A hybrid adaptive MCMC algorithm in function spaces

The preconditioned Crank-Nicolson (pCN) method is a Markov Chain Monte Carlo (MCMC) scheme, specifically designed to perform Bayesian inferences in function spaces. Unlike many standard MCMC algorithms, the pCN method can preserve the sampling efficiency under the mesh refinement, a property referred to as being dimension independent. In this work we consider an adaptive strategy to further improve the efficiency of pCN. In particular we develop a hybrid adaptive MCMC method: the algorithm performs an adaptive Metropolis scheme in a chosen finite dimensional subspace, and a standard pCN algorithm in the complement space of the chosen subspace. We show that the proposed algorithm satisfies certain important ergodicity conditions. Finally with numerical examples we demonstrate that the proposed method has competitive performance with existing adaptive algorithms.Comment: arXiv admin note: text overlap with arXiv:1511.0583

The Non-Perturbative Quantum Nature of the Dislocation-Phonon Interaction

Despite the long history of dislocation-phonon interaction studies, there are many problems that have not been fully resolved during this development. These include an incompatibility between a perturbative approach and the long-range nature of a dislocation, the relation between static and dynamic scattering, and the nature of dislocation-phonon resonance. Here by introducing a fully quantized dislocation field, the "dislon"[1], a phonon is renormalized as a quasi-phonon, with shifted quasi-phonon energy, and accompanied by a finite quasi-phonon lifetime that is reducible to classical results. A series of outstanding legacy issues including those above can be directly explained within this unified phonon renormalization approach. In particular, a renormalized phonon naturally resolves the decades-long debate between dynamic and static dislocation-phonon scattering approaches.Comment: 5 pages main text, 3 figures, 10 pages supplemental material

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

7-Ketocholesterol Induces Cell Apoptosis by Activation of Nuclear Factor kappa B in Mouse Macrophages

We investigated the molecular mechanisms responsible for the induction of apoptosis in mouse monocytic macrophage cell line J774A.1 stimulated by 7-ketocholesterol (7-KC). Cell apoptosis was detected by Annexin V-propidium iodide (PI) staining. The DNA-binding activity of nuclear factor kappa B (NF-kappaB) was assessed by electrophoretic mobility shift assay (EMSA). Results showed that 7-KC-stimulation in J774A.1 cells activated NF-kappaB, which is involved in cell apoptosis, in a time- and dose-dependent manners. 7-KC was also found to increase the binding activity of NF-kappaB to specific DNA binding sites, a possible mechanism for the induction of the cell apoptosis. Moreover, these effects were partially inhibited by pyrrolidine dithiocarbamate (PDTC), an NF-kappaB inhibitor. Taken together, 7-KC may be an important factor in atherosclerosis due to the ability of 7-KC to induce cell apoptosis, which is at least partially mediated through the activation of NF-kappaB.</p

2D Spatial Distributions for Measures of Random Sequences Using Conjugate Maps

Advanced visual tools are useful to provide additional information for modern information warfare. 2D spatial distributions of random sequences play an important role to understand properties of complex sequences. This paper proposes time-sequences from a given logical function of 1D Cellular Automata in both Poincare map and conjugate map. Multiple measure sequences of Markov chains can be used to display spatial distributions using conjugate maps. Measure sequences recursively produced by different logical functions generating maps. Possible complementary feature exits between pair functions, Conjugate symmetry relationships between a pair of logical functions in conjugate maps can be observed

Crystal structure of rhodopsin bound to arrestin by femtosecond X-ray laser.

G-protein-coupled receptors (GPCRs) signal primarily through G proteins or arrestins. Arrestin binding to GPCRs blocks G protein interaction and redirects signalling to numerous G-protein-independent pathways. Here we report the crystal structure of a constitutively active form of human rhodopsin bound to a pre-activated form of the mouse visual arrestin, determined by serial femtosecond X-ray laser crystallography. Together with extensive biochemical and mutagenesis data, the structure reveals an overall architecture of the rhodopsin-arrestin assembly in which rhodopsin uses distinct structural elements, including transmembrane helix 7 and helix 8, to recruit arrestin. Correspondingly, arrestin adopts the pre-activated conformation, with a ∼20° rotation between the amino and carboxy domains, which opens up a cleft in arrestin to accommodate a short helix formed by the second intracellular loop of rhodopsin. This structure provides a basis for understanding GPCR-mediated arrestin-biased signalling and demonstrates the power of X-ray lasers for advancing the frontiers of structural biology

Combination of sonic wave velocity, density and electrical resistivity for joint estimation of gas-hydrate reservoir parameters and their uncertainties

Gas-hydrate saturation and porosity are the most crucial reservoir parameters for gas-hydrate resource assessment. Numerous academics have put forward elastic and electrical petrophysical models for calculating the saturation and porosity of gas-hydrate. However, owing to the limitations of a single petrophysical model, the estimation of gas-hydrate saturation and porosity using single elastic or electrical measurement data appears to be inconsistent and uncertain. In this study, the sonic wave velocity, density and resistivity well log data are combined with a Bayesian linear inversion method for the simultaneous estimation of gas-hydrate saturation and porosity. The sonic wave velocity, density and resistivity data of the Shenhu area in the South China Sea are used to estimate the gas-hydrate saturation and porosity. To validate the accuracy of this method, the estimation results are compared with the saturation obtained from pore water chemistry and porosity obtained from density logs. The well log data examples show that the joint estimation method not only provides a rapid estimation of the gas-hydrate reservoir parameters but also improves the accuracy of results and determines their uncertainty.Document Type: Original articleCited as: Zhang, X., Li, Q., Li, L., Fan, Q., Geng, J. Combination of sonic wave velocity, density and electrical resistivity for joint estimation of gas-hydrate reservoir parameters and their uncertainties. Advances in Geo-Energy Research, 2023, 10(2): 133-140. https://doi.org/10.46690/ager.2023.11.0