Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in $${\mathbb R^d}$$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential

A nonlinear hydrodynamical approach to granular materials

We propose a nonlinear hydrodynamical model of granular materials. We show how this model describes the formation of a sand pile from a homogeneous distribution of material under gravity, and then discuss a simulation of a rotating sandpile which shows, in qualitative agreement with experiment, a static and dynamic angle of repose.Comment: 17 pages, 14 figures, RevTeX4; minor changes to wording and some additional discussion. Accepted by Phys. Rev.

Modeling magnetospheric fields in the Jupiter system

The various processes which generate magnetic fields within the Jupiter system are exemplary for a large class of similar processes occurring at other planets in the solar system, but also around extrasolar planets. Jupiter's large internal dynamo magnetic field generates a gigantic magnetosphere, which is strongly rotational driven and possesses large plasma sources located deeply within the magnetosphere. The combination of the latter two effects is the primary reason for Jupiter's main auroral ovals. Jupiter's moon Ganymede is the only known moon with an intrinsic dynamo magnetic field, which generates a mini-magnetosphere located within Jupiter's larger magnetosphere including two auroral ovals. Ganymede's magnetosphere is qualitatively different compared to the one from Jupiter. It possesses no bow shock but develops Alfv\'en wings similar to most of the extrasolar planets which orbit their host stars within 0.1 AU. New numerical models of Jupiter's and Ganymede's magnetospheres presented here provide quantitative insight into the processes that maintain these magnetospheres. Jupiter's magnetospheric field is approximately time-periodic at the locations of Jupiter's moons and induces secondary magnetic fields in electrically conductive layers such as subsurface oceans. In the case of Ganymede, these secondary magnetic fields influence the oscillation of the location of its auroral ovals. Based on dedicated Hubble Space Telescope observations, an analysis of the amplitudes of the auroral oscillations provides evidence that Ganymede harbors a subsurface ocean. Callisto in contrast does not possess a mini-magnetosphere, but still shows a perturbed magnetic field environment. Callisto's ionosphere and atmospheric UV emission is different compared to the other Galilean satellites as it is primarily been generated by solar photons compared to magnetospheric electrons.Comment: Chapter for Book: Planetary Magnetis

Stuart Warren (24 Dec 1938–22 Mar 2020)

Celebrating the life of Stuart Warren

FGF receptor genes and breast cancer susceptibility: results from the Breast Cancer Association Consortium

Background:Breast cancer is one of the most common malignancies in women. Genome-wide association studies have identified FGFR2 as a breast cancer susceptibility gene. Common variation in other fibroblast growth factor (FGF) receptors might also modify risk. We tested this hypothesis by studying genotyped single-nucleotide polymorphisms (SNPs) and imputed SNPs in FGFR1, FGFR3, FGFR4 and FGFRL1 in the Breast Cancer Association Consortium. Methods:Data were combined from 49 studies, including 53 835 cases and 50 156 controls, of which 89 050 (46 450 cases and 42 600 controls) were of European ancestry, 12 893 (6269 cases and 6624 controls) of Asian and 2048 (1116 cases and 932 controls) of African ancestry. Associations with risk of breast cancer, overall and by disease sub-type, were assessed using unconditional logistic regression. Results:Little evidence of association with breast cancer risk was observed for SNPs in the FGF receptor genes. The strongest evidence in European women was for rs743682 in FGFR3; the estimated per-allele odds ratio was 1.05 (95 confidence interval=1.02-1.09, P=0.0020), which is substantially lower than that observed for SNPs in FGFR2. Conclusion:Our results suggest that common variants in the other FGF receptors are not associated with risk of breast cancer to the degree observed for FGFR2. © 2014 Cancer Research UK

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa

Interactions of Pleckstrin Homology Domains with Membranes: Adding Back the Bilayer via High-Throughput Molecular Dynamics

A molecular simulation pipeline for determining the mode of interaction of pleckstrin homology (PH) domains with phosphatidylinositol phosphate (PIP)-containing lipid bilayers is presented. We evaluate our methodology for the GRP1 PH domain via comparison with structural and biophysical data. Coarse-grained simulations yield a 2D density landscape for PH/membrane interactions alongside residue contact profiles. Predictions of the membrane localization and interactions of 13 PH domains reveal canonical, non-canonical, and dual PIP-binding sites on the proteins. Thus, the PH domains associate with the PIP molecules in the membrane via a highly positively charged loop. Some PH domains exhibit modes of interaction with PIP-containing membranes additional to this canonical binding mode. All 13 PH domains cause a degree of local clustering of PIP molecules upon binding to the membrane. This provides a global picture of PH domain interactions with membranes. The high-throughput approach could be extended to other families of peripheral membrane proteins

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Spatial linear dark field control and holographic modal wavefront sensing with a vAPP coronagraph on MagAO-X

The Magellan Extreme Adaptive Optics (MagAO-X) Instrument is an extreme AO system coming online at the end of 2019 that will be operating within the visible and near-IR. With state-of-the-art wavefront sensing and coronagraphy, MagAO-X will be optimized for high-contrast direct exoplanet imaging at challenging visible wavelengths, particularly Hα. To enable high-contrast imaging, the instrument hosts a vector apodizing phase plate (vAPP) coronagraph. The vAPP creates a static region of high contrast next to the star that is referred to as a dark hole; on MagAO-X, the expected dark hole raw contrast is ∼4  ×  10  −  6. The ability to maintain this contrast during observations, however, is limited by the presence of non-common path aberrations (NCPA) and the resulting quasi-static speckles that remain unsensed and uncorrected by the primary AO system. These quasi-static speckles within the dark hole degrade the high contrast achieved by the vAPP and dominate the light from an exoplanet. The aim of our efforts here is to demonstrate two focal plane wavefront sensing (FPWFS) techniques for sensing NCPA and suppressing quasi-static speckles in the final focal plane. To sense NCPA to which the primary AO system is blind, the science image is used as a secondary wavefront sensor. With the vAPP, a static high-contrast dark hole is created on one side of the PSF, leaving the opposite side of the PSF unocculted. In this unobscured region, referred to as the bright field, the relationship between modulations in intensity and low-amplitude pupil plane phase aberrations can be approximated as linear. The bright field can therefore be used as a linear wavefront sensor to detect small NCPA and suppress quasi-static speckles. This technique, known as spatial linear dark field control (LDFC), can monitor the bright field for aberrations that will degrade the high-contrast dark hole. A second form of FPWFS, known as holographic modal wavefront sensing (hMWFS), is also employed with the vAPP. This technique uses hologram-generated PSFs in the science image to monitor the presence of low-order aberrations. With LDFC and the hMWFS, high contrast across the dark hole can be maintained over long observations, thereby allowing planet light to remain visible above the stellar noise over the course of observations on MagAO-X. Here, we present simulations and laboratory demonstrations of both spatial LDFC and the hMWFS with a vAPP coronagraph at the University of Arizona Extreme Wavefront Control Laboratory. We show both in simulation and in the lab that the hMWFS can be used to sense low-order aberrations and reduce the wavefront error (WFE) by a factor of 3  −  4  ×  . We also show in simulation that, in the presence of a temporally evolving pupil plane phase aberration with 27-nm root-mean-square (RMS) WFE, LDFC can reduce the WFE to 18-nm RMS, resulting in factor of 6 to 10 gain in contrast that is kept stable over time. This performance is also verified in the lab, showing that LDFC is capable of returning the dark hole to the average contrast expected under ideal lab conditions. These results demonstrate the power of the hMWFS and spatial LDFC to improve MagAO-X’s high-contrast imaging capabilities for direct exoplanet imaging.Instrumentatio