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

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

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

Directional emission from asymmetric microlaser resonators of ∏-conjugated polymers

Journal ArticleA ∏-conjugated polymer film was fabricated into an asymmetric microlaser resonator having a quadrapole deformation with irregular boundaries and a Q factor of 600. At high excitation intensities above the threshold for lasing, we observed multimode laser emission spectra and directional emission at four different angles. Chaotic ray dynamics explains the observed emission pattern

Spectral analysis of polymer microring lasers

Journal ArticleThe emission spectra of microring lasers made of p-conjugated polymer films that coat glass optical fibers are analyzed with the help of a Fourier transform. This method allows for the assignment of photopumped emission lines to integral Bessel functions and a more precise determination of the laser threshold excitation intensity based on harmonic analysis

Multiple resonances in microdisk lasers of ∏-conjugated polymers

Journal ArticleWe have fabricated microdisk lasers from p-conjugated polymers that show multiline emission spectrum upon optical excitation. Using Fourier transform analysis, each emission line is assigned integer to an interger Bessel function that helps to estimate the field distribution inside the photoexcited polymer microdisk. We found that the microdisk can sustain two different laser modes with different, though complementary, field distributions and that the index of refraction decreases with increasing excitation intensity

Universal properties of random lasers

Journal ArticleThe design and fabrication of laser resonators is often difficult. However, random lasers occur in gain media with numerous scatterers and produce coherent laser emission without any predesigned cavity. The generation of coherent emission from multiple scattering is quite general and its basic principles are shown here using two model systems, namely rr-conjugated polymer films and rhodamine-TiO2 suspensions. Above a threshold excitation intensity, both systems show narrow emission lines (<0.5 nm), coherence that is determined by photon statistics, and a fundamental cavity length in the disordered material that is revealed by averaging multiple power Fourier transform spectra

Spectral analysis of near threshold random lasers

ManuscriptEmission spectra from random lasing systems typically have numerous narrow resonant lines. When excited very near to the laser threshold there are fewer resonant lines which clarify the emission spectrum analysis. We studied three different random lasing systems including ?-conjugated polymer films, zinc oxide and TiO2 scatterers in dye solution. Fourier transform analysis of the laser emission spectra near threshold of each system shows that all the sharp lines are highly correlated, indicating that they originate from a single high symmetry resonant structure. The naturally formed microresonators have a circular geometry in the two-dimensional films, and transient spherical geometry in the scatterers/dye suspension