Advanced clustering techniques for the IDU cross-match in the ESA Gaia mission

Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Rosa Maria Miró RoigThe cross-match (XM) is a sophisticated process that provides a link between every Gaia observation and the corresponding source in the catalogue. In this work, we describe a generalized method based on clustering analysis for a clustering stage of the Gaia XM, including additional parameters such as magnitude and proper motion. The performance of the implemented algorithm is assessed through real-case examples using Gaia data, and the successful results that were obtained demonstrates that the system behaves as expected

Energy levels in a symmetric triple well

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Josep TaronWe show, by analogy with the double square well, the energy levels of the triple square well. More specifically, it is interesting the analysis of the lowest energy levels when E < V0 because the three lowest energy levels are non-degenerate in contrast with the classical solution, and the transition between different wells is possible. As a result, we develop the corresponding energy formulae which are confirmed numerically and the tunnel effect is also described

Combinatorial properties of convex polygons in point sets

The Erd&#337;s-Szekeres theorem is a famous result in Discrete geometry that inspired a lot of research and motivated new problems. The theorem states that for every integer n &#8805; 3 there is another integer N_0 such that any set of N &#8805; N_0 points in general position in the plane contains the vertex set of a convex n-gon. Related is the question on the number of empty (without interior points) convex k-gons, X_k, in a set of n points, for k=3,4,5,... . A known result states that the alternating sum of the X_k's only depends on the number n of points, but not on the precise positions of the points. A proof was given by Pinchasi, Radoi&#269;i&#263;, and Sharir in 2006. In this thesis we extend this result to the numbers of convex k-gons with l interior points, X_{k,l}, and provide several formulas involving these numbers. All these formulas only depend on the number n of points of the set. The proofs are based on a continuous motion argument. We further show that with this proof technique at most n-2 linearly independent equations for the X_{k,l}'s can be obtained and we provide n-2 such equations. We also obtain several other formulas, building upon a work by Huemer, Oliveros, Pérez-Lantero, and Vogtenhuber. The obtained formulas could further be useful to solve some open problems related to the Erd&#337;s-Szekeres theorem. This thesis also surveys several known results and questions related to this classical problem for point sets in the plane

Analysis of the 2021 GeV flare of PSR B1259-63

Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2021, Tutor: Pol Bordas ComaPSR B1259-63/LS 2883 is a gamma-ray binary in which the compact object (a pulsar) crosses the disk of the massive companion twice during its 3.4 years orbit, when it is close to periastron. The GeV flare detected by Fermi-LAT around 30-40 days after the periastron passage in 2010, 2014 and 2017 was not detected until 60 days after the most recent periastron on 9th February 2021 and lasted more than the previous flares. An unbinned likelihood analysis was performed with the Python 3 version of the Fermi-Tools, HEAsoft 6.28 and making use of pass 8 Fermi-LAT data obtained up to 112 days after periastron (1st June 2021). Modelling PSR B1259-63 with a power law, a photon index of 2.76 ± 0.09 and a Test Statistics significance level of 170.3 were obtained during the flare, similar to the values in papers referring to the previous flares. Although several models have been proposed to explain this phenomenon that is likely related to the pulsar crossing the disk, the origin of the GeV is still unclea

Low cost fingerprint matching system for biometric identification

We plan to devise low cost techniques for figerprint identification in a reduced community, where sensibility and specificity have different importance. Techniques should be easily implementable in apps running in android machines.The objective of this project is to develop a system required by the Doctors Without Borders NGO that consists in managing the medical histories of a refugee camp in an easier way. Specifically, this system was already designed in another final degree project with the objective of storing the medical histories in a database, managing them by an application, and using the fingerprint for the patient’s identification. Due to the poor results obtained in the fingerprint identification, this project is focused in developing a low complexity technique (that should run in an Android device) with low mismatching error. Two minutiae-based matching methods have been developed but only one of them reaches sufficiently good results. It is based in the vectors between the minutiae in the frequency domain and it has reached a correct recognition probability of 70% and a correct rejection probability of 71.4286% with a processing time of 5 seconds in a database compounded by 60 people.El objetivo de este proyecto es desarrollar un sistema solicitado para la ONG Médicos Sin Fronteras que consiste en gestionar más fácilmente los historiales médicos de un campo de refugiados. En concreto este sistema fue diseñado en otro trabajo fin de grado y consiste en guardar los historiales médicos en una base de datos, gestionarlos a través de una aplicación y utilizar la huella dactilar para la identificación de los pacientes. Debido a los pobres resultados obtenidos en la identificación con la huella dactilar, este proyecto está centrado en mejorar esta parte. Se han desarrollado dos métodos de matching basados en minucias pero solo una de ellos logra resultados suficientemente buenos. Este método se basa en los vectores que unen las minucias en el dominio frecuencial y ha logrado una probabilidad de reconocimiento correcto del 70% y una probabilidad de rechazar correctamente del 71.4286% con un tiempo de procesado de 5 segundos en una base de datos formada por 60 personas.L’objectiu d’aquest projecte és desenvolupar un sistema sol·licitat per la ONG Metges Sense Fronteres que consisteix en gestionar més fàcilment els historials mèdics d’un camp de refugiats. En concret, aquest sistema va ser dissenyat en un altre treball fi de grau i consisteix en guardar els historials mèdics en una base de dades, gestionar-els a través d’un aplicació i utilitzar l’empremta dactilar per la identificació dels pacients. Degut als pobres resultats obtinguts en la identificació amb l’empremta dactilar, aquest projecte està centrat en millorar aquesta part. S’han desenvolupat dos mètodes de matching basats en minúcies però només un d’ells assoleix resultats suficientment bons. Aquest mètode es basa en els vectors que uneixen les minúcies en el domini freqüencial i ha assolit una probabilitat de reconèixer correctament del 70% i una probabilitat de rebutjar correctament del 71.4286% amb un temps de processat de 5 segons en una base de dades formada per 60 persones

A service-constrained positioning strategy for an autonomous fleet of airborne base stations

This paper proposes a positioning strategy for a fleet of unmanned aerial vehicles (UAVs) airlifting wireless base stations driven by communication constraints. First, two schedulers that model the distribution of resources among users within a single cell are analyzed. Then, an UAV autonomous positioning strategy is developed, based on a fair distribution of the radio resources among all the users of all the cells in a given scenario, in such a way that the user bitrate is the same regardless the users’ distribution and spatial density. Moreover, two realistic constraints are added related to capacity of the backhaul link among the UAVs and the ground station: the bitrate delivered per UAV and the total backhaul bandwidth shared among all the UAVs. Additionally, an energy consumption model is considered to evaluate the efficiency and viability of the proposed strategy. Finally, numerical results in different scenarios are provided to assess both the schedulers performance and the proposed coordinated positioning strategy for the UAVs.Peer ReviewedPostprint (published version

On weighted sums of numbers of convex polygons in point sets

The version of record of this article, first published in Discrete & Computational Geometry, is available online at Publisher’s website: https://doi.org/10.1007/s00454-022-00395-8Let S be a set of n points in general position in the plane, and let Xk,(S) be the number of convex k-gons with vertices in S that have exactly points of S in their interior. We prove several equalities for the numbers Xk,(S). This problem is related to the Erd¿os–Szekeres theorem. Some of the obtained equations also extend known equations for the numbers of empty convex polygons to polygons with interior points. Analogous results for higher dimension are shown as well.Research of C.H. was partially supported by project MTM2015-63791-R (MINECO/ FEDER), PID-2019-104129GB-I00/MCIN/AEI/10.13039/501100011033, and by project Gen. Cat. DGR 2017SGR1336. D.O. was partially supported by project PAPIIT IG100721 and CONACyT 282280. P. P-L. was partially supported by project DICYT 041933PL Vicerrectoría de Investigación, Desarrollo e Innovación USACH (Chile), and Programa Regional STICAMSUD 19-STIC-02. Research of B.V. was partially supported by the Austrian Science Fund (FWF) within the collaborative DACH project Arrangements and Drawings as FWF Project I 3340-N35. We thank an anonymous referee for helpful comments. This project has been supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 734922Postprint (author's final draft

Comparative analysis of tools to predict rapid progression in autosomal dominant polycystic kidney disease

Background: Autosomal dominant polycystic kidney disease (ADPKD) is the most common genetic kidney disease and shows a wide phenotype. Only patients with rapid progression (RP) are included in clinical trials or are approved to receive disease-modifying drugs. This study aims at comparing different available predictive tools in ADPKD with the Mayo classification (MC) identification of rapid progressors based on high total kidney volume (TKV) according to age. Methods: A total of 164 ADPKD patients were recruited retrospectively from a single centre. The performance of diverse tools to identify RP defined as being in MC categories 1C-1E was assessed. Results: A total of 118 patients were MC 1C-1E. The algorithm developed by the European Renal Association-European Dialysis and Transplant Association Working Group on Inherited Kidney Disorders/European Renal Best Practice had a low sensitivity in identifying MC 1C-1E. The sensitivity and specificity of TKV to predict RP depend on the cut-off used. A kidney length of >16.5 cm before age 45 years has high specificity but low sensitivity. Assessing the MC by ultrasonography had high levels of agreement with magnetic resonance imaging (MRI) data, especially for 1A, 1D and 1E. The estimated glomerular filtration rate (eGFR) decline was very sensitive but had low specificity. In contrast, the Predicting Renal Outcome in Polycystic Kidney Disease (PROPKD) score was very specific but had poor sensitivity. Having hypertension before 35 years of age is a good clinical predictor of MC 1C-1E. Family history can be of help in suggesting RP, but by itself it lacks sufficient sensitivity and specificity. Conclusions: The MC by ultrasonography could be an option in hospitals with limited access to MRI as it performs well generally, and especially at the extremes of the MC, i.e. classes 1A, 1D and 1E. The eGFR decline is sensitive but not very specific when compared with the MC, whereas the PROPKD score is very specific but has low sensitivity. Integrating the different tools currently available to determine RP should facilitate the identification of rapid progressors among patients with ADPKD

Gaia Early Data Release 3: The astrometric solution

[Context] Gaia Early Data Release 3 (Gaia EDR3) contains results for 1.812 billion sources in the magnitude range G = 3-21 based on observations collected by the European Space Agency Gaia satellite during the first 34 months of its operational phase. [Aims] We describe the input data, the models, and the processing used for the astrometric content of Gaia EDR3, as well as the validation of these results performed within the astrometry task. [Methods] The processing broadly followed the same procedures as for Gaia DR2, but with significant improvements to the modelling of observations. For the first time in the Gaia data processing, colour-dependent calibrations of the line- and point-spread functions have been used for sources with well-determined colours from DR2. In the astrometric processing these sources obtained five-parameter solutions, whereas other sources were processed using a special calibration that allowed a pseudocolour to be estimated as the sixth astrometric parameter. Compared with DR2, the astrometric calibration models have been extended, and the spin-related distortion model includes a self-consistent determination of basic-angle variations, improving the global parallax zero point. [Results] Gaia EDR3 gives full astrometric data (positions at epoch J2016.0, parallaxes, and proper motions) for 1.468 billion sources (585 millionwith five-parameter solutions, 882 million with six parameters), and mean positions at J2016.0 for an additional 344 million.Solutions with five parameters are generally more accurate than six-parameter solutions, and are available for 93% of the sources brighter than the 17th magnitude. The median uncertainty in parallax and annual proper motion is 0.02-0.03 mas at magnitude G = 9-14, and around 0.5 mas at G = 20. Extensive characterisation of the statistical properties of the solutions is provided, including the estimated angular power spectrum of parallax bias from the quasars.This work was financially supported by the European Space Agency (ESA) in the framework of the Gaia project; the German Aerospace Agency (Deutsches Zentrum für Luft- und Raumfahrt e.V., DLR) through grants 50QG0501, 50QG0601, 50QG0901, 50QG1401 and 50QG1402; the Spanish Ministry of Economy (MINECO/FEDER, UE) through grants ESP2016-80079-C2-1-R, RTI2018-095076-B-C21 and the Institute of Cosmos Sciences University of Barcelona (ICCUB, Unidad de Excelencia “María de Maeztu”) through grants MDM-2014-0369 and CEX2019-000918-M; the Swedish National Space Agency (SNSA/Rymdstyrelsen); and the United Kingdom Particle Physics and Astronomy Research Council (PPARC), the United Kingdom Science and Technology Facilities Council (STFC), and the United Kingdom Space Agency (UKSA) through the following grants to the University of Bristol, the University of Cambridge, the University of Edinburgh, the University of Leicester, the Mullard Space Sciences Laboratory of University College London, and the United Kingdom Rutherford Appleton Laboratory (RAL): PP/D006511/1, PP/D006546/1, PP/D006570/1, ST/I000852/1, ST/J005045/1, ST/K00056X/1, ST/K000209/1, ST/K000756/1, ST/L006561/1, ST/N000595/1, ST/N000641/1, ST/N000978/1, ST/N001117/1, ST/S000089/1, ST/S000976/1, ST/S001123/1, ST/S001948/1, ST/S002103/1, and ST/V000969/1