Mini-Workshop: Recent Developments in Statistical Methods with Applications to Genetics and Genomics

Recent progress in high-throughput genomic technologies has revolutionized the field of human genetics and promises to lead to important scientific advances. With new improvements in massively parallel biotechnologies, it is becoming increasingly more efficient to generate vast amounts of information at the genomics, transcriptomics, proteomics, metabolomics etc. levels, opening up as yet unexplored opportunities in the search for the genetic causes of complex traits. Despite this tremendous progress in data generation, it remains very challenging to analyze, integrate and interpret these data. The resulting data are high-dimensional and very sparse, and efficient statistical methods are critical in order to extract the rich information contained in these data. The major focus of the mini-workshop, entitled “Recent Developments in Statistical Methods with Applications to Genetics and Genomics”, has been on integrative methods. Relevant research questions included the optimal study design for integrative genomic analyses; appropriate handling and pre-processing of different types of omics data; statistical methods for integration of multiple types of omics data; adjustment for confounding due to latent factors such as cell or tissue heterogeneity; the optimal use of omics data to enhance or make sense of results identified through genetic studies; and statistical and computational strategies for analysis of multiple types of high-dimensional data

Blind Estimation of OFDM System Parameters for Automatic Signal Identification

Orthogonal frequency division multiplexing (OFDM) has gained worldwide popular­ ity in broadband wireless communications recently due to its high spectral efficiency and robust performance in multipath fading channels. A growing trend of smart receivers which can support and adapt to multiple OFDM based standards auto­ matically brings the necessity of identifying different standards by estimating OFDM system parameters without a priori information. Consequently, blind estimation and identification of OFDM system parameters has received considerable research atten­ tions. Many techniques have been developed for blind estimation of various OFDM parameters, whereas estimation of the sampling frequency is often ignored. Further­ more, the estimated sampling frequency of an OFDM signal has to be very accurate for data recovery due to the high sensitivity of OFDM signals to sampling clock offset. To address the aforementioned problems, we propose a two-step cyclostation- arity based algorithm with low computational complexity to precisely estimate the sampling frequency of a received oversampled OFDM signal. With this estimated sampling frequency and oversampling ratio, other OFDM system parameters, i.e., the number of subcarriers, symbol duration and cyclic prefix (CP) length can be es­ timated based on the cyclic property from CP sequentially. In addition, modulation scheme used in the OFDM can be classified based on the higher-order statistics (HOS) of the frequency domain OFDM signal. All the proposed algorithms are verified by a lab testing system including a vec­ tor signal generator, a spectrum analyzer and a high speed digitizer. The evaluation results confirm the high precision and efficacy of the proposed algorithm in realistic scenarios

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Tensor Networks for Dimensionality Reduction and Large-Scale Optimizations. Part 2 Applications and Future Perspectives

Part 2 of this monograph builds on the introduction to tensor networks and their operations presented in Part 1. It focuses on tensor network models for super-compressed higher-order representation of data/parameters and related cost functions, while providing an outline of their applications in machine learning and data analytics. A particular emphasis is on the tensor train (TT) and Hierarchical Tucker (HT) decompositions, and their physically meaningful interpretations which reflect the scalability of the tensor network approach. Through a graphical approach, we also elucidate how, by virtue of the underlying low-rank tensor approximations and sophisticated contractions of core tensors, tensor networks have the ability to perform distributed computations on otherwise prohibitively large volumes of data/parameters, thereby alleviating or even eliminating the curse of dimensionality. The usefulness of this concept is illustrated over a number of applied areas, including generalized regression and classification (support tensor machines, canonical correlation analysis, higher order partial least squares), generalized eigenvalue decomposition, Riemannian optimization, and in the optimization of deep neural networks. Part 1 and Part 2 of this work can be used either as stand-alone separate texts, or indeed as a conjoint comprehensive review of the exciting field of low-rank tensor networks and tensor decompositions.Comment: 232 page

Diffusion MRI for Well-posed and Optimal White Matter Microstructure Characterisation: Beyond Single Diffusion Encoding

The human brain hosts a colossal number of water molecules which are constantly moving due to Brownian motion. Their movement, random by nature, is restricted by the brain tissue walls. Magnetic Resonance Imaging (MRI) provides macroscopic measurements of the diffusion process in a non-invasive manner, i.e. diffusion MRI. Hidden in these measurements lies information about the underlying architecture. The ability to unravel tissue microstructure from the coarse-grained diffusion measurements is extremely valuable since this information is 2-3 orders of magnitude below typical MRI resolution. This makes diffusion MRI sensitive to pathological and developmental processes occurring at the mesoscopic scale, in the order of microns. Accessing this level of detail can lead to clinical biomarkers specific to early stages of neurodegenerative diseases or brain development. Computational models of biophysical tissue properties have been widely used in diffusion MRI research to elucidate the link between microstructural properties and MR signal formation. The potential increase in sensitivity and specificity in detecting brain microstructural changes is their major driving force. However, these models establish complex relationships between biophysical properties and the MR signal, making the inverse problem of recovering model parameters from noisy measurements ill-conditioned with conventional diffusion MRI acquisitions. This thesis explores ways to make diffusion MRI biophysical modelling more robust while maintaining time and hardware requirements that are feasible in clinical conditions. Firstly, we explore theoretically the benefits of incorporating functionally independent measurements, such as double diffusion encoding. Secondly, we propose an optimal experiment design framework that gives us, after exploring the whole multidimensional diffusion MRI measurement space, the acquisition that maximises accuracy and precision in the parameter estimation. Finally, we extract relevant information from histology images that can be used to feed or benchmark diffusion MRI models

Blind channel estimation for space-time block codes : novel methods and performance Studies

[abstract] This work is based on a study of blind source separation techniques in order to estimate coe cients in transmission systems using Alamouti codi cation with two transmit antennas and one receive antenna. Most of present standards include pilot symbols to estimate the channel in reception. Since these symbols do not deliver user's data, their use decrease transferring quantity and also the system capacity. On the other hand, algorithms of blind separation are less precise when estimating channel coe cients than those supervised, but achieving a higher transferring rate. In this work we will deal with Alamouti codi cation system as a typical problem of blind sources separation where the signals transmitted and the channel coe cients must be estimated according to lineal and instantaneous mixtures (observations). Orthogonal structure required by Alamouti codi cation allows us to solve this problem by decomposing eigenvalues and eigenvectors of matrices calculated from di erent statistics of the observations. These algorithms could be classi ed as those using second order statistics and those using higher order statistics. Algorithms based on second order statistics work with correlation matrix of observations. They are computationally less expensive, but require a lineal precoder in order to balance the power of the signals transmitted. One of our contributions is being able to determine in an empirical way how the power decompensation should be done in order to reduce the proabibility of error in the system. On the other hand, algorithms dealing with high level statistics are based on diagonalize one or several high level cumulant matrices deriving into a major computational cost in the receiver. As an advantage we must point out that they do not require to include a lineal precoder to do the power decompensation. In this work we will prove that the output of these techniques depends on the level of eigenvalue of the diagonalized matrix spreading. This idea will be used by us in order to achieve the optimal cumulant matrix and also to propose a new algorithm that increases the output in relation to those already proposed by other authors. Another important contribution of this present study is to propose a detailed comparison between channel estimation techniques in simulated scenarios, considering channels with Rayleigh and Rice distribution, and in real scenarios in ISM of 2.4 GHz band, by using a MIMO testbed developed in Universidade da Coruña. [Resumen] En este trabajo se realiza un estudio de técnicas de separación ciega de fuentes para la estimación de los coeficientes en sistemas de transmisión que emplean la codificación de Alamouti con 2 antenas transmisoras y 1 antena receptora. La mayoría de los estándares actuales incluyen símbolos piloto para estimar el canal en recepción. Dado que estos símbolos no transportan datos del usuario, su utilización decrementa la tasa de transferencia y degrada el rendimiento del sistema. Por otro lado, los algoritmos de separación ciega son menos precisos en la estimación de los coeficientes de canal que los supervisados pero consiguen una tasa de transferencia mayor. En el presente trabajo, modelaremos el sistema de codificación de Alamouti como un problema típico de separación ciega de fuentes donde las se~nales transmitidas y los coeficientes del canal deben ser estimados a partir de mezclas lineales e instantáneas (observaciones). La estructura ortogonal impuesta por la codificación de Alamouti permite resolver este problema mediante la descomposición de autovalores y autovectores de matrices calculadas a partir de diferentes estadísticos de las observaciones. Estos algoritmos pueden ser clasificados en aquellos que utilizan estadísticos de segundo orden y aquellos que emplean estadísticos de orden superior. Los algoritmos que emplean estadísticos de segundo orden trabajan con la matriz de correlación de las observaciones, son computacionalmente poco costosos pero requieren de un precodificador lineal para descompensar la potencia de las se~nales transmitidas. Una de nuestras aportaciones es la de determinar de forma empírica cómo debe realizarse la descompesación de potencia de cara a reducir la probabilidad de error del sistema. Por otro lado, los algoritmos que trabajan con estadísticos de orden superior se basan en diagonalizar una o varias matrices de cumulantes de orden superior, lo que conlleva un mayor coste computacional en el receptor. Como ventaja debe resaltarse que no requieren incluir un precodificador lineal que realice la descompensación de potencia. En este trabajo mostraremos que el rendimiento de estas técnicas depende del grado de dispersión de los autovalores de la matriz que se diagonaliza. Utilizaremos esta idea para obtener la matriz de cumulantes óptima y para formular un nuevo algoritmo que supera en rendimiento a los propuestos previamente por otros autores. Otra aportación relevante del presente trabajo es presentar una detallada comparación de las técnicas de estimación de canal en entornos simulados, considerando canales con ditribución Rayleigh y Rice, y en entornos reales en la banda ISM de 2.4 GHz mediante el empleo de una plataforma de transmisión MIMO desarrollada en la Universidade da Coruña