Free energy of a folded polymer under cylindrical confinement

Monte Carlo computer simulations are used to study the conformational free energy of a folded polymer confined to a long cylindrical tube. The polymer is modeled as a hard-sphere chain. Its conformational free energy $F$ is measured as a function of $\lambda$, the end-to-end distance of the polymer. In the case of a flexible linear polymer, $F(\lambda)$ is a linear function in the folded regime with a gradient that scales as $f\equiv |dF/d\lambda| \sim N^0 D^{-1.20\pm 0.01}$ for a tube of diameter $D$ and a polymer of length $N$. This is close to the prediction $f \sim N^0 D^{-1}$ obtained from simple scaling arguments. The discrepancy is due in part to finite-size effects associated with the de-Gennes blob model. A similar discrepancy was observed for the folding of a single arm of a three-arm star polymer. We also examine backfolding of a semiflexible polymer of persistence length $P$ in the classic Odijk regime. In the overlap regime, the derivative scales $f \sim N^0 D^{-1.72\pm 0.02} P^{-0.35\pm 0.01}$, which is close to the prediction $f \sim N^0 D^{-5/3} P^{-1/3}$ obtained from a scaling argument that treats interactions between deflection segments at the second virial level. In addition, the measured free energy cost of forming a hairpin turn is quantitatively consistent with a recent theoretical calculation. Finally, we examine the scaling of $F(\lambda)$ for a confined semiflexible chain in the presence of an S-loop composed of two hairpins. While the predicted scaling of the free energy gradient is the same as that for a single hairpin, we observe a scaling of $f \sim D^{-1.91\pm 0.03} P^{-0.36\pm 0.01}$. Thus, the quantitative discrepancy between this measurement and the predicted scaling is somewhat greater for S-loops than for single hairpins.Comment: 17 papes, 12 figure

Spike-and-Slab Priors for Function Selection in Structured Additive Regression Models

Structured additive regression provides a general framework for complex Gaussian and non-Gaussian regression models, with predictors comprising arbitrary combinations of nonlinear functions and surfaces, spatial effects, varying coefficients, random effects and further regression terms. The large flexibility of structured additive regression makes function selection a challenging and important task, aiming at (1) selecting the relevant covariates, (2) choosing an appropriate and parsimonious representation of the impact of covariates on the predictor and (3) determining the required interactions. We propose a spike-and-slab prior structure for function selection that allows to include or exclude single coefficients as well as blocks of coefficients representing specific model terms. A novel multiplicative parameter expansion is required to obtain good mixing and convergence properties in a Markov chain Monte Carlo simulation approach and is shown to induce desirable shrinkage properties. In simulation studies and with (real) benchmark classification data, we investigate sensitivity to hyperparameter settings and compare performance to competitors. The flexibility and applicability of our approach are demonstrated in an additive piecewise exponential model with time-varying effects for right-censored survival times of intensive care patients with sepsis. Geoadditive and additive mixed logit model applications are discussed in an extensive appendix

Fluctuations of radiation from a chaotic laser below threshold

Radiation from a chaotic cavity filled with gain medium is considered. A set of coupled equations describing the photon density and the population of gain medium is proposed and solved. The spectral distribution and fluctuations of the radiation are found. The full noise is a result of a competition between positive correlations of photons with equal frequencies (due to stimulated emission and chaotic scattering) which increase fluctuations, and a suppression due to interaction with a gain medium which leads to negative correlations between photons. The latter effect is responsible for a pronounced suppression of the photonic noise as compared to the linear theory predictions.Comment: 7 pages, 5 figures; expanded version, to appear in Phys. Rev.

Freezing by Monte Carlo Phase-Switch

We describe a Monte Carlo procedure which allows sampling of the disjoint configuration spaces associated with crystalline and fluid phases, within a single simulation. The method utilises biased sampling techniques to enhance the probabilities of gateway states (in each phase) which are such that a global switch (to the other phase) can be implemented. Equilibrium freezing-point parameters can be determined directly; statistical uncertainties prescribed transparently; and finite-size effects quantified systematically. The method is potentially quite general; we apply it to the freezing of hard spheres.Comment: 5 pages, 2 figure

Bottom mixed layer oxygen dynamics in the Celtic Sea

The seasonally stratified continental shelf seas are highly productive, economically important environments which are under considerable pressure from human activity. Global dissolved oxygen concentrations have shown rapid reductions in response to anthropogenic forcing since at least the middle of the twentieth century. Oxygen consumption is at the same time linked to the cycling of atmospheric carbon, with oxygen being a proxy for carbon remineralisation and the release of CO2. In the seasonally stratified seas the bottom mixed layer (BML) is partially isolated from the atmosphere and is thus controlled by interplay between oxygen consumption processes, vertical and horizontal advection. Oxygen consumption rates can be both spatially and temporally dynamic, but these dynamics are often missed with incubation based techniques. Here we adopt a Bayesian approach to determining total BML oxygen consumption rates from a high resolution oxygen time-series. This incorporates both our knowledge and our uncertainty of the various processes which control the oxygen inventory. Total BML rates integrate both processes in the water column and at the sediment interface. These observations span the stratified period of the Celtic Sea and across both sandy and muddy sediment types. We show how horizontal advection, tidal forcing and vertical mixing together control the bottom mixed layer oxygen concentrations at various times over the stratified period. Our muddy-sand site shows cyclic spring-neap mediated changes in oxygen consumption driven by the frequent resuspension or ventilation of the seabed. We see evidence for prolonged periods of increased vertical mixing which provide the ventilation necessary to support the high rates of consumption observed