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Outlier detection is one of the standard exploratory analysis tasks in functional data analysis. We present the R package fdaoutlier which contains implementations of some of the latest techniques for detecting functional outliers. The package makes it easy to detect different types of outliers (magnitude, shape, and amplitude) in functional data, and some of the implemented methods can be applied to both univariate and multivariate functional data. We illustrate the main functionality of the R package with common functional datasets in the literature.

Even when neural networks are widely used in a large number of applications, they are still considered as black boxes and present some difficulties for dimensioning or evaluating their prediction error. This has led to an increasing interest in the overlapping area between neural networks and more traditional statistical methods, which can help overcome those problems. In this article, a mathematical framework relating neural networks and polynomial regression is explored by building an explicit expression for the coefficients of a polynomial regression from the weights of a given neural network, using a Taylor expansion approach. This is achieved for single hidden layer neural networks in regression problems. The validity of the proposed method depends on different factors like the distribution of the synaptic potentials or the chosen activation function. The performance of this method is empirically tested via simulation of synthetic data generated from polynomials to train neural networks with different structures and hyperparameters, showing that almost identical predictions can be obtained when certain conditions are met. Lastly, when learning from polynomial generated data, the proposed method produces polynomials that approximate correctly the data locally., Comment: 39 pages, 15 figures

We demonstrate a new fabrication process for hybrid semiconductor-superconductor heterostructures based on anodic oxidation (AO), allowing controlled thinning of epitaxial Al films. Structural and transport studies of oxidized epitaxial Al films grown on insulating GaAs substrates reveal spatial non-uniformity and enhanced critical temperature and magnetic fields. Oxidation of epitaxial Al on hybrid InAs heterostructures with a conducting quantum well show similarly enhanced superconducting properties transferred to the two-dimensional electron gas (2DEG) by proximity effect, with critical perpendicular magnetic fields up to 3.5 T. An insulating AlOx film, that passivates the heterostructure from exposure to air, is obtained by complete oxidation of the Al. It simultaneously removes the need to strip Al which damages the underlying semiconductor. AO passivation yielded 2DEG mobilities two times higher than similar devices with Al removed by wet etching. An AO-passivated Hall bar showed quantum Hall features emerging at a transverse field of 2.5 T, below the critical transverse field of thinned films, eventually allowing transparent coupling of quantum Hall effect and superconductivity. AO thinning and passivation are compatible with standard lithographic techniques, giving lateral resolution below <50 nm. We demonstrate local patterning of AO by realizing a semiconductor-based Josephson junction operating up to 0.3 T perpendicular.

Digital mammogram inspection is the most popular technique for early detection of abnormalities in human breast tissue. When mammograms are analyzed through a computational method, the presence of the pectoral muscle might affect the results of breast lesions detection. This problem is particularly evident in the mediolateral oblique view (MLO), where pectoral muscle occupies a large part of the mammography. Therefore, identifying and eliminating the pectoral muscle are essential steps for improving the automatic discrimination of breast tissue. In this paper, we propose an approach based on anatomical features to tackle this problem. Our method consists of two steps: (1) a process to remove the noisy elements such as labels, markers, scratches and wedges, and (2) application of an intensity transformation based on the Beta distribution. The novel methodology is tested with 322 digital mammograms from the Mammographic Image Analysis Society (mini-MIAS) database and with a set of 84 mammograms for which the area normalized error was previously calculated. The results show a very good performance of the method.

We propose two new outlier detection methods, for identifying and classifying different types of outliers in (big) functional data sets. The proposed methods are based on an existing method called Massive Unsupervised Outlier Detection (MUOD). MUOD detects and classifies outliers by computing for each curve, three indices, all based on the concept of linear regression and correlation, which measure outlyingness in terms of shape, magnitude and amplitude, relative to the other curves in the data. 'Semifast-MUOD', the first method, uses a sample of the observations in computing the indices, while 'Fast-MUOD', the second method, uses the point-wise or $L_1$ median in computing the indices. The classical boxplot is used to separate the indices of the outliers from those of the typical observations. Performance evaluation of the proposed methods using simulated data show significant improvements compared to MUOD, both in outlier detection and computational time. We show that Fast-MUOD is especially well suited to handling big and dense functional datasets with very small computational time compared to other methods. Further comparisons with some recent outlier detection methods for functional data also show superior or comparable outlier detection accuracy of the proposed methods. We apply the proposed methods on weather, population growth, and video data.

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

The large Land\'{e} g-factor, high spin-orbit coupling, and low effective mass of the two-dimensional electron gas in InSb quantum wells combined with proximal superconductivity may realize a scalable platform for topological quantum computation. Aluminum thin films directly deposited on top of InSb planar structures result in the formation of a reactive AlInSb layer at the interface. This interlayer progressively consumes the whole Al film, resulting in a disordered AlInSb layer after few months at room temperature. We report on a heterostructure design that results in a significant increase of the durability of these hybrid Al-InSb heterostructures with the preservation of a pure Al film and sharp superconductor-semiconductor interface for more than one year. Two monolayers of epitaxial InAs at the superconductor-semiconductor interface prevent interfacial reactivity as evidenced by X-ray reflectivity and energy dispersive spectroscopy measurements. Structural characterizations of the Al films by transmission electron microscopy reveal the presence of tens of nanometers wide grains predominantly oriented with Al(110) parallel to InSb(001).

A robust estimator is proposed for the parameters that characterize the linear regression problem. It is based on the notion of shrinkages, often used in Finance and previously studied for outlier detection in multivariate data. A thorough simulation study is conducted to investigate: the efficiency with normal and heavy-tailed errors, the robustness under contamination, the computational times, the affine equivariance and breakdown value of the regression estimator. Two classical data-sets often used in the literature and a real socio-economic data-set about the Living Environment Deprivation of areas in Liverpool (UK), are studied. The results from the simulations and the real data examples show the advantages of the proposed robust estimator in regression.

A collection of robust Mahalanobis distances for multivariate outlier detection is proposed, based on the notion of shrinkage. Robust intensity and scaling factors are optimally estimated to define the shrinkage. Some properties are investigated, such as affine equivariance and breakdown value. The performance of the proposal is illustrated through the comparison to other techniques from the literature, in a simulation study and with a real dataset. The behavior when the underlying distribution is heavy-tailed or skewed, shows the appropriateness of the method when we deviate from the common assumption of normality. The resulting high correct detection rates and low false detection rates in the vast majority of cases, as well as the significantly smaller computation time shows the advantages of our proposal.

Two-dimensional electron gases (2DEGs) coupled to superconductors offer the opportunity to explore a variety of quantum phenomena. These include the study of novel Josephson effects, superconducting correlations in quantum (spin) Hall systems, hybrid superconducting qubits and emergent topological states in semiconductors with spin-orbit interaction (SOI). InSb is a well-known example of such a strong SOI semiconductor, however hybrid superconducting devices in InSb quantum wells remain unexplored. Here, we interface InSb 2DEGs with a superconductor (NbTiN) to create Josephson junctions (JJs), thus providing the first evidence of induced superconductivity in high quality InSb quantum wells. The JJs support supercurrent transport over several microns and display clear signatures of ballistic superconductivity. Furthermore, we exploit the large Land\'{e} g-factor and gate tunability of the junctions to control the current-phase relation, and drive transitions between the $0$ and $\pi$-states. This control over the free energy landscape allows us to construct a phase diagram identifying these $0$ and $\pi$-regions, in agreement with theory. Our results establish InSb quantum wells as a promising new material platform to study the interplay between superconductivity, SOI and magnetism., Comment: Includes supplementary information. Data files available at: https://doi.org/10.4121/uuid:5fab8273-8794-4cd7-96d4-ba8ec00a62cf