On local comparison between various metrics on Teichmüller spaces

International audienceThere are several Teichmüller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint ( a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal Teichmüller space, the length spectrum Teichmüller space, the Fenchel-Nielsen Teichmüller space, and there are others. In general, these spaces are set-theoretically different. An important question is therefore to understand relations between these spaces. Each of these spaces is equipped with its own metric, and under some hypotheses, there are inclusions between these spaces. In this paper, we obtain local metric comparison results on these inclusions, namely, we show that the inclusions are locally bi-Lipschitz under certain hypotheses. To obtain these results, we use some hyperbolic geometry estimates that give new results also for surfaces of finite type. We recall that in the case of a surface of finite type, all these Teichmüller spaces coincide setwise. In the case of a surface of finite type with no boundary components (and possibly with punctures), we show that the restriction of the identity map to any thick part of Teichmüller space is globally bi-Lipschitz with respect to the length spectrum metric and the classical Teichmüller metric on the domain and on the range respectively. In the case of a surface of finite type with punctures and boundary components, there is a metric on the Teichmüller space which we call the arc metric, whose definition is analogous to the length spectrum metric, but which uses lengths of geodesic arcs instead of lengths of closed geodesics. We show that the restriction of the identity map restricted to any ``relative thick" part of Teichmüller space is globally bi-Lipschitz, with respect to any of the three metrics: the length spectrum metric, the Teichmüller metric and the arc metric on the domain and on the range

Fundamental Strings as Black Bodies

We show that the decay spectrum of massive excitations in perturbative string theories is thermal when averaged over the (many) initial degenerate states. We first compute the inclusive photon spectrum for open strings at the tree level showing that a black body spectrum with the Hagedorn temperature emerges in the averaging. A similar calculation for a massive closed string state with winding and Kaluza-Klein charges shows that the emitted graviton spectrum is thermal with a "grey-body" factor, which approaches one near extremality. These results uncover a simple physical meaning of the Hagedorn temperature and provide an explicit microscopic derivation of the black body spectrum from a unitary $S$ matrix.Comment: some changes in the Discussion section and in the reference list. 11 pages, Late

Sewing Constraints and Non-Orientable Open Strings

We extend to non-orientable surfaces previous work on sewing constraints in Conformal Field Theory. A new constraint, related to the real projective plane, is described and is used to illustrate the correspondence with a previous construction of open-string spectra.Comment: phyzzx, 11 pages and 4 figures, ROM2F-93/3

Characterization of ellipses as uniformly dense sets with respect to a family of convex bodies

Let K \subset R^N be a convex body containing the origin. A measurable set G \subset R^N with positive Lebesgue measure is said to be uniformly K-dense if, for any fixed r > 0, the measure of G \cap (x + rK) is constant when x varies on the boundary of G (here, x + rK denotes a translation of a dilation of K). We first prove that G must always be strictly convex and at least C1,1-regular; also, if K is centrally symmetric, K must be strictly convex, C1,1-regular and such that K = G - G up to homotheties; this implies in turn that G must be C2,1- regular. Then for N = 2, we prove that G is uniformly K-dense if and only if K and G are homothetic to the same ellipse. This result was already proven by Amar, Berrone and Gianni in [3]. However, our proof removes their regularity assumptions on K and G and, more importantly, it is susceptible to be generalized to higher dimension since, by the use of Minkowski's inequality and an affine inequality, avoids the delicate computations of the higher-order terms in the Taylor expansion near r = 0 for the measure of G\cap(x+rK) (needed in [3])

Influence of Blackberry Plants on the Aroma Profile of Vitis vinifera L. cv. Pinot Noir

V. vinifera cv. Pinot noir vines were grown in pots together with blackberry plants and the effect of this association on the grape aroma was assessed. Preliminary data showed that vines that cohabited with blackberry had a different aroma profile compared to vine grown alone. The association with blackberry increased the concentration of 30 out 74 free aroma compounds and of 24 out 95 bound ones. No aroma compound was identified exclusively in the treated grapes

Path integral evaluation of Dbrane amplitudes

We extend Polchinski's evaluation of the measure for the one-loop closed string path integral to open string tree amplitudes with boundaries and crosscaps embedded in Dbranes. We explain how the nonabelian limit of near-coincident Dbranes emerges in the path integral formalism. We give a careful path integral derivation of the cylinder amplitude including the modulus dependence of the volume of the conformal Killing group.Comment: Extended version replacing hep-th/9903184, includes discussion of nonabelian limit, Latex, 10 page

Can One Teach Old Drugs New Tricks? Reformulating to Repurpose Chloroquine and Hydroxychloroquine

The outbreak of the novel corona virus disease, COVID-19, has presented health care professionals with the unique challenges of trying to select appropriate pharmacological treatments with little time available for drug testing. Given the development times and manufacturing requirements for new products, Value Added Medicines (repurposing – reformulation of existing drugs) could be one possibility to beat the COVID-19 outbreak. This review explores reformulation alternatives which could be progressed with chloroquine and hydroxychloroquine; two antimalarial drugs, that are being tested on a global scale as a potential therapeutic option. The key areas for improvement have been reviewed and the potential solutions to the problems and limitations of current formulations are discussed. The pharmaceutical challenges discussed are those of highly soluble drugs, needed to be given at high doses and presenting a real bitter taste challenge with significant gastrointestinal side effects that could be translated and repurposed into fit for purpose reformulations

Impaired postural control in patients affected by tension-type headache.

Sixteen subjects, affected by chronic tension-type headache (TTH) accordingly to the International Headache Society Classification (1988) criteria, in presence of tenderness in pericranial muscles,with a mean age of 37+/-11.8 years, and ten healthy volunteer subjects, age and sex matched, were submitted to postural analysis by Static Posturography (S.Ve.P. Amplaid). Aim of the study was to evaluate whether patients with TTH have disturbed postural control, as compared to normal subjects. Postural analysis considered all posturographic variables but focused on spectral frequency analysis of body sway. In both open (OE) and closed eyes (CE) condition, spectral frequency analysis showed a significantly increased body sway at low (OE= p < or = 0.01; CE= p < or = 0.01) and middle (OE= p < or = 0.01; CE= p < or = 0.01) frequencies on the antero-posterior (y) plane and at low frequencies (OE= p < or = 0.05; CE= p < or = 0.05) on the lateral (x) plane. Statistical analysis was performed using the Student's t test for unpaired data, p value 0.05 defined significant. The proprioceptive input seems to be predominant at middle and high frequencies in maintaining posture, our results seem then to suggest a proprioceptive disturbance in TTH patients. The disturbance is likely related to chronic pericranial muscle contraction and tenderness. Posturography and spectral analysis may help not only in the diagnosis of a postural disturbance but even more in the follow-up of TTH patients, during and after a medical and/or a rehabilitative treatment

Dynamics near the critical point: the hot renormalization group in quantum field theory

The perturbative approach to the description of long wavelength excitations at high temperature breaks down near the critical point of a second order phase transition. We study the \emph{dynamics} of these excitations in a relativistic scalar field theory at and near the critical point via a renormalization group approach at high temperature and an $\epsilon$ expansion in $d=5-\epsilon$ space-time dimensions. The long wavelength physics is determined by a non-trivial fixed point of the renormalization group. At the critical point we find that the dispersion relation and width of quasiparticles of momentum $p$ is $\omega_p \sim p^{z}$ and $\Gamma_p \sim (z-1) \omega_p$ respectively, the group velocity of quasiparticles $v_g \sim p^{z-1}$ vanishes in the long wavelength limit at the critical point. Away from the critical point for $T\gtrsim T_c$ we find $\omega_p \sim \xi^{-z}[1+(p \xi)^{2z}]^{{1/2}}$ and $\Gamma_p \sim (z-1) \omega_p \frac{(p \xi)^{2z}}{1+(p \xi)^{2z}}$ with $\xi$ the finite temperature correlation length $\xi \propto |T-T_c|^{-\nu}$. The new \emph{dynamical} exponent $z$ results from anisotropic renormalization in the spatial and time directions. For a theory with O(N) symmetry we find $z=1+ \epsilon \frac{N+2}{(N+8)^2}+\mathcal{O}(\epsilon^2)$. Critical slowing down, i.e, a vanishing width in the long-wavelength limit, and the validity of the quasiparticle picture emerge naturally from this analysis.Comment: Discussion on new dynamical universality class. To appear in Phys. Rev.