Input-output relations for a 3-port grating coupled Fabry-Perot cavity

We analyze an optical 3-port reflection grating by means of a scattering matrix formalism. Amplitude and phase relations between the 3 ports, i.e. the 3 orders of diffraction are derived. Such a grating can be used as an all-reflective, low-loss coupler to Fabry-Perot cavities. We derive the input output relations of a 3-port grating coupled cavity and find distinct properties not present in 2-port coupled cavities. The cavity relations further reveal that the 3-port coupler can be designed such that the additional cavity port interferes destructively. In this case the all-reflective, low-loss, single-ended Fabry-Perot cavity becomes equivalent to a standard transmissive, 2-port coupled cavity

Three-port beam splitters-combiners for interferometer applications

We derive generic phase and amplitude coupling relations for beam splitters-combiners that couple a single port with three output ports or input ports, respectively. We apply the coupling relations to a reflection grating that serves as a coupler to a single-ended Fabry-Perot ring cavity. In the impedance-matched case such an interferometer can act as an all-reflective ring mode cleaner. It is further shown that in the highly undercoupled case almost complete separation of carrier power and phase signal from a cavity strain can be achieved

An Analysis of Alcohol and Tobacco Advertising on Billboards by Ethnicity and Income in Omaha, Nebraska

The purpose of this study was to examine the extent to which alcohol and tobacco billboard advertising and vendors are differentially targeted toward African American, Hispanic, White, and/or poor census tracts in the city of Omaha, Nebraska. Using census tract data, differences between tobacco and alcohol billboard advertising found in African American, Hispanic, and White census tracts were analyzed. Differences between high and low income neighborhoods billboard advertising of tobacco and alcohol products were also analyzed. In addition, the content of all tobacco and alcohol billboard advertisements in Omaha was summarized. Tobacco and alcohol vendor information was analyzed in the same way as the billboard advertisements. The data revealed the following conclusions. (1) African American census tracts had the highest rates of tobacco and alcohol billboards per 1,000 people, followed by Hispanic census tracts, while White census tracts had the lowest rates of tobacco and alcohol billboards per 1,000 people. (2) Low income census tracts had greater rates of tobacco and alcohol billboard advertisements per 1,000 people than high income census tracts. (3) Hispanic census tracts had the highest rates of tobacco and alcohol vendors per 1,000 people, followed by African American census tracts, while White census tracts had the lowest rates of tobacco and alcohol vendors per 1,000 people. (4) Low income census tracts had greater rates of tobacco vendors per 1,000 people than high income census tracts. High income census tracts had greater rates of alcohol vendors per 1,000 people than low income census tracts. (5) Billboard advertising in African American and Hispanic census tracts did not contain more racial/ethnic-specific language and models than White census tracts. (6) The trends in tobacco and alcohol billboard advertising in Omaha, Nebraska included very few models in the ads, cigarettes were the only type of tobacco advertised, a large amount of low cost cigarettes were advertised, beer advertising dominated the alcohol product advertising, no malt liquor was advertised, and tobacco and alcohol advertisements were found on 11.7% of all billboards

Sustained coevolution of phage Lambda and Escherichia coli involves inner- as well as outer- membrane defences and counter- defences

Bacteria often evolve resistance to phage through the loss or modification of cell surface receptors. In Escherichia coli and phage λ, such resistance can catalyze a coevolutionary arms race focused on host and phage structures that interact at the outer membrane. Here, we analyse another facet of this arms race involving interactions at the inner membrane, whereby E. coli evolves mutations in mannose permease- encoding genes manY and manZ that impair λ’s ability to eject its DNA into the cytoplasm. We show that these man mutants arose concurrently with the arms race at the outer membrane. We tested the hypothesis that λ evolved an additional counter- defence that allowed them to infect bacteria with deleted man genes. The deletions severely impaired the ancestral λ, but some evolved phage grew well on the deletion mutants, indicating that they regained infectivity by evolving the ability to infect hosts independently of the mannose permease. This coevolutionary arms race fulfils the model of an inverse gene- for- gene infection network. Taken together, the interactions at both the outer and inner membranes reveal that coevolutionary arms races can be richer and more complex than is often appreciated

Plagiocephaly Perception and Prevention: A Need to Intervene Early to Educate Parents

Background: Plagiocephaly is a condition where the cranium has been malformed because of external forces or premature cranial suture fusion. This study’s objective was to gather and examine data regarding parent and caregiver awareness of plagiocephaly and its potential impact on development as well as to determine their rate of concern for positional flattening. Method: A cross-sectional survey study was conducted. Categorical variables were described by frequency and proportions. The study was conducted across eight outpatient pediatric sites. Approximately 1,100 parents and caregivers were targeted. Inclusion criteria required participants to be willing to answer the questionnaire, to be 18 years of age or older, and to have an infant 12 months of age or younger. Results: There were 404 participants, most of whom were female (89.8%) and 30–39 years of age (61.1%). Nineteen children (4.7%) were reported to have plagiocephaly, torticollis, and/or muscle weakness (PTM). A greater percentage of the participants with a child with PTM knew of positional flattening or plagiocephaly (73.3%) compared to those without (53.8%). The respondents with a child with PTM had a greater concern about plagiocephaly than those without (p = .03). Many of the respondents (65.3%) would use a device designed to prevent plagiocephaly. Conclusion: Many parents and caregivers were unaware of plagiocephaly and its potential impact on facial symmetry. A greater percentage of the participants with a child with PTM knew of positional flattening and also had a greater concern about plagiocephaly than those without

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.Comment: LaTeX, 19 page

Towards Collaborative Conceptual Exploration

In domains with high knowledge distribution a natural objective is to create principle foundations for collaborative interactive learning environments. We present a first mathematical characterization of a collaborative learning group, a consortium, based on closure systems of attribute sets and the well-known attribute exploration algorithm from formal concept analysis. To this end, we introduce (weak) local experts for subdomains of a given knowledge domain. These entities are able to refute and potentially accept a given (implicational) query for some closure system that is a restriction of the whole domain. On this we build up a consortial expert and show first insights about the ability of such an expert to answer queries. Furthermore, we depict techniques on how to cope with falsely accepted implications and on combining counterexamples. Using notions from combinatorial design theory we further expand those insights as far as providing first results on the decidability problem if a given consortium is able to explore some target domain. Applications in conceptual knowledge acquisition as well as in collaborative interactive ontology learning are at hand.Comment: 15 pages, 2 figure

Demonstration of 3-port grating phase relations

We experimentally demonstrate the phase relations of 3-port gratings by investigating 3-port coupled Fabry-Perot cavities. Two different gratings which have the same 1st order diffraction efficiency but differ substantially in their 2nd order diffraction efficiency have been designed and manufactured. Using the gratings as couplers to Fabry-Perot cavities we could validate the results of an earlier theoretical description of the phases at a three port grating