Nonparametric Information Geometry

The differential-geometric structure of the set of positive densities on a given measure space has raised the interest of many mathematicians after the discovery by C.R. Rao of the geometric meaning of the Fisher information. Most of the research is focused on parametric statistical models. In series of papers by author and coworkers a particular version of the nonparametric case has been discussed. It consists of a minimalistic structure modeled according the theory of exponential families: given a reference density other densities are represented by the centered log likelihood which is an element of an Orlicz space. This mappings give a system of charts of a Banach manifold. It has been observed that, while the construction is natural, the practical applicability is limited by the technical difficulty to deal with such a class of Banach spaces. It has been suggested recently to replace the exponential function with other functions with similar behavior but polynomial growth at infinity in order to obtain more tractable Banach spaces, e.g. Hilbert spaces. We give first a review of our theory with special emphasis on the specific issues of the infinite dimensional setting. In a second part we discuss two specific topics, differential equations and the metric connection. The position of this line of research with respect to other approaches is briefly discussed.Comment: Submitted for publication in the Proceedings od GSI2013 Aug 28-30 2013 Pari

Dolore post-operatorio nei pazienti affetti da neoplasia testa-collo: fattori predittivi ed efficacia della terapia

Negli anni è aumentata l’attenzione verso i molteplici aspetti associati alla “sfera” dolore, anche nei pazienti oncologici sottoposti a chirurgia testa-collo. Il dolore, definito infatti da diverse caratteristiche, quali l’esperienza personale, gli aspetti qualitativi della percezione, l’intensità, l’impatto emotivo, riconosce un’eziologia “multifattoriale”. Scopo del presente lavoro è stato: (i) valutare l’efficacia della terapia analgesica in pazienti affetti da tumore testa-collo e sottoposti a trattamento chirurgico; (ii) studiare le possibili variabili ed i fattori predittivi che possano influenzare l’insorgenza di dolore. Sono stati studiati 164 pazienti, affetti da neoplasia maligna del distretto testa-collo, trattati chirurgicamente tra il dicembre 2009 ed il dicembre 2013. I dati raccolti comprendono l’età, il sesso, la valutazione del rischio anestesiologico, la sede del tumore, la stadiazione TNM, il tipo di intervento effettuato, la complessità e la durata dell’intervento, le eventuali complicanze post-operatorie, i giorni di degenza post-intervento, la valutazione del dolore nei giorni 0, 1, 3 e 5 post-chirurgia. L’adeguatezza della terapia analgesica è stata espressa in termini di incidenza e prevalenza del dolore post-operatorio, le variabili legate al paziente, alla malattia, al trattamento chirurgico e farmacologico, sono state poi associate all’insorgenza del dolore così da poter descrivere eventuali fattori predittivi. Dai dati ottenuti emerge che la popolazione studiata ha ricevuto un’adeguata terapia antalgica, sia nell’immediato post-operatorio che nei giorni successivi. Non sono risultate associazioni statisticamente significative tra sesso, età ed incidenza del dolore post-chirurgico, mentre lo stadio del tumore, la complessità dell’intervento chirurgico e la sede della neoplasia hanno presentano correlazione significativa con il rischio di insorgenza di dolore post-operatorio. L’elevata prevalenza del dolore in ambito oncologico testa-collo, fa sì che un’appropriata ed attenta gestione del dolore risulti fondamentale. Nel futuro pertanto si auspica una sempre migliore comprensione dei fattori biologici, sociali e psicologici che caratterizzano la percezione del dolore ai fini di migliorarne il controllo

Effective Properties of a Binary Magnonic Crystal - Conferenza internazionale

In this paper the effective properties of a two-dimensional periodic binary magnetic system are studied. The magnetic system is composed by cobalt cylindrical dots embedded into a permalloy film. The dot diameter is 310 nm and the periodicity of the system is 600 nm. Since the dot diameter is smaller than the characteristic mode wavelength, it is possible to describe the collective excitations through effective quantities. In particular, for each collective mode an effective wavelength and a small effective wave vector not necessarily equal to the corresponding Bloch wavelength and Bloch wave vector can be defined. The introduction of these effective quantities characterizing collective mode dynamics allows us to describe the binary periodic magnetic system as a magnonic metamaterial

A note on the border of an exponential family

Short paper presented at the 45th Scientific Meeting Italian Statistical Society, June 16-18, 2010

A note on the border of an exponential family

Short paper presented at the 45th Scientific Meeting Italian Statistical Society, June 16-18, 2010

Perpendicularly Magnetized Antidot Lattice as a Two-Dimensional Magnonic Metamaterial - Presentazione poster by R. Zivieri - Conferenza internazionale

The effective properties of a perpendicularly magnetized two-dimensional antidot lattice having periodicity and hole size in the nanometric range are studied. The effective rules involving the effective wavelength and the effective wave vector of collective modes characterize these magnonic crystals as magnonic metamaterials

Perpendicularly magnetized antidot lattice as a two-dimensional magnonic metamaterial

In this paper the effective properties of a perpendicularly magnetized magnonic crystal are theoretically studied. The magnonic crystal is a two-dimensional antidot lattice composed by circular holes embedded into a ferromagnetic film. Both the periodicity of the magnonic crystal and the diameter of the holes are in the nanometric range and the external magnetic field is applied perpendicularly to the plane. It is shown, according to a micromagnetic approach and analytical calculations, that the effective rules linking the effective wavelength and effective wave vector of collective modes to the corresponding Bloch quantities characterizing the dynamics of in-plane magnetized periodic systems remain valid also in this geometry. It is thus possible to classify two-dimensional antidot lattices with perpendicular magnetization as magnonic metamaterials. Other metamaterial properties arising from the band structure calculation such as the band gap amplitudes at the Brillouin zone boundaries are also discussed

Size effects on spin dynamics in 2D ferromagnetic antidot lattices -- Presentazione poster by R. Zivieri - Conferenza internazionale

The size effects on frequencies of collective modes in two-dimensional (2D) arrays of periodic circular antidots (holes) embedded into a ferromagnetic Permalloy material are investigated. The study is performed by calculating the frequency behaviour as a function of the intensity H of the external magnetic field applied in the plane of the system along the ydirection for vanishing Bloch wave vector. The antidot periodicity is a = 420 nm, the thickness is L = 30 nm, whereas the diameters of the holes are d1 = 140 nm, d2 = 180 nm, d3= 220 nm and d4= 260 nm, respectively [1]. The two relevant modes, having an appreciable calculated scattering cross-section, are: 1) the resonant mode of the spectrum, the so-called Fundamental (F) mode, whose spatial profile is confined in the channels; 2) the equivalent mode mainly localized in the horizontal rows of ADs, the Floc mode. Frequencies of collective modes monotonically increase with increasing the mean internal field. However, at a fixed external field the frequencies of F and Floc mode have on opposite behavior as a function of the hole size as shown in Figure 1. Indeed, the mean demagnetizing field experienced by the F mode is anti-parallel to the external field lowering the mean internal field, while for the Floc mode it is parallel and has the effect to increase the internal field. Moreover, at the centre of the first Brillouin zone, the two lowest spin-wave mode frequencies, namely the edge mode (EM) localized at the antidot borders [2] and the F mode, become soft at a given critical field showing a deep minimum. The intensity of the critical field depends on the hole size and both soft modes do exhibit a finite gap. The softening mechanism is strictly related to the rotation of the static magnetization from the hard to the easy axis marking a reorientational and continuous phase transition [3]. [1] J. Ding, D. Tripathy, A. O. Adeyeye, J. Appl. Phys. 109, (2011) 07D304-1-3. [2] S. Tacchi, M. Madami, G. Gubbiotti, G. Carlotti, A.O. Adeyeye, S. Neusser, B. Botters, D. Grundler, IEEE Trans. Magn. 46, (2010) 172-178