Superclasses and supercharacters of normal pattern subgroups of the unipotent upper triangular matrix group

Let $U_n$ denote the group of $n\times n$ unipotent upper-triangular matrices over a fixed finite field \FF_q, and let U_\cP denote the pattern subgroup of $U_n$ corresponding to the poset \cP. This work examines the superclasses and supercharacters, as defined by Diaconis and Isaacs, of the family of normal pattern subgroups of $U_n$. After classifying all such subgroups, we describe an indexing set for their superclasses and supercharacters given by set partitions with some auxiliary data. We go on to establish a canonical bijection between the supercharacters of U_\cP and certain \FF_q-labeled subposets of \cP. This bijection generalizes the correspondence identified by Andr\'e and Yan between the supercharacters of $U_n$ and the \FF_q-labeled set partitions of $\{1,2,...,n\}$. At present, few explicit descriptions appear in the literature of the superclasses and supercharacters of infinite families of algebra groups other than \{U_n : n \in \NN\}. This work signficantly expands the known set of examples in this regard.Comment: 28 page

Selección masal por prolificidad y rendimiento en la variedad de maíz ICA V 552.

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Robust nonparametric detection of objects in noisy images

We propose a novel statistical hypothesis testing method for detection of objects in noisy images. The method uses results from percolation theory and random graph theory. We present an algorithm that allows to detect objects of unknown shapes in the presence of nonparametric noise of unknown level and of unknown distribution. No boundary shape constraints are imposed on the object, only a weak bulk condition for the object's interior is required. The algorithm has linear complexity and exponential accuracy and is appropriate for real-time systems. In this paper, we develop further the mathematical formalism of our method and explore important connections to the mathematical theory of percolation and statistical physics. We prove results on consistency and algorithmic complexity of our testing procedure. In addition, we address not only an asymptotic behavior of the method, but also a finite sample performance of our test.Comment: This paper initially appeared in 2010 as EURANDOM Report 2010-049. Link to the abstract at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-abstract.pdf Link to the paper at EURANDOM repository: http://www.eurandom.tue.nl/reports/2010/049-report.pd

NOD2 Modulates Serotonin Transporter and Interacts with TLR2 and TLR4 in Intestinal Epithelial Cells

Background/Aims: Serotonin (5-HT) is a chief modulator of intestinal activity. The effects of 5-HT depend on its extracellular availability, which is mainly controlled by serotonin transporter (SERT), expressed in enterocytes. On the other hand, innate immunity, mediated by Toll-like receptors (TLRs) and nucleotide oligomerization domain (NOD)-like receptors (NLRs), is known to control intestinal microbiota and maintain intestinal homeostasis. The dysregulation of the intestinal serotonergic system and innate immunity has been observed in in ammatory bowel diseases (IBD), the incidence of which has severely increased all over the world. The aim of the present study, therefore, was to analyze the effect of NOD2 on intestinal SERT activity and expression, as well as to study the crosstalk of NOD2 with TLR2 and TLR4. Methods: Intestinal epithelial cell line Caco-2/TC7 was used to analyze SERT activity and SERT, NOD2, TLR2 and TLR4 molecular expression by real-time PCR and western blotting. Moreover, intestinal tract (ileum and colon) from mice de cient in TLR2, TLR4 or TLR2/4 receptors was used to test the interdependence of NOD2 with these TLR receptors. Results: NOD2 activation inhibits SERT activity in Caco-2/TC7 cells, mainly due to the decrement of SERT molecular expression, with RIP2/RICK being the intracellular pathway involved in this effect. This inhibitory effect on SERT would yield an increment of extracellular 5-HT availability. In this sense, 5-HT strongly inhibits NOD2 expression. In addition, NOD2 showed greater interdependence with TLR2 than with TLR4. Indeed, NOD2 expression signi cantly increased in both cells treated with TLR2 agonists and the intestinal tract of Tlr2-/- mice. Conclusions: It may be inferred from our data that NOD2 could play a role in intestinal pathophysiology not only through its inherent innate immune role but also due to its interaction with other receptors as TLR2 and the modulation of the intestinal serotonergic system decreasing SERT activity and expression

lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their corresponding unit spheres). We also assume mixture weights for the different components. We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces. We study the recovery of the most significant subspace by minimizing the lp-averaged distances of data points from d-dimensional subspaces, where p>0. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 0<p<=1, then for any fraction of outliers the most significant subspace can be recovered by lp minimization with overwhelming probability (which depends on the generating distribution and its parameters). We show that when adding small noise around the underlying subspaces the most significant subspace can be nearly recovered by lp minimization for any 0<p<=1 with an error proportional to the noise level. On the other hand, if p>1 and there is more than one underlying subspace, then with overwhelming probability the most significant subspace cannot be recovered or nearly recovered. This last result does not require spherically symmetric outliers.Comment: This is a revised version of the part of 1002.1994 that deals with single subspace recovery. V3: Improved estimates (in particular for Lemma 3.1 and for estimates relying on it), asymptotic dependence of probabilities and constants on D and d and further clarifications; for simplicity it assumes uniform distributions on spheres. V4: minor revision for the published versio

Non-homogeneous polygonal Markov fields in the plane: graphical representations and geometry of higher order correlations

We consider polygonal Markov fields originally introduced by Arak and Surgailis (1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of features with the two-dimensional Ising model. We introduce non-homogeneous version of polygonal fields in anisotropic enviroment. For these fields we provide a class of new graphical constructions and random dynamics. These include a generalised dynamic representation, generalised and defective disagreement loop dynamics as well as a generalised contour birth and death dynamics. Next, we use these constructions as tools to obtain new exact results on the geometry of higher order correlations of polygonal Markov fields in their consistent regime.Comment: 54 page

Application of the Fisher-Rao metric to ellipse detection

The parameter space for the ellipses in a two dimensional image is a five dimensional manifold, where each point of the manifold corresponds to an ellipse in the image. The parameter space becomes a Riemannian manifold under a Fisher-Rao metric, which is derived from a Gaussian model for the blurring of ellipses in the image. Two points in the parameter space are close together under the Fisher-Rao metric if the corresponding ellipses are close together in the image. The Fisher-Rao metric is accurately approximated by a simpler metric under the assumption that the blurring is small compared with the sizes of the ellipses under consideration. It is shown that the parameter space for the ellipses in the image has a finite volume under the approximation to the Fisher-Rao metric. As a consequence the parameter space can be replaced, for the purpose of ellipse detection, by a finite set of points sampled from it. An efficient algorithm for sampling the parameter space is described. The algorithm uses the fact that the approximating metric is flat, and therefore locally Euclidean, on each three dimensional family of ellipses with a fixed orientation and a fixed eccentricity. Once the sample points have been obtained, ellipses are detected in a given image by checking each sample point in turn to see if the corresponding ellipse is supported by the nearby image pixel values. The resulting algorithm for ellipse detection is implemented. A multiresolution version of the algorithm is also implemented. The experimental results suggest that ellipses can be reliably detected in a given low resolution image and that the number of false detections can be reduced using the multiresolution algorithm

Calidad de vida y función sexual en mujeres con disfunción del piso-pélvico del sur de Chile

Antecedentes/Objetivos: La disfunción del piso pélvico (DPP) es muy prevalente, afectando a un tercio de las mujeres adultas. Estas patologías no suponen un riesgo vital, pero sus síntomas pueden interferir con las actividades de la vida diaria incluyendo aspectos físicos, sociales y sexuales. En el sur de Chile, en el Hospital de alta complejidad (Regional-Concepción), se ha implementado la Unidad de Piso Pélvico (UPP). No hay evidencia sobre el efecto que supone en la calidad de vida y la función sexual de las mujeres que la padecen Describir la calidad de vida y función sexual de mujeres controladas en la Unidad de Piso Pélvico de un Hospital de alta complejidad en Chile. Métodos: Estudio transversal. Población: usuarias con DPP de la UPP del H. Regional-Concepción. Muestra 173. Variables: Caract. sociodemográficas, antecedentes obstétricos, tipo de DPP, Variables de Calidad de Vida (percepción del estado de salud, limitación emocional, limitación de actividades cotidianas, alteraciones de actividades sociales) (Short Form-12 Health Survey) y función sexual (PISQ-12). Análisis: medidas de dispersión, frecuencia absoluta- relativa. Resultados: Edad media 57 años, 88% con ingreso menor a 357€. 91% con IMC-sobrepeso y obesidad, 64% ≥ 3 hijos. Tipos DPP: 53% incontinencia de orina (IO), 35% prolapso vaginal (Pp), 12% IO+Pp. Calidad de vida (n = 173): Mala percepción de salud: 95%. Limitación emocional: 37%. Limitación de actividades cotidianas: 67%. Alteraciones de actividades sociales: 57% Función sexual (n = 95): Disfunción alta: 8,4%, moderada: 41,1%, baja 50,5%. El 15% nunca tuvo deseo-sexual los últimos 6 meses. El 14% admite no haber alcanzado el orgasmo en los últimos 6 meses, el mismo porcentaje admite no sentir excitación en el mismo período. El 19% admite no estar satisfechas con las actividades sexuales actuales, el 15% siente dolor durante las relaciones sexuales, el 40% admite sufrir de pérdidas de orina durante la actividad sexual, y el mismo número admite restringir su vida sexual debido al miedo de pérdida de orina durante el acto sexual. El 27% admite tener reacciones emocionales negativas durante las relaciones sexuales. El 10% y el 13% admite que sus parejas sufrían de disfunción eréctil y eyaculación, respectivamente. Por último, el 42% de las mujeres admite que sus orgasmos en los últimos 6 meses son más intensos. Conclusiones: Las mujeres con DPP presentan una alteración negativa de su calidad de vida y de su función sexual, aunque existe cierta incongruencia al valorar positivamente la calidad de los orgasmos cuando los demás aspectos de la vida sexual son negativos