Coisotropic Variational Problems

In this article we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then the extremal curves can be found by quadratures. Our proof is constructive and relies on the reduction theory for coisotropic optimal control problems. This gives a unified explanation of the integrability of several classical variational problems such as the total squared curvature functional, the projective, conformal and pseudo-conformal arc-length functionals, the Delaunay and the Poincar{\'e} variational problems

Hamiltonian flows on null curves

The local motion of a null curve in Minkowski 3-space induces an evolution equation for its Lorentz invariant curvature. Special motions are constructed whose induced evolution equations are the members of the KdV hierarchy. The null curves which move under the KdV flow without changing shape are proven to be the trajectories of a certain particle model on null curves described by a Lagrangian linear in the curvature. In addition, it is shown that the curvature of a null curve which evolves by similarities can be computed in terms of the solutions of the second Painlev\'e equation.Comment: 14 pages, v2: final version; minor changes in the expositio

Binary trees, coproducts, and integrable systems

We provide a unified framework for the treatment of special integrable systems which we propose to call "generalized mean field systems". Thereby previous results on integrable classical and quantum systems are generalized. Following Ballesteros and Ragnisco, the framework consists of a unital algebra with brackets, a Casimir element, and a coproduct which can be lifted to higher tensor products. The coupling scheme of the iterated tensor product is encoded in a binary tree. The theory is exemplified by the case of a spin octahedron.Comment: 15 pages, 6 figures, v2: minor correction in theorem 1, two new appendices adde

Effective holographic theory of charge density waves

We use gauge/gravity duality to write down an effective low energy holographic theory of charge density waves. We consider a simple gravity model which breaks translations spontaneously in the dual field theory in a homogeneous manner, capturing the low energy dynamics of phonons coupled to conserved currents. We first focus on the leading two-derivative action, which leads to excited states with nonzero strain. We show that including subleading quartic derivative terms leads to dynamical instabilities of AdS2 translation invariant states and to stable phases breaking translations spontaneously. We compute analytically the real part of the electric conductivity. The model allows to construct Lifshitz-like hyperscaling violating quantum critical ground states breaking translations spontaneously. At these critical points, the real part of the dc conductivity can be metallic or insulating

Cosmological diagrammatic rules

A simple set of diagrammatic rules is formulated for perturbative evaluation of ``in-in" correlators, as is needed in cosmology and other nonequilibrium problems. These rules are both intuitive, and efficient for calculational purposes.Comment: 7 pages, 3 figure

Uso Tópico do Alendronato de Sódio Associado ao Bio-oss® no Reparo de Defeitos Òsseos - Estudo Histomorfométrico em Calvária de Ratos

O alendronato de sódio (ALN) tem demostrado um efeito anabólico no reparo ósseo quando associado aos enxertos provenientes de osso bovino liofilizado, porém a forma de administração e a concentração ainda são objeto de investigação. Objetivo: Esta pesquisa avaliou o efeito do uso tópico do ALN a 0,5%, utilizado isoladamente ou associado ao osso bovino liofilizado (Bio-Oss®), sobre o percentual de neoformação óssea e a absorção dos grânulos do enxerto. Metodologia: Duas cavidades de 5mm de diâmetro foram confeccionadas na calvária de 18 ratos Wistar e preenchidas com: ALN 0,5% veiculado em esponja de gelatina (grupo A - GA); BioOss® (grupo B - GB); Bio-Oss® embebido em ALN 0,5% (grupo AB - GAB); coágulo sanguíneo (grupo controle - GC). Os animais foram eutanasiados aos 90 dias pósoperatórios. Os espécimes foram analisados histologicamente (hematoxilina/eosina) e por histomorfometria com auxílio do software AutoCAD®, quanto ao percentual de neoformação óssea e de remanescentes de grânulos de Bio-Oss®. Na análise estatística, os grupos foram comparados utilizando o teste t de Student para amostras pareadas (p ≤ 0,05). Resultados: As médias dos percentuais de neoformação óssea foram: GA = 40,4 ± 22,2; GB = 46,0 ± 22,0; GAB = 29,9 ± 17,8; GC = 49,9 ± 16,4, enquanto a média dos percentuais de remanescentes de grânulos de Bio-Oss® foram: GB = 9,2 ± 4,5 e GAB = 12,2 ± 7,2%. Houve diferença estatisticamente significativa no percentual de neoformação óssea apenas entre o grupo GC e GAB (p = 0,025), com preenchimento tecidual do defeito ósseo sem diferença estatística em virtude da presença dos grânulos do enxerto. Não houve diferença estatisticamente significativa no percentual de remanescentes de grânulos entre os grupos. Conclusão: O uso do ALN 0,5% tópico isoladamente nas cavidades ósseas não alterou o percentual de neoformação óssea. Quando associado ao Bio-Oss®, diminuiu o percentual de neoformação óssea e não interferiu na reabsorção dos grânulos do enxerto. Descritores

Videogame Addiction Scale for Children: Psychometric Properties and Gamer Profiles in the Italian Context

Given the few studies examining the evaluation of screening tools for videogame addiction among children aged 12 years and under, the present study analyzed (i) the psychometric properties (factorial structure, reliability indices and criterion validity) of the Italian version of the Videogame Addiction Scale for Children (VASC) and (ii) its construct validity using a person-centered approach. Two studies were carried out. In study 1, 728 participants completed a survey including demographic information, questions concerning the amount of time spent in playing videogames, and the Italian version of the VASC. In study 2, 1008 participants completed a survey comprising demographic information, the Italian version of the VASC, the Big Five Questionnaire for Children, and the social dimension subscale of the Multidimensional Self-Concept Scale. Findings supported (i) the four-dimensional first-order factor structure, (ii) full scalar invariance across age groups and partial scalar equivalence across gender, and (iii) reliability and criterion validity of the VASC. The construct validity of the VASC was confirmed by the identification of two distinct profiles (high videogame players vs. low videogame players) and their specific patterns of associations with personality traits and social self-concept. Interaction effects of gender × profiles on personality traits were evidenced. Overall, the findings provided validity for the use of the Italian version of the VASC and extending the body of literature on videogame addiction

Gaudin Models and Bending Flows: a Geometrical Point of View

In this paper we discuss the bihamiltonian formulation of the (rational XXX) Gaudin models of spin-spin interaction, generalized to the case of sl(r)-valued spins. In particular, we focus on the homogeneous models. We find a pencil of Poisson brackets that recursively define a complete set of integrals of the motion, alternative to the set of integrals associated with the 'standard' Lax representation of the Gaudin model. These integrals, in the case of su(2), coincide wih the Hamiltonians of the 'bending flows' in the moduli space of polygons in Euclidean space introduced by Kapovich and Millson. We finally address the problem of separability of these flows and explicitly find separation coordinates and separation relations for the r=2 case.Comment: 27 pages, LaTeX with amsmath and amssym

Excursion Sets and Non-Gaussian Void Statistics

Primordial non-Gaussianity (NG) affects the large scale structure (LSS) of the universe by leaving an imprint on the distribution of matter at late times. Much attention has been focused on using the distribution of collapsed objects (i.e. dark matter halos and the galaxies and galaxy clusters that reside in them) to probe primordial NG. An equally interesting and complementary probe however is the abundance of extended underdense regions or voids in the LSS. The calculation of the abundance of voids using the excursion set formalism in the presence of primordial NG is subject to the same technical issues as the one for halos, which were discussed e.g. in arXiv:1005.1203. However, unlike the excursion set problem for halos which involved random walks in the presence of one barrier $\delta_c$, the void excursion set problem involves two barriers $\delta_v$ and $\delta_c$. This leads to a new complication introduced by what is called the "void-in-cloud" effect discussed in the literature, which is unique to the case of voids. We explore a path integral approach which allows us to carefully account for all these issues, leading to a rigorous derivation of the effects of primordial NG on void abundances. The void-in-cloud issue in particular makes the calculation conceptually rather different from the one for halos. However, we show that its final effect can be described by a simple yet accurate approximation. Our final void abundance function is valid on larger scales than the expressions of other authors, while being broadly in agreement with those expressions on smaller scales.Comment: 28 pages (18+appendices), 7 figures; v2 -- minor changes in sec 3.2, version published in PR

Teaching mathematics at distance: A challenge for universities

The focus of this research is how Sicilian state university mathematics professors faced the challenge of teaching via distance education during the first wave of the COVID-19 pandemic. Since the pandemic entered our lives suddenly, the professors found themselves having to lecture using an e-learning platform that they had never used before, and for which they could not receive training due to the health emergency. In addition to the emotional aspects related to the particular situation of the pandemic, there are two aspects to consider when teaching mathematics at a distance. The first is related to the fact that at university level, lecturers generally teach mathematics in a formal way, using many symbols and formulas that they are used to writing. The second aspect is that the way mathematics is taught is also related to the students to whom the teaching is addressed. In fact, not only online, but also in face-to-face modality, the teaching of mathematics to students on the mathematics degree course involves a different approach to lessons (as well as to the choice of topics to explain) than teaching mathematics in another degree course. In order to investigate how the Sicilian State university mathematics professors taught mathematics at distance, a questionnaire was prepared and administered one month after the beginning of the lockdown in Italy. Both quantitative and qualitative analyses were made, which allowed us to observe the way that university professors have adapted to the new teaching modality: they started to appropriate new artifacts (writing tablets, mathematical software, e-learning platform) to replicate their face-to-face teaching modality, mostly maintaining their blackboard teacher status. Their answers also reveal their beliefs related to teaching mathematics at university level, noting what has been an advantageous or disadvantageous for them in distance teaching