Search

Resistive Random Access Memories (RRAMs) are being studied by the industry and academia because it is widely accepted that they are promising candidates for the next generation of high density nonvolatile memories. Taking into account the stochastic nature of mechanisms behind resistive switching, a new technique based on the use of functional data analysis has been developed to accurately model resistive memory device characteristics. Functional principal component analysis (FPCA) based on Karhunen-Loeve expansion is applied to obtain an orthogonal decomposition of the reset process in terms of uncorrelated scalar random variables. Then, the device current has been accurately described making use of just one variable presenting a modeling approach that can be very attractive from the circuit simulation viewpoint. The new method allows a comprehensive description of the stochastic variability of these devices by introducing a probability distribution that allows the simulation of the main parameter that is employed for the model implementation. A rigorous description of the mathematical theory behind the technique is given and its application for a broad set of experimental measurements is explained.

A functional linear discriminant analysis approach to classify a set of kinematic data (human movement curves of individuals performing different physical activities) is performed. Kinematic data, usually collected in linear acceleration or angular rotation format, can be identified with functions in a continuous domain (time, percentage of gait cycle, etc.). Since kinematic curves are measured in the same sample of individuals performing different activities, they are a clear example of functional data with repeated measures. On the other hand, the sample curves are observed with noise. Then, a roughness penalty might be necessary in order to provide a smooth estimation of the discriminant functions, which would make them more interpretable. Moreover, because of the infinite dimension of functional data, a reduction dimension technique should be considered. To solve these problems, we propose a multi-class approach for penalized functional partial least squares (FPLS) regression. Then linear discriminant analysis (LDA) will be performed on the estimated FPLS components. This methodology is motivated by two case studies. The first study considers the linear acceleration recorded every two seconds in 30 subjects, related to three different activities (walking, climbing stairs and down stairs). The second study works with the triaxial angular rotation, for each joint, in 51 children when they completed a cycle walking under three conditions (walking, carrying a backpack and pulling a trolley). A simulation study is also developed for comparing the performance of the proposed functional LDA with respect to the corresponding multivariate and non-penalized approaches.

Functional principal component analysis based on Karhunen Loeve expansion allows to describe the stochastic evolution of the main characteristics associated to multiple systems and devices. Identifying the probability distribution of the principal component scores is fundamental to characterize the whole process. The aim of this work is to consider a family of statistical distributions that could be accurately adjusted to a previous transformation. Then, a new class of distributions, the linear-phase-type, is introduced to model the principal components. This class is studied in detail in order to prove, through the KL expansion, that certain linear transformations of the process at each time point are phase-type distributed. This way, the one-dimensional distributions of the process are in the same linear-phase-type class. Finally, an application to model the reset process associated with resistive memories is developed and explained.

The homogeneity problem for testing if more than two different samples come from the same population is considered for the case of functional data. The methodological results are motivated by the study of homogeneity of electronic devices fabricated by different materials and active layer thicknesses. In the case of normality distribution of the stochastic processes associated with each sample, this problem is known as Functional ANOVA problem and is reduced to test the equality of the mean group functions (FANOVA). The problem is that the current/voltage curves associated with Resistive Random Access Memories (RRAM) are not generated by a Gaussian process so that a different approach is necessary for testing homogeneity. To solve this problem two different parametric and nonparametric approaches based on basis expansion of the sample curves are proposed. The first consists of testing multivariate homogeneity tests on a vector of basis coefficients of the sample curves. The second is based on dimension reduction by using functional principal component analysis of the sample curves (FPCA) and testing multivariate homogeneity on a vector of principal components scores. Different approximation numerical techniques are employed to adapt the experimental data for the statistical study. An extensive simulation study is developed for analyzing the performance of both approaches in the parametric and non-parametric cases. Finally, the proposed methodologies are applied on three samples of experimental reset curves measured in three different RRAM technologies.

Physical activity plays a significant role in the well-being of individuals with Chronic obstructive Pulmonary Disease (COPD). Specifically, it has been directly associated with changes in hospitalization rates for these patients. However, previous investigations have primarily been conducted in a cross-sectional or longitudinal manner and have not considered a continuous perspective. Using the telEPOC program we use telemonitoring data to analyze the impact of physical activity adopting a functional data approach. However, Traditional functional data methods, including functional regression models, typically assume a consistent data domain. However, the data in the telEPOC program exhibits variable domains, presenting a challenge since the majority of functional data methods, are based on the fact that data are observed in the same domain. To address this challenge, we introduce a novel fully functional methodology tailored to variable domain functional data, eliminating the need for data alignment, which can be computationally taxing. Although models designed for variable domain data are relatively scarce and may have inherent limitations in their estimation methods, our approach circumvents these issues. We substantiate the effectiveness of our methodology through a simulation study, comparing our results with those obtained using established methodologies. Finally, we apply our methodology to analyze the impact of physical activity in COPD patients using the telEPOC program's data. Software for our method is available in the form of R code on request at \url{https://github.com/Pavel-Hernadez-Amaro/V.D.F.R.M-new-estimation-approach.git}.

Asg is a Python package that solves penalized linear regression and quantile regression models for simultaneous variable selection and prediction, for both high and low dimensional frameworks. It makes very easy to set up and solve different types of lasso-based penalizations among which the asgl (adaptive sparse group lasso, that gives name to the package) is remarked. This package is built on top of cvxpy, a Python-embedded modeling language for convex optimization problems and makes extensive use of multiprocessing, a Python module for parallel computing that significantly reduces computation times of asgl., Comment: 31 pages, 1 figure, 1 table

Partial least squares (PLS) is a dimensionality reduction technique used as an alternative to ordinary least squares (OLS) in situations where the data is colinear or high dimensional. Both PLS and OLS provide mean based estimates, which are extremely sensitive to the presence of outliers or heavy tailed distributions. In contrast, quantile regression is an alternative to OLS that computes robust quantile based estimates. In this work, the multivariate PLS is extended to the quantile regression framework, obtaining a theoretical formulation of the problem and a robust dimensionality reduction technique that we call fast partial quantile regression (fPQR), that provides quantile based estimates. An efficient implementation of fPQR is also derived, and its performance is studied through simulation experiments and the chemometrics well known biscuit dough dataset, a real high dimensional example., Comment: 22 pages, 5 figures and 5 tables

Sparse group LASSO (SGL) is a penalization technique used in regression problems where the covariates have a natural grouped structure and provides solutions that are both between and within group sparse. In this paper the SGL is introduced to the quantile regression (QR) framework, and a more flexible version, the adaptive sparse group LASSO (ASGL), is proposed. This proposal adds weights to the penalization improving prediction accuracy. Usually, adaptive weights are taken as a function of the original nonpenalized solution model. This approach is only feasible in the n > p framework. In this work, a solution that allows using adaptive weights in high-dimensional scenarios is proposed. The benefits of this proposal are studied both in synthetic and real datasets., Comment: 9 figures, 5 tables