NOVI MAGISTRAT Jože Plečnik, progetti per il centro monumentale di Lubiana

This research work analyzes the theme of the architecture of the city and aims at establishing, by studying the urban project of the new town hall in Ljubljana made by the Slovenian architect Jože Plečnik, the idea that the construction of the city must be carried out through a type of architecture directed at the planning of collective urban spaces. The plan for the new town hall building, drew in three versions – 1932, 1939, and 1940-41 –, is part of a large set of plans concerning the area that Plečnik defines to be the “osrčje” (heart) of Ljubljana, that is, the central area within the castle hill and the distinctive arc of the Ljubljanica River, on the eastern boundary of the old “mesto” (town). Among the Plečnik's projects on urban scale for Ljubljana, the above-mentioned plans, unbuilt and scarcely published, must be considered to be ones of the least known, despite their importance in the professional activity of the architect. The work consists of three parts: the first part describes the background of theories and projects which shaped Plečnik's urban culture, during the years of his education in Vienna and before the beginning of the planning activities this work focuses on; the second part studies the plans for the “heart” of the city; the third part investigates the plan for the new town hall building by means of the graphical reconstruction of the three plan versions made by Plečnik, and it provides insights into the relationships among form, significance and motivation of his work. Since the plans have never been built, the digital tridimensional reconstruction of the building models allowed to show unknown spaces and confirm that Architecture has a particular significance when its goal is the planning of collective urban spaces.

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.