On the geometry of the spin-statistics connection in quantum mechanics

The Spin-Statistics theorem states that the statistics of a system of identical particles is determined by their spin: Particles of integer spin are Bosons (i.e. obey Bose-Einstein statistics), whereas particles of half-integer spin are Fermions (i.e. obey Fermi-Dirac statistics). Since the original proof by Fierz and Pauli, it has been known that the connection between Spin and Statistics follows from the general principles of relativistic Quantum Field Theory. In spite of this, there are different approaches to Spin-Statistics and it is not clear whether the theorem holds under assumptions that are different, and even less restrictive, than the usual ones (e.g. Lorentz-covariance). Additionally, in Quantum Mechanics there is a deep relation between indistinguishabilty and the geometry of the configuration space. This is clearly illustrated by Gibbs' paradox. Therefore, for many years efforts have been made in order to find a geometric proof of the connection between Spin and Statistics. Recently, various proposals have been put forward, in which an attempt is made to derive the Spin-Statistics connection from assumptions different from the ones used in the relativistic, quantum field theoretic proofs. Among these, there is the one due to Berry and Robbins (BR), based on the postulation of a certain single-valuedness condition, that has caused a renewed interest in the problem. In the present thesis, we consider the problem of indistinguishability in Quantum Mechanics from a geometric-algebraic point of view. An approach is developed to study configuration spaces Q having a finite fundamental group, that allows us to describe different geometric structures of Q in terms of spaces of functions on the universal cover of Q. In particular, it is shown that the space of complex continuous functions over the universal cover of Q admits a decomposition into C(Q)-submodules, labelled by the irreducible representations of the fundamental group of Q, that can be interpreted as the spaces of sections of certain flat vector bundles over Q. With this technique, various results pertaining to the problem of quantum indistinguishability are reproduced in a clear and systematic way. Our method is also used in order to give a global formulation of the BR construction. As a result of this analysis, it is found that the single-valuedness condition of BR is inconsistent. Additionally, a proposal aiming at establishing the Fermi-Bose alternative, within our approach, is made.

"Making Sense of Figures": Statistics, Computing and Information Technologies in Agriculture and Biology in Britain, 1920s-1960s

Throughout the twentieth century statistical methods have increasingly become part of experimental research. In particular, statistics has made quantification processes meaningful in the soft sciences, which had traditionally relied on activities such as collecting and describing diversity rather than timing variation. The thesis explores this change in relation to agriculture and biology, focusing on analysis of variance and experimental design, the statistical methods developed by the mathematician and geneticist Ronald Aylmer Fisher during the 1920s. The role that Fisher’s methods acquired as tools of scientific research, side by side with the laboratory equipment and the field practices adopted by research workers, is here investigated bottom-up, beginning with the computing instruments and the information technologies that were the tools of the trade for statisticians. Four case studies show under several perspectives the interaction of statistics, computing and information technologies, giving on the one hand an overview of the main tools – mechanical calculators, statistical tables, punched and index cards, standardised forms, digital computers – adopted in the period, and on the other pointing out how these tools complemented each other and were instrumental for the development and dissemination of analysis of variance and experimental design. The period considered is the half-century from the early 1920s to the late 1960s, the institutions investigated are Rothamsted Experimental Station and the Galton Laboratory, and the statisticians examined are Ronald Fisher and Frank Yates.

Antipodal random sequences with prescribed second-order statistics: application to Compressive Sensing and UWB system based on DS-CDMA

It is usual to hear a strange short sentence: «Random is better than...». Why is randomness a good solution to a certain engineering problem? There are many possible answers, and all of them are related to the considered topic. In this thesis I will discuss about two crucial topics that take advantage by randomizing some waveforms involved in signals manipulations. In particular, advantages are guaranteed by shaping the second order statistic of antipodal sequences involved in an intermediate signal processing stages. The first topic is in the area of analog-to-digital conversion, and it is named Compressive Sensing (CS). CS is a novel paradigm in signal processing that tries to merge signal acquisition and compression at the same time. Consequently it allows to direct acquire a signal in a compressed form. In this thesis, after an ample description of the CS methodology and its related architectures, I will present a new approach that tries to achieve high compression by design the second order statistics of a set of additional waveforms involved in the signal acquisition/compression stage. The second topic addressed in this thesis is in the area of communication system, in particular I focused the attention on ultra-wideband (UWB) systems. An option to produce and decode UWB signals is direct-sequence spreading with multiple access based on code division (DS-CDMA). Focusing on this methodology, I will address the coexistence of a DS-CDMA system with a narrowband interferer. To do so, I minimize the joint effect of both multiple access (MAI) and narrowband (NBI) interference on a simple matched filter receiver. I will show that, when spreading sequence statistical properties are suitably designed, performance improvements are possible with respect to a system exploiting chaos-based sequences minimizing MAI only.

Integration of Internet of Things and Cloud computing. A case study on vital signs monitoring.

Il progresso scientifico e le innovazioni tecnologiche nei campi dell'elettronica, informatica e telecomunicazioni, stanno aprendo la strada a nuove visioni e concetti. L'obiettivo della tesi è quello d'introdurre il modello del Cloud computing per rendere possibile l'attuale visione di Internet of Thing. Nel primo capitolo si introduce Ubiquitous computing come un nuovo modo di vedere i computer, cercando di fare chiarezza sulla sua definizione, la sua nascita e fornendo un breve quadro storico. Nel secondo capitolo viene presentata la visione di Internet of Thing (Internet delle “cose”) che si avvale di concetti e di problematiche in parte già considerate con Ubiquitous computing. Internet of Thing è una visione in cui la rete Internet viene estesa agli oggetti di tutti i giorni. Tracciare la posizione degli oggetti, monitorare pazienti da remoto, rilevare dati ambientali sono solo alcuni esempi. Per realizzare questo tipo di applicazioni le tecnologie wireless sono da considerare necessarie, sebbene questa visione non assuma nessuna specifica tecnologia di comunicazione. Inoltre, anche schede di sviluppo possono agevolare la prototipazione di tali applicazioni. Nel terzo capitolo si presenta Cloud computing come modello di business per utilizzare su richiesta risorse computazionali. Nel capitolo, vengono inizialmente descritte le caratteristiche principali e i vari tipi di modelli di servizio, poi viene argomentato il ruolo che i servizi di Cloud hanno per Internet of Thing. Questo modello permette di accelerare lo sviluppo e la distribuzione di applicazioni di Internet of Thing, mettendo a disposizione capacità di storage e di calcolo per l'elaborazione distribuita dell'enorme quantità di dati prodotta da sensori e dispositivi vari. Infine, nell'ultimo capitolo viene considerato, come esempio pratico, l'integrazione di tecnologie di Cloud computing in una applicazione IoT. Il caso di studio riguarda il monitoraggio remoto dei parametri vitali, considerando Raspberry Pi e la piattaforma e-Health sviluppata da Cooking Hacks per lo sviluppo di un sistema embedded, e utilizzando PubNub come servizio di Cloud per distribuire i dati ottenuti dai sensori. Il caso di studio metterà in evidenza sia i vantaggi sia le eventuali problematiche che possono scaturire utilizzando servizi di Cloud in applicazioni IoT.

Blood aspiration as a vital sign detected by postmortem computed tomography imaging

Blood aspiration is a significant forensic finding. In this study, we examined the value of postmortem computed tomography (CT) imaging in evaluating findings of blood aspiration. We selected 37 cases with autopsy evidence of blood in the lungs and/or in the airways previously submitted to total-body CT scanning. The CT-images were retrospectively analyzed. In one case with pulmonary blood aspiration, biopsy specimens were obtained under CT guide for histological examination. In six cases, CT detected pulmonary abnormalities suggestive of blood aspiration, not mentioned in the autopsy reports. CT reconstructions provided additional data about the distribution and extent of aspiration. In one needle-biopsied case, the pulmonary specimens showed blood in the alveoli. We suggest the use of CT imaging as a tool complementary to traditional techniques in cases of blood aspiration to avoid misdiagnosis, to guide the investigation of lung tissue, and to allow for more evidence-based inferences on the cause of death.

Tissue response and wound healing after placement of two types of bioengineered grafts containing vital cells in submucosal maxillary pouches: an experimental pilot study in rabbits

PURPOSE: This pilot study evaluated the wound healing and tissue response after placement of two different skin substitutes in subgingival mucosal pouches in rabbits. MATERIALS AND METHODS: Four rabbits were selected to receive a commercially available skin substitute consisting of a collagen matrix with fibroblasts and an epithelial layer (test membrane 1) and a prototype device consisting of a collagen matrix with fibroblasts only (test membrane 2). In each rabbit, two horizontal incisions were made in the buccal alveolar mucosa of the maxilla bilaterally to create submucosal pouches. Three pouches in each animal were filled with either the test 1 or test 2 membranes, and one pouch was left without a membrane (sham-operated control). All rabbits were sacrificed after a healing period of 4 weeks, and histologic samples were prepared and examined. RESULTS: After a healing period of 1 month, both tested membranes were still visible in the sections. Test membrane 1 was still bilayered, contained inflammatory cells in its center, and was encapsulated by a thick fibrous tissue. Numerous ectopic calcifications were evident in the collagenous part of the membrane and in association with some basal epithelial cells. Test membrane 2 was also encapsulated in fibrous tissue, with inflammatory cells present only between the fibrous encapsulation and the remnants of the membrane. For test membrane 2, no calcifications were visible. CONCLUSIONS: Test membrane 1 seemed to be more resistant to degradation, but there was also a more pronounced inflammatory reaction in comparison to test membrane 2, especially in the vicinity of the keratinocytes. The significance of the ectopic calcifications, along with that of the resorption or degradation processes of both tested membranes, must be evaluated in future experimental studies, with different time points after implantation examine

A project-oriented course in probability and statistics for undergraduate electrical engineering students

An introductory course in probability and statistics for third-year and fourth-year electrical engineering students is described. The course is centered around several computer-based projects that are designed to achieve two objectives. First, the projects illustrate the course topics and provide hands-on experience for the students. The second and equally important objective of the projects is to convey the relevance and usefulness of probability and statistics to practical problems that undergraduate students can appreciate. The benefit of this course as to motivate electrical engineering students to excel in the study of probability concepts, instead of viewing the subject as one more course requirement toward graduation. The authors co-teach the course, and MATLAB is used for mast of the computer-based projects

From Unsuitable Ally to Vital Parter: The Case of US-Korean Relations and The Vietnam War, 1954-1966

This is the history of the decade prior to the entrance of Korean troops into the Vietnam War, roughly covering the years 1953-1965.

Simultaneous Multiscale Polyaffine Registration by Incorporating Deformation Statistics

Locally affine (polyaffine) image registration methods capture intersubject non-linear deformations with a low number of parameters, while providing an intuitive interpretation for clinicians. Considering the mandible bone, anatomical shape differences can be found at different scales, e.g. left or right side, teeth, etc. Classically, sequential coarse to fine registration are used to handle multiscale deformations, instead we propose a simultaneous optimization of all scales. To avoid local minima we incorporate a prior on the polyaffine transformations. This kind of groupwise registration approach is natural in a polyaffine context, if we assume one configuration of regions that describes an entire group of images, with varying transformations for each region. In this paper, we reformulate polyaffine deformations in a generative statistical model, which enables us to incorporate deformation statistics as a prior in a Bayesian setting. We find optimal transformations by optimizing the maximum a posteriori probability. We assume that the polyaffine transformations follow a normal distribution with mean and concentration matrix. Parameters of the prior are estimated from an initial coarse to fine registration. Knowing the region structure, we develop a blockwise pseudoinverse to obtain the concentration matrix. To our knowledge, we are the first to introduce simultaneous multiscale optimization through groupwise polyaffine registration. We show results on 42 mandible CT images.