A principal component approach to space-based gravitational wave astronomy

The current approach to data analysis for the Laser Interferometry Space Antenna (LISA) depends on the time delay interferometry observables (TDI) which have to be generated before any weak signal detection can be performed. These are linear combinations of the raw data with appropriate time shifts that lead to the cancellation of the laser frequency noises. This is possible because of the multiple occurrences of the same noises in the different raw data. Originally, these observables were manually generated starting with LISA as a simple stationary array and then adjusted to incorporate the antenna's motions. However, none of the observables survived the flexing of the arms in that they did not lead to cancellation with the same structure. The principal component approach is another way of handling these noises that was presented by Romano and Woan which simplified the data analysis by removing the need to create them before the analysis. This method also depends on the multiple occurrences of the same noises but, instead of using them for cancellation, it takes advantage of the correlations that they produce between the different readings. These correlations can be expressed in a noise (data) covariance matrix which occurs in the Bayesian likelihood function when the noises are assumed be Gaussian. Romano and Woan showed that performing an eigendecomposition of this matrix produced two distinct sets of eigenvalues that can be distinguished by the absence of laser frequency noise from one set. The transformation of the raw data using the corresponding eigenvectors also produced data that was free from the laser frequency noises. This result led to the idea that the principal components may actually be time delay interferometry observables since they produced the same outcome, that is, data that are free from laser frequency noise. The aims here were (i) to investigate the connection between the principal components and these observables, (ii) to prove that the data analysis using them is equivalent to that using the traditional observables and (ii) to determine how this method adapts to real LISA especially the flexing of the antenna. For testing the connection between the principal components and the TDI observables a 10x 10 covariance matrix containing integer values was used in order to obtain an algebraic solution for the eigendecomposition. The matrix was generated using fixed unequal arm lengths and stationary noises with equal variances for each noise type. Results confirm that all four Sagnac observables can be generated from the eigenvectors of the principal components. The observables obtained from this method however, are tied to the length of the data and are not general expressions like the traditional observables, for example, the Sagnac observables for two different time stamps were generated from different sets of eigenvectors. It was also possible to generate the frequency domain optimal AET observables from the principal components obtained from the power spectral density matrix. These results indicate that this method is another way of producing the observables therefore analysis using principal components should give the same results as that using the traditional observables. This was proven by fact that the same relative likelihoods (within 0.3%) were obtained from the Bayesian estimates of the signal amplitude of a simple sinusoidal gravitational wave using the principal components and the optimal AET observables. This method fails if the eigenvalues that are free from laser frequency noises are not generated. These are obtained from the covariance matrix and the properties of LISA that are required for its computation are the phase-locking, arm lengths and noise variances. Preliminary results of the effects of these properties on the principal components indicate that only the absence of phase-locking prevented their production. The flexing of the antenna results in time varying arm lengths which will appear in the covariance matrix and, from our toy model investigations, this did not prevent the occurrence of the principal components. The difficulty with flexing, and also non-stationary noises, is that the Toeplitz structure of the matrix will be destroyed which will affect any computation methods that take advantage of this structure. In terms of separating the two sets of data for the analysis, this was not necessary because the laser frequency noises are very large compared to the photodetector noises which resulted in a significant reduction in the data containing them after the matrix inversion. In the frequency domain the power spectral density matrices were block diagonals which simplified the computation of the eigenvalues by allowing them to be done separately for each block. The results in general showed a lack of principal components in the absence of phase-locking except for the zero bin. The major difference with the power spectral density matrix is that the time varying arm lengths and non-stationarity do not show up because of the summation in the Fourier transform.

Sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution

Understanding how virus strains offer protection against closely related emerging strains is vital for creating effective vaccines. For many viruses, including Foot-and-Mouth Disease Virus (FMDV) and the Influenza virus where multiple serotypes often co-circulate, in vitro testing of large numbers of vaccines can be infeasible. Therefore the development of an in silico predictor of cross-protection between strains is important to help optimise vaccine choice. Vaccines will offer cross-protection against closely related strains, but not against those that are antigenically distinct. To be able to predict cross-protection we must understand the antigenic variability within a virus serotype, distinct lineages of a virus, and identify the antigenic residues and evolutionary changes that cause the variability. In this thesis we present a family of sparse hierarchical Bayesian models for detecting relevant antigenic sites in virus evolution (SABRE), as well as an extended version of the method, the extended SABRE (eSABRE) method, which better takes into account the data collection process. The SABRE methods are a family of sparse Bayesian hierarchical models that use spike and slab priors to identify sites in the viral protein which are important for the neutralisation of the virus. In this thesis we demonstrate how the SABRE methods can be used to identify antigenic residues within different serotypes and show how the SABRE method outperforms established methods, mixed-effects models based on forward variable selection or l1 regularisation, on both synthetic and viral datasets. In addition we also test a number of different versions of the SABRE method, compare conjugate and semi-conjugate prior specifications and an alternative to the spike and slab prior; the binary mask model. We also propose novel proposal mechanisms for the Markov chain Monte Carlo (MCMC) simulations, which improve mixing and convergence over that of the established component-wise Gibbs sampler. The SABRE method is then applied to datasets from FMDV and the Influenza virus in order to identify a number of known antigenic residue and to provide hypotheses of other potentially antigenic residues. We also demonstrate how the SABRE methods can be used to create accurate predictions of the important evolutionary changes of the FMDV serotypes. In this thesis we provide an extended version of the SABRE method, the eSABRE method, based on a latent variable model. The eSABRE method takes further into account the structure of the datasets for FMDV and the Influenza virus through the latent variable model and gives an improvement in the modelling of the error. We show how the eSABRE method outperforms the SABRE methods in simulation studies and propose a new information criterion for selecting the random effects factors that should be included in the eSABRE method; block integrated Widely Applicable Information Criterion (biWAIC). We demonstrate how biWAIC performs equally to two other methods for selecting the random effects factors and combine it with the eSABRE method to apply it to two large Influenza datasets. Inference in these large datasets is computationally infeasible with the SABRE methods, but as a result of the improved structure of the likelihood, we are able to show how the eSABRE method offers a computational improvement, leading it to be used on these datasets. The results of the eSABRE method show that we can use the method in a fully automatic manner to identify a large number of antigenic residues on a variety of the antigenic sites of two Influenza serotypes, as well as making predictions of a number of nearby sites that may also be antigenic and are worthy of further experiment investigation.

Inversion of ambient seismic noise HVSR to evaluate velocity and structural models of the Lower Tagus Basin, Portugal

During its history, several significant earthquakes have shaken the Lower Tagus Valley (Portugal). These earthquakes were destructive; some strong earthquakes were produced by large ruptures in offshore structures located southwest of the Portuguese coastline, and other moderate earthquakes were produced by local faults. In recent years, several studies have successfully obtained strong-ground motion syntheses for the Lower Tagus Valley using the finite difference method. To confirm the velocity model of this sedimentary basin obtained from geophysical and geological data, we analysed the ambient seismic noise measurements by applying the horizontal to vertical spectral ratio (HVSR) method. This study reveals the dependence of the frequency and amplitude of the low-frequency (HVSR) peaks (0.2–2 Hz) on the sediment thickness. We have obtained the depth of the Cenozoic basement along a profile transversal to the basin by the inversion of these ratios, imposing constraints from seismic reflection, boreholes, seismic sounding and gravimetric and magnetic potentials. This technique enables us to improve the existing three-dimensional model of the Lower Tagus Valley structure. The improved model will be decisive for the improvement of strong motion predictions in the earthquake hazard analysis of this highly populated basin. The methodology discussed can be applied to any other sedimentary basin.

Using a Bayesian model for estimating air borne infection risks: Fusarium head blight.

2016

Using a bayesian model for estimating air borne infection risks: wheat blast.

2016

Bayesian estimates of genetic parameters for reproductive traits in Nellore cows raised on pasture in tropical regions.

2016

Genetic parameters for carcass traits and body weight using a Bayesian approach in the Canchim cattle.

Correlation between genetic parameters and factors such as backfat thickness (BFT), rib eye area (REA), and body weight (BW) were estimated for Canchim beef cattle raised in natural pastures of Brazil. Data from 1648 animals were analyzed using multi-trait (BFT, REA, and BW) animal models by the Bayesian approach. This model included the effects of contemporary group, age, and individual heterozygosity as covariates. In addition, direct additive genetic and random residual effects were also analyzed. Heritability estimated for BFT (0.16), REA (0.50), and BW (0.44) indicated their potential for genetic improvements and response to selection processes. Furthermore, genetic correlations between BW and the remaining traits were high (P > 0.50), suggesting that selection for BW could improve REA and BFT. On the other hand, genetic correlation between BFT and REA was low (P = 0.39 ± 0.17), and included considerable variations, suggesting that these traits can be jointly included as selection criteria without influencing each other. We found that REA and BFT responded to the selection processes, as measured by ultrasound. Therefore, selection for yearling weight results in changes in REA and BFT.

Subsidence history, thermal maturity, and structural inversion of the Greater Caucasus-Kura-Adjara-Trialeti basin system of central-eastern Georgia

This study aims at defining the tectonic evolution of a portion of the Caucasian region, in Georgia, which experienced a complex pattern of deformation events throughout Mesozoic and Cenozoic times. An integrated approach was applied to unravel the thermo-tectonic history of three inverted sedimentary basins from burial to exhumation. Additionally, this dissertation provides examples of structural inversion of sedimentary basins in response to far-field transmission of compressional stresses away from collision zones, contributing to elucidate the dynamics of stress partitioning during continental collisions. The Adjara-Trialeti fold-and-thrust belt in south-western Georgia results from the structural inversion of a Middle Eocene continental back-arc rift basin opened as a consequence of the Northern Neotethys slab rollback. This study quantitatively defines the subsidence and exhumation history of the Adjara-Trialeti basin, constraining its Middle Miocene inception of structural inversion. The western Kura Basin is a flexural foreland basin trapped between the Lesser Caucasus to the south and the Greater Caucasus to the north. This study constrains successive and competing episodes of flexural subsidence during Oligocene-Miocene times, followed by partial inversion through thick- and thin-skinned tectonics in response to continued convergence between the adjacent, oppositely verging orogenic belts. The Greater Caucasus results from the structural inversion of a Jurassic continental back-arc basin, but the timing of its growth is still debated. An across-strike transect in its southern central domain was studied, indicating that this sector of the Greater Caucasus experienced two phases of structural inversion during Late Cretaceous-Paleocene and Late Miocene times. Overall, the dataset presented in this dissertation points to a complex and episodic history of incremental deformation, characterised by successive phases of extensional and compressional tectonics which developed in response to sequential terrane accretion at the southwestern margin of Eurasia since Late Cretaceous times, eventually determining the current configuration of the Arabia-Eurasia collision zone.

Bayesian Linear Regression for estimation of the Fractal Dimension of the Cerebral Cortex

The cerebral cortex presents self-similarity in a proper interval of spatial scales, a property typical of natural objects exhibiting fractal geometry. Its complexity therefore can be characterized by the value of its fractal dimension (FD). In the computation of this metric, it has usually been employed a frequentist approach to probability, with point estimator methods yielding only the optimal values of the FD. In our study, we aimed at retrieving a more complete evaluation of the FD by utilizing a Bayesian model for the linear regression analysis of the box-counting algorithm. We used T1-weighted MRI data of 86 healthy subjects (age 44.2 ± 17.1 years, mean ± standard deviation, 48% males) in order to gain insights into the confidence of our measure and investigate the relationship between mean Bayesian FD and age. Our approach yielded a stronger and significant (P < .001) correlation between mean Bayesian FD and age as compared to the previous implementation. Thus, our results make us suppose that the Bayesian FD is a more truthful estimation for the fractal dimension of the cerebral cortex compared to the frequentist FD.

Anisotropic seismic tomography with the reversible jump Markov chain Monte Carlo

The established isotropic tomographic models show the features of subduction zones in terms of seismic velocity anomalies, but they are generally subjected to the generation of artifacts due to the lack of anisotropy in forward modelling. There is evidence for the significant influence of seismic anisotropy in the mid-upper mantle, especially for boundary layers like subducting slabs. As consequence, in isotropic models artifacts may be misinterpreted as compositional or thermal heterogeneities. In this thesis project the application of a trans-dimensional Metropolis-Hastings method is investigated in the context of anisotropic seismic tomography. This choice arises as a response to the important limitations introduced by traditional inversion methods which use iterative procedures of optimization of a function object of the inversion. On the basis of a first implementation of the Bayesian sampling algorithm, the code is tested with some cartesian two-dimensional models, and then extended to polar coordinates and dimensions typical of subduction zones, the main focus proposed for this method. Synthetic experiments with increasing complexity are realized to test the performance of the method and the precautions for multiple contexts, taking into account also the possibility to apply seismic ray-tracing iteratively. The code developed is tested mainly for 2D inversions, future extensions will allow the anisotropic inversion of seismological data to provide more realistic imaging of real subduction zones, less subjected to generation of artifacts.

Synthetic generation of amyloid PET images by non-linear dimensionality reduction inversion

Privacy issues and data scarcity in PET field call for efficient methods to expand datasets via synthetic generation of new data that cannot be traced back to real patients and that are also realistic. In this thesis, machine learning techniques were applied to 1001 amyloid-beta PET images, which had undergone a diagnosis of Alzheimer’s disease: the evaluations were 540 positive, 457 negative and 4 unknown. Isomap algorithm was used as a manifold learning method to reduce the dimensions of the PET dataset; a numerical scale-free interpolation method was applied to invert the dimensionality reduction map. The interpolant was tested on the PET images via LOOCV, where the removed images were compared with the reconstructed ones with the mean SSIM index (MSSIM = 0.76 ± 0.06). The effectiveness of this measure is questioned, since it indicated slightly higher performance for a method of comparison using PCA (MSSIM = 0.79 ± 0.06), which gave clearly poor quality reconstructed images with respect to those recovered by the numerical inverse mapping. Ten synthetic PET images were generated and, after having been mixed with ten originals, were sent to a team of clinicians for the visual assessment of their realism; no significant agreements were found either between clinicians and the true image labels or among the clinicians, meaning that original and synthetic images were indistinguishable. The future perspective of this thesis points to the improvement of the amyloid-beta PET research field by increasing available data, overcoming the constraints of data acquisition and privacy issues. Potential improvements can be achieved via refinements of the manifold learning and the inverse mapping stages during the PET image analysis, by exploring different combinations in the choice of algorithm parameters and by applying other non-linear dimensionality reduction algorithms. A final prospect of this work is the search for new methods to assess image reconstruction quality.

Phylogenetics, Ancestral State Reconstruction, And A New Infrafamilial Classification Of The Pantropical Ochnaceae (medusagynaceae, Ochnaceae S.str., Quiinaceae) Based On Five Dna Regions.

Ochnaceae s.str. (Malpighiales) are a pantropical family of about 500 species and 27 genera of almost exclusively woody plants. Infrafamilial classification and relationships have been controversial partially due to the lack of a robust phylogenetic framework. Including all genera except Indosinia and Perissocarpa and DNA sequence data for five DNA regions (ITS, matK, ndhF, rbcL, trnL-F), we provide for the first time a nearly complete molecular phylogenetic analysis of Ochnaceae s.l. resolving most of the phylogenetic backbone of the family. Based on this, we present a new classification of Ochnaceae s.l., with Medusagynoideae and Quiinoideae included as subfamilies and the former subfamilies Ochnoideae and Sauvagesioideae recognized at the rank of tribe. Our data support a monophyletic Ochneae, but Sauvagesieae in the traditional circumscription is paraphyletic because Testulea emerges as sister to the rest of Ochnoideae, and the next clade shows Luxemburgia+Philacra as sister group to the remaining Ochnoideae. To avoid paraphyly, we classify Luxemburgieae and Testuleeae as new tribes. The African genus Lophira, which has switched between subfamilies (here tribes) in past classifications, emerges as sister to all other Ochneae. Thus, endosperm-free seeds and ovules with partly to completely united integuments (resulting in an apparently single integument) are characters that unite all members of that tribe. The relationships within its largest clade, Ochnineae (former Ochneae), are poorly resolved, but former Ochninae (Brackenridgea, Ochna) are polyphyletic. Within Sauvagesieae, the genus Sauvagesia in its broad circumscription is polyphyletic as Sauvagesia serrata is sister to a clade of Adenarake, Sauvagesia spp., and three other genera. Within Quiinoideae, in contrast to former phylogenetic hypotheses, Lacunaria and Touroulia form a clade that is sister to Quiina. Bayesian ancestral state reconstructions showed that zygomorphic flowers with adaptations to buzz-pollination (poricidal anthers), a syncarpous gynoecium (a near-apocarpous gynoecium evolved independently in Quiinoideae and Ochninae), numerous ovules, septicidal capsules, and winged seeds with endosperm are the ancestral condition in Ochnoideae. Although in some lineages poricidal anthers were lost secondarily, the evolution of poricidal superstructures secured the maintenance of buzz-pollination in some of these genera, indicating a strong selective pressure on keeping that specialized pollination system.

Mucopolysaccharidosis Type Ii: Identification Of 30 Novel Mutations Among Latin American Patients.

In this study, 103 unrelated South-American patients with mucopolysaccharidosis type II (MPS II) were investigated aiming at the identification of iduronate-2-sulfatase (IDS) disease causing mutations and the possibility of some insights on the genotype-phenotype correlation The strategy used for genotyping involved the identification of the previously reported inversion/disruption of the IDS gene by PCR and screening for other mutations by PCR/SSCP. The exons with altered mobility on SSCP were sequenced, as well as all the exons of patients with no SSCP alteration. By using this strategy, we were able to find the pathogenic mutation in all patients. Alterations such as inversion/disruption and partial/total deletions of the IDS gene were found in 20/103 (19%) patients. Small insertions/deletions/indels (<22 bp) and point mutations were identified in 83/103 (88%) patients, including 30 novel mutations; except for a higher frequency of small duplications in relation to small deletions, the frequencies of major and minor alterations found in our sample are in accordance with those described in the literature.

Exploring Iris Colour Prediction And Ancestry Inference In Admixed Populations Of South America.

New DNA-based predictive tests for physical characteristics and inference of ancestry are highly informative tools that are being increasingly used in forensic genetic analysis. Two eye colour prediction models: a Bayesian classifier - Snipper and a multinomial logistic regression (MLR) system for the Irisplex assay, have been described for the analysis of unadmixed European populations. Since multiple SNPs in combination contribute in varying degrees to eye colour predictability in Europeans, it is likely that these predictive tests will perform in different ways amongst admixed populations that have European co-ancestry, compared to unadmixed Europeans. In this study we examined 99 individuals from two admixed South American populations comparing eye colour versus ancestry in order to reveal a direct correlation of light eye colour phenotypes with European co-ancestry in admixed individuals. Additionally, eye colour prediction following six prediction models, using varying numbers of SNPs and based on Snipper and MLR, were applied to the study populations. Furthermore, patterns of eye colour prediction have been inferred for a set of publicly available admixed and globally distributed populations from the HGDP-CEPH panel and 1000 Genomes databases with a special emphasis on admixed American populations similar to those of the study samples.

Ssr-based Genetic Diversity And Structure Of Garlic Accessions From Brazil.

Garlic is a spice and a medicinal plant; hence, there is an increasing interest in 'developing' new varieties with different culinary properties or with high content of nutraceutical compounds. Phenotypic traits and dominant molecular markers are predominantly used to evaluate the genetic diversity of garlic clones. However, 24 SSR markers (codominant) specific for garlic are available in the literature, fostering germplasm researches. In this study, we genotyped 130 garlic accessions from Brazil and abroad using 17 polymorphic SSR markers to assess the genetic diversity and structure. This is the first attempt to evaluate a large set of accessions maintained by Brazilian institutions. A high level of redundancy was detected in the collection (50 % of the accessions represented eight haplotypes). However, non-redundant accessions presented high genetic diversity. We detected on average five alleles per locus, Shannon index of 1.2, HO of 0.5, and HE of 0.6. A core collection was set with 17 accessions, covering 100 % of the alleles with minimum redundancy. Overall FST and D values indicate a strong genetic structure within accessions. Two major groups identified by both model-based (Bayesian approach) and hierarchical clustering (UPGMA dendrogram) techniques were coherent with the classification of accessions according to maturity time (growth cycle): early-late and midseason accessions. Assessing genetic diversity and structure of garlic collections is the first step towards an efficient management and conservation of accessions in genebanks, as well as to advance future genetic studies and improvement of garlic worldwide.