Topics in geometry, analysis and inverse problems

The thesis consists of three independent parts. Part I: Polynomial amoebas We study the amoeba of a polynomial, as de ned by Gelfand, Kapranov and Zelevinsky. A central role in the treatment is played by a certain convex function which is linear in each complement component of the amoeba, which we call the Ronkin function. This function is used in two di erent ways. First, we use it to construct a polyhedral complex, which we call a spine, approximating the amoeba. Second, the Monge-Ampere measure of the Ronkin function has interesting properties which we explore. This measure can be used to derive an upper bound on the area of an amoeba in two dimensions. We also obtain results on the number of complement components of an amoeba, and consider possible extensions of the theory to varieties of codimension higher than 1. Part II: Differential equations in the complex plane We consider polynomials in one complex variable arising as eigenfunctions of certain differential operators, and obtain results on the distribution of their zeros. We show that in the limit when the degree of the polynomial approaches innity, its zeros are distributed according to a certain probability measure. This measure has its support on the union of nitely many curve segments, and can be characterized by a simple condition on its Cauchy transform. Part III: Radon transforms and tomography This part is concerned with different weighted Radon transforms in two dimensions, in particular the problem of inverting such transforms. We obtain stability results of this inverse problem for rather general classes of weights, including weights of attenuation type with data acquisition limited to a 180 degrees range of angles. We also derive an inversion formula for the exponential Radon transform, with the same restriction on the angle.

Topics in financial econometrics

In the first chapter, we consider the joint estimation of objective and risk-neutral parameters for SV option pricing models. We propose a strategy which exploits the information contained in large heterogeneous panels of options, and we apply it to S&P 500 index and index call options data. Our approach breaks the stochastic singularity between contemporaneous option prices by assuming that every observation is affected by measurement error. We evaluate the likelihood function by using a MC-IS strategy combined with a Particle Filter algorithm. The second chapter examines the impact of different categories of traders on market transactions. We estimate a model which takes into account traders’ identities at the transaction level, and we find that the stock prices follow the direction of institutional trading. These results are carried out with data from an anonymous market. To explain our estimates, we examine the informativeness of a wide set of market variables and we find that most of them are unambiguously significant to infer the identity of traders. The third chapter investigates the relationship between the categories of market traders and three definitions of financial durations. We consider trade, price and volume durations, and we adopt a Log-ACD model where we include information on traders at the transaction level. As to trade durations, we observe an increase of the trading frequency when informed traders and the liquidity provider intensify their presence in the market. For price and volume durations, we find the same effect to depend on the state of the market activity. The fourth chapter proposes a strategy to express order aggressiveness in quantitative terms. We consider a simultaneous equation model to examine price and volume aggressiveness at Euronext Paris, and we analyse the impact of a wide set of order book variables on the price-quantity decision.

Topics in Local Economic Development

This thesis contributes to the current debate in literature about local economic development by considering two different topics: quality of institutions, and the role of clusters in innovation and productivity growth. The research is built upon three papers. The first paper deals with the analysis of the effect of administrative continuity on administrative efficiency. The analysis underlines the importance of different typologies of social capital. Findings reveal a positive impact on administrative efficiency (AE) by administrative continuity (AC) when it is coupled by bridging and linking social capital. On the contrary, bonding social capital influences negatively the effect by AC on AE. The second paper investigates the spatial interaction in levels of quality of government (QoG) among European regions. Notwithstanding the largely recognised role by institutions in the design of regional policies, no study has been conducted about the mechanisms of interaction and diffusion of QoG at regional level. This research wants to overcome this knowledge gap in literature. Findings reveal a heterogeneity in spatial interaction among groups of regions, i.e. ‘leader regions’ (Northern regions) and ‘lagging regions’ (Southern regions), when considering different mechanisms of interaction (learning / imitating competition and pure competition). Moreover, the effect of wealth on the levels of QoG is nonlinear. Finally, the third paper analyses the relation among specialization and productivity within the agricultural sector. In literature, the study of clusters dynamics has long neglected agriculture. The analysis describes the changes in sectorial specialization for eight main crop groups in Italian regions (NUTS 3), assessing the existence of spatial autocorrelations by using an exploratory data analysis. Furthermore, the effect of specialization on productivity is analysed within the main crop groups using a spatial panel data model. Findings reveal a marked tendency to specialization in the Italian agriculture, and a heterogeneous effect by specialization on productivity.

State of the science on controversial topics: missing maxillary lateral incisors - a report of the Angle Society of Europe 2012 meeting

BACKGROUND The optimal long-term management of the congenitally missing maxillary lateral incisor continues to cause controversy within the specialty. The Angle Society of Europe meeting 2012 dedicated a day to address some of the current controversies relating to the management of these missing lateral incisors. FINDINGS The format of the day consisted of morning presentations and afternoon breakout sessions to discuss a variety of questions related to the management of missing lateral incisors. CONCLUSIONS The consensus viewpoint from this day was that the care of patients with congenitally missing lateral incisors is best achieved through a multi-disciplinary approach. The current evidence base is weak, and further well-designed, prospective trials are needed.

State of the science on controversial topics: orthodontic therapy and gingival recession (a report of the Angle Society of Europe 2013 meeting)

BACKGROUND Controversy exists in the literature between the role of orthodontic treatment and gingival recession. Whilst movement of teeth outside the alveolar bone has been reported as a risk factor for gingival recession, others have found no such association. FINDINGS The Angle Society of Europe devoted a study day to explore the evidence surrounding these controversies. The aim of the day was for a panel of experts to evaluate the current evidence base in relation to either the beneficial or detrimental effects of orthodontic treatment on the gingival tissue. CONCLUSIONS There remains a relatively weak evidence base for the role of orthodontic treatment and gingival recession and thus a need to undertake a risk assessment and appropriate consent prior to the commencement of treatment. In further prospective, well designed trials are needed.

Identifying Topics in Social Media Posts using DBpedia

This paper describes a method for identifying topics in text published in social media, by applying topic recognition techniques that exploit DBpedia. We evaluate such method for social media in Spanish and we provide the results of the evaluation performed.