String theory and the Kauffman polynomial

We propose a new, precise integrality conjecture for the colored Kauffman polynomial of knots and links inspired by large N dualities and the structure of topological string theory on orientifolds. According to this conjecture, the natural knot invariant in an unoriented theory involves both the colored Kauffman polynomial and the colored HOMFLY polynomial for composite representations, i.e. it involves the full HOMFLY skein of the annulus. The conjecture sheds new light on the relationship between the Kauffman and the HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide various non-trivial tests of the conjecture and we sketch the string theory arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos corrected, final version to appear in CM

Chern-Simons Invariants of Torus Links

We compute the vacuum expectation values of torus knot operators in Chern-Simons theory, and we obtain explicit formulae for all classical gauge groups and for arbitrary representations. We reproduce a known formula for the HOMFLY invariants of torus links and we obtain an analogous formula for Kauffman invariants. We also derive a formula for cable knots. We use our results to test a recently proposed conjecture that relates HOMFLY and Kauffman invariants.Comment: 20 pages, 5 figures; v2: minor changes, version submitted to AHP. The final publication is available at http://www.springerlink.com/content/a2614232873l76h6

Instanton counting, Macdonald function and the moduli space of D-branes

We argue the connection of Nekrasov's partition function in the \Omega background and the moduli space of D-branes, suggested by the idea of geometric engineering and Gopakumar-Vafa invariants. In the instanton expansion of N=2 SU(2) Yang-Mills theory the Nakrasov's partition function with equivariant parameters \epsilon_1, \epsilon_2 of toric action on C^2 factorizes correctly as the character of SU(2)_L \times SU(2)_R spin representation. We show that up to two instantons the spin contents are consistent with the Lefschetz action on the moduli space of D2-branes on (local) F_0. We also present an attempt at constructing a refined topological vertex in terms of the Macdonald function. The refined topological vertex with two parameters of T^2 action allows us to obtain the generating functions of equivariant \chi_y and elliptic genera of the Hilbert scheme of n points on C^2 by the method of topological vertex.Comment: 33 pages, 2 figures, (v2) minor changes, references added, (v3) Comments and more references adde

Torus knots and mirror symmetry

We propose a spectral curve describing torus knots and links in the B-model. In particular, the application of the topological recursion to this curve generates all their colored HOMFLY invariants. The curve is obtained by exploiting the full Sl(2, Z) symmetry of the spectral curve of the resolved conifold, and should be regarded as the mirror of the topological D-brane associated to torus knots in the large N Gopakumar-Vafa duality. Moreover, we derive the curve as the large N limit of the matrix model computing torus knot invariants.Comment: 30 pages + appendix, 3 figure

Cognitive endpoints for therapy development for neuronopathic mucopolysaccharidoses: Results of a consensus procedure

The design and conduct of clinical studies to evaluate the effects of novel therapies on central nervous system manifestations in children with neuronopathic mucopolysaccharidoses is challenging. Owing to the rarity of these disorders, multinational studies are often needed to recruit enough patients to provide meaningful data and statistical power. This can make the consistent collection of reliable data across study sites difficult. To address these challenges, an International MPS Consensus Conference for Cognitive Endpoints was convened to discuss approaches for evaluating cognitive and adaptive function in patients with mucopolysaccharidoses. The goal was to develop a consensus on best practice for the design and conduct of clinical studies investigating novel therapies for these conditions, with particular focus on the most appropriate outcome measures for cognitive function and adaptive behavior. The outcomes from the consensus panel discussion are reported here

Measurement of the CP-Violating Asymmetry Amplitude sin2β\beta

We present results on time-dependent CP-violating asymmetries in neutral B decays to several CP eigenstates. The measurements use a data sample of about 88 million Y(4S) --> B Bbar decays collected between 1999 and 2002 with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. We study events in which one neutral B meson is fully reconstructed in a final state containing a charmonium meson and the other B meson is determined to be either a B0 or B0bar from its decay products. The amplitude of the CP-violating asymmetry, which in the Standard Model is proportional to sin2beta, is derived from the decay-time distributions in such events. We measure sin2beta = 0.741 +/- 0.067 (stat) +/- 0.033 (syst) and |lambda| = 0.948 +/- 0.051 (stat) +/- 0.017 (syst). The magnitude of lambda is consistent with unity, in agreement with the Standard Model expectation of no direct CP violation in these modes

The HERMES Spectrometer

The HERMES experiment is collecting data on inclusive and semi-inclusive deep inelastic scattering of polarised positrons from polarised targets of Il, D, and He-3. These data give information on the spin structure of the nucleon. This paper describes the forward angle spectrometer built for this purpose. The spectrometer includes numerous tracking chambers (micro-strip gas chambers, drift and proportional chambers) in front of and behind a 1.3 T.m magnetic field, as well as an extensive set of detectors for particle identification (a lead-glass calorimeter, a pre-shower detector, a transition radiation detector, and a threshold Cherenkov detector). Two of the main features of the spectrometer are its good acceptance and identification of both positrons and hadrons, in particular pions. These characteristics, together with the purity of the targets, are allowing HERMES to make unique contributions to the understanding of how the spins of the quarks contribute to the spin of the nucleon. (C) 1998 Elsevier Science B.V. All rights reserved

Performance of reconstruction and identification of τ leptons decaying to hadrons and vτ in pp collisions at √s=13 TeV

The algorithm developed by the CMS Collaboration to reconstruct and identify τ leptons produced in proton-proton collisions at √s=7 and 8 TeV, via their decays to hadrons and a neutrino, has been significantly improved. The changes include a revised reconstruction of π⁰ candidates, and improvements in multivariate discriminants to separate τ leptons from jets and electrons. The algorithm is extended to reconstruct τ leptons in highly Lorentz-boosted pair production, and in the high-level trigger. The performance of the algorithm is studied using proton-proton collisions recorded during 2016 at √s=13 TeV, corresponding to an integrated luminosity of 35.9 fb¯¹. The performance is evaluated in terms of the efficiency for a genuine τ lepton to pass the identification criteria and of the probabilities for jets, electrons, and muons to be misidentified as τ leptons. The results are found to be very close to those expected from Monte Carlo simulation