Canard Cycles and Poincar\'e Index of Non-Smooth Vector Fields on the Plane

This paper is concerned with closed orbits of non-smooth vector fields on the plane. For a subclass of non-smooth vector fields we provide necessary and sufficient conditions for the existence of canard kind solutions. By means of a regularization we prove that the canard cycles are singular orbits of singular perturbation problems which are limit periodic sets of a sequence of limit cycles. Moreover, we generalize the Poincar\'e Index for non-smooth vector fields.Comment: 20 pages, 25 figure

Mechanical oscillations in lasing microspheres

We investigate the feasibility of activating coherent mechanical oscillations in lasing microspheres by modulating the laser emission at a mechanical eigenfrequency. To this aim, 1.5% Nd3+:Barium-Titanium-Silicate microspheres with diameters around 50 {\mu}m were used as high quality factor (Q>10^6) whispering gallery mode lasing cavities. We have implemented a pump-and-probe technique in which the pump laser used to excite the Nd3+ ions is focused on a single microsphere with a microscope objective and a probe laser excites a specific optical mode with the evanescent field of a tapered fibre. The studied microspheres show monomode and multi-mode lasing action, which can be modulated in the best case up to 10 MHz. We have optically transduced thermally-activated mechanical eigenmodes appearing in the 50-70 MHz range, the frequency of which decreases with increasing the size of the microspheres. In a pump-and-probe configuration we observed modulation of the probe signal up to the maximum pump modulation frequency of our experimental setup, i.e., 20 MHz. This modulation decreases with frequency and is unrelated to lasing emission, pump scattering or thermal effects. We associate this effect to free-carrier-dispersion induced by multiphoton pump light absorption. On the other hand, we conclude that, in our current experimental conditions, it was not possible to resonantly excite the mechanical modes. Finally, we discuss on how to overcome these limitations by increasing the modulation frequency of the lasing emission and decreasing the frequency of the mechanical eigenmodes displaying a strong degree of optomechanical coupling.Comment: 17 pages, 5 figure

Group Strategyproof Pareto-Stable Marriage with Indifferences via the Generalized Assignment Game

We study the variant of the stable marriage problem in which the preferences of the agents are allowed to include indifferences. We present a mechanism for producing Pareto-stable matchings in stable marriage markets with indifferences that is group strategyproof for one side of the market. Our key technique involves modeling the stable marriage market as a generalized assignment game. We also show that our mechanism can be implemented efficiently. These results can be extended to the college admissions problem with indifferences

Anderson Photon-Phonon Colocalization in Certain Random Superlattices

International audienceFundamental observations in physics ranging from gravitational wave detection to laser cooling of a nanomechanical oscillator into its quantum ground state rely on the interaction between the optical and the mechanical degrees of freedom. A key parameter to engineer this interaction is the spatial overlap between the two fields, optimized in carefully designed resonators on a case-by-case basis. Disorder is an alternative strategy to confine light and sound at the nanoscale. However, it lacks an a priori mechanism guaranteeing a high degree of colocalization due to the inherently complex nature of the underlying interference processes. Here, we propose a way to address this challenge by using GaAs=AlAs vertical distributed Bragg reflectors with embedded geometrical disorder. Because of a remarkable coincidence in the physical parameters governing light and motion propagation in these two materials, the equations for both longitudinal acoustic waves and normal-incidence light become practically equivalent for excitations of the same wavelength. This guarantees spatial overlap between the electromagnetic and displacement fields of specific photon-phonon pairs, leading to strong light-matter interaction. In particular, a statistical enhancement in the vacuum optomechanical coupling rate, g o , is found, making this system a promising candidate to explore Anderson localization of high frequency (∼20 GHz) phonons enabled by cavity optomechanics. The colocalization effect shown here unlocks the access to unexplored localization phenomena and the engineering of light-matter interactions mediated by Anderson-localized states

Somatotype and digital dermatoglyphic in mexican football players

La valoración de la forma corporal y de las capacidades físicas es una necesidad para la selección, clasificación y entrenamiento de los jugadores de futbol. El presente estudio examinó en futbolistas profesionales mexicanos (N = 49) la relación entre clases de somatotipo y clases de capacidades físicas de acuerdo a dermatoglifia dactilar. Las frecuencias de clases de somatotipo y clases de capacidad física fueron comparadas entre subgrupos de futbolistas. Una mayor proporción de futbolistas se caracterizó por somatotipo mesomorfo balanceado con dermatoglifia tipo 2 y 3 correspondiente a fuerza, fuerza explosiva y velocidad. Esto es consistente con hallazgos previos en futbolistas chilenos y brasileños, extendiendo por tanto la evidencia disponible acerca de somatotipo y dermatoglifia en futbolistas latinoamericanosEvaluating body shape and capacities is needed for selection, classification and training of football players. The present study examined in Mexican male football players (N = 49) the relationship between types of somatotype and types of physical capacities according to digital dermatoglyphics. The frequencies of types of somatotype and of physical capacities were compared between football players subgroups. A higher proportion of football players was characterised by a balanced mesomorph somatotype with dermatoglyphic type 2 and 3 corresponding to strength, explosive strength and velocity. This is consistent with previous findings in Chilenean and Brazilian footballers, Therefore extending the available evidence of somatotype and dermatoglyphics in Latin American football player

Order quantification of hexagonal periodic arrays fabricated by in situ solvent-assisted nanoimprint lithography of block copolymers

arXiv:1403.2250v1Directed self-assembly of block copolymer polystyrene-b-polyethylene oxide (PS-b-PEO) thin film was achieved by a one-pot methodology of solvent vapor assisted nanoimprint lithography (SAIL). Simultaneous solvent-anneal and imprinting of a PS-b-PEO thin film on silicon without surface pre-treatments yielded a 250 nm line grating decorated with 20 nm diameter nanodots array over a large surface area of up to 4' wafer scale. The grazing-incidence small-angle x-ray scattering diffraction pattern showed the fidelity of the NIL stamp pattern replication and confirmed the periodicity of the BCP of 40 nm. The order of the hexagonally arranged nanodot lattice was quantified by SEM image analysis using the opposite partner method and compared to conventionally solvent-annealed block copolymer films. The imprint-based SAIL methodology thus demonstrated an improvement in ordering of the nanodot lattice of up to 50%, and allows significant time and cost reduction in the processing of these structures.The research leading to these results received funding from the European Union FP7 under the project LAMAND (grant agreement n° 245565), NANOFUNCTION (grant agreement no. 257375, FP7-ICT-2009-5) and by the Spanish Ministry of Economics and Competitiveness under project TAPHOR contract no. MAT2012-31392 (Plan Nacional de I + D + I (2008–2011)Peer Reviewe

Mechanical oscillations in lasing microspheres

We investigate the feasibility of activating coherent mechanical oscillations in lasing microspheres by modulating the laser emission at a mechanical eigenfrequency. To this aim, 1.5%Nd3+:Barium-Titanium-Silicate microspheres with diameters around 50 μm were used as high quality factor (Q>106) whispering gallery mode lasing cavities. We have implemented a pump-and-probe technique in which the pump laser used to excite the Nd3+ ions is focused on a single microsphere with a microscope objective and a probe laser excites a specific optical mode with the evanescent field of a tapered fibre. The studied microspheres show monomode and multi-mode lasing action, which can be modulated in the best case up to 10 MHz. We have optically transduced thermally-activated mechanical eigenmodes appearing in the 50-70 MHz range, the frequency of which decreases with increasing the size of the microspheres. In a pump-and-probe configuration we observed modulation of the probe signal up to the maximum pump modulation frequency of our experimental setup, i.e., 20 MHz. This modulation decreases with frequency and is unrelated to lasing emission, pump scattering or thermal effects. We associate this effect to free-carrier-dispersion induced by multiphoton pump light absorption. On the other hand, we conclude that, in our current experimental conditions, it was not possible to resonantly excite the mechanical modes. Finally, we discuss on how to overcome these limitations by increasing the modulation frequency of the lasing emission and decreasing the frequency of the mechanical eigenmodes displaying a strong degree of optomechanical coupling

Medical resource use in patients with psoriatic arthritis in a comprehensive rheumatological center in Colombia

Psoriatic arthritis (PsA), a chronic systemic inflammatory disorder, impairs the quality of life of patients. The aim of this study was to describe the medical resource use in patients with PsA in a comprehensive rheumatological center in Colombia. We retrospectively analyzed patients diagnosed with PsA who were attended in a center of excellence for rheumatic diseases located in Bogotá, D.C. Colombia, from January to December 2019. A database of medical records was analyzed to identify the use of medical resources classified by specialized physician visits, medications and ambulatory services (e.g., diagnostic, laboratory or image procedures, physical therapy). We reported absolute and relative frequencies among diagnostic groups. This study had no risk for patients. Ninety-six patients with PsA were studied, 57% were women. The mean age was 58.08 (±12.3 years), 90.63% of diagnostic was arthropathic psoriasis, other diagnostics were rheumatoid arthritis without rheumatoid factor, unspecified site (2.08%) and psoriasis, unspecified (2.08%) (ICD-10 code L405, M060, L409, respectively). In terms of treatments, most of the patients used a conventional disease-modifying antirheumatic drugs (DMARDs), methotrexate was the most frequent (represented the 14% of prescription and 78% of patients). On the other hand, 56.25% of patients receive treatment with biological DMARDs (10% of prescription). Among these biologicals, adalimumab (17.71%) and secukinumab (16.67%) were the most used. Regarding other health services, the visit to the specialist and the RX were the most common (83.33% of patients). Chest RX and column RX (17.71% each) had the highest frequency. This is one of the first approaches to the estimation of use of medical resources of PsA in Colombia. Frequency of DMARS use was associated to the severity and medical control of patients

Piecewise smooth systems near a co-dimension 2 discontinuity manifold: can one say what should happen?

We consider a piecewise smooth system in the neighborhood of a co-dimension 2 discontinuity manifold $\Sigma$. Within the class of Filippov solutions, if $\Sigma$ is attractive, one should expect solution trajectories to slide on $\Sigma$. It is well known, however, that the classical Filippov convexification methodology is ambiguous on $\Sigma$. The situation is further complicated by the possibility that, regardless of how sliding on $\Sigma$ is taking place, during sliding motion a trajectory encounters so-called generic first order exit points, where $\Sigma$ ceases to be attractive. In this work, we attempt to understand what behavior one should expect of a solution trajectory near $\Sigma$ when $\Sigma$ is attractive, what to expect when $\Sigma$ ceases to be attractive (at least, at generic exit points), and finally we also contrast and compare the behavior of some regularizations proposed in the literature. Through analysis and experiments we will confirm some known facts, and provide some important insight: (i) when $\Sigma$ is attractive, a solution trajectory indeed does remain near $\Sigma$, viz. sliding on $\Sigma$ is an appropriate idealization (of course, in general, one cannot predict which sliding vector field should be selected); (ii) when $\Sigma$ loses attractivity (at first order exit conditions), a typical solution trajectory leaves a neighborhood of $\Sigma$; (iii) there is no obvious way to regularize the system so that the regularized trajectory will remain near $\Sigma$ as long as $\Sigma$ is attractive, and so that it will be leaving (a neighborhood of) $\Sigma$ when $\Sigma$ looses attractivity. We reach the above conclusions by considering exclusively the given piecewise smooth system, without superimposing any assumption on what kind of dynamics near $\Sigma$ (or sliding motion on $\Sigma$) should have been taking place.Comment: 19 figure

Luminescence from Semiconductor Quantum Wires, Quantum Dots, and Monolayer Quantum Wells: Bottleneck and Localization Issues

Semiconductors nanostructures are fabricated using a range of techniques which inevitably have an impact in the resulting optical properties. Multilayers are grown by epitaxial techniques with a varying degree of uniformity in thickness, composition, etc., all leading to localisation effects in two-dimension. These multilayers are patterned to fabricate wires and dots using, in this case, electron beam lithography and dry etching. The fabrication steps contribute to modifications of the optical properties, beyond the expected purely confinement-related effects. An overview of linear and modulation spectroscopy is presented to demonstrate the impact of fabrication steps as well as of lateral confinement upon the emission from wires and dots. We focus on photoreflectance of GaAs-GaA1As dots and Si-SiGe wires as a probe of strain relaxation. Near-field scanning optical microscopy of single dots of GaAs-GaA1As at helium temperatures illustrates the potentials of using scanning probe techniques to study the underlying quantum mechanics of nanostructures. Finally, we suggest that a combination of lateral exciton confinement and exciton localization is a possible way forward to realise high emission efficiency nanostructures