Measuring the convergence of Monte Carlo free energy calculations

The nonequilibrium work fluctuation theorem provides the way for calculations of (equilibrium) free energy based on work measurements of nonequilibrium, finite-time processes and their reversed counterparts by applying Bennett's acceptance ratio method. A nice property of this method is that each free energy estimate readily yields an estimate of the asymptotic mean square error. Assuming convergence, it is easy to specify the uncertainty of the results. However, sample sizes have often to be balanced with respect to experimental or computational limitations and the question arises whether available samples of work values are sufficiently large in order to ensure convergence. Here, we propose a convergence measure for the two-sided free energy estimator and characterize some of its properties, explain how it works, and test its statistical behavior. In total, we derive a convergence criterion for Bennett's acceptance ratio method.Comment: 14 pages, 17 figure

Using bijective maps to improve free energy estimates

We derive a fluctuation theorem for generalized work distributions, related to bijective mappings of the phase spaces of two physical systems, and use it to derive a two-sided constraint maximum likelihood estimator of their free energy difference which uses samples from the equilibrium configurations of both systems. As an application, we evaluate the chemical potential of a dense Lennard-Jones fluid and study the construction and performance of suitable maps.Comment: 17 pages, 11 figure

Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lam\'e equation. We also show that the two pairs of orbits created at period-doubling bifurcations of touch-and-go type are given by two different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper, accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of bifurcations "touch-and-go" replaced by "island-chain

Can one hear the shape of the Universe?

It is shown that the recent observations of NASA's explorer mission "Wilkinson Microwave Anisotropy Probe" (WMAP) hint that our Universe may possess a non-trivial topology. As an example we discuss the Picard space which is stretched out into an infinitely long horn but with finite volume.Comment: 4 page

Are GSTM1 Null and GSTT1 Null Risk Factor of Autism Spectrum Disorder? a Preliminary Study

Background: Low plasma total glutathione (tGSH) levels, elevated levels of oxidized glutathione (GSSG) and low ratios of tGSH to GSSG in autism were reported. Glutathione S-transferases (GST) are antioxidant enzymes that play important role in cellular detoxification and the excretion of environmental pollutants including heavy metals. Glutathione S-transferase mu (GSTM1) and Glutathione S-transferase theta (GSTT1) are known to be highly polymorphic. Homozygous deletions of these genes result in lack ofenzyme activity and impaired the ability to excrete metals including mercury. Combined effects of mercury (Hg) accumulation coupled with decreased levels of antioxidants (low glutathione and antioxidant enzymes) contribute to the phenotypic presentation of autism spectrum disorder (ASD). Association of GSTM1 null genotype with autism has been reported. Therefore the preliminary study was performed to investigate the role of GSTM1 null and GSTT1 null as risk factor of ASD associated with phenotype expression.Method: Fifty one ASD patients were recruited from special need & autism school and 45 controls from Semarang & Solo. Blood veins samples were collected and genomic DNA was extracted by salting-out method in CEBIOR Semarang. Genotyping for GSTM1 and GSTT1 gene was done in UMBI Malaysia. Multiplex PCR was performed and PCR products were separated on 1.2 % agarose gel, stained with ethidium bromide and visualized on UV transiluminator. GSTM1 & GSTT1 gene product is about 625 bp and 459 bp. Absence of GSTM1 and GSTT1 gene band was interpreted as GSTM1 null & GSTT1 null.Results: The frequency of GSTM1 null and GSTT1 null in ASD higher compared with control group but the difference is not statistically significant (p=0.357, OR=0.504; 95% CI 0.117-2.168 and p=0.364, OR=0.674; 95% CI 0.287-1.580). There is also no statistically different in the distribution of GSTM1 null and GSTT1 null between mild to moderately autistic and severely autistic (p=0.983, OR=0.980; 95% CI 0.158-6.095 and p=0.439, OR=1.633; 95% CI 0.471-5.656).Conclusion: GSTM1 null and GSTT1 null are not risk factor of ASD. Further investigations are needed with a bigger sample size, analyzing multiple GST genes and GST activity determination to find out the gene susceptibility of ASD and factors that contribute to the phenotype expression of ASD

About ergodicity in the family of limacon billiards

By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limacon billiards. The statistics of these bifurcation shows that the size of the stable intervals decreases with approximately the same rate as their number increases with the period. In particular, we give numerical evidence that arbitrarily close to the cardioid there are elliptic islands due to orbits created in saddle node bifurcations. This shows explicitly that if in this one parameter family of maps ergodicity occurs for more than one parameter the set of these parameter values has a complicated structure.Comment: 17 pages, 9 figure

Closed orbits and spatial density oscillations in the circular billiard

We present a case study for the semiclassical calculation of the oscillations in the particle and kinetic-energy densities for the two-dimensional circular billiard. For this system, we can give a complete classification of all closed periodic and non-periodic orbits. We discuss their bifurcations under variation of the starting point r and derive analytical expressions for their properties such as actions, stability determinants, momentum mismatches and Morse indices. We present semiclassical calculations of the spatial density oscillations using a recently developed closed-orbit theory [Roccia J and Brack M 2008 Phys. Rev. Lett. 100 200408], employing standard uniform approximations from perturbation and bifurcation theory, and test the convergence of the closed-orbit sum.Comment: LaTeX, 42 pp., 17 figures (24 *.eps files, 1 *.tex file); final version (v3) to be published in J. Phys.

Steroid Pathway Genes and Neonatal Respiratory Distress After Betamethasone Use in Anticipated Preterm Birth

Objective: To test several key glucocorticoid genes that are enhanced in lung development for associations with respiratory distress syndrome (RDS) after antenatal corticosteroid use. Methods: A prospective cohort of women received betamethasone to accelerate fetal lung maturity for threatened preterm delivery. DNA was obtained from mothers and newborns. Neonatal RDS was the primary outcome. Genotyping for single-nucleotide polymorphisms (SNPs) in 68 glucocorticoid genes found to be differentially expressed during lung development was performed. Multivariable analysis tested for associations of SNPs in the candidate genes with RDS. Results: Genotypic results for 867 SNPs in 96 mothers and 73 babies were included. Thirty-nine (53.4%) babies developed RDS. Maternal SNPs in the centromeric protein E (CENPE), GLRX, CD9, and AURKA genes provided evidence of association with RDS (P < .01). In newborns, SNPs in COL4A3, BHLHE40, and SRGN provided evidence of association with RDS (P < .01). Conclusion: Single-nucleotide polymorphisms in several glucocorticoid responsive genes suggest association with neonatal RDS after antenatal corticosteroid use

Utilization of photon orbital angular momentum in the low-frequency radio domain

We show numerically that vector antenna arrays can generate radio beams which exhibit spin and orbital angular momentum characteristics similar to those of helical Laguerre-Gauss laser beams in paraxial optics. For low frequencies (< 1 GHz), digital techniques can be used to coherently measure the instantaneous, local field vectors and to manipulate them in software. This opens up for new types of experiments that go beyond those currently possible to perform in optics, for information-rich radio physics applications such as radio astronomy, and for novel wireless communication concepts.Comment: 4 pages, 5 figures. Changed title, identical to the paper published in PR