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2022/2023, 2n quadrimestre

Graph topology inference is a research field that studies how to learn the structure of a graph from data related to it. It is a very popular research topic in which algorithms are being developed faster and more efficient year after year. Graphs are a mathematical tool that allows us to model relationships between data obtained from complex structures, such as the human brain. In this thesis, we have developed a graph topology inference algorithm based on the estimation of the precision matrix with Laplacian constraints, where we have used real data obtained by f-MRI to evaluate the algorithm. Then, we have applied network science parameters, such as the small-world parameter, in order to compare different graph network topologies and provide valuable information about the structure of these graphs., La inferencia de topología de grafos es un campo de investigación en el que se estudia cómo aprender la estructura de un grafo a partir de datos relacionados con él. Es un tema de investigación muy popular en el que se desarrollan algoritmos cada vez más rápidos y eficientes año tras año. Los grafos son una herramienta matemática que nos permite modelar las relaciones entre datos obtenidos en estructuras complejas, como por ejemplo el cerebro humano. En esta tesis, hemos desarrollado un algoritmo de inferencia de topología de grafos basado en la estimación de la matriz de precisión con restricciones de Laplaciana, donde hemos utilizado datos reales obtenidos por f-MRI para evaluar el algoritmo. Después, hemos aplicado parámetros de ciencia de redes, como por ejemplo el parámetro "small-world", para poder comparar diferentes topologías de grafos y proporcionar una información valiosa sobre la estructura de estos grafos., La inferència de topologia de grafs és un camp de recerca en el qual s'estudia com aprendre l'estructura d'un graf a partir de dades relacionades amb ell. És un tema de recerca molt popular en el qual es desenvolupen algorismes cada vegada més ràpids i eficients any rere any. Els grafs són una eina matemàtica que ens permet modelar les relacions entre dades obtingudes en estructures complexes, com per exemple el cervell humà. En aquesta tesi, hem dut a terme un algorisme d'inferència de topologia de grafs basat en l'estimació de la matriu de precisió amb restriccions de Laplaciana, on hem utilitzat dades reals aconseguides per f-MRI per avaluar l'algorisme. Després, hem aplicat paràmetres de ciència de xarxes, com per exemple el paràmetre "small-world", per poder comparar diferents topologies de grafs i proporcionar una informació valuosa sobre l'estructura d'aquests grafs.

Utilitzar filtre en grafs per a predir la topologia d'un graf., This project will focus on the development of methods to predict relations (links) between elements (nodes) of a network structured in a graph. In order to study these systems, the graphs will be understood as a signal domain. Therefore, the aim of the project becomes to design a signal processing method to predict missing or future links of a graph, Este proyecto se centra en el desarrollo de métodos para predecir las relaciones (enlaces) entre elementos (nodos) de una red estructurada en un grafo. Para estudiar estos sistemas, los grafos se entenderán como un dominio de señales. Por lo tanto, el objetivo del proyecto se convierte a diseñar un método de procesamiento de señales para predeci enlaces futuros o desconocidos de un grafo, Aquest projecte se centra en el desenvolupament de mètodes per predir les relacions (enllaços) entre elements (nodes) d'una xarxa estructurada en un graf. Per tal d'estudiar aquests sistemes, els grafs s'entendran com un domini de senyals. Per tant, l'objectiu del projecte es converteix en dissenyar un mètode de processament de senyals per predir enllaços futurs o desconeguts d'un graf

Higher-order link prediction (HOLP) seeks missing links capturing dependencies among three or more network nodes. Predicting high-order links (HOLs) can for instance reveal hyperlinks in the structure of drug substance and metabolic networks. Existing methods either make restrictive assumptions regarding the emergence of HOLs, or, they rely on reduced dimensionality models of limited expressiveness. To overcome these limitations, the HOLP approach developed here leverages distribution similarities across embeddings as captured by a learnable probability metric. The intuition underpinning the novel approach is that sets of nodes whose embeddings are less similar in distribution, are less likely to be connected by a HOL. Specifically, nonlinear dimensionality reduction is effected through a Gaussian process latent variable model that yields nodal embeddings, and also learns a data-driven similarity function (kernel). This kernel forms the core of a maximum mean discrepancy probability metric. Tests on benchmark datasets illustrate the potential of the proposed approach., This work was supported in part by NSF grants 1901134, 2126052, 2212318, 2220292. A. Pages-Zamora was supported by grants PID 2019-104958RB-C41 and RED2018-102668-T funded by MCIN/AEI/10.13039/501100011033; and by 2021 SGR 01033 funded by Dept. de Recerca i Univ. de la Generalitat de Catalunya 10.13039/501100002809., Peer Reviewed, Postprint (author's final draft)

Resolved, 2021/2022

With Differential GNSS (DGNSS), Single Differentiation (SD) of GNSS pseudorange mea- surements is computed with the aim of correcting harmful errors such as ionospheric and tropospheric delays. These errors can be mitigated to up to very few centimeters, which denotes a performance improvement with respect to the Standard Point Positioning (SPP) solution, widely used in GNSS receivers. However, with DGNSS it is necessary to have a very precise knowledge of the coordinates of a reference station in order to experience this performance improvement. We propose the Massive User-Centric Single Differentiation (MUCSD) algorithm, which is proven to have a comparable performance to DGNSS with- out the need of a reference station. Instead, N cooperative receivers which provide noisy observations of their position and clock bias are introduced in the model. The MUCSD algorithm is mathematically derived with an Iterative Weighted Least Squares (WLS) Estimator. The estimator lower bound is calculated with the Cramér-Rao Bound (CRB). Several scenarios are simulated to test the MUCSD algorithm with the MassiveCoop-Sim simulator. Results show that if the observations provided by the cooperative users have a noise of up to 10 meters, DGNSS performance can be obtained with N = 10. When observations are very noisy, the MUCSD performance still approaches DGNSS for high values of N.

Unsupervised ensemble learning refers to methods devised for a particular task that combine data provided by decision learners taking into account their reliability, which is usually inferred from the data. Here, the variant calling step of the next generation sequencing technologies is formulated as an unsupervised ensemble classification problem. A variant calling algorithm based on the expectation-maximization algorithm is further proposed that estimates the maximum-a-posteriori decision among a number of classes larger than the number of different labels provided by the learners. Experimental results with real human DNA sequencing data show that the proposed algorithm is competitive compared to state-of-the-art variant callers as GATK, HTSLIB, and Platypus., This work has been funded by the Agencia Estatal de Investigación, Ministerio de Ciencia, Innovación y Universidades of the Spanish Government and ERDF funds (PID2019-104958RB-C41, RED2018-102668-T); and by Gipuzkoa Fellows grant and Ramon y Cajal grant., Peer Reviewed, Postprint (published version)

This paper deals with the selection of the training dataset in kernel-based methods for function reconstruction, with a focus on kernel ridge regression. A functional analysis is performed which, in the absence of noise, links the optimal sampling distribution to the one minimizing the difference between the kernel matrix and its low-rank Nyström approximation. From this standpoint, a statistical passive sampling approach is derived which uses the leverage scores of the columns of the kernel matrix to design a sampling distribution that minimizes an upper bound of the risk function. The proposed approach constitutes a passive method, able to select the optimal subset of training samples using only information provided by the input set and the kernel, but without needing to know the values of the function to be approximated. Furthermore, the proposed approach is backed up by numerical tests on real datasets., This work has been funded by the Ministerio de Ciencia e Innovación (MICINN) of the Spanish Government and by the Agencia Estatal de Investigación (AEI/10.13039/501100011033) and ERDF funds (PID 2019-104958RB-C41/C43, RED2018-102668-T); and by the Catalan Government (2017 SGR 578)., Peer Reviewed, Postprint (author's final draft)

We consider the quantum multiple hypothesis testing problem, focusing on the case of hypothesis represented by pure states. A sequential adaptive algorithm is derived and analyzed first. This strategy exhibits a decay rate in the error probability with respect to the expected value of measurements greater than the optimal decay rate of the fixed-length methods. A more elaborated scheme is developed next, by serially concatenating multiple implementations of the first scheme. In this case each stage considers as a priori hypothesis probability the a posteriori probability of the previous stage. We show that, by means of a fixed number of concatenations, the expected value of measurements to be performed decreases considerably. We also analyze one strategy based on an asymptotically large concatenation of the initial scheme, demonstrating that the expected number of measurements in this case is upper bounded by a constant, even in the case of zero average error probability. A lower bound for the expected number of measurements in the zero error probability setting is also derived., This work was supported in part by the Agencia Estatal de Investigación, Ministerio de Ciencia e Innovación, of the Spanish Government, under Grant RED2018-102668-T and Grant PID2019-104958RB-C41; in part by the Catalan Government under Grant 2017 SGR 578 AGAUR; and in part by the QuantumCAT within the European Regional Development Fund (ERDF) Program of Catalunya under Grant 001-P-001644., Postprint (published version)

In recent years, second generation artificial neural networks (ANNs) have revolutionized the field of machine learning. These networks are mainly trained using supervised learning algorithms, e.g. back-propagation, and their neurons have a static activation that represents the spike rate of a biological neuron. However, physiological evidence suggests that biological neurons also take into account spike timing to encode information, and that their learning mechanisms are unsupervised. These difference motivated the exploration of spiking neural networks (SNNs) as third generation ANNs, that employ spiking neurons as computational units and are endowed with bio-inspired Hebbian learning mechanisms, e.g. spike timing dependent plasticity (STDP). In parallel, a growing interest to extend neural networks to machine learning tasks involving non-Euclidean data has led to the development of graph neural networks (GNNs). However, the research on SNNs is very recent and a third generation GNN implementation is still lacking. In this work, we develop a new learning rule for SNNs that we call GraphSTDP, which represents a first step towards the implementation of a third generation GNN.

This paper presents a method to estimate the direction of arrival (DOA) of multiple sources received by a uniform linear array (ULA) with a reduced number of radio-frequency (RF) chains. The receiving array relies on antenna switching so that at every time instant only the signals received by a randomly selected subset of antennas are downconverted to baseband and sampled. Low-rank matrix completion (MC) techniques are then used to reconstruct the missing entries of the signal data matrix to keep the angular resolution of the original large-scale array. The proposed MC algorithm exploits not only the low- rank structure of the signal subspace, but also the shift-invariance property of ULAs, which results in a better estimation of the signal subspace. Further, the effect of MC on DOA estimation is discussed under the perturbation theory framework. The simulation results suggest that the proposed method provides accurate DOA estimates even in the small-sample regime with a significant reduction in the number of RF chains required for a given spatial resolution., This work was supported by the Ministerio de Ciencia e Innovación (MICINN) of Spain, and AEI/FEDER funds of the E.U., under grants TEC2016-75067-C4-4-R /2-R (CARMEN), PID2019-104958RB-C43/C41 (ADELE) and BES-2017-080542., Peer Reviewed, Postprint (author's final draft)

This letter addresses the problem of order estimation for uniform linear arrays (ULAs) with multi-switch antenna selection in the small-sample regime. Multi-switch antenna selection results in a data matrix with missing entries, a scenario for which existing order estimation methods that build on the eigenvalues of the sample covariance matrix do not perform well. A direct application of the Davis-Kahan theorem allows us to show that the signal subspace is quite robust in the presence of missing entries. Based on this finding, this letter proposes a matrix completion (MC) subspace-based order estimation criterion that exploits the shift-invariance property of ULAs. A recently proposed shift-invariant matrix completion (SIMC) method is used for reconstructing the data matrix, and the proposed order estimation criterion is based on the chordal subspace distance between two submatrices extracted from the reconstructed matrix for increasing values of the dimension of the signal subspace. Our simulation results show that the method provides accurate order estimates with percentages of missing entries higher than 50 %., This work was supported by the Ministerio de Ciencia e Innovación (MICINN) of Spain, and AEI/FEDER funds of the E.U., under Grants PID2019-104958RB-C43/C41 (ADELE) and BES-2017-080542., Peer Reviewed, Postprint (author's final draft)

Resolved

This paper presents the benefits of using the random-walk normalized Laplacian matrix as a graph-shift operator and defines the frequencies of a graph by the eigenvalues of this matrix. A criterion to order these frequencies is proposed based on the Euclidean distance between a graph signal and its shifted version with the transition matrix as shift operator. Further, the frequencies of a periodic graph built through the repeated concatenation of a basic graph are studied. We show that when a graph is replicated, the graph frequency domain is interpolated by an upsampling factor equal to the number of replicas of the basic graph, similarly to the effect of zero-padding in digital signal processing., This work has been funded by the Agencia Estatal de Investigación, Ministerio de Ciencia, Innovación y Universidades of the Spanish Government and ERDF funds (PID2019-104958RB-C41, RED2018-102668-T); and by the Catalan Government-Secretaria d'Universitats i Recerca, Departament d'Empresa i Coneixement, Generalitat de Catalunya, AGAUR (2020 FI_B 00495, 2017 SGR 578)., Peer Reviewed, Postprint (published version)

Resolved

In matrix completion, the objective is to recover an unknown matrix from a small subset of observed entries. Most successful methods for recovering the unknown entries are based on the assumption that the unknown full matrix has low rank. By having low rank, each of its entries are obtained as a function of a small number of coefficients which can be accurately estimated provided that there are enough available observations. Hence, in low-rank matrix completion the estimate is given by the matrix of minimum rank that fits the observed entries. Besides low rankness, the unknown matrix might exhibit other structural properties which can be leveraged in the recovery process. In a smooth matrix, it can be expected that entries that are close in index distance will have similar values. Similarly, groups of rows or columns can be known to contain similarly valued entries according to certain relational structures. This relational information is conveyed through different means such as covariance matrices or graphs, with the inconvenient that these cannot be derived from the data matrix itself since it is incomplete. Hence, any knowledge on how the matrix entries are related among them must be derived from prior information. This thesis deals with matrix completion with prior information, and presents an outlook that generalizes to many situations. In the first part, the columns of the unknown matrix are cast as graph signals with a graph known beforehand. In this, the adjacency matrix of the graph is used to calculate an initial point for a proximal gradient algorithm in order to reduce the iterations needed to converge to a solution. Then, under the assumption that the graph signals are smooth, the graph Laplacian is incorporated into the problem formulation with the aim to enforce smoothness on the solution. This results in an effective denoising of the observed matrix and reduced error, which is shown through theoretical analysis of the proximal gradient coupled with L, A matrix completion, l'objectiu és recuperar una matriu a partir d'un subconjunt d'entrades observables. Els mètodes més eficaços es basen en la idea que la matriu desconeguda és de baix rang. Al ser de baix rang, les seves entrades són funció d'uns pocs coeficients que poden ser estimats sempre que hi hagi suficients observacions. Així, a matrix completion la solució s'obté com la matriu de mínim rang que millor s'ajusta a les entrades visibles. A més de baix rang, la matriu desconeguda pot tenir altres propietats estructurals que poden ser aprofitades en el procés de recuperació. En una matriu suau, pot esperar-se que les entrades en posicions pròximes tinguin valor similar. Igualment, grups de columnes o files poden saber-se similars. Aquesta informació relacional es proporciona a través de diversos mitjans com ara matrius de covariància o grafs, amb l'inconvenient que aquests no poden ser derivats a partir de la matriu de dades ja que està incompleta. Aquesta tesi tracta sobre matrix completion amb informació prèvia, i presenta metodologies que poden aplicar-se a diverses situacions. En la primera part, les columnes de la matriu desconeguda s'identifiquen com a senyals en un graf conegut prèviament. Llavors, la matriu d'adjacència del graf s'usa per calcular un punt inicial per a un algorisme de gradient pròxim amb la finalitat de reduir les iteracions necessàries per arribar a la solució. Després, suposant que els senyals són suaus, la matriu laplaciana del graf s'incorpora en la formulació del problema amb tal forçar suavitat en la solució. Això resulta en una reducció de soroll en la matriu observada i menor error, la qual cosa es demostra a través d'anàlisi teòrica i simulacions numèriques. La segona part de la tesi introdueix eines per a aprofitar informació prèvia mitjançant reproducing kernel Hilbert spaces. Atès que un kernel mesura la similitud entre dos punts en un espai, permet codificar qualsevol tipus d'informació tal com vectors de característiques, Postprint (published version)

Quantum computing over the past few decades has experienced a huge boost, due in part to the discovery of algorithms such as the Shor's algorithm which promises a significant reduction in complexity compared to its analogues of classical computing. The main objective of this thesis is to introduce improvements in some algorithms based on the quantum Fourier transform, more specifically in the phase estimation algorithm and the order-finding algorithm. In addition to this, the problem of efficient generation of quantum states is also studied, where as a result a method has been developed for the efficient generation of quantum states., La computación cuántica ha experimentado un gran avance durante las últimas décadas, en parte debido al descubrimiento de algoritmos como el algoritmo de Shor, el cual promete una reducción en la complejidad comparado con su análogo en computación clásica. El objetivo principal de la tesis es introducir mejoras en algunos algoritmos basados en la transformada cuántica de Fourier, concretamente en el algoritmo de estimación de fase y el algoritmo de order-finding. Además, se estudia el problema de la generación eficiente de estados cuánticos, donde como resultado se ha desarrollado un método para la generación eficiente de estados cuánticos., La computació quàntica ha experimentat un gran impuls durant les últimes dècades, en part debut al descobriment d'algoritmes com l'algoritme de Shor, el qual promet una reducció en la complexitat comparat amb el seu anàleg en computació clàssica. L'objectiu principal de la tesi és introduir millores en alguns algoritmes basats en la transformada quàntica de Fourier, concretament en l'algoritme d'estimació de fase i l'algoritme de order-finding. A més, s'estudia el problema de la generació eficient d'estats quàntics, on com a resultat s'ha desenvolupat un mètode per a la generació eficient d'estats quàntics.

© 2020 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., Prior information can be incorporated in matrix completion to improve estimation accuracy and extrapolate the missing entries. Reproducing kernel Hilbert spaces provide tools to leverage the said prior information, and derive more reliable algorithms. This paper analyzes the generalization error of such approaches, and presents numerical tests confirming the theoretical results, This work is supported by ERDF funds (TEC2013-41315-R and TEC2016-75067-C4-2), the Catalan Government (2017 SGR 578), and NSF grants(1500713, 1514056, 1711471 and 1509040)., Peer Reviewed, Postprint (published version)

© 2020 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., This paper addresses the problem of source enumeration by an array of sensors in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances, referred to non-iid noise hereafter, when the sources are uncorrelated. The diagonal terms of the sample covariance matrix are removed and, after applying Toeplitz rectification as a denoising step, the signal covariance matrix is reconstructed by using a low-rank matrix completion method adapted to enforce the Toeplitz structure of the sought solution. The proposed source enumeration criterion is based on the Frobenius norm of the reconstructed signal covariance matrix obtained for increasing rank values. As illustrated by simulation examples, the proposed method performs robustly for both small and large-scale arrays with few snapshots, i.e. small-sample regime., This work was supported by the Ministerio de Econom ́ıa y Competi-tividad (MINECO) of Spain, and AEI/FEDER funds of the E.U., undergrants TEC2016-75067-C4-4-R (CARMEN), PID2019-104958RB-C43/C41(ADELE) and BES-2017-080542, Peer Reviewed, Postprint (author's final draft)

Detecting anomalous behaviors in a specific environment is a challenge and a necessity, since by detecting an anomaly we can soon avoid wasting time to solve a specific problem. For example, in a domestic environment we can intercept a thief, or in an industry we would be able to know if a machine is not working properly. To solve this challenge, many fields of research have been opened, some based on video recordings and others on the ambient sound of the specific area to be analyzed. In this Thesis, an anomaly sound detection system is proposed for signals that have been subjected to blind source separation using ICA methods. The system is built with a neural network called Autoencoder, in order to use the reconstruction error that it returns. This reconstruction error is the difference between the original signal and the one reconstructed by the Autoencoder. By using and combining it with the error added to the signal after applying the ICA method, it has been demonstrated that the system can detect whether or not an audio signal is anomalous., Detectar comportamientos anómalos en un entorno específico es un desafío y una necesidad, ya que al detectar una anomalía, podemos evitar con antelación perder tiempo resolviendo un problema específico. Por ejemplo, en un entorno doméstico podemos interceptar a un ladrón, o en una industria podríamos saber si una máquina no funciona correctamente. Para resolver este problema, se han abierto muchos campos de investigación, algunos basados en el análisis de grabaciones de video y otros en el sonido ambiental del área específica a analizar. En esta Tesis, se propone un sistema de detección de sonido de anomalías para señales que han sido sometidas a la separación ciega de fuente utilizando métodos ICA. El sistema está construido con una red neuronal llamada Autoencoder, para utilizar el error de reconstrucción que devuelve. Este error de reconstrucción es la diferencia entre la señal original y la reconstruida por el Autoencoder. Al usarlo y combinarlo con el error agregado a la señal después de aplicar el método ICA, se ha demostrado que el sistema puede detectar si una señal de audio es anómala o no., La detecció de conductes anòmales en un entorn concret és un repte i una necessitat, ja que, detectant una anomalia amb antelació, podem evitar perdre el temps intentant resoldre un problema. Per exemple, en un entorn domèstic podem interceptar un lladre, o en una indústria podríem identificar si una màquina no funciona adequadament. Per resoldre aquest repte, s'han obert molts camps de recerca, alguns basats en enregistraments de vídeo i d'altres en el so ambient de l'àrea específica a analitzar. En aquesta Tesi, es proposa un sistema de detecció de sons anòmales per a senyals que han estat sotmesos a una separació cega de fonts mitjançant mètodes ICA. El sistema està construït amb una xarxa neuronal anomenada Autoencoder, per tal d'utilitzar l'error de reconstrucció que aquest retorna. Aquest error de reconstrucció és la diferència entre el senyal original i el reconstruït per l'Autoencoder. Mitjançant l'ús i la combinació amb l'error afegit al senyal després d'aplicar el mètode ICA, s'ha demostrat que el sistema pot detectar si un senyal d'àudio és o no anòmal.

Ground penetrating radars have been tested for detecting trapped alive victims from the ruins of collapsed building, for example due to a mining disaster, rock slide or natural catastrophe. The priority of the rescue teams is to find alive people as fast as they can. Rescue radars are designed with the primary objective of quickly finding survivors trapped beneath the surface. Researchers in the Department of Microsystems Engineering (IMTEK), at the Albert-Ludwigs University of Freiburg, have been working on experiments about antenna designing and measuring systems for rescue radar through the years. Currently, IMTEK is working in a project which objective is to develop a sensor system for the localization of buried people. This thesis has been developed there, that is why it is focused on their needs and possibilities. The aim of the thesis is to develop a mobile GPR antenna assembly which can be used as a rescue radar. The project is composed of three fundamental parts: different kinds of HF-simulations software for GPR applications comparison, while verifying if MATLAB openEMS open free source can be used for designing antennas in IMTEK department projects; designing and optimizing the GPR antenna assembly while analyzing different techniques for crosstalk isolation enhancement such us adding rings, meander-line and Electromagnetic Band Gap; and once the prototype is defined and manufactured, testing the GPR antenna in different scenarios. As a conclusion of the work, the simulations results of both software used were very close from the antenna prototype datasheet diagrams as well as from the experimental tests did. Therefore, Matlab openEMS software has also proved to be very competent in antenna designing sector, obtaining practically identical results as the CST Studio Suit software. Furthermore, after analyzing the performance of different GPR antenna modifications and the isolation enhancement structures added to the design, we concluded that the Electromag, Los georadares se han probado para detectar víctimas atrapadas en las ruinas de edificios derrumbados por causas diversas, como desastres en una mina, desprendimientos de rocas o catástrofes naturales. En estos casos, la prioridad de los equipos de rescate es encontrar los supervivientes atrapados debajo de la superficie lo más rápido posible. Los radares de rescate están diseñados con el objetivo principal de satisfacer esta necesidad. Durante los últimos años, investigadores del Departamento de Ingeniería de Microsistemas (IMTEK) de la Universidad Albert-Ludwigs de Friburg han realizado experimentos e investigaciones sobre antenas y sistemas de medida para radares de rescate. Actualmente, el IMTEK trabaja en un proyecto enfocado a desarrollar sistemas con sensores incorporados para la localización de personas enterradas debajo de la superficie. La presente tesis, realizada en este departamento, se centra en las necesidades y posibilidades. El objetivo principal de esta tesis es desarrollar un georadar móvil con aplicación directa a los radares de rescate. El trabajo está compuesto por tres partes principales: comparar diferentes tipos de programas de simulación HF para aplicaciones de georadares, mientras al mismo tiempo verificar si el software gratuito MATLAB open EMS puede ser útil para diseñar antenas en los proyectos de departamento IMTEK; diseñar y optimizar el montaje del georadar mientras se analizan diferentes técnicas de aislamiento de la comunicación cruzada y, en último lugar, cuando el prototipo este definido y fabricado, realizar diferentes pruebas de escenarios específicos para georadares. Los resultados obtenidos por los dos programas de simulación empleados en el proyecto fueron muy similares al datasheet de la antena utilizada y a los experimentos realizados. Por tanto, se puede concluir que MATLAB openEMS es igual de competente que el software CST Studio Suit en el sector del diseño de antenas. Finalmente, después de analizar el desarrollo de la, Els georadars han estat provats per detectar víctimes vives atrapades a les ruïnes d?edificis esfondrats per diverses causes, com desastres en una mina, despreniments de roques o catàstrofes naturals. En aquests casos, la prioritat dels equips de rescat és trobar els supervivents atrapats sota la superfície el més ràpid possible. Els radars de rescat estan dissenyats amb l?objectiu principal de satisfer aquesta necessitat. Durant els darrers anys, investigadors del Departament d?Enginyeria de Microsistemes (IMTEK) de la Universitat Albert-Ludwigs de Friburg han realitzat experiments i investigacions sobre antenes i sistemes de mesura per a radars de rescat. Actualment, l?IMTEK treballa en un projecte enfocat a desenvolupar sistemes amb sensors incorporats per a la localització de persones enterrades sota la superfície. La present tesi, realitzada en aquest departament, es centra en les seves necessitats i possibilitats. L?objectiu principal d'aquesta tesi és desenvolupar un georadar mòbil amb aplicació directa als radars de rescat. El treball està compost per tres parts principals: comparar diferents tipus de programaris de simulació HF per a aplicacions de georadars, mentre al mateix temps verificar si el software obert MATLAB openEMS pot ser útil per dissenyar antenes en els projectes del departament IMTEK; dissenyar i optimitzar el muntatge del georadar mentre s?analitzen diferents tècniques d?isolació de la comunicació creuada i, en darrer lloc, quan el prototip estigui definit i fabricat, realitzar diferents proves d?escenaris específics per a georadars. Els resultats obtinguts pels dos programes de simulació emprats en el projecte van ser molt similars al datasheet de l?antena utilitzada i als experiments efectuats. Per tant, es pot concloure que MATLAB openEMS és igual de competent que el software CST Studio Suit en el sector del disseny d?antenes. Finalment, després d?analitzar el desenvolupament de les diferents modificacions fetes al georadar i afegir dife

Graphs are a mathematical tools that allow us to model relationships between data obtained in complex structures, such as the brain, expression of genomes, sensor networks, and more. This project investigates signal processing techniques in graphs to infer the topology of them from observed data. In particular, different inference techniques of graph topology are tested using real data. One of the main goals was to find a suitable database for the experiment. This search led us to a database of EEG's (Electroencephalograms) in a human brain. In addition, it has been studied the usefulness of the resulting topology of the graphs to classify the data., Los grafos son una herramienta matemática que nos permite modelar las relaciones entre datos obtenidos en estructuras complejas, como por ejemplo el cerebro, la expresión de los genomas, redes de sensores, entre otros. En este proyecto se investigan técnicas de procesamiento de señal en grafos para inferir la topología de éstos a partir de datos observados. En particular se testean diferentes técnicas de inferencia de la topología de los grafos usando datos reales. Uno de los principales objetivos consistió en encontrar una base de datos idónea para realizar el experimento. Esta búsqueda nos llevó hasta una base de datos de EEG's (Electroencefalogramas) de un cerebro humano. Como tarea adicional también se ha estudiado la utilidad de la topología de los grafos resultantes para clasificar los datos., Els grafs són una eina matemàtica que ens permet modelar les relacions entre dades obtingudes en estructures complexes, com per exemple el cervell, l'expressió dels genomes, xarxes de sensors, entre d'altres. En aquest projecte s'investiguen tècniques de processament de senyal en grafs per inferir la topologia d'aquests a partir de dades observades. En particular es testegen diferents tècniques d'inferència de la topologia dels grafs usant dades reals. Un dels principals objectius va consistir en trobar una base de dades idònia per a realitzar l'experiment. Aquesta cerca ens va portar fins a una base de dades d'EEG's (Electroencefalogrames) d'un cervell humà. Com a tasca addicional també s'ha estudiat la utilitat de la topologia dels grafs resultants per a classificar les dades.

Estimating the unknown parameters of a statistical model based on the observations collected by a sensor network is an important problem with application in multiple fields. In this setting, distributed processing, by which computations are carried out within the network in order to avoid raw data transmission to a fusion centre, is a desirable feature resulting in improved robustness and energy savings. In the presence of incomplete data, the expectation-maximisation (EM) algorithm is a popular means to iteratively compute the maximum likelihood (ML) estimate. It has found application in diverse fields such as computational biology, anomaly detection, speech segmentation, reinforcement learning, and motion estimation, among others. In this chapter we will review the formulation of the centralised EM estimation algorithm as a starting point and then discuss distributed versions well suited for implementation in sensor networks. The first class of these distributed versions requires specialised routing through the network in terms of a linear or circular path visiting all nodes, whereas the second class does away with this requirement by using the concept of network consensus to diffuse information through the network. Our focus will be on a relevant sensor network application, in which the parameter of a linear model is to be estimated in the presence of an unknown number of randomly malfunctioning sensors., Peer Reviewed, Postprint (author's final draft)

In this work, the 3D spatial organization of a human Jurkat cell, an immune cell who is one ofthe main targets of the human immunodeficiency virus (HIV), is analyzed through the clusteringof genome interactions networks provided by the Hi-C data, a 3D massive sequencing technologycapable of quantifying interactions among regions of the genome inside the nucleus of a cell. Thedata analysis approach consists on a graph theoretic modelling of these networks and the clusteringanalysis is performed by the use of spectral clustering methods, a family of clustering techniquesbased on the spectral decomposition of Laplacian matrices of graph networks. By inferring the3D structure of the Jurkat cell at the nuclear scale, the distribution of HIV integration sites onthe Jurkat genome is analyzed and contrasted with the current knowledge of the the integrationmechanisms and their relationship with the 3D genomic context. The clustering results are alsoevaluated through a common set of metrics, which serve to objectively asses the 3D structure ofthe nucleus of the Jurkat cell. With the proposed data analysis, the main findings are: the 3Dspatial structure is not prominent, the global interaction genomic network contains just a fewcommunities and the insertion pattern of HIV, contrasted on the detected communities, confirmsthe established knowledge of HIV integration mechanisms.

© 2019 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., Decision-making procedures when a set of individual binary labels is processed to produce a unique joint decision can be approached modeling the individual labels as multivariate independent Bernoulli random variables. This probabilistic model allows an unsupervised solution using EM-based algorithms, which basically estimate the distribution model parameters and take a joint decision using a Maximum a Posteriori criterion. These methods usually assume that individual decision agents are conditionally independent, an assumption that might not hold in practical setups. Therefore, in this work we formulate and solve the decision-making problem using an EM-based approach but assuming correlated decision agents. Improved performance is obtained on synthetic and real datasets, compared to classical and state-of-the-art algorithms., Peer Reviewed, Postprint (author's final draft)

© <2018>. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0, Crowdsourced data in science might be severely error-prone due to the inexperience of annotators participating in the project. In this work, we present a procedure to detect specific structures in an image given tags provided by multiple annotators and collected through a crowdsourcing methodology. The procedure consists of two stages based on the Expectation–Maximization (EM) algorithm, one for clustering and the other one for detection, and it gracefully combines data coming from annotators with unknown reliability in an unsupervised manner. An online implementation of the approach is also presented that is well suited to crowdsourced streaming data. Comprehensive experimental results with real data from the MalariaSpot project are also included., Peer Reviewed, Preprint

Resolved

© 2019 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., Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a fast and low-complexity solver, the task is formulated as one of kernel ridge regression. The resultant MCEX algorithm can also afford online implementation, while the class of kernel functions also encompasses several existing approaches to MC with prior information. Numerical tests on synthetic and real datasets show that the novel approach is faster than widespread methods such as alternating least-squares (ALS) or stochastic gradient descent (SGD), and that the recovery error is reduced, especially when dealing with noisy data., Peer Reviewed, Postprint (author's final draft)

Resolved

© 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 rising interest in pattern recognition and data analytics has spurred the development of innovative machine learning algorithms and tools. However, as each algorithm has its strengths and limitations, one is motivated to judiciously fuse multiple algorithms in order to find the “best” performing one, for a given dataset. Ensemble learning aims at such highperformance meta-algorithm, by combining the outputs from multiple algorithms. The present work introduces a blind scheme for learning from ensembles of classifiers, using a moment matching method that leverages joint tensor and matrix factorization. Blind refers to the combiner who has no knowledge of the groundtruth labels that each classifier has been trained on. A rigorous performance analysis is derived and the proposed scheme is evaluated on synthetic and real datasets., Peer Reviewed, Postprint (author's final draft)

Development of an antenna characterization system, software and hardware parts. As a result, the radiation pattern of an antenna is obtained together with other relevant values., Desarrollo de un sistema de caracterización de antenas, parte de software y hardware. Como resultado se obtiene el diagrama de radiación de una antena y otros valores relevantes., Desenvolupament d'un sistema de caracterització d'antenes, part de software i hardware. Com a resultat s'obté el diagrama de radiació d'una antena i altres valors rellevants.

We address the problem of distributed estimation of a vector-valued parameter performed by a wireless sensor network in the presence of noisy observations which may be unreliable due to faulty transducers. The proposed distributed estimator is based on the Expectation-Maximization (EM) algorithm and combines consensus and diffusion techniques: a term for information diffusion is gradually turned off, while a term for updated information averaging is turned on so that all nodes in the network approach the same value of the estimate. The proposed method requires only local exchanges of information among network nodes and, in contrast with previous approaches, it does not assume knowledge of the a priori probability of transducer failures or the noise variance. A convergence analysis is provided, showing that the convergent points of the centralized EM iteration are locally asymptotically convergent points of the proposed distributed scheme. Numerical examples show that the distributed algorithm asymptotically attains the performance of the centralized EM method., Peer Reviewed, Preprint

© 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 rising interest in pattern recognition and data analytics has spurred the development of a plethora of machine learning algorithms and tools. However, as each algorithm has its strengths and weaknesses, one is motivated to judiciously fuse multiple algorithms in order to find the “best” performing one, for a given dataset. Ensemble learning aims to create a high- performance meta-algorithm, by combining the outputs from multiple algorithms. The present work introduces a simple blind scheme for learning from ensembles of classifiers, using joint matrix factorization. Blind refers to the combiner who has no knowledge of the ground-truth labels that each classifier has been trained on. Performance is evaluated on synthetic and real datasets., Peer Reviewed, Postprint (author's final draft)

Resolved

2017/2018

Malaria eradication of the worldwide is currently one of the main WHO’s global goals. In this work, we focus on the use of human-machine interaction strategies for lowcost fast reliable malaria diagnostic based on a crowdsourced approach. The addressed technical problem consists in detecting spots in images even under very harsh conditions when positive objects are very similar to some artifacts. The clicks or tags delivered by several annotators labeling an image are modeled as a robust finite mixture, and techniques based on the Expectation-Maximization (EM) algorithm are proposed for accurately counting malaria parasites on thick blood smears obtained by microscopic Giemsa-stained techniques. This approach outperforms other traditional methods as it is shown through experimentation with real data., Peer Reviewed, Postprint (published version)

Community identification with rank tensor decomposition, Conceive, design, implement and test an algorithm for community detection in networks based on the construction of a tensor that contains information from the network and its factorization using the Concebir, diseñar, implememtar y operar un algoritmo de identificación de comunidades en redes basado en la construcción de un tensor que contiene información sobre la red y su factorización usando la Canonical Polyadic Decomposition (CPD)., Concebir, diseñar, implememtar y operar un algoritmo de identificación de comunidades en redes basado en la construcción de un tensor que contiene información sobre la red y su factorización usando la Canonical Polyadic Decomposition (CPD)., Concebre, dissenyar, implementar i avaluar un algorisme per a la identificació de comunitats en xarxes basat en la construcció d'un tensor que conté informació sobre la xarxa i la seva factorització utilitzant la Canonical Polyadic Decomposition (CPD).

We live in a world in which medicine and technology are more united than ever. That is why in the last few years, lots of research groups initially dedicated to the development of technologies, have started to investigate in a field in which progresses are needed in order to protect the humanity against diseases, an this field is the medicine one. This work, following this trend, is focused on one of the diseases that affects the bast majority of tropical countries, Malaria. Along this final Degree Thesis, this disease will be the center of the work, firstly trying to sensitize the reader about its importance and after that, once the objectives have been defined, develop signal processing techniques and algorithms that in the end will count and detect malaria parasites via crowdsourcing, system that is explained in the Introduction chapter., Vivimos en un mundo en el que medicina y tecnología cada vez van más de la mano. Es por ello que durante los últimos años, muchos grupos de investigación inicialmente dedicados al desarrollo de tecnología, han desembarcado en un campo en el cual se necesitan avances para poder proteger al ser humano de enfermedades, es decir, el campo de la medicina. Este proyecto, siguiendo esta tendencia, se centra en una de las enfermedades que más afecta a países de zonas tropicales, la Malaria. A lo largo de este trabajo final de grado se hablará de esta enfermedad y se podrá sensibilizar al lector de su importancia. Una vez se han fijado los objetivos, se desarrollaran técnicas y algoritmos de procesado de señal cuya finalidad será la de contar y detectar parásitos de malaria mediante crowdsourcing, sistema explicado en la introducción., Vivim en un món el qual medicina i tecnologia cada cop estan més units. És per això que durant els últims anys, molts grups de recerca que inicialment es dedicaven al desenvolupament de tecnologia, s'han submergit en un camp en el qual es necessiten mes avenços per poder protegir l'ésser humà d'enfermetats, és a dir, el món de la medicina. Aquest treball, seguint aquesta tendència, es centra en una de les enfermetats que més afecta a països de zones tropicals, la Malaria. Durant aquest projecte de final de grau es parlarà sobre aquesta enfermetat i es podrà sensibilitzar el lector de la seva importancia. Un cop els objectius del treball han estat fixats es desenvoluparan tècniques i algorismes de processament del senyal la finalitat dels qual serà la de contar i detectar paràsits de malaria mitjançant crowdsourcing, sistema explicat a la introducció.

©2017 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., This paper takes on the problem of recovering the missing entries of an incomplete matrix, which is known as matrix completion, when the columns of the matrix are signals that lie on a graph and the available observations are noisy. We solve a version of the problem regularized with the Laplacian quadratic form by means of the proximal gradient method, and derive theoretical bounds on the recovery error. Moreover, in order to speed up the convergence of the proximal gradient, we propose an initialization method that utilizes the structural information contained in the Laplacian matrix of the graph., Peer Reviewed, Postprint (author's final draft)

© 2017 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, Crowdsourcing approaches rely on the collection of multiple individuals to solve problems that require analysis of large data sets in a timely accurate manner. The inexperience of participants or annotators motivates well robust techniques. Focusing on clustering setups, the data provided by all an- notators is suitably modeled here as a mixture of Gaussian components plus a uniformly distributed random variable to capture outliers. The proposed algorithm is based on the expectation-maximization algorithm and allows for soft as- signments of data to clusters, to rate annotators according to their performance, and to estimate the number of Gaussian components in the non-Gaussian/Gaussian mixture model, in a jointly manner., Peer Reviewed, Postprint (author's final draft)

We consider the problem of estimating the coefficients in a multivariable linear model by means of a wireless sensor network which may be affected by anomalous measurements. The noise covariance matrices at the different sensors are assumed unknown. Treating outlying samples, and their support, as additional nuisance parameters, the Maximum Likelihood estimate is investigated, with the number of outliers being estimated according to the Minimum Description Length principle. A distributed implementation based on iterative consensus techniques is then proposed, and it is shown effective for managing outliers in the data., Peer Reviewed, Postprint (author's final draft)

This paper focuses on the problem of the distributed estimation of a parameter vector based on noisy observations regularly acquired by the nodes of a wireless sensor network and assuming that some of the nodes have faulty sensors. We propose two online schemes, both centralized and distributed, based on the Expectation-Maximization (EM) algorithm. These algorithms are able to identify and disregard the faulty nodes, and provide a refined estimate of the parameters each time instant after a new set of observations is acquired. Simulation results demonstrate that the centralized versions of the proposed online algorithms attain the same estimation error as the centralized batch EM, whereas the distributed versions come very close to matching the batch EM., Peer Reviewed, Postprint (published version)

The work is framed in an European project participated by six companies that aims at developing a product for locating people in emergency situations like earthquakes or avalanches.

This paper addresses the problem of distributed estimation of a parameter vector in the presence of noisy input and noisy output data, as well as data faults, performed by a wireless sensor network in which only local interactions among the nodes are allowed. In the presence of unreliable observations, standard estimators become biased and perform poorly in low signal-to-noise ratios. We propose therefore two different distributed approaches based on the Expectation-Maximization algorithm: in the first one the regressors are estimated at each iteration, whereas the second one does not require explicit regressor estimation. Numerical results show that the proposed methods approach the performance of a clairvoyant scheme with knowledge of the random data faults., Peer Reviewed, Postprint (published version)

Once the RESCUECELL system was integrated, all the functionalities were tested in terms of accuracy, and performance under real scenarios in collapsed structures 1 and snow. For this purpose, a set of tests and procedures were defined based on the preliminary tests under WP3 and WP5. This deliverable describes the results of the procedure 2 followed to analyse the data recorded in the test in Line of Sight (LoS) scenario as well as the snow scenario. The results obtained in by the Positioning Algorithm in booth scenarios are also described. The deliverable ends with a summary of the results of the tests carried out under task 6.2. Furthermore, some recommendations for further research are pointed out., Peer Reviewed, Preprint

RESCUECELL. Seventh Framework Programme Research for the Benefit of the SMEs. Grant Agreement Number 315007. Deliverable: D6.1 Report of final validation in collapsed structures., Preprint

©2016 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., This paper focuses on the problem of positioning a source using angle-of-arrival measurements taken by a wireless sensor network in which some of the nodes experience non lineof-sight (LOS) propagation conditions. In order to mitigate the errors induced by the nodes in NLOS, we derive an algorithm that combines the expectation-maximization algorithm with a weighted least-squares estimation of the source position so that the nodes in NLOS are eventually identified and discarded. Moreover, a distributed version of this algorithm based on a diffusion strategy that iteratively refines the position estimate while driving the network to a consensus is presented., Peer Reviewed, Postprint (author's final draft)