Split Sampling: Expectations, Normalisation and Rare Events

In this paper we develop a methodology that we call split sampling methods to estimate high dimensional expectations and rare event probabilities. Split sampling uses an auxiliary variable MCMC simulation and expresses the expectation of interest as an integrated set of rare event probabilities. We derive our estimator from a Rao-Blackwellised estimate of a marginal auxiliary variable distribution. We illustrate our method with two applications. First, we compute a shortest network path rare event probability and compare our method to estimation to a cross entropy approach. Then, we compute a normalisation constant of a high dimensional mixture of Gaussians and compare our estimate to one based on nested sampling. We discuss the relationship between our method and other alternatives such as the product of conditional probability estimator and importance sampling. The methods developed here are available in the R package: SplitSampling

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

Being Prepared and Staying Connected: Scouting’s Influence on Social Capital and Community Involvement

Objectives In recent years, scholars have become concerned about the effects that declining levels of social capital are having on community life in the United States. Data suggest that Americans are less likely to interact with neighbors and less likely to participate in community groups than they were in the past. Nevertheless, researchers have found that participation in some types of organizations has a positive impact on social capital and civic involvement. Each year, millions of American youth participate in programs designed to promote positive youth development. Here, we examine the effect that participation in one of the largest youth organizations, the Boy Scouts of America (BSA), has on adult social capital and community involvement. Methods Utilizing a national survey of adult males, we compare measures of social capital and community involvement for former Scouts and non‐Scouts. Results Our findings suggest that level of involvement in the Boy Scouts is significantly related to measures of adult social capital and community engagement. Conclusion Scouting tends to have a significant impact on the lives of its most committed members. Future research must continue to explore the long‐term effects of participation in youth organizations

Evaluating the Applicability of the Fokker-Planck Equation in Polymer Translocation: A Brownian Dynamics Study

Brownian dynamics (BD) simulations are used to study the translocation dynamics of a coarse-grained polymer through a cylindrical nanopore. We consider the case of short polymers, with a polymer length, N, in the range N=21-61. The rate of translocation is controlled by a tunable friction coefficient, gamma_{0p}, for monomers inside the nanopore. In the case of unforced translocation, the mean translocation time scales with polymer length N as ~ (N-N_p)^alpha, where N_p is the average number of monomers in the nanopore. The exponent approaches the value alpha=2 when the pore friction is sufficiently high, in accord with the prediction for the case of the quasi-static regime where pore friction dominates. In the case of forced translocation, the polymer chain is stretched and compressed on the cis and trans sides, respectively, for low gamma_{0p}. However, the chain approaches conformational quasi-equilibrium for sufficiently large gamma_{0p}. In this limit the observed scaling of with driving force and chain length supports the FP prediction that is proportional to N/f_d for sufficiently strong driving force. Monte Carlo simulations are used to calculate translocation free energy functions for the system. The free energies are used with the Fokker-Planck equation to calculate translocation time distributions. At sufficiently high gamma_{0p}, the predicted distributions are in excellent agreement with those calculated from the BD simulations. Thus, the FP equation provides a valid description of translocation dynamics for sufficiently high pore friction for the range of polymer lengths considered here. Increasing N will require a corresponding increase in pore friction to maintain the validity of the FP approach. Outside the regime of low N and high pore friction, the polymer is out of equilibrium, and the FP approach is not valid.Comment: 13 pages, 11 figure

Structured Voluntary Youth Activities and Positive Outcomes in Adulthood: An Exploratory Study of Involvement in Scouting and Subjective Well-Being

This study explores whether youth involvement in Scouting has positive consequences later in life. We examine whether the number of years of participation in Scouting is positively associated with human and social capital and recreational lifestyles in adulthood, and whether these are linked to subjective well-being: relational, emotional, and physical health. To explore this potential relationship, we estimated a structural equation model, analyzing data from a national sample of adult males. We found that youth involvement in Scouting is positively related to subjective well-being indirectly via the positive adult outcomes

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.

Groundtruthing next-gen sequencing for microbial ecology-biases and errors in community structure estimates from PCR amplicon pyrosequencing

Analysis of microbial communities by high-throughput pyrosequencing of SSU rRNA gene PCR amplicons has transformed microbial ecology research and led to the observation that many communities contain a diverse assortment of rare taxa-a phenomenon termed the Rare Biosphere. Multiple studies have investigated the effect of pyrosequencing read quality on operational taxonomic unit (OTU) richness for contrived communities, yet there is limited information on the fidelity of community structure estimates obtained through this approach. Given that PCR biases are widely recognized, and further unknown biases may arise from the sequencing process itself, a priori assumptions about the neutrality of the data generation process are at best unvalidated. Furthermore, post-sequencing quality control algorithms have not been explicitly evaluated for the accuracy of recovered representative sequences and its impact on downstream analyses, reducing useful discussion on pyrosequencing reads to their diversity and abundances. Here we report on community structures and sequences recovered for in vitro-simulated communities consisting of twenty 16S rRNA gene clones tiered at known proportions. PCR amplicon libraries of the V3-V4 and V6 hypervariable regions from the in vitro-simulated communities were sequenced using the Roche 454 GS FLX Titanium platform. Commonly used quality control protocols resulted in the formation of OTUs with >1% abundance composed entirely of erroneous sequences, while over-aggressive clustering approaches obfuscated real, expected OTUs. The pyrosequencing process itself did not appear to impose significant biases on overall community structure estimates, although the detection limit for rare taxa may be affected by PCR amplicon size and quality control approach employed. Meanwhile, PCR biases associated with the initial amplicon generation may impose greater distortions in the observed community structure

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

The TIGRE gamma-ray telescope

TIGRE is an advanced telescope for gamma-ray astronomy with a few arcmin resolution. From 0.3 to 10 MeV it is a Compton telescope. Above 1 MeV, its multi-layers of double sided silicon strip detectors allow for Compton recoil electron tracking and the unique determination for incident photon direction. From 10 to 100 MeV the tracking feature is utilized for gamma-ray pair event reconstruction. Here we present TIGRE energy resolutions, background simulations and the development of the electronics readout system