Zeta and L-functions of elliptic curves

In questa tesi si studiano alcune proprietà fondamentali delle funzioni Zeta e L associate ad una curva ellittica. In particolare, si dimostra la razionalità della funzione Zeta e l'ipotesi di Riemann per due famiglie specifiche di curve ellittiche. Si studia poi il problema dell'esistenza di un prolungamento analitico al piano complesso della funzione L di una curva ellittica con moltiplicazione complessa, attraverso l'analisi diretta di due casi particolari.

The velocity dispersion profile of the globular cluster 47Tucanae

Gli ammassi globulari rappresentano i laboratori ideali nei quali studiare la dinamica di sistemi ad N-corpi ed i suoi effetti sull’evoluzione stellare. Infatti, gli ammassi globulari sono gli unici sistemi astrofisici che, entro il tempo scala dell’età dell’Universo, sperimentano quasi tutti i processi di dinamica stellare noti. Questo lavoro di tesi si inserisce in un progetto a lungo termine volto a fornire una dettagliata caratterizzazione delle proprietà dinamiche degli ammassi globulari galattici. In questa ricerca, strumenti di fondamentale importanza sono il profilo di dispersione di velocità del sistema e la sua curva di rotazione. Per determinare le componenti radiali di questi profili cinematici in ammassi globulari galattici è necessario misurare la velocità lungo la linea di vista di un ampio campione di stelle membre, a differenti distanze dal centro. Seguendo un approccio multi-strumentale, è possibile campionare l’intera estensione radiale dell’ammasso utilizzando spettrografi multi-oggetto ad alta risoluzione spettrale nelle regioni intermedie/esterne, e spettrografi IFU con ottiche adattive per le regioni centrali (pochi secondi d’arco dal centro). Questo lavoro di tesi è volto a determinare il profilo di dispersione di velocità dell’ammasso globulare 47 Tucanae, campionando un’estensione radiale compresa tra circa 20'' e 13' dal centro. Per questo scopo sono state misurate le velocità radiali di circa un migliaio di stelle nella direzione di 47 Tucanae, utilizzando spettri ad alta risoluzione ottenuti con lo spettrografo multi-oggetto FLAMES montato al Very Large Telescope dell’ESO. Le velocità radiali sono state misurate utilizzando la tecnica di cross-correlazione tra gli spettri osservati e appropriati spettri teorici, e sono state ottenute accuratezze inferiori a 0.5km/s. Il campione così ottenuto (complementare a quello raccolto con strumenti IFU nelle regioni centrali) è fondamentale per costruire il profilo di dispersione di velocità dell’ammasso e la sua eventuale curva di rotazione. Questi dati, combinati col profilo di densità dell’ammasso precedentemente determinato, permetteranno di vincolare opportunamente modelli teorici come quelli di King (1966) o di Wilson (1975), e di arrivare così alla prima solida determinazione dei parametri strutturali e dinamici (raggi di core e di metà massa, tempo di rilassamento, parametro collisionale, etc.) e della massa totale e distribuzione di massa del sistema.

Relating the physicochemical characteristics and dispersion of multiwalled carbon nanotubes in different suspension media to their oxidative reactivity in vitro and inflammation in vivo

Reactive oxygen species (ROS) production is important in the toxicity of pathogenic particles such as fibres. We examined the oxidative potential of straight (50 microm and 10 microm) and tangled carbon nanotubes in a cell free assay, in vitro and in vivo using different dispersants. The cell free oxidative potential of tangled nanotubes was higher than for the straight fibres. In cultured macrophages tangled tubes exhibited significantly more ROS at 30 min, while straight tubes increased ROS at 4 h. ROS was significantly higher in bronchoalveolar lavage cells of animals instilled with tangled and 10 mum straight fibres, whereas the number of neutrophils increased only in animals treated with the long tubes. Addition of dispersants in the suspension media lead to enhanced ROS detection by entangled tubes in the cell-free system. Tangled fibres generated more ROS in a cell-free system and in cultured cells, while straight fibres generated a slower but more prolonged effect in animals.

Different Learning Curves for Axillary Brachial Plexus Block: Ultrasound Guidance versus Nerve Stimulation

Little is known about the learning of the skills needed to perform ultrasound- or nerve stimulator-guided peripheral nerve blocks. The aim of this study was to compare the learning curves of residents trained in ultrasound guidance versus residents trained in nerve stimulation for axillary brachial plexus block. Ten residents with no previous experience with using ultrasound received ultrasound training and another ten residents with no previous experience with using nerve stimulation received nerve stimulation training. The novices' learning curves were generated by retrospective data analysis out of our electronic anaesthesia database. Individual success rates were pooled, and the institutional learning curve was calculated using a bootstrapping technique in combination with a Monte Carlo simulation procedure. The skills required to perform successful ultrasound-guided axillary brachial plexus block can be learnt faster and lead to a higher final success rate compared to nerve stimulator-guided axillary brachial plexus block.

Efficient fabrication of polymer nanocomposites with effective exfoliation and dispersion by solid-state/melt extrusion

In this communication, solid-state/melt extrusion (SSME) is introduced as a novel technique that combines solid-state shear pulverization (SSSP) and conventional twin screw extrusion (TSE) in a single extrusion system. The morphology and property enhancements in a model linear low-density polyethylene/organically modified clay nanocomposite sample fabricated via SSME were compared to those fabricated via SSSP and TSE. The results show that SSME is capable of exfoliating and dispersing the nanofillers similarly to SSSP, while achieving a desirable output rate and producing extrudate similar in form to that from TSE.

Closed Time-like Curves and Inertial Frame Dragging: How to Time Travel via Spacetime Rotation

As the number of solutions to the Einstein equations with realistic matter sources that admit closed time-like curves (CTC's) has grown drastically, it has provoked some authors [10] to call for a physical interpretation of these seemingly exotic curves that could possibly allow for causality violations. A first step in drafting a physical interpretation would be to understand how CTC's are created because the recent work of [16] has suggested that, to follow a CTC, observers must counter-rotate with the rotating matter, contrary to the currently accepted explanation that it is due to inertial frame dragging that CTC's are created. The exact link between inertialframe dragging and CTC's is investigated by simulating particle geodesics and the precession of gyroscopes along CTC's and backward in time oriented circular orbits in the van Stockum metric, known to have CTC's that could be traversal, so the van Stockum cylinder could be exploited as a time machine. This study of gyroscopeprecession, in the van Stockum metric, supports the theory that CTC's are produced by inertial frame dragging due to rotating spacetime metrics.

Short anterior correction of the thoracolumbar/lumbar curve in King 1 idiopathic scoliosis: the behaviour of the instrumented and non-instrumented curves and the trunk balance

This is a retrospective clinical, radiological and patient outcome assessment of 21 consecutive patients with King 1 idiopathic adolescent scoliosis treated by short anterior selective fusion of the major thoracolumbar/lumbar (TL/L) curve. Three-dimensional changes of both curves, changes in trunk balance and rib hump were evaluated. The minimal follow-up was 24 months (max. 83). The Cobb angle of the TL/L curve was 52 degrees (45-67 degrees) with a flexibility of 72% (40-100%). The average length of the main curve was 5 (3-8) segments. An average of 3 (2-4) segments was fused using rigid single rod implants with side-loading screws. The Cobb angle of the thoracic curve was 33 degrees (18-50 degrees) with a flexibility of 69% (29-100%). The thoracic curve in bending was less than 20 degrees in 17 patients, and 20-25 degrees in 4 patients. In the TL/L curve there was an improvement of the Cobb angle of 67%, of the apex vertebral rotation of 51% and of the apex vertebral translation of 74%. The Cobb angle of the thoracic curve improved 29% spontaneously. Shoulder balance improved significantly from an average preoperative imbalance of 14.5-3.1 mm at the last follow-up. Seventy-five percent of the patients with preoperative positive shoulder imbalance (higher on the side of the thoracic curve) had levelled shoulders at the last follow-up. C7 offset improved from a preoperative 19.8 (0-40) to 4.8 (0-18) mm at the last follow-up. There were no significant changes in rotation, translation of the thoracic curve and the clinical rib hump. There were no significant changes in thoracic kyphosis or lumbar lordosis. The average score of the SRS-24 questionnaire at the last follow-up was 91 points (max. 120). We conclude that short anterior selective fusion of the TL/L curve in King 1 scoliosis with a thoracic curve bending to 25 degrees or less (Type 5 according to Lenke classification) results in a satisfactory correction and a balanced spine. Short fusions leave enough mobile lumbar segments for the establishment of global spinal balance. A positive shoulder imbalance is not a contraindication for this procedure. Structural interbody grafts are not necessary to maintain lumbar lordosis.

A CASE STUDY IN PHARMACOLOGIC IMAGING USING PRINCIPAL CURVES IN SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY

In this manuscript we are concerned with functional imaging of the colon to assess the kinetics of a microbicide lubricant. The overarching goal is to understand the distribution of the lubricant in the colon. Such information is crucial for understanding the potential impact of the microbicide on HIV viral transmission. The experiment was conducted by imaging a radiolabeled lubricant distributed in the subject’s colon. The tracer imaging was conducted via single photon emission computed tomography (SPECT), a non-invasive, in-vivo functional imaging technique. We develop a novel principal curve algorithm to construct a three dimensional curve through the colon images. The developed algorithm is tested and debugged on several difficult two dimensional images of familiar curves where the original principal curve algorithm does not apply. The final curve fit to the colon data is compared with experimental sigmoidoscope collection.

Confidence Bands for Convex Median Curves using Sign-Tests

Suppose that one observes pairs (x1,Y1), (x2,Y2), ..., (xn,Yn), where x1 < x2 < ... < xn are fixed numbers while Y1, Y2, ..., Yn are independent random variables with unknown distributions. The only assumption is that Median(Yi) = f(xi) for some unknown convex or concave function f. We present a confidence band for this regression function f using suitable multiscale sign tests. While the exact computation of this band seems to require O(n4) steps, good approximations can be obtained in O(n2) steps. In addition the confidence band is shown to have desirable asymptotic properties as the sample size n tends to infinity.