Analyzing the dependence structure of microarray data: a copula–based approach

The main aim of this Ph.D. dissertation is the study of clustering dependent data by means of copula functions with particular emphasis on microarray data. Copula functions are a popular multivariate modeling tool in each field where the multivariate dependence is of great interest and their use in clustering has not been still investigated. The first part of this work contains the review of the literature of clustering methods, copula functions and microarray experiments. The attention focuses on the K–means (Hartigan, 1975; Hartigan and Wong, 1979), the hierarchical (Everitt, 1974) and the model–based (Fraley and Raftery, 1998, 1999, 2000, 2007) clustering techniques because their performance is compared. Then, the probabilistic interpretation of the Sklar’s theorem (Sklar’s, 1959), the estimation methods for copulas like the Inference for Margins (Joe and Xu, 1996) and the Archimedean and Elliptical copula families are presented. In the end, applications of clustering methods and copulas to the genetic and microarray experiments are highlighted. The second part contains the original contribution proposed. A simulation study is performed in order to evaluate the performance of the K–means and the hierarchical bottom–up clustering methods in identifying clusters according to the dependence structure of the data generating process. Different simulations are performed by varying different conditions (e.g., the kind of margins (distinct, overlapping and nested) and the value of the dependence parameter ) and the results are evaluated by means of different measures of performance. In light of the simulation results and of the limits of the two investigated clustering methods, a new clustering algorithm based on copula functions (‘CoClust’ in brief) is proposed. The basic idea, the iterative procedure of the CoClust and the description of the written R functions with their output are given. The CoClust algorithm is tested on simulated data (by varying the number of clusters, the copula models, the dependence parameter value and the degree of overlap of margins) and is compared with the performance of model–based clustering by using different measures of performance, like the percentage of well–identified number of clusters and the not rejection percentage of H0 on . It is shown that the CoClust algorithm allows to overcome all observed limits of the other investigated clustering techniques and is able to identify clusters according to the dependence structure of the data independently of the degree of overlap of margins and the strength of the dependence. The CoClust uses a criterion based on the maximized log–likelihood function of the copula and can virtually account for any possible dependence relationship between observations. Many peculiar characteristics are shown for the CoClust, e.g. its capability of identifying the true number of clusters and the fact that it does not require a starting classification. Finally, the CoClust algorithm is applied to the real microarray data of Hedenfalk et al. (2001) both to the gene expressions observed in three different cancer samples and to the columns (tumor samples) of the whole data matrix.

The physical city and the urban structure: detecting amenity zones and applying urban morphology to New York

The city is a collection of built structures and infrastructure embedded in socio-cultural processes: any investigation into a city’s transformations involves considerations on the degree to which its composite elements respond to socio-economical changes. The main purpose of this research is to investigate how transformations in the functional requirements of New York’s society have spurred, since the 1970s, changes in both the city’s urban structure and physical form. The present work examines the rise of Amenity Zones in New York, and investigates the transformations that have occurred in New York’s built environment since the 1970s. By applying qualitative measures and analyzing the relationship between urban amenities and the creative class, the present work has investigated changes in the urban structure and detected a hierarchical series of amenity zones classes, namely, Super Amenity Zones (SAZs), Nodal Amenity Zones (NAZs) and Peripheral Amenity Zones (PAZs). This series allows for a more comprehensive reading of the urban structure in a complex city like New York, bringing advancements to the amenity zone’s methodology. In order to examine the manner in which the other component of the city, the physical form, has changed or adapted to the new socio-economic condition, the present research has applied Conzenian analysis to a select study area, Atlantic Avenue. The results of this analysis reveal that, contrary to the urban structure, which changes rapidly, the physical form of New York is hard to modify completely, due to the resilience of the town plan and its elements, and to preservation laws; the city rather adapts to socio-economical changes through process of adaptive reuses or conversion. Concluding, this research has examined the dialectic between the ever-changing needs of society and the complexity of the built environment and urban structure, showing the different degrees to which the urban landscape modifies, reacts and sometimes adapts to the population’s functional requirements.

A journey through the capital structure of the banking sector: Empirical evidence for Europe from 2008 to 2012

Systemic risk is the protagonist of the recent financial crisis. This thesis proposes a definition and a propagation mechanism for systemic risk. Risk management has a direct linkage with capital management, when addressing the question that the risk handled by a financial institution is compatible with the amount of equity available. This thesis proposes a risk management of liquid market variables, which compose the assets of a bank, based on the statistical tool of PCA. The principal component analysis will define the PCR, or Principal Components of Risk. Such definition of Risk will be adopted to test if the risk represented by PCR is explanatory of the movements of equity and/or debt for the banks included in the in the index Itraxx financial senior: the results of these regressions will be compared with a formal Capital Adequacy test in order to assess the financial soundness of the main financial European institutions.

Neural network modelling of the wave-structure interaction processes

This thesis presents a new Artificial Neural Network (ANN) able to predict at once the main parameters representative of the wave-structure interaction processes, i.e. the wave overtopping discharge, the wave transmission coefficient and the wave reflection coefficient. The new ANN has been specifically developed in order to provide managers and scientists with a tool that can be efficiently used for design purposes. The development of this ANN started with the preparation of a new extended and homogeneous database that collects all the available tests reporting at least one of the three parameters, for a total amount of 16’165 data. The variety of structure types and wave attack conditions in the database includes smooth, rock and armour unit slopes, berm breakwaters, vertical walls, low crested structures, oblique wave attacks. Some of the existing ANNs were compared and improved, leading to the selection of a final ANN, whose architecture was optimized through an in-depth sensitivity analysis to the training parameters of the ANN. Each of the selected 15 input parameters represents a physical aspect of the wave-structure interaction process, describing the wave attack (wave steepness and obliquity, breaking and shoaling factors), the structure geometry (submergence, straight or non-straight slope, with or without berm or toe, presence or not of a crown wall), or the structure type (smooth or covered by an armour layer, with permeable or impermeable core). The advanced ANN here proposed provides accurate predictions for all the three parameters, and demonstrates to overcome the limits imposed by the traditional formulae and approach adopted so far by some of the existing ANNs. The possibility to adopt just one model to obtain a handy and accurate evaluation of the overall performance of a coastal or harbor structure represents the most important and exportable result of the work.

Assessment of the population structure and temporal changes in spatial dynamics and genetic characteristics of the Atlantic bluefin tuna under a fishery independent framework.

As a large and long-lived species with high economic value, restricted spawning areas and short spawning periods, the Atlantic bluefin tuna (BFT; Thunnus thynnus) is particularly susceptible to over-exploitation. Although BFT have been targeted by fisheries in the Mediterranean Sea for thousands of years, it has only been in these last decades that the exploitation rate has reached far beyond sustainable levels. An understanding of the population structure, spatial dynamics, exploitation rates and the environmental variables that affect BFT is crucial for the conservation of the species. The aims of this PhD project were 1) to assess the accuracy of larval identification methods, 2) determine the genetic structure of modern BFT populations, 3) assess the self-recruitment rate in the Gulf of Mexico and Mediterranean spawning areas, 4) estimate the immigration rate of BFT to feeding aggregations from the various spawning areas, and 5) develop tools capable of investigating the temporal stability of population structuring in the Mediterranean Sea. Several weaknesses in modern morphology-based taxonomy including demographic decline of expert taxonomists, flawed identification keys, reluctance of the taxonomic community to embrace advances in digital communications and a general scarcity of modern user-friendly materials are reviewed. Barcoding of scombrid larvae revealed important differences in the accuracy of the taxonomic identifications carried out by different ichthyoplanktologists following morphology-based methods. Using a Genotyping-by-Sequencing a panel of 95 SNPs was developed and used to characterize the population structuring of BFT and composition of adult feeding aggregations. Using novel molecular techniques, DNA was extracted from bluefin tuna vertebrae excavated from late iron age, ancient roman settlements Byzantine-era Constantinople and a 20th century collection. A second panel of 96 SNPs was developed to genotype historical and modern samples in order to elucidate changes in population structuring and allele frequencies of loci associated with selective traits.