On properties of the numbers coprime with the primes up to p_n

In this paper we investigate about the effective distribution of the numbers coprime with the primes up to p_n . More precisely we prove that these numbers form a periodically monotone sequence . Then we examine some properties of this sequence which, in a certain sense, are transferred to the sequence of primes. Moreover we study the distribution of twin and cousin terms within the above sequence . This study also makes furthermore strongly plausible that the set of twin primes as well as the set of cousin primes is infinite

A general framework for penalized mixed-effects multitask learning with applications on DNA methylation surrogate biomarkers creation

Recent evidence highlights the usefulness of DNA methylation (DNAm) biomarkers as surrogates for exposure to risk factors for noncommunicable diseases in epidemiological studies and randomized trials. DNAm variability has been demonstrated to be tightly related to lifestyle behavior and exposure to environmental risk factors, ultimately providing an unbiased proxy of an individual state of health. At present, the creation of DNAm surrogates relies on univariate penalized regression models, with elastic-net regularizer being the gold standard when accomplishing the task. Nonetheless, more advanced modeling procedures are required in the presence of multivariate outcomes with a structured dependence pattern among the study samples. In this work we propose a general framework for mixed-effects multitask learning in presence of high-dimensional predictors to develop a multivariate DNAm biomarker from a multicenter study. A penalized estimation scheme, based on an expectation-maximization algorithm, is devised in which any penalty criteria for fixed-effects models can be conveniently incorporated in the fitting process. We apply the proposed methodology to create novel DNAm surrogate biomarkers for multiple correlated risk factors for cardiovascular diseases and comorbidities. We show that the proposed approach, modeling multiple outcomes together, outperforms state-of-the-art alternatives both in predictive power and biomolecular interpretation of the results

A Deep Survival EWAS approach estimating risk profile based on pre-diagnostic DNA methylation: An application to breast cancer time to diagnosis

Previous studies for cancer biomarker discovery based on pre-diagnostic blood DNA methylation (DNAm) profiles, either ignore the explicit modeling of the Time To Diagnosis (TTD), or provide inconsistent results. This lack of consistency is likely due to the limitations of standard EWAS approaches, that model the effect of DNAm at CpG sites on TTD independently. In this work, we aim to identify blood DNAm profiles associated with TTD, with the aim to improve the reliability of the results, as well as their biological meaningfulness. We argue that a global approach to estimate CpG sites effect profile should capture the complex (potentially non-linear) relationships interplaying between sites. To prove our concept, we develop a new Deep Learning-based approach assessing the relevance of individual CpG Islands (i.e., assigning a weight to each site) in determining TTD while modeling their combined effect in a survival analysis scenario. The algorithm combines a tailored sampling procedure with DNAm sites agglomeration, deep non-linear survival modeling and SHapley Additive exPlanations (SHAP) values estimation to aid robustness of the derived effects profile. The proposed approach deals with the common complexities arising from epidemiological studies, such as small sample size, noise, and low signal-to-noise ratio of blood-derived DNAm. We apply our approach to a prospective case-control study on breast cancer nested in the EPIC Italy cohort and we perform weighted gene-set enrichment analyses to demonstrate the biological meaningfulness of the obtained results. We compared the results of Deep Survival EWAS with those of a traditional EWAS approach, demonstrating that our method performs better than the standard approach in identifying biologically relevant pathways

Multifunctional bioinspired sol-gel coatings for architectural glasses

Although several multinational companies have recently released products incorporating bioinspired functional coatings, their practical integration in building envelopes is still an open issue. High production costs associated to the existing vacuum deposition technologies, as well as the difficulties in extending the number of functions achievable by a single coating, represent to date the main limitations to their diffusion on a large scale. This review summarizes the key topics in the field of functional coatings for architectural glasses, focusing in particular on the potential applications of sol-gel based antireflective and self-cleaning coatings, that have received a tremendous attention in the last years. It provides an overview of the recent research efforts aimed to improve their properties and to extend their range of applicability. The bioinspired principles, upon which such coatings are based, are also described and are related to the chemical and morphological properties of such surfaces. (C) 2009 Elsevier Ltd. All rights reserved

The Italian genome reflects the history of Europe and the Mediterranean basin

Recent scientific literature has highlighted the relevance of population genetic studies both for disease association mapping in admixed populations and for understanding the history of human migrations. Deeper insight into the history of the Italian population is critical for understanding the peopling of Europe. Because of its crucial position at the centre of the Mediterranean basin, the Italian peninsula has experienced a complex history of colonization and migration whose genetic signatures are still present in contemporary Italians. In this study, we investigated genomic variation in the Italian population using 2.5 million single-nucleotide polymorphisms in a sample of more than 300 unrelated Italian subjects with well-defined geographical origins. We combined several analytical approaches to interpret genome-wide data on 1272 individuals from European, Middle Eastern, and North African populations. We detected three major ancestral components contributing different proportions across the Italian peninsula, and signatures of continuous gene flow within Italy, which have produced remarkable genetic variability among contemporary Italians. In addition, we have extracted novel details about the Italian population's ancestry, identifying the genetic signatures of major historical events in Europe and the Mediterranean basin from the Neolithic (e.g., peopling of Sardinia) to recent times (e.g., ‘barbarian invasion' of Northern and Central Italy). These results are valuable for further genetic, epidemiological and forensic studies in Italy and in Europe