Rudiments of Holography

An elementary introduction to Maldacena's AdS/CFT correspondence is given, with some emphasis in the Fefferman-Graham construction. This is based on lectures given by one of us (E.A.) at the Universidad Autonoma de Madrid.Comment: 60 pages, additional misprints corrected, references adde

Screening of charged spheroidal colloidal particles

We study the effective screened electrostatic potential created by a spheroidal colloidal particle immersed in an electrolyte, within the mean field approximation, using Poisson--Botzmann equation in its linear and nonlinear forms, and also beyond the mean field by means of Monte Carlo computer simulation. The anisotropic shape of the particle has a strong effect on the screened potential, even at large distances (compared to the Debye length) from it. To quantify this anisotropy effect, we focus our study on the dependence of the potential on the position of the observation point with respect with the orientation of the spheroidal particle. For several different boundary conditions (constant potential, or constant surface charge) we find that, at large distance, the potential is higher in the direction of the large axis of the spheroidal particle

Riemannian Geometry of Noncommutative Surfaces

A Riemannian geometry of noncommutative n-dimensional surfaces is developed as a first step towards the construction of a consistent noncommutative gravitational theory. Historically, as well, Riemannian geometry was recognized to be the underlying structure of Einstein's theory of general relativity and led to further developments of the latter. The notions of metric and connections on such noncommutative surfaces are introduced and it is shown that the connections are metric-compatible, giving rise to the corresponding Riemann curvature. The latter also satisfies the noncommutative analogue of the first and second Bianchi identities. As examples, noncommutative analogues of the sphere, torus and hyperboloid are studied in detail. The problem of covariance under appropriately defined general coordinate transformations is also discussed and commented on as compared with other treatments.Comment: 28 pages, some clarifications, examples and references added, version to appear in J. Math. Phy

Double scaling limits of random matrices and minimal (2m,1) models: the merging of two cuts in a degenerate case

In this article, we show that the double scaling limit correlation functions of a random matrix model when two cuts merge with degeneracy $2m$ (i.e. when $y\sim x^{2m}$ for arbitrary values of the integer $m$) are the same as the determinantal formulae defined by conformal $(2m,1)$ models. Our approach follows the one developed by Berg\`{e}re and Eynard in \cite{BergereEynard} and uses a Lax pair representation of the conformal $(2m,1)$ models (giving Painlev\'e II integrable hierarchy) as suggested by Bleher and Eynard in \cite{BleherEynard}. In particular we define Baker-Akhiezer functions associated to the Lax pair to construct a kernel which is then used to compute determinantal formulae giving the correlation functions of the double scaling limit of a matrix model near the merging of two cuts.Comment: 37 pages, 4 figures. Presentation improved, typos corrected. Published in Journal Of Statistical Mechanic

Asymptomatic Carotid Stenosis and Cognitive Improvement using Transcervical Stenting with Protective Flow Reversal Technique

ObjectivesThe relationship between carotid artery stenosis and cognitive function in individuals without a history of stroke is not clear. The possible pathomechanisms of cognitive impairment include silent embolization and hypoperfusion. In this study the aim was to assess cognitive changes after transcervical carotid artery stenting with proximal cerebral protection by flow reversal in patients with asymptomatic carotid stenosis, a novel technique that has been proved to decrease the number intraoperative emboli.Methods25 consecutive patients were assessed, of which 22 were men (88%) mean age of 74 years with severe asymptomatic carotid stenosis who underwent revascularization by carotid artery stenting (CAS) with flow reversal. Patients were evaluated 1 day before and 6 months after the procedure using a standardized neuropsychological battery. Test scores were adjusted according to age, sex, education level and were standardized (0–100). The mean of all the cognitive function scores yielded the global cognitive score (GCS).ResultsThere were no neurological complications during the procedure or during hospitalization in any patient. No deaths or cardiac complications occurred in any patient. The pre-procedure neuropsychological study showed cognitive impairment in: information processing speed in 15 patients (62.5%), visuospatial function in 14 (56.0%), memory in 18 (72.0%), executive functions in 14 (56.0%), language in three (12.0%), attention in 10 (40.0%), and global cognitive performance in eight (32.0%). Comparison of these scores with those obtained 6-month post-procedure showed significant improvement in GCS in all patients (p = .002), with a particularly marked gain in information processing speed (p = .018). Although significant improvement was not found for the remaining cognitive functions assessed, some gain was documented, and there was no deterioration.ConclusionsRevascularization by transcervical CAS with flow reversal for cerebral protection results in improved neurocognitive performance in asymptomatic elderly patients with severe carotid artery stenosis

Breaking a chaos-noise-based secure communication scheme

This paper studies the security of a secure communication scheme based on two discrete-time intermittently-chaotic systems synchronized via a common random driving signal. Some security defects of the scheme are revealed: 1) the key space can be remarkably reduced; 2) the decryption is insensitive to the mismatch of the secret key; 3) the key-generation process is insecure against known/chosen-plaintext attacks. The first two defects mean that the scheme is not secure enough against brute-force attacks, and the third one means that an attacker can easily break the cryptosystem by approximately estimating the secret key once he has a chance to access a fragment of the generated keystream. Yet it remains to be clarified if intermittent chaos could be used for designing secure chaotic cryptosystems.Comment: RevTeX4, 11 pages, 15 figure

The relevance of grated inlets within surface drainage systems in the field of urban flood resilience. A review of several experimental and numerical simulation approaches

Urban drainage networks should be designed and operated preferably under open channel flow conditions without flux return, backwater, or overflows. In the case of extreme storm events, urban pluvial flooding is generated by the excess of surface runoff that could not be conveyed by pressurized sewer pipes, due to its limited capacity or, many times, due to the poor efficiency of surface drainage systems to collect uncontrolled overland flow. Generally, the hydraulic design of sewer systems is addressed more for underground networks, neglecting the surface drainage system, although inadequate inlet spacings and locations can cause dangerous flooding with rele-vant socio-economic impacts and the interruption of critical services and urban activities. Several experimental and numerical studies carried out at the Technical University of Catalonia (UPC) and other research institutions demonstrated that the hydraulic efficiency of inlets can be very low under critical conditions (e.g., high circulating overland flow on steep areas). In these cases, the hydraulic efficiency of conventional grated inlets and continuous transverse elements can be around 10–20%. Their hydraulic capacity, expressed in terms of discharge coefficients, shows the same criticism with values quite far from those that are usually used in several project practice phases. The grate clogging phenomenon and more intense storm events produced by climate change could further reduce the inlets’ performance. In this context, in order to improve the flood urban resilience of our cities, the relevance of the hydraulic behavior of surface drainage systems is clear