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 knots and 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 invariant

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

Quantum computing based on semiconductor nanowires

A quantum computer will have computational power beyond that of conventional computers, which can be exploited for solving important and complex problems, such as predicting the conformations of large biological molecules. Materials play a major role in this emerging technology, as they can enable sophisticated operations, such as control over single degrees of freedom and their quantum states, as well as preservation and coherent transfer of these states between distant nodes. Here we assess the potential of semiconductor nanowires grown from the bottom-up as a materials platform for a quantum computer. We review recent experiments in which small bandgap nanowires are used to manipulate single spins in quantum dots and experiments on Majorana fermions, which are quasiparticles relevant for topological quantum computing

From InSb Nanowires to Nanocubes: Looking for the Sweet Spot

High aspect ratios are highly desired to fully exploit the one-dimensional properties of indium antimonide nanowires. Here we systematically investigate the growth mechanisms and find parameters leading to long and thin nanowires. Variation of the V/III ratio and the nanowire density are found to have the same influence on the “local” growth conditions and can control the InSb shape from thin nanowires to nanocubes. We propose that the V/III ratio controls the droplet composition and the radial growth rate and these parameters determine the nanowire shape. A sweet spot is found for nanowire interdistances around 500 nm leading to aspect ratios up to 35. High electron mobilities up to 3.5 × 10^4 cm^2 V^(–1) s^(–1) enable the realization of complex spintronic and topological devices

Knot invariants, Chern–Simons theory and the topological recursion

Cette thèse concerne la théorie de Chern-Simons, les invariants de noeuds, les intégrales matricielles formelles et à la théorie des cordes topologiques, ainsi que les relations entre ces différents domaines. Dans un premier temps, nous étudions les polynômes de HOMFLY et de Kauffman colorés des noeuds du tore àl'aide de la théorie de Chern–Simons. Nous obtenons une généralisation de la formule de Rosso-Jones, valable pour les noeuds du tore dans les espaces lenticulaires. Dans une deuxième partie, nous effectuons des vérification d'une conjecture sur la structure des invariants de noeuds, inspirée par la théorie des cordes. Par la suite, nous abordons la relation entre noeuds et courbes algébriques, qui provient de la dualité entre théorie de Chern-Simons et théorie des cordes topologiques de type B. Nous étendons cette relation aux noeuds du tore dans les espaces lenticulaires. Finalement, nous étudions une déformation à un paramètre des modèles de matrices

Knot Operators in Chern-Simons Gauge Theory

Ce travail concerne l'invariant quantique de HOMFLY défini dans le cadre de la théorie de Chern-Simons avec groupe de jauge SU(N). Le but est de reproduire une formule simple pour les invariants [Lin & Zheng 2006] en utilisant le formalisme des opérateurs de noeuds [Labastida et al. 1991]. Notre approche emploie exclusivement la théorie des représentations, en particulier l'opération d'Adams, et un opérateur diagonal que nous identifions à un twist fractionnaire [Morton & Manchon 2008]

The uses of the refined matrix model recursion

We study matrix models in the β-ensemble by building on the refined recursion relation proposed by Chekhov and Eynard. We present explicit results for the first β-deformed corrections in the one-cut and the two-cut cases, as well as two applications to supersymmetric gauge theories: the calculation of superpotentials in N=1gauge theories, and the calculation of vevs of surface operators in superconformal N=2theories and their Liouville duals. Finally, we study the β-deformation of the Chern–Simons matrix model. Our results indicate that this model does not provide an appropriate description of the Ω-deformed topological string on the resolved conifold, and therefore that the β-deformation might provide a different generalization of topological string theory in toric Calabi–Yau backgrounds

Probability of major depression classification based on the SCID, CIDI, and MINI diagnostic interviews: A synthesis of three individual participant data meta-analyses

Introduction: Three previous individual participant data meta-analyses (IPDMAs) reported that, compared to the Structured Clinical Interview for the DSM (SCID), alternative reference standards, primarily the Composite International Diagnostic Interview (CIDI) and the Mini International Neuropsychiatric Interview (MINI), tended to misclassify major depression status, when controlling for depression symptom severity. However, there was an important lack of precision in the results. Objective: To compare the odds of the major depression classification based on the SCID, CIDI, and MINI. Methods: We included and standardized data from 3 IPDMA databases. For each IPDMA, separately, we fitted binomial generalized linear mixed models to compare the adjusted odds ratios (aORs) of major depression classification, controlling for symptom severity and characteristics of participants, and the interaction between interview and symptom severity. Next, we synthesized results using a DerSimonian-Laird random-effects meta-analysis. Results: In total, 69,405 participants (7,574 [11%] with major depression) from 212 studies were included. Controlling for symptom severity and participant characteristics, the MINI (74 studies; 25,749 participants) classified major depression more often than the SCID (108 studies; 21,953 participants; aOR 1.46; 95% confidence interval [CI] 1.11-1.92]). Classification odds for the CIDI (30 studies; 21,703 participants) and the SCID did not differ overall (aOR 1.19; 95% CI 0.79-1.75); however, as screening scores increased, the aOR increased less for the CIDI than the SCID (interaction aOR 0.64; 95% CI 0.52-0.80). Conclusions: Compared to the SCID, the MINI classified major depression more often. The odds of the depression classification with the CIDI increased less as symptom levels increased. Interpretation of research that uses diagnostic interviews to classify depression should consider the interview characteristics.</p