synucleinopathies. In fact no deficits in motor function or cognition were observed at 3 or 6 months of age. Taken together, these findings show that transduction of neonatal mouse with AAV-αsyn can successfully lead to rapid, whole brain transduction of wild-type human αsyn, but increased levels of wildtype αsyn do not induce behavior changes at an early time point (6 months), despite pathological changes in several neurons populations as early as 1 month