A hidden symmetry of a branching law

We consider branching laws for the restriction of some irreducible unitary representations $\Pi$ of $G=O(p,q)$ to its subgroup $H=O(p-1,q)$. In Kobayashi (arXiv:1907.07994), the irreducible subrepresentations of $O(p-1,q)$ in the restriction of the unitary $\Pi|_{O(p-1,q) }$ are determined. By considering the restriction of packets of irreducible representations we obtain another very simple branching law, which was conjectured in Orsted-Speh (arXiv:1907.07544).Comment: 16 page

Pair Interaction Potentials of Colloids by Extrapolation of Confocal Microscopy Measurements of Collective Structure

A method for measuring the pair interaction potential between colloidal particles by extrapolation measurement of collective structure to infinite dilution is presented and explored using simulation and experiment. The method is particularly well suited to systems in which the colloid is fluorescent and refractive index matched with the solvent. The method involves characterizing the potential of mean force between colloidal particles in suspension by measurement of the radial distribution function using 3D direct visualization. The potentials of mean force are extrapolated to infinite dilution to yield an estimate of the pair interaction potential, $U(r)$. We use Monte Carlo (MC) simulation to test and establish our methodology as well as to explore the effects of polydispersity on the accuracy. We use poly-12-hydroxystearic acid-stabilized poly(methyl methacrylate) (PHSA-PMMA) particles dispersed in the solvent dioctyl phthalate (DOP) to test the method and assess its accuracy for three different repulsive systems for which the range has been manipulated by addition of electrolyte.Comment: 35 pages, 14 figure

Using the local density approximation and the LYP, BLYP, and B3LYP functionals within Reference--State One--Particle Density--Matrix Theory

For closed-shell systems, the local density approximation (LDA) and the LYP, BLYP, and B3LYP functionals are shown to be compatible with reference-state one-particle density-matrix theory, where this recently introduced formalism is based on Brueckner-orbital theory and an energy functional that includes exact exchange and a non-universal correlation-energy functional. The method is demonstrated to reduce to a density functional theory when the exchange-correlation energy-functional has a simplified form, i.e., its integrand contains only the coordinates of two electron, say r1 and r2, and it has a Dirac delta function -- delta(r1 - r2) -- as a factor. Since Brueckner and Hartree--Fock orbitals are often very similar, any local exchange functional that works well with Hartree--Fock theory is a reasonable approximation with reference-state one-particle density-matrix theory. The LDA approximation is also a reasonable approximation. However, the Colle--Salvetti correlation-energy functional, and the LYP variant, are not ideal for the method, since these are universal functionals. Nevertheless, they appear to provide reasonable approximations. The B3LYP functional is derived using a linear combination of two functionals: One is the BLYP functional; the other uses exact exchange and a correlation-energy functional from the LDA.Comment: 26 Pages, 0 figures, RevTeX 4, Submitted to Mol. Phy

Stability data, irregular connections and tropical curves

We study a class of meromorphic connections nabla(Z) on P^1, parametrised by the central charge Z of a stability condition, with values in a Lie algebra of formal vector fields on a torus. Their definition is motivated by the work of Gaiotto, Moore and Neitzke on wall-crossing and three-dimensional field theories. Our main results concern two limits of the families nabla(Z) as we rescale the central charge Z to RZ. In the R to 0 ``conformal limit'' we recover a version of the connections introduced by Bridgeland and Toledano Laredo (and so the Joyce holomorphic generating functions for enumerative invariants), although with a different construction yielding new explicit formulae. In the R to infty ``large complex structure" limit the connections nabla(Z) make contact with the Gross-Pandharipande-Siebert approach to wall-crossing based on tropical geometry. Their flat sections display tropical behaviour, and also encode certain tropical/relative Gromov-Witten invariants

Sense and nonsense in sensors

Continuous subcutaneous glucose monitoring (CGM) is a developing technology in the treatment of diabetes mellitus. The first randomised controlled trials on its efficacy have been performed. In several studies, CGM lowered HbA1c in adult patients with suboptimally controlled type 1 diabetes mellitus, when selecting compliant patients who tolerate the device. However, as a preventive tool for hypoglycaemia, CGM has not fulfilled the great expectations. Increasing reimbursement of CGM is expected in the near future, awaiting studies on cost-effectiveness

Bim and Bmf synergize to induce apoptosis in Neisseria gonorrhoeae infection

Abstract: Bcl-2 family proteins including the pro-apoptotic BH3-only proteins are central regulators of apoptotic cell death. Here we show by a focused siRNA miniscreen that the synergistic action of the BH3-only proteins Bim and Bmf is required for apoptosis induced by infection with Neisseria gonorrhoeae (Ngo). While Bim and Bmf were associated with the cytoskeleton of healthy cells, they both were released upon Ngo infection. Loss of Bim and Bmf from the cytoskeleton fraction required the activation of Jun-N-terminal kinase-1 (JNK-1), which in turn depended on Rac-1. Depletion and inhibition of Rac-1, JNK-1, Bim, or Bmf prevented the activation of Bak and Bax and the subsequent activation of caspases. Apoptosis could be reconstituted in Bim-depleted and Bmf-depleted cells by additional silencing of antiapoptotic Mcl-1 and Bcl-XL, respectively. Our data indicate a synergistic role for both cytoskeletal-associated BH3-only proteins, Bim, and Bmf, in an apoptotic pathway leading to the clearance of Ngo-infected cells. Author Summary: A variety of physiological death signals, as well as pathological insults, trigger apoptosis, a genetically programmed form of cell death. Pathogens often induce host cell apoptosis to establish a successful infection. Neisseria gonorrhoeae (Ngo), the etiological agent of the sexually transmitted disease gonorrhoea, is a highly adapted obligate human-specific pathogen and has been shown to induce apoptosis in infected cells. Here we unveil the molecular mechanisms leading to apoptosis of infected cells. We show that Ngo-mediated apoptosis requires a special subset of proapoptotic proteins from the group of BH3-only proteins. BH3-only proteins act as stress sensors to translate toxic environmental signals to the initiation of apoptosis. In a siRNA-based miniscreen, we found Bim and Bmf, BH3-only proteins associated with the cytoskeleton, necessary to induce host cell apoptosis upon infection. Bim and Bmf inactivated different inhibitors of apoptosis and thereby induced cell death in response to infection. Our data unveil a novel pathway of infection-induced apoptosis that enhances our understanding of the mechanism by which BH3-only proteins control apoptotic cell death

Spondin-2 (SPON2), a More Prostate-Cancer-Specific Diagnostic Biomarker

BACKGROUND: Prostate-specific antigen (PSA) screening, although common, has recently been called into question. To find prostate cancer (PCa) diagnostic biomarkers that can make up for the defects of PSA, we compared the secretomes of several benign and PCa cell lines, selected candidate molecules, and then confirmed their clinical value. METHODOLOGY/PRINCIPAL FINDINGS: We first identified extracellular proteins by two-dimensional gel electrophoresis (2-DE) coupled with liquid chromatography-tandem mass spectrometry (LC-MS/MS) identification. We then validated the secreted proteins on a cellular level, and finally determined whether they could be used as PCa diagnostic biomarkers using prostate tissue and serum specimens of Chinese volunteers by immunohistostaining and sandwich ELISA. We obtained credible extracellular protein 2-DE graphs of prostate cell lines. The 5 spots that showed superior repeatability were selected for LC-MS/MS analysis, which identified seven candidate molecules. One of the candidate molecules, spondin-2 (SPON2), was only expressed in the conditioned media (CM) of androgen receptor (AR) positive PCa cell lines. Using tissue microarray by immunohistostaining, we found SPON2 to be over-expressed in PCa. SPON2 staining was more intense in Gleason score sum 7-8 and in PCa patients with metastasis. By receiver operator characteristic (ROC) curve analysis, we found that the serum SPON2 level was elevated in PCa patients, showing sensitivity and specificity suitable for diagnostic use. We also found that SPON2 could be used to identify PCa patients with serum PSA levels no higher than 10 ng/ml from healthy elderly men. CONCLUSION/SIGNIFICANCE: SPON2 is a new serum and histological diagnostic biomarker for PCa. It can avoid some of the problems of PSA testing and was here found to offer relatively high sensitivity and specificity relative to PSA

Experiences of baby-led weaning: trust, control, and renegotiation

Baby-led weaning (Rapley 2013) is an approach to introducing solid foods that relies on the presence of self-feeding skills and is increasing in popularity in the UK and New Zealand. This study aimed to investigate the reported experiences and feelings of mothers using a BLW approach in order to better understand the experiences of the mother and infant, the benefits and challenges of the approach, and the beliefs which underpin these experiences. 15 UK Mothers were interviewed over the course of a series of five emails using a semi-structured approach. The email transcripts were anonymised and analysed using thematic analysis (Braun & Clarke 2006). There were four main themes which were identified from the analysis: i) Trusting the child, ii) Parental control and responsibility, iii) Precious milk and, iv) Renegotiating baby-led weaning. The themes identified reflect a range of different ideals and pressures that this group of mothers tried to negotiate in order to provide their infants with a positive and healthy introduction to solid foods. One of the key issues of potential concern is the timing at which some of the children ingested complementary foods. Although complementary foods were made available to the infants at 6 months of age, in many cases they were not ingested until much later. These findings have potentially important implications for mother’s decision-making, health professional policy and practice, and future research