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

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

Swings between rotation and accretion power in a millisecond binary pulsar

It is thought that neutron stars in low-mass binary systems can accrete matter and angular momentum from the companion star and be spun-up to millisecond rotational periods. During the accretion stage, the system is called a low-mass X-ray binary, and bright X-ray emission is observed. When the rate of mass transfer decreases in the later evolutionary stages, these binaries host a radio millisecond pulsar whose emission is powered by the neutron star's rotating magnetic field. This evolutionary model is supported by the detection of millisecond X-ray pulsations from several accreting neutron stars and also by the evidence for a past accretion disc in a rotation-powered millisecond pulsar. It has been proposed that a rotation-powered pulsar may temporarily switch on during periods of low mass inflow in some such systems. Only indirect evidence for this transition has hitherto been observed. Here we report observations of accretion-powered, millisecond X-ray pulsations from a neutron star previously seen as a rotation-powered radio pulsar. Within a few days after a month-long X-ray outburst, radio pulses were again detected. This not only shows the evolutionary link between accretion and rotation-powered millisecond pulsars, but also that some systems can swing between the two states on very short timescales.Comment: 43 pages, 9 figures, 4 table. Published by Nature on 26 Sep 2013. Includes Supplementary information. Minor differences with published version may exis

Space-like (vs. time-like) collinear limits in QCD: is factorization violated?

We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e.g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum and colour charge of the non-collinear partons. We present explicit results on one-loop and two-loop amplitudes for both the two-parton and multiparton collinear limits. At the level of square amplitudes and, more generally, cross sections in hadron--hadron collisions, the violation of strict collinear factorization has implications on the non-abelian structure of logarithmically-enhanced terms in perturbative calculations (starting from the next-to-next-to-leading order) and on various factorization issues of mass singularities (starting from the next-to-next-to-next-to-leading order).Comment: 81 pages, 5 figures, typos corrected in the text, few comments added and inclusion of NOTE ADDED on recent development

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

The Songbird Neurogenomics (SoNG) Initiative: Community-based tools and strategies for study of brain gene function and evolution

BACKGROUND: Songbirds hold great promise for biomedical, environmental and evolutionary research. A complete draft sequence of the zebra finch genome is imminent, yet a need remains for application of genomic resources within a research community traditionally focused on ethology and neurobiological methods. In response, we developed a core set of genomic tools and a novel collaborative strategy to probe gene expression in diverse songbird species and natural contexts. RESULTS: We end-sequenced cDNAs from zebra finch brain and incorporated additional sequences from community sources into a database of 86,784 high quality reads. These assembled into 31,658 non-redundant contigs and singletons, which we annotated via BLAST search of chicken and human databases. The results are publicly available in the ESTIMA:Songbird database. We produced a spotted cDNA microarray with 20,160 addresses representing 17,214 non-redundant products of an estimated 11,500–15,000 genes, validating it by analysis of immediate-early gene (zenk) gene activation following song exposure and by demonstrating effective cross hybridization to genomic DNAs of other songbird species in the Passerida Parvorder. Our assembly was also used in the design of the "Lund-zfa" Affymetrix array representing ~22,000 non-redundant sequences. When the two arrays were hybridized to cDNAs from the same set of male and female zebra finch brain samples, both arrays detected a common set of regulated transcripts with a Pearson correlation coefficient of 0.895. To stimulate use of these resources by the songbird research community and to maintain consistent technical standards, we devised a "Community Collaboration" mechanism whereby individual birdsong researchers develop experiments and provide tissues, but a single individual in the community is responsible for all RNA extractions, labelling and microarray hybridizations. CONCLUSION: Immediately, these results set the foundation for a coordinated set of 25 planned experiments by 16 research groups probing fundamental links between genome, brain, evolution and behavior in songbirds. Energetic application of genomic resources to research using songbirds should help illuminate how complex neural and behavioral traits emerge and evolve

"Best fit" framework synthesis: refining the method

Background Following publication of the first worked example of the “best fit” method of evidence synthesis for the systematic review of qualitative evidence in this journal, the originators of the method identified a need to specify more fully some aspects of this particular derivative of framework synthesis. Methods and Results We therefore present a second such worked example in which all techniques are defined and explained, and their appropriateness is assessed. Specified features of the method include the development of new techniques to identify theories in a systematic manner; the creation of an a priori framework for the synthesis; and the “testing” of the synthesis. An innovative combination of existing methods of quality assessment, analysis and synthesis is used to complete the process. This second worked example was a qualitative evidence synthesis of employees’ views of workplace smoking cessation interventions, in which the “best fit” method was found to be practical and fit for purpose. Conclusions The method is suited to producing context-specific conceptual models for describing or explaining the decision-making and health behaviours of patients and other groups. It offers a pragmatic means of conducting rapid qualitative evidence synthesis and generating programme theories relating to intervention effectiveness, which might be of relevance both to researchers and policy-makers

Accreting Millisecond X-Ray Pulsars

Accreting Millisecond X-Ray Pulsars (AMXPs) are astrophysical laboratories without parallel in the study of extreme physics. In this chapter we review the past fifteen years of discoveries in the field. We summarize the observations of the fifteen known AMXPs, with a particular emphasis on the multi-wavelength observations that have been carried out since the discovery of the first AMXP in 1998. We review accretion torque theory, the pulse formation process, and how AMXP observations have changed our view on the interaction of plasma and magnetic fields in strong gravity. We also explain how the AMXPs have deepened our understanding of the thermonuclear burst process, in particular the phenomenon of burst oscillations. We conclude with a discussion of the open problems that remain to be addressed in the future.Comment: Review to appear in "Timing neutron stars: pulsations, oscillations and explosions", T. Belloni, M. Mendez, C.M. Zhang Eds., ASSL, Springer; [revision with literature updated, several typos removed, 1 new AMXP added