Diffusive Nested Sampling

We introduce a general Monte Carlo method based on Nested Sampling (NS), for sampling complex probability distributions and estimating the normalising constant. The method uses one or more particles, which explore a mixture of nested probability distributions, each successive distribution occupying ~e^-1 times the enclosed prior mass of the previous distribution. While NS technically requires independent generation of particles, Markov Chain Monte Carlo (MCMC) exploration fits naturally into this technique. We illustrate the new method on a test problem and find that it can achieve four times the accuracy of classic MCMC-based Nested Sampling, for the same computational effort; equivalent to a factor of 16 speedup. An additional benefit is that more samples and a more accurate evidence value can be obtained simply by continuing the run for longer, as in standard MCMC.Comment: Accepted for publication in Statistics and Computing. C++ code available at http://lindor.physics.ucsb.edu/DNes

Rate constants for diffusive processes by partial path sampling

We introduce a path sampling method for the computation of rate constants for systems with a highly diffusive character. Based on the recently developed algorithm of transition interface sampling (TIS) this procedure increases the efficiency by sampling only parts of complete transition trajectories confined within a certain region. The algorithm assumes the loss of memory for highly diffusive progression along the reaction coordinate. We compare the new technique to the TIS method for a simple diatomic system and show that the computation time of the new method scales linearly, instead of quadraticaly, with the length of the diffusive barrier. The validity of the memory loss assumption is also discussed.Comment: 12 pages, including 8 figures, RevTeX

Sampling diffusive transition paths

We address the problem of sampling double-ended diffusive paths. The ensemble of paths is expressed using a symmetric version of the Onsager-Machlup formula, which only requires evaluation of the force field and which, upon direct time discretization, gives rise to a symmetric integrator that is accurate to second order. Efficiently sampling this ensemble requires avoiding the well-known stiffness problem associated with sampling infinitesimal Brownian increments of the path, as well as a different type of stiffness associated with sampling the coarse features of long paths. The fine-feature sampling stiffness is eliminated with the use of the fast sampling algorithm (FSA), and the coarse-feature sampling stiffness is avoided by introducing the sliding and sampling (S&S) algorithm. A key feature of the S&S algorithm is that it enables massively parallel computers to sample diffusive trajectories that are long in time. We use the algorithm to sample the transition path ensemble for the structural interconversion of the 38-atom Lennard-Jones cluster at low temperature.Comment: 13 pages 5 figure

The influence of macrofaunal burrow spacing and diffusive scaling on sedimentary nitrification and denitrification: An experimental simulation and model approach

The influence of burrow spacing on nitrification and denitrification was simulated experimentally using sediment plugs of different thicknesses immersed in aerated seawater reservoirs. Different plug thicknesses mimic different distances between oxygenated burrow centers and produce similar changes in aerobic–anaerobic reaction balances as a function of diffusive transport scaling. The thicknesses used were roughly equivalent to transport scales (interburrow spacing) that could be produced by burrow abundances of ~400 to 50,000 m-2, depending on burrow lumen radii (e.g., 0.05–1 cm). Following the exposure of anoxic sediment plugs to aerated water, an efficient aerobic nitrification zone was established within the first ~2–3 millimeters of sediment. At pseudo-steady state, the thinnest plug (2 mm) simulating highest burrow density, was entirely oxic and the denitrification rate nil. Denitrification was stimulated in anoxic regions of the thicker plugs (5, 10, and 20 mm) compared to the initial value in experimental sediment. Maximum nitrification rates and the highest denitrification/nitrification ratio between oxic nitrification and adjacent denitrification zones occurred for the intermediate plug thickness of 5 mm. Of the oxic/anoxic composites, the thickest plug showed the least efficient coupling between nitrification/denitrification zones (lowest denitrification/nitrification ratio). Both the thickness of the oxic layer and the total net remineralization of dissolved inorganic N varied inversely with plug thickness. A set of diffusion–reaction models was formulated assuming a range of possible nitrification kinetic functions. All model forms predicted optimal nitrification–denitrification and ammonification–denitrification coupling with relative oxic–anoxic zonation scales comparable to intermediate plug thicknesses (5–6 mm). However, none of the commonly assumed kinetic forms for nitrification could produce the observed NO-3 profiles in detail, implying that natural sediment populations of nitrifiers may be less sensitive to O2 than laboratory strains. Our experimental and model results clearly show that rates of N remineralization and the balance between stimulation/inhibition of denitrification are highly dependent on sedimentary biogenic structure and the particular geometries of irrigated burrow distributions

Evaluation of diffusive gradients in thin-films using a Diphonix® resin for monitoring dissolved uranium in natural waters

Commercially available Diphonix® resin (TrisKem International) was evaluated as a receiving phase for use with the diffusive gradients in thin-films (DGT) passive sampler for measuring uranium. This resin has a high partition coefficient for actinides and is used in the nuclear industry. Other resins used as receiving phases with DGT for measuring uranium have been prone to saturation and significant chemical interferences. The performance of the device was evaluated in the laboratory and in field trials. In laboratory experiments uptake of uranium (all 100% efficiency) by the resin was unaffected by varying pH (4–9), ionic strength (0.01–1.00 M, as NaNO3) and varying aqueous concentrations of Ca2+ (100–500 mg L−1) and HCO3− (100–500 mg L−1). Due to the high partition coefficient of Diphonex®, several elution techniques for uranium were evaluated. The optimal eluent mixture was 1 M NaOH/1 M H2O2, eluting 90% of the uranium from the resin. Uptake of uranium was linear (R2 = 0.99) over time (5 days) in laboratory experiments using artificial freshwater showing no saturation effects of the resin. In field deployments (River Lambourn, UK) the devices quantitatively accumulated uranium for up to 7 days. In both studies uptake of uranium matched that theoretically predicted for the DGT. Similar experiments in seawater did not follow the DGT theoretical uptake and the Diphonix® appeared to be capacity limited and also affected by matrix interferences. Isotopes of uranium (U235/U238) were measured in both environments with a precision and accuracy of 1.6–2.2% and 1.2–1.4%, respectively. This initial study shows the potential of using Diphonix®-DGT for monitoring of uranium in the aquatic environment

Diffusive MIMO Molecular Communications: Channel Estimation, Equalization and Detection

In diffusion-based communication, as for molecular systems, the achievable data rate is low due to the stochastic nature of diffusion which exhibits a severe inter-symbol-interference (ISI). Multiple-Input Multiple-Output (MIMO) multiplexing improves the data rate at the expense of an inter-link interference (ILI). This paper investigates training-based channel estimation schemes for diffusive MIMO (D-MIMO) systems and corresponding equalization methods. Maximum likelihood and least-squares estimators of mean channel are derived, and the training sequence is designed to minimize the mean square error (MSE). Numerical validations in terms of MSE are compared with Cramer-Rao bound derived herein. Equalization is based on decision feedback equalizer (DFE) structure as this is effective in mitigating diffusive ISI/ILI. Zero-forcing, minimum MSE and least-squares criteria have been paired to DFE, and their performances are evaluated in terms of bit error probability. Since D-MIMO systems are severely affected by the ILI because of short transmitters inter-distance, D-MIMO time interleaving is exploited as countermeasure to mitigate the ILI with remarkable performance improvements. The feasibility of a block-type communication including training and data equalization is explored for D-MIMO, and system-level performances are numerically derived.Comment: Accepted paper at IEEE transaction on Communicatio

Inferring diffusion in single live cells at the single molecule level

The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single molecule and single cell level can add significant insight into understanding molecular architectures of diffusing molecules and the nanoscale environment in which the molecules diffuse. The tool of choice for monitoring dynamic molecular localization in live cells is fluorescence microscopy, especially so combining total internal reflection fluorescence (TIRF) with the use of fluorescent protein (FP) reporters in offering exceptional imaging contrast for dynamic processes in the cell membrane under relatively physiological conditions compared to competing single molecule techniques. There exist several different complex modes of diffusion, and discriminating these from each other is challenging at the molecular level due to underlying stochastic behaviour. Analysis is traditionally performed using mean square displacements of tracked particles, however, this generally requires more data points than is typical for single FP tracks due to photophysical instability. Presented here is a novel approach allowing robust Bayesian ranking of diffusion processes (BARD) to discriminate multiple complex modes probabilistically. It is a computational approach which biologists can use to understand single molecule features in live cells.Comment: combined ms (1-37 pages, 8 figures) and SI (38-55, 3 figures