Construction of Markov processes and associated multiplicative functionals from given harmonic measures

Let E be a noncompact locally compact second countable Hausdorff space. We consider the question when, given a family of finite nonzero measures on E that behave like harmonic measures associated with all relatively compact open sets in E (i.e. that satisfy a certain consistency condition), one can construct a Markov process on E and a multiplicative functional with values in [0, ∞) such that the hitting distributions of the process “inflated” by the multiplicative functional yield the given harmonic measures. We achieve this construction under weak continuity and local transience conditions on these measures that are natural in the theory of Markov processes, and a mild growth restriction on them. In particular, if the space E equipped with the measures satisfies the conditions of a harmonic space, such a Markov process and associated multiplicative functional exist. The result extends in a new direction the work of many authors, in probability and in axiomatic potential theory, on constructing Markov processes from given hitting distributions (i.e. from harmonic measures that have total mass no more than 1).Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/47657/1/440_2005_Article_BF01192513.pd

Very High Resolution Solar X-ray Imaging Using Diffractive Optics

This paper describes the development of X-ray diffractive optics for imaging solar flares with better than 0.1 arcsec angular resolution. X-ray images with this resolution of the \geq10 MK plasma in solar active regions and solar flares would allow the cross-sectional area of magnetic loops to be resolved and the coronal flare energy release region itself to be probed. The objective of this work is to obtain X-ray images in the iron-line complex at 6.7 keV observed during solar flares with an angular resolution as fine as 0.1 arcsec - over an order of magnitude finer than is now possible. This line emission is from highly ionized iron atoms, primarily Fe xxv, in the hottest flare plasma at temperatures in excess of \approx10 MK. It provides information on the flare morphology, the iron abundance, and the distribution of the hot plasma. Studying how this plasma is heated to such high temperatures in such short times during solar flares is of critical importance in understanding these powerful transient events, one of the major objectives of solar physics. We describe the design, fabrication, and testing of phase zone plate X-ray lenses with focal lengths of \approx100 m at these energies that would be capable of achieving these objectives. We show how such lenses could be included on a two-spacecraft formation-flying mission with the lenses on the spacecraft closest to the Sun and an X-ray imaging array on the second spacecraft in the focal plane \approx100 m away. High resolution X-ray images could be obtained when the two spacecraft are aligned with the region of interest on the Sun. Requirements and constraints for the control of the two spacecraft are discussed together with the overall feasibility of such a formation-flying mission

Reducing Computational Costs in the Basic Perturbation Lemma

Homological Perturbation Theory [11, 13] is a well-known general method for computing homology, but its main algorithm, the Basic Perturbation Lemma, presents, in general, high computational costs. In this paper, we propose a general strategy in order to reduce the complexity in some important formulas (those following a specific pattern) obtained by this algorithm. Then, we show two examples of application of this methodology.

Urgent Considerations for the Neuro-oncologic Treatment of Patients with Gliomas During the COVID-19 Pandemic.

The COVID-19 outbreak is posing unprecedented risks and challenges for all communities and healthcare systems, worldwide. There are unique considerations for many adult patients with gliomas who are vulnerable to the novel coronavirus due to older age and immunosuppression. As patients with terminal illnesses, they present ethical challenges for centers that may need to ration access to ventilator care due to insufficient critical care capacity. It is urgent for the neuro-oncology community to develop a pro-active and coordinated approach to the care of adults with gliomas in order to provide them with the best possible oncologic care while also reducing their risk of viral infection during times of potential healthcare system failure. In this article, we present an approach developed by an international multi-disciplinary group to optimize the care of adults with gliomas during this pandemic. We recommend measures to promote strict social distancing and minimize exposures for patients, address risk and benefit of all therapeutic interventions, pro-actively develop end of life plans, educate patients and caregivers and ensure the health of the multi-disciplinary neuro-oncology workforce. This pandemic is already changing neuro-oncologic care delivery around the globe. It is important to highlight opportunities to maximize the benefit and minimize the risk of glioma management during this pandemic and potentially, in the future

RR-symmetric Gauge Mediation With Fayet-Iliopoulos Term

We have studied $R$-symmetrc gauge mediation models with Fayet-Iliopoulos terms. We give a concrete example of hidden sector with an $U(1)_H$ gauge theory and a Fayet-Iliopoulos term, which can induce distinctive soft terms in the visible sector, and help solving fine tuning problems in models of $R$-symmetric gauge mediation.Comment: 11 pages, 1 figur

Logarithmic Corrections to Rotating Extremal Black Hole Entropy in Four and Five Dimensions

We compute logarithmic corrections to the entropy of rotating extremal black holes using quantum entropy function i.e. Euclidean quantum gravity approach. Our analysis includes five dimensional supersymmetric BMPV black holes in type IIB string theory on T^5 and K3 x S^1 as well as in the five dimensional CHL models, and also non-supersymmetric extremal Kerr black hole and slowly rotating extremal Kerr-Newmann black holes in four dimensions. For BMPV black holes our results are in perfect agreement with the microscopic results derived from string theory. In particular we reproduce correctly the dependence of the logarithmic corrections on the number of U(1) gauge fields in the theory, and on the angular momentum carried by the black hole in different scaling limits. We also explain the shortcomings of the Cardy limit in explaining the logarithmic corrections in the limit in which the (super)gravity description of these black holes becomes a valid approximation. For non-supersymmetric extremal black holes, e.g. for the extremal Kerr black hole in four dimensions, our result provides a stringent testing ground for any microscopic explanation of the black hole entropy, e.g. Kerr/CFT correspondence.Comment: LaTeX file, 50 pages; v2: added extensive discussion on the relation between boundary condition and choice of ensemble, modified analysis for slowly rotating black holes, all results remain unchanged, typos corrected; v3: minor additions and correction

Logarithmic Corrections to N=2 Black Hole Entropy: An Infrared Window into the Microstates

Logarithmic corrections to the extremal black hole entropy can be computed purely in terms of the low energy data -- the spectrum of massless fields and their interaction. The demand of reproducing these corrections provides a strong constraint on any microscopic theory of quantum gravity that attempts to explain the black hole entropy. Using quantum entropy function formalism we compute logarithmic corrections to the entropy of half BPS black holes in N=2 supersymmetric string theories. Our results allow us to test various proposals for the measure in the OSV formula, and we find agreement with the measure proposed by Denef and Moore if we assume their result to be valid at weak topological string coupling. Our analysis also gives the logarithmic corrections to the entropy of extremal Reissner-Nordstrom black holes in ordinary Einstein-Maxwell theory.Comment: LaTeX file, 66 page

Numerical resolution of the hyperbolic heat equation using smoothed mathematical functions instead of Heaviside and Dirac delta distributions

The hyperbolic bioheat equation (HBE) has been used to model heating applications involving very short power pulses. This equation includes two mathematical distributions (Heaviside and Delta) which have to be necessarily substituted for smoothed mathematical functions when the HBE is solved by numerical methods. This study focuses on which type of smoothed functions would be suitable for this purpose, i.e. those which would provide solutions similar to those obtained analytically from the original Heaviside and Delta distributions. The logistic function was considered as a substitute for the Heaviside function, while its derivative and the probabilistic Gaussian function were considered as substitutes for the Delta distribution. We also considered polynomial interpolation functions, in particular, the families of smoothed functions with continuous second derivative without overshoot used by COMSOL Multiphysics. All the smoothed functions were used to solve the HBE by the Finite Element Method (COMSOL Multiphysics), and the solutions were compared to those obtained analytically from the original Heaviside and Delta distributions. The results showed that only the COMSOL smoothed functions provide a numerical solution almost identical to the analytical one. Finally, we demonstrated mathematically that in order to find a suitable smoothed function (f) that must adequately substitute any mathematical distribution (D) in the HBE, the difference D - f must have compact support. (c) 2013 Elsevier Ltd. All rights reserved.This work received financial support from the Spanish "Plan Nacional de I + D + I del Ministerio de Ciencia e Innovacion" Grant No. TEC2011-27133-C02-01 and from Universitat Politenica de Valencia (PAID-06-11 Ref. 1988). V. Romero Garcia is grateful for the support of "Programa de Contratos Post-Doctorales con Movilidad UPV del Campus de Excelencia (CEI-01-11)" and FEDER Project MAT2009-09438.Rivera Ortun, MJ.; Trujillo Guillen, M.; Romero García, V.; López Molina, JA.; Berjano Zanón, E. (2013). Numerical resolution of the hyperbolic heat equation using smoothed mathematical functions instead of Heaviside and Dirac delta distributions. International Communications in Heat and Mass Transfer. 46:7-12. https://doi.org/10.1016/j.icheatmasstransfer.2013.05.017S7124

Markerless monocular tracking system for guided external eye surgery

This paper presents a novel markerless monocular tracking system aimed at guiding ophthalmologists during external eye surgery. This new tracking system performs a very accurate tracking of the eye by detecting invariant points using only textures that are present in the sclera, i.e., without using traditional features like the pupil and/or cornea reflections, which remain partially or totally occluded in most surgeries. Two known algorithms that compute invariant points and correspondences between pairs of images were implemented in our system: Scalable Invariant Feature Transforms (SIFT) and Speed Up Robust Features (SURF). The results of experiments performed on phantom eyes show that, with either algorithm, the developed system tracks a sphere at a 360◦ rotation angle with an error that is lower than 0.5%. Some experiments have also been carried out on images of real eyes showing promising behavior of the system in the presence of blood or surgical instruments during real eye surgery. © 2014 Elsevier Ltd. All rights reserved.Monserrat Aranda, C.; Rupérez Moreno, MJ.; Alcañiz Raya, ML.; Mataix, J. (2014). Markerless monocular tracking system for guided external eye surgery. Computerized Medical Imaging and Graphics. 38(8):785-792. doi:10.1016/j.compmedimag.2014.08.001S78579238

States and transitions in black-hole binaries

With the availability of the large database of black-hole transients from the Rossi X-Ray Timing Explorer, the observed phenomenology has become very complex. The original classification of the properties of these systems in a series of static states sorted by mass accretion rate proved not to be able to encompass the new picture. I outline here a summary of the current situation and show that a coherent picture emerges when simple properties such as X-ray spectral hardness and fractional variability are considered. In particular, fast transition in the properties of the fast time variability appear to be crucial to describe the evolution of black-hole transients. Based on this picture, I present a state-classification which takes into account the observed transitions. I show that, in addition to transients systems, other black-hole binaries and Active Galactic Nuclei can be interpreted within this framework. The association between these states and the physics of the accretion flow around black holes will be possible only through modeling of the full time evolution of galactic transient systems.Comment: 30 pages, 11 figures, To appear in Belloni, T. (ed.): The Jet Paradigm - From Microquasars to Quasars, Lect. Notes Phys. 794 (2009