An infinitesimally nonrigid polyhedron with nonstationary volume in the Lobachevsky 3-space

We give an example of an infinitesimally nonrigid polyhedron in the Lobachevsky 3-space and construct an infinitesimal flex of that polyhedron such that the volume of the polyhedron isn't stationary under the flex.Comment: 10 pages, 2 Postscript figure

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators

In this letter,we present our conjecture on the connection between the Kontsevich--Witten and the Hurwitz tau-functions. The conjectural formula connects these two tau-functions by means of the $GL(\infty)$ group element. An important feature of this group element is its simplicity: this is a group element of the Virasoro subalgebra of $gl(\infty)$. If proved, this conjecture would allow to derive the Virasoro constraints for the Hurwitz tau-function, which remain unknown in spite of existence of several matrix model representations, as well as to give an integrable operator description of the Kontsevich--Witten tau-function.Comment: 13 page

Rigidity and volume preserving deformation on degenerate simplices

Given a degenerate $(n+1)$-simplex in a $d$-dimensional space $M^d$ (Euclidean, spherical or hyperbolic space, and $d\geq n$), for each $k$, $1\leq k\leq n$, Radon's theorem induces a partition of the set of $k$-faces into two subsets. We prove that if the vertices of the simplex vary smoothly in $M^d$ for $d=n$, and the volumes of $k$-faces in one subset are constrained only to decrease while in the other subset only to increase, then any sufficiently small motion must preserve the volumes of all $k$-faces; and this property still holds in $M^d$ for $d\geq n+1$ if an invariant $c_{k-1}(\alpha^{k-1})$ of the degenerate simplex has the desired sign. This answers a question posed by the author, and the proof relies on an invariant $c_k(\omega)$ we discovered for any $k$-stress $\omega$ on a cell complex in $M^d$. We introduce a characteristic polynomial of the degenerate simplex by defining $f(x)=\sum_{i=0}^{n+1}(-1)^{i}c_i(\alpha^i)x^{n+1-i}$, and prove that the roots of $f(x)$ are real for the Euclidean case. Some evidence suggests the same conjecture for the hyperbolic case.Comment: 27 pages, 2 figures. To appear in Discrete & Computational Geometr

HOMFLY and superpolynomials for figure eight knot in all symmetric and antisymmetric representations

Explicit answer is given for the HOMFLY polynomial of the figure eight knot $4_1$ in arbitrary symmetric representation R=[p]. It generalizes the old answers for p=1 and 2 and the recently derived results for p=3,4, which are fully consistent with the Ooguri-Vafa conjecture. The answer can be considered as a quantization of the \sigma_R = \sigma_{[1]}^{|R|} identity for the "special" polynomials (they define the leading asymptotics of HOMFLY at q=1), and arises in a form, convenient for comparison with the representation of the Jones polynomials as sums of dilogarithm ratios. In particular, we construct a difference equation ("non-commutative A-polynomial") in the representation variable p. Simple symmetry transformation provides also a formula for arbitrary antisymmetric (fundamental) representation R=[1^p], which also passes some obvious checks. Also straightforward is a deformation from HOMFLY to superpolynomials. Further generalizations seem possible to arbitrary Young diagrams R, but these expressions are harder to test because of the lack of alternative results, even partial.Comment: 14 page

Molecular and Microbial Microenvironments in Chronically Diseased Lungs Associated with Cystic Fibrosis.

To visualize the personalized distributions of pathogens and chemical environments, including microbial metabolites, pharmaceuticals, and their metabolic products, within and between human lungs afflicted with cystic fibrosis (CF), we generated three-dimensional (3D) microbiome and metabolome maps of six explanted lungs from three cystic fibrosis patients. These 3D spatial maps revealed that the chemical environments differ between patients and within the lungs of each patient. Although the microbial ecosystems of the patients were defined by the dominant pathogen, their chemical diversity was not. Additionally, the chemical diversity between locales in the lungs of the same individual sometimes exceeded interindividual variation. Thus, the chemistry and microbiome of the explanted lungs appear to be not only personalized but also regiospecific. Previously undescribed analogs of microbial quinolones and antibiotic metabolites were also detected. Furthermore, mapping the chemical and microbial distributions allowed visualization of microbial community interactions, such as increased production of quorum sensing quinolones in locations where Pseudomonas was in contact with Staphylococcus and Granulicatella, consistent with in vitro observations of bacteria isolated from these patients. Visualization of microbe-metabolite associations within a host organ in early-stage CF disease in animal models will help elucidate the complex interplay between the presence of a given microbial structure, antibiotics, metabolism of antibiotics, microbial virulence factors, and host responses.IMPORTANCE Microbial infections are now recognized to be polymicrobial and personalized in nature. Comprehensive analysis and understanding of the factors underlying the polymicrobial and personalized nature of infections remain limited, especially in the context of the host. By visualizing microbiomes and metabolomes of diseased human lungs, we reveal how different the chemical environments are between hosts that are dominated by the same pathogen and how community interactions shape the chemical environment or vice versa. We highlight that three-dimensional organ mapping methods represent hypothesis-building tools that allow us to design mechanistic studies aimed at addressing microbial responses to other microbes, the host, and pharmaceutical drugs

Ground-State of Charged Bosons Confined in a Harmonic Trap

We study a system composed of N identical charged bosons confined in a harmonic trap. Upper and lower energy bounds are given. It is shown in the large N limit that the ground-state energy is determined within an accuracy of $\pm 8$ and that the mean field theory provides a reasonable result with relative error of less than 16% for the binding energy .Comment: 15 page

Superpolynomials for toric knots from evolution induced by cut-and-join operators

The colored HOMFLY polynomials, which describe Wilson loop averages in Chern-Simons theory, possess an especially simple representation for torus knots, which begins from quantum R-matrix and ends up with a trivially-looking split W representation familiar from character calculus applications to matrix models and Hurwitz theory. Substitution of MacDonald polynomials for characters in these formulas provides a very simple description of "superpolynomials", much simpler than the recently studied alternative which deforms relation to the WZNW theory and explicitly involves the Littlewood-Richardson coefficients. A lot of explicit expressions are presented for different representations (Young diagrams), many of them new. In particular, we provide the superpolynomial P_[1]^[m,km\pm 1] for arbitrary m and k. The procedure is not restricted to the fundamental (all antisymmetric) representations and the torus knots, still in these cases some subtleties persist.Comment: 23 pages + Tables (51 pages

Head Position in Stroke Trial (HeadPoST)- sitting-up vs lying-flat positioning of patients with acute stroke: study protocol for a cluster randomised controlled trial

Background Positioning a patient lying-flat in the acute phase of ischaemic stroke may improve recovery and reduce disability, but such a possibility has not been formally tested in a randomised trial. We therefore initiated the Head Position in Stroke Trial (HeadPoST) to determine the effects of lying-flat (0°) compared with sitting-up (≥30°) head positioning in the first 24 hours of hospital admission for patients with acute stroke. Methods/Design We plan to conduct an international, cluster randomised, crossover, open, blinded outcome-assessed clinical trial involving 140 study hospitals (clusters) with established acute stroke care programs. Each hospital will be randomly assigned to sequential policies of lying-flat (0°) or sitting-up (≥30°) head position as a ‘business as usual’ stroke care policy during the first 24 hours of admittance. Each hospital is required to recruit 60 consecutive patients with acute ischaemic stroke (AIS), and all patients with acute intracerebral haemorrhage (ICH) (an estimated average of 10), in the first randomised head position policy before crossing over to the second head position policy with a similar recruitment target. After collection of in-hospital clinical and management data and 7-day outcomes, central trained blinded assessors will conduct a telephone disability assessment with the modified Rankin Scale at 90 days. The primary outcome for analysis is a shift (defined as improvement) in death or disability on this scale. For a cluster size of 60 patients with AIS per intervention and with various assumptions including an intracluster correlation coefficient of 0.03, a sample size of 16,800 patients at 140 centres will provide 90 % power (α 0.05) to detect at least a 16 % relative improvement (shift) in an ordinal logistic regression analysis of the primary outcome. The treatment effect will also be assessed in all patients with ICH who are recruited during each treatment study period. Discussion HeadPoST is a large international clinical trial in which we will rigorously evaluate the effects of different head positioning in patients with acute stroke. Trial registration ClinicalTrials.gov identifier: NCT02162017 (date of registration: 27 April 2014); ANZCTR identifier: ACTRN12614000483651 (date of registration: 9 May 2014). Protocol version and date: version 2.2, 19 June 2014

Challenges in QCD matter physics - The Compressed Baryonic Matter experiment at FAIR

Substantial experimental and theoretical efforts worldwide are devoted to explore the phase diagram of strongly interacting matter. At LHC and top RHIC energies, QCD matter is studied at very high temperatures and nearly vanishing net-baryon densities. There is evidence that a Quark-Gluon-Plasma (QGP) was created at experiments at RHIC and LHC. The transition from the QGP back to the hadron gas is found to be a smooth cross over. For larger net-baryon densities and lower temperatures, it is expected that the QCD phase diagram exhibits a rich structure, such as a first-order phase transition between hadronic and partonic matter which terminates in a critical point, or exotic phases like quarkyonic matter. The discovery of these landmarks would be a breakthrough in our understanding of the strong interaction and is therefore in the focus of various high-energy heavy-ion research programs. The Compressed Baryonic Matter (CBM) experiment at FAIR will play a unique role in the exploration of the QCD phase diagram in the region of high net-baryon densities, because it is designed to run at unprecedented interaction rates. High-rate operation is the key prerequisite for high-precision measurements of multi-differential observables and of rare diagnostic probes which are sensitive to the dense phase of the nuclear fireball. The goal of the CBM experiment at SIS100 (sqrt(s_NN) = 2.7 - 4.9 GeV) is to discover fundamental properties of QCD matter: the phase structure at large baryon-chemical potentials (mu_B > 500 MeV), effects of chiral symmetry, and the equation-of-state at high density as it is expected to occur in the core of neutron stars. In this article, we review the motivation for and the physics programme of CBM, including activities before the start of data taking in 2022, in the context of the worldwide efforts to explore high-density QCD matter.Comment: 15 pages, 11 figures. Published in European Physical Journal