Attaching handlebodies to 3-manifolds

The main theorem of this paper is a generalisation of well known results about Dehn surgery to the case of attaching handlebodies to a simple 3-manifold. The existence of a finite set of `exceptional' curves on the boundary of the 3-manifold is established. Provided none of these curves is attached to the boundary of a disc in a handlebody, the resulting manifold is shown to be word hyperbolic and `hyperbolike'. We then give constructions of gluing maps satisfying this condition. These take the form of an arbitrary gluing map composed with powers of a suitable homeomorphism of the boundary of the handlebodies.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol6/paper26.abs.htm

Local ensemble transform Kalman filter, a fast non-stationary control law for adaptive optics on ELTs: theoretical aspects and first simulation results

We propose a new algorithm for an adaptive optics system control law, based on the Linear Quadratic Gaussian approach and a Kalman Filter adaptation with localizations. It allows to handle non-stationary behaviors, to obtain performance close to the optimality defined with the residual phase variance minimization criterion, and to reduce the computational burden with an intrinsically parallel implementation on the Extremely Large Telescopes (ELTs).Comment: This paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://www.opticsinfobase.org/oe/ . Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under la

An algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary

We provide an algorithm to determine the Heegaard genus of simple 3-manifolds with non-empty boundary. More generally, we supply an algorithm to determine (up to ambient isotopy) all the Heegaard splittings of any given genus for the manifold. As a consequence, the tunnel number of a hyperbolic link is algorithmically computable. Our techniques rely on Rubinstein's work on almost normal surfaces, and also a new structure called a partially flat angled ideal triangulation.Comment: 23 pages, 14 figure

Local Ensemble Transform Kalman Filter: a non-stationary control law for complex adaptive optics systems on ELTs

We propose a new algorithm for an adaptive optics system control law which allows to reduce the computational burden in the case of an Extremely Large Telescope (ELT) and to deal with non-stationary behaviors of the turbulence. This approach, using Ensemble Transform Kalman Filter and localizations by domain decomposition is called the local ETKF: the pupil of the telescope is split up into various local domains and calculations for the update estimate of the turbulent phase on each domain are performed independently. This data assimilation scheme enables parallel computation of markedly less data during this update step. This adapts the Kalman Filter to large scale systems with a non-stationary turbulence model when the explicit storage and manipulation of extremely large covariance matrices are impossible. First simulation results are given in order to assess the theoretical analysis and to demonstrate the potentiality of this new control law for complex adaptive optics systems on ELTs.Comment: Proceedings of the AO4ELT3 conference; 8 pages, 3 figure

Different routes in which protein P27KIP1 is involved in oncogenesis

Treballs Finals de Grau de Farmàcia, Facultat de Farmàcia i Ciències de l'Alimentació, Universitat de Barcelona, 2022. Tutor/a: María Jesús Pujol Sobreví

Achieving Very High PV Penetration

This article argues that optimally deployed intermittency solutions could affordably transform solar power generation into the firm power delivery system modern economies require, thereby enabling very high solar penetration and the displacement conventional power generation. The optimal deployment of these high‐penetration enabling solutions imply the existence of a healthy power grid, and therefore imply a central role for utilities and grid operators. This article also argues that a value‐based electricity compensation mechanism, recognizing the multifaceted, penetration‐dependent value and cost of solar energy, and capable of shaping consumption patterns to optimally match resource and demand, would be an effective vehicle to enable high solar penetration and deliver affordable firm power generation

Phase-stable source of polarization-entangled photons in a linear double-pass configuration

We demonstrate a compact, robust, and highly efficient source of polarization-entangled photons, based on linear bi-directional down-conversion in a novel 'folded sandwich' configuration. Bi-directionally pumping a single periodically poled KTiOPO$_4$ (ppKTP) crystal with a 405-nm laser diode, we generate entangled photon pairs at the non-degenerate wavelengths 784 nm (signal) and 839 nm (idler), and achieve an unprecedented detection rate of 11.8 kcps for 10.4 $\mu$W of pump power (1.1 million pairs / mW), in a 2.9-nm bandwidth, while maintaining a very high two-photon entanglement quality, with a Bell-state fidelity of $99.3\pm0.3$%