Implicit renewal theory for exponential functionals of L\'evy processes

We establish a new functional relation for the probability density function of the exponential functional of a L\'evy process, which allows to significantly simplify the techniques commonly used in the study of these random variables and hence provide quick proofs of known results, derive new results, as well as sharpening known estimates for the distribution. We apply this formula to provide another look to the Wiener-Hopf type factorisation for exponential functionals obtained in a series of papers by Pardo, Patie and Savov, derive new identities in law, and to describe the behaviour of the tail distribution at infinity and of the distribution at zero in a rather large set of situations

Sliding to predict: vision-based beating heart motion estimation by modeling temporal interactions

Purpose: Technical advancements have been part of modern medical solutions as they promote better surgical alternatives that serve to the benefit of patients. Particularly with cardiovascular surgeries, robotic surgical systems enable surgeons to perform delicate procedures on a beating heart, avoiding the complications of cardiac arrest. This advantage comes with the price of having to deal with a dynamic target which presents technical challenges for the surgical system. In this work, we propose a solution for cardiac motion estimation. Methods: Our estimation approach uses a variational framework that guarantees preservation of the complex anatomy of the heart. An advantage of our approach is that it takes into account different disturbances, such as specular reflections and occlusion events. This is achieved by performing a preprocessing step that eliminates the specular highlights and a predicting step, based on a conditional restricted Boltzmann machine, that recovers missing information caused by partial occlusions. Results: We carried out exhaustive experimentations on two datasets, one from a phantom and the other from an in vivo procedure. The results show that our visual approach reaches an average minima in the order of magnitude of 10-7 while preserving the heart’s anatomical structure and providing stable values for the Jacobian determinant ranging from 0.917 to 1.015. We also show that our specular elimination approach reaches an accuracy of 99% compared to a ground truth. In terms of prediction, our approach compared favorably against two well-known predictors, NARX and EKF, giving the lowest average RMSE of 0.071. Conclusion: Our approach avoids the risks of using mechanical stabilizers and can also be effective for acquiring the motion of organs other than the heart, such as the lung or other deformable objects.Peer ReviewedPostprint (published version

Asesorando a centros educativos implicados en procesos de mejora escolar

Presentamos algunas reflexiones sobre el asesoramiento para la mejora escolar, a partir de la experiencia vivida con distintos centros a lo largo de los cursos 01-02 al 03-04, como consecuencia de la aplicación del Plan de Evaluación de Centros de Canarias (PECCAN) que aplicó el Instituto Canario de Evaluación y Calidad Educativa (ICEC) en nuestra comunidad autónoma. Durante esos tres años hemos trabajado -con distinto grado de intensidad- en más de una decena de centros, tanto de educación infantil-primaria como de secundaria, desempeñando el papel de asesores externos en labores de apoyo a los claustros, a partir del momento en que -en el marco del PECCAN- recibían los resultados y conclusiones de la evaluación externa por parte del inspector de la zona y la escuela debía iniciar la elaboración del plan de mejora. A lo largo de esta aportación presentaremos de modo sintético el modelo de asesoramiento que ha servido de referencia a lo largo del proceso, para luego centrarnos de manera más específica en dos de los casos que nos han parecido más ilustrativos de la experiencia. Para terminar propondremos algunas conclusiones en forma de reflexiones y sugerencias de cara a mejorar este tipo de intervenciones en las escuela

Interplay between the magnetic anisotropy contributions of Cobalt nanowires

We report on the magnetic properties and the crystallographic structure of the cobalt nanowire arrays as a function of their nanoscale dimensions. X-ray diffraction measurements show the appearance of an in-plane HCP-Co phase for nanowires with 50 nm diameter, suggesting a partial reorientation of the magnetocrystalline anisotropy axis along the membrane plane with increasing pore diameter. No significant changes in the magnetic behavior of the nanowire system are observed with decreasing temperature, indicating that the effective magnetoelastic anisotropy does not play a dominant role in the remagnetization processes of individual nanowires. An enhancement of the total magnetic anisotropy is found at room temperature with a decreasing nanowire diameter-to-length ratio (d/L), a result that is quantitatively analyzed on the basis of a simplified shape anisotropy model.Comment: 8 pages, 4 figure