Design, fabrication, and characterization of deep-etched waveguide gratings

One-dimensional (1-D) deep-etched gratings on a specially grown AlGaAs wafer were designed and fabricated. The gratings were fabricated using state-of-the-art electron beam lithography and high-aspect-ratio reactive ion etching (RIE) in order to achieve the required narrow deep air slots with good accuracy and reproducibility. Since remarkable etch depths (up to 1.5 /spl mu/m), which completely cut through the waveguide core layer, have been attained, gratings composed of only five periods (and, thus, shorter than 6 /spl mu/m) have a bandgap larger than 100 nm. A defect was introduced by increasing the width of the central semiconductor tooth to create microcavities that exhibit a narrow transmission peak (less than 7 nm) around the wavelength of 1530 nm. The transmission spectra between 1460 and 1580 nm have been systematically measured, and the losses have been estimated for a set of gratings, both with and without a defect, for different periods and air slot dimensions. Numerical results obtained via a bidirectional beam propagation code allowed the evaluation of transmissivity, reflectivity, and diffraction losses. By comparing experimental results with the authors' numerical findings, a clear picture of the role of the grating's geometric parameters in determining its spectral features and diffractive losses is illustrated

The orbifold transform and its applications

We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the theory of permutation orbifolds is addressed, and the general results illustrated on the example of torus partition functions

Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio

Discrete molecular dynamics simulations of peptide aggregation

We study the aggregation of peptides using the discrete molecular dynamics simulations. At temperatures above the alpha-helix melting temperature of a single peptide, the model peptides aggregate into a multi-layer parallel beta-sheet structure. This structure has an inter-strand distance of 0.48 nm and an inter-sheet distance of 1.0 nm, which agree with experimental observations. In this model, the hydrogen bond interactions give rise to the inter-strand spacing in beta-sheets, while the Go interactions among side chains make beta-strands parallel to each other and allow beta-sheets to pack into layers. The aggregates also contain free edges which may allow for further aggregation of model peptides to form elongated fibrils.Comment: 15 pages, 8 figure

Statistical Properties of Cross-Correlation in the Korean Stock Market

We investigate the statistical properties of the correlation matrix between individual stocks traded in the Korean stock market using the random matrix theory (RMT) and observe how these affect the portfolio weights in the Markowitz portfolio theory. We find that the distribution of the correlation matrix is positively skewed and changes over time. We find that the eigenvalue distribution of original correlation matrix deviates from the eigenvalues predicted by the RMT, and the largest eigenvalue is 52 times larger than the maximum value among the eigenvalues predicted by the RMT. The $\beta_{473}$ coefficient, which reflect the largest eigenvalue property, is 0.8, while one of the eigenvalues in the RMT is approximately zero. Notably, we show that the entropy function $E(\sigma)$ with the portfolio risk $\sigma$ for the original and filtered correlation matrices are consistent with a power-law function, $E(\sigma) \sim \sigma^{-\gamma}$, with the exponent $\gamma \sim 2.92$ and those for Asian currency crisis decreases significantly

Overriding water table control on managed peatland greenhouse gas emissions

Global peatlands store more carbon than is naturally present in the atmosphere1,2. However, many peatlands are under pressure from drainage-based agriculture, plantation development and fire, with the equivalent of around 3% of all anthropogenic greenhouse gases emitted from drained peatland3–5. Efforts to curb such emissions are intensifying through the conservation of undrained peatlands and rewetting of drained systems6. Here we report CO2 eddy covariance data from 16 locations and CH4 data from 41 locations in the British Isles, and combine them with published data from sites across all major peatland biomes. We find that the mean annual effective water-table depth (WTDe; that is, the average depth of the aerated peat layer) overrides all other ecosystem- and management-related controls on greenhouse gas fluxes. We estimate that every 10 cm of reduction in WTDe could reduce the net warming impact of CO2 and CH4 emissions (100-year Global Warming Potentials) by at least 3 t CO2e ha-1 yr-1, until WTDe is < 30 cm. Raising water levels further would continue to have a net cooling effect until WTDe is < 10 cm. Our results suggest that greenhouse gas emissions from peatlands drained for agriculture could be greatly reduced without necessarily halting their productive use. Halving WTDe in all drained agricultural peatlands, for example, could reduce emissions by the equivalent of over 1% of global anthropogenic emissions

Validation and optimization of host immunological bio-signatures for a point-of-care test for TB disease

The development of a non-sputum-based, point-of-care diagnostic test for tuberculosis (TB) is a priority in the global effort to combat this disease, particularly in resource-constrained settings. Previous studies have identified host biomarker signatures which showed potential, but there is a need to validate and refine these for development as a test. We recruited 1,403 adults presenting with symptoms suggestive of pulmonary TB at primary healthcare clinics in six countries from West, East and Southern Africa. Of the study cohort, 326 were diagnosed with TB and 787 with other respiratory diseases, from whom we randomly selected 1005 participants. Using Luminex(R) technology, we measured the levels of 20 host biomarkers in serum samples which we used to evaluate the diagnostic accuracy of previously identified and novel bio-signatures. Our previously identified seven-marker bio-signature did not perform well (sensitivity: 89%, specificity: 60%). We also identified an optimal, two-marker bio-signature with a sensitivity of 94% and specificity of 69% in patients with no history of previous TB. This signature performed slightly better than C-reactive protein (CRP) alone. The cut-off value for a positive diagnosis differed for human immuno-deficiency virus (HIV)-positive and -negative individuals. Notably, we also found that no signature was able to diagnose TB adequately in patients with a prior history of the disease. We have identified a two-marker, pan-African bio-signature which is more robust than CRP alone and meets the World Health Organization (WHO) target product profile requirements for a triage test in both HIV-negative and HIV-positive individuals. This signature could be incorporated into a point-of-care device, greatly reducing the necessity for expensive confirmatory diagnostics and potentially reducing the number of cases currently lost to follow-up. It might also potentially be useful with individuals unable to provide sputum or with paucibacillary disease. We suggest that the performance of TB diagnostic signatures can be improved by incorporating the HIV-status of the patient. We further suggest that only patients who have never had TB be subjected to a triage test and that those with a history of previous TB be evaluated using more direct diagnostic techniques.Cancer Signaling networks and Molecular Therapeutic

25 Years of Self-organized Criticality: Concepts and Controversies

Introduced by the late Per Bak and his colleagues, self-organized criticality (SOC) has been one of the most stimulating concepts to come out of statistical mechanics and condensed matter theory in the last few decades, and has played a significant role in the development of complexity science. SOC, and more generally fractals and power laws, have attracted much comment, ranging from the very positive to the polemical. The other papers (Aschwanden et al. in Space Sci. Rev., 2014, this issue; McAteer et al. in Space Sci. Rev., 2015, this issue; Sharma et al. in Space Sci. Rev. 2015, in preparation) in this special issue showcase the considerable body of observations in solar, magnetospheric and fusion plasma inspired by the SOC idea, and expose the fertile role the new paradigm has played in approaches to modeling and understanding multiscale plasma instabilities. This very broad impact, and the necessary process of adapting a scientific hypothesis to the conditions of a given physical system, has meant that SOC as studied in these fields has sometimes differed significantly from the definition originally given by its creators. In Bak’s own field of theoretical physics there are significant observational and theoretical open questions, even 25 years on (Pruessner 2012). One aim of the present review is to address the dichotomy between the great reception SOC has received in some areas, and its shortcomings, as they became manifest in the controversies it triggered. Our article tries to clear up what we think are misunderstandings of SOC in fields more remote from its origins in statistical mechanics, condensed matter and dynamical systems by revisiting Bak, Tang and Wiesenfeld’s original papers