Entanglement entropy in restricted integrable spin-chains

In questa tesi abbiamo presentato il calcolo dell’Entropia di Entanglement di un sistema quantistico unidimensionale integrabile la cui rappresentazione statistica é data dal modello RSOS, il cui punto critico é una realizzazione su reticolo di tutti i modelli conformi minimali. Sfruttando l’integrabilitá di questi modelli, abbiamo svolto il calcolo utilizzando la tecnica delle Corner Transfer Matrices (CTM). Il risultato ottenuto si discosta leggermente dalla previsione di J. Cardy e P. Calabrese ricavata utilizzando la teoria dei campi conformi descriventi il punto critico. Questa differenza é stata imputata alla non-unitarietá del modello studiato, in quanto la tecnica CTM studia il ground state, mentre la previsione di Cardy e Calabrese si focalizza sul vuoto conforme del modello: nel caso dei sistemi non-unitari questi due stati non coincidono, ma possono essere visti come eccitazioni l’uno dell’altro. Dato che l’Entanglement é un fenomeno genuinamente quantistico e il modello RSOS descrive un sistema statistico classico bidimensionale, abbiamo proposto una Hamiltoniana quantistica unidimensionale integrabile la cui rappresentazione statistica é data dal modello RSOS.

Statistical Physics and Modeling of Human Mobility

In this thesis, we extend some ideas of statistical physics to describe the properties of human mobility. By using a database containing GPS measures of individual paths (position, velocity and covered space at a spatial scale of 2 Km or a time scale of 30 sec), which includes the 2% of the private vehicles in Italy, we succeed in determining some statistical empirical laws pointing out "universal" characteristics of human mobility. Developing simple stochastic models suggesting possible explanations of the empirical observations, we are able to indicate what are the key quantities and cognitive features that are ruling individuals' mobility. To understand the features of individual dynamics, we have studied different aspects of urban mobility from a physical point of view. We discuss the implications of the Benford's law emerging from the distribution of times elapsed between successive trips. We observe how the daily travel-time budget is related with many aspects of the urban environment, and describe how the daily mobility budget is then spent. We link the scaling properties of individual mobility networks to the inhomogeneous average durations of the activities that are performed, and those of the networks describing people's common use of space with the fractional dimension of the urban territory. We study entropy measures of individual mobility patterns, showing that they carry almost the same information of the related mobility networks, but are also influenced by a hierarchy among the activities performed. We discover that Wardrop's principles are violated as drivers have only incomplete information on traffic state and therefore rely on knowledge on the average travel-times. We propose an assimilation model to solve the intrinsic scattering of GPS data on the street network, permitting the real-time reconstruction of traffic state at a urban scale.

Implementation of network entropy algorithms on hpc machines, with application to high-dimensional experimental data

Network Theory is a prolific and lively field, especially when it approaches Biology. New concepts from this theory find application in areas where extensive datasets are already available for analysis, without the need to invest money to collect them. The only tools that are necessary to accomplish an analysis are easily accessible: a computing machine and a good algorithm. As these two tools progress, thanks to technology advancement and human efforts, wider and wider datasets can be analysed. The aim of this paper is twofold. Firstly, to provide an overview of one of these concepts, which originates at the meeting point between Network Theory and Statistical Mechanics: the entropy of a network ensemble. This quantity has been described from different angles in the literature. Our approach tries to be a synthesis of the different points of view. The second part of the work is devoted to presenting a parallel algorithm that can evaluate this quantity over an extensive dataset. Eventually, the algorithm will also be used to analyse high-throughput data coming from biology.

Horizon entropy from scratch

Scopo di questo lavoro di tesi è lo studio di alcune proprietà delle teorie generali della gravità in relazione alla meccanica e la termodinamica dei buchi neri. In particolare, la trattazione che seguirà ha lo scopo di fornire un percorso autoconsistente che conduca alla nozione di entropia di un orizzonte descritta in termini delle carica di Noether associata all'invarianza del funzionale d'azione, che descrive la teoria gravitazionale in considerazione, per trasformazioni di coordinate generali. Si presterà particolare attenzione ad alcune proprietà geometriche della Lagrangiana, proprietà che sono indipendenti dalla particolare forma della teoria che si sta prendendo in considerazione; trattasi cioè non di proprietà dinamiche, legate cioè alla forma delle equazioni del moto del campo gravitazionale, ma piuttosto caratteristiche proprie di qualunque varietà rappresentante uno spaziotempo curvo. Queste caratteristiche fanno sì che ogni teoria generale della gravità possieda alcune grandezze definite localmente sullo spaziotempo, in particolare una corrente di Noether e la carica ad essa associata. La forma esplicita della corrente e della carica dipende invece dalla Lagrangiana che si sceglie di adottare per descrivere il campo gravitazionale. Il lavoro di tesi sarà orientato prima a descrivere come questa corrente di Noether emerge in qualunque teoria della gravità invariante per trasformazioni generali e come essa viene esplicitata nel caso di Lagrangiane particolari, per poi identificare la carica ad essa associata come una grandezza connessa all' entropia di un orizzonte in qualunque teoria generale della gravità.

Entanglement entropy in 1-d quantum spin chains

In questa tesi abbiamo studiato il comportamento delle entropie di Entanglement e dello spettro di Entanglement nel modello XYZ attraverso delle simulazioni numeriche. Le formule per le entropie di Von Neumann e di Renyi nel caso di una catena bipartita infinita esistevano già, ma mancavano ancora dei test numerici dettagliati. Inoltre, rispetto alla formula per l'Entropia di Entanglement di J. Cardy e P. Calabrese per sistemi non critici, tali relazioni presentano delle correzioni che non hanno ancora una spiegazione analitica: i risultati delle simulazioni numeriche ne hanno confermato la presenza. Abbiamo inoltre testato l'ipotesi che lo Schmidt Gap sia proporzionale a uno dei parametri d'ordine della teoria, e infine abbiamo simulato numericamente l'andamento delle Entropie e dello spettro di Entanglement in funzione della lunghezza della catena di spin. Ciò è stato possibile solo introducendo dei campi magnetici ''ad hoc'' nella catena, con la proprietà che l'andamento delle suddette quantità varia a seconda di come vengono disposti tali campi. Abbiamo quindi discusso i vari risultati ottenuti.

Accretion of Mass and Angular Momentum onto The Discs of Spiral Galaxies

In this Thesis, we study the accretion of mass and angular momentum onto the disc of spiral galaxies from a global and a local perspective and comparing theory predictions with several observational data. First, we propose a method to measure the specific mass and radial growth rates of stellar discs, based on their star formation rate density profiles and we apply it to a sample of nearby spiral galaxies. We find a positive radial growth rate for almost all galaxies in our sample. Our galaxies grow in size, on average, at one third of the rate at which they grow in mass. Our results are in agreement with theoretical expectations if known scaling relations of disc galaxies are not evolving with time. We also propose a novel method to reconstruct accretion profiles and the local angular momentum of the accreting material from the observed structural and chemical properties of spiral galaxies. Applied to the Milky Way and to one external galaxy, our analysis indicates that accretion occurs at relatively large radii and has a local deficit of angular momentum with respect to the disc. Finally, we show how structure and kinematics of hot gaseous coronae, which are believed to be the source of mass and angular momentum of massive spiral galaxies, can be reconstructed from their angular momentum and entropy distributions. We find that isothermal models with cosmologically motivated angular momentum distributions are compatible with several independent observational constraints. We also consider more complex baroclinic equilibria: we describe a new parametrization for these states, a new self-similar family of solution and a method for reconstructing structure and kinematics from the joint angular momentum/entropy distribution.

The Effect of Grade Point Average on Undergraduates' Understanding of Heat Transfer

Engineering students continue to develop and show misconceptions due to prior knowledge and experiences (Miller, Streveler, Olds, Chi, Nelson, & Geist, 2007). Misconceptions have been documented in students’ understanding of heat transfer(Krause, Decker, Niska, Alford, & Griffin, 2003) by concept inventories (e.g., Jacobi,Martin, Mitchell, & Newell, 2003; Nottis, Prince, Vigeant, Nelson, & Hartsock, 2009). Students’ conceptual understanding has also been shown to vary by grade point average (Nottis et al., 2009). Inquiry-based activities (Nottis, Prince, & Vigeant, 2010) haveshown some success over traditional instructional methods (Tasoglu & Bakac, 2010) in altering misconceptions. The purpose of the current study was to determine whether undergraduate engineering students’ understanding of heat transfer concepts significantly changed after instruction with eight inquiry-based activities (Prince & Felder, 2007) supplementing instruction and whether students’ self reported GPA and prior knowledge, as measured by completion of specific engineering courses, affected these changes. The Heat and Energy Concept Inventory (Prince, Vigeant, & Nottis, 2010) was used to assess conceptual understanding. It was found that conceptual understanding significantly increased from pre- to post-test. It was also found that GPA had an effect on conceptual understanding of heat transfer; significant differences were found in post-test scores onthe concept inventory between GPA groups. However, there were mixed results when courses previously taken were analyzed. Future research should strive to analyze how prior knowledge effects conceptual understanding and aim to reduce the limitations of the current study such as, sampling method and methods of measuring GPA and priorknowledge.

Predicting perceived vulnerability for breast cancer among women with an average breast cancer risk

OBJECTIVES: The purpose of the present study was to investigate predictors of perceived vulnerability for breast cancer in women with an average risk for breast cancer. On the basis of empirical findings that suggested which variables might be associated with perceived vulnerability for breast cancer, we investigated whether knowledge of breast cancer risk factors, cancer worry, intrusions about breast cancer, optimism about not getting cancer and perceived health status have a predictive value for perceived breast cancer vulnerability. DESIGN: In a 3-step approach, we recruited 292 women from the general public in Germany who had neither a family history of breast cancer nor breast cancer themselves. After receiving an initial informational letter about study objectives, the women were interviewed by telephone and then asked to fill in a self-administered questionnaire. METHODS: We used structural equation modelling and hypothesized that each of the included variables has a direct influence on perceived vulnerability for breast cancer. RESULTS: We found a valid model with acceptable fit indices. Optimism about not getting cancer, intrusions about breast cancer and women's perceived health status explained 32% of the variance of perceived vulnerability for breast cancer. Cancer worry and knowledge about breast cancer did not influence perceived vulnerability for breast cancer. CONCLUSION: Perceived vulnerability for breast cancer is associated with health-related variables more than with knowledge about breast cancer risk factors.

Flow cytometry and FISH to measure the average length of telomeres (flow FISH)

Telomeres have emerged as crucial cellular elements in aging and various diseases including cancer. To measure the average length of telomere repeats in cells, we describe our protocols that use fluorescent in situ hybridization (FISH) with labeled peptide nucleic acid (PNA) probes specific for telomere repeats in combination with fluorescence measurements by flow cytometry (flow FISH). Flow FISH analysis can be performed using commercially available flow cytometers, and has the unique advantage over other methods for measuring telomere length of providing multi-parameter information on the length of telomere repeats in thousands of individual cells. The accuracy and reproducibility of the measurements is augmented by the automation of most pipetting (aspiration and dispensing) steps, and by including an internal standard (control cells) with a known telomere length in every tube. The basic protocol for the analysis of nucleated blood cells from 22 different individuals takes about 12 h spread over 2-3 days.

Soft tissue profile changes following mandibular advancement and setback surgery an average of 12 years postoperatively

PURPOSE: The aim of this study was to assess long-term changes in position of soft tissue landmarks following mandibular advancement and setback surgery. MATERIALS AND METHODS: Twenty-seven patients (14 women, 13 men; mean age, 36 years) who had undergone either mandibular advancement (15 patients) or setback surgery (12 patients), were available for a long-term follow-up an average of 12 years postoperatively. In all of these cases, lateral cephalometric radiographs taken immediately before operation, at 1 week, 14 months, and 12 years postoperatively, were studied. RESULTS: During the 14 months postoperatively, soft tissue chin and mentolabial fold followed its underlying hard tissue in all patients. A continuous skeletal relapse was observable 12 years after mandibular advancement, but soft tissue chin moved more in an anterior direction. After mandibular setback, soft and hard tissue landmarks remained almost unchanged. Over the entire observation period, a thickening of soft tissue at pogonion was generally seen, and particularly a thickening of the whole chin in the setback group. All patients showed a significant lengthening and thinning of the upper lip. In all except 2 males, the patient's body weight increased markedly. CONCLUSION: In contrast to the immediate postoperative stage, soft tissue changes observed an average of 12 years after the primary operation do not directly follow the movements of the underlying skeletal structure. The soft tissue profile changes observed over such a long term seem to be influenced not only by the underlying skeletal structure but also by other factors such as weight gain and aging process.

Entropy and bispectral index for assessment of sedation, analgesia and the effects of unpleasant stimuli in critically ill patients: an observational study

INTRODUCTION: Sedative and analgesic drugs are frequently used in critically ill patients. Their overuse may prolong mechanical ventilation and length of stay in the intensive care unit. Guidelines recommend use of sedation protocols that include sedation scores and trials of sedation cessation to minimize drug use. We evaluated processed electroencephalography (response and state entropy and bispectral index) as an adjunct to monitoring effects of commonly used sedative and analgesic drugs and intratracheal suctioning. METHODS: Electrodes for monitoring bispectral index and entropy were placed on the foreheads of 44 critically ill patients requiring mechanical ventilation and who previously had no brain dysfunction. Sedation was targeted individually using the Ramsay Sedation Scale, recorded every 2 hours or more frequently. Use of and indications for sedative and analgesic drugs and intratracheal suctioning were recorded manually and using a camera. At the end of the study, processed electroencephalographical and haemodynamic variables collected before and after each drug application and tracheal suctioning were analyzed. Ramsay score was used for comparison with processed electroencephalography when assessed within 15 minutes of an intervention. RESULTS: The indications for boli of sedative drugs exhibited statistically significant, albeit clinically irrelevant, differences in terms of their association with processed electroencephalographical parameters. Electroencephalographical variables decreased significantly after bolus, but a specific pattern in electroencephalographical variables before drug administration was not identified. The same was true for opiate administration. At both 30 minutes and 2 minutes before intratracheal suctioning, there was no difference in electroencephalographical or clinical signs in patients who had or had not received drugs 10 minutes before suctioning. Among patients who received drugs, electroencephalographical parameters returned to baseline more rapidly. In those cases in which Ramsay score was assessed before the event, processed electroencephalography exhibited high variation. CONCLUSIONS: Unpleasant or painful stimuli and sedative and analgesic drugs are associated with significant changes in processed electroencephalographical parameters. However, clinical indications for drug administration were not reflected by these electroencephalographical parameters, and barely by sedation level before drug administration or tracheal suction. This precludes incorporation of entropy and bispectral index as target variables for sedation and analgesia protocols in critically ill patients.

Auditory event-related potentials, bispectral index, and entropy for the discrimination of different levels of sedation in intensive care unit patients

BACKGROUND: Sedation protocols, including the use of sedation scales and regular sedation stops, help to reduce the length of mechanical ventilation and intensive care unit stay. Because clinical assessment of depth of sedation is labor-intensive, performed only intermittently, and interferes with sedation and sleep, processed electrophysiological signals from the brain have gained interest as surrogates. We hypothesized that auditory event-related potentials (ERPs), Bispectral Index (BIS), and Entropy can discriminate among clinically relevant sedation levels. METHODS: We studied 10 patients after elective thoracic or abdominal surgery with general anesthesia. Electroencephalogram, BIS, state entropy (SE), response entropy (RE), and ERPs were recorded immediately after surgery in the intensive care unit at Richmond Agitation-Sedation Scale (RASS) scores of -5 (very deep sedation), -4 (deep sedation), -3 to -1 (moderate sedation), and 0 (awake) during decreasing target-controlled sedation with propofol and remifentanil. Reference measurements for baseline levels were performed before or several days after the operation. RESULTS: At baseline, RASS -5, RASS -4, RASS -3 to -1, and RASS 0, BIS was 94 [4] (median, IQR), 47 [15], 68 [9], 75 [10], and 88 [6]; SE was 87 [3], 46 [10], 60 [22], 74 [21], and 87 [5]; and RE was 97 [4], 48 [9], 71 [25], 81 [18], and 96 [3], respectively (all P < 0.05, Friedman Test). Both BIS and Entropy had high variabilities. When ERP N100 amplitudes were considered alone, ERPs did not differ significantly among sedation levels. Nevertheless, discriminant ERP analysis including two parameters of principal component analysis revealed a prediction probability PK value of 0.89 for differentiating deep sedation, moderate sedation, and awake state. The corresponding PK for RE, SE, and BIS was 0.88, 0.89, and 0.85, respectively. CONCLUSIONS: Neither ERPs nor BIS or Entropy can replace clinical sedation assessment with standard scoring systems. Discrimination among very deep, deep to moderate, and no sedation after general anesthesia can be provided by ERPs and processed electroencephalograms, with similar P(K)s. The high inter- and intraindividual variability of Entropy and BIS precludes defining a target range of values to predict the sedation level in critically ill patients using these parameters. The variability of ERPs is unknown.