Explaining legal norm transmission using an epidemiological model : the case of employment drug testing

Dans cette thèse, nous construisons un modèle épidémiologique de la dissémina- tion de normes juridiques. L’objectif est d’expliquer la transmission de normes juridiques américaines régissant les tests de dépistages pour drogues au travail vers le Canada ainsi que la propagation subséquente de ces normes à travers la jurisprudence canadienne. La propagation des normes régissant les tests de dépistages pour drogues au travail sert donc à la fois de point de départ pour une réflexion théorique sur la transmission de normes juridiques et pour une étude de cas empirique. Nous partons de la prémisse que les explications du changement juridique, telles celle de la transplantation et celle de l’harmonisation, sont essentiellement métaphoriques. Ces métaphores explicatives fonctionnent en invitant des comparaisons entre les domaines connus et inconnus. Quand ce processus de comparaison est systématisé, la métaphore devient un modèle. Dans la thèse, nous appliquons cette procédure de systématisation afin de transformer la métaphore de la propagation virale en modèle épidémiologique. Après une revue de la littérature sur les épidémies sociales, nous décrivons les éléments pertinents de la théorie épidémiologique pour, ensuite, les transposer au domaine juridique. Le modèle est alors opérationnalisé en l’appliquant à une base de données composée de la jurisprudence pertinente (n=187). Les résultats soutiennent les hypothèses du modèle. 90 % des décisions qui citent les sources américaines sont infectées selon les critères du modèle, alors que seulement 64 % des décisions qui ne citent pas de sources américaines sont infectées. Cela soutient l’hypothèse d’une épidémie dite de « réservoir commun ». Nous avons également démontré une corrélation positive entre la référence à ces décisions et l’état d’infection! : 87 % des décisions qui citent des décisions qui réfèrent aux sources américaines sont infectées, alors que le taux d’infection parmi la population restante est de seulement 53 %. Les résultats semblables ont été obtenus pour les décisions de troisième génération. Cela soutient l’hypothèse selon laquelle il y a eu propagation à travers la jurisprudence suite aux contacts initiaux avec le réservoir commun. Des corrélations positives ont aussi été démontrées entre l’état d’infection et l’appartenance à l’une ou l’autre de sous-populations particulières qui seraient, par hypothèse, des points d’infection. En conclusion de la thèse, nous avançons que c’est seulement après avoir construit un modèle et d’avoir constaté ses limites que nous pouvons vraiment comprendre le rôle des métaphores et des modèles dans l’explication de phénomènes juridiques.

Factor Analysis of a Large DSGE Model

We study the workings of the factor analysis of high-dimensional data using artificial series generated from a large, multi-sector dynamic stochastic general equilibrium (DSGE) model. The objective is to use the DSGE model as a laboratory that allow us to shed some light on the practical benefits and limitations of using factor analysis techniques on economic data. We explain in what sense the artificial data can be thought of having a factor structure, study the theoretical and finite sample properties of the principal components estimates of the factor space, investigate the substantive reason(s) for the good performance of di¤usion index forecasts, and assess the quality of the factor analysis of highly dissagregated data. In all our exercises, we explain the precise relationship between the factors and the basic macroeconomic shocks postulated by the model.

A new avalanche model for solar flares

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

Estimation of State Space Models and Stochastic Volatility

Ma thèse est composée de trois chapitres reliés à l'estimation des modèles espace-état et volatilité stochastique. Dans le première article, nous développons une procédure de lissage de l'état, avec efficacité computationnelle, dans un modèle espace-état linéaire et gaussien. Nous montrons comment exploiter la structure particulière des modèles espace-état pour tirer les états latents efficacement. Nous analysons l'efficacité computationnelle des méthodes basées sur le filtre de Kalman, l'algorithme facteur de Cholesky et notre nouvelle méthode utilisant le compte d'opérations et d'expériences de calcul. Nous montrons que pour de nombreux cas importants, notre méthode est plus efficace. Les gains sont particulièrement grands pour les cas où la dimension des variables observées est grande ou dans les cas où il faut faire des tirages répétés des états pour les mêmes valeurs de paramètres. Comme application, on considère un modèle multivarié de Poisson avec le temps des intensités variables, lequel est utilisé pour analyser le compte de données des transactions sur les marchés financières. Dans le deuxième chapitre, nous proposons une nouvelle technique pour analyser des modèles multivariés à volatilité stochastique. La méthode proposée est basée sur le tirage efficace de la volatilité de son densité conditionnelle sachant les paramètres et les données. Notre méthodologie s'applique aux modèles avec plusieurs types de dépendance dans la coupe transversale. Nous pouvons modeler des matrices de corrélation conditionnelles variant dans le temps en incorporant des facteurs dans l'équation de rendements, où les facteurs sont des processus de volatilité stochastique indépendants. Nous pouvons incorporer des copules pour permettre la dépendance conditionnelle des rendements sachant la volatilité, permettant avoir différent lois marginaux de Student avec des degrés de liberté spécifiques pour capturer l'hétérogénéité des rendements. On tire la volatilité comme un bloc dans la dimension du temps et un à la fois dans la dimension de la coupe transversale. Nous appliquons la méthode introduite par McCausland (2012) pour obtenir une bonne approximation de la distribution conditionnelle à posteriori de la volatilité d'un rendement sachant les volatilités d'autres rendements, les paramètres et les corrélations dynamiques. Le modèle est évalué en utilisant des données réelles pour dix taux de change. Nous rapportons des résultats pour des modèles univariés de volatilité stochastique et deux modèles multivariés. Dans le troisième chapitre, nous évaluons l'information contribuée par des variations de volatilite réalisée à l'évaluation et prévision de la volatilité quand des prix sont mesurés avec et sans erreur. Nous utilisons de modèles de volatilité stochastique. Nous considérons le point de vue d'un investisseur pour qui la volatilité est une variable latent inconnu et la volatilité réalisée est une quantité d'échantillon qui contient des informations sur lui. Nous employons des méthodes bayésiennes de Monte Carlo par chaîne de Markov pour estimer les modèles, qui permettent la formulation, non seulement des densités a posteriori de la volatilité, mais aussi les densités prédictives de la volatilité future. Nous comparons les prévisions de volatilité et les taux de succès des prévisions qui emploient et n'emploient pas l'information contenue dans la volatilité réalisée. Cette approche se distingue de celles existantes dans la littérature empirique en ce sens que ces dernières se limitent le plus souvent à documenter la capacité de la volatilité réalisée à se prévoir à elle-même. Nous présentons des applications empiriques en utilisant les rendements journaliers des indices et de taux de change. Les différents modèles concurrents sont appliqués à la seconde moitié de 2008, une période marquante dans la récente crise financière.

Patient-specific model of a scoliotic torso for surgical planning

A method for the construction of a patient-specific model of a scoliotic torso for surgical planning via inter- patient registration is presented. Magnetic Resonance Images (MRI) of a generic model are registered to surface topography (TP) and X-ray data of a test patient. A partial model is first obtained via thin-plate spline registration between TP and X-ray data of the test patient. The MRIs from the generic model are then fit into the test patient using articulated model registration between the vertebrae of the generic model’s MRIs in prone position and the test patient’s X-rays in standing position. A non-rigid deformation of the soft tissues is performed using a modified thin-plate spline constrained to maintain bone rigidity and to fit in the space between the vertebrae and the surface of the torso. Results show average Dice values of 0.975 ± 0.012 between the MRIs following inter-patient registration and the surface topography of the test patient, which is comparable to the average value of 0.976 ± 0.009 previously obtained following intra-patient registration. The results also show a significant improvement compared to rigid inter-patient registration. Future work includes validating the method on a larger cohort of patients and incorporating soft tissue stiffness constraints. The method developed can be used to obtain a geometric model of a patient including bone structures, soft tissues and the surface of the torso which can be incorporated in a surgical simulator in order to better predict the outcome of scoliosis surgery, even if MRI data cannot be acquired for the patient.

Statistical model based 3D shape prediction of postoperative trunks for non-invasive scoliosis surgery planning

One of the major concerns of scoliosis patients undergoing surgical treatment is the aesthetic aspect of the surgery outcome. It would be useful to predict the postoperative appearance of the patient trunk in the course of a surgery planning process in order to take into account the expectations of the patient. In this paper, we propose to use least squares support vector regression for the prediction of the postoperative trunk 3D shape after spine surgery for adolescent idiopathic scoliosis. Five dimensionality reduction techniques used in conjunction with the support vector machine are compared. The methods are evaluated in terms of their accuracy, based on the leave-one-out cross-validation performed on a database of 141 cases. The results indicate that the 3D shape predictions using a dimensionality reduction obtained by simultaneous decomposition of the predictors and response variables have the best accuracy.

Studies on Pseudoscalar Meson Bound States and Semileptonic Decays in a Relativistic Potential Model

In this thesis quark-antiquark bound states are considered using a relativistic two-body equation for Dirac particles. The mass spectrum of mesons includes bound states involving two heavy quarks or one heavy and one light quark. In order to analyse these states within a unified formalism, it is desirable to have a two-fermion equation that limits to one body Dirac equation with a static interaction for the light quark when the other particle's mass tends to infinity. A suitable two-body equation has been developed by Mandelzweig and Wallace. This equation is solved in momentum space and is used to describe the complete spectrum of mesons. The potential used in this work contains a short range one-gluon exchange interaction and a long range linear confining and constant potential terms. This model is used to investigate the decay processes of heavy mesons. Semileptonic decays are more tractable since there is no final state interactions between the leptons and hadrons that would otherwise complicate the situation. Studies on B and D meson decays are helpful to understand the nonperturbative strong interactions of heavy mesons, which in turn is useful to extract the details of weak interaction process. Calculation of form factors of these semileptonic decays of pseudo scalar mesons are also presented.

Finite-size scaling analysis of the avalanches in the three-dimensional Gaussian random-field Ising model with metastable dynamics

A numerical study is presented of the third-dimensional Gaussian random-field Ising model at T=0 driven by an external field. Standard synchronous relaxation dynamics is employed to obtain the magnetization versus field hysteresis loops. The focus is on the analysis of the number and size distribution of the magnetization avalanches. They are classified as being nonspanning, one-dimensional-spanning, two-dimensional-spanning, or three-dimensional-spanning depending on whether or not they span the whole lattice in different space directions. Moreover, finite-size scaling analysis enables identification of two different types of nonspanning avalanches (critical and noncritical) and two different types of three-dimensional-spanning avalanches (critical and subcritical), whose numbers increase with L as a power law with different exponents. We conclude by giving a scenario for avalanche behavior in the thermodynamic limit.

Using Neural Network Classifier Support Vector Machine Regression for the prediction of Melting Point of Drug – like compounds

In our study we use a kernel based classification technique, Support Vector Machine Regression for predicting the Melting Point of Drug – like compounds in terms of Topological Descriptors, Topological Charge Indices, Connectivity Indices and 2D Auto Correlations. The Machine Learning model was designed, trained and tested using a dataset of 100 compounds and it was found that an SVMReg model with RBF Kernel could predict the Melting Point with a mean absolute error 15.5854 and Root Mean Squared Error 19.7576

A Trainable Object Detection System: Car Detection in Static Images

This paper describes a general, trainable architecture for object detection that has previously been applied to face and peoplesdetection with a new application to car detection in static images. Our technique is a learning based approach that uses a set of labeled training data from which an implicit model of an object class -- here, cars -- is learned. Instead of pixel representations that may be noisy and therefore not provide a compact representation for learning, our training images are transformed from pixel space to that of Haar wavelets that respond to local, oriented, multiscale intensity differences. These feature vectors are then used to train a support vector machine classifier. The detection of cars in images is an important step in applications such as traffic monitoring, driver assistance systems, and surveillance, among others. We show several examples of car detection on out-of-sample images and show an ROC curve that highlights the performance of our system.

Comparing Support Vector Machines with Gaussian Kernels to Radial Basis Function Classifiers

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

Properties of Support Vector Machines

Support Vector Machines (SVMs) perform pattern recognition between two point classes by finding a decision surface determined by certain points of the training set, termed Support Vectors (SV). This surface, which in some feature space of possibly infinite dimension can be regarded as a hyperplane, is obtained from the solution of a problem of quadratic programming that depends on a regularization parameter. In this paper we study some mathematical properties of support vectors and show that the decision surface can be written as the sum of two orthogonal terms, the first depending only on the margin vectors (which are SVs lying on the margin), the second proportional to the regularization parameter. For almost all values of the parameter, this enables us to predict how the decision surface varies for small parameter changes. In the special but important case of feature space of finite dimension m, we also show that there are at most m+1 margin vectors and observe that m+1 SVs are usually sufficient to fully determine the decision surface. For relatively small m this latter result leads to a consistent reduction of the SV number.

Notes on PCA, Regularization, Sparsity and Support Vector Machines

We derive a new representation for a function as a linear combination of local correlation kernels at optimal sparse locations and discuss its relation to PCA, regularization, sparsity principles and Support Vector Machines. We first review previous results for the approximation of a function from discrete data (Girosi, 1998) in the context of Vapnik"s feature space and dual representation (Vapnik, 1995). We apply them to show 1) that a standard regularization functional with a stabilizer defined in terms of the correlation function induces a regression function in the span of the feature space of classical Principal Components and 2) that there exist a dual representations of the regression function in terms of a regularization network with a kernel equal to a generalized correlation function. We then describe the main observation of the paper: the dual representation in terms of the correlation function can be sparsified using the Support Vector Machines (Vapnik, 1982) technique and this operation is equivalent to sparsify a large dictionary of basis functions adapted to the task, using a variation of Basis Pursuit De-Noising (Chen, Donoho and Saunders, 1995; see also related work by Donahue and Geiger, 1994; Olshausen and Field, 1995; Lewicki and Sejnowski, 1998). In addition to extending the close relations between regularization, Support Vector Machines and sparsity, our work also illuminates and formalizes the LFA concept of Penev and Atick (1996). We discuss the relation between our results, which are about regression, and the different problem of pattern classification.

Categorization in IT and PFC: Model and Experiments

In a recent experiment, Freedman et al. recorded from inferotemporal (IT) and prefrontal cortices (PFC) of monkeys performing a "cat/dog" categorization task (Freedman 2001 and Freedman, Riesenhuber, Poggio, Miller 2001). In this paper we analyze the tuning properties of view-tuned units in our HMAX model of object recognition in cortex (Riesenhuber 1999) using the same paradigm and stimuli as in the experiment. We then compare the simulation results to the monkey inferotemporal neuron population data. We find that view-tuned model IT units that were trained without any explicit category information can show category-related tuning as observed in the experiment. This suggests that the tuning properties of experimental IT neurons might primarily be shaped by bottom-up stimulus-space statistics, with little influence of top-down task-specific information. The population of experimental PFC neurons, on the other hand, shows tuning properties that cannot be explained just by stimulus tuning. These analyses are compatible with a model of object recognition in cortex (Riesenhuber 2000) in which a population of shape-tuned neurons provides a general basis for neurons tuned to different recognition tasks.

Robust Factor Analysis for Compositional Data

Factor analysis as frequent technique for multivariate data inspection is widely used also for compositional data analysis. The usual way is to use a centered logratio (clr) transformation to obtain the random vector y of dimension D. The factor model is then y = Λf + e (1) with the factors f of dimension k < D, the error term e, and the loadings matrix Λ. Using the usual model assumptions (see, e.g., Basilevsky, 1994), the factor analysis model (1) can be written as Cov(y) = ΛΛT + ψ (2) where ψ = Cov(e) has a diagonal form. The diagonal elements of ψ as well as the loadings matrix Λ are estimated from an estimation of Cov(y). Given observed clr transformed data Y as realizations of the random vector y. Outliers or deviations from the idealized model assumptions of factor analysis can severely effect the parameter estimation. As a way out, robust estimation of the covariance matrix of Y will lead to robust estimates of Λ and ψ in (2), see Pison et al. (2003). Well known robust covariance estimators with good statistical properties, like the MCD or the S-estimators (see, e.g. Maronna et al., 2006), rely on a full-rank data matrix Y which is not the case for clr transformed data (see, e.g., Aitchison, 1986). The isometric logratio (ilr) transformation (Egozcue et al., 2003) solves this singularity problem. The data matrix Y is transformed to a matrix Z by using an orthonormal basis of lower dimension. Using the ilr transformed data, a robust covariance matrix C(Z) can be estimated. The result can be back-transformed to the clr space by C(Y ) = V C(Z)V T where the matrix V with orthonormal columns comes from the relation between the clr and the ilr transformation. Now the parameters in the model (2) can be estimated (Basilevsky, 1994) and the results have a direct interpretation since the links to the original variables are still preserved. The above procedure will be applied to data from geochemistry. Our special interest is on comparing the results with those of Reimann et al. (2002) for the Kola project data