An approximate empirical Bayesian method for large-scale linear-Gaussian inverse problems

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often determined via an empirical Bayesian method that maximizes the marginal likelihood function, i.e., the probability density of the data conditional on the hyperparameters. Evaluating the marginal likelihood, however, is computationally challenging for large-scale problems. In this work, we present a method to approximately evaluate marginal likelihood functions, based on a low-rank approximation of the update from the prior covariance to the posterior covariance. We show that this approximation is optimal in a minimax sense. Moreover, we provide an efficient algorithm to implement the proposed method, based on a combination of the randomized SVD and a spectral approximation method to compute square roots of the prior covariance matrix. Several numerical examples demonstrate good performance of the proposed method

The IAS-MEEG Package: A Flexible Inverse Source Reconstruction Platform for Reconstruction and Visualization of Brain Activity from M/EEG Data

We present a standalone Matlab software platform complete with visualization for the reconstruction of the neural activity in the brain from MEG or EEG data. The underlying inversion combines hierarchical Bayesian models and Krylov subspace iterative least squares solvers. The Bayesian framework of the underlying inversion algorithm allows to account for anatomical information and possible a priori belief about the focality of the reconstruction. The computational efficiency makes the software suitable for the reconstruction of lengthy time series on standard computing equipment. The algorithm requires minimal user provided input parameters, although the user can express the desired focality and accuracy of the solution. The code has been designed so as to favor the parallelization performed automatically by Matlab, according to the resources of the host computer. We demonstrate the flexibility of the platform by reconstructing activity patterns with supports of different sizes from MEG and EEG data. Moreover, we show that the software reconstructs well activity patches located either in the subcortical brain structures or on the cortex. The inverse solver and visualization modules can be used either individually or in combination. We also provide a version of the inverse solver that can be used within Brainstorm toolbox. All the software is available online by Github, including the Brainstorm plugin, with accompanying documentation and test data

Fast Gibbs sampling for high-dimensional Bayesian inversion

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to explore and quantify its uncertainties. In applications where the inverse solution is subject to further analysis procedures, this can be a significant advantage. Alongside theoretical progress, various new computational techniques allow to sample very high dimensional posterior distributions: In [Lucka2012], a Markov chain Monte Carlo (MCMC) posterior sampler was developed for linear inverse problems with $\ell_1$-type priors. In this article, we extend this single component Gibbs-type sampler to a wide range of priors used in Bayesian inversion, such as general $\ell_p^q$ priors with additional hard constraints. Besides a fast computation of the conditional, single component densities in an explicit, parameterized form, a fast, robust and exact sampling from these one-dimensional densities is key to obtain an efficient algorithm. We demonstrate that a generalization of slice sampling can utilize their specific structure for this task and illustrate the performance of the resulting slice-within-Gibbs samplers by different computed examples. These new samplers allow us to perform sample-based Bayesian inference in high-dimensional scenarios with certain priors for the first time, including the inversion of computed tomography (CT) data with the popular isotropic total variation (TV) prior.Comment: submitted to "Inverse Problems

The anisotropy of granular materials

The effect of the anisotropy on the elastoplastic response of two dimensional packed samples of polygons is investigated here, using molecular dynamics simulation. We show a correlation between fabric coefficients, characterizing the anisotropy of the granular skeleton, and the anisotropy of the elastic response. We also study the anisotropy induced by shearing on the subnetwork of the sliding contacts. This anisotropy provides an explanation to some features of the plastic deformation of granular media.Comment: Submitted to PR

Stress and Strain in Flat Piling of Disks

We have created a flat piling of disks in a numerical experiment using the Distinct Element Method (DEM) by depositing them under gravity. In the resulting pile, we then measured increments in stress and strain that were associated with a small decrease in gravity. We first describe the stress in terms of the strain using isotropic elasticity theory. Then, from a micro-mechanical view point, we calculate the relation between the stress and strain using the mean strain assumption. We compare the predicted values of Young's modulus and Poisson's ratio with those that were measured in the numerical experiment.Comment: 9 pages, 1 table, 8 figures, and 2 pages for captions of figure

Immune-related adverse events (irAEs) in advanced non-small cell lung cancer (aNSCLC): Platelet-to-lymphocyte ratio (PLR) predicts the risk of development and relapse

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Inverse Modeling for MEG/EEG data

We provide an overview of the state-of-the-art for mathematical methods that are used to reconstruct brain activity from neurophysiological data. After a brief introduction on the mathematics of the forward problem, we discuss standard and recently proposed regularization methods, as well as Monte Carlo techniques for Bayesian inference. We classify the inverse methods based on the underlying source model, and discuss advantages and disadvantages. Finally we describe an application to the pre-surgical evaluation of epileptic patients.Comment: 15 pages, 1 figur

QUALIDADE DE VIDA, SAÚDE E ENFERMAGEM NA PERSPECTIVA ECOSSISTÊMICA

The quality of life in the present context can be seen under various perspectives. So, this aims to reflect on the quality of life, health and nursing concepts from an ecosystemic perspective. It was built from a theoretical and philosophical reflection, and in analogy with authors who study and discuss the concept of health, nursing and quality of life in the light of systems thinking. It allowed the questioning of how the quality of life and health, in an expanded set of elements, relate to aspects of the ecosystem. In this way, it permits seeing daily life in a context of the unique environment of the subject involved in this space. However, in a broader context, numerous collective spaces, which are related, similar or different actions and activities are built and rebuilt differently corroborating for dialogue, discussion, construction/reconstruction of knowledge from the perspective of health promotion and quality of life.  La calidad de vida en el contexto actual puede percibirse desde diversos puntos de vista. Así este estudio tiene como objetivo reflexionar sobre el concepto de calidad de vida, salud y enfermería en una perspectiva ecosistémica. Fue construido a partir de una reflexión teórica y filosófica, y en analogía con los autores que estudian y discuten el concepto de salud, enfermería y calidad de vida a la luz del pensamiento sistémico. Ello permitió el cuestionamiento de cómo la calidad de vida y la salud, en un conjunto más amplio de elementos, se relacionan con los aspectos del ecosistema. De esta manera, permite percibir el diario vivir en un contexto ambiental que es único a la persona involucrada en este espacio. Al mismo tiempo, en un contexto más amplio, numerosos espacios colectivos, con los cuales se relaciona, las acciones y actividades similares o diferentes, se construyen y reconstruyen de manera diferente corroborando para el diálogo, el debate, a la construcción y reconstrucción del conocimiento desde la perspectiva de promoción de la salud y de la calidad de vida.A qualidade de vida no contexto atual pode ser percebida sob diveersas óticas. Assim este estudo objetiva refletir acerca do constructo qualidade de vida, saúde e enfermagem na perspectiva ecossistêmica. Foi construído a partir de uma reflexão teórico-filosófica, e em analogia com autores que trabalham e discutem o conceito de saúde, enfermagem e qualidade de vida à luz do pensamento sistêmico. Ela possibilitou a problematização de como a qualidade de vida e a saúde, em um conjunto de elementos ampliados, se relacionam com os aspectos ecossistêmicos. Assim, permite perceber o viver cotidiano em um contexto ambiental que é único ao sujeito envolvido nesse espaço. Entretanto, ao mesmo tempo, num contexto mais amplo, inúmeros espaços coletivos, com os quais se relaciona, as ações e atividades semelhantes ou diferentes se constroem e reconstroem de modo diferenciado corroborando para o diálogo, a discussão, a construção/reconstrução de saberes na perspectiva da promoção da saúde e da qualidade de vida

Determination of the branching ratios Γ(KL→3π0)/Γ(KL→π+π−π0)\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi^+ \pi^- \pi^0) and Γ(KL→3π0)/Γ(KL→πeν)\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi e \nu )

Improved branching ratios were measured for the $K_L \to 3 \pi^0$ decay in a neutral beam at the CERN SPS with the NA31 detector: $\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi^+ \pi^- \pi^0) = 1.611 \pm 0.037$ and $\Gamma (K_L \to 3 \pi^0) / \Gamma (K_L \to \pi e \nu ) = 0.545 \pm 0.010$. From the first number an upper limit for $\Delta I =5/2$ and $\Delta I = 7/2$ transitions in neutral kaon decay is derived. Using older results for the Ke3/K$\mu$3 fraction, the 3$\pi^0$ branching ratio is found to be $\Gamma (K_L \to 3 \pi^0 )/ \Gamma_{tot} = (0.211 \pm 0.003)$, about a factor three more precise than from previous experiments