A variational principle for cyclic polygons with prescribed edge lengths

We provide a new proof of the elementary geometric theorem on the existence and uniqueness of cyclic polygons with prescribed side lengths. The proof is based on a variational principle involving the central angles of the polygon as variables. The uniqueness follows from the concavity of the target function. The existence proof relies on a fundamental inequality of information theory. We also provide proofs for the corresponding theorems of spherical and hyperbolic geometry (and, as a byproduct, in $1+1$ spacetime). The spherical theorem is reduced to the euclidean one. The proof of the hyperbolic theorem treats three cases separately: Only the case of polygons inscribed in compact circles can be reduced to the euclidean theorem. For the other two cases, polygons inscribed in horocycles and hypercycles, we provide separate arguments. The hypercycle case also proves the theorem for "cyclic" polygons in $1+1$ spacetime.Comment: 18 pages, 6 figures. v2: typos corrected, final versio

Haplotype and isoform specific expression estimation using multi-mapping RNA-seq reads

We present a novel pipeline and methodology for simultaneously estimating isoform expression and allelic imbalance in diploid organisms using RNA-seq data. We achieve this by modeling the expression of haplotype-specific isoforms. If unknown, the two parental isoform sequences can be individually reconstructed. A new statistical method, MMSEQ, deconvolves the mapping of reads to multiple transcripts (isoforms or haplotype-specific isoforms). Our software can take into account non-uniform read generation and works with paired-end reads

Blow-up profile of rotating 2D focusing Bose gases

We consider the Gross-Pitaevskii equation describing an attractive Bose gas trapped to a quasi 2D layer by means of a purely harmonic potential, and which rotates at a fixed speed of rotation $\Omega$. First we study the behavior of the ground state when the coupling constant approaches $a\_*$ , the critical strength of the cubic nonlinearity for the focusing nonlinear Schr{\"o}dinger equation. We prove that blow-up always happens at the center of the trap, with the blow-up profile given by the Gagliardo-Nirenberg solution. In particular, the blow-up scenario is independent of $\Omega$, to leading order. This generalizes results obtained by Guo and Seiringer (Lett. Math. Phys., 2014, vol. 104, p. 141--156) in the non-rotating case. In a second part we consider the many-particle Hamiltonian for $N$ bosons, interacting with a potential rescaled in the mean-field manner $--a\_N N^{2\beta--1} w(N^{\beta} x), with$w$a positive function such that$\int\_{\mathbb{R}^2} w(x) dx = 1$. Assuming that$\beta < 1/2$and that$a\_N \to a\_*$sufficiently slowly, we prove that the many-body system is fully condensed on the Gross-Pitaevskii ground state in the limit$N \to \infty$

Special Values of Generalized Polylogarithms

We study values of generalized polylogarithms at various points and relationships among them. Polylogarithms of small weight at the points 1/2 and -1 are completely investigated. We formulate a conjecture about the structure of the linear space generated by values of generalized polylogarithms.Comment: 32 page

Mechanism of resonant electron emission from the deprotonated GFP chromophore and its biomimetics

The Green Fluorescent Protein (GFP), which is widely used in bioimaging, is known to undergo light-induced redox transformations. Electron transfer is thought to occur resonantly through excited states of its chromophore; however, a detailed understanding of the electron gateway states of the chromophore is still missing. Here, we use photoelectron spectroscopy and high-level quantum chemistry calculations to show that following UV excitation, the ultrafast electron dynamics in the chromophore anion proceeds via an excited shape resonance strongly coupled to the open continuum. The impact of this state is found across the entire 355–315 nm excitation range, from above the first bound–bound transition to below the opening of higher-lying continua. By disentangling the electron dynamics in the photodetachment channels, we provide an important reference for the adiabatic position of the electron gateway state, which is located at 348 nm, and discover the source of the curiously large widths of the photoelectron spectra that have been reported in the literature. By introducing chemical modifications to the GFP chromophore, we show that the detachment threshold and the position of the gateway state, and hence the underlying excited-state dynamics, can be changed systematically. This enables a fine tuning of the intrinsic electron emission properties of the GFP chromophore and has significant implications for its function, suggesting that the biomimetic GFP chromophores are more stable to photooxidation

SUPPORT Tools for Evidence-informed Policymaking in health 6: Using research evidence to address how an option will be implemented

This article is part of a series written for people responsible for making decisions about health policies and programmes and for those who support these decision makers

SUPPORT Tools for evidence-informed health Policymaking (STP) 7: Finding systematic reviews

This article is part of a series written for people responsible for making decisions about health policies and programmes and for those who support these decision makers

EXO 0748-676 Rules out Soft Equations of State for Neutron Star Matter

The interiors of neutron stars contain matter at very high densities, in a state that differs greatly from those found in the early universe or achieved at terrestrial experiments. Matter in these conditions can only be probed through astrophysical observations that measure the mass and radius of neutron stars with sufficient precision. Here I report for the first time a unique determination of the mass and radius of the neutron star EXO 0748-676, which appears to rule out all the soft equations of state of neutron star matter. If this object is typical, then condensates and unconfined quarks do not exist in the centers of neutron stars.Comment: To appear in Nature, press embargo until publicatio

Large scale analytic calculations in quantum field theories

We present a survey on the mathematical structure of zero- and single scale quantities and the associated calculation methods and function spaces in higher order perturbative calculations in relativistic renormalizable quantum field theories.Comment: 25 pages Latex, 1 style fil