Variance-based sensitivity of Bayesian inverse problems to the prior distribution

The formulation of Bayesian inverse problems involves choosing prior distributions; choices that seem equally reasonable may lead to significantly different conclusions. We develop a computational approach to better understand the impact of the hyperparameters defining the prior on the posterior statistics of the quantities of interest. Our approach relies on global sensitivity analysis (GSA) of Bayesian inverse problems with respect to the hyperparameters defining the prior. This, however, is a challenging problem--a naive double loop sampling approach would require running a prohibitive number of Markov chain Monte Carlo (MCMC) sampling procedures. The present work takes a foundational step in making such a sensitivity analysis practical through (i) a judicious combination of efficient surrogate models and (ii) a tailored importance sampling method. In particular, we can perform accurate GSA of posterior prediction statistics with respect to prior hyperparameters without having to repeat MCMC runs. We demonstrate the effectiveness of the approach on a simple Bayesian linear inverse problem and a nonlinear inverse problem governed by an epidemiological model

Extreme events driven glassy behaviour in granular media

Motivated by recent experiments on the approach to jamming of a weakly forced granular medium using an immersed torsion oscillator [Nature 413 (2001) 407], we propose a simple model which relates the microscopic dynamics to macroscopic rearrangements and accounts for the following experimental facts: (1) the control parameter is the spatial amplitude of the perturbation and not its reduced peak acceleration; (2) a Vogel-Fulcher-Tammann-like form for the relaxation time. The model draws a parallel between macroscopic rearrangements in the system and extreme events whose probability of occurrence (and thus the typical relaxation time) is estimated using extreme-value statistics. The range of validity of this description in terms of the control parameter is discussed as well as the existence of other regimes.Comment: 7 pages, to appear in Europhys. Let

Statistics of S-matrix poles in Few-Channel Chaotic Scattering: Crossover from Isolated to Overlapping Resonances

We derive the explicit expression for the distribution of resonance widths in a chaotic quantum system coupled to continua via M equivalent open channels. It describes a crossover from the $\chi^2$ distribution (regime of isolated resonances) to a broad power-like distribution typical for the regime of overlapping resonances. The first moment is found to reproduce exactly the Moldauer-Simonius relation between the mean resonance width and the transmission coefficient. This fact may serve as another manifestation of equivalence between the spectral and the ensemble averaging.Comment: 4 two-column pages, RevTex. text is slightly modified; some misprints are correcte

Electronic structure and optical properties of lightweight metal hydrides

We study the electronic structures and dielectric functions of the simple hydrides LiH, NaH, MgH2 and AlH3, and the complex hydrides Li3AlH6, Na3AlH6, LiAlH4, NaAlH4 and Mg(AlH4)2, using first principles density functional theory and GW calculations. All these compounds are large gap insulators with GW single particle band gaps varying from 3.5 eV in AlH3 to 6.5 eV in the MAlH4 compounds. The valence bands are dominated by the hydrogen atoms, whereas the conduction bands have mixed contributions from the hydrogens and the metal cations. The electronic structure of the aluminium compounds is determined mainly by aluminium hydride complexes and their mutual interactions. Despite considerable differences between the band structures and the band gaps of the various compounds, their optical responses are qualitatively similar. In most of the spectra the optical absorption rises sharply above 6 eV and has a strong peak around 8 eV. The quantitative differences in the optical spectra are interpreted in terms of the structure and the electronic structure of the compounds.Comment: 13 pages, 10 figure

DFT Study of Planar Boron Sheets: A New Template for Hydrogen Storage

We study the hydrogen storage properties of planar boron sheets and compare them to those of graphene. The binding of molecular hydrogen to the boron sheet (0.05 eV) is stronger than that to graphene. We find that dispersion of alkali metal (AM = Li, Na, and K) atoms onto the boron sheet markedly increases hydrogen binding energies and storage capacities. The unique structure of the boron sheet presents a template for creating a stable lattice of strongly bonded metal atoms with a large nearest neighbor distance. In contrast, AM atoms dispersed on graphene tend to cluster to form a bulk metal. In particular the boron-Li system is found to be a good candidate for hydrogen storage purposes. In the fully loaded case this compound can contain up to 10.7 wt. % molecular hydrogen with an average binding energy of 0.15 eV/H2.Comment: 19 pages, 7 figures, and 3 table

Effect of internal friction on transformation twin dynamics in SrxBa1-xSnO3 perovskite

The dynamics of transformation twins in SrxBa1-xSnO3 (x=0.6,0.8) perovskite has been studied by dynamical mechanical analysis in three-point bend geometry. This material undergoes phase transitions from orthorhombic to tetragonal and cubic structures on heating. The mechanical loss signatures of the transformation twins include relaxation and frequency-independent peaks in the orthorhombic and tetragonal phases, with no observed energy dissipation in the cubic phase. The macroscopic shape, orientation and relative displacements of twin walls have been calculated from bending and anisotropy energies. The mechanical loss angle and distribution of relaxation time are discussed in term of bending modes of domain walls.Comment: 20 pages, 4 figure

Vibration-induced "thermally activated" jamming transition in granular media

The quasi-static frequency response of a granular medium is measured by a forced torsion oscillator method, with forcing frequency $f_{p}$ in the range $10^{-4}$ Hz to 5 Hz, while weak vibrations at high-frequency $f_{s}$, in the range 50 Hz to 200 Hz, are generated by an external shaker. The intensity of vibration, $\Gamma$, is below the fluidization limit. A loss factor peak is observed in the oscillator response as a function of $\Gamma$ or $f_{p}$. In a plot of $\ln f_{p}$ against $1/\Gamma$, the position of the peak follows an Arrhenius-like behaviour over four orders of magnitude in $f_{p}$. The data can be described as a stochastic hopping process involving a probability factor $\exp(-\Gamma_{j}/\Gamma)$ with $\Gamma_{j}$ a $f_{s}$-dependent characteristic vibration intensity. A $f_{s}$-independent description is given by $\exp(-\tau_{j}/\tau)$, with $\tau_{j}$ an intrinsic characteristic time, and $\tau =\Gamma ^{n}/2\pi f_{s}$, n=0.5-0.6, an empirical control parameter with unit of time. $\tau$ is seen as the effective average time during which the perturbed grains can undergo structural rearrangement. The loss factor peak appears as a crossover in the dynamic behaviour of the vibrated granular system, which, at the time-scale $1/f_{p}$, is solid-like at low $\Gamma$, and the oscillator is jammed into the granular material, and is fluid-like at high $\Gamma$, where the oscillator can slide viscously.Comment: Final version to appear in PR

Immunolymphoscintigraphy for Metastatic Sentinel Nodes: Test of a Model

Aim. To develop a method and obtain proof-of-principle for immunolymphoscintigraphy for identification of metastatic sentinel nodes. Methods. We selected one of four tumour-specific antibodies against human breast cancer and investigated (1), in immune-deficient (nude) mice with xenograft human breast cancer expressing the antigen if specific binding of the intratumorally injected, radioactively labelled, monoclonal antibody could be scintigraphically visualized, and (2) transportation to and retention in regional lymph nodes of the radioactively labelled antibody after subcutaneous injection in healthy rabbits. Results and Conclusion. Our paper suggests the theoretical possibility of a model of dual isotope immuno-lymphoscintigraphy for noninvasive, preoperative, malignant sentinel node imaging

A Model for the Development of the Rhizobial and Arbuscular Mycorrhizal Symbioses in Legumes and Its Use to Understand the Roles of Ethylene in the Establishment of these two Symbioses

We propose a model depicting the development of nodulation and arbuscular mycorrhizae. Both processes are dissected into many steps, using Pisum sativum L. nodulation mutants as a guideline. For nodulation, we distinguish two main developmental programs, one epidermal and one cortical. Whereas Nod factors alone affect the cortical program, bacteria are required to trigger the epidermal events. We propose that the two programs of the rhizobial symbiosis evolved separately and that, over time, they came to function together. The distinction between these two programs does not exist for arbuscular mycorrhizae development despite events occurring in both root tissues. Mutations that affect both symbioses are restricted to the epidermal program. We propose here sites of action and potential roles for ethylene during the formation of the two symbioses with a specific hypothesis for nodule organogenesis. Assuming the epidermis does not make ethylene, the microsymbionts probably first encounter a regulatory level of ethylene at the epidermis–outermost cortical cell layer interface. Depending on the hormone concentrations there, infection will either progress or be blocked. In the former case, ethylene affects the cortex cytoskeleton, allowing reorganization that facilitates infection; in the latter case, ethylene acts on several enzymes that interfere with infection thread growth, causing it to abort. Throughout this review, the difficulty of generalizing the roles of ethylene is emphasized and numerous examples are given to demonstrate the diversity that exists in plants