Assessment of the quality of brain regions and neuroimaging metrics as biomarkers of Alzheimer’s disease

Alzheimer Disease (AD) is characterized by progressive cognitive decline and dementia. Earlier diagnosis and classification of different stages of the disease are currently the main challenges and can be assessed by neuroimaging. With this work we aim to evaluate the quality of brain regions and neuroimaging metrics as biomarkers of AD. Multimodal Imaging Brain Connectivity Analysis (MIBCA) toolbox functionalities were used to study AD by T1weighted, Diffusion Tensor Imaging and 18FAV45 PET, with data obtained from the AD Neuroimaging Initiative database, specifically 12 healthy controls (CTRL) and 33 patients with early mild cognitive impairment (EMCI), late MCI (LMCI) and AD (11 patients/group). The metrics evaluated were gray-matter volume (GMV), cortical thickness (CThk), mean diffusivity (MD), fractional anisotropy (FA), fiber count (FiberConn), node degree (Deg), cluster coefficient (ClusC) and relative standard-uptake-values (rSUV). Receiver Operating Characteristic (ROC) curves were used to evaluate and compare the diagnostic accuracy of the most significant metrics and brain regions and expressed as area under the curve (AUC). Comparisons were performed between groups. The RH-Accumbens/Deg demonstrated the highest AUC when differentiating between CTRLEMCI (82%), whether rSUV presented it in several brain regions when distinguishing CTRL-LMCI (99%). Regarding CTRL-AD, highest AUC were found with LH-STG/FiberConn and RH-FP/FiberConn (~100%). A larger number of neuroimaging metrics related with cortical atrophy with AUC>70% was found in CTRL-AD in both hemispheres, while in earlier stages, cortical metrics showed in more confined areas of the temporal region and mainly in LH, indicating an increasing of the spread of cortical atrophy that is characteristic of disease progression. In CTRL-EMCI several brain regions and neuroimaging metrics presented AUC>70% with a worst result in later stages suggesting these indicators as biomarkers for an earlier stage of MCI, although further research is necessary.

Spatial metrics and Landsat data for urban landuse change detection: case of Addis Ababa, Ethiopia.

Dissertation submitted in partial fulfilment of the requirements for the Degree of Master of Science in Geospatial Technologies.

A go-to-market strategy for vertebral metrics

Dissertação para obtenção do Grau de Mestre em Engenharia Biomédica

Dynamic stability metrics for the container loading problem

The Container Loading Problem (CLP) literature has traditionally evaluated the dynamic stability of cargo by applying two metrics to box arrangements: the mean number of boxes supporting the items excluding those placed directly on the floor (M1) and the percentage of boxes with insufficient lateral support (M2). However, these metrics, that aim to be proxies for cargo stability during transportation, fail to translate real-world cargo conditions of dynamic stability. In this paper two new performance indicators are proposed to evaluate the dynamic stability of cargo arrangements: the number of fallen boxes (NFB) and the number of boxes within the Damage Boundary Curve fragility test (NB_DBC). Using 1500 solutions for well-known problem instances found in the literature, these new performance indicators are evaluated using a physics simulation tool (StableCargo), replacing the real-world transportation by a truck with a simulation of the dynamic behaviour of container loading arrangements. Two new dynamic stability metrics that can be integrated within any container loading algorithm are also proposed. The metrics are analytical models of the proposed stability performance indicators, computed by multiple linear regression. Pearson’s r correlation coefficient was used as an evaluation parameter for the performance of the models. The extensive computational results show that the proposed metrics are better proxies for dynamic stability in the CLP than the previous widely used metrics.

Assessing the performance of macroinvertebrate metrics in the Challhuaco-Ñireco System (Northern Patagonia, Argentina)

ABSTRACT Seven sites were examined in the Challhuaco-Ñireco system, located in the reserve of the Nahuel Huapi National Park, however part of the catchment is urbanized, being San Carlos de Bariloche (150,000 inhabitants) placed in the lower part of the basin. Physico-chemical variables were measured and benthic macroinvertebrates were collected during three consecutive years at seven sites from the headwater to the river outlet. Sites near the source of the river were characterised by Plecoptera, Ephemeroptera, Trichoptera and Diptera, whereas sites close to the river mouth were dominated by Diptera, Oligochaeta and Mollusca. Regarding functional feeding groups, collector-gatherers were dominant at all sites and this pattern was consistent among years. Ordination Analysis (RDA) revealed that species assemblages distribution responded to the climatic and topographic gradient (temperature and elevation), but also were associated with variables related to human impact (conductivity, nitrate and phosphate contents). Species assemblages at headwaters were mostly represented by sensitive insects, whereas tolerant taxa such as Tubificidae, Lumbriculidae, Chironomidae and crustacean Aegla sp. were dominant at urbanised sites. Regarding macroinvertebrate metrics employed, total richness, EPT taxa, Shannon diversity index and Biotic Monitoring Patagonian Stream index resulted fairly consistent and evidenced different levels of disturbances at the stream, meaning that this measures are suitable for evaluation of the status of Patagonian mountain streams.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Metrics on diagram groups and uniform embeddings in a Hilbert space

"Vegeu el resum a l'inici del document del fitxer adjunt".

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.

Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds

"Vegeu el resum a l'inici del document del fitxer adjunt."

IQRray, a new method for Affymetrix microarray quality control, and the homologous organ conservation score, a new benchmark method for quality control metrics.

MOTIVATION: Microarray results accumulated in public repositories are widely reused in meta-analytical studies and secondary databases. The quality of the data obtained with this technology varies from experiment to experiment, and an efficient method for quality assessment is necessary to ensure their reliability. RESULTS: The lack of a good benchmark has hampered evaluation of existing methods for quality control. In this study, we propose a new independent quality metric that is based on evolutionary conservation of expression profiles. We show, using 11 large organ-specific datasets, that IQRray, a new quality metrics developed by us, exhibits the highest correlation with this reference metric, among 14 metrics tested. IQRray outperforms other methods in identification of poor quality arrays in datasets composed of arrays from many independent experiments. In contrast, the performance of methods designed for detecting outliers in a single experiment like Normalized Unscaled Standard Error and Relative Log Expression was low because of the inability of these methods to detect datasets containing only low-quality arrays and because the scores cannot be directly compared between experiments. AVAILABILITY AND IMPLEMENTATION: The R implementation of IQRray is available at: ftp://lausanne.isb-sib.ch/pub/databases/Bgee/general/IQRray.R. CONTACT: Marta.Rosikiewicz@unil.ch SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Parallel spinors on pseudo-riemannian spin(q) manifolds

We study simply-connected irreducible non-locally symmetric pseudo-Riemannian Spin(q) manifolds admitting parallel quaternionic spinors.

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

Modified differentials and basic cohomology for Riemannian foliations

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincaré duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.

Index theory for basic Dirac operators on Riemannian foliations

In this paper we prove a formula for the analytic index of a basic Dirac-type operator on a Riemannian foliation, solving a problem that has been open for many years. We also consider more general indices given by twisting the basic Dirac operator by a representation of the orthogonal group. The formula is a sum of integrals over blowups of the strata of the foliation and also involves eta invariants of associated elliptic operators. As a special case, a Gauss-Bonnet formula for the basic Euler characteristic is obtained using two independent proofs.