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 three-dimensional single-bin-size bin packing problem: combining metaheuristic and machine learning approaches

The Three-Dimensional Single-Bin-Size Bin Packing Problem is one of the most studied problem in the Cutting & Packing category. From a strictly mathematical point of view, it consists of packing a finite set of strongly heterogeneous “small” boxes, called items, into a finite set of identical “large” rectangles, called bins, minimizing the unused volume and requiring that the items are packed without overlapping. The great interest is mainly due to the number of real-world applications in which it arises, such as pallet and container loading, cutting objects out of a piece of material and packaging design. Depending on these real-world applications, more objective functions and more practical constraints could be needed. After a brief discussion about the real-world applications of the problem and a exhaustive literature review, the design of a two-stage algorithm to solve the aforementioned problem is presented. The algorithm must be able to provide the spatial coordinates of the placed boxes vertices and also the optimal boxes input sequence, while guaranteeing geometric, stability, fragility constraints and a reduced computational time. Due to NP-hard complexity of this type of combinatorial problems, a fusion of metaheuristic and machine learning techniques is adopted. In particular, a hybrid genetic algorithm coupled with a feedforward neural network is used. In the first stage, a rich dataset is created starting from a set of real input instances provided by an industrial company and the feedforward neural network is trained on it. After its training, given a new input instance, the hybrid genetic algorithm is able to run using the neural network output as input parameter vector, providing as output the optimal solution. The effectiveness of the proposed works is confirmed via several experimental tests.

Biomass Gasification - Process analysis and dimensioning aspects for downdraft units and gas cleaning lines

In such territories where food production is mostly scattered in several small / medium size or even domestic farms, a lot of heterogeneous residues are produced yearly, since farmers usually carry out different activities in their properties. The amount and composition of farm residues, therefore, widely change during year, according to the single production process periodically achieved. Coupling high efficiency micro-cogeneration energy units with easy handling biomass conversion equipments, suitable to treat different materials, would provide many important advantages to the farmers and to the community as well, so that the increase in feedstock flexibility of gasification units is nowadays seen as a further paramount step towards their wide spreading in rural areas and as a real necessity for their utilization at small scale. Two main research topics were thought to be of main concern at this purpose, and they were therefore discussed in this work: the investigation of fuels properties impact on gasification process development and the technical feasibility of small scale gasification units integration with cogeneration systems. According to these two main aspects, the present work was thus divided in two main parts. The first one is focused on the biomass gasification process, that was investigated in its theoretical aspects and then analytically modelled in order to simulate thermo-chemical conversion of different biomass fuels, such as wood (park waste wood and softwood), wheat straw, sewage sludge and refuse derived fuels. The main idea is to correlate the results of reactor design procedures with the physical properties of biomasses and the corresponding working conditions of gasifiers (temperature profile, above all), in order to point out the main differences which prevent the use of the same conversion unit for different materials. At this scope, a gasification kinetic free model was initially developed in Excel sheets, considering different values of air to biomass ratio and the downdraft gasification technology as particular examined application. The differences in syngas production and working conditions (process temperatures, above all) among the considered fuels were tried to be connected to some biomass properties, such elementary composition, ash and water contents. The novelty of this analytical approach was the use of kinetic constants ratio in order to determine oxygen distribution among the different oxidation reactions (regarding volatile matter only) while equilibrium of water gas shift reaction was considered in gasification zone, by which the energy and mass balances involved in the process algorithm were linked together, as well. Moreover, the main advantage of this analytical tool is the easiness by which the input data corresponding to the particular biomass materials can be inserted into the model, so that a rapid evaluation on their own thermo-chemical conversion properties is possible to be obtained, mainly based on their chemical composition A good conformity of the model results with the other literature and experimental data was detected for almost all the considered materials (except for refuse derived fuels, because of their unfitting chemical composition with the model assumptions). Successively, a dimensioning procedure for open core downdraft gasifiers was set up, by the analysis on the fundamental thermo-physical and thermo-chemical mechanisms which are supposed to regulate the main solid conversion steps involved in the gasification process. Gasification units were schematically subdivided in four reaction zones, respectively corresponding to biomass heating, solids drying, pyrolysis and char gasification processes, and the time required for the full development of each of these steps was correlated to the kinetics rates (for pyrolysis and char gasification processes only) and to the heat and mass transfer phenomena from gas to solid phase. On the basis of this analysis and according to the kinetic free model results and biomass physical properties (particles size, above all) it was achieved that for all the considered materials char gasification step is kinetically limited and therefore temperature is the main working parameter controlling this step. Solids drying is mainly regulated by heat transfer from bulk gas to the inner layers of particles and the corresponding time especially depends on particle size. Biomass heating is almost totally achieved by the radiative heat transfer from the hot walls of reactor to the bed of material. For pyrolysis, instead, working temperature, particles size and the same nature of biomass (through its own pyrolysis heat) have all comparable weights on the process development, so that the corresponding time can be differently depending on one of these factors according to the particular fuel is gasified and the particular conditions are established inside the gasifier. The same analysis also led to the estimation of reaction zone volumes for each biomass fuel, so as a comparison among the dimensions of the differently fed gasification units was finally accomplished. Each biomass material showed a different volumes distribution, so that any dimensioned gasification unit does not seem to be suitable for more than one biomass species. Nevertheless, since reactors diameters were found out quite similar for all the examined materials, it could be envisaged to design a single units for all of them by adopting the largest diameter and by combining together the maximum heights of each reaction zone, as they were calculated for the different biomasses. A total height of gasifier as around 2400mm would be obtained in this case. Besides, by arranging air injecting nozzles at different levels along the reactor, gasification zone could be properly set up according to the particular material is in turn gasified. Finally, since gasification and pyrolysis times were found to considerably change according to even short temperature variations, it could be also envisaged to regulate air feeding rate for each gasified material (which process temperatures depend on), so as the available reactor volumes would be suitable for the complete development of solid conversion in each case, without even changing fluid dynamics behaviour of the unit as well as air/biomass ratio in noticeable measure. The second part of this work dealt with the gas cleaning systems to be adopted downstream the gasifiers in order to run high efficiency CHP units (i.e. internal engines and micro-turbines). Especially in the case multi–fuel gasifiers are assumed to be used, weightier gas cleaning lines need to be envisaged in order to reach the standard gas quality degree required to fuel cogeneration units. Indeed, as the more heterogeneous feed to the gasification unit, several contaminant species can simultaneously be present in the exit gas stream and, as a consequence, suitable gas cleaning systems have to be designed. In this work, an overall study on gas cleaning lines assessment is carried out. Differently from the other research efforts carried out in the same field, the main scope is to define general arrangements for gas cleaning lines suitable to remove several contaminants from the gas stream, independently on the feedstock material and the energy plant size The gas contaminant species taken into account in this analysis were: particulate, tars, sulphur (in H2S form), alkali metals, nitrogen (in NH3 form) and acid gases (in HCl form). For each of these species, alternative cleaning devices were designed according to three different plant sizes, respectively corresponding with 8Nm3/h, 125Nm3/h and 350Nm3/h gas flows. Their performances were examined on the basis of their optimal working conditions (efficiency, temperature and pressure drops, above all) and their own consumption of energy and materials. Successively, the designed units were combined together in different overall gas cleaning line arrangements, paths, by following some technical constraints which were mainly determined from the same performance analysis on the cleaning units and from the presumable synergic effects by contaminants on the right working of some of them (filters clogging, catalysts deactivation, etc.). One of the main issues to be stated in paths design accomplishment was the tars removal from the gas stream, preventing filters plugging and/or line pipes clogging At this scope, a catalytic tars cracking unit was envisaged as the only solution to be adopted, and, therefore, a catalytic material which is able to work at relatively low temperatures was chosen. Nevertheless, a rapid drop in tars cracking efficiency was also estimated for this same material, so that an high frequency of catalysts regeneration and a consequent relevant air consumption for this operation were calculated in all of the cases. Other difficulties had to be overcome in the abatement of alkali metals, which condense at temperatures lower than tars, but they also need to be removed in the first sections of gas cleaning line in order to avoid corrosion of materials. In this case a dry scrubber technology was envisaged, by using the same fine particles filter units and by choosing for them corrosion resistant materials, like ceramic ones. Besides these two solutions which seem to be unavoidable in gas cleaning line design, high temperature gas cleaning lines were not possible to be achieved for the two larger plant sizes, as well. Indeed, as the use of temperature control devices was precluded in the adopted design procedure, ammonia partial oxidation units (as the only considered methods for the abatement of ammonia at high temperature) were not suitable for the large scale units, because of the high increase of reactors temperature by the exothermic reactions involved in the process. In spite of these limitations, yet, overall arrangements for each considered plant size were finally designed, so that the possibility to clean the gas up to the required standard degree was technically demonstrated, even in the case several contaminants are simultaneously present in the gas stream. Moreover, all the possible paths defined for the different plant sizes were compared each others on the basis of some defined operational parameters, among which total pressure drops, total energy losses, number of units and secondary materials consumption. On the basis of this analysis, dry gas cleaning methods proved preferable to the ones including water scrubber technology in al of the cases, especially because of the high water consumption provided by water scrubber units in ammonia adsorption process. This result is yet connected to the possibility to use activated carbon units for ammonia removal and Nahcolite adsorber for chloride acid. The very high efficiency of this latter material is also remarkable. Finally, as an estimation of the overall energy loss pertaining the gas cleaning process, the total enthalpy losses estimated for the three plant sizes were compared with the respective gas streams energy contents, these latter obtained on the basis of low heating value of gas only. This overall study on gas cleaning systems is thus proposed as an analytical tool by which different gas cleaning line configurations can be evaluated, according to the particular practical application they are adopted for and the size of cogeneration unit they are connected to.

CT perfusion image processing: analysis of liver tumors

Perfusion CT imaging of the liver has potential to improve evaluation of tumour angiogenesis. Quantitative parameters can be obtained applying mathematical models to Time Attenuation Curve (TAC). However, there are still some difficulties for an accurate quantification of perfusion parameters due, for example, to algorithms employed, to mathematical model, to patient’s weight and cardiac output and to the acquisition system. In this thesis, new parameters and alternative methodologies about liver perfusion CT are presented in order to investigate the cause of variability of this technique. Firstly analysis were made to assess the variability related to the mathematical model used to compute arterial Blood Flow (BFa) values. Results were obtained implementing algorithms based on “ maximum slope method” and “Dual input one compartment model” . Statistical analysis on simulated data demonstrated that the two methods are not interchangeable. Anyway slope method is always applicable in clinical context. Then variability related to TAC processing in the application of slope method is analyzed. Results compared with manual selection allow to identify the best automatic algorithm to compute BFa. The consistency of a Standardized Perfusion Index (SPV) was evaluated and a simplified calibration procedure was proposed. At the end the quantitative value of perfusion map was analyzed. ROI approach and map approach provide related values of BFa and this means that pixel by pixel algorithm give reliable quantitative results. Also in pixel by pixel approach slope method give better results. In conclusion the development of new automatic algorithms for a consistent computation of BFa and the analysis and definition of simplified technique to compute SPV parameter, represent an improvement in the field of liver perfusion CT analysis.

Joint value at risk: a new conditional risk measure

In this PhD thesis a new firm level conditional risk measure is developed. It is named Joint Value at Risk (JVaR) and is defined as a quantile of a conditional distribution of interest, where the conditioning event is a latent upper tail event. It addresses the problem of how risk changes under extreme volatility scenarios. The properties of JVaR are studied based on a stochastic volatility representation of the underlying process. We prove that JVaR is leverage consistent, i.e. it is an increasing function of the dependence parameter in the stochastic representation. A feasible class of nonparametric M-estimators is introduced by exploiting the elicitability of quantiles and the stochastic ordering theory. Consistency and asymptotic normality of the two stage M-estimator are derived, and a simulation study is reported to illustrate its finite-sample properties. Parametric estimation methods are also discussed. The relation with the VaR is exploited to introduce a volatility contribution measure, and a tail risk measure is also proposed. The analysis of the dynamic JVaR is presented based on asymmetric stochastic volatility models. Empirical results with S&P500 data show that accounting for extreme volatility levels is relevant to better characterize the evolution of risk. The work is complemented by a review of the literature, where we provide an overview on quantile risk measures, elicitable functionals and several stochastic orderings.

Novel methods of state estimation and parameter identification for high-performance motorcycles

This research activity aims at providing a reliable estimation of particular state variables or parameters concerning the dynamics and performance optimization of a MotoGP-class motorcycle, integrating the classical model-based approach with new methodologies involving artificial intelligence. The first topic of the research focuses on the estimation of the thermal behavior of the MotoGP carbon braking system. Numerical tools are developed to assess the instantaneous surface temperature distribution in the motorcycle's front brake discs. Within this application other important brake parameters are identified using Kalman filters, such as the disc convection coefficient and the power distribution in the disc-pads contact region. Subsequently, a physical model of the brake is built to estimate the instantaneous braking torque. However, the results obtained with this approach are highly limited by the knowledge of the friction coefficient (μ) between the disc rotor and the pads. Since the value of μ is a highly nonlinear function of many variables (namely temperature, pressure and angular velocity of the disc), an analytical model for the friction coefficient estimation appears impractical to establish. To overcome this challenge, an innovative hybrid solution is implemented, combining the benefit of artificial intelligence (AI) with classical model-based approach. Indeed, the disc temperature estimated through the thermal model previously implemented is processed by a machine learning algorithm that outputs the actual value of the friction coefficient thus improving the braking torque computation performed by the physical model of the brake. Finally, the last topic of this research activity regards the development of an AI algorithm to estimate the current sideslip angle of the motorcycle's front tire. While a single-track motorcycle kinematic model and IMU accelerometer signals theoretically enable sideslip calculation, the presence of accelerometer noise leads to a significant drift over time. To address this issue, a long short-term memory (LSTM) network is implemented.