Robust high-dimensional precision matrix estimation

The dependency structure of multivariate data can be analyzed using the covariance matrix $\Sigma$. In many fields the precision matrix $\Sigma^{-1}$ is even more informative. As the sample covariance estimator is singular in high-dimensions, it cannot be used to obtain a precision matrix estimator. A popular high-dimensional estimator is the graphical lasso, but it lacks robustness. We consider the high-dimensional independent contamination model. Here, even a small percentage of contaminated cells in the data matrix may lead to a high percentage of contaminated rows. Downweighting entire observations, which is done by traditional robust procedures, would then results in a loss of information. In this paper, we formally prove that replacing the sample covariance matrix in the graphical lasso with an elementwise robust covariance matrix leads to an elementwise robust, sparse precision matrix estimator computable in high-dimensions. Examples of such elementwise robust covariance estimators are given. The final precision matrix estimator is positive definite, has a high breakdown point under elementwise contamination and can be computed fast

A statistical data-based approach to instability detection and wear prediction in radial turning processes

Radial turning forces for tool-life improvements are studied, with the emphasis on predictive rather than preventive maintenance. A tool for wear prediction in various experimental settings of instability is proposed through the application of two statistical approaches to process data on tool-wear during turning processes: three sigma edit rule analysis and Principal Component Analysis (PCA). A Linear Mixed Model (LMM) is applied for wear prediction. These statistical approaches to instability detection generate results of acceptable accuracy for delivering expert opinion. They may be used for on-line monitoring to improve the processing of different materials. The LMM predicted significant differences for tool wear when turning different alloys and with different lubrication systems. It also predicted the degree to which the turning process could be extended while conserving stability. Finally, it should be mentioned that tool force in contact with the material was not considered to be an important input variable for the model.The work was performed as a part of the HIMMOVAL (Grant Agreement Number: 620134) project within the CLEAN-SKY program, linked to the SAGE2 project for geared open-rotor development and the delivery of the demonstrator part. Funding through grant IT900-16 is also acknowledged from the Basque Government Department of Education, Universities and Research

Morphology is not always useful for diagnosis, and that’s ok: Species hypotheses should not be bound to a class of data. Reply to Brown and Gibbons (S Afr J Sci. 2022;118(9/10), Art. #12590)

This paper serves as a reply to the Commentary by Brown and Gibbons (S Afr J Sci. 2022;118(9/10), Art. #12590) on our recently published paper on systematics of the moon jellyfish genus Aurelia (Lawley et al. PeerJ 2021;9, e11954)). We emphasise that we are not advocating for the routine use of molecular data alone in taxonomic diagnoses, rather that it is a valid approach in cases where, after detailed analyses, morphological features are shown to be unreliable

Phylogeny and chromosomal diversification in the <i>Dichroplus elongatus</i> species group (Orthoptera, Melanoplinae)

In an attempt to track the chromosomal differentiation in the Dichroplus elongatus species group, we analyzed the karyotypes of four species with classical cytogenetic and mapping several multigene families through fluorescent in situ hybridization (FISH). We improved the taxon sampling of the D. elongatus species group adding new molecular data to infer the phylogeny of the genus and reconstruct the karyotype evolution. Our molecular analyses recovered a fully resolved tree with no evidence for the monophyly of Dichroplus. However, we recovered several stable clades within the genus, including the D. elongatus species group, under the different strategies of tree analyses (Maximum Parsimony and Maximum Likelihood). The chromosomal data revealed minor variation in the D. elongatus species group's karyotypes caused by chromosome rearrangements compared to the phylogenetically related D. maculipennis species group. The karyotypes of D. intermedius and D. exilis described herein showed the standard characteristics found in most Dichroplini, 2n = 23/24, X0♂ XX♀, Fundamental number (FN) = 23/24. However, we noticed two established pericentric inversions in D. intermedius karyotype, raising the FN to 27♂/28♀. A strong variation in the heterochromatic blocks distribution was evidenced at interespecific level. The multigene families' mapping revealed significant variation, mainly in rDNA clusters. These variations are probably caused by micro chromosomal changes, such as movement of transposable elements (TEs) and ectopic recombination. These observations suggest a high genomic dynamism for these repetitive DNA sequences in related species. The reconstruction of the chromosome character "variation in the FN" posits the FN = 23/24 as the ancestral state, and it is hypothesized that variations due to pericentric inversions has arisen independently three times in the evolutionary history of Dichroplus. One of these independent events occurred in the D. elongatus species group, where D. intermedius is the unique case with the highest FN described in the tribe Dichroplini.Centro de Estudios Parasitológicos y de VectoresFacultad de Ciencias Naturales y Muse

The importance of molecular characters when morphological variability hinders diagnosability: systematics of the moon jellyfish genus Aurelia (Cnidaria: Scyphozoa)

Cryptic species have been detected across Metazoa, and while no apparent morphological features distinguish them, it should not impede taxonomists from formal descriptions. We accepted this challenge for the jellyfish genus Aurelia, which has a long and confusing taxonomic history. We demonstrate that morphological variability in Aurelia medusae overlaps across very distant geographic localities. Even though some morphological features seem responsible for most of the variation, regional geographic patterns of dissimilarities are lacking. This is further emphasized by morphological differences found when comparing lab-cultured Aurelia coerulea medusae with the diagnostic features in its recent redescription. Previous studies have also highlighted the difficulties in distinguishing Aurelia polyps and ephyrae, and their morphological plasticity. Therefore, mostly based on genetic data, we recognize 28 species of Aurelia, of which seven were already described, 10 are formally described herein, four are resurrected and seven remain undescribed. We present diagnostic genetic characters for all species and designate type materials for newly described and some resurrected species. Recognizing moon jellyfish diversity with formal names is vital for conservation efforts and other studies. This work clarifies the practical implications of molecular genetic data as diagnostic characters, and sheds light on the patterns and processes that generate crypsis.Fil: Lawley, Jonathan W.. Universidade de Sao Paulo; Brasil. Griffith University; AustraliaFil: Gamero Mora, Edgar. Universidade de Sao Paulo; BrasilFil: Maronna, Maximiliano Manuel. Universidade de Sao Paulo; BrasilFil: Chiaverano, Luciano Martin. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; Argentina. Instituto Nacional de Investigaciones y Desarrollo Pesquero; ArgentinaFil: Stampar, Sérgio N.. Universidade Estadual Paulista Julio de Mesquita Filho; BrasilFil: Hopcroft, Russell R.. University of Alaska; Estados UnidosFil: Collins, Allen G.. National Museum of Natural History; Estados UnidosFil: Morandini, André C.. Universidade de Sao Paulo; Brasi

Robust Modal Filtering and Control of the X-56A Model with Simulated Fiber Optic Sensor Failures

The X-56A aircraft is a remotely-piloted aircraft with flutter modes intentionally designed into the flight envelope. The X-56A program must demonstrate flight control while suppressing all unstable modes. A previous X-56A model study demonstrated a distributed-sensing-based active shape and active flutter suppression controller. The controller relies on an estimator which is sensitive to bias. This estimator is improved herein, and a real-time robust estimator is derived and demonstrated on 1530 fiber optic sensors. It is shown in simulation that the estimator can simultaneously reject 230 worst-case fiber optic sensor failures automatically. These sensor failures include locations with high leverage (or importance). To reduce the impact of leverage outliers, concentration based on a Mahalanobis trim criterion is introduced. A redescending M-estimator with Tukey bisquare weights is used to improve location and dispersion estimates within each concentration step in the presence of asymmetry (or leverage). A dynamic simulation is used to compare the concentrated robust estimator to a state-of-the-art real-time robust multivariate estimator. The estimators support a previously-derived mu-optimal shape controller. It is found that during the failure scenario, the concentrated modal estimator keeps the system stable

Optical polarization observations of NGC 6231: evidence for a past SN fingerprint

We present the first linear multicolor polarization observations for a sample of 35 stars in the direction of the Galactic cluster NGC 6231. We have found a complex pattern in the angles of the polarimetric vectors. Near the core of this cluster the structure shows a semi-circular pattern that we have interpreted as a re-orientation of the dust particles, showing the morphology of the magnetic field. We propose that a supernova event has occurred some time ago and produced a shock on the local ISM. We discuss in this paper independent confirmations othis event, both from the studies on the diffuse interstellar absorptions Crawford (2001) and the results of the pre-main sequence stars (PMS) given by Sung et al. (1998). We also show that a supernova is supported by the evolutive status of the cluster.Comment: 24 pages, 4 figures, ApJ Accepte

Application of median-equation approach for outlier detection in geodetic networks

In geodetic measurements some outliers may occur sometimes in data sets, depending on different reasons. There are two main approaches to detect outliers as Tests for outliers (Baarda's and Pope's Tests) and robust methods (Danish method, Huber method etc.). These methods use the Least Squares Estimation (LSE). The outliers affect the LSE results, especially it smears the effects of the outliers on the good observations and sometimes wrong results may be obtained. To avoid these effects, a method that does not use LSE should be preferred. The median is a high breakdown point estimator and if it is applied for the outlier detection, reliable results can be obtained. In this study, a robust method which uses median with or as a treshould value on median residuals that are obtained from median equations is proposed. If the a priori variance of the observations is known, the reliability of the new approch is greater than the one in the case where the a priori variance is unknown

Robust Henderson III estimators of variance components in the nested error model

Common methods for estimating variance components in Linear Mixed Models include Maximum Likelihood (ML) and Restricted Maximum Likelihood (REML). These methods are based on the strong assumption of multivariate normal distribution and it is well know that they are very sensitive to outlying observations with respect to any of the random components. Several robust altematives of these methods have been proposed (e.g. Fellner 1986, Richardson and Welsh 1995). In this work we present several robust alternatives based on the Henderson method III which do not rely on the normality assumption and provide explicit solutions for the variance components estimators. These estimators can later be used to derive robust estimators of regression coefficients. Finally, we describe an application of this procedure to small area estimation, in which the main target is the estimation of the means of areas or domains when the within-area sample sizes are small