Frobenius structures on double Hurwitz spaces

We construct Frobenius structures of "dual type" on the moduli space of ramified coverings of $\mathbb{P}^1$ with given ramification type over two points, generalizing a construction of Dubrovin. A complete hierarchy of hydrodynamic type is obtained from the corresponding deformed flat connection. This provides a suitable framework for the Whitham theory of an enlarged class of integrable hierarchies; we treat as examples the q-deformed Gelfand-Dickey hierarchy and the sine-Gordon equation, and compute the corresponding solutions of the WDVV equations.Comment: 28 page

Biorthogonal ensembles with two-particle interactions

We investigate determinantal point processes on $[0,+\infty)$ of the form \begin{equation*}\label{probability distribution} \frac{1}{Z_n}\prod_{1\leq i<j\leq n}(\lambda_j-\lambda_i)\prod_{1\leq i<j\leq n}(\lambda_j^\theta-\lambda_i^\theta) \prod_{j=1}^n w(\lambda_j)d\lambda_j,\qquad \theta\geq 1. \end{equation*} We prove that the biorthogonal polynomials associated to such models satisfy a recurrence relation and a Christoffel-Darboux formula if $\theta\in\mathbb Q$, and that they can be characterized in terms of $1\times 2$ vector-valued Riemann-Hilbert problems which exhibit some non-standard properties. In addition, we obtain expressions for the equilibrium measure associated to our model if $w(\lambda)=e^{-nV(\lambda)}$ in the one-cut case with and without hard edge.Comment: 28 pages, 6 figure

Torque-Controlled Stepping-Strategy Push Recovery: Design and Implementation on the iCub Humanoid Robot

One of the challenges for the robotics community is to deploy robots which can reliably operate in real world scenarios together with humans. A crucial requirement for legged robots is the capability to properly balance on their feet, rejecting external disturbances. iCub is a state-of-the-art humanoid robot which has only recently started to balance on its feet. While the current balancing controller has proved successful in various scenarios, it still misses the capability to properly react to strong pushes by taking steps. This paper goes in this direction. It proposes and implements a control strategy based on the Capture Point concept [1]. Instead of relying on position control, like most of Capture Point related approaches, the proposed strategy generates references for the momentum-based torque controller already implemented on the iCub, thus extending its capabilities to react to external disturbances, while retaining the advantages of torque control when interacting with the environment. Experiments in the Gazebo simulator and on the iCub humanoid robot validate the proposed strategy

The Time of Intersection - Time dynamics in the relationship between architecture and artworks in public space.

Time has always fascinated men for its (apparently) inviolable structure and for the poetic dimension that this concept brings with it, during the history of civilization, time has been a crucial concept to understanding reality. At the beginning of the Twentieth century, thanks to the scientific discoveries, above all, Albert Einstein’s general relativity theory, the notion of time became an important element also for science for understanding the structure of the universe. The continuous and ever-faster scientific discoveries have also dissolved the linearity of time and its very nature, offering new possibilities to rethink space-time, as a series of connected, but not necessarily linear, events. Something we are experiencing today through the multi-temporality of the digital world, but which at the same time also shifts our way of perceiving physical reality. A reality made of natural objects but also objects crafted by man, from utensils to symbolic and artistic objects, from the simplest refuge to the city. Everything we do and produce is inevitably part of a space-time dimension. In this manytemporal reality in which we live, we can therefore interpret time - also - as a distinctive structural element of the things that human beings build, whether small or large, from tools to metropolises. In this background, it is very interesting to understand how time works in two of the most symbolic categories of objects of human creation, architecture and art, specifically, art in public space. How time influences their realization, thinking of it as a constructive and fundamental category of the project itself. The time that works into the artwork is naturally different from the time that works into architecture, but the overlapping of these two different times, by structure and perception, inevitably creates a third time, that we will call a “Time of Intersection”, which becomes the subject of this thesis.Il tempo ha sempre affascinato gli uomini per la sua struttura (apparentemente) inviolabile e per la dimensione poetica che questo concetto porta con sé; nel corso della storia della civiltà, il tempo è stato un concetto cruciale per la comprensione della realtà. All’inizio del XX secolo, grazie alle scoperte scientifiche, prima fra tutte la teoria della relatività generale di Albert Einstein, la nozione di tempo è diventata un elemento importante anche per la scienza per comprendere la struttura dell’universo. Le continue e sempre più rapide scoperte scientifiche hanno dissolto anche la linearità del tempo e la sua stessa natura, offrendo nuove possibilità di ripensare lo spazio-tempo, come una serie di eventi collegati, ma non necessariamente lineari. Qualcosa che oggi sperimentiamo attraverso la multitemporalità del mondo digitale, ma che allo stesso tempo sposta anche il nostro modo di percepire la realtà fisica. Una realtà fatta di oggetti naturali ma anche di oggetti creati dall’uomo, dagli utensili agli oggetti simbolici e artistici, dal più semplice rifugio alla città. Tutto ciò che facciamo e produciamo fa inevitabilmente parte di una dimensione spazio- temporale. In questa realtà pluritemporale in cui viviamo, possiamo quindi interpretare il tempo - anche - come un elemento strutturale distintivo delle cose che gli esseri umani costruiscono, siano esse piccole o grandi, dagli utensili alle metropoli. In questo contesto, è molto interessante capire come funziona il tempo in due delle categorie più simboliche di oggetti di creazione umana, l’architettura e l’arte, in particolare l’arte nello spazio pubblico. Come il tempo influenzi la loro realizzazione, pensandolo come categoria costruttiva e fondamentale del progetto stesso. Il tempo che opera nell’opera d’arte è naturalmente diverso dal tempo che opera nell’architettura, ma la sovrapposizione di questi due tempi diversi, per struttura e percezione, crea inevitabilmente un terzo tempo, che chiameremo “Tempo di Intersezione”, che diventa l’oggetto di questa tesi

CMB anomalies and the effects of local features of the inflaton potential

Recent analysis of the WMAP and Planck data have shown the presence of a dip and a bump in the spectrum of primordial perturbations at the scales $k=0.002$ Mpc${}^{-1}$ and $k=0.0035$ Mpc${}^{-1}$ respectively. We analyze for the first time the effects a local feature in the inflaton potential to explain the observed deviations from scale invariance in the primordial spectrum. We perform a best fit analysis of the cosmic microwave background (CMB) radiation temperature and polarization data. The effects of the features can improve the agreement with observational data respect to the featureless model. The best fit local feature affects the primordial curvature spectrum mainly in the region of the bump, leaving the spectrum unaffected on other scales.Comment: 18 pages, 8figures, published in EPJ

Manual therapy as a conservative treatment for adolescent idiopathic scoliosis: a systematic review

<p>Abstract</p> <p>Background</p> <p>The treatment of adolescent idiopathic scoliosis is contingent upon many variables. Simple observation is enough for less serious curvatures, but for very serious cases surgical intervention could be proposed. Between these there is a wide range of different treatments. Manual therapy is commonly used: the aim of this paper is to verify the data existing in the literature on the efficacy of this approach.</p> <p>Methods</p> <p>A systematic review of the scientific literature published internationally has been performed. We have included in the term manual therapy all the manipulative and generally passive techniques performed by an external operator. In a more specific meaning, osteopathic, chiropractic and massage techniques have been considered as manipulative therapeutic methods. We performed our systematic research in Medline, Embase, Cinhal, Cochrane Library, Pedro with the following terms: idiopathic scoliosis combined with chiropractic; manipulation; mobilization; manual therapy; massage; osteopathy; and therapeutic manipulation. The criteria for inclusion were as follows: Any kind of research; diagnosis of adolescent idiopathic scoliosis; patients treated exclusively by one of the procedures established as a standard for this review (chiropractic manipulation, osteopathic techniques, massage); and outcome in Cobb degrees.</p> <p>Results</p> <p>We founded 145 texts, but only three papers were relevant to our study. However, no one of the three satisfied all the required inclusion criteria because they were characterized by a combination of manual techniques and other therapeutic approaches.</p> <p>Conclusion</p> <p>The lack of any kind of serious scientific data does not allow us to draw any conclusion on the efficacy of manual therapy as an efficacious technique for the treatment of Adolescent idiopathic scoliosis.</p