1,826 research outputs found
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
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 âPlan Estatal de Investigacio Ìn, Desarrollo e Innovacio Ìn Orientada a los Retos de la Sociedadâ 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
The role of bone morphogenetic proteins and their signalling in human cancers
Both endogenous and exogenous GDF-9 led to a promotion in prostate cancer cell adhesion, invasion, motility, and growth. GDF-9 mediated growth promotion was shown to correlate with an increase in cell cycle progression via up-regulation of Cyclin D1, and protection from apoptosis in a Smad-independent manner. Furthermore, GDF-9 associated cell adhesion, motility, and invasion was shown to involve FAK, paxillin, and Rho-ROCK signalling, as well as EMT and its associated inducers. These effects promote the aggressiveness of PC-3 cells, aiding in their progression and possibly metastasis. These results suggest that GDF-9 is involved in prostate cancer progression by activation of a complex network of signalling pathways and molecules. This provides further proof of the importance of BMP signalling, and suggests that perhaps novel treatments for prostate cancer based on BMPs should be investigated. In addition, it sheds some light on the use of BMPs as prognostic indicators of disease, aiding in diagnosis, and perhaps future forms of treatment.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
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
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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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.
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
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
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