On the inversion of the density gradient at the fringe of the convection zone

Introduction. It is well known that the total pressure and the temperature increase as one goes inward from the surface to the center of a star. That the density, on the other hand, does not necessarily increase with depth below the surface was pointed out by Hoyle and Schwarzschild (1955) and was borne out quite clearly by the numerical integrations of the solar surface layers by Faulkner, Griffiths, and Hoyle (1963). The question was raised by Tayler and Gough (1963) as to whether the density gradient inversion was real or whether it was due to the particular model of convection adopted by Faulkner et al. It is the purpose of this note to show that the inversion is indeed genuine and results from the steep temperature gradient that exists in the outermost layers of the convection zone where convection is not fully efficient and carries only a fraction (<1/2) of the total energy flux. Also, the electron pressure-temperature plane can be divided into regions where dp/dT is negative and positive. The dividing line depends, in an insensitive manner, on the assumed model and efficiency of convection. In the case of the sun it is the hydrogen ionization at about 10^4 °K that causes the opacity to go up sharply and as a result the temperature gradient steepens there by inverting the density gradient. The inversion necessarily results in a Rayleigh-Taylor instability

Sample Complexity of Dictionary Learning and other Matrix Factorizations

Many modern tools in machine learning and signal processing, such as sparse dictionary learning, principal component analysis (PCA), non-negative matrix factorization (NMF), $K$-means clustering, etc., rely on the factorization of a matrix obtained by concatenating high-dimensional vectors from a training collection. While the idealized task would be to optimize the expected quality of the factors over the underlying distribution of training vectors, it is achieved in practice by minimizing an empirical average over the considered collection. The focus of this paper is to provide sample complexity estimates to uniformly control how much the empirical average deviates from the expected cost function. Standard arguments imply that the performance of the empirical predictor also exhibit such guarantees. The level of genericity of the approach encompasses several possible constraints on the factors (tensor product structure, shift-invariance, sparsity \ldots), thus providing a unified perspective on the sample complexity of several widely used matrix factorization schemes. The derived generalization bounds behave proportional to $\sqrt{\log(n)/n}$ w.r.t.\ the number of samples $n$ for the considered matrix factorization techniques.Comment: to appea

Structural and magnetic investigations of two spreading systems around the Rodriguez Triple Junction with respect to hydrothermal activities

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Las conjeturas y la construcción de conocimiento en clase de geometría

En el cursillo Las conjeturas y la construcción de conocimiento geométrico en clase de geometría los asistentes deben resolver un problema empleando geometría dinámica. El proceso de solución y las conjeturas que proponen ambientan la discusión sobre dos aspectos que contribuyen a la participación autónoma, relevante y genuina (Perry, Samper, Camargo, Echeverry y Molina, 2008) de los estudiantes en la construcción de conocimiento: el papel del instrumento usado para resolver el problema y la mediación semiótica del profesor. El provecho didáctico que puede sacarse de estos aspectos se fundamenta en dos marcos de referencia y se ilustra con el análisis de segmentos del proceso y de las conjeturas producidas por un grupo de estudiantes de un curso de geometría plana de la Universidad Pedagógica Nacional

Trajectory Specification for High-Capacity Air Traffic Control

In the current air traffic management system, the fundamental limitation on airspace capacity is the cognitive ability of human air traffic controllers to maintain safe separation with high reliability. The doubling or tripling of airspace capacity that will be needed over the next couple of decades will require that tactical separation be at least partially automated. Standardized conflict-free four-dimensional trajectory assignment will be needed to accomplish that objective. A trajectory specification format based on the Extensible Markup Language is proposed for that purpose. This format can be used to downlink a trajectory request, which can then be checked on the ground for conflicts and approved or modified, if necessary, then uplinked as the assigned trajectory. The horizontal path is specified as a series of geodetic waypoints connected by great circles, and the great-circle segments are connected by turns of specified radius. Vertical profiles for climb and descent are specified as low-order polynomial functions of along-track position, which is itself specified as a function of time. Flight technical error tolerances in the along-track, cross-track, and vertical axes define a bounding space around the reference trajectory, and conformance will guarantee the required separation for a period of time known as the conflict time horizon. An important safety benefit of this regimen is that the traffic will be able to fly free of conflicts for at least several minutes even if all ground systems and the entire communication infrastructure fail. Periodic updates in the along-track axis will adjust for errors in the predicted along-track winds

The Division of Ownership in New Ventures

The current study investigates a tripartite incentive contract between an innovator supplying an intellectual asset, a professional assigned to productive tasks, and a consulting firm specializing in matching ideas and professional skills. A rather simple pure tripartite partnership implements the consultant´s expected profit maximum and maximizes the project`s expected surplus. The liquidity-constrained professional is compensated by receiving a share of one half in the new venture. The consultant´s and the innovator´s shares reflect the relative value of search. However, the consultant´s optimal search effort to find an appropriate production partner is inefficiently low.New ventures, tripartite incentive contract, consulting contract, partnerships