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

In vivo evaluation of operative torque generated by two Nickel-Titanium rotary instruments during root canal preparation

Objectives This in vivo study evaluated the operative torque and preparation time of ProTaper NEXT (Dentsply Maillefer; Ballaigues, Switzerland) and EdgeFile X7 (EdgeEndo; Albuquerque, New Mexico, United States) rotary systems during root canal preparation of maxillary premolars. Materials and Methods Ten double-rooted maxillary premolars with independent canals were selected. Each canal in each tooth was prepared with one of the rotary systems (n = 10), ProTaper NEXT or EdgeFile X7. The instruments were rotated at 300 rpm with maximum torque set at 2 N.cm using an electric motor (KaVo; Biberach, Germany) that automatically recorded torque values at every 1/10th of a second (ds). Statistical Analysis Operative torque (N.cm) and preparation time (s) of the first shaping instrument (size 17/.04) of both rotary systems were recorded and statistically compared using the Mann-Whiney U test with a significance level set at 5%. Results No instrument exhibited flute deformation or underwent intracanal failure. No differences were found between the instruments regarding the maximum (peak) torque values (p > 0.05). EdgeFile X7 17/.04 required significantly less preparation time (3.75 seconds interquartile range [IQR]: 3.2-9.0) than ProTaper NEXT X1 (15.45 seconds IQR: 8.35-21.1) (p < 0.05). The median operative torque values of ProTaper NEXT X1 (0.26 N.cm; IQR: 0.18-0.49) were significantly higher compared with EdgeFile X7 17/.04 (0.09 N.cm; IQR: 0.05-0.17) (p < 0.05). Conclusions Although no difference was found between the median peak torque values of ProTaper NEXT X1 and EdgeFile X7 17/.04 instruments, the operative torque and instrumentation time results were impacted by their different designs and alloys during clinical preparation of root canals

Testing the “Black Code”: does having white close friends elicit identity denial and decreased empathy from black ingroup members?

The present experiment examined identity denial and reduced empathy for ingroup (vs. outgroup) targets as a function of the racial composition of their social networks. Black participants rated ingroup (Black) targets as more weakly racially identified and expressed less empathy for ingroup targets with cross-race close friends vs. same-race close friends or no friends. Furthermore, the effect of social network composition on empathy was mediated by perceived racial identity. These findings were limited to the ingroup target. Although the outgroup (White) target was rated as more weakly identified when shown with cross-race close friends vs. same-race close friends or no friends, neither social network composition nor perceived racial identity predicted empathy for the outgroup target. These findings extend previous research on identity denial and suggest that, for Blacks, closely associating with Whites undermines the usually robust pattern of ingroup empathy

Fatigue resistance of new and used nickel-titanium rotary instruments: a comparative study

Aim of the present study was twofold. First, to evaluate in vitro, the performance of two different NiTi rotary instruments in one molar case; then, to evaluate their resistance to cyclic fatigue, compared to new ones

Finite Temperature Effective Potential for Gauge Models in de Sitter Space

The one-loop effective potential for gauge models in static de Sitter space at finite temperatures is computed by means of the $\zeta$--function method. We found a simple relation which links the effective potentials of gauge and scalar fields at all temperatures. In the de Sitter invariant and zero-temperature states the potential for the scalar electrodynamics is explicitly obtained, and its properties in these two vacua are compared. In this theory the two states are shown to behave similarly in the regimes of very large and very small radii a of the background space. For the gauge symmetry broken in the flat limit ($a \to \infty$) there is a critical value of a for which the symmetry is restored in both quantum states. Moreover, the phase transitions which occur at large or at small a are of the first or of the second order, respectively, regardless the vacuum considered. The analytical and numerical analysis of the critical parameters of the above theory is performed. We also established a class of models for which the kind of phase transition occurring depends on the choice of the vacuum.Comment: 23 pages, LaTeX, 5 figure.ep