Mathematical open problems in Projected Entangled Pair States

Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad mathematical audience, some mathematical questions about PEPS.Comment: Notes associated to the Santal\'o Lecture 2017, Universidad Complutense de Madrid (UCM), minor typos correcte

Tailoring electronic and optical properties of TiO2: nanostructuring, doping and molecular-oxide interactions

Titanium dioxide is one of the most widely investigated oxides. This is due to its broad range of applications, from catalysis to photocatalysis to photovoltaics. Despite this large interest, many of its bulk properties have been sparsely investigated using either experimental techniques or ab initio theory. Further, some of TiO2's most important properties, such as its electronic band gap, the localized character of excitons, and the localized nature of states induced by oxygen vacancies, are still under debate. We present a unified description of the properties of rutile and anatase phases, obtained from ab initio state of the art methods, ranging from density functional theory (DFT) to many body perturbation theory (MBPT) derived techniques. In so doing, we show how advanced computational techniques can be used to quantitatively describe the structural, electronic, and optical properties of TiO2 nanostructures, an area of fundamental importance in applied research. Indeed, we address one of the main challenges to TiO2-photocatalysis, namely band gap narrowing, by showing how to combine nanostructural changes with doping. With this aim we compare TiO2's electronic properties for 0D clusters, 1D nanorods, 2D layers, and 3D bulks using different approximations within DFT and MBPT calculations. While quantum confinement effects lead to a widening of the energy gap, it has been shown that substitutional doping with boron or nitrogen gives rise to (meta-)stable structures and the introduction of dopant and mid-gap states which effectively reduce the band gap. Finally, we report how ab initio methods can be applied to understand the important role of TiO2 as electron-acceptor in dye-sensitized solar cells. This task is made more difficult by the hybrid organic-oxide structure of the involved systems.Comment: 32 pages, 8 figure

Chromosomal analysis of selected lines of Drosophila melanogaster with a new level of bristle canalization

International audienc

Introducing keytagging, a novel technique for the protection of medical image-based tests

This paper introduces keytagging, a novel technique to protect medical image-based tests by implementing image authentication, integrity control and location of tampered areas, private captioning with role-based access control, traceability and copyright protection. It relies on the association of tags (binary data strings) to stable, semistable or volatile features of the image, whose access keys (called keytags) depend on both the image and the tag content. Unlike watermarking, this technique can associate information to the most stable features of the image without distortion. Thus, this method preserves the clinical content of the image without the need for assessment, prevents eavesdropping and collusion attacks, and obtains a substantial capacity-robustness tradeoff with simple operations. The evaluation of this technique, involving images of different sizes from various acquisition modalities and image modifications that are typical in the medical context, demonstrates that all the aforementioned security measures can be implemented simultaneously and that the algorithm presents good scalability. In addition to this, keytags can be protected with standard Cryptographic Message Syntax and the keytagging process can be easily combined with JPEG2000 compression since both share the same wavelet transform. This reduces the delays for associating keytags and retrieving the corresponding tags to implement the aforementioned measures to only ¿30 and ¿90. ms respectively. As a result, keytags can be seamlessly integrated within DICOM, reducing delays and bandwidth when the image test is updated and shared in secure architectures where different users cooperate, e.g. physicians who interpret the test, clinicians caring for the patient and researchers

Anderson localization in carbon nanotubes: defect density and temperature effects

The role of irradiation induced defects and temperature in the conducting properties of single-walled (10,10) carbon nanotubes has been analyzed by means of a first-principles approach. We find that di-vacancies modify strongly the energy dependence of the differential conductance, reducing also the number of contributing channels from two (ideal) to one. A small number of di-vacancies (5-9) brings up strong Anderson localization effects and a seemly universal curve for the resistance as a function of the number of defects. It is also shown that low temperatures, around 15-65 K, are enough to smooth out the fluctuations of the conductance without destroying the exponential dependence of the resistivity as a function of the tube length.Comment: 4 pages, 4 figure

First-Principle Description of Correlation Effects in Layered Materials

We present a first-principles description of anisotropic materials characterized by having both weak (dispersion-like) and strong covalent bonds, based on the Adiabatic--Connection Fluctuation--Dissipation Theorem within Density Functional Theory. For hexagonal boron nitride the in-plane and out of plane bonding as well as vibrational dynamics are well described both at equilibrium and when the layers are pulled apart. Also bonding in covalent and ionic solids is described. The formalism allows to ping-down the deficiencies of common exchange-correlation functionals and provides insight towards the inclusion of dispersion interactions into the correlation functional.Comment: Accepted for publication in Physical Review Letter

Collective unambiguous positioning with high-order BOC signals

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.The unambiguous estimation of high-order BOC signals in harsh propagation conditions is still an open problem in the literature. This paper proposes to overcome the limitations observed in state-of-the-art unambiguous estimation techniques based on the application of existing direct positioning techniques and the exploitation of the spatial diversity introduced by arrays of antennas. In particular, the ambiguity problem is solved as a multiple-input multiple-output (MIMO) estimation problem in the position domain.Peer ReviewedPostprint (author's final draft