The Degrees of Freedom of Partial Least Squares Regression

The derivation of statistical properties for Partial Least Squares regression can be a challenging task. The reason is that the construction of latent components from the predictor variables also depends on the response variable. While this typically leads to good performance and interpretable models in practice, it makes the statistical analysis more involved. In this work, we study the intrinsic complexity of Partial Least Squares Regression. Our contribution is an unbiased estimate of its Degrees of Freedom. It is defined as the trace of the first derivative of the fitted values, seen as a function of the response. We establish two equivalent representations that rely on the close connection of Partial Least Squares to matrix decompositions and Krylov subspace techniques. We show that the Degrees of Freedom depend on the collinearity of the predictor variables: The lower the collinearity is, the higher the Degrees of Freedom are. In particular, they are typically higher than the naive approach that defines the Degrees of Freedom as the number of components. Further, we illustrate how the Degrees of Freedom approach can be used for the comparison of different regression methods. In the experimental section, we show that our Degrees of Freedom estimate in combination with information criteria is useful for model selection.Comment: to appear in the Journal of the American Statistical Associatio

Spatially Resolved Magnetization in the Bose-Einstein Condensed State of BaCuSi2O6: Evidence for Imperfect Frustration

In order to understand the nature of the two-dimensional Bose-Einstein condensed (BEC) phase in BaCuSi2O6, we performed detailed 63Cu and 29Si NMR above the critical magnetic field, Hc1= 23.4 T. The two different alternating layers present in the system have very different local magnetizations close to Hc1; one is very weak, and its size and field dependence are highly sensitive to the nature of inter-layer coupling. Its precise value could only be determined by "on-site" 63Cu NMR, and the data are fully reproduced by a model of interacting hard-core bosons in which the perfect frustration associated to tetragonal symmetry is slightly lifted, leading to the conclusion that the population of the less populated layers is not fully incoherent but must be partially condensed

Free-electron Model for Mesoscopic Force Fluctuations in Nanowires

When two metal electrodes are separated, a nanometer sized wire (nanowire) is formed just before the contact breaks. The electrical conduction measured during this retraction process shows signs of quantized conductance in units of G_0=2e^2/h. Recent experiments show that the force acting on the wire during separation fluctuates, which has been interpreted as being due to atomic rearrangements. In this report we use a simple free electron model, for two simple geometries, and show that the electronic contribution to the force fluctuations is comparable to the experimentally found values, about 2 nN.Comment: 4 pages, 3 figures, reference correcte

Incipient charge order observed by NMR in the normal state of YBa2Cu3Oy

The pseudogap regime of high-temperature cuprates harbours diverse manifestations of electronic ordering whose exact nature and universality remain debated. Here, we show that the short-ranged charge order recently reported in the normal state of YBa2Cu3Oy corresponds to a truly static modulation of the charge density. We also show that this modulation impacts on most electronic properties, that it appears jointly with intra-unit-cell nematic, but not magnetic, order, and that it exhibits differences with the charge density wave observed at lower temperatures in high magnetic fields. These observations prove mostly universal, they place new constraints on the origin of the charge density wave and they reveal that the charge modulation is pinned by native defects. Similarities with results in layered metals such as NbSe2, in which defects nucleate halos of incipient charge density wave at temperatures above the ordering transition, raise the possibility that order-parameter fluctuations, but no static order, would be observed in the normal state of most cuprates if disorder were absent.Comment: Updated version. Free download at Nature Comm. website (doi below

Clinical effectiveness of restorative materials for the restoration of carious primary teeth without pulp therapy: a systematic review.

PURPOSE To systematically search the available evidence and evaluate the clinical effectiveness of restorative materials for restoration of carious primary teeth. The findings aimed to support the European Academy of Paediatric Dentistry (EAPD) guidelines development. METHODS Literature search was performed by searching 4 electronic databases for eligible randomised controlled clinical trials (RCTs) comparing restorative materials for the restoration of carious primary teeth up to December 28th, 2020. Quality assessment was performed with the revised Cochrane risk-of-bias tool for randomized trials (RoB 2). RESULTS Of 1685 identified articles 29 RCTs were finally deemed as eligible for inclusion. Annual failure rates were: Amalgam 1-28%; atraumatic restorative treatment 1.2-37.1%; glass-ionomer cement (GIC) 7.6-16.6%, metal-reinforced GIC 29.9%, resin-modified GIC 1.9-16.9%, high-viscosity GIC 2.9-25.6%; glass carbomer ≤ 46.2%; compomer 0-14.7%; composite resin (CR) 0-19.5%, bulk-fill CR 0-16.9%; zirconia crowns 3.3%, composite strip crowns 15%, and preformed metal crowns (Hall-Technique) 3.1%. Secondary caries, poor marginal adaptation, loss of retention, and fracture of restoration were reported as reasons for failure. Four studies were evaluated at unclear and 25 at high risk of bias. Clinical and methodological heterogeneity, and the diversity of tested materials across included studies did not allow for meta-analyses. CONCLUSIONS Within the limitations of this systematic review, namely, the heterogeneity and the overall high risk of bias among included studies, clear recommendations based on solid evidence for the best restorative approach in primary teeth cannot be drawn. There is a need for future thoroughly implemented RCTs evaluating restorations in primary teeth to close this knowledge gap

Clinical effectiveness of pit and fissure sealants in primary and permanent teeth of children and adolescents: an umbrella review.

PURPOSE This umbrella review aimed to critically appraise the evidence published in systematic reviews (SRs) on the clinical effectiveness of sealants compared with each other/the non-use in primary/permanent teeth of children and adolescents with at least 12-month follow-up. METHODS A systematic literature search on 4 electronic databases was conducted up to January 18th, 2023. Following handsearching, two review authors independently screened retrieved articles, extracted data, and assessed the risk of bias (RoB) using the risk of bias in systematic reviews (ROBIS) tool. Based on a citation matrix, the overlap was interpreted by the corrected covered area (CCA). RESULTS Of 239 retrieved records, 7 SRs met the eligibility criteria with a moderate overlap among them (CCA = 7.4%). For primary molars, in 1120 1.5- to 8-year-old children, data on the clinical effectiveness of sealants were inconclusive. For permanent molars, 3 SRs found a significant caries risk reduction for sealants versus non-use (≤ 36-month follow-up). There was insufficient evidence to proof superiority of sealants over fluoride varnish for caries prevention (3 SRs), and to rank sealant materials according to the best clinical effectiveness in permanent molars. One study was rated at low and 6 at high RoB, which did not allow for a valid quantitative synthesis. CONCLUSION Considering the limitations of this umbrella review, sealants are more effective for caries prevention in children's permanent molars compared to no treatment. Future well-implemented RCTs are needed to draw reliable conclusions on the clinical effectiveness of sealants in primary and permanent teeth of children and adolescents

Clinical effectiveness of restorative materials for the restoration of carious lesions in pulp treated primary teeth: a systematic review.

PURPOSE To systematically review the clinical performance of restorative materials after pulp therapy of carious primary teeth. It is part 2 of a systematic review on the clinical effectiveness of restorative materials for the management of carious primary teeth supporting the European Academy of Paediatric Dentistry (EAPD) guideline development. METHODS Four electronic databases were systematically searched up to December 28th, 2020. Randomised controlled clinical trials (RCTs) on restorative materials for the restoration of carious primary teeth after pulp therapy were included. Failure rate, annual failure rate (AFR) and reasons for failure were recorded. Studies were sorted by restorative materials. The Cochrane Risk of bias tool for randomised trials (RoB 2.0) was used for quality assessment. RESULTS After identification of 1685 articles and screening of 41 papers from EAPD review group 1, 5 RCTs were included. Restored primary molars with pulpotomy presented the following AFRs: composite resin (CR) 0%, preformed metal crowns (PMCs) 2.4-2.5%, resin-modified glass-ionomer cement combined with CR 3.8%, compomer 8.9%, and amalgam 14.3%. Maxillary primary incisors receiving pulpectomy exhibited AFRs of 0-2.3% for composite strip crowns (CSCs) depending on the post chosen. Reasons for failure were secondary caries, poor marginal adaptation, loss of retention and fracture of restoration. All studies were classified as high risk of bias. Meta-analyses were not feasible given the clinical/methodological heterogeneity amongst studies. CONCLUSION Considering any limitations of this review, CR and PMCs can be recommended for primary molars after pulpotomy, and CSCs for primary incisors receiving pulpectomy. However, a need for further well-designed RCTs was observed