Groups of tree-expanded series

We describe the proalgebraic groups represented by three Hopf algebras on planar binary trees previously introduced by the author and Christian Brouder in relation with the renormalization of quantum electrodynamics. Using two monoidal structures and a set-operad structure on planar binary trees, we show that these groups can be realized on formal series expanded over trees, and that the group laws are generalization of the multiplication and the composition of usual series in one variable. All the constructions are done in a general operad-theoretic setting, and then applied to the duplicial operad on trees.Comment: 30 pages; added references, to appear in J.Algebr

Orthodontic treatment need and prevalence of malocclusions in the Orthodontic Unit of "Sapienza - University of Rome" : a six - year clinical experience

AIM The objective of this epidemiological survey was to investigate the dental-skeletal features of subjects attending the Public Dental Service in U.O.C. (Orthodontic Department of “La Sapienza University of Rome) and compare them with the existing body of evidence coming from other surveys. Accordingly, the Index of Orthodontic Treatment Need (I.O.T.N.) was employed, in order to achieve a common framework to allow the shaping of public health prevention practices. MATERIALS & METHODS A sample of 3491 subjects in the Orthodontic Department of “La Sapienza- University of Rome” (UOC) was evaluated with the adoption of I.O.T.N. to define malocclusion severity. RESULTS In the result analysis, it was observed that class II malocclusion was more frequent in the sample (40%), and a large part of the examined population also presented mandibular dental crowding (43%), increased overjet (41%), increased overbite (38%). Only 26,44% (20,17% IOTN 4; 6,27% IOTN 5) had strong need for orthodontic treatment. CONCLUSION The realization of epidemiologic investigations to establish priority for treatment need is therefore particularly useful, not only to estimate the prevalence of some clinical conditions in the observed population, but also to plan targeted interventions, such as interceptive and corrective therapies in growing children. CLINICAL SIGNIFICANCE These interventions could solve specific clinical situations and/or prevent their escalation. Only in this way it’s possible to avoid fragmenting the limited resources available, using them for patients with an objective need

Naturalizing Qualia

Hill (2014) argues that perceptual qualia, i.e. the ways in which things look from a viewpoint, are physical properties of objects. They are relational in nature, that is, they are functions of objects’ intrinsic properties, viewpoints, and observers. Hill also claims that his kind of representationalism is the only view capable of “naturalizing qualia”. After discussing a worry with Hill’s account, I put forward an alternative, which is just as “naturalization-friendly”. I build upon Chirimuuta’s color adverbialism (2015), and I argue that we would better serve the “naturalizing project” if we abandoned representationalism and preferred a broadly adverbialist view of perceptual qualia

TASI Lectures on Gravitational Waves from the Early Universe

These lectures discuss how the direct detection of gravitational waves can be used to probe the very early Universe. We review the main cosmological mechanisms which could have produced relic gravitational waves, and compare theoretical predictions with capabilities and time scales of current and upcoming experiments.Comment: 37 pages, 8 figures; typos correcte

Glauber dynamics on nonamenable graphs: Boundary conditions and mixing time

We study the stochastic Ising model on finite graphs with n vertices and bounded degree and analyze the effect of boundary conditions on the mixing time. We show that for all low enough temperatures, the spectral gap of the dynamics with (+)-boundary condition on a class of nonamenable graphs, is strictly positive uniformly in n. This implies that the mixing time grows at most linearly in n. The class of graphs we consider includes hyperbolic graphs with sufficiently high degree, where the best upper bound on the mixing time of the free boundary dynamics is polynomial in n, with exponent growing with the inverse temperature. In addition, we construct a graph in this class, for which the mixing time in the free boundary case is exponentially large in n. This provides a first example where the mixing time jumps from exponential to linear in n while passing from free to (+)-boundary condition. These results extend the analysis of Martinelli, Sinclair and Weitz to a wider class of nonamenable graphs.Comment: 31 pages, 4 figures; added reference; corrected typo