Using self organizing maps on compositional data

Self-organizing maps (Kohonen 1997) is a type of artificial neural network developed to explore patterns in high-dimensional multivariate data. The conventional version of the algorithm involves the use of Euclidean metric in the process of adaptation of the model vectors, thus rendering in theory a whole methodology incompatible with non-Euclidean geometries. In this contribution we explore the two main aspects of the problem: 1. Whether the conventional approach using Euclidean metric can shed valid results with compositional data. 2. If a modification of the conventional approach replacing vectorial sum and scalar multiplication by the canonical operators in the simplex (i.e. perturbation and powering) can converge to an adequate solution. Preliminary tests showed that both methodologies can be used on compositional data. However, the modified version of the algorithm performs poorer than the conventional version, in particular, when the data is pathological. Moreover, the conventional ap- proach converges faster to a solution, when data is \well-behaved". Key words: Self Organizing Map; Artificial Neural networks; Compositional data

A eletrodinâmica escalar generalizada de Duffin-Kemmer-Petiau, uma análise funcional de sua dinâmica quântica covariante e o equilíbrio termodinâmico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Materno-fetal nutrient transfer across primary human trophoblast layer.

MATERNO-FETAL NUTRIENT TRANSFER ACROSS PRIMARY HUMAN TROPHOBLAST MONOLAYER Objectives: Polarized trophoblasts represent the transport and metabolic barrier between the maternal and fetal circulation. Currently human placental nutrient transfer in vitro is mainly investigated unidirectionallyon cultured primary trophoblasts, or bidirectionally on the Transwell® system using BeWo cells treated with forskolin. As forskolin can induce various gene alterations (e.g. cAMP response element genes), we aimed to establish a physiological primary trophoblast model for materno-fetal nutrient exchange studies without forskolin application. Methods: Human term cytotrophoblasts were isolated by enzymatic digestion and Percoll® gradient separation. The purity of the primary cells was assessed by flow cytometry using the trophoblast-specific marker cytokeratin-7. After screening different coating matrices, we optimized the growth conditions for the primary cytotrophoblasts on Transwell/ inserts. The morphology of 5 days cultured trophoblasts was determined by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Membrane makers were visualized using confocal microscopy. Additionally transport studies were performed on the polarized trophoblasts in the Transwell® system. Results: During 5 days culture, the trophoblasts (>90% purity) developed a modest trans-epithelial electrical resistance (TEER) and a sizedependent apparent permeability coefficient (Papp) to fluorescently labeled compounds (MW ~400-70’000D). SEM analyses confirmed a confluent trophoblast layer with numerous microvilli at day six, and TEM revealed a monolayer with tight junctions. Immunocytochemistry on the confluent trophoblasts showed positivity for the cell-cell adhesion molecule E-cadherin, the tight junction protein ZO-1, and the membrane proteins ABCA1 and Na+/K+-ATPase. Vectorial glucose and cholesterol transport studies confirmed functionality of the cultured trophoblast barrier. Conclusion: Evidence from cell morphology, biophysical parameters and cell marker expressions indicate the successful and reproducible establishment of a primary trophoblast monolayer model suitable for transport studies. Application of this model to pathological trophoblasts will help to better understand the mechanism underlying gestational diseases, and to define the consequences of placental pathology on materno-fetal nutrient transport.

Electromagnetic theory.

Date of first publication of each article is given.

Probabilistic topographic information visualisation

The focus of this thesis is the extension of topographic visualisation mappings to allow for the incorporation of uncertainty. Few visualisation algorithms in the literature are capable of mapping uncertain data with fewer able to represent observation uncertainties in visualisations. As such, modifications are made to NeuroScale, Locally Linear Embedding, Isomap and Laplacian Eigenmaps to incorporate uncertainty in the observation and visualisation spaces. The proposed mappings are then called Normally-distributed NeuroScale (N-NS), T-distributed NeuroScale (T-NS), Probabilistic LLE (PLLE), Probabilistic Isomap (PIso) and Probabilistic Weighted Neighbourhood Mapping (PWNM). These algorithms generate a probabilistic visualisation space with each latent visualised point transformed to a multivariate Gaussian or T-distribution, using a feed-forward RBF network. Two types of uncertainty are then characterised dependent on the data and mapping procedure. Data dependent uncertainty is the inherent observation uncertainty. Whereas, mapping uncertainty is defined by the Fisher Information of a visualised distribution. This indicates how well the data has been interpolated, offering a level of ‘surprise’ for each observation. These new probabilistic mappings are tested on three datasets of vectorial observations and three datasets of real world time series observations for anomaly detection. In order to visualise the time series data, a method for analysing observed signals and noise distributions, Residual Modelling, is introduced. The performance of the new algorithms on the tested datasets is compared qualitatively with the latent space generated by the Gaussian Process Latent Variable Model (GPLVM). A quantitative comparison using existing evaluation measures from the literature allows performance of each mapping function to be compared. Finally, the mapping uncertainty measure is combined with NeuroScale to build a deep learning classifier, the Cascading RBF. This new structure is tested on the MNist dataset achieving world record performance whilst avoiding the flaws seen in other Deep Learning Machines.

A mathematical model for the maneuvering simulation of a propelled SPAR vessel

To predict the maneuvering performance of a propelled SPAR vessel, a mathematical model was established as a path simulator. A system-based mathematical model was chosen as it offers advantages in cost and time over full Computational Fluid Dynamics (CFD) simulations. The model is intended to provide a means of optimizing the maneuvering performance of this new vessel type. In this study the hydrodynamic forces and control forces are investigated as individual components, combined in a vectorial setting, and transferred to a body-fixed basis. SPAR vessels are known to be very sensitive to large amplitude motions during maneuvers due to the relatively small hydrostatic restoring forces. Previous model tests of SPAR vessels have shown significant roll and pitch amplitudes, especially during course change maneuvers. Thus, a full 6 DOF equation of motion was employed in the current numerical model. The mathematical model employed in this study was a combination of the model introduced by the Maneuvering Modeling Group (MMG) and the Abkowitz (1964) model. The new model represents the forces applied to the ship hull, the propeller forces and the rudder forces independently, as proposed by the MMG, but uses a 6DOF equation of motion introduced by Abkowitz to describe the motion of a maneuvering ship. The mathematical model was used to simulate the trajectory and motions of the propelled SPAR vessel in 10˚/10˚, 20˚/20˚ and 30˚/30˚ standard zig-zag maneuvers, as well as turning circle tests at rudder angles of 20˚ and 30˚. The simulation results were used to determine the maneuverability parameters (e.g. advance, transfer and tactical diameter) of the vessel. The final model provides the means of predicting and assessing the performance of the vessel type and can be easily adapted to specific vessel configurations based on the generic SPAR-type vessel used in this study.

The average mixing matrix signature

Laplacian-based descriptors, such as the Heat Kernel Signature and the Wave Kernel Signature, allow one to embed the vertices of a graph onto a vectorial space, and have been successfully used to find the optimal matching between a pair of input graphs. While the HKS uses a heat di↵usion process to probe the local structure of a graph, the WKS attempts to do the same through wave propagation. In this paper, we propose an alternative structural descriptor that is based on continuoustime quantum walks. More specifically, we characterise the structure of a graph using its average mixing matrix. The average mixing matrix is a doubly-stochastic matrix that encodes the time-averaged behaviour of a continuous-time quantum walk on the graph. We propose to use the rows of the average mixing matrix for increasing stopping times to develop a novel signature, the Average Mixing Matrix Signature (AMMS). We perform an extensive range of experiments and we show that the proposed signature is robust under structural perturbations of the original graphs and it outperforms both the HKS and WKS when used as a node descriptor in a graph matching task.

Attainment of O/W emulsions containing liquid crystal from annatto oil (Bixa orellana), coffee oil, and tea tree oil (Melaleuca alternifolia) as oily phase using HLB system and ternary phase diagram

Emulsions containing liquid crystals present interesting properties and advantages such as the skin moisturize increase, active release modulation, and emulsion stabilization. In this work, emulsions containing annatto, coffee and tea tree oils, and nonionic surfactants were developed. The HLB method was used for selection of surfactants. The required HLB value was established (9.0). Liquid crystals were attained when used the surfactant mixture Ceteareth-5 and Steareth-2 and identified as lamellar. The emulsions showed pseudoplastic behavior and tixotropy. The ternary diagram was useful in the selection of the proportion of surfactant and oily phase considering skin compatibility and liquid crystal presence.

Phase diagram for a class of spin-1/2 Heisenberg models interpolating between the square-lattice, the triangular-lattice, and the linear-chain limits

We study the spin-1/2 Heisenberg models on an anisotropic two-dimensional lattice which interpolates between the square lattice at one end, a set of decoupled spin chains on the other end, and the triangular-lattice Heisenberg model in between. By series expansions around two different dimer ground states and around various commensurate and incommensurate magnetically ordered states, we establish the phase diagram for this model of a frustrated antiferromagnet. We find a particularly rich phase diagram due to the interplay of magnetic frustration, quantum fluctuations, and varying dimensionality. There is a large region of the usual two-sublattice Neel phase, a three-sublattice phase for the triangular-lattice model, a region of incommensurate magnetic order around the triangular-lattice model, and regions in parameter space where there is no magnetic order. We find that the incommensurate ordering wave vector is in general altered from its classical value by quantum fluctuations. The regime of weakly coupled chains is particularly interesting and appears to be nearly critical. [S0163-1829(99)10421-1].

High-pressure phase diagram of the drug mitotane in compressed and/or supercritical CO(2)

This work provides experimental phase diagram of mitotane, a drug used in the chemotherapy treatment of adrenocortical carcinoma, in compressed and/or supercritical CO(2). The synthetic-static method in a high-pressure variable-volume view cell coupled with a transmitted-light intensity probe was used to measure the solid-fluid (SF) equilibrium data. The phase equilibrium experiments were determined in temperature ranging from (298.2 to 333.1) K and pressure up to 22 MPa. Peng-Robinson equation of state (PR-EoS) with classical mixing rule was used to correlate the experimental data. Excellent agreement was found between experimental and calculated values. (C) 2009 Elsevier Ltd. All rights reserved.

Variation of the physicochemical and morphological characteristics of solvent casted poly(vinylidene fluoride) along its binary phase diagram with dimethylformamide

Poly(vinylidene fluoride), PVDF, films and membranes were prepared by solvent casting from dimethylformamide, DMF, by systematically varying polymer/solvent ratio and solvent evaporation temperature. The effect of the processing conditions on the morphology, degree of porosity, mechanical and thermal properties and crystalline phase of the polymer were evaluated. The obtained microstructure is explained by the Flory-Huggins theory. For the binary system, the porous membrane formation is attributed to a spinodal decomposition of the liquid-liquid phase separation. The morphological features were simulated through the correlation between the Gibbs total free energy and the Flory-Huggins theory. This correlation allowed the calculation of the PVDF/DMF phase diagram and the evolution of the microstructure in different regions of the phase diagram. Varying preparation conditions allow tailoring polymer 2 microstructure while maintaining a high degree of crystallinity and a large β crystalline phase content. Further, the membranes show adequate mechanical properties for applications in filtration or battery separator membranes.

Tailoring poly(vinylidene fluoride-co-chlorotrifluoroethylene) microstructure and physicochemical properties by exploring its binary phase diagram with dimethylformamide

Poly(vinylidene fluoride-co-chlorotrifluoroethylene), PVDF-CTFE, membranes were prepared by solven casting from dimethylformamide, DMF. The preparation conditions involved a systematic variation of polymer/solvent ratio and solvent evaporation temperature. The microstructural variations of the PVDF-CTFE membranes depend on the different regions of the PVDF-CTFE/DMF phase diagram, explained by the Flory-Huggins theory. The effect of the polymer/solvent ratio and solvent evaporation temperature on the morphology, degree of porosity, β-phase content, degree of crystallinity, mechanical, dielectric and piezoelectric properties of the PVDF-CTFE polymer were evaluated. In this binary system, the porous microstructure is attributed to a spinodal decomposition of the liquid-liquid phase separation. For a given polymer/solvent ratio, 20 wt%, and higher evaporation solvent temperature, the β-phase content is around 82% and the piezoelectric coefficient, d33, is - 4 pC/N.

Metrics on diagram groups and uniform embeddings in a Hilbert space

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

Stationary states and phase diagram for a model of the Gunn effect under realistic boundary conditions

A general formulation of boundary conditions for semiconductor-metal contacts follows from a phenomenological procedure sketched here. The resulting boundary conditions, which incorporate only physically well-defined parameters, are used to study the classical unipolar drift-diffusion model for the Gunn effect. The analysis of its stationary solutions reveals the presence of bistability and hysteresis for a certain range of contact parameters. Several types of Gunn effect are predicted to occur in the model, when no stable stationary solution exists, depending on the value of the parameters of the injecting contact appearing in the boundary condition. In this way, the critical role played by contacts in the Gunn effect is clearly established.