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

Electromagnetic penguin operators and direct CP violation in K --> pi l^+ l^-

Supersymmetric extensions of the Standard Model predict a large enhancement of the Wilson coefficients of the dimension-five electromagnetic penguin operators affecting the direct CP violation in K_L --> pi^0 e^+ e^- and the charge asymmetry in K^\pm --> pi^\pm l^+ l^-. Here we compute the relevant matrix elements in the chiral quark model and compare these with the ones given by lattice calculationsComment: 12 pages, JHEP style, gluonic corrections to B_T adde

A computational model integrating brain electrophysiology and metabolism highlights the key role of extracellular potassium and oxygen

The human brain is a small organ which uses a disproportional amount of the total metabolic energy pro- duction in the body. While it is well understood that the most significant energy sink is the maintenance of the neuronal membrane potential during the brain signaling activity, the role of astrocytes in the energy balance continues to be the topic of a lot of research. A key function of astrocytes, besides clearing glutamate from the synaptic clefts, is the potassium clearing after neuronal activation. Extracellular potassium plays a significant role in triggering neuronal firing, and elevated concentration of potassium may lead to abnormal firing pattern, e.g., seizures, thus emphasizing the importance of the glial K+ buffering role. The predictive mathematical model proposed in this paper elucidates the role of glial potassium clearing in brain energy metabolism, integrating a detailed model of the ion dynamics which regulates neuronal firing with a three compartment metabolic model. Because of the very different characteristic time scales of electrophysiology and metabolism, care must be taken when coupling the two models to ensure that the predictions, e.g., neuronal firing frequencies and the oxygen- glucose index (OGI) of the brain during activation and rest, are in agreement with empirical observations. The temporal multi-scale nature of the problem requires the design of new computational tools to ensure a stable and accurate numerical treatment of the problem. The model predictions for different protocols, including combinations of elevated activation and ischemic episodes, are in good agreement with experimental observations reported in the literature.This work was supported by the Bizkaia Talent and European Commission through CO- FUND under the grant CIPAS: Computational Inverse Problems Across Scales (AYD-000-278, 2015), by the Basque Government through the BERC 2014-2017 program, and by the Spanish Ministry of Economics and Competitive- ness MINECO through the BCAM Severo Ochoa excellence accreditation SEV-2013-0323 and the Spanish ”Plan Estatal de Investigacio ́n, Desarrollo e Innovacio ́n Orientada a los Retos de la Sociedad” under Grant BELEMET - Brain ELEctro-METabolic modeling and numerical approximation (MTM2015-69992-R). The work of Daniela Cal- vetti was partly supported by Grant Number 246665 from the Simons Foundation, and the work of Erkki Somersalo was partly supported by NSF Grant DMS 1016183. Daniela Calvetti and Erkki Somersalo were partly supported by NIH, grant 1U01GM111251-01

Brain energetics plays a key role in the coordination of electrophysiology, metabolism and hemodynamics: evidence from an integrated computational model

The energetic needs of brain cells at rest and during elevated neuronal activation has been the topic of many investigations where mathematical models have played a significant role providing a context for the interpretation of experimental findings. A recently proposed mathematical model, comprising a double feedback between cellular metabolism and electrophysiology, sheds light on the interconnections between the electrophysiological details associated with changes in the frequency of neuronal firing and the corresponding metabolic activity. We propose a new extended mathematical model comprising a three-way feedback connecting metabolism, electrophysiology and hemodynamics. Upon specifying the time intervals of higher neuronal activation, the model generates a potassium based signal leading to the concomitant increase in cerebral blood flow with associated vasodilation and metabolic changes needed to sustain the increased energy demand. The predictions of the model are in good qualitative and quantitative agreement with experimental findings reported in the literature, even predicting a slow after-hyperpolarization of a duration of approximately 16 s matching experimental observations.The work of Daniela Calvetti was partly support by NSF grants DMS-1522334 and NIH grant 1U01 GM111251-01. The work of Erkki Somersalo was partly support by NSF grants DMS 1714617 and NIH grant 1U01GM111251-01

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

Stochastic modelling of muscle recruitment during activity

Muscle forces can be selected from a space of muscle recruitment strategies that produce stable motion and variable muscle and joint forces. However, current optimization methods provide only a single muscle recruitment strategy. We modelled the spectrum of muscle recruitment strategies while walking. The equilibrium equations at the joints, muscle constraints, static optimization solutions and 15-channel electromyography (EMG) recordings for seven walking cycles were taken from earlier studies. The spectrum of muscle forces was calculated using Bayesian statistics and Markov chain Monte Carlo (MCMC) methods, whereas EMG-driven muscle forces were calculated using EMG-driven modelling. We calculated the differences between the spectrum and EMG-driven muscle force for 1–15 input EMGs, and we identified the muscle strategy that best matched the recorded EMG pattern. The best-fit strategy, static optimization solution and EMG-driven force data were compared using correlation analysis. Possible and plausible muscle forces were defined as within physiological boundaries and within EMG boundaries. Possible muscle and joint forces were calculated by constraining the muscle forces between zero and the peak muscle force. Plausible muscle forces were constrained within six selected EMG boundaries. The spectrum to EMG-driven force difference increased from 40 to 108 N for 1–15 EMG inputs. The best-fit muscle strategy better described the EMG-driven pattern (R2 = 0.94; RMSE = 19 N) than the static optimization solution (R2 = 0.38; RMSE = 61 N). Possible forces for 27 of 34 muscles varied between zero and the peak muscle force, inducing a peak hip force of 11.3 body-weights. Plausible muscle forces closely matched the selected EMG patterns; no effect of the EMG constraint was observed on the remaining muscle force ranges. The model can be used to study alternative muscle recruitment strategies in both physiological and pathophysiological neuromotor conditions

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

Ab-initio calculation of Kerr spectra for semi-infinite systems including multiple reflections and optical interferences

Based on Luttinger's formulation the complex optical conductivity tensor is calculated within the framework of the spin-polarized relativistic screened Korringa-Kohn-Rostoker method for layered systems by means of a contour integration technique. For polar geometry and normal incidence ab-initio Kerr spectra of multilayer systems are then obtained by including via a 2x2 matrix technique all multiple reflections between layers and optical interferences in the layers. Applications to Co|Pt5 and Pt3|Co|Pt5 on the top of a semi-infinite fcc-Pt(111) bulk substrate show good qualitative agreement with the experimental spectra, but differ from those obtained by applying the commonly used two-media approach.Comment: 32 pages (LaTeX), 5 figures (Encapsulated PostScript), submitted to Phys. Rev.