On two subgroups of U(n), useful for quantum computing

As two basic building blocks for any quantum circuit, we consider the 1-qubit PHASOR circuit Phi(theta) and the 1-qubit NEGATOR circuit N(theta). Both are roots of the IDENTITY circuit. Indeed: both (NO) and N(0) equal the 2 x 2 unit matrix. Additionally, the NEGATOR is a root of the classical NOT gate. Quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2(w)); quantum circuits consisting of controlled NEGATORs are represented by matrices from XU(2(w)). Here, ZU(n) and XU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n x n unitary matrices with all 2n line sums (i.e. all n row sums and all n column sums) equal to 1 and the group ZU(n) consists of all n x n unitary diagonal matrices with first entry equal to 1. Any U(n) matrix can be decomposed into four parts: U = exp(i alpha) Z(1)XZ(2), where both Z(1) and Z(2) are ZU(n) matrices and X is an XU(n) matrix. We give an algorithm to find the decomposition. For n = 2(w) it leads to a four-block synthesis of an arbitrary quantum computer

Optical extinction due to intrinsic structural variations of photonic crystals

Unavoidable variations in size and position of the building blocks of photonic crystals cause light scattering and extinction of coherent beams. We present a new model for both 2 and 3-dimensional photonic crystals that relates the extinction length to the magnitude of the variations. The predicted lengths agree well with our new experiments on high-quality opals and inverse opals, and with literature data analyzed by us. As a result, control over photons is limited to distances up to 50 lattice parameters ($\sim 15 \mu$m) in state-of-the-art structures, thereby impeding large-scale applications such as integrated circuits. Conversely, scattering in photonic crystals may lead to novel physics such as Anderson localization and non-classical diffusion.Comment: 10 pages, 3 figures. Changes include: added Lagendijk as author; simplified and generalized the tex

Cross-talk between signaling pathways leading to defense against pathogens and insects

In nature, plants interact with a wide range of organisms, some of which are harmful (e.g. pathogens, herbivorous insects), while others are beneficial (e.g. growth-promoting rhizobacteria, mycorrhizal fungi, and predatory enemies of herbivores). During the evolutionary arms race between plants and their attackers, primary and secondary immune responses evolved to recognize common or highly specialized features of microbial pathogens (Chisholm et al., 2006), resulting in sophisticated mechanisms of defense

The relevance of spatial variation in ecotourism attributes for the economic sustainability of protected areas

In contemporary society, protected areas are increasingly expected to justify their existence through the services that they provide to society. Protected areas offer many important cultural services, but appraisal of these nonmaterial benefits has generally proven difficult and most studies have focused on single case studies. Data on tourist numbers across multiple camps and protected areas provide a tractable and previously unexploited case study for better understanding the economic sustainability of cultural service provision and the relevance of potentially confounding variables (e.g., location and infrastructure) for park sustainability. We used redundancy analysis and linear models to relate a 5-yr monthly data set (2007–2012) of tourist numbers and tourism-derived income in all camps in South African national parks to a set of largely GIS-derived, determinant attributes that captured key elements of location, biodiversity, infrastructure, and accommodation cost at a camp level. Our analysis suggests that the degree to which cultural services can be converted into revenue for conservation is strongly contingent on infrastructure, location, and the business model that the park adopts. When considered alone, ecological attributes explained 14.2% and 3% of day and overnight visitation rates, respectively. In contrast, models that considered ecosystems in combination with other elements could explain 53% and 67% of variation. Linear models confirmed the existence of complex interactions between groups of variables and highlighted individual covariates that affected visitation rates. Significant variables included ecological features that provided aesthetic services, number of water bodies, elevation, available units, unit costs, and distance to the coast, airports, and other national parks. Taken in context our results suggest that it may be simpler than expected to make predictions about the potential future economic viability of protected areas under alternative models of management, illustrate how ecological variables may represent the “supply” side in cultural services, and highlight the complex interplay between ecological and built infrastructure. Encouragingly, this in turn suggests that relatively small, targeted investments in infrastructure could lead to disproportionate increases in tourist visitation rates and hence in increased revenue for conservation

Gravity-mode period spacings as seismic diagnostic for a sample of gamma Doradus stars from Kepler space photometry and high-resolution ground-based spectroscopy

Gamma Doradus stars (hereafter gamma Dor stars) are gravity-mode pulsators of spectral type A or F. Such modes probe the deep stellar interior, offering a detailed fingerprint of their structure. Four-year high-precision space-based Kepler photometry of gamma Dor stars has become available, allowing us to study these stars with unprecedented detail. We selected, analysed, and characterized a sample of 67 gamma Dor stars for which we have Kepler observations available. For all the targets in the sample we assembled high-resolution spectroscopy to confirm their F-type nature. We found fourteen binaries, among which four single-lined binaries, five double-lined binaries, two triple systems and three binaries with no detected radial velocity variations. We estimated the orbital parameters whenever possible. For the single stars and the single-lined binaries, fundamental parameter values were determined from spectroscopy. We searched for period spacing patterns in the photometric data and identified this diagnostic for 50 of the stars in the sample, 46 of which are single stars or single-lined binaries. We found a strong correlation between the spectroscopic vsini and the period spacing values, confirming the influence of rotation on gamma Dor-type pulsations as predicted by theory. We also found relations between the dominant g-mode frequency, the longest pulsation period detected in series of prograde modes, vsini, and log Teff.Comment: 61 pages, 61 figures, 6 tables, accepted for publication in ApJ