Interaction patterns of brain activity across space, time and frequency. Part I: methods

We consider exploratory methods for the discovery of cortical functional connectivity. Typically, data for the i-th subject (i=1...NS) is represented as an NVxNT matrix Xi, corresponding to brain activity sampled at NT moments in time from NV cortical voxels. A widely used method of analysis first concatenates all subjects along the temporal dimension, and then performs an independent component analysis (ICA) for estimating the common cortical patterns of functional connectivity. There exist many other interesting variations of this technique, as reviewed in [Calhoun et al. 2009 Neuroimage 45: S163-172]. We present methods for the more general problem of discovering functional connectivity occurring at all possible time lags. For this purpose, brain activity is viewed as a function of space and time, which allows the use of the relatively new techniques of functional data analysis [Ramsay & Silverman 2005: Functional data analysis. New York: Springer]. In essence, our method first vectorizes the data from each subject, which constitutes the natural discrete representation of a function of several variables, followed by concatenation of all subjects. The singular value decomposition (SVD), as well as the ICA of this new matrix of dimension [rows=(NT*NV); columns=NS] will reveal spatio-temporal patterns of connectivity. As a further example, in the case of EEG neuroimaging, Xi of size NVxNW may represent spectral density for electric neuronal activity at NW discrete frequencies from NV cortical voxels, from the i-th EEG epoch. In this case our functional data analysis approach would reveal coupling of brain regions at possibly different frequencies.Comment: Technical report 2011-March-15, The KEY Institute for Brain-Mind Research Zurich, KMU Osak

Family violence and practices of the legal practitioners of criminal law: analysis of five cases of Santa Rosa, Argentina

El artículo analiza la vinculación entre derecho penal y violencia familiar y procura describir yexplicar cómo funciona el discurso jurídico y cómo influyen las prácticas judiciales en la aplicaciónde las leyes de violencia de género    The article analyzes the link between criminal law and family violence by describing how legaldiscourses influence the legal practices in the enforcement of gender violence.  

Group Lasso estimation of high-dimensional covariance matrices

In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the process has a sparse representation in a large dictionary of basis functions. Using a matrix regression model, we propose a new methodology for high-dimensional covariance matrix estimation based on empirical contrast regularization by a group Lasso penalty. Using such a penalty, the method selects a sparse set of basis functions in the dictionary used to approximate the process, leading to an approximation of the covariance matrix into a low dimensional space. Consistency of the estimator is studied in Frobenius and operator norms and an application to sparse PCA is proposed

Nonparametric estimation of covariance functions by model selection

We propose a model selection approach for covariance estimation of a multi-dimensional stochastic process. Under very general assumptions, observing i.i.d replications of the process at fixed observation points, we construct an estimator of the covariance function by expanding the process onto a collection of basis functions. We study the non asymptotic property of this estimate and give a tractable way of selecting the best estimator among a possible set of candidates. The optimality of the procedure is proved via an oracle inequality which warrants that the best model is selected

Adaptive estimation of spectral densities via wavelet thresholding and information projection

In this paper, we study the problem of adaptive estimation of the spectral density of a stationary Gaussian process. For this purpose, we consider a wavelet-based method which combines the ideas of wavelet approximation and estimation by information projection in order to warrants that the solution is a nonnegative function. The spectral density of the process is estimated by projecting the wavelet thresholding expansion of the periodogram onto a family of exponential functions. This ensures that the spectral density estimator is a strictly positive function. Then, by Bochner's theorem, the corresponding estimator of the covariance function is semidefinite positive. The theoretical behavior of the estimator is established in terms of rate of convergence of the Kullback-Leibler discrepancy over Besov classes. We also show the excellent practical performance of the estimator in some numerical experiments

Klipsun Magazine, 1982, Volume 12, Issue 07 - November

https://cedar.wwu.edu/klipsun_magazine/1066/thumbnail.jp

Modélisation moléculaire d'interfaces liquide-vapeur à haute pression et prédiction de la tension interfaciale

surface tension;Monte Carlo molecular simulation; alkanes; aromatics;binary mixture water-acid gases; long range corrections;CO2The knowledge of the phase equilibria of petroleum compounds is crucial for most applications in the oil industry. Many projects such as the acid gases (H2S, CO2) storage require full control of interfacial properties of systems involved. The surface tension is a fundamental property to control the safety of the CO2 geological storage. Interfacial properties depend on a certain number of factors such as temperature, pressure and composition of fluids, and are difficult to measure under geological temperature and pressure conditions. Moreover, very few data are available in the literature for systems with H2S or CO2 under pressure because of the toxicity and/or the corrosiveness of these gases. The molecular simulation is an efficient tool for the prediction of the interfacial properties under high temperature and pressure.We performed methodological checks concerning the impact of different parameters of simulation (size effects, truncation effects, long range corrections) on the surface tension calculation. We established procedures to make the surface tension independent of the setup. We focused on the surface tension calculation of liquid-vapour interfaces of alkanes and aromatics. We extended our study to the interfacial tension of binary mixtures (CH4-H2O, H2O-H2S and H2O-CO2). The dependence of the surface tension with the temperature has been reproduced for different hydrocarbons. We also showed the dependence of the interfacial tension of binary mixtures with pressure. The molecular description of the surfaces and the composition of each phase were determined.La connaissance du comportement des équilibres de phase des hydrocarbures est primordiale pour la plupart des applications dans le domaine pétrolier. De nombreux projets tels que la réinjection des gaz acides (H2S, CO2) nécessitent d'avoir une parfaite maîtrise des propriétés interfaciales des systèmes impliqués. La tension interfaciale est donc une propriété indispensable à connaître pour la sureté du stockage géologique du CO2. Les propriétés interfaciales dépendent de plusieurs facteurs tels que la température, la pression et la composition des fluides en présence, et sont délicates à mesurer dans les conditions thermodynamiques proches de celles caractéristiques des gisements ou des puits. De plus, l'acquisition de données pour des systèmes contenant CO2 ou H2S sous pression est difficile en raison des caractères corrosifs et/ou toxiques de ces gaz. La conséquence de ces difficultés est un déficit de données expérimentales de tension interfaciale pour de nombreux systèmes. La modélisation moléculaire est un outil efficace pour la prévision des propriétés interfaciales à des températures et pressions élevées. Nous avons mené une étude méthodologique sur les paramètres de simulation qui peuvent influencer le calcul de la tension superficielle dans le cas d'une simulation Monte Carlo avec présence explicite de l'interface. Nous avons établi des dépendances entre la tension superficielle et certains paramètres (effets de taille, troncature du potentiel, corrections à longue distance), ainsi qu'un protocole pour maitriser la simulation de tels systèmes. Puis, nous nous sommes concentrés sur l'étude de l'interface liquide-vapeur d'hydrocarbures purs (n-alcanes, alcanes ramifiés, cycloalcanes et aromatiques), mais aussi de mélanges binaires (CH4-H2O, H2O-H2S et H2O-CO2). Nous avons reproduit la dépendance de la tension superficielle de plusieurs familles d'hydrocarbures avec la température. Nous avons également vérifié la dépendance de la tension interfaciale de systèmes binaires avec la pression. Les descriptions moléculaires des interfaces et la composition des différentes phases ont également été étudiées