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

Definition of critical conditions for obtaining of a macromodel of ceramic matrix composites

The necessity for development of an approach to studying the phase composition and physico-chemical processes occurring during the firing of ceramic materials with a matrix structure based on technogenic and natural materials is substantiated. The study results on definition of critical conditions for obtaining of a ceramic matrix composites macromodel are presented

A hierarchical Bayesian perspective on majorization-minimization for non-convex sparse regression: Application to M/EEG source imaging

Majorization-minimization (MM) is a standard iterative optimization technique which consists in minimizing a sequence of convex surrogate functionals. MM approaches have been particularly successful to tackle inverse problems and statistical machine learning problems where the regularization term is a sparsity-promoting concave function. However, due to non-convexity, the solution found by MM depends on its initialization. Uniform initialization is the most natural and often employed strategy as it boils down to penalizing all coefficients equally in the first MM iteration. Yet, this arbitrary choice can lead to unsatisfactory results in severely under-determined inverse problems such as source imaging with magneto- and electro-encephalography (M/EEG). The framework of hierarchical Bayesian modeling (HBM) is an alternative approach to encode sparsity. This work shows that for certain hierarchical models, a simple alternating scheme to compute fully Bayesian maximum a posteriori (MAP) estimates leads to the exact same sequence of updates as a standard MM strategy (see the adaptive lasso). With this parallel outlined, we show how to improve upon these MM techniques by probing the multimodal posterior density using Markov Chain Monte-Carlo (MCMC) techniques. Firstly, we show that these samples can provide well-informed initializations that help MM schemes to reach better local minima. Secondly, we demonstrate how it can reveal the different modes of the posterior distribution in order to explore and quantify the inherent uncertainty and ambiguity of such ill-posed inference procedure. In the context of M/EEG, each mode corresponds to a plausible configuration of neural sources, which is crucial for data interpretation, especially in clinical contexts. Results on both simulations and real datasets show how the number or the type of sensors affect the uncertainties on the estimates

Using reciprocity for relating the simulation of transcranial current stimulation to the EEG forward problem

To explore the relationship between transcranial current stimulation (tCS) and the electroencephalography (EEG) forward problem, we investigate and compare accuracy and efficiency of a reciprocal and a direct EEG forward approach for dipolar primary current sources both based on the finite element method (FEM), namely the adjoint approach (AA) and the partial integration approach in conjunction with a transfer matrix concept (PI). By analyzing numerical results, comparing to analytically derived EEG forward potentials and estimating computational complexity in spherical shell models, AA turns out to be essentially identical to PI. It is then proven that AA and PI are also algebraically identical even for general head models. This relation offers a direct link between the EEG forward problem and tCS. We then demonstrate how the quasi-analytical EEG forward solutions in sphere models can be used to validate the numerical accuracies of FEM-based tCS simulation approaches. These approaches differ with respect to the ease with which they can be employed for realistic head modeling based on MRI-derived segmentations. We show that while the accuracy of the most easy to realize approach based on regular hexahedral elements is already quite high, it can be significantly improved if a geometry-adaptation of the elements is employed in conjunction with an isoparametric FEM approach. While the latter approach does not involve any additional difficulties for the user, it reaches the high accuracies of surface-segmentation based tetrahedral FEM, which is considerably more difficult to implement and topologically less flexible in practice. Finally, in a highly realistic head volume conductor model and when compared to the regular alternative, the geometry-adapted hexahedral FEM is shown to result in significant changes in tCS current flow orientation and magnitude up to 45° and a factor of 1.66, respectively

Electrical Stimulation of the Human Cerebral Cortex by Extracranial Muscle Activity: Effect Quantification With Intracranial EEG and FEM Simulations

Objective: Electric fields (EF) of approx. 0.2 V/m have been shown to be sufficiently strong to both modulate neuronal activity in the cerebral cortex and have measurable effects on cognitive performance. We hypothesized that the EF caused by the electrical activity of extracranial muscles during natural chewing may reach similar strength in the cerebral cortex and hence might act as an endogenous modality of brain stimulation. Here, we present first steps toward validating this hypothesis. Methods: Using a realistic volume conductor head model of an epilepsy patient having undergone intracranial electrode placement and utilizing simultaneous intracranial and extracranial electrical recordings during chewing, we derive predictions about the chewing-related cortical EF strength to be expected in healthy individuals. Results: We find that in the region of the temporal poles, the expected EF strength may reach amplitudes in the order of 0.1-1 V/m. Conclusion: The cortical EF caused by natural chewing could be large enough to modulate ongoing neural activity in the cerebral cortex and influence cognitive performance. Significance: The present study lends first support for the assumption that extracranial muscle activity might represent an endogenous source of electrical brain stimulation. This offers a new potential explanation for the puzzling effects of gum chewing on cognition, which have been repeatedly reported in the literature

Lewis X antigen mediates adhesion of human breast carcinoma cells to activated endothelium. Possible involvement of the endothelial scavenger receptor C-Type lectin

Lewis x (Lex, CD15), also known as SSEA-1 (stage specific embryonic antigen-1), is a trisaccharide with the structure Galβ(1–4)Fucα(1–3)GlcNAc, which is expressed on glycoconjugates in human polymorphonuclear granulocytes and various tumors such as colon and breast carcinoma. We have investigated the role of Lex in the adhesion of MCF-7 human breast cancer cells and PMN to human umbilical endothelial cells (HUVEC) and the effects of two different anti-Lex mAbs (FC-2.15 and MCS-1) on this adhesion. We also analyzed the cytolysis of Lex+-cells induced by anti-Lex mAbs and complement when cells were adhered to the endothelium, and the effect of these antibodies on HUVEC. The results indicate that MCF-7 cells can bind to HUVEC, and that MCS-1 but not FC-2.15 mAb inhibit this interaction. Both mAbs can efficiently lyse MCF-7 cells bound to HUVEC in the presence of complement without damaging endothelial cells. We also found a Lex-dependent PMN interaction with HUVEC. Although both anti-Lex mAbs lysed PMN in suspension and adhered to HUVEC, PMN aggregation was only induced by mAb FC-2.15. Blotting studies revealed that the endothelial scavenger receptor C-type lectin (SRCL), which binds Lex-trisaccharide, interacts with specific glycoproteins of Mr␣∼␣28 kD and 10 kD from MCF-7 cells. The interaction between Lex+-cancer cells and vascular endothelium is a potential target for cancer treatment.Fil: Elola, Maria Teresa. Fundación Instituto Leloir; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Capurro, Mariana Isabel. University of Toronto; CanadáFil: Barrio, Maria Marcela. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Fundación para la Investigación, Docencia y Prevención del Cáncer; ArgentinaFil: Coombs, Peter J.. Imperial College London; Reino UnidoFil: Taylor, Maureen E.. Imperial College London; Reino UnidoFil: Drickamer, Kurt. Imperial College London; Reino UnidoFil: Mordoh, Jose. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Fundación para la Investigación, Docencia y Prevención del Cáncer; Argentin

Three dimensional photoacoustic tomography in Bayesian framework

The image reconstruction problem (or inverse problem) in photoacoustic tomography is to resolve the initial pressure distribution from detected ultrasound waves generated within an object due to an illumination by a short light pulse. Recently, a Bayesian approach to photoacoustic image reconstruction with uncertainty quantification was proposed and studied with two dimensional numerical simulations. In this paper, the approach is extended to three spatial dimensions and, in addition to numerical simulations, experimental data are considered. The solution of the inverse problem is obtained by computing point estimates, i.e., maximum a posteriori estimate and posterior covariance. These are computed iteratively in a matrix-free form using a biconjugate gradient stabilized method utilizing the adjoint of the acoustic forward operator. The results show that the Bayesian approach can produce accurate estimates of the initial pressure distribution in realistic measurement geometries and that the reliability of these estimates can be assessed

Ginsenosides act as positive modulators of P2X4 receptors

We investigated the selectivity of protopanaxadiol ginsenosides from Panax ginseng acting as positive allosteric modulators on P2X receptors. ATP-induced responses were measured in stable cell lines overexpressing human P2X4 using a YOPRO-1 dye uptake assay, intracellular calcium measurements, and whole-cell patch-clamp recordings. Ginsenosides CK and Rd were demonstrated to enhance ATP responses at P2X4 by ∼twofold, similar to potentiation by the known positive modulator ivermectin. Investigations into the role of P2X4 in mediating a cytotoxic effect showed that only P2X7 expression in HEK-293 cells induces cell death in response to high concentrations of ATP, and that ginsenosides can enhance this process. Generation of a P2X7-deficient clone of BV-2 microglial cells using CRISPR/ Cas9 gene editing enabled an investigation of endogenous P2X4 in a microglial cell line. Compared with parental BV-2 cells, P2X7-deficient BV-2 cells showed minor potentiation of ATP responses by ginsenosides, and insensitivity to ATP 2 or ATP 1 ginsenoside-induced cell death, indicating a primary role for P2X7 receptors in both of these effects. Computational docking to a homology model of human P2X4, based on the open state of zfP2X4, yielded evidence of a putative ginsenoside binding site in P2X4 in the central vestibule region of the large ectodomain

Design and characterization of superpotent bivalent ligands targeting oxytocin receptor dimers via a channel-like structure

Dimeric/oligomeric states of G-protein coupled receptors have been difficult to target. We report here bivalent ligands consisting of two identical oxytocin-mimetics that induce a three order magnitude boost in G-protein signaling of oxytocin receptors (OTRs) in vitro and a 100- and 40-fold gain in potency in vivo in the social behavior of mice and zebrafish. Through receptor mutagenesis and interference experiments with synthetic peptides mimicking transmembrane helices (TMH), we show that such superpotent behavior follows from the binding of the bivalent ligands to dimeric receptors based on a TMH1-TMH2 interface. Moreover, in this arrangement, only the analogues with a well-defined spacer length (∼25 Å) precisely fit inside a channel-like passage between the two protomers of the dimer. The newly discovered oxytocin bivalent ligands represent a powerful tool for targeting dimeric OTR in neurodevelopmental and psychiatric disorders and, in general, provide a framework to untangle specific arrangements of G-protein coupled receptor dimers

Fully three-dimensional sound speed-corrected multi-wavelength photoacoustic breast tomography

Photoacoustic tomography is a contrast agent-free imaging technique capable of visualizing blood vessels and tumor-associated vascularization in breast tissue. While sophisticated breast imaging systems have been recently developed, there is yet much to be gained in imaging depth, image quality and tissue characterization capability before clinical translation is possible. In response, we have developed a hybrid photoacoustic and ultrasound-transmission tomographic system PAM3. The photoacoustic component has for the first time three-dimensional multi-wavelength imaging capability, and implements substantial technical advancements in critical hardware and software sub-systems. The ultrasound component enables for the first time, a three-dimensional sound speed map of the breast to be incorporated in photoacoustic reconstruction to correct for inhomogeneities, enabling accurate target recovery. The results demonstrate the deepest photoacoustic breast imaging to date namely 48 mm, with a more uniform field of view than hitherto, and an isotropic spatial resolution that rivals that of Magnetic Resonance Imaging. The in vivo performance achieved, and the diagnostic value of interrogating angiogenesis-driven optical contrast as well as tumor mass sound speed contrast, gives confidence in the system's clinical potential.Comment: 33 pages Main Body, 9 pages Supplementary Materia