A symbolic method for k-statistics

Trough the classical umbral calculus, we provide new, compact and easy to handle expressions of k-statistics, and more in general of U-statistics. In addition such a symbolic method can be naturally extended to multivariate case and to generalized k-statistics.Comment: Extended abstract with corrected typos and change conten

Cumulants and convolutions via Abel polynomials

We provide an unifying polynomial expression giving moments in terms of cumulants, and viceversa, holding in the classical, boolean and free setting. This is done by using a symbolic treatment of Abel polynomials. As a by-product, we show that in the free cumulant theory the volume polynomial of Pitman and Stanley plays the role of the complete Bell exponential polynomial in the classical theory. Moreover via generalized Abel polynomials we construct a new class of cumulants, including the classical, boolean and free ones, and the convolutions linearized by them. Finally, via an umbral Fourier transform, we state a explicit connection between boolean and free convolution

Natural statistics for spectral samples

Spectral sampling is associated with the group of unitary transformations acting on matrices in much the same way that simple random sampling is associated with the symmetric group acting on vectors. This parallel extends to symmetric functions, k-statistics and polykays. We construct spectral k-statistics as unbiased estimators of cumulants of trace powers of a suitable random matrix. Moreover we define normalized spectral polykays in such a way that when the sampling is from an infinite population they return products of free cumulants.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1107 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A review on the prevention of inflammatory periimplant diseases

Background: An impressive number of dental implants are inserted worldwide. Evolution in dental implants and simplification of surgical techniques allowed a significant increase in the number of dentists involved in implant surgery. Most of them are general dentists, are not always sufficiently formed and experienced, frequently use low-quality implants, do not adopt the proper patient selective criteria, do not adequately monitor and maintain the inserted implants, and do not report their own statistics to the dental community. Consequently, the incidence of inflammatory periimplant diseases (IPDs) has progressively increased to values significantly higher than those previously indicated by the scientific literature. Materials and Methods: Two main literature searches were undertaken in October 2018 in the PubMed Website database. Only articles written in English and published from 2008 onward were considered; 'Clinical Trial,' 'Meta analysis,' 'Observational study,' 'Review,' and 'Validation study' were selected as article type filters. The following keywords were used in the searches: 'Peri implantitis prevention' and 'Dental implant failure prevention.'Results: Preventive measures are analyzed according to the different factors that can favor the occurrence of an infection. The factors are divided into (i) implant dependent, (ii) patient dependent, and (iii) surgeon dependent. Conclusions: Scientific and clinical data confirm that when materials are selected with care, patients are carefully evaluated for factors of risk and attitude to adhere to the necessary maintenance program, and operative protocols and maintenance programs are respected dental implants can be attractive and effective tools for oral rehabilitation. Nevertheless, dentists and patients should have greater awareness that in many cases the decision to utilize dental implants cannot be taken lightly

Probiotic streptococcus salivarius reduces symptoms of denture stomatitis and oral colonization by Candida Albicans

Denture stomatitis (DS) is an inflammatory status of oral mucosae frequently observed in denture wearers, and mainly associated with oral overgrowth of Candida albicans. DS is the cause of multiple visits to the dental office and is thought to enhance the risk of systemic infections. The treatment of DS mainly relies upon improvement of oral hygiene measures and prescription of topical or systemic antifungal agents, and disinfectants that, although effective, are not without drawbacks. Since, in recent years, some probiotics were investigated as a means to contrast oral colonization by Candida spp., this study was designed to preliminarily evaluate the effects of probiotic strain Streptococcus salivarius K12, in subjects affected by DS, and the duration of these effects. Fifty adult denture wearers affected by DS were enrolled and randomly divided into two groups: the experimental group was instructed to perform careful oral and denture hygiene and to assume the probiotic preparation for 30 days; the control group received only oral hygiene instructions. Patients were evaluated for signs of DS at the beginning of the study, at the end of treatment and 30 days later. Microbiological samples were obtained at the beginning of the study and at the end of treatment to quantify Candida albicans cells. Experimental treatment reduced clinical signs and symptoms of DS and the count of C. albicans. The clinical effects of experimental treatment were still evident after 30 days, suggesting that administration of probiotic strain Streptococcus salivarius K12 could be a promising approach in the treatment of DS

The influence of a new clinical motion for endodontic instruments on the incidence of postoperative pain

Previous studies showed that motor motions play an important role in determining apical extrusion of debris. Therefore a new clinical motion (MIMERACI) has been proposed. The basic idea is to progress slowly (1mm advancement), and after each 1mm, to remove the instrument from the canal, clean flutes and irrigate. The aim of the study was to prove whether the clinical use of MIMERACI technique would influence or not postoperative pain.MATERIALS AND METHODS: 100 teeth requesting endodontic treatment were selected for the study and divided into two similar groups based on anatomy, pre-operative symptoms and vitality, presence or absence of periapical lesion. All teeth were shaped, cleaned and obturated by the same operator, using the same NiTi instruments. The only difference between the two groups was the instrumentation technique: tradional (group A) vs MIMERACI (group B). Assessment of postoperative pain was performed 3 days after treatment. Presence, absence and degree of pain were recorded with a visual analogue scale (VAS), validated in previous studies. Collected data statistically analyzed using one-way ANOVA post hoc Tukey test. RESULTS: For VAS pain scores MIMERACI technique showed significantly better results than group A (p=0,031). Overall, both incidence and intensity of symptoms were significantly lower. Flare ups occurred in 3 patients, but none treated with the MIMERACI Technique. CONCLUSIONS: Since extruded debris can elicit more postoperative pain, results obtained by using MIMERACI technique are probably due to many factors: better mechanical removal and less production of debris and more efficient irrigation during instrumentation

The evolution of man–machine interaction: the role of human in Industry 4.0 paradigm

ndustry 4.0 is a new paradigm in the manufacturing world and it has deeply changed the Human–machine interaction. This paper focus is on the nature of this interaction, which is made possible thanks to the Internet of Things (IoT), and Cyber-Physical System (CPS). These Industry 4.0 key technologies are studied related to the standard Deming cycle, in order to underline the importance of Human–machine interaction. The Fourth Industrial Revolution involves several changes in the workforce’s key features. In this paper, a new perspective based on the centrality of humans is given in the new Industry era. The importance of the human factor will be deeply studied through the implementation of the ‘Sand Cone Model’. A new framework is proposed in order to explain the quality measures addiction on the workforce quality skills, and how it engraves on improving efficiency and effectiveness of an industrial process