Legendrian Distributions with Applications to Poincar\'e Series

Let $X$ be a compact Kahler manifold and $L\to X$ a quantizing holomorphic Hermitian line bundle. To immersed Lagrangian submanifolds $\Lambda$ of $X$ satisfying a Bohr-Sommerfeld condition we associate sequences $\{ |\Lambda, k\rangle \}_{k=1}^\infty$, where $\forall k$ $|\Lambda, k\rangle$ is a holomorphic section of $L^{\otimes k}$. The terms in each sequence concentrate on $\Lambda$, and a sequence itself has a symbol which is a half-form, $\sigma$, on $\Lambda$. We prove estimates, as $k\to\infty$, of the norm squares $\langle \Lambda, k|\Lambda, k\rangle$ in terms of $\int_\Lambda \sigma\overline{\sigma}$. More generally, we show that if $\Lambda_1$ and $\Lambda_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting cleanly, the inner products $\langle\Lambda_1, k|\Lambda_2, k\rangle$ have an asymptotic expansion as $k\to\infty$, the leading coefficient being an integral over the intersection $\Lambda_1\cap\Lambda_2$. Our construction is a quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove that the Poincar\'e series on hyperbolic surfaces are a particular case, and therefore obtain estimates of their norms and inner products.Comment: 41 pages, LaTe

Two-phase densification of cohesive granular aggregates

When poured into a container, cohesive granular materials form low-density, open granular aggregates. If pressed upon with a ram, these aggregates densify by particle rearrangement. Here we introduce experimental evidence to the effect that particle rearrangement is a spatially heterogeneous phenomenon, which occurs in the form of a phase transformation between two configurational phases of the granular aggregate. We then show that the energy landscape associated with particle rearrangement is consistent with our interpretation of the experimental results. Besides affording insight into the physics of the granular state, our conclusions are relevant to many engineering processes and natural phenomena.Comment: 7 pages, 3 figure

Evidence for spin-triplet superconducting correlations in metal-oxide heterostructures with non-collinear magnetization

Heterostructures composed of ferromagnetic La0.7Sr0.3MnO3, ferromagnetic SrRuO3, and superconducting YBa2Cu3Ox were studied experimentally. Structures of composition Au/La0.7Sr0.3MnO3/SrRuO3/YBa2Cu3Ox were prepared by pulsed laser deposition, and their high quality was confirmed by X-ray diffraction and reflectometry. A non-collinear magnetic state of the heterostructures was revealed by means of SQUID magnetometry and polarized neutron reflectometry. We have further observed superconducting currents in mesa-structures fabricated by deposition of a second superconducting Nb layer on top of the heterostructure, followed by patterning with photolithography and ion-beam etching. Josephson effects observed in these mesa-structures can be explained by the penetration of a triplet component of the superconducting order parameter into the magnetic layers.Comment: 10 pages, 6 figure

Strengthening the Cohomological Crepant Resolution Conjecture for Hilbert-Chow morphisms

Given any smooth toric surface S, we prove a SYM-HILB correspondence which relates the 3-point, degree zero, extended Gromov-Witten invariants of the n-fold symmetric product stack [Sym^n(S)] of S to the 3-point extremal Gromov-Witten invariants of the Hilbert scheme Hilb^n(S) of n points on S. As we do not specialize the values of the quantum parameters involved, this result proves a strengthening of Ruan's Cohomological Crepant Resolution Conjecture for the Hilbert-Chow morphism from Hilb^n(S) to Sym^n(S) and yields a method of reconstructing the cup product for Hilb^n(S) from the orbifold invariants of [Sym^n(S)].Comment: Revised versio

Diversidad de pseudomonas fluorescentes en cultivos de papa de la region cundiboyacense y su actividad antagonista in vitro sobre rhizoctonia solani

Las pseudomonas fluorescentes son unas de las bacterias benéficas más importantes a nivel de la rizosfera gracias a que pueden controlar algunos fitopatógenos habituales del suelo como resultado de su capacidad antagonista. Hay muy pocos trabajos realizados para conocer la composición y diversidad de pseudomonas fluorescentes en países tropicales. En este trabajo se determinó la composición de pseudomonas fluorescentes provenientes de dife-rentes cultivos de papa ubicados en la región Cundiboyacense, entre 2.100 y 3.200 msnm, la cual es considerada la zona de mayor producción de papa de Colombia. Así mismo se evaluó el efecto de algunas prácticas de cultivo sobre dicha composición. Finalmente se determinó la capacidad de antagonismo de algunos aislamientos de pseudomonas fluorescentes contra Rhizoctonia solani. Fueron evaluadas 45 muestras de rizosfera y rizoplano de cultivos de papa provenientes de 15 campos de papa diferentes. Las muestras se procesaron usando una modificación del medio King B, la cual resultó ser más eficiente para aislar pseudomonas fluorescentes, que otras reportadas en la literatura. El 80,7% y 82,7% de las pseudomonas fluorescentes aisladas en rizosfera y rizoplano, respectivamente, fueron Pseudomonas fluorescens, mostrando poca diversidad en las muestras evaluadas. Por otra parte se observó un efecto de la estrategia de rotación de cultivo maíz-papa, sobre el número de pseudomonas fluorescentes aisladas de la rizosfera. Estos resultados tienen implicaciones para el diseño de estrategias de manejo integrado de plagas en los cultivos de los países tropicales. Finalmente se encontraron aisla-mientos nativos con actividad antagonista sobre anteriores, si bien no aseguran un control eficaz del pató-geno en condiciones de campo, sí dan una idea del poten-cial biocontrolador de la especie aplicados como comuni-dades bacterianas, cepas o subproductos de éstas.Fluorescent Pseudomonas are one of the most important benefic bacteria of the rizhosphere. It is because they can control some soil borne phytopatogen agents as a result of their antagonistic capacity. There are few works about the composition and diversity of fluorescent Pseudomonas in tropical countries. In this work we studied the composition of fluorescent Pseudomonas form different potato crops located at the Cundiboyacense región between 2100 and 3200 mosl, which is the most important area of potato production in Colombia. This study also assesses the effect of some crop practices variables on rizosphere bacteria richness and diversity. Finally, it was determined the antagonistic capacity of some Pseudomonas fluorescens isolates against Rhizoctonia solani. A total of 45 rhizosphere samples were taken from 15 potato fields. To isolate the Pseudomonas it was used king B medium modified by us. Our results showed that this modified medium consistently allowed a more efficient recovery of the fluorescent Pseudomonas than the media reported in the literature. 80.7% and 82.7% of the fluorescent Pseudomonas isolated from the rizosphere and rizoplane respectively were Pseudomonas fluorescens. It suggest a low fluorescent pseudomonas diversity. Our work also denotes an effect of the maize-potato crop rotation strategy on the amount of the fluorescent Pseudomonas isolated from the rizosphere. These results may have importance in designing appropriate strategies for bio-controlling soil borne phytopathogens. In tropical countries like Colombia, this knowledge might help to improve crop yields. Finally it was found native isolates with antagonistic activity against Rhizoctonia solani in the bioassays in vitro, such results if not assure an efficient control of the pathogen in field conditions, may give an idea of the potentiality of P.fluorescens to be applied as bacterial community, strains or derived products of them

Algunas Estrategias Útiles en el Salón de Clase

El término \solución de problemas" se refiere a la tarea matemática que tiene el potencial para proveer retos intelectuales que ayudan a mejorar el entendimiento y el desarrollo de las matemáticas en los estudiantes. Tal tarea, un problema puede promover en los estudiantes el entendimiento conceptual y fomentar sus habilidades para razonar y comunicarse matemáticamente, capturando su interés y curiosidad. En este cursillo mostramos algunas estrategias, como buscar un patrón de comportamiento, explotar la paridad, el principio del palomar o de las casillas e invariantes. Estas estrategias son útiles en solución de problemas y son la esencia del quehacer matemático. Además al trabajar en forma de taller se muestra un modo de ense~nanza que posibilita y anima a la participación de cada estudiante. Se escogieron estas cuatro estrategias, ya que para utilizarlas cada participante no requiere mucho conocimiento y es más ellas motivan a la exploración y la abstración de propiedades de un tema relacionado

Quantifying Robotic Swarm Coverage

In the field of swarm robotics, the design and implementation of spatial density control laws has received much attention, with less emphasis being placed on performance evaluation. This work fills that gap by introducing an error metric that provides a quantitative measure of coverage for use with any control scheme. The proposed error metric is continuously sensitive to changes in the swarm distribution, unlike commonly used discretization methods. We analyze the theoretical and computational properties of the error metric and propose two benchmarks to which error metric values can be compared. The first uses the realizable extrema of the error metric to compute the relative error of an observed swarm distribution. We also show that the error metric extrema can be used to help choose the swarm size and effective radius of each robot required to achieve a desired level of coverage. The second benchmark compares the observed distribution of error metric values to the probability density function of the error metric when robot positions are randomly sampled from the target distribution. We demonstrate the utility of this benchmark in assessing the performance of stochastic control algorithms. We prove that the error metric obeys a central limit theorem, develop a streamlined method for performing computations, and place the standard statistical tests used here on a firm theoretical footing. We provide rigorous theoretical development, computational methodologies, numerical examples, and MATLAB code for both benchmarks.Comment: To appear in Springer series Lecture Notes in Electrical Engineering (LNEE). This book contribution is an extension of our ICINCO 2018 conference paper arXiv:1806.02488. 27 pages, 8 figures, 2 table

Semi-Parametric Drift and Diffusion Estimation for Multiscale Diffusions

We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective equation describing the dynamics on the longer diffusive time scale, i.e. in a homogenization framework. We examine the case where both the drift and the diffusion coefficients in the effective dynamics are space-dependent and depend on multiple unknown parameters. It is known that classical estimators, such as Maximum Likelihood and Quadratic Variation of the Path Estimators, fail to obtain reasonable estimates for parameters in the effective dynamics when based on observations of the underlying multiscale diffusion. We propose a novel algorithm for estimating both the drift and diffusion coefficients in the effective dynamics based on a semi-parametric framework. We demonstrate by means of extensive numerical simulations of a number of selected examples that the algorithm performs well when applied to data from a multiscale diffusion. These examples also illustrate that the algorithm can be used effectively to obtain accurate and unbiased estimates.Comment: 32 pages, 10 figure

Casimir-like tunneling-induced electronic forces

We study the quantum forces that act between two nearby conductors due to electronic tunneling. We derive an expression for these forces by calculating the flux of momentum arising from the overlap of evanescent electronic fields. Our result is written in terms of the electronic reflection amplitudes of the conductors and it has the same structure as Lifshitz's formula for the electromagnetically mediated Casimir forces. We evaluate the tunneling force between two semiinfinite conductors and between two thin films separated by an insulating gap. We discuss some applications of our results.Comment: 8 pages, 3 figs, submitted to Proc. of QFEXT'05, to be published in J. Phys.

Efecto de las fuentes de polen sobre el rendimiento en la extracción de aceite y perfil de ácidos grasos de las semillas de dátil (Phoenix dactylifera L.) cultivar Medjool de México

The present investigation aimed to assess the effect of pollen sources on the mass, dimension, oil content and fatty acid profile of the seeds from female palms of the Medjool date cultivar. The palms were pollinated with Deglet Noor, Khadrawy, Medjool and Zahidi cultivars. In addition, three palms were pollinated as the treatment control. The fatty acids were evaluated by gas chromatography-mass spectrometry. The surface morphology of date seed powder was examined using SEM, before and after n-hexane interaction. The seeds of the Medjool treatment had the greatest mass (1.42 g), but the lowest oil content (5.37% w/w); the control seeds showed smaller mass (1.21 g), but higher oil content (13.57% w/w). The proportion of fatty acids varied significantly among the treatments with respect to the control. The most abundant fatty acids were oleic (C18:1), lauric (C12:0), myristic (C14:0), palmitic (C16:0), linoleic (C18:2), and stearic (C18:0). Together these fatty acids presented a composition between 98.3 and 98.67% for treatments, and 99.0% for the control. The results indicate that the pollen sources from Deglet Noor, Khadrawy, Medjool and Zahidi cultivars had a significant effect on mass, dimension, oil content and fatty acid profile of the seeds of the date cultivar Medjool. The date seed oil could be used as edible oil, in food products, and in pharmaceutical and cosmetic applications.La presente investigación tuvo como objetivo evaluar el efecto de las fuentes de polen, sobre la masa, dimensión, contenido de aceite y el perfil de ácidos grasos de las semillas de dátil del cultivar Medjool. Las palmas hembras del cultivar Medjool fueron polinizadas con cultivares Deglet Noor, Khadrawy, Medjool y Zahidi. Además, tres palmas fueron polinizadas como tratamiento control. Los ácidos grasos se evaluaron por cromatografía de gases-espectrometría de masas. La morfología de la superficie del polvo de semillas de dátil se examinó utilizando un equipo SEM, antes y después de la interacción n-hexano. Las semillas del tratamiento Medjool resultaron con mayor masa (1,42 g), pero menor contenido de aceite (5,37% p/p); la semilla control, mostró una masa más pequeña (1,21 g), pero un mayor contenido de aceite (13,57% p/p). La composición de ácidos grasos varió significativamente entre los tratamientos con respecto al control. Los ácidos grasos mayoritarios fueron: oleico (C18:1), láurico (C12:0), mirístico (C14:0), palmítico (C16:0), linoleico (C18:2) and esteárico (C18:0). En total, estos ácidos grasos alcanzan una composición entre 98.3 y 98.67% para los tratamientos, y 99.0% para el control. Los resultados indican que la fuente de polen de los cultivares Deglet Noor, Khadrawy, Medjool y Zahidi tiene un efecto significativo sobre la masa, dimensión, contenido de aceite y el perfil de ácidos grasos de la semilla del cultivar de dátil Medjool. El aceite de la semilla de dátil, podría usarse como aceite comestible, productos alimenticios, aplicaciones farmacéuticas y cosméticas