Essays on Bayesian Inference for Social Networks

This thesis presents Bayesian solutions to inference problems for three types of social network data structures: a single observation of a social network, repeated observations on the same social network, and repeated observations on a social network developing through time. A social network is conceived as being a structure consisting of actors and their social interaction with each other. A common conceptualisation of social networks is to let the actors be represented by nodes in a graph with edges between pairs of nodes that are relationally tied to each other according to some definition. Statistical analysis of social networks is to a large extent concerned with modelling of these relational ties, which lends itself to empirical evaluation. The first paper deals with a family of statistical models for social networks called exponential random graphs that takes various structural features of the network into account. In general, the likelihood functions of exponential random graphs are only known up to a constant of proportionality. A procedure for performing Bayesian inference using Markov chain Monte Carlo (MCMC) methods is presented. The algorithm consists of two basic steps, one in which an ordinary Metropolis-Hastings up-dating step is used, and another in which an importance sampling scheme is used to calculate the acceptance probability of the Metropolis-Hastings step. In paper number two a method for modelling reports given by actors (or other informants) on their social interaction with others is investigated in a Bayesian framework. The model contains two basic ingredients: the unknown network structure and functions that link this unknown network structure to the reports given by the actors. These functions take the form of probit link functions. An intrinsic problem is that the model is not identified, meaning that there are combinations of values on the unknown structure and the parameters in the probit link functions that are observationally equivalent. Instead of using restrictions for achieving identification, it is proposed that the different observationally equivalent combinations of parameters and unknown structure be investigated a posteriori. Estimation of parameters is carried out using Gibbs sampling with a switching devise that enables transitions between posterior modal regions. The main goal of the procedures is to provide tools for comparisons of different model specifications. Papers 3 and 4, propose Bayesian methods for longitudinal social networks. The premise of the models investigated is that overall change in social networks occurs as a consequence of sequences of incremental changes. Models for the evolution of social networks using continuos-time Markov chains are meant to capture these dynamics. Paper 3 presents an MCMC algorithm for exploring the posteriors of parameters for such Markov chains. More specifically, the unobserved evolution of the network in-between observations is explicitly modelled thereby avoiding the need to deal with explicit formulas for the transition probabilities. This enables likelihood based parameter inference in a wider class of network evolution models than has been available before. Paper 4 builds on the proposed inference procedure of Paper 3 and demonstrates how to perform model selection for a class of network evolution models.

On some Banach space constants arising in nonlinear fixed point and eigenvalue theory

[EN] As is well known, in any infinite-dimensional Banach space one may find fixed point free self-maps of the unit ball, retractions of the unit ball onto its boundary, contractions of the unit sphere, and nonzero maps without positive eigenvalues and normalized eigenvectors. In this paper, we give upper and lower estimates, or even explicit formulas, for the minimal Lipschitz constant and measure of noncompactness of such maps.

Constraint handling rules. Compositional semantics and program transformation

This thesis intends to investigate two aspects of Constraint Handling Rules (CHR). It proposes a compositional semantics and a technique for program transformation. CHR is a concurrent committed-choice constraint logic programming language consisting of guarded rules, which transform multi-sets of atomic formulas (constraints) into simpler ones until exhaustion [Frü06] and it belongs to the declarative languages family. It was initially designed for writing constraint solvers but it has recently also proven to be a general purpose language, being as it is Turing equivalent [SSD05a]. Compositionality is the first CHR aspect to be considered. A trace based compositional semantics for CHR was previously defined in [DGM05]. The reference operational semantics for such a compositional model was the original operational semantics for CHR which, due to the propagation rule, admits trivial non-termination. In this thesis we extend the work of [DGM05] by introducing a more refined trace based compositional semantics which also includes the history. The use of history is a well-known technique in CHR which permits us to trace the application of propagation rules and consequently it permits trivial non-termination avoidance [Abd97, DSGdlBH04]. Naturally, the reference operational semantics, of our new compositional one, uses history to avoid trivial non-termination too. Program transformation is the second CHR aspect to be considered, with particular regard to the unfolding technique. Said technique is an appealing approach which allows us to optimize a given program and in more detail to improve run-time efficiency or spaceconsumption. Essentially it consists of a sequence of syntactic program manipulations which preserve a kind of semantic equivalence called qualified answer [Frü98], between the original program and the transformed ones. The unfolding technique is one of the basic operations which is used by most program transformation systems. It consists in the replacement of a procedure-call by its definition. In CHR every conjunction of constraints can be considered as a procedure-call, every CHR rule can be considered as a procedure and the body of said rule represents the definition of the call. While there is a large body of literature on transformation and unfolding of sequential programs, very few papers have addressed this issue for concurrent languages. We define an unfolding rule, show its correctness and discuss some conditions in which it can be used to delete an unfolded rule while preserving the meaning of the original program. Finally, confluence and termination maintenance between the original and transformed programs are shown. This thesis is organized in the following manner. Chapter 1 gives some general notion about CHR. Section 1.1 outlines the history of programming languages with particular attention to CHR and related languages. Then, Section 1.2 introduces CHR using examples. Section 1.3 gives some preliminaries which will be used during the thesis. Subsequentely, Section 1.4 introduces the syntax and the operational and declarative semantics for the first CHR language proposed. Finally, the methodologies to solve the problem of trivial non-termination related to propagation rules are discussed in Section 1.5. Chapter 2 introduces a compositional semantics for CHR where the propagation rules are considered. In particular, Section 2.1 contains the definition of the semantics. Hence, Section 2.2 presents the compositionality results. Afterwards Section 2.3 expounds upon the correctness results. Chapter 3 presents a particular program transformation known as unfolding. This transformation needs a particular syntax called annotated which is introduced in Section 3.1 and its related modified operational semantics !0t is presented in Section 3.2. Subsequently, Section 3.3 defines the unfolding rule and prove its correctness. Then, in Section 3.4 the problems related to the replacement of a rule by its unfolded version are discussed and this in turn gives a correctness condition which holds for a specific class of rules. Section 3.5 proves that confluence and termination are preserved by the program modifications introduced. Finally, Chapter 4 concludes by discussing related works and directions for future work.

Application of different instrumental techniques to the selective evaluation of bio-sensible compounds in foodstuff of animal and vegetable origin

This PhD thesis describes the application of some instrumental analytical techniques suitable to the study of fundamental food products for the human diet, such as: extra virgin olive oil and dairy products. These products, widely spread in the market and with high nutritional values, are increasingly recognized healthy properties although their lipid fraction might contain some unfavorable components to the human health. The research activity has been structured in the following investigations: “Comparison of different techniques for trans fatty acids analysis” “Fatty acids analysis of outcrop milk cream samples, with particular emphasis on the content of Conjugated Linoleic Acid (CLA) and trans Fatty Acids (TFA), by using 100m high-polarity capillary column” “Evaluation of the oxidited fatty acids (OFA) content during the Parmigiano-Reggiano cheese seasoning” “Direct analysis of 4-desmethyl sterols and two dihydroxy triterpenes in saponified vegetal oils (olive oil and others) using liquid chromatography-mass spectrometry” “Quantitation of long chain poly-unsatured fatty acids (LC-PUFA) in base infant formulas by Gas Chromatography, and evaluation of the blending phases accuracy during their preparation” “Fatty acids composition of Parmigiano Reggiano cheese samples, with emphasis on trans isomers (TFA)”

Epos orale russo tra oralità e scrittura: problemi e proposte di traduzione

In the present thesis, I discuss the role of orality in translation, taking into account the problems arising while translating Russian folk epics. I investigate the meaning of orality in the context of folkloristic translation, trying to define a concept of oral poetry, and exploring its consequences for translation. In the first chapter, I try to identify the main differences between written literature and oral modes of expression, with special reference to folklore. Oral verbal art is performed, sung or recited, and based on a vital and dynamic interrelation between kinesics, sound, speech and gestures. According to Muhawi (2006), performance provides an interpretive frame enabling a correct interpretation of the message conveyed beyond the literal meaning. Transposing certain performance elements into print is one of the most controversial problems in folklore studies. However, formulas and formal stylistic devices may be rendered in transcription, building a bridge between oral and written elements. In the translation of oral poetry in transcription, this interconnection between orality and literacy might be emphasized, thus creating a hybrid dimension where oral and literary features coexist. In the second chapter, I introduce and describe the genre of Russian folk epics, transmitted orally, and transcribed between the 19th and 20th centuries, from a historical, linguistic and stylistic point of view. In the third and fourth chapters, I explore the issue of translation of Russian oral poetry. I first analyse existing Italian translations of Russian epics, and then present and discuss my own translation, based on a philological, scholarly approach. Thus, in my translation, which is followed by a rich commentary, I try to focus on the rendering of formulas as one of the most relevant aspects of Russian epics. At the same time, oral devices combine with literary features, thus creating a sort of frozen orality.

Numeralklassifikatoren im Thai

Wie viele andere Sprachen Ost- und Südostasiens ist das Thai eine numerusneutrale Sprache, in der ein Nomen lediglich das Konzept benennt und keinen Hinweis auf die Anzahl der Objekte liefert. Um Nomina im Thai zählen zu können, ist der Klassifikator (Klf) nötig, der die Objekte anhand ihrer semantischen Schlüsseleigenschaft herausgreift und individualisiert. Neben der Klassifikation stellt die Individualisierung die Hauptfunktion des Klf dar. Weitere Kernfunktionen des Klf außerhalb des Zählkontextes sind die Markierung der Definitheit, des Numerus sowie des Kontrasts. Die wichtigsten neuen Ergebnisse dieser Arbeit, die sowohl die Ebenen der Grammatik und Semantik als auch die der Logik und Pragmatik integriert, sind folgende: Im Thai kann der Klf sowohl auf der Element- als auch auf der Mengenebene agieren. In der Verbindung mit einem Demonstrativ kann der Klf auch eine pluralische Interpretation hervorrufen, wenn er auf eine als pluralisch präsupponierte Gesamtmenge referiert oder die Gesamtmenge in einer Teil-Ganzes-Relation individualisiert. In einem Ausdruck, der bereits eine explizite Zahlangabe enthält, bewirkt die Klf-Demonstrativ-Konstruktion eine Kontrastierung von Mengen mit gleichen Eigenschaften. Wie auch der Individualbegriff besitzt der Klf Intension und Extension. Intension und Extension von Thai-Klf verhalten sich umgekehrt proportional, d.h. je spezifischer der Inhalt eines Klf ist, desto kleiner ist sein Umfang. Der Klf signalisiert das Schlüsselmerkmal, das mit der Intension des Nomens der Identifizierung des Objekts dient. Der Klf individualisiert das Nomen, indem er Teilmengen quantifiziert. Er kann sich auf ein Objekt, eine bestimmte Anzahl von Objekten oder auf alle Objekte beziehen. Formal logisch lassen sich diese Funktionen mithilfe des Existenz- und des Allquantors darstellen. Auch die Nullstelle (NST) läßt sich formal logisch darstellen. Auf ihren jeweiligen Informationsgehalt reduziert, ergeben sich für Klf und NST abhängig von ihrer Positionierung verschiedene Informationswerte: Die Opposition von Klf und NST bewirkt in den Fragebögen ausschließlich skalare Q-Implikaturen, die sich durch die Informationsformeln in Form einer Horn-Skala darstellen lassen. In einem sich aufbauenden Kontext transportieren sowohl Klf als auch NST in der Kontextmitte bekannte Informationen, wodurch Implikaturen des M- bzw. I-Prinzips ausgelöst werden. Durch die Verbindung der Informationswerte mit den Implikaturen des Q-, M- und I-Prinzips lässt sich anhand der Positionierung direkt erkennen, wann der Klf die Funktion der Numerus-, der Definitheits- oder der Kontrast-Markierung erfüllt.

Toeplitz operators on finite and infinite dimensional spaces with associated psi *-Fréchet algebras

The present thesis is a contribution to the multi-variable theory of Bergman and Hardy Toeplitz operators on spaces of holomorphic functions over finite and infinite dimensional domains. In particular, we focus on certain spectral invariant Frechet operator algebras F closely related to the local symbol behavior of Toeplitz operators in F. We summarize results due to B. Gramsch et.al. on the construction of Psi_0- and Psi^*-algebras in operator algebras and corresponding scales of generalized Sobolev spaces using commutator methods, generalized Laplacians and strongly continuous group actions. In the case of the Segal-Bargmann space H^2(C^n,m) of Gaussian square integrable entire functions on C^n we determine a class of vector-fields Y(C^n) supported in complex cones K. Further, we require that for any finite subset V of Y(C^n) the Toeplitz projection P is a smooth element in the Psi_0-algebra constructed by commutator methods with respect to V. As a result we obtain Psi_0- and Psi^*-operator algebras F localized in cones K. It is an immediate consequence that F contains all Toeplitz operators T_f with a symbol f of certain regularity in an open neighborhood of K. There is a natural unitary group action on H^2(C^n,m) which is induced by weighted shifts and unitary groups on C^n. We examine the corresponding Psi^*-algebra A of smooth elements in Toeplitz-C^*-algebras. Among other results sufficient conditions on the symbol f for T_f to belong to A are given in terms of estimates on its Berezin-transform. Local aspects of the Szegö projection P_s on the Heisenbeg group and the corresponding Toeplitz operators T_f with symbol f are studied. In this connection we apply a result due to Nagel and Stein which states that for any strictly pseudo-convex domain U the projection P_s is a pseudodifferential operator of exotic type (1/2, 1/2). The second part of this thesis is devoted to the infinite dimensional theory of Bergman and Hardy spaces and the corresponding Toeplitz operators. We give a new proof of a result observed by Boland and Waelbroeck. Namely, that the space of all holomorphic functions H(U) on an open subset U of a DFN-space (dual Frechet nuclear space) is a FN-space (Frechet nuclear space) equipped with the compact open topology. Using the nuclearity of H(U) we obtain Cauchy-Weil-type integral formulas for closed subalgebras A in H_b(U), the space of all bounded holomorphic functions on U, where A separates points. Further, we prove the existence of Hardy spaces of holomorphic functions on U corresponding to the abstract Shilov boundary S_A of A and with respect to a suitable boundary measure on S_A. Finally, for a domain U in a DFN-space or a polish spaces we consider the symmetrizations m_s of measures m on U by suitable representations of a group G in the group of homeomorphisms on U. In particular,in the case where m leads to Bergman spaces of holomorphic functions on U, the group G is compact and the representation is continuous we show that m_s defines a Bergman space of holomorphic functions on U as well. This leads to unitary group representations of G on L^p- and Bergman spaces inducing operator algebras of smooth elements related to the symmetries of U.

Polarization in heavy quark decays

In this thesis I concentrate on the angular correlations in top quark decays and their next--to--leading order (NLO) QCD corrections. I also discuss the leading--order (LO) angular correlations in unpolarized and polarized hyperon decays. In the first part of the thesis I calculate the angular correlation between the top quark spin and the momentum of decay products in the rest frame decay of a polarized top quark into a charged Higgs boson and a bottom quark in Two-Higgs-Doublet-Models: $t(uparrow)rightarrow b+H^{+}$. The decay rate in this process is split into an angular independent part (unpolarized) and an angular dependent part (polar correlation). I provide closed form formulae for the ${mathcal O}(alpha_{s})$ radiative corrections to the unpolarized and the polar correlation functions for $m_{b}neq 0$ and $m_{b}=0$. The results for the unpolarized rate agree with the existing results in the literature. The results for the polarized correlations are new. I found that, for certain values of $tanbeta$, the ${mathcal O}(alpha_s)$ radiative corrections to the unpolarized, polarized rates, and the asymmetry parameter can become quite large. In the second part I concentrate on the semileptonic rest frame decay of a polarized top quark into a bottom quark and a lepton pair: $t(uparrow) to X_b + ell^+ + nu_ell$. I analyze the angular correlations between the top quark spin and the momenta of the decay products in two different helicity coordinate systems: system 1a with the $z$--axis along the charged lepton momentum, and system 3a with the $z$--axis along the neutrino momentum. The decay rate then splits into an angular independent part (unpolarized), a polar angle dependent part (polar correlation) and an azimuthal angle dependent part (azimuthal correlation). I present closed form expressions for the ${mathcal O}(alpha_{s})$ radiative corrections to the unpolarized part and the polar and azimuthal correlations in system 1a and 3a for $m_{b}neq 0$ and $m_{b}=0$. For the unpolarized part and the polar correlation I agree with existing results. My results for the azimuthal correlations are new. In system 1a I found that the azimuthal correlation vanishes in the leading order as a consequence of the $(V-A)$ nature of the Standard Model current. The ${mathcal O}(alpha_{s})$ radiative corrections to the azimuthal correlation in system 1a are very small (around 0.24% relative to the unpolarized LO rate). In system 3a the azimuthal correlation does not vanish at LO. The ${mathcal O}(alpha_{s})$ radiative corrections decreases the LO azimuthal asymmetry by around 1%. In the last part I turn to the angular distribution in semileptonic hyperon decays. Using the helicity method I derive complete formulas for the leading order joint angular decay distributions occurring in semileptonic hyperon decays including lepton mass and polarization effects. Compared to the traditional covariant calculation the helicity method allows one to organize the calculation of the angular decay distributions in a very compact and efficient way. This is demonstrated by the specific example of the polarized hyperon decay $Xi^0(uparrow) to Sigma^+ + l^- + bar{nu}_l$ ,($l^-=e^-, mu^-$) followed by the nonleptonic decay $Sigma^+ to p + pi^0$, which is described by a five--fold angular decay distribution.

Mass measurements on neutron-deficient nuclides at SHIPTRAP and commissioning of a cryogenic narrow-band FT-ICR mass spectrometer

The dissertation presented here deals with high-precision Penning trap mass spectrometry on short-lived radionuclides. Owed to the ability of revealing all nucleonic interactions, mass measurements far off the line of ß-stability are expected to bring new insight to the current knowledge of nuclear properties and serve to test the predictive power of mass models and formulas. In nuclear astrophysics, atomic masses are fundamental parameters for the understanding of the synthesis of nuclei in the stellar environments. This thesis presents ten mass values of radionuclides around A = 90 interspersed in the predicted rp-process pathway. Six of them have been experimentally determined for the first time. The measurements have been carried out at the Penning-trap mass spectrometer SHIPTRAP using the destructive time-of-fligh ion-cyclotron-resonance (TOF-ICR) detection technique. Given the limited performance of the TOF-ICR detection when trying to investigate heavy/superheavy species with small production cross sections (σ< 1 μb), a new detection system is found to be necessary. Thus, the second part of this thesis deals with the commissioning of a cryogenic double-Penning trap system for the application of a highly-sensitive, narrow-band Fourier-transform ion-cyclotron-resonance (FT-ICR) detection technique. With the non-destructive FT-ICR detection method a single singly-charged trapped ion will provide the required information to determine its mass. First off-line tests of a new detector system based on a channeltron with an attached conversion dynode, of a cryogenic pumping barrier, to guarantee ultra-high vacuum conditions during mass determination, and of the detection electronics for the required single-ion sensitivity are reported.

Nondestructive evaluation of concrete compression strength by means of Artificial Neural Network (ANN)

The evaluation of structural performance of existing concrete buildings, built according to standards and materials quite different to those available today, requires procedures and methods able to cover lack of data about mechanical material properties and reinforcement detailing. To this end detailed inspections and test on materials are required. As a consequence tests on drilled cores are required; on the other end, it is stated that non-destructive testing (NDT) cannot be used as the only mean to get structural information, but can be used in conjunction with destructive testing (DT) by a representative correlation between DT and NDT. The aim of this study is to verify the accuracy of some formulas of correlation available in literature between measured parameters, i.e. rebound index, ultrasonic pulse velocity and compressive strength (SonReb Method). To this end a relevant number of DT and NDT tests has been performed on many school buildings located in Cesena (Italy). The above relationships have been assessed on site correlating NDT results to strength of core drilled in adjacent locations. Nevertheless, concrete compressive strength assessed by means of NDT methods and evaluated with correlation formulas has the advantage of being able to be implemented and used for future applications in a much more simple way than other methods, even if its accuracy is strictly limited to the analysis of concretes having the same characteristics as those used for their calibration. This limitation warranted a search for a different evaluation method for the non-destructive parameters obtained on site. To this aim, the methodology of neural identification of compressive strength is presented. Artificial Neural Network (ANN) suitable for the specific analysis were chosen taking into account the development presented in the literature in this field. The networks were trained and tested in order to detect a more reliable strength identification methodology.

Edizione commentata della Cronaca di Venezia di Giovanni Tiepolo (XVI-XVII sec.)

Il seguente studio propone l'esame di una cronaca veneziana del XVI secolo, inedita, dalle origini al 1538/39, che parte della tradizione manoscritta attribuisce al Patriarca di Venezia Giovanni Tiepolo (1619-1631), parte ad Agostino degli Agostini, (1530-1574), un patrizio veneziano il cui nome è legato essenzialmente ad una cronaca dal 421 al 1570. Indipendentemente da chi sia il primitivo autore, la cronaca, di discreto pregio per la storia interna e il funzionamento delle istituzioni veneziane, presenta elementi di spiccata originalità dal punto di vista compositivo e formale che la pongono in una prospettiva storiografica alternativa al dualismo tra la storiografia ufficiale promossa per pubblico decreto e l'iniziativa privata dei diaria del XV-XVI. La cronaca veneziana, abbandonata per formule più sofisticate e innovative di diffusione dell'informazione pubblica, sopravvive, formalmente immutata nella sua arcaicità, rinnovandosi nella tendenza a creare compendi ricchi di documenti e di elenchi, destinati ad aiutare la nobiltà ad orientarsi nel mondo socio-politico contemporaneo. Si consuma così il divorzio fra l'informazione tecnico-politica utile al patriziato nello svolgimento del suo lavoro e la storiografia pubblica che, di fronte alle varie esigenze e ai diversi generi letterari, sceglie ideologicamente di abbracciare il genere delle laus civitatis e della storiografia laudativa ed encomiastica. In questo contesto si inserisce la Cronaca esemplata dal Patriarca Giovanni Tiepolo, chiaro esempio di un tentativo di razionalizzazione dell'informazione in cui le notizie e gli elementi non ritenuti immediatamente utili come le lunghe liste dei 41 elettori, le promissioni ducali, nonchè singoli episodi ed eventi trattati, trovano una collocazione esterna alla cronaca, in quello che Reines definisce l'ormai nascente archivio politico del XVI secolo.

Analisi e ottimizzazione del servizio di raccolta e trasporto dei rifiuti anche in relazione alle tematiche ambientali: un'applicazione alla rete urbana di Bologna

Questo studio, che è stato realizzato in collaborazione con Hera, è un'analisi della gestione dei rifiuti a Bologna. La ricerca è stata effettuata su diversi livelli: un livello strategico il cui scopo è quello di identificare nuovi metodi per la raccolta dei rifiuti in funzione delle caratteristiche del territorio della città, un livello analitico che riguarda il miglioramento delle applicazioni informatiche di supporto, e livello ambientale che riguarda il calcolo delle emissioni in atmosfera di veicoli adibiti alla raccolta e al trasporto dei rifiuti. innanzitutto è stato necessario studiare Bologna e lo stato attuale dei servizi di raccolta dei rifiuti. È incrociando questi componenti che in questi ultimi tre anni sono state effettuate modifiche nel settore della gestione dei rifiuti. I capitoli seguenti sono inerenti le applicazioni informatiche a sostegno di tali attività: Siget e Optit. Siget è il programma di gestione del servizio, che attualmente viene utilizzato per tutte le attività connesse alla raccolta di rifiuti. È un programma costituito da moduli diversi, ma di sola la gestione dati. la sperimentazione con Optit ha aggiunto alla gestione dei dati la possibilità di avere tali dati in cartografia e di associare un algoritmo di routing. I dati archiviati in Siget hanno rappresentato il punto di partenza, l'input, e il raggiungimento di tutti punti raccolta l'obiettivo finale. L'ultimo capitolo è relativo allo studio dell'impatto ambientale di questi percorsi di raccolta dei rifiuti. Tale analisi, basata sulla valutazione empirica e sull'implementazione in Excel delle formule del Corinair mostra la fotografia del servizio nel 2010. Su questo aspetto Optit ha fornito il suo valore aggiunto, implementando nell'algoritmo anche le formule per il calcolo delle emissioni.

Frobenius polynomials for Calabi-Yau equations

Sei $\pi:X\rightarrow S$ eine \&quot;uber $\Z$ definierte Familie von Calabi-Yau Varietaten der Dimension drei. Es existiere ein unter dem Gauss-Manin Zusammenhang invarianter Untermodul $M\subset H^3_{DR}(X/S)$ von Rang vier, sodass der Picard-Fuchs Operator $P$ auf $M$ ein sogenannter {\em Calabi-Yau } Operator von Ordnung vier ist. Sei $k$ ein endlicher K\&quot;orper der Charaktetristik $p$, und sei $\pi_0:X_0\rightarrow S_0$ die Reduktion von $\pi$ \uber $k$. F\ur die gew\ohnlichen (ordinary) Fasern $X_{t_0}$ der Familie leiten wir eine explizite Formel zur Berechnung des charakteristischen Polynoms des Frobeniusendomorphismus, des {\em Frobeniuspolynoms}, auf dem korrespondierenden Untermodul $M_{cris}\subset H^3_{cris}(X_{t_0})$ her. Sei nun $f_0(z)$ die Potenzreihenl\osung der Differentialgleichung $Pf=0$ in einer Umgebung der Null. Da eine reziproke Nullstelle des Frobeniuspolynoms in einem Teichm\uller-Punkt $t$ durch $f_0(z)/f_0(z^p)|_{z=t}$ gegeben ist, ist ein entscheidender Schritt in der Berechnung des Frobeniuspolynoms die Konstruktion einer $p-$adischen analytischen Fortsetzung des Quotienten $f_0(z)/f_0(z^p)$ auf den Rand des $p-$adischen Einheitskreises. Kann man die Koeffizienten von $f_0$ mithilfe der konstanten Terme in den Potenzen eines Laurent-Polynoms, dessen Newton-Polyeder den Ursprung als einzigen inneren Gitterpunkt enth\alt, ausdr\ucken,so beweisen wir gewisse Kongruenz-Eigenschaften unter den Koeffizienten von $f_0$. Diese sind entscheidend bei der Konstruktion der analytischen Fortsetzung. Enth\alt die Faser $X_{t_0}$ einen gew\ohnlichen Doppelpunkt, so erwarten wir im Grenz\ubergang, dass das Frobeniuspolynom in zwei Faktoren von Grad eins und einen Faktor von Grad zwei zerf\allt. Der Faktor von Grad zwei ist dabei durch einen Koeffizienten $a_p$ eindeutig bestimmt. Durchl\auft nun $p$ die Menge aller Primzahlen, so erwarten wir aufgrund des Modularit\atssatzes, dass es eine Modulform von Gewicht vier gibt, deren Koeffizienten durch die Koeffizienten $a_p$ gegeben sind. Diese Erwartung hat sich durch unsere umfangreichen Rechnungen best\atigt. Dar\uberhinaus leiten wir weitere Formeln zur Bestimmung des Frobeniuspolynoms her, in welchen auch die nicht-holomorphen L\osungen der Gleichung $Pf=0$ in einer Umgebung der Null eine Rolle spielen.

Forward implied volatility expansions in LSV models

In this work we address the problem of finding formulas for efficient and reliable analytical approximation for the calculation of forward implied volatility in LSV models, a problem which is reduced to the calculation of option prices as an expansion of the price of the same financial asset in a Black-Scholes dynamic. Our approach involves an expansion of the differential operator, whose solution represents the price in local stochastic volatility dynamics. Further calculations then allow to obtain an expansion of the implied volatility without the aid of any special function or expensive from the computational point of view, in order to obtain explicit formulas fast to calculate but also as accurate as possible.

L(ocus) d(atos) d(ecreto) d(ecurionum): La concessione di spazi pubblici nelle comunita' cittadine dell'italia romana

La tesi riguarda la concessione di spazi di proprietà pubblica a privati, intesi come singole persone o enti, quali ad esempio i collegi, da parte delle autorità cittadine. Le fonti a disposizione per indagare tale pratica burocratica sono quasi totalmente di natura epigrafica, per lo più attestanti l’espressione locus datus decreto decurionum, variamente abbreviata, o formule similari. Questo aspetto della vita civica è stata cursoriamente oggetto di studio in diversi contributi, ma si tratta di articoli che circoscrivono il tema, analizzandolo in relazione a ristrette aree geografiche, oppure considerandone determinati aspetti (ad esempio l’ambito sacro o quello funerario). Si è perciò ritenuto utile proseguire questa linea di ricerca affrontando uno studio di più ampio raggio, che comprenda la documentazione epigrafica dell’intero territorio italico (costituito dalle undici regioni augustee ad esclusione di Roma), per tutte le tipologie testuali (iscrizioni sacre, funerarie, onorarie, su opera pubblica, exempla decreti), allo scopo di formulare osservazioni più precise e puntuali sulla procedura burocratica in esame, pur con tutti i limiti noti a chi affronti questo genere di indagine. Tra le conclusioni raggiunte, è emerso come durante il I-II sec. d.C. vi fosse la tendenza a concedere, sporadicamente, dei loca sepulturae extraurbani a membri delle famiglie delle élites cittadine, anche donne e fanciulli, mentre il foro e le altre aree pubbliche interne alla città erano soprattutto utilizzate direttamente dai decurioni per l’elevazione di dediche e statue. Nel corso del II sec. d.C., con massima diffusione nell’età antonina e poi in quella severiana, prese invece piede l’uso privato a scopo onorario degli spazi pubblici siti all’interno delle città, ovvero in aree prima pressoché precluse all’intervento di singoli cittadini: familiari e liberti, collegi e altri organismi commissionavano statue dedicate prevalentemente agli amministratori locali, magistrati cittadini spesso divenuti anche cavalieri.