Subspace averaging and order determination for source enumeration

In this paper, we address the problem of subspace averaging, with special emphasis placed on the question of estimating the dimension of the average. The results suggest that the enumeration of sources in a multi-sensor array, which is a problem of estimating the dimension of the array manifold, and as a consequence the number of radiating sources, may be cast as a problem of averaging subspaces. This point of view stands in contrast to conventional approaches, which cast the problem as one of identifiying covariance models in a factor model. We present a robust formulation of the proposed order fitting rule based on majorization-minimization algorithms. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. By means of simulation examples, we show that the proposed SA criterion is especially effective in high-dimensional scenarios with low sample support.The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yuejie Chi. The work of V. Garg and I. Santamaria was supported in part by the Ministerio de Economía y Competitividad (MINECO) of Spain, and in part by the AEI/FEDER funds of the E.U., under Grants TEC2016-75067-C4-4-R (CARMEN), TEC2015-69648-REDC, and BES-2017-080542. The work of D. Ramírez was supported in part by the Ministerio de Ciencia, Innovación y Universidades under Grant TEC2017-92552-EXP (aMBITION), in part by the Ministerio de Ciencia, Innovación y Universidades, jointly with the European Commission (ERDF), under Grants TEC2015-69868-C2-1-R (ADVENTURE) and TEC2017-86921-C2-2-R (CAIMAN), and in part by The Comunidad de Madrid under Grant Y2018/TCS-4705 (PRACTICOCM). The work of L. L. Scharf was supported in part by the U.S. NSF under Contract CISE-1712788

Subspace-based order estimation techniques in massive MIMO

Order estimation, also known as source enumeration, is a classical problem in array signal processing which consists in estimating the number of signals received by an array of sensors. In the last decades, numerous approaches to this problem have been proposed. However, the need of working with large-scale arrays (like in massive MIMO systems), low signal-to-noise- ratios, and poor sample regime scenarios, introduce new challenges to order estimation problems. For instance, most of the classical approaches are based on information theoretic criteria, which usually require a large sample size, typically several times larger than the number of sensors. Obtaining a number of samples several times larger than the number of sensors is not always possible with large-scale arrays. In addition, most of the methods found in literature assume that the noise is spatially white, which is very restrictive for many practical scenarios. This dissertation deals with the problem of source enumeration for large-scale arrays, and proposes solutions that work robustly in the small sample regime under various noise models. The first part of the dissertation solves the problem by applying the idea of subspace averaging. The input data are modelled as subspaces, and an average or central subspace is computed. The source enumeration problem can be seen as an estimation of the dimension of the central subspace. A key element of the proposed method is to construct a bootstrap procedure, based on a newly proposed discrete distribution on the manifold of projection matrices, for stochastically generating subspaces from a function of experimentally determined eigenvalues. In this way, the proposed subspace averaging (SA) technique determines the order based on the eigenvalues of an average projection matrix, rather than on the likelihood of a covariance model, penalized by functions of the model order. The proposed SA criterion is especially effective in high-dimensional scenarios with low sample support for uniform linear arrays in the presence of white noise. Further, the proposed SA method is extended for: i) non-white noises, and ii) non-uniform linear arrays. The SA criterion is sensitive with the chosen dimension of extracted subspaces. To solve this problem, we combine the SA technique with a majority vote approach. The number of sources is detected for increasing dimensions of the SA technique and then a majority vote is applied to determine the final estimate. Further, to extend SA for arrays with arbitrary geometries, the SA is combined with a sparse reconstruction (SR) step. In the first step, each received snapshot is approximated by a sparse linear combination of the rest of snapshots. The SR problem is regularized by the logarithm-based surrogate of the l-0 norm and solved using a majorization-minimization approach. Based on the SR solution, a sampling mechanism is proposed in the second step to generate a collection of subspaces, all of which approximately span the same signal subspace. Finally, the dimension of the average of this collection of subspaces provides a robust estimate for the number of sources. The second half of the dissertation introduces a completely different approach to the order estimation for uniform linear arrays, which is based on matrix completion algorithms. This part first discusses the problem of order estimation in the presence of noise whose spatial covariance structure is a diagonal matrix with possibly different variances. 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. The proposed method performs robustly for both small and large-scale arrays with few snapshots. Finally, an approach to work with a reduced number of radio–frequency (RF) chains is proposed. 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 uniform linear arrays, which results in a better estimation of the signal subspace. In addition, the effect of MC on DOA estimation is discussed under the perturbation theory framework. Further, this approach is extended to devise a novel order estimation criterion for missing data scenario. The proposed source enumeration criterion is based on the chordal subspace distance between two sub-matrices extracted from the reconstructed matrix after using MC for increasing rank values. We show that the proposed order estimation criterion performs consistently with a very few available entries in the data matrix.This work was supported by the Ministerio de Ciencia e Innovación (MICINN) of Spain, under grants TEC2016-75067-C4-4-R (CARMEN) and BES-2017-080542

Speech enhancement algorithms for audiological applications

Texto en inglés y resumen en inglés y españolPremio Extraordinario de Doctorado de la UAH en el año académico 2013-2014La mejora de la calidad de la voz es un problema que, aunque ha sido abordado durante muchos años, aún sigue abierto. El creciente auge de aplicaciones tales como los sistemas manos libres o de reconocimiento de voz automático y las cada vez mayores exigencias de las personas con pérdidas auditivas han dado un impulso definitivo a este área de investigación. Esta tesis doctoral se centra en la mejora de la calidad de la voz en aplicaciones audiológicas. La mayoría del trabajo de investigación desarrollado en esta tesis está dirigido a la mejora de la inteligibilidad de la voz en audífonos digitales, teniendo en cuenta las limitaciones de este tipo de dispositivos. La combinación de técnicas de separación de fuentes y filtrado espacial con técnicas de aprendizaje automático y computación evolutiva ha originado novedosos e interesantes algoritmos que son incluidos en esta tesis. La tesis esta dividida en dos grandes bloques. El primer bloque contiene un estudio preliminar del problema y una exhaustiva revisión del estudio del arte sobre algoritmos de mejora de la calidad de la voz, que sirve para definir los objetivos de esta tesis. El segundo bloque contiene la descripción del trabajo de investigación realizado para cumplir los objetivos de la tesis, así como los experimentos y resultados obtenidos. En primer lugar, el problema de mejora de la calidad de la voz es descrito formalmente en el dominio tiempo-frecuencia. Los principales requerimientos y restricciones de los audífonos digitales son definidas. Tras describir el problema, una amplia revisión del estudio del arte ha sido elaborada. La revisión incluye algoritmos de mejora de la calidad de la voz mono-canal y multi-canal, considerando técnicas de reducción de ruido y técnicas de separación de fuentes. Además, la aplicación de estos algoritmos en audífonos digitales es evaluada. El primer problema abordado en la tesis es la separación de fuentes sonoras en mezclas infra-determinadas en el dominio tiempo-frecuencia, sin considerar ningún tipo de restricción computacional. El rendimiento del famoso algoritmo DUET, que consigue separar fuentes de voz con solo dos mezclas, ha sido evaluado en diversos escenarios, incluyendo mezclas lineales y binaurales no reverberantes, mezclas reverberantes, y mezclas de voz con otro tipo de fuentes tales como ruido y música. El estudio revela la falta de robustez del algoritmo DUET, cuyo rendimiento se ve seriamente disminuido en mezclas reverberantes, mezclas binaurales, y mezclas de voz con música y ruido. Con el objetivo de mejorar el rendimiento en estos casos, se presenta un novedoso algoritmo de separación de fuentes que combina la técnica de clustering mean shift con la base del algoritmo DUET. La etapa de clustering del algoritmo DUET, que esta basada en un histograma ponderado, es reemplazada por una modificación del algoritmo mean shift, introduciendo el uso de un kernel Gaussiano ponderado. El análisis de los resultados obtenidos muestran una clara mejora obtenida por el algoritmo propuesto en relación con el algoritmo DUET original y una modificación que usa k-means. Además, el algoritmo propuesto ha sido extendido para usar un array de micrófonos de cualquier tamaño y geometría. A continuación se ha abordado el problema de la enumeración de fuentes de voz, que esta relacionado con el problema de separación de fuentes. Se ha propuesto un novedoso algoritmo basado en un criterio de teoría de la información y en la estimación de los retardos relativos causados por las fuentes entre un par de micrófonos. El algoritmo ha obtenido excelente resultados y muestra robustez en la enumeración de mezclas no reverberantes de hasta 5 fuentes de voz. Además se demuestra la potencia del algoritmo para la enumeración de fuentes en mezclas reverberantes. El resto de la tesis esta centrada en audífonos digitales. El primer problema tratado es el de la mejora de la inteligibilidad de la voz en audífonos monoaurales. En primer lugar, se realiza un estudio de los recursos computacionales disponibles en audífonos digitales de ultima generación. Los resultados de este estudio se han utilizado para limitar el coste computacional de los algoritmos de mejora de la calidad de la voz para audífonos propuestos en esta tesis. Para resolver este primer problema se propone un algoritmo mono-canal de mejora de la calidad de la voz de bajo coste computacional. El objetivo es la estimación de una mascara tiempo-frecuencia continua para obtener el mayor parámetro PESQ de salida. El algoritmo combina una versión generalizada del estimador de mínimos cuadrados con un algoritmo de selección de características a medida, utilizando un novedoso conjunto de características. El algoritmo ha obtenido resultados excelentes incluso con baja relación señal a ruido. El siguiente problema abordado es el diseño de algoritmos de mejora de la calidad de la voz para audífonos binaurales comunicados de forma inalámbrica. Estos sistemas tienen un problema adicional, y es que la conexión inalámbrica aumenta el consumo de potencia. El objetivo en esta tesis es diseñar algoritmos de mejora de la calidad de la voz de bajo coste computacional que incrementen la eficiencia energética en audífonos binaurales comunicados de forma inalámbrica. Se han propuesto dos soluciones. La primera es un algoritmo de extremado bajo coste computacional que maximiza el parámetro WDO y esta basado en la estimación de una mascara binaria mediante un discriminante cuadrático que utiliza los valores ILD e ITD de cada punto tiempo-frecuencia para clasificarlo entre voz o ruido. El segundo algoritmo propuesto, también de bajo coste, utiliza además la información de puntos tiempo-frecuencia vecinos para estimar la IBM mediante una versión generalizada del LS-LDA. Además, se propone utilizar un MSE ponderado para estimar la IBM y maximizar el parámetro WDO al mismo tiempo. En ambos algoritmos se propone un esquema de transmisión eficiente energéticamente, que se basa en cuantificar los valores de amplitud y fase de cada banda de frecuencia con un numero distinto de bits. La distribución de bits entre frecuencias se optimiza mediante técnicas de computación evolutivas. El ultimo trabajo incluido en esta tesis trata del diseño de filtros espaciales para audífonos personalizados a una persona determinada. Los coeficientes del filtro pueden adaptarse a una persona siempre que se conozca su HRTF. Desafortunadamente, esta información no esta disponible cuando un paciente visita el audiólogo, lo que causa perdidas de ganancia y distorsiones. Con este problema en mente, se han propuesto tres métodos para diseñar filtros espaciales que maximicen la ganancia y minimicen las distorsiones medias para un conjunto de HRTFs de diseño

Valid Post-Selection Inference

In the classical theory of statistical inference, data is assumed to be generated from a known model, and the properties of the parameters in the model are of interest. In applications, however, it is often the case that the model that generates the data is unknown, and as a consequence a model is often chosen based on the data. In my dissertation research, we study how to achieve valid inference when the model or hypotheses are data-driven. We study three scenarios, which are summarized in the three chapters. In the first chapter, we study the common practice to perform data-driven variable selection and derive statistical inference from the resulting model. We find such inference enjoys none of the guarantees that classical statistical theory provides for tests and confidence intervals when the model has been chosen a priori. We propose to produce valid post-selection inference by reducing the problem to one of simultaneous inference. Simultaneity is required for all linear functions that arise as coefficient estimates in all submodels. By purchasing simultaneity insurance for all possible submodels, the resulting post-selection inference is rendered universally valid under all possible model selection procedures. This inference is therefore generally conservative for particular selection procedures, but it is always more precise than full Scheffé protection. Importantly it does not depend on the truth of the selected submodel, and hence it produces valid inference even in wrong models. We describe the structure of the simultaneous inference problem and give some asymptotic results. In the second chapter of this thesis, we propose a different approach to achieve valid post-selection inference which corresponds to the treatment of the design matrix predictors as random. Our methodology is based on two techniques, namely split samples and the bootstrap. Split-sample methodology generally involves dividing the observations randomly into two parts: one part for exploratory model building, a.k.a. the training set or planning sample, and the other part for confirmatory statistical inference, a.k.a. holdout set or analysis sample. We use a training sample only to seek a subset of predictors, and then perform the estimation and inference on the holdout set. As far as inference after selection in linear models is concerned, the main advantage of this technique is, roughly speaking, that it separates the data for exploratory analysis from the data for confirmatory analysis, thereby removing the contaminating effect of selection on inference. We show that the our procedure achieves valid inference asymptotically for any selection rule. The third part of the thesis is an application of the split samples method to an observational study on the effect of obstetric unit closures in Philadelphia. The splitting was successful twice over: (i) it successfully identified an interesting and moderately insensitive conclusion, (ii) by comparison of the planning and analysis samples, it is clearly seen to have avoided an exaggerated claim of insensitivity to unmeasured bias that might have occurred by focusing on the least sensitive of many findings. Under the assumption of no unmeasured confounding, we found strong evidence that obstetric unit closures caused birth injuries. We also showed this conclusion to be insensitive to bias from a moderate amount of unmeasured confounding

Speech enhancement algorithms for audiological applications

Texto en inglés y resumen en inglés y españolPremio Extraordinario de Doctorado de la UAH en el año académico 2013-2014La mejora de la calidad de la voz es un problema que, aunque ha sido abordado durante muchos años, aún sigue abierto. El creciente auge de aplicaciones tales como los sistemas manos libres o de reconocimiento de voz automático y las cada vez mayores exigencias de las personas con pérdidas auditivas han dado un impulso definitivo a este área de investigación. Esta tesis doctoral se centra en la mejora de la calidad de la voz en aplicaciones audiológicas. La mayoría del trabajo de investigación desarrollado en esta tesis está dirigido a la mejora de la inteligibilidad de la voz en audífonos digitales, teniendo en cuenta las limitaciones de este tipo de dispositivos. La combinación de técnicas de separación de fuentes y filtrado espacial con técnicas de aprendizaje automático y computación evolutiva ha originado novedosos e interesantes algoritmos que son incluidos en esta tesis. La tesis esta dividida en dos grandes bloques. El primer bloque contiene un estudio preliminar del problema y una exhaustiva revisión del estudio del arte sobre algoritmos de mejora de la calidad de la voz, que sirve para definir los objetivos de esta tesis. El segundo bloque contiene la descripción del trabajo de investigación realizado para cumplir los objetivos de la tesis, así como los experimentos y resultados obtenidos. En primer lugar, el problema de mejora de la calidad de la voz es descrito formalmente en el dominio tiempo-frecuencia. Los principales requerimientos y restricciones de los audífonos digitales son definidas. Tras describir el problema, una amplia revisión del estudio del arte ha sido elaborada. La revisión incluye algoritmos de mejora de la calidad de la voz mono-canal y multi-canal, considerando técnicas de reducción de ruido y técnicas de separación de fuentes. Además, la aplicación de estos algoritmos en audífonos digitales es evaluada. El primer problema abordado en la tesis es la separación de fuentes sonoras en mezclas infra-determinadas en el dominio tiempo-frecuencia, sin considerar ningún tipo de restricción computacional. El rendimiento del famoso algoritmo DUET, que consigue separar fuentes de voz con solo dos mezclas, ha sido evaluado en diversos escenarios, incluyendo mezclas lineales y binaurales no reverberantes, mezclas reverberantes, y mezclas de voz con otro tipo de fuentes tales como ruido y música. El estudio revela la falta de robustez del algoritmo DUET, cuyo rendimiento se ve seriamente disminuido en mezclas reverberantes, mezclas binaurales, y mezclas de voz con música y ruido. Con el objetivo de mejorar el rendimiento en estos casos, se presenta un novedoso algoritmo de separación de fuentes que combina la técnica de clustering mean shift con la base del algoritmo DUET. La etapa de clustering del algoritmo DUET, que esta basada en un histograma ponderado, es reemplazada por una modificación del algoritmo mean shift, introduciendo el uso de un kernel Gaussiano ponderado. El análisis de los resultados obtenidos muestran una clara mejora obtenida por el algoritmo propuesto en relación con el algoritmo DUET original y una modificación que usa k-means. Además, el algoritmo propuesto ha sido extendido para usar un array de micrófonos de cualquier tamaño y geometría. A continuación se ha abordado el problema de la enumeración de fuentes de voz, que esta relacionado con el problema de separación de fuentes. Se ha propuesto un novedoso algoritmo basado en un criterio de teoría de la información y en la estimación de los retardos relativos causados por las fuentes entre un par de micrófonos. El algoritmo ha obtenido excelente resultados y muestra robustez en la enumeración de mezclas no reverberantes de hasta 5 fuentes de voz. Además se demuestra la potencia del algoritmo para la enumeración de fuentes en mezclas reverberantes. El resto de la tesis esta centrada en audífonos digitales. El primer problema tratado es el de la mejora de la inteligibilidad de la voz en audífonos monoaurales. En primer lugar, se realiza un estudio de los recursos computacionales disponibles en audífonos digitales de ultima generación. Los resultados de este estudio se han utilizado para limitar el coste computacional de los algoritmos de mejora de la calidad de la voz para audífonos propuestos en esta tesis. Para resolver este primer problema se propone un algoritmo mono-canal de mejora de la calidad de la voz de bajo coste computacional. El objetivo es la estimación de una mascara tiempo-frecuencia continua para obtener el mayor parámetro PESQ de salida. El algoritmo combina una versión generalizada del estimador de mínimos cuadrados con un algoritmo de selección de características a medida, utilizando un novedoso conjunto de características. El algoritmo ha obtenido resultados excelentes incluso con baja relación señal a ruido. El siguiente problema abordado es el diseño de algoritmos de mejora de la calidad de la voz para audífonos binaurales comunicados de forma inalámbrica. Estos sistemas tienen un problema adicional, y es que la conexión inalámbrica aumenta el consumo de potencia. El objetivo en esta tesis es diseñar algoritmos de mejora de la calidad de la voz de bajo coste computacional que incrementen la eficiencia energética en audífonos binaurales comunicados de forma inalámbrica. Se han propuesto dos soluciones. La primera es un algoritmo de extremado bajo coste computacional que maximiza el parámetro WDO y esta basado en la estimación de una mascara binaria mediante un discriminante cuadrático que utiliza los valores ILD e ITD de cada punto tiempo-frecuencia para clasificarlo entre voz o ruido. El segundo algoritmo propuesto, también de bajo coste, utiliza además la información de puntos tiempo-frecuencia vecinos para estimar la IBM mediante una versión generalizada del LS-LDA. Además, se propone utilizar un MSE ponderado para estimar la IBM y maximizar el parámetro WDO al mismo tiempo. En ambos algoritmos se propone un esquema de transmisión eficiente energéticamente, que se basa en cuantificar los valores de amplitud y fase de cada banda de frecuencia con un numero distinto de bits. La distribución de bits entre frecuencias se optimiza mediante técnicas de computación evolutivas. El ultimo trabajo incluido en esta tesis trata del diseño de filtros espaciales para audífonos personalizados a una persona determinada. Los coeficientes del filtro pueden adaptarse a una persona siempre que se conozca su HRTF. Desafortunadamente, esta información no esta disponible cuando un paciente visita el audiólogo, lo que causa perdidas de ganancia y distorsiones. Con este problema en mente, se han propuesto tres métodos para diseñar filtros espaciales que maximicen la ganancia y minimicen las distorsiones medias para un conjunto de HRTFs de diseño

Advances in parameter estimation, source enumeration, and signal identification for wireless communications

Parameter estimation and signal identification play an important role in modern wireless communication systems. In this thesis, we address different parameter estimation and signal identification problems in conjunction with the Internet of Things (IoT), cognitive radio systems, and high speed mobile communications. The focus of Chapter 2 of this thesis is to develop a new uplink multiple access (MA) scheme for the IoT in order to support ubiquitous massive uplink connectivity for devices with sporadic traffic pattern and short packet size. The proposed uplink MA scheme removes the Media Access Control (MAC) address through the signal identification algorithms which are employed at the gateway. The focus of Chapter 3 of this thesis is to develop different maximum Doppler spread (MDS) estimators in multiple-input multiple-output (MIMO) frequency-selective fading channel. The main idea behind the proposed estimators is to reduce the computational complexity while increasing system capacity. The focus of Chapter 4 and Chapter 5 of this thesis is to develop different antenna enumeration algorithms and signal-to-noise ratio (SNR) estimators in MIMO timevarying fading channels, respectively. The main idea is to develop low-complexity algorithms and estimators which are robust to channel impairments. The focus of Chapter 6 of this thesis is to develop a low-complexity space-time block codes (STBC)s identification algorithms for cognitive radio systems. The goal is to design an algorithm that is robust to time-frequency transmission impairments

Electronic correlations in inhomogeneous model systems: numerical simulation of spectra and transmission

Many fascinating features in condensed matter systems emerge due to the interaction between electrons. Magnetism is such a paramount consequence, which is explained in terms of the exchange interaction of electrons. Another prime example is the metal-to-Mott-insulator transition, where the energy cost of Coulomb repulsion competes against the kinetic energy, the latter favoring delocalization. While systems of correlated electrons are exciting and show remarkable and technologically promising physical properties, they are difficult to treat theoretically. A single-particle description is insufficient; the quantum many-body problem of interacting electrons has to be solved. In the present thesis, we study physical properties of half-metallic ferromagnets which are used in spintronic devices. Half-metals exhibit a metallic spin channel, while the other spin channel is insulating; they are characterized by a high spin polarization. This thesis contributes to the development of numerical methods and applies them to models of half-metallic ferromagnets. Throughout this work, the single-band Hubbard Hamiltonian is considered, and electronic correlations are treated within dynamical mean-field theory. Instead of directly solving the lattice model, the dynamical mean-field theory amounts to solving a local, effective impurity problem that is determined self-consistently. At finite temperatures, this impurity problem is solved employing continuous-time quantum Monte Carlo algorithms formulated in the action formalism. As these algorithms are formulated in imaginary time, an analytic continuation is required to obtain spectral functions. We formulate a version of the N-point Padé algorithm that calculates the location of the poles in a least-squares sense. To directly obtain spectra for real frequencies, we employ Hamiltonian-based tensor network methods at zero temperature. We also summarize the ideas of the density matrix renormalization group algorithm, and of the time evolution using the time-dependent variational principle, employing a diagrammatic notation. Real materials never display perfect translational symmetry. Thus, realistic models require the inclusion of disorder effects. In this work, we discuss these within a single-site approximation, the coherent potential approximation, and combine it with the dynamical mean-field theory, allowing to treat interacting electrons in multicomponent alloys on a local level. We extend this combined scheme to off-diagonal disorder, that is, disorder in the hopping amplitudes, by employing the Blackman–Esterling–Berk formalism. For this purpose, we illustrate the ideas of this formalism using tensor diagrams and provide an efficient implementation. The structure of the effective medium is discussed, and a concentration scaling is proposed that resolves some of its peculiarities. The limit of vanishing hopping between different components is discussed and solved analytically for the Bethe lattice with a general coordination number. We exemplify the combined algorithm for a Bethe lattice, showing results that exhibit alloy-band-insulator to correlated-metal to Mott-insulator transitions. We study models of half-metallic ferromagnets to elucidate the effects of local electronic correlations on the spectral function. To model half-metallicity, a static spin splitting is used to produce the half-metallic density of states. Applying the Padé analytic continuation to the self-energy instead of the Green’s function produces reliable spectral functions agreeing with the zero-temperature results obtained for real frequencies. To address transport properties, we investigate the interface of a half-metallic layer and a metallic, band insulating, or Mott insulating layer. We observe charge reconstruction which induces metallicity at the interface; quasiparticle states are present in the Mott insulating layer even for a large Hubbard interaction. The transmission through a barrier made of such a single interacting half-metallic layer sandwiched by metallic leads is studied employing the Meir–Wingreen formalism. This allows for a transparent calculation of the transmission in the presence of the Hubbard interaction. For a strong coupling of the central layer to the leads, we identify high intensity bound states which do not contribute to the transmission. For small coupling, on the other hand, we find resonant states which enhance the transmission. In particular, we demonstrate that even for a single half-metallic layer, highly polarized transmissions are achievable

Improving Monitoring and Diagnosis for Process Control using Independent Component Analysis

Statistical Process Control (SPC) is the general field concerned with monitoring the operation and performance of systems. SPC consists of a collection of techniques for characterizing the operation of a system using a probability distribution consistent with the system\u27s inputs and outputs. Classical SPC monitors a single variable to characterize the operation of a single machine tool or process step using tools such as Shewart charts. The traditional approach works well for simple small to medium size processes. For more complex processes a number of multivariate SPC techniques have been developed in recent decades. These advanced methods suffer from several disadvantages compared to univariate techniques: they tend to be statistically less powerful, and they tend to complicate process diagnosis when a disturbance is detected. This research introduces a general method for simplifying multivariate process monitoring in such a manner as to allow the use of traditional SPC tools while facilitating process diagnosis. Latent variable representations of complex processes are developed which directly relate disturbances with process steps or segments. The method models disturbances in the process rather than the process itself. The basic tool used is Independent Component Analysis (ICA). The methodology is illustrated on the problem of monitoring Electrical Test (E-Test) data from a semiconductor manufacturing process. Development and production data from a working semiconductor plant are used to estimate a factor model that is then used to develop univariate control charts for particular types of process disturbances. Detection and false alarm rates for data with known disturbances are given. The charts correctly detect and classify all the disturbance cases with a very low false alarm rate. A secondary contribution is the introduction of a method for performing an ICA like analysis using possibilistic data instead of probabilistic data. This technique extends the general ICA framework to apply to a broader range of uncertainty types. Further development of this technique could lead to the capability to use extremely sparse data to estimate ICA process models

Permutation Invariant Gaussian Matrix Models

Matrix models are ubiquitous in physics. Commonly arising due to the presence of gauge symmetries in a system, they play an important role in establishing results within the context of the AdS/CFT correspondence. They also capture the statistics of complex systems in a remarkably diverse range of fields within the framework of random matrix theory (RMT), these include nuclear physics, chaos, condensed matter physics, financial correlations and biological networks. Inspired by both of these applications, and motivated by the existence of physical matrix systems possessing discrete symmetries, is the study of Gaussian matrix models invariant under SN , the symmetric group of all permutations of N objects. We specialise the most general of these models to the case of symmetric matrices with vanishing diagonal elements. This model is used to study an ensemble of financial correlation matrices and as a tool to detect market states. This problem has a natural per- mutation symmetry, and the observables of interest are permutation invariant polynomials of the matrix variables (PIMOs). We find that the values of low order PIMOs are generally closely matched by the predictions by the model, and vectors of PIMOs are shown to be efficient indicators of the market state. Turning our attention to the general structure of permutation invariant Gaussian matrix (PIGM) models of general matrices of size N, we show that PIMOs of degree k are in one-to-one correspondence with equivalence classes of the diagrammatic partition algebra Pk(N). On a subspace of the 13-parameter space of general PIGM models there is an enhanced O(N) symmetry. At a special point within this subspace exists the simplest O(N) invariant action, which we furnish with an inner product on the PIMOs. We prove the large N factorisation of this inner product. Lastly, we study the implications of permutation symmetry for the state space and dynamics of quantum mechanical matrix systems. The general permutation invariant matrix quantum harmonic oscillator Hamiltonian is solved and families of interacting Hamiltonians, which are diagonalised by a representation theoretic basis for the permutation invariant subspace, are described. These include Hamiltonians for which low-energy states are SN invariant and can give rise to large ground state degeneracies related to the dimensions of partition algebras

Divergence Measures

Data science, information theory, probability theory, statistical learning and other related disciplines greatly benefit from non-negative measures of dissimilarity between pairs of probability measures. These are known as divergence measures, and exploring their mathematical foundations and diverse applications is of significant interest. The present Special Issue, entitled “Divergence Measures: Mathematical Foundations and Applications in Information-Theoretic and Statistical Problems”, includes eight original contributions, and it is focused on the study of the mathematical properties and applications of classical and generalized divergence measures from an information-theoretic perspective. It mainly deals with two key generalizations of the relative entropy: namely, the R_ényi divergence and the important class of f -divergences. It is our hope that the readers will find interest in this Special Issue, which will stimulate further research in the study of the mathematical foundations and applications of divergence measures