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.

A partial dependence factorial analysis to deal with selection bias in observational studis

This thesis presents a creative and practical approach to dealing with the problem of selection bias. Selection bias may be the most important vexing problem in program evaluation or in any line of research that attempts to assert causality. Some of the greatest minds in economics and statistics have scrutinized the problem of selection bias, with the resulting approaches – Rubin’s Potential Outcome Approach(Rosenbaum and Rubin,1983; Rubin, 1991,2001,2004) or Heckman’s Selection model (Heckman, 1979) – being widely accepted and used as the best fixes. These solutions to the bias that arises in particular from self selection are imperfect, and many researchers, when feasible, reserve their strongest causal inference for data from experimental rather than observational studies. The innovative aspect of this thesis is to propose a data transformation that allows measuring and testing in an automatic and multivariate way the presence of selection bias. The approach involves the construction of a multi-dimensional conditional space of the X matrix in which the bias associated with the treatment assignment has been eliminated. Specifically, we propose the use of a partial dependence analysis of the X-space as a tool for investigating the dependence relationship between a set of observable pre-treatment categorical covariates X and a treatment indicator variable T, in order to obtain a measure of bias according to their dependence structure. The measure of selection bias is then expressed in terms of inertia due to the dependence between X and T that has been eliminated. Given the measure of selection bias, we propose a multivariate test of imbalance in order to check if the detected bias is significant, by using the asymptotical distribution of inertia due to T (Estadella et al. 2005) , and by preserving the multivariate nature of data. Further, we propose the use of a clustering procedure as a tool to find groups of comparable units on which estimate local causal effects, and the use of the multivariate test of imbalance as a stopping rule in choosing the best cluster solution set. The method is non parametric, it does not call for modeling the data, based on some underlying theory or assumption about the selection process, but instead it calls for using the existing variability within the data and letting the data to speak. The idea of proposing this multivariate approach to measure selection bias and test balance comes from the consideration that in applied research all aspects of multivariate balance, not represented in the univariate variable- by-variable summaries, are ignored. The first part contains an introduction to evaluation methods as part of public and private decision process and a review of the literature of evaluation methods. The attention is focused on Rubin Potential Outcome Approach, matching methods, and briefly on Heckman’s Selection Model. The second part focuses on some resulting limitations of conventional methods, with particular attention to the problem of how testing in the correct way balancing. The third part contains the original contribution proposed , a simulation study that allows to check the performance of the method for a given dependence setting and an application to a real data set. Finally, we discuss, conclude and explain our future perspectives.

Isospin dependence of the Ar+Ni fusion-evaporation cross section

The fundamental goal of this thesis is the determination of the isospin dependence of the Ar+Ni fusion-evaporation cross section. Three Ar isotope beams, with energies of about 13AMeV, have been accelerated and impinged onto isotopically enriched Ni targets, in order to produce Pd nuclei, with mass number varying from 92 to 104. The measurements have been performed by the high performance 4pi detector INDRA, coupled with the magnetic spectrometer VAMOS. Even if the results are very preliminary, the obtained fusion-evaporation cross sections behaviour gives a hint at the possible isospin dependence of the fusion-evaporation cross sections.

Synthesis and application of new ion-tagged ligands and organocatalysts

We report the synthesis and application of some ion-tagged catalysts in organometallic catalysis and organocatalysis. With the installation of an ionic group on the backbone of a known catalyst, two main effects are generally obtained. i) a modification of the solubility of the catalyst: if judicious choice of the ion pair is made, the ion-tag can confer to the catalyst a solubility profile suitable for catalyst recycling. ii) the ionic group can play a non-innocent role in the process considered: if stabilizing interaction between the ionic group and the developing charges in the transition state are established, the reaction can speed up. We describe the use of ion-tagged diphenylprolinol as Zn ligand. The chiral ligand grafted onto an ionic liquid (IL) was recycled 10 times with no loss of reactivity and selectivity, when it was employed in the first example of enantioselective addition of ZnEt2 to aldehydes in ILs. An ammonium-tagged phosphine displayed the capability to stabilize Pd catalysts for the Suzuki reaction in ILs. The ionic phase was recycled 6 times with no detectable loss of activity and very low Pd leaching in the organic phase. This catalytic system was also employed for the functionalization of the challenging substrate 5,11-dibromotetracene. In the field of organocatalysis, we prepared two ion-tagged derivatives of the McMillan imidazolidinone. The results of the asymmetric Diels-Alder reaction between trans-cinnamaldehyde and cyclopentadiene exhibited great dependence on the position and nature of the ionic group. Finally, when O-TMS-diphenylprolinol was tagged with an imidazolium ion, exploiting a silyl ether linker, an efficient catalyst for the asymmetric addition of aldehydes to nitroolefins was achieved. The catalyst displayed enhanced reactivity and the same high level of selectivity of the untagged parent catalyst and it could be employed in a wide range of reaction conditions, included use of water as solvent.

The coupling between electron transfer and Protein/Solvent Dynamics in Photosynthetic Reaction Centers: Spectroscopic Studies in Amorphous Matrices

We investigated at the molecular level protein/solvent interactions and their relevance in protein function through the use of amorphous matrices at room temperature. As a model protein, we used the bacterial photosynthetic reaction center (RC) of Rhodobacter sphaeroides, a pigment protein complex which catalyzes the light-induced charge separation initiating the conversion of solar into chemical energy. The thermal fluctuations of the RC and its dielectric conformational relaxation following photoexcitation have been probed by analyzing the recombination kinetics of the primary charge-separated (P+QA-) state, using time resolved optical and EPR spectroscopies. We have shown that the RC dynamics coupled to this electron transfer process can be progressively inhibited at room temperature by decreasing the water content of RC films or of RC-trehalose glassy matrices. Extensive dehydration of the amorphous matrices inhibits RC relaxation and interconversion among conformational substates to an extent comparable to that attained at cryogenic temperatures in water-glycerol samples. An isopiestic method has been developed to finely tune the hydration level of the system. We have combined FTIR spectral analysis of the combination and association bands of residual water with differential light-minus-dark FTIR and high-field EPR spectroscopy to gain information on thermodynamics of water sorption, and on structure/dynamics of the residual water molecules, of protein residues and of RC cofactors. The following main conclusions were reached: (i) the RC dynamics is slaved to that of the hydration shell; (ii) in dehydrated trehalose glasses inhibition of protein dynamics is most likely mediated by residual water molecules simultaneously bound to protein residues and sugar molecules at the protein-matrix interface; (iii) the local environment of cofactors is not involved in the conformational dynamics which stabilizes the P+QA-; (iv) this conformational relaxation appears to be rather delocalized over several aminoacidic residues as well as water molecules weakly hydrogen-bonded to the RC.

Thermodynamic and mechanical properties of polymer-solvent systems

This work presents the results of theoretical and experimental characterization of thermodynamic, mechanical and transport properties in polymer solvent systems. The polymer solvent pairs considered ranged to those in which the polymer is rubbery, to those in which the initially glassy polymeric matrix is plasticized by the action of the low molecular weight species. Advanced Equation of State models have been adopted for thermodynamic modeling,along with a rigorous procedure that enables to extend their applicability to the non equilibrium, glassy region. Mass sorption kinetics had been modeled with phenomenological models and with advanced kinetic models.

Structure-property relations in polymers from renewable resources

The present research project focuses its attention on the study of structure-property relations in polymers from renewable sources (bio-based polymers) such as polymers microbially produced, i.e. polyhydrohyalkanoates (PHAs) or chemically synthesized using monomers from renewable sources, i.e. polyammide 11 (PA11). By means of a broad spectrum of experimental techniques, the influence of different modifications on bio-based polymers such as blending with other components, copolymerization with different co-monomers and introduction of branching to yield complex architectures have been investigated. The present work on PHAs focused on the study of the dependence of polymer properties on both the fermentation process conditions (e.g. bacterial strain and carbon substrate used) and the method adopted to recover PHAs from cells. Furthermore, a solvent-free method using an enzyme and chemicals in an aqueous medium, was developed in order to recover PHAs from cells. Such a method allowed to recover PHA granules in their amorphous state, i.e. in native form useful for specific applications (e.g. paper coating). In addition, a commercial PHA was used as polymeric matrix to develop biodegradable and bio-based composites for food packaging applications. Biodegradable, non-toxic, food contact plasticizers and low cost, widely available lignocellulosic fibers (wheat straw fibers) were incorporated in such a polymeric matrix, in order to decrease PHA brittleness and the polymer cost, respectively. As concerns the study of polyamide 11, both the rheological and the solid-state behavior of PA11 star samples with different arm number and length was studied. Introduction of arms in a polymer molecule allows to modulate melt viscosity behavior which is advantageous for industrial applications. Also, several important solid-state properties, in particular mechanical properties, are affected by the presence of branching. Given the importance of using ‘green’ synthetic strategies in polymer chemistry, novel poly(-amino esters), synthesized via enzymatic-catalyzed polymerization, have also been investigated in this work.