A Female Rabbi in Fourteenth Century Zaragoza?

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A simple expression for the ADM mass

We show by an almost elementary calculation that the ADM mass of an asymptotically flat space can be computed as a limit involving a rate of change of area of a closed 2-surface. The result is essentially the same as that given by Brown and York. We will prove this result in two ways, first by direct calculation from the original formula as given by Arnowitt, Deser and Misner and second as a corollary of an earlier result by Brewin for the case of simplicial spaces.Comment: 9 pages, 1 figur

An Acidic Motif Retains Vesicular Monoamine Transporter 2 on Large Dense Core Vesicles

The release of biogenic amines from large dense core vesicles (LDCVs) depends on localization of the vesicular monoamine transporter VMAT2 to LDCVs. We now find that a cluster of acidic residues including two serines phosphorylated by casein kinase 2 is required for the localization of VMAT2 to LDCVs. Deletion of the acidic cluster promotes the removal of VMAT2 from LDCVs during their maturation. The motif thus acts as a signal for retention on LDCVs. In addition, replacement of the serines by glutamate to mimic phosphorylation promotes the removal of VMAT2 from LDCVs, whereas replacement by alanine to prevent phosphorylation decreases removal. Phosphorylation of the acidic cluster thus appears to reduce the localization of VMAT2 to LDCVs by inactivating a retention mechanism

Generalised Gagliardo–Nirenberg inequalities using weak Lebesgue spaces and BMO

Using elementary arguments based on the Fourier transform we prove that for $1 \leq q n(1/2-1/p)$, if $f \in L^{q,\infty}(\R^n) \cap \dot{H}^s(\R^n)$ then $f \in L^p(\R^n)$ and there exists a constant $c_{p,q,s}$ such that $$\|f\|_{L^p} \leq c_{p,q,s} \|f\|_{L^{q,\infty}}^\theta \|f\|_{\dot H^s}^{1-\theta},$$ where $1/p = \theta/q + (1-\theta)(1/2-s/n)$. In particular, in $\R^2$ we obtain the generalised Ladyzhenskaya inequality $\|f\|_{L^4}\le c\|f\|_{L^{2,\infty}}^{1/2}\|f\|_{\dot H^1}^{1/2}$. We also show that for $s=n/2$ the norm in $\|f\|_{\dot H^{n/2}}$ can be replaced by the norm in BMO. As well as giving relatively simple proofs of these inequalities, this paper provides a brief primer of some basic concepts in harmonic analysis, including weak spaces, the Fourier transform, the Lebesgue Differentiation Theorem, and Calderon-Zygmund decompositions

On Generalized Stam Inequalities and Fisher–Rényi Complexity Measures

Information-theoretic inequalities play a fundamental role in numerous scientific and technological areas (e.g., estimation and communication theories, signal and information processing, quantum physics, …) as they generally express the impossibility to have a complete description of a system via a finite number of information measures. In particular, they gave rise to the design of various quantifiers (statistical complexity measures) of the internal complexity of a (quantum) system. In this paper, we introduce a three-parametric Fisher–Rényi complexity, named ( p , β , λ ) -Fisher–Rényi complexity, based on both a two-parametic extension of the Fisher information and the Rényi entropies of a probability density function ρ characteristic of the system. This complexity measure quantifies the combined balance of the spreading and the gradient contents of ρ , and has the three main properties of a statistical complexity: the invariance under translation and scaling transformations, and a universal bounding from below. The latter is proved by generalizing the Stam inequality, which lowerbounds the product of the Shannon entropy power and the Fisher information of a probability density function. An extension of this inequality was already proposed by Bercher and Lutwak, a particular case of the general one, where the three parameters are linked, allowing to determine the sharp lower bound and the associated probability density with minimal complexity. Using the notion of differential-escort deformation, we are able to determine the sharp bound of the complexity measure even when the three parameters are decoupled (in a certain range). We determine as well the distribution that saturates the inequality: the ( p , β , λ ) -Gaussian distribution, which involves an inverse incomplete beta function. Finally, the complexity measure is calculated for various quantum-mechanical states of the harmonic and hydrogenic systems, which are the two main prototypes of physical systems subject to a central potential.The authors are very grateful to the CNRS (Steeve Zozor) and the Junta de Andalucía and the MINECO–FEDER under the grants FIS2014–54497 and FIS2014–59311P (Jesús Sánchez-Dehesa) for partial financial support

Systematics of Hypocrea citrina and related taxa

Morphological studies and phylogenetic analyses of DNA sequences from three genomic regions – the internal transcribed spacer (ITS) regions of the nuclear ribosomal gene repeat, a partial sequence of RNA polymerase II subunit (rpb2), and a partial sequence of translation elongation factor (tef1) – were used to investigate the systematics of Hypocrea citrina and related species. A neotype specimen is designated for H. citrina that conforms to Persoon's description of a yellow effuse fungus occurring on leaf litter. Historical information and results obtained in this study provide the foundation for selection of a lectotype specimen from Fries's herbarium for H. lactea. The results indicate that (1) Hypocrea citrina and H. pulvinata are distinct species; (2) H. lactea sensu Fries is a synonym of the older name H. citrina; (3) H. pulvinata, H. protopulvinata, and H. americana are phylogenetically distinct species that form a well-supported polyporicolous clade; (4) H. citrina is situated in a clade closely related to H. pulvinata; and (5) H. microcitrina and H. pseudostraminea reside in a highly supported clade phylogenetically distinct from H. citrina. Hypocrea protopulvinata, H. microcitrina, H. megalocitrina, H. pseudostraminea, and a new species, H. aurantiistroma, are reported and described from North America. Variation in rpb2 and tef1 gene sequences suggests geographical subgroupings between European and North American isolates of H. pulvinata. The phylogenies inferred from ITS, rpb2, and tef1 gene sequences are concordant. Hypocrea citrina var. americana is elevated to species status, Hypocrea americana

iPSC-Derived Dopamine Neurons Reveal Differences between Monozygotic Twins Discordant for Parkinson’s Disease

SummaryParkinson’s disease (PD) has been attributed to a combination of genetic and nongenetic factors. We studied a set of monozygotic twins harboring the heterozygous glucocerebrosidase mutation (GBA N370S) but clinically discordant for PD. We applied induced pluripotent stem cell (iPSC) technology for PD disease modeling using the twins’ fibroblasts to evaluate and dissect the genetic and nongenetic contributions. Utilizing fluorescence-activated cell sorting, we obtained a homogenous population of “footprint-free” iPSC-derived midbrain dopaminergic (mDA) neurons. The mDA neurons from both twins had ∼50% GBA enzymatic activity, ∼3-fold elevated α-synuclein protein levels, and a reduced capacity to synthesize and release dopamine. Interestingly, the affected twin’s neurons showed an even lower dopamine level, increased monoamine oxidase B (MAO-B) expression, and impaired intrinsic network activity. Overexpression of wild-type GBA and treatment with MAO-B inhibitors normalized α-synuclein and dopamine levels, suggesting a combination therapy for the affected twin

MAO-B Elevation in Mouse Brain Astrocytes Results in Parkinson's Pathology

Age-related increases in monoamine oxidase B (MAO-B) may contribute to neurodegeneration associated with Parkinson's disease (PD). The MAO-B inhibitor deprenyl, a long-standing antiparkinsonian therapy, is currently used clinically in concert with the dopamine precursor L-DOPA. Clinical studies suggesting that deprenyl treatment alone is not protective against PD associated mortality were targeted to symptomatic patients. However, dopamine loss is at least 60% by the time PD is symptomatically detectable, therefore lack of effect of MAO-B inhibition in these patients does not negate a role for MAO-B in pre-symptomatic dopaminergic loss. In order to directly evaluate the role of age-related elevations in astroglial MAO-B in the early initiation or progression of PD, we created genetically engineered transgenic mice in which MAO-B levels could be specifically induced within astroglia in adult animals. Elevated astrocytic MAO-B mimicking age related increase resulted in specific, selective and progressive loss of dopaminergic neurons in the substantia nigra (SN), the same subset of neurons primarily impacted in the human condition. This was accompanied by other PD-related alterations including selective decreases in mitochondrial complex I activity and increased mitochondrial oxidative stress. Along with a global astrogliosis, we observed local microglial activation within the SN. These pathologies correlated with decreased locomotor activity. Importantly, these events occurred even in the absence of the PD-inducing neurotoxin MPTP. Our data demonstrates that elevation of murine astrocytic MAO-B by itself can induce several phenotypes of PD, signifying that MAO-B could be directly involved in multiple aspects of disease neuropathology. Mechanistically this may involve increases in membrane permeant H2O2 which can oxidize dopamine within dopaminergic neurons to dopaminochrome which, via interaction with mitochondrial complex I, can result in increased mitochondrial superoxide. Our inducible astrocytic MAO-B transgenic provides a novel model for exploring pathways involved in initiation and progression of several key features associated with PD pathology and for therapeutic drug testing