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.

Stellar Relics of the hierarchical assembly of the Galaxy

This PhD Thesis is part of a long-term wide research project, carried out by the "Osservatorio Astronomico di Bologna (INAF-OABO)", that has as primary goal the comprehension and reconstruction of formation mechanism of galaxies and their evolution history. There is now substantial evidence, both from theoretical and observational point of view, in favor of the hypothesis that the halo of our Galaxy has been at least partially, built up by the progressive accretion of small fragments, similar in nature to the present day dwarf galaxies of the Local Group. In this context, the photometric and spectroscopic study of systems which populate the halo of our Galaxy (i.e. dwarf spheroidal galaxy, tidal streams, massive globular cluster, etc) permits to discover, not only the origin and behaviour of these systems, but also the structure of our Galactic halo, combined with its formation history. In fact, the study of the population of these objects and also of their chemical compositions, age, metallicities and velocity dispersion, permit us not only an improvement in the understanding of the mechanisms that govern the Galactic formation, but also a valid indirect test for cosmological model itself. Specifically, in this Thesis we provided a complete characterization of the tidal Stream of the Sagittarius dwarf spheroidal galaxy, that is the most striking example of the process of tidal disruption and accretion of a dwarf satellite in to our Galaxy. Using Red Clump stars, extracted from the catalogue of the Sloan Digital Sky Survey (SDSS) we obtained an estimate of the distance, the depth along the line of sight and of the number density for each detected portion of the Stream (and more in general for each detected structure along our line of sight). Moreover comparing the relative number (i.e. the ratio) of Blue Horizontal Branch stars and Red Clump stars (the two features are tracers of different age/different metallicity populations) in the main body of the galaxy and in the Stream, in order to verify the presence of an age-metallicity gradient along the Stream. We also report the detection of a population of Red Clump stars probably associated with the recently discovered Bootes III stellar system. Finally, we also present the results of a survey of radial velocities over a wide region, extending from r ~ 10' out to r ~ 80' within the massive star cluster Omega Centauri. The survey was performed with FLAMES@VLT, to study the velocity dispersion profile in the outer regions of this stellar system. All the results presented in this Thesis, have already been published in refeered journals.

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.

Morphological-molecular taxonomy and population genetic structure of common and Egyptian soles of the Adriatic Sea

A total of 352 specimens were analyzed to achieve the different aims of this thesis. 255 central-northern Adriatic specimens of S. solea and S. aegyptiaca were molecularly analysed using microsatellite locus Sos(AC)40 and 205 also morphologically due to evaluate the abundance and the distribution of the cryptic species S. aegyptiaca and to confirm morphologic analyses. Morphological and molecular analyses comparated show a correspondence of 96%. A combined morphologic approach could be proposed to apply multiple criteria on the analyzed external morphological keys. The Adriatic Egyptian soles may lives in shallow waters (up 30 m) and in brackish lagoon. 127 samples of Adriatic common sole added to 326 samples of previous studies showed, using mitochondrial marker (CytB), that the Adriatic Sea as contact zone between Tyrrhenian and Aegean Sea, the divergence within the Adriatic Sea is low but significant between central-north and south, with a longitudinal strong gene flow in central-northern side. It’s also showed as in the Adriatic Sea two near-panmictic populations of common sole exist.

Structure and properties of nanostructures from polyelectrolytes and porphyrins: Self-Assembly in aqueous solution

In this work self-assembling model systems in aqueous solution were studied. The systems contained charged polymers, polyelectrolytes, that were combined with oppositely charged counterions to build up supramolecular structures. With imaging, scattering and spectroscopic techniques it was investigated how the structure of building units influences the structure of their assemblies. Polyelectrolytes with different chemical structure, molecular weight and morphology were investigated. In addition to linear polyelectrolytes, semi-flexible cylindrical bottle-brush polymers that possess a defined cross-section and a relatively high persistence along the backbone were studied. The polyelectrolytes were combined with structural organic counterions having charge numbers one to four. Especially the self-assembly of polyelectrolytes with different tetravalent water-soluble porphyrins was studied. Porphyrins have a rigid aromatic structure that has a structural effect on their self-assembly behavior and through which porphyrins are capable of self-aggregation via π-π interaction. The main focus of the thesis is the self-assembly of cylindrical bottle-brush polyelectrolytes with tetravalent porphyrins. It was shown that the addition of porphyrins to oppositely charged brush molecules induces a hierarchical formation of stable nanoscale brush-porphyrin networks. The networks can be disconnected by addition of salt and single porphyrin-decoratedrncylindrical brush polymers are obtained. These two new morphologies, brush-porphyrin networks and porphyrin-decorated brush polymers, may have potential as functional materials with interesting mechanical and optical properties.

Analysis and mathematical modeling of wave-structure interaction

The aim of this thesis, included within the THESEUS project, is the development of a mathematical model 2DV two-phase, based on the existing code IH-2VOF developed by the University of Cantabria, able to represent together the overtopping phenomenon and the sediment transport. Several numerical simulations were carried out in order to analyze the flow characteristics on a dike crest. The results show that the seaward/landward slope does not affect the evolution of the flow depth and velocity over the dike crest whereas the most important parameter is the relative submergence. Wave heights decrease and flow velocities increase while waves travel over the crest. In particular, by increasing the submergence, the wave height decay and the increase of the velocity are less marked. Besides, an appropriate curve able to fit the variation of the wave height/velocity over the dike crest were found. Both for the wave height and for the wave velocity different fitting coefficients were determined on the basis of the submergence and of the significant wave height. An equation describing the trend of the dimensionless coefficient c_h for the wave height was derived. These conclusions could be taken into consideration for the design criteria and the upgrade of the structures. In the second part of the thesis, new equations for the representation of the sediment transport in the IH-2VOF model were introduced in order to represent beach erosion while waves run-up and overtop the sea banks during storms. The new model allows to calculate sediment fluxes in the water column together with the sediment concentration. Moreover it is possible to model the bed profile evolution. Different tests were performed under low-intensity regular waves with an homogeneous layer of sand on the bottom of a channel in order to analyze the erosion-deposition patterns and verify the model results.

German validation of the Conners Adult ADHD Rating Scales–self-report (CAARS-S) I: Factor structure and normative data

Attention-deficit/hyperactivity disorder (ADHD) often persists into adulthood. Instruments for diagnosing ADHD in childhood are well validated and reliable, but diagnosis of ADHD in adults remains problematic. Attempts have been made to develop criteria specific for adult ADHD, resulting in the development of self-report and observer-rated questionnaires. To date, the Conners Adult ADHD Rating Scales (CAARS) are the international standard for questionnaire assessment of ADHD. The current study evaluates a German version of the CAARS self-report (CAARS-S).

From Craton to Rift: Empirically Based Ground-Truth Criteria for Local Events Recorded on Regional Networks

Region-specific empirically based ground-truth (EBGT) criteria used to estimate the epicentral-location accuracy of seismic events have been developed for the Main Ethiopian Rift and the Tibetan plateau. Explosions recorded during the Ethiopia-Afar Geoscientific Lithospheric Experiment (EAGLE), the International Deep Profiling of Tibet, and the Himalaya (INDEPTH III) experiment provided the necessary GT0 reference events. In each case, the local crustal structure is well known and handpicked arrival times were available, facilitating the establishment of the location accuracy criteria through the stochastic forward modeling of arrival times for epicentral locations. In the vicinity of the Main Ethiopian Rift, a seismic event is required to be recorded on at least 8 stations within the local Pg/Pn crossover distance and to yield a network-quality metric of less than 0.43 in order to be classified as EBGT5(95%) (GT5 with 95% confidence). These criteria were subsequently used to identify 10 new GT5 events with magnitudes greater than 2.1 recorded on the Ethiopian Broadband Seismic Experiment (EBSE) network and 24 events with magnitudes greater than 2.4 recorded on the EAGLE broadband network. The criteria for the Tibetan plateau are similar to the Ethiopia criteria, yet slightly less restrictive as the network-quality metric needs to be less than 0.45. Twenty-seven seismic events with magnitudes greater than 2.5 recorded on the INDEPTH III network were identified as GT5 based on the derived criteria. When considered in conjunction with criteria developed previously for the Kaapvaal craton in southern Africa, it is apparent that increasing restrictions on the network-quality metric mirror increases in the complexity of geologic structure from craton to plateau to rift. Accession Number: WOS:000322569200012

Spatial and temporal variation in population genetic structure of wild Nile tilapia (Oreochromis niloticus) across Africa

Background: Reconstructing the evolutionary history of a species is challenging. It often depends not only on the past biogeographic and climatic events but also the contemporary and ecological factors, such as current connectivity and habitat heterogeneity. In fact, these factors might interact with each other and shape the current species distribution. However, to what extent the current population genetic structure reflects the past and the contemporary factors is largely unknown. Here we investigated spatio-temporal genetic structures of Nile tilapia (Oreochromis niloticus) populations, across their natural distribution in Africa. While its large biogeographic distribution can cause genetic differentiation at the paleo-biogeographic scales, its restricted dispersal capacity might induce a strong genetic structure at micro-geographic scales. Results: Using nine microsatellite loci and 350 samples from ten natural populations, we found the highest genetic differentiation among the three ichthyofaunal provinces and regions (Ethiopian, Nilotic and Sudano-Sahelian) (R(ST) = 0.38 - 0.69). This result suggests the predominant effect of paleo-geographic events at macro-geographic scale. In addition, intermediate divergences were found between rivers and lakes within the regions, presumably reflecting relatively recent interruptions of gene flow between hydrographic basins (R(ST) = 0.24 - 0.32). The lowest differentiations were observed among connected populations within a basin (R(ST) = 0.015 in the Volta basin). Comparison of temporal sample series revealed subtle changes in the gene pools in a few generations (F = 0 - 0.053). The estimated effective population sizes were 23 - 143 and the estimated migration rate was moderate (m similar to 0.094 - 0.097) in the Volta populations. Conclusions: This study revealed clear hierarchical patterns of the population genetic structuring of O. niloticus in Africa. The effects of paleo-geographic and climatic events were predominant at macro-geographic scale, and the significant effect of geographic connectivity was detected at micro-geographic scale. The estimated effective population size, the moderate level of dispersal and the rapid temporal change in genetic composition might reflect a potential effect of life history strategy on population dynamics. This hypothesis deserves further investigation. The dynamic pattern revealed at micro-geographic and temporal scales appears important from a genetic resource management as well as from a biodiversity conservation point of view.

Bayesian Hierarchical Distributed Lag Models for Summer Ozone Exposure and Cardio-Respiratory Mortality

In this paper, we develop Bayesian hierarchical distributed lag models for estimating associations between daily variations in summer ozone levels and daily variations in cardiovascular and respiratory (CVDRESP) mortality counts for 19 U.S. large cities included in the National Morbidity Mortality Air Pollution Study (NMMAPS) for the period 1987 - 1994. At the first stage, we define a semi-parametric distributed lag Poisson regression model to estimate city-specific relative rates of CVDRESP associated with short-term exposure to summer ozone. At the second stage, we specify a class of distributions for the true city-specific relative rates to estimate an overall effect by taking into account the variability within and across cities. We perform the calculations with respect to several random effects distributions (normal, t-student, and mixture of normal), thus relaxing the common assumption of a two-stage normal-normal hierarchical model. We assess the sensitivity of the results to: 1) lag structure for ozone exposure; 2) degree of adjustment for long-term trends; 3) inclusion of other pollutants in the model;4) heat waves; 5) random effects distributions; and 6) prior hyperparameters. On average across cities, we found that a 10ppb increase in summer ozone level for every day in the previous week is associated with 1.25 percent increase in CVDRESP mortality (95% posterior regions: 0.47, 2.03). The relative rate estimates are also positive and statistically significant at lags 0, 1, and 2. We found that associations between summer ozone and CVDRESP mortality are sensitive to the confounding adjustment for PM_10, but are robust to: 1) the adjustment for long-term trends, other gaseous pollutants (NO_2, SO_2, and CO); 2) the distributional assumptions at the second stage of the hierarchical model; and 3) the prior distributions on all unknown parameters. Bayesian hierarchical distributed lag models and their application to the NMMAPS data allow us estimation of an acute health effect associated with exposure to ambient air pollution in the last few days on average across several locations. The application of these methods and the systematic assessment of the sensitivity of findings to model assumptions provide important epidemiological evidence for future air quality regulations.

A BAYESIAN HIERARCHICAL FRAMEWORK FOR SPATIAL MODELING OF fMRI DATA

Functional neuroimaging techniques enable investigations into the neural basis of human cognition, emotions, and behaviors. In practice, applications of functional magnetic resonance imaging (fMRI) have provided novel insights into the neuropathophysiology of major psychiatric,neurological, and substance abuse disorders, as well as into the neural responses to their treatments. Modern activation studies often compare localized task-induced changes in brain activity between experimental groups. One may also extend voxel-level analyses by simultaneously considering the ensemble of voxels constituting an anatomically defined region of interest (ROI) or by considering means or quantiles of the ROI. In this work we present a Bayesian extension of voxel-level analyses that offers several notable benefits. First, it combines whole-brain voxel-by-voxel modeling and ROI analyses within a unified framework. Secondly, an unstructured variance/covariance for regional mean parameters allows for the study of inter-regional functional connectivity, provided enough subjects are available to allow for accurate estimation. Finally, an exchangeable correlation structure within regions allows for the consideration of intra-regional functional connectivity. We perform estimation for our model using Markov Chain Monte Carlo (MCMC) techniques implemented via Gibbs sampling which, despite the high throughput nature of the data, can be executed quickly (less than 30 minutes). We apply our Bayesian hierarchical model to two novel fMRI data sets: one considering inhibitory control in cocaine-dependent men and the second considering verbal memory in subjects at high risk for Alzheimer’s disease. The unifying hierarchical model presented in this manuscript is shown to enhance the interpretation content of these data sets.

Hierarchical segmentation-assisted multimodal registration for MR brain images

Information theory-based metric such as mutual information (MI) is widely used as similarity measurement for multimodal registration. Nevertheless, this metric may lead to matching ambiguity for non-rigid registration. Moreover, maximization of MI alone does not necessarily produce an optimal solution. In this paper, we propose a segmentation-assisted similarity metric based on point-wise mutual information (PMI). This similarity metric, termed SPMI, enhances the registration accuracy by considering tissue classification probabilities as prior information, which is generated from an expectation maximization (EM) algorithm. Diffeomorphic demons is then adopted as the registration model and is optimized in a hierarchical framework (H-SPMI) based on different levels of anatomical structure as prior knowledge. The proposed method is evaluated using Brainweb synthetic data and clinical fMRI images. Both qualitative and quantitative assessment were performed as well as a sensitivity analysis to the segmentation error. Compared to the pure intensity-based approaches which only maximize mutual information, we show that the proposed algorithm provides significantly better accuracy on both synthetic and clinical data.

Selection criteria for selective dorsal rhizotomy in children with spastic cerebral palsy: a systematic review of the literature

AIM Information regarding the selection procedure for selective dorsal rhizotomy (SDR) in children with spastic cerebral palsy (CP) is scarce. Therefore, the aim of this study was to summarize the selection criteria for SDR in children with spastic CP. METHOD A systematic review was carried out using the following databases: MEDLINE, CINAHL, EMBASE, PEDro, and the Cochrane Library. Additional studies were identified in the reference lists. Search terms included 'selective dorsal rhizotomy', 'functional posterior rhizotomy', 'selective posterior rhizotomy', and 'cerebral palsy'. Studies were selected if they studied mainly children (<18y of age) with spastic CP, if they had an intervention of SDR, if they had a detailed description of the selection criteria, and if they were in English. The levels of evidence, conduct of studies, and selection criteria for SDR were scored. RESULTS Fifty-two studies were included. Selection criteria were reported in 16 International Classification of Functioning, Disability and Health model domains including 'body structure and function' (details concerning spasticity [94%], other movement abnormalities [62%], and strength [54%]), 'activity' (gross motor function [27%]), and 'personal and environmental factors' (age [44%], diagnosis [50%], motivation [31%], previous surgery [21%], and follow-up therapy [31%]). Most selection criteria were not based on standardized measurements. INTERPRETATION Selection criteria for SDR vary considerably. Future studies should describe clearly the selection procedure. International meetings of experts should develop more uniform consensus guidelines, which could form the basis for selecting candidates for SDR.

A Hierarchical Bayesian Model for Measuring Motion Adaptation

Previous research has shown that motion imagery draws on the same neural circuits that are involved in perception of motion, thus leading to a motion aftereffect (Winawer et al., 2010). Imagined stimuli can induce a similar shift in participants’ psychometric functions as neural adaptation due to a perceived stimulus. However, these studies have been criticized on the grounds that they fail to exclude the possibility that the subjects might have guessed the experimental hypothesis, and behaved accordingly (Morgan et al., 2012). In particular, the authors claim that participants can adopt arbitrary response criteria, which results in similar changes of the central tendency μ of psychometric curves as those shown by Winawer et al. (2010).

Estimating Diagnostic Test Accuracies for Brachyspira hyodysenteriae Accounting for the Complexities of Population Structure in Food Animals

For swine dysentery, which is caused by Brachyspira hyodysenteriae infection and is an economically important disease in intensive pig production systems worldwide, a perfect or error-free diagnostic test ("gold standard") is not available. In the absence of a gold standard, Bayesian latent class modelling is a well-established methodology for robust diagnostic test evaluation. In contrast to risk factor studies in food animals, where adjustment for within group correlations is both usual and required for good statistical practice, diagnostic test evaluation studies rarely take such clustering aspects into account, which can result in misleading results. The aim of the present study was to estimate test accuracies of a PCR originally designed for use as a confirmatory test, displaying a high diagnostic specificity, and cultural examination for B. hyodysenteriae. This estimation was conducted based on results of 239 samples from 103 herds originating from routine diagnostic sampling. Using Bayesian latent class modelling comprising of a hierarchical beta-binomial approach (which allowed prevalence across individual herds to vary as herd level random effect), robust estimates for the sensitivities of PCR and culture, as well as for the specificity of PCR, were obtained. The estimated diagnostic sensitivity of PCR (95% CI) and culture were 73.2% (62.3; 82.9) and 88.6% (74.9; 99.3), respectively. The estimated specificity of the PCR was 96.2% (90.9; 99.8). For test evaluation studies, a Bayesian latent class approach is well suited for addressing the considerable complexities of population structure in food animals.