STRUCTURE AND BIFURCATION OF PULLBACK ATTRACTORS IN A NON-AUTONOMOUS CHAFEE-INFANTE EQUATION

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, u(t) = u(xx) + lambda(xx) - lambda u beta(t)u(3), and investigate the bifurcations that this attractor undergoes as A is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.

Parametric resonances in a base-excited double pendulum

Two parametrically-induced phenomena are addressed in the context of a double pendulum subject to a vertical base excitation. First, the parametric resonances that cause the stable downward vertical equilibrium to bifurcate into large-amplitude periodic solutions are investigated extensively. Then the stabilization of the unstable upward equilibrium states through the parametric action of the high-frequency base motion is documented in the experiments and in the simulations. It is shown that there is a region in the plane of the excitation frequency and amplitude where all four unstable equilibrium states can be stabilized simultaneously in the double pendulum. The parametric resonances of the two modes of the base-excited double pendulum are studied both theoretically and experimentally. The transition curves (i.e., boundaries of the dynamic instability regions) are constructed asymptotically via the method of multiple scales including higher-order effects. The bifurcations characterizing the transitions from the trivial equilibrium to the periodic solutions are computed by either continuation methods and or by time integration and compared with the theoretical and experimental results.

Correlation between carotid bifurcation calcium burden on non-enhanced CT and percentage stenosis, as confirmed by digital subtraction angiography

Objectives: Previous evidence supports a direct relationship between the calcium burden (volume) on post-contrast CT with the percent internal carotid artery (ICA) stenosis at the carotid bifurcation. We sought to further investigate this relationship by comparing non-enhanced CT (NECT) and digital subtraction angiography (DSA). Methods: 50 patients (aged 41-82 years) were retrospectively identified who had undergone cervical NECT and DSA. A 64-multidetector array CT (MDCT) scanner was utilised and the images reviewed using preset window widths/levels (30/300) optimised to calcium, with the volumes measured via three-dimensional reconstructive software. Stenosis measurements were performed on DSA and luminal diameter stenoses >40% were considered "significant". Volume thresholds of 0.01, 0.03, 0.06, 0.09 and 0.12 cm(3) were utilised and Pearson's correlation coefficient (r) was calculated to correlate the calcium volume with percent stenosis. Results: Of 100 carotid bifurcations, 88 were available and of these 7 were significantly stenotic. The NECT calcium volume moderately correlated with percent stenosis on DSA r=0.53 (p<0.01). A moderate-strong correlation was found between the square root of calcium volume on NECT with percent stenosis on DSA (r=0.60, p<0.01). Via a receiver operating characteristic curve, 0.06 cm(3) was determined to be the best threshold (sensitivity 100%, specificity 90.1%, negative predictive value 100% and positive predictive value 46.7%) for detecting significant stenoses. Conclusion: This preliminary investigation confirms a correlation between carotid bifurcation calcium volume and percent ICA stenosis and is promising for the optimal threshold for stenosis detection. Future studies could utilise calcium volumes to create a "score" that could predict high grade stenosis.

Analysis of nonlinear dynamics of vocal folds using high-speed video observation and biomechanical modeling

Primary voice production occurs in the larynx through vibrational movements carried out by vocal folds. However, many problems can affect this complex system resulting in voice disorders. In this context, time-frequency-shape analysis based on embedding phase space plots and nonlinear dynamics methods have been used to evaluate the vocal fold dynamics during phonation. For this purpose, the present work used high-speed video to record the vocal fold movements of three subjects and extract the glottal area time series using an image segmentation algorithm. This signal is used for an optimization method which combines genetic algorithms and a quasi-Newton method to optimize the parameters of a biomechanical model of vocal folds based on lumped elements (masses, springs and dampers). After optimization, this model is capable of simulating the dynamics of recorded vocal folds and their glottal pulse. Bifurcation diagrams and phase space analysis were used to evaluate the behavior of this deterministic system in different circumstances. The results showed that this methodology can be used to extract some physiological parameters of vocal folds and reproduce some complex behaviors of these structures contributing to the scientific and clinical evaluation of voice production. (C) 2010 Elsevier Inc. All rights reserved.

Bifurcation effects on the plasma edge of tokamaks with ergodic limiter.

In the present paper, we solve a twist symplectic map for the action of an ergodic magnetic limiter in a large aspect-ratio tokamak. In this model, we study the bifurcation scenarios that occur in the remnants regular islands that co-exist with chaotic magnetic surfaces. The onset of atypical local bifurcations created by secondary shearless tori are identified through numerical profiles of internal rotation number and we observe that their rupture can reduce the usual magnetic field line escape at the tokamak plasma edge.

The effects of hypocalcemia on spatial alternans and ventricular fibrillation studied with the optical mapping technique

The heart is a wonderful but complex organ: it uses electrochemical mechanisms in order to produce mechanical energy to pump the blood throughout the body and allow the life of humans and animals. This organ can be subject to several diseases and sudden cardiac death (SCD) is the most catastrophic manifestation of these diseases, responsible for the death of a large number of people throughout the world. It is estimated that 325000 Americans annually die for SCD. SCD most commonly occurs as a result of reentrant tachyarrhythmias (ventricular tachycardia (VT) and ventricular fibrillation (VF)) and the identification of those patients at higher risk for the development of SCD has been a difficult clinical challenge. Nowadays, a particular electrocardiogram (ECG) abnormality, “T-wave alternans” (TWA), is considered a precursor of lethal cardiac arrhythmias and sudden death, a sensitive indicator of risk for SCD. TWA is defined as a beat-to-beat alternation in the shape, amplitude, or timing of the T-wave on the ECG, indicative of the underlying repolarization of cardiac cells [5]. In other words TWA is the macroscopic effect of subcellular and celluar mechanisms involving ionic kinetics and the consequent depolarization and repolarization of the myocytes. Experimental activities have shown that TWA on the ECG is a manifestation of an underlying alternation of long and short action potential durations (APDs), the so called APD-alternans, of cardiac myocytes in the myocardium. Understanding the mechanism of APDs-alternans is the first step for preventing them to occur. In order to investigate these mechanisms it’s very important to understand that the biological systems are complex systems and their macroscopic properties arise from the nonlinear interactions among the parts. The whole is greater than the sum of the parts, and it cannot be understood only by studying the single parts. In this sense the heart is a complex nonlinear system and its way of working follows nonlinear dynamics; alternans also, they are a manifestation of a phenomenon typical in nonlinear dynamical systems, called “period-dubling bifurcation”. Over the past decade, it has been demonstrated that electrical alternans in cardiac tissue is an important marker for the development of ventricular fibrillation and a significant predictor for mortality. It has been observed that acute exposure to low concentration of calcium does not decrease the magnitude of alternans and sustained ventricular Fibrillation (VF) is still easily induced under these condition. However with prolonged exposure to low concentration of calcium, alternans disappears, but VF is still inducible. This work is based on this observation and tries to make it clearer. The aim of this thesis is investigate the effect of hypocalcemia spatial alternans and VF doing experiments with canine hearts and perfusing them with a solution with physiological ionic concentration and with a solution with low calcium concentration (hypocalcemia); in order to investigate the so called memory effect, the experimental activity was modified during the way. The experiments were performed with the optical mapping technique, using voltage-sensitive dye, and a custom made Java code was used in post-processing. Finding the Nolasco and Dahlen’s criterion [8] inadequate for the prediction of alternans, and takin into account the experimental results, another criterion, which consider the memory effect, has been implemented. The implementation of this criterion could be the first step in the creation of a method, AP-based, discriminating who is at risk if developing VF. This work is divided into four chapters: the first is a brief presentation of the physiology of the heart; the second is a review of the major theories and discovers in the study of cardiac dynamics; the third chapter presents an overview on the experimental activity and the optical mapping technique; the forth chapter contains the presentation of the results and the conclusions.

Lamellar body ultrastructure revisited: high-pressure freezing and cryo-electron microscopy of vitreous sections

Lamellar bodies are the storage sites for lung surfactant within type II alveolar epithelial cells. The structure-function models of lamellar bodies are based on microscopic analyses of chemically fixed tissue. Despite available alternative fixation methods that are less prone to artifacts, such as cryofixation by high-pressure freezing, the nature of the lung, being mostly air filled, makes it difficult to take advantage of these improved methods. In this paper, we propose a new approach and show for the first time the ultrastructure of intracellular lamellar bodies based on cryo-electron microscopy of vitreous sections in the range of nanometer resolution. Thus, unspoiled by chemical fixation, dehydration and contrasting agents, a close to native structure is revealed. Our approach uses perfluorocarbon to substitute the air in the alveoli. Lung tissue was subsequently high-pressure frozen, cryosectioned and observed in a cryo-electron microscope. The lamellar bodies clearly show a tight lamellar morphology. The periodicity of these lamellae was 7.3 nm. Lamellar bifurcations were observed in our cryosections. The technical approach described in this paper allows the examination of the native cellular ultrastructure of the surfactant system under near in vivo conditions, and therefore opens up prospectives for scrutinizing various theories of lamellar body biogenesis, exocytosis and recycling.

Electroporation enhances reporter gene expression following delivery of naked plasmid DNA to the lung

BACKGROUND: Existing methods of non-viral airway gene transfer suffer from low levels of efficiency. Electroporation has been used to enhance gene transfer in a range of tissues. Here we assess the usefulness of electroporation for enhancing gene transfer in the lungs of mice and sheep. METHODS: Naked plasmid DNA (pDNA) expressing either luciferase or green fluorescent protein (GFP) was delivered to mouse lungs by instillation. Following surgical visualisation, the lungs were directly electroporated and the level and duration of luciferase activity was assessed and cell types that were positive for GFP were identified in lung cryosections. Naked pDNA was nebulised to the sheep lung and electrodes attached to the tip of a bronchoscope were used to electroporate airway segment bifurcations, Luciferase activity was assessed in electroporated and control non-electroporated regions, after 24 h. RESULTS: Following delivery of naked pDNA to the mouse lung, electroporation resulted in up to 400-fold higher luciferase activity than naked pDNA alone when luciferase was under the control of a cytomegalovirus (CMV) promoter. Following delivery of a plasmid containing the human polyubiquitin C (UbC) promoter, electroporation resulted in elevated luciferase activity for at least 28 days. Visualisation of GFP indicated that electroporation resulted in increased GFP detection compared with non-electroporated controls. In the sheep lung electroporation of defined sites in the airways resulted in luciferase activity 100-fold greater than naked pDNA alone. CONCLUSIONS: These results indicate that electroporation can be used to enhance gene transfer in the lungs of mice and sheep without compromising the duration of expression.

A numerical model for inert gas transport in the lung based on fractal airway morphology

Patients suffering from cystic fibrosis (CF) show thick secretions, mucus plugging and bronchiectasis in bronchial and alveolar ducts. This results in substantial structural changes of the airway morphology and heterogeneous ventilation. Disease progression and treatment effects are monitored by so-called gas washout tests, where the change in concentration of an inert gas is measured over a single or multiple breaths. The result of the tests based on the profile of the measured concentration is a marker for the severity of the ventilation inhomogeneity strongly affected by the airway morphology. However, it is hard to localize underlying obstructions to specific parts of the airways, especially if occurring in the lung periphery. In order to support the analysis of lung function tests (e.g. multi-breath washout), we developed a numerical model of the entire airway tree, coupling a lumped parameter model for the lung ventilation with a 4th-order accurate finite difference model of a 1D advection-diffusion equation for the transport of an inert gas. The boundary conditions for the flow problem comprise the pressure and flow profile at the mouth, which is typically known from clinical washout tests. The natural asymmetry of the lung morphology is approximated by a generic, fractal, asymmetric branching scheme which we applied for the conducting airways. A conducting airway ends when its dimension falls below a predefined limit. A model acinus is then connected to each terminal airway. The morphology of an acinus unit comprises a network of expandable cells. A regional, linear constitutive law describes the pressure-volume relation between the pleural gap and the acinus. The cyclic expansion (breathing) of each acinus unit depends on the resistance of the feeding airway and on the flow resistance and stiffness of the cells themselves. Special care was taken in the development of a conservative numerical scheme for the gas transport across bifurcations, handling spatially and temporally varying advective and diffusive fluxes over a wide range of scales. Implicit time integration was applied to account for the numerical stiffness resulting from the discretized transport equation. Local or regional modification of the airway dimension, resistance or tissue stiffness are introduced to mimic pathological airway restrictions typical for CF. This leads to a more heterogeneous ventilation of the model lung. As a result the concentration in some distal parts of the lung model remains increased for a longer duration. The inert gas concentration at the mouth towards the end of the expirations is composed of gas from regions with very different washout efficiency. This results in a steeper slope of the corresponding part of the washout profile.

Automatic generation of models for abdominal aortic aneurysms and intraluminal thrombus based on hexahedral meshes

To propose an automated patient-specific algorithm for the creation of accurate and smooth meshes of the aortic anatomy, to be used for evaluating rupture risk factors of abdominal aortic aneurysms (AAA). Finite element (FE) analyses and simulations require meshes to be smooth and anatomically accurate, capturing both the artery wall and the intraluminal thrombus (ILT). The two main difficulties are the modeling of the arterial bifurcations, and of the ILT, which has an arbitrary shape that is conforming to the aortic wall.

Damping models in the truncated derivative nonlinear Schrödinger equation

Four-dimensional flow in the phase space of three amplitudes of circularly polarized Alfven waves and one relative phase, resulting from a resonant three-wave truncation of the derivative nonlinear Schrödinger equation, has been analyzed; wave 1 is linearly unstable with growth rate , and waves 2 and 3 are stable with damping 2 and 3, respectively. The dependence of gross dynamical features on the damping model as characterized by the relation between damping and wave-vector ratios, 2 /3, k2 /k3, and the polarization of the waves, is discussed; two damping models, Landau k and resistive k2, are studied in depth. Very complex dynamics, such as multiple blue sky catastrophes and chaotic attractors arising from Feigenbaum sequences, and explosive bifurcations involving Intermittency-I chaos, are shown to be associated with the existence and loss of stability of certain fixed point P of the flow. Independently of the damping model, P may only exist as against flow contraction just requiring.In the case of right-hand RH polarization, point P may exist for all models other than Landau damping; for the resistive model, P may exist for RH polarization only if 2+3/2.

Contributions to Bayesian network learning with applications to neuroscience

Neuronal morphology is a key feature in the study of brain circuits, as it is highly related to information processing and functional identification. Neuronal morphology affects the process of integration of inputs from other neurons and determines the neurons which receive the output of the neurons. Different parts of the neurons can operate semi-independently according to the spatial location of the synaptic connections. As a result, there is considerable interest in the analysis of the microanatomy of nervous cells since it constitutes an excellent tool for better understanding cortical function. However, the morphologies, molecular features and electrophysiological properties of neuronal cells are extremely variable. Except for some special cases, this variability makes it hard to find a set of features that unambiguously define a neuronal type. In addition, there are distinct types of neurons in particular regions of the brain. This morphological variability makes the analysis and modeling of neuronal morphology a challenge. Uncertainty is a key feature in many complex real-world problems. Probability theory provides a framework for modeling and reasoning with uncertainty. Probabilistic graphical models combine statistical theory and graph theory to provide a tool for managing domains with uncertainty. In particular, we focus on Bayesian networks, the most commonly used probabilistic graphical model. In this dissertation, we design new methods for learning Bayesian networks and apply them to the problem of modeling and analyzing morphological data from neurons. The morphology of a neuron can be quantified using a number of measurements, e.g., the length of the dendrites and the axon, the number of bifurcations, the direction of the dendrites and the axon, etc. These measurements can be modeled as discrete or continuous data. The continuous data can be linear (e.g., the length or the width of a dendrite) or directional (e.g., the direction of the axon). These data may follow complex probability distributions and may not fit any known parametric distribution. Modeling this kind of problems using hybrid Bayesian networks with discrete, linear and directional variables poses a number of challenges regarding learning from data, inference, etc. In this dissertation, we propose a method for modeling and simulating basal dendritic trees from pyramidal neurons using Bayesian networks to capture the interactions between the variables in the problem domain. A complete set of variables is measured from the dendrites, and a learning algorithm is applied to find the structure and estimate the parameters of the probability distributions included in the Bayesian networks. Then, a simulation algorithm is used to build the virtual dendrites by sampling values from the Bayesian networks, and a thorough evaluation is performed to show the model’s ability to generate realistic dendrites. In this first approach, the variables are discretized so that discrete Bayesian networks can be learned and simulated. Then, we address the problem of learning hybrid Bayesian networks with different kinds of variables. Mixtures of polynomials have been proposed as a way of representing probability densities in hybrid Bayesian networks. We present a method for learning mixtures of polynomials approximations of one-dimensional, multidimensional and conditional probability densities from data. The method is based on basis spline interpolation, where a density is approximated as a linear combination of basis splines. The proposed algorithms are evaluated using artificial datasets. We also use the proposed methods as a non-parametric density estimation technique in Bayesian network classifiers. Next, we address the problem of including directional data in Bayesian networks. These data have some special properties that rule out the use of classical statistics. Therefore, different distributions and statistics, such as the univariate von Mises and the multivariate von Mises–Fisher distributions, should be used to deal with this kind of information. In particular, we extend the naive Bayes classifier to the case where the conditional probability distributions of the predictive variables given the class follow either of these distributions. We consider the simple scenario, where only directional predictive variables are used, and the hybrid case, where discrete, Gaussian and directional distributions are mixed. The classifier decision functions and their decision surfaces are studied at length. Artificial examples are used to illustrate the behavior of the classifiers. The proposed classifiers are empirically evaluated over real datasets. We also study the problem of interneuron classification. An extensive group of experts is asked to classify a set of neurons according to their most prominent anatomical features. A web application is developed to retrieve the experts’ classifications. We compute agreement measures to analyze the consensus between the experts when classifying the neurons. Using Bayesian networks and clustering algorithms on the resulting data, we investigate the suitability of the anatomical terms and neuron types commonly used in the literature. Additionally, we apply supervised learning approaches to automatically classify interneurons using the values of their morphological measurements. Then, a methodology for building a model which captures the opinions of all the experts is presented. First, one Bayesian network is learned for each expert, and we propose an algorithm for clustering Bayesian networks corresponding to experts with similar behaviors. Then, a Bayesian network which represents the opinions of each group of experts is induced. Finally, a consensus Bayesian multinet which models the opinions of the whole group of experts is built. A thorough analysis of the consensus model identifies different behaviors between the experts when classifying the interneurons in the experiment. A set of characterizing morphological traits for the neuronal types can be defined by performing inference in the Bayesian multinet. These findings are used to validate the model and to gain some insights into neuron morphology. Finally, we study a classification problem where the true class label of the training instances is not known. Instead, a set of class labels is available for each instance. This is inspired by the neuron classification problem, where a group of experts is asked to individually provide a class label for each instance. We propose a novel approach for learning Bayesian networks using count vectors which represent the number of experts who selected each class label for each instance. These Bayesian networks are evaluated using artificial datasets from supervised learning problems. Resumen La morfología neuronal es una característica clave en el estudio de los circuitos cerebrales, ya que está altamente relacionada con el procesado de información y con los roles funcionales. La morfología neuronal afecta al proceso de integración de las señales de entrada y determina las neuronas que reciben las salidas de otras neuronas. Las diferentes partes de la neurona pueden operar de forma semi-independiente de acuerdo a la localización espacial de las conexiones sinápticas. Por tanto, existe un interés considerable en el análisis de la microanatomía de las células nerviosas, ya que constituye una excelente herramienta para comprender mejor el funcionamiento de la corteza cerebral. Sin embargo, las propiedades morfológicas, moleculares y electrofisiológicas de las células neuronales son extremadamente variables. Excepto en algunos casos especiales, esta variabilidad morfológica dificulta la definición de un conjunto de características que distingan claramente un tipo neuronal. Además, existen diferentes tipos de neuronas en regiones particulares del cerebro. La variabilidad neuronal hace que el análisis y el modelado de la morfología neuronal sean un importante reto científico. La incertidumbre es una propiedad clave en muchos problemas reales. La teoría de la probabilidad proporciona un marco para modelar y razonar bajo incertidumbre. Los modelos gráficos probabilísticos combinan la teoría estadística y la teoría de grafos con el objetivo de proporcionar una herramienta con la que trabajar bajo incertidumbre. En particular, nos centraremos en las redes bayesianas, el modelo más utilizado dentro de los modelos gráficos probabilísticos. En esta tesis hemos diseñado nuevos métodos para aprender redes bayesianas, inspirados por y aplicados al problema del modelado y análisis de datos morfológicos de neuronas. La morfología de una neurona puede ser cuantificada usando una serie de medidas, por ejemplo, la longitud de las dendritas y el axón, el número de bifurcaciones, la dirección de las dendritas y el axón, etc. Estas medidas pueden ser modeladas como datos continuos o discretos. A su vez, los datos continuos pueden ser lineales (por ejemplo, la longitud o la anchura de una dendrita) o direccionales (por ejemplo, la dirección del axón). Estos datos pueden llegar a seguir distribuciones de probabilidad muy complejas y pueden no ajustarse a ninguna distribución paramétrica conocida. El modelado de este tipo de problemas con redes bayesianas híbridas incluyendo variables discretas, lineales y direccionales presenta una serie de retos en relación al aprendizaje a partir de datos, la inferencia, etc. En esta tesis se propone un método para modelar y simular árboles dendríticos basales de neuronas piramidales usando redes bayesianas para capturar las interacciones entre las variables del problema. Para ello, se mide un amplio conjunto de variables de las dendritas y se aplica un algoritmo de aprendizaje con el que se aprende la estructura y se estiman los parámetros de las distribuciones de probabilidad que constituyen las redes bayesianas. Después, se usa un algoritmo de simulación para construir dendritas virtuales mediante el muestreo de valores de las redes bayesianas. Finalmente, se lleva a cabo una profunda evaluaci ón para verificar la capacidad del modelo a la hora de generar dendritas realistas. En esta primera aproximación, las variables fueron discretizadas para poder aprender y muestrear las redes bayesianas. A continuación, se aborda el problema del aprendizaje de redes bayesianas con diferentes tipos de variables. Las mixturas de polinomios constituyen un método para representar densidades de probabilidad en redes bayesianas híbridas. Presentamos un método para aprender aproximaciones de densidades unidimensionales, multidimensionales y condicionales a partir de datos utilizando mixturas de polinomios. El método se basa en interpolación con splines, que aproxima una densidad como una combinación lineal de splines. Los algoritmos propuestos se evalúan utilizando bases de datos artificiales. Además, las mixturas de polinomios son utilizadas como un método no paramétrico de estimación de densidades para clasificadores basados en redes bayesianas. Después, se estudia el problema de incluir información direccional en redes bayesianas. Este tipo de datos presenta una serie de características especiales que impiden el uso de las técnicas estadísticas clásicas. Por ello, para manejar este tipo de información se deben usar estadísticos y distribuciones de probabilidad específicos, como la distribución univariante von Mises y la distribución multivariante von Mises–Fisher. En concreto, en esta tesis extendemos el clasificador naive Bayes al caso en el que las distribuciones de probabilidad condicionada de las variables predictoras dada la clase siguen alguna de estas distribuciones. Se estudia el caso base, en el que sólo se utilizan variables direccionales, y el caso híbrido, en el que variables discretas, lineales y direccionales aparecen mezcladas. También se estudian los clasificadores desde un punto de vista teórico, derivando sus funciones de decisión y las superficies de decisión asociadas. El comportamiento de los clasificadores se ilustra utilizando bases de datos artificiales. Además, los clasificadores son evaluados empíricamente utilizando bases de datos reales. También se estudia el problema de la clasificación de interneuronas. Desarrollamos una aplicación web que permite a un grupo de expertos clasificar un conjunto de neuronas de acuerdo a sus características morfológicas más destacadas. Se utilizan medidas de concordancia para analizar el consenso entre los expertos a la hora de clasificar las neuronas. Se investiga la idoneidad de los términos anatómicos y de los tipos neuronales utilizados frecuentemente en la literatura a través del análisis de redes bayesianas y la aplicación de algoritmos de clustering. Además, se aplican técnicas de aprendizaje supervisado con el objetivo de clasificar de forma automática las interneuronas a partir de sus valores morfológicos. A continuación, se presenta una metodología para construir un modelo que captura las opiniones de todos los expertos. Primero, se genera una red bayesiana para cada experto y se propone un algoritmo para agrupar las redes bayesianas que se corresponden con expertos con comportamientos similares. Después, se induce una red bayesiana que modela la opinión de cada grupo de expertos. Por último, se construye una multired bayesiana que modela las opiniones del conjunto completo de expertos. El análisis del modelo consensuado permite identificar diferentes comportamientos entre los expertos a la hora de clasificar las neuronas. Además, permite extraer un conjunto de características morfológicas relevantes para cada uno de los tipos neuronales mediante inferencia con la multired bayesiana. Estos descubrimientos se utilizan para validar el modelo y constituyen información relevante acerca de la morfología neuronal. Por último, se estudia un problema de clasificación en el que la etiqueta de clase de los datos de entrenamiento es incierta. En cambio, disponemos de un conjunto de etiquetas para cada instancia. Este problema está inspirado en el problema de la clasificación de neuronas, en el que un grupo de expertos proporciona una etiqueta de clase para cada instancia de manera individual. Se propone un método para aprender redes bayesianas utilizando vectores de cuentas, que representan el número de expertos que seleccionan cada etiqueta de clase para cada instancia. Estas redes bayesianas se evalúan utilizando bases de datos artificiales de problemas de aprendizaje supervisado.

Analytical Calculation of Stall-inception and Surge Points for an Axial-flow Compresor Rotor

Recently, a theoretical criterion to calculate the stability of an axial-flow compressor rotor has been presented in the scientific literature. This theoretical criterion was used for determining the locus of the stability line over the rotor map and for predicting the post-stall evolution of the constant-speed line of a rotor. The main objective of this paper is to improve the predictions of such a model. To do that, the paper proposes a different characterization of the characteristic azimuthal length and a calculation of the ratio of specific heats based on a polytropic exponent. Thanks to these new values, the model predicts two bifurcation points in the behaviour of the flow: the inception point of the instability and the surge point. Experimental data from a pure axial compressor are used to validate the model showing that the prediction of the flow coefficient at the surge point has an error inferior to 5%. For the rotor studied, the paper provides a quantitative and qualitative description of the inception of the instability and of the mechanism involved in the instable region of the compressor map. The paper also discusses the role of rotor efficiency in the position of the bifurcations and gives a sensitivity analysis of its position. Finally, it presents a discussion about how the model can explain the different behaviours exhibited by the same rotor when the flow coefficient is reduced

Long wave theory for experimental devices with compressed/expanded surfactant monolayers

Surfactant monolayers are of interest in a variety of phenomena, including thin film dynamics and the formation and dynamics of foams. Measurement of surface properties has received a continuous attention and requires good theoretical models to extract the relevant physico- chemical information from experimental data. A common experimental set up consists in a shallow liquid layer whose free surface is slowly com- pressed/expanded in periodic fashion by moving two slightly immersed solid barriers, which varies the free surface area and thus the surfactant concentration. The simplest theory ignores the fluid dynamics in the bulk fluid, assuming spatially uniform surfactant concentration, which requires quite small forcing frequencies and provides reversible dynamics in the compression/expansion cycles. Sometimes, it is not clear whether depar- ture from reversibility is due to non-equilibrium effects or to the ignored fluid dynamics. Here we present a long wave theory that takes the fluid dynamics and the symmetries of the problem into account. In particular, the validity of the spatially-uniform-surfactant-concentration assumption is established and a nonlinear diffusion equation is derived. This allows for calculating spatially nonuniform monolayer dynamics and uncovering the physical mechanisms involved in the surfactant behavior. Also, this analysis can be considered a good means for extracting more relevant information from each experimental run.

Estudio de la dinámica no lineal de vórtices magnéticos en nanodots

En el presente trabajo se ha realizado un estudio sobre el comportamiento dinámico de vórtices magnéticos en su aplicación en osciladores de espín-torque. A partir de los modelos matemáticos elaborados en [4] sobre estos osciladores de espín-torque, se han simulado y estudiado usando MATLAB, entre otras herramientas, para tratar de verificar su concordancia con el comportamiento físico observado en el laboratorio. Es importante señalar que el estudio tiene en cuenta la dinámica no lineal, esencial para describir correctamente un sistema oscilante en la práctica. El análisis matemático del sistema que describe la órbita del núcleo de un vórtice magnético sometido a la acción de un campo magnético externo oscilatorio, muestra la posibilidad de la existencia de hasta tres soluciones especiales, según la geometría del dot y el valor del campo magnético de excitación, tanto de su frecuencia como de su amplitud. Estas soluciones corresponden a estados estacionarios del vórtice caracterizados como una órbita circular, aunque en el caso de existir tres equilibrios uno de ellos es inestable. El modelo matemático ha sido estudiado y analizado para reproducir los resultados obtenidos en [4] y adicionalmente se ha implementado el caso de la energía potencial del vórtice con el término no lineal distinto de [4] (con una constante β negativa). Los resultados obtenidos bajo esta suposición muestran una cierta disparidad respecto al caso de β positiva y reflejan la existencia de comportamientos muy diferentes. En la dinámica del vórtice bajo la suposición de β negativa también surgen bifurcaciones de pliegue (fold-over) en la trayectoria del núcleo del vórtice: siempre se obtienen tres equilibrios a bajas frecuencias y aparecen a veces dos intervalos con tres equilibrios en lugar de uno solo, a diferencia del caso de β positiva. El comportamiento del núcleo del vórtice sigue un proceso de histéresis en ambos casos, cuando se dan ciertas condiciones. ABSTRACT. This work is a study about the dynamic behaviour of magnetic vortex in its application in spin-torque oscillators. Starting from mathematical models developed in [4] on this subject, a further analysis has been performed using MATLAB to simulate the behaviour of vortex-based spin-torque oscillators as different relevant parameters vary. The main aim of the study is to check if the obtained results can explain the observed physical behaviour, and an important observation is that fully nonlinear effects are taken into consideration. The mathematical analysis of the system that describes the orbit of the vortex core under the influence of an external oscillatory magnetic field shows that there are up to three possible special solutions depending on the dot geometry and the magnetic driving field value, both on its amplitude as well as its frequency. These solutions correspond to a stable circular orbit of the vortex core, but when the system has three solutions one of them is unstable. This mathematical model has been analyzed and studied to reproduce the results obtained in [4] and, additionally, the effect of a negative value of the nonlinear part of the vortex potential (constant β). Results derived from this assumption exhibit certain differences with respect to the case of a positive constant (β) and reflect the existence of very different patterns. Vortex dynamics under the supposition of a negative β also yield fold-over bifurcations in the trajectory of the vortex core: there are always three solutions at low frequencies and there may be two different intervals with three solutions as opposed to the case of positive β. The vortex core follows a hysteresis process in both cases, when certain conditions are met.