Efficient Krylov subspace methods for uncertainty quantification in large Bayesian linear inverse problems

Uncertainty quantification for linear inverse problems remains a challenging task, especially for problems with a very large number of unknown parameters (e.g., dynamic inverse problems) and for problems where computation of the square root and inverse of the prior covariance matrix are not feasible. This work exploits Krylov subspace methods to develop and analyze new techniques for large‐scale uncertainty quantification in inverse problems. In this work, we assume that generalized Golub‐Kahan‐based methods have been used to compute an estimate of the solution, and we describe efficient methods to explore the posterior distribution. In particular, we use the generalized Golub‐Kahan bidiagonalization to derive an approximation of the posterior covariance matrix, and we provide theoretical results that quantify the accuracy of the approximate posterior covariance matrix and of the resulting posterior distribution. Then, we describe efficient methods that use the approximation to compute measures of uncertainty, including the Kullback‐Liebler divergence. We present two methods that use the preconditioned Lanczos algorithm to efficiently generate samples from the posterior distribution. Numerical examples from dynamic photoacoustic tomography demonstrate the effectiveness of the described approaches.     

Sharp melting of polymer-DNA hybrids: an associative phase separation approach

An associative equilibrium theory describing the sharp melting behavior of polymer-DNA hybrids is developed. The theory considers linear polymers with attached DNAs on each polymer that serve as "stickers" and with a two-state model governing the DNA melting equilibrium. For three or more oligonucleotides on each polymer, solutions of polymer-DNA hybrids are found to undergo phase separation at sufficiently low temperatures. The dense phase dissolves as temperature increases, which leads to a sharp increase in the fraction of non-hybridized DNA near the phase transition temperature, in agreement with experimental absorbance profiles at 260 nm. The melting temperature is predicted to have the same dependence on salt concentration as a solution of unattached DNAs and be weakly sensitive to the concentration of DNA in solution. The melting temperature is predicted to be higher than that of unattached DNA in solution, with the magnitude of the increase sensitive to the DNA hybridization cooperativity. The theoretical predictions are generally in good quantitative agreement with new experimental data (also presented here), which show the effect of the polymer-DNA hybrid length and salt concentration on the melting profiles.     

Multifunctional polymeric nanoparticles from diverse bioactive agents

We present a rational approach for assembling diverse bioactive agents, such as DNA, proteins, and drug molecules, into core-shell multifunctional polymeric nanoparticles (PNPs) that can be internalized in human breast cancer cells. Using ring-opening metathesis polymerization (ROMP), block copolymers containing small-molecule drug segments (>50% w/w) and tosylated hexaethylene glycol segments were prepared and assembled into PNPs that allowed for the surface conjugation of single-stranded DNA sequences and/or tumor-targeting antibodies. The resulting antibody-functionalized particles were readily uptaken by breast cancer cells that overexpressed the corresponding antigens.     

General continuum boundary conditions for miscible binary fluids from molecular dynamics simulations

Molecular dynamics simulations are used to explore the flow behavior and diffusion of miscible fluids near solid surfaces. The solid produces deviations from bulk fluid behavior that decay over a distance of the order of the fluid correlation length. Atomistic results are mapped onto two types of continuum model: Mesoscopic models that follow this decay and conventional sharp interface boundary conditions for the stress and velocity. The atomistic results, and mesoscopic models derived from them, are consistent with the conventional Marangoni stress boundary condition. However, there are deviations from the conventional Navier boundary condition that states that the slip velocity between wall and fluid is proportional to the strain rate. A general slip boundary condition is derived from the mesoscopic model that contains additional terms associated with the Marangoni stress and diffusion, and is shown to describe the atomistic simulations. The additional terms lead to strong flows when there is a concentration gradient. The potential for using this effect to make a nanomotor or pump is evaluated.     

Planar nitric oxide (NO)-selective ultramicroelectrode sensor for measuring localized NO surface concentrations at xerogel microarrays

A planar ultramicroelectrode nitric oxide (NO) sensor was fabricated to measure the local NO surface concentrations from NO-releasing microarrays of varying geometries. The sensor consisted of platinized Pt (25 microm) working electrode and a silver paint reference electrode coated with a thin silicone rubber gas permeable membrane. An internal hydrogel layer separated the Pt working electrode and gas permeable membrane. The total diameter of the sensor was 相似文献   

n-Particle Quantum Statistics on Graphs

We develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. For 2-connected graphs the independence of quantum statistics with respect to the number of particles is proven. For non-planar 3-connected graphs we identify bosons and fermions as the only possible statistics, whereas for planar 3-connected graphs we show that one anyon phase exists. Our approach also yields an alternative proof of the structure theorem for the first homology group of n-particle graph configuration spaces. Finally, we determine the topological gauge potentials for 2-connected graphs.