Isomorphisms of algebras of Colombeau generalized functions

We show that for smooth manifolds X and Y, any isomorphism between the special algebra of Colombeau generalized functions on X, resp. Y is given by composition with a unique Colombeau generalized function from Y to X. We also identify the multiplicative linear functionals from the special algebra of Colombeau generalized functions on X to the ring of Colombeau generalized numbers. Up to multiplication with an idempotent generalized number, they are given by an evaluation map at a compactly supported generalized point on X.Comment: 10 page

Growth Bands in Test Plates of the Sea Urchins Arbacia punctulata and Lytechinus variegatus (Echinodermata) on the Central Florida Gulf Coast Shelf

Growth bands in test plates provide information about the biology and ecology of sea urchins. We documented the bands in the test plates of Arbacia punctulata and Lytechinus variegatus at different seasons and locations on the central Florida Gulf Coast shelf. The number of growth bands in test plates is significantly correlated with test diameter for A. punctulata. The number of growth bands is not significantly correlated with test diameter for L. variegatus. The condition of the outermost growth band was recorded along with the month and reproductive state to investigate the effect of variation in reproduction and temperature on growth. Growth bands in A. punctulata are well defined and appear to be related to the reproductive cycle. Growth bands in L. variegatus are less well defined and may be more closely related to food availability

An algebraic approach to manifold-valued generalized functions

We discuss the nature of structure-preserving maps of varies function algebras. In particular, we identify isomorphisms between special Colombeau algebras on manifolds with invertible manifold-valued generalized functions in the case of smooth parametrization. As a consequence, and to underline the consistency and validity of this approach, we see that this generalized version on algebra isomorphisms in turn implies the classical result on algebras of smooth functions.Comment: 7 page

H-alpha Emission Variability in the gamma-ray Binary LS I +61 303

LS I +61 303 is an exceptionally rare example of a high mass X-ray binary (HMXB) that also exhibits MeV-TeV emission, making it one of only a handful of "gamma-ray binaries". Here we present H-alpha spectra that show strong variability during the 26.5 day orbital period and over decadal time scales. We detect evidence of a spiral density wave in the Be circumstellar disk over part of the orbit. The H-alpha line profile also exhibits a dramatic emission burst shortly before apastron, observed as a redshifted shoulder in the line profile, as the compact source moves almost directly away from the observer. We investigate several possible origins for this red shoulder, including an accretion disk, mass transfer stream, and a compact pulsar wind nebula that forms via a shock between the Be star's wind and the relativistic pulsar wind.Comment: Accepted to Ap

The use of D-chiro-inositol in clinical practice

OBJECTIVE: D-chiro-Inositol has been widely used in clinical practice to induce ovulation in women with polycystic ovary syndrome. Only recent evidence established that this molecule acts through two different mechanisms, with potentially different outcomes. On the one hand, under a metabolic perspective, D-chiro-Inositol improves insulin signaling, thus restoring physiological insulin levels in resistant subjects. On the other hand, at a cellular level, it downregulates the expression of steroidogenic enzyme aromatase, which is responsible for the conversion of androgens to estrogens. MATERIALS AND METHODS: We reviewed current literature in different databases, searching for D-chiro-Inositol in relation with one of the following keywords: myo-inositol, PCOS, infertility, insulin resistance, aromatase, androgen and inositol, testosterone, estrogen and inositol, estradiol, hypogonadotropic hypogonadism, fat tissue, estrogens and cancer, anovulation, uterine myoma, endometriosis, endometrial hyperplasia. RESULTS: D-Chiro-Inositol treatment may be helpful in restoring physiological hormonal levels in various clinical disorders. However, D-Chiro-Inositol intervention should be carefully designed to avoid possible undesired side effects stemming from its multiple mechanisms of action. CONCLUSIONS: We evaluated the optimal D Chiro-Inositol administration for different pathologies, defining dosages and timing. Even though further studies are required to validate our preliminary results, this paper is primarily intended to guide researchers through some of the pathways of D-Chiro-Inositol

Total flow intensity, active flow intensity and volume related flow intensity as new quantitative metrics in optical coherence tomography angiography

Optical coherence tomography (OCT) angiography (OCTA) is a non-invasive tool for the in-vivo study of the intraretinal vascular network. It is based on the analysis of motion particles within the retina to reconstruct the paths followed by the erythrocytes, i.e. retinal capillaries. To date, qualitative and quantitative information are based on the morphological features disclosed by retinal capillaries. In the present study, we proposed new quantitative functional metrics, named Total Flow Intensity (TFI), Active Flow Intensity (AFI), and Volume-related Flow Intensity (VFI), based on the processing of the blood flow signal detected by OCTA. We studied these metrics in a cohort of healthy subjects, and we assessed their clinical utility by including a cohort of age-matched patients affected by Stargardt disease. Moreover, we compared TFI, AFI, and VFI to the widely used vessel density (VD) parameter. TFI, AFI, and VFI were able to describe in detail the different properties of the retinal vascular compartment. In particular, TFI was intended as the overall amount of volumetric retinal blood flow. AFI represented a selective measure of voxels disclosing blood flow signal. VFI was developed to put in relationship the volumetric blood flow information with the not vascularized retinal volume. In conclusion, TFI, AFI, and VFI were proposed as feasible functional OCTA biomarkers based on the analysis of retinal blood flow signal

Introductions to the Community: Early-Career Researchers in the Time of COVID-19

COVID-19 has unfortunately halted lab work, conferences, and in-person networking, which is especially detrimental to researchers just starting their labs. Through social media and our reviewer networks, we met some early-career stem cell investigators impacted by the closures. Here, they introduce themselves and their research to our readers