A direct approach to quaternionic manifolds

The recent definition of slice regular function of several quaternionic variables suggests a new notion of quaternionic manifold. We give the definition of quaternionic regular manifold, as a space locally modeled on $\mathbb{H}^n$, in a slice regular sense. We exhibit some significant classes of examples, including manifolds which carry a quaternionic affine structure.Comment: 13 page

The Role of Vision on Spatial Competence

Several pieces of evidence indicate that visual experience during development is fundamental to acquire long-term spatial capabilities. For instance, reaching abilities tend to emerge at 5 months of age in sighted infants, while only later at 10 months of age in blind infants. Moreover, other spatial skills such as auditory localization and haptic orientation discrimination tend to be delayed or impaired in visually impaired children, with a huge impact on the development of sighted-like perceptual and cognitive asset. Here, we report an overview of studies showing that the lack of vision can interfere with the development of coherent multisensory spatial representations and highlight the contribution of current research in designing new tools to support the acquisition of spatial capabilities during childhood

Comparison of Distances for Supervised Segmentation of White Matter Tractography

Tractograms are mathematical representations of the main paths of axons within the white matter of the brain, from diffusion MRI data. Such representations are in the form of polylines, called streamlines, and one streamline approximates the common path of tens of thousands of axons. The analysis of tractograms is a task of interest in multiple fields, like neurosurgery and neurology. A basic building block of many pipelines of analysis is the definition of a distance function between streamlines. Multiple distance functions have been proposed in the literature, and different authors use different distances, usually without a specific reason other than invoking the "common practice". To this end, in this work we want to test such common practices, in order to obtain factual reasons for choosing one distance over another. For these reasons, in this work we compare many streamline distance functions available in the literature. We focus on the common task of automatic bundle segmentation and we adopt the recent approach of supervised segmentation from expert-based examples. Using the HCP dataset, we compare several distances obtaining guidelines on the choice of which distance function one should use for supervised bundle segmentation

A Strong Version of the Hilbert Nullstellensatz for slice regular polynomials in several quaternionic variables

In this paper we prove a strong version of the Hilbert Nullstellensatz in the ring $\mathbb H[q_1,\ldots,q_n]$ of slice regular polynomials in several quaternionic variables. Our proof deeply depends on a detailed analysis of the common zeros of slice regular polynomials which belong to an ideal in $\mathbb H[q_1,\ldots,q_n]$. This study motivates the introduction of a new notion of algebraic set in the quaternionic setting, which allows us to define a Zariski-type topology on $\mathbb H^n$.Comment: Under review, submitted on 11th January 202

On compact affine quaternionic curves and surfaces

This paper is devoted to the study of affine quaternionic manifolds and to a possible classification of all compact affine quaternionic curves and surfaces. It is established that on an affine quaternionic manifold there is one and only one affine quaternionic structure. A direct result, based on the celebrated Kodaira Theorem that studies compact complex manifolds in complex dimension 2, states that the only compact affine quaternionic curves are the quaternionic tori and the primary Hopf surface S^3 x S^1. As for compact affine quaternionic surfaces, we restrict to the complete ones: the study of their fundamental groups, together with the inspection of all nilpotent hypercomplex simply connected 8-dimensional Lie Groups, identifies a path towards their classification.Comment: 20 pages, accepted for publication in The Journal of Geometric Analysi

Resultants of slice regular polynomials in two quaternionic variables

We introduce a non-commutative resultant, for slice regular polynomials in two quaternionic variables, defined in terms of a suitable Dieudonn\'e determinant.We use this tool to investigate the existence of common zeros of slice regular polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:2212.0230

DEVELOPMENT OF AN IN VITRO BIOMIMETIC DEVICE AIMED AT REPRODUCING THE INTESTINAL BARRIER

Lo scopo della tesi è il design e la caratterizzazione di un sistema biomimetico di simulazione in vitro della barriera intestinale. Il device simula le proprietà della barriera intestinale sia in termini di interfaccia permeabile che consente il trasporto di sostanze e l'assorbimento di farmaci, sia come attuatore bioibrido ingegnerizzato che riproduce la peristalsi intestinale. Lo scopo del lavoro nasce dalla necessità di avere uno strumento in vitro per modellare le caratteristiche fisiologiche e patologiche della barriera intestinale e i meccanismi di assorbimento attraverso di essa

Development and validation of flight control laws for a small-scale helicopter

University of Pisa is performing a research finalized to develop Rotary Unmanned Aerial Vehicles (RUAV) starting from a small commercial RC helicopters. These vehicles will be capable to perform planned missions in autonomous or automatic flight, including the take-off and landing phase, also thanks to sense and avoid system capabilities. At the moment the activities are focused on a small helicopter, T_REX 500 ESP equipped with a GPS, inertial sensor and a data acquisition system, avaiable at the department. In the first part of this work, a non-linear open-loop analytic model of the rotor craft (developed and identificated in a previous thesis at the department)will be modified and linerized. The procedure of linearization is based on a Matlab automatic tool which creates a linear model directly from the non-linear one. In the second part of this work the control laws will be evaluated and compared with the corresponding laws created for a model based on the aerodynamic derivatives (developed in a previous thesis)in order to understand better the dynamic of the helicopter. As a final validation the control laws will be implemented on the non linear model to verify the stability and the beahaviour of the T-Rex 500 after inputs in velocity (capability to reach a new condition of trim)

Il ruolo della metodica CGH array nella diagnostica delle sindromi dismorfogenetiche con disabilità neuropsichica in eta evolutiva

La tesi è strutturata in una parte generale che tratta le sindromi dismorfogenetiche e la disabilità intellettiva e le modalità più innovative di diagnosi. La parte sperimentale si concentra su pazienti affetti da disturbi del neurosviluppo e/o anomalie congenite multiple di natura da determinare studiati al CGH array. In maniera esemplificativa, viene poi studiato un campione di pazienti affetti da sindrome Di George