On Cournot-Nash equilibria with exogenous uncertainty

A large body of literature has accumulated which examines how the optimal solution of an agent maximizing the expectation of a real-valued function, depending on a random parameterp and the agent's behaviorx, reacts to perturbations in the first and second moments ofp. Here, by an approximation valid for small uncertainty, we allow many agents and consider their behavior in a Cournot-Nash equilibrium. We also allowp to depend on the behaviors of the participating agents. We apply the analysis to two models, one of a Cournot oligopoly, the other of a cooperative of individuals where there is uncertainty in the return to communal work

Two Wide Planetary-mass Companions to Solar-type Stars in Upper Scorpius

At wide separations, planetary-mass and brown dwarf companions to solar-type stars occupy a curious region of parameter space not obviously linked to binary star formation or solar system scale planet formation. These companions provide insight into the extreme case of companion formation (either binary or planetary), and due to their relative ease of observation when compared to close companions, they offer a useful template for our expectations of more typical planets. We present the results from an adaptive optics imaging survey for wide (~50–500 AU) companions to solar-type stars in Upper Scorpius. We report one new discovery of a ~14 M_J companion around GSC 06214−00210and confirm that the candidate planetary-mass companion 1RXS J160929.1−210524 detected by Lafrenière et al. is in fact comoving with its primary star. In our survey, these two detections correspond to ~4% of solar-type stars having companions in the 6–20 M_J mass and ~200–500 AU separation range. This figure is higher than would be expected if brown dwarfs and planetary-mass companions were drawn from an extrapolation of the binary mass function. Finally, we discuss implications for the formation of these objects

Secondary Metabolic Gene Cluster Silencing in Aspergillus Nidulans

In contrast to most primary metabolism genes, the genes involved in secondary metabolism and certain nutrient utilization pathways are clustered in fungi. Recently a nuclear protein, LaeA, was found to be required for the transcription of several secondary metabolite gene clusters in Aspergillus nidulans. Here we show that LaeA regulation does not extend to nutrient utilization or the spoC1 sporulation clusters. One of the secondary metabolite clusters regulated by LaeA contains the positive regulatory (i.e. aflR) and biosynthetic genes required for biosynthesis of sterigmatocystin (ST), a carcinogenic toxin. Analysis of ST gene cluster expression indicates LaeA regulation of the cluster is location specific as transcription of genes bordering the ST cluster are unaffected in a ΔlaeA mutant and placement of a primary metabolic gene, argB, in the ST cluster resulted in argB silencing in the ΔlaeA background. ST cluster gene expression was remediated when an additional copy of aflR was placed outside of the cluster but not when placed in the cluster. Site-specific mutation of an s-adenosyl methionine (AdoMet) binding site in LaeA generated a ΔlaeA phenotype suggesting the protein to be a methyltransferase

Developments in PF-HPLC (pneumatic-fluoropolymer high performance liquid chromatography)

Return missions are providing unique opportunities to deepen our knowledge of the formation and evolution of the solar system. The six Apollo missions have been critical in shaping our understanding of the Earth-Moon history [1], and the recent Genesis (solar wind; e.g., [2]), Stardust (cometary dust from Wild 2; e.g., [3,4]) and Hayabusa (dust from S-type asteroid from Itokawa; e.g., [5]) missions brought in a wealth of data

The REE isotopic compositions of the Earth

Lanthanides are a group of 14 naturally occurring elements with atomic numbers ranging from 57 (La) to 74 (Lu), which are also known as rare earth elements (REE). REEs are ubiquitous in minerals and rocks. The chemical properties of REEs vary as smooth functions of their atomic numbers, a phenomenon known as the contraction of the lanthanides. This is the main control behind REE fractionation in minerals and rocks. The relative abundance of REEs is usually presented as the REE pattern by normalizing the concentrations in the sample to those in reference materials such as chondrites and shales

Starlight Demonstration of the Dragonfly Instrument: an Integrated Photonic Pupil Remapping Interferometer for High Contrast Imaging

In the two decades since the first extra-solar planet was discovered, the detection and characterization of extra-solar planets has become one of the key endeavors in all of modern science. Recently direct detection techniques such as interferometry or coronography have received growing attention because they reveal the population of exoplanets inaccessible to Doppler or transit techniques, and moreover they allow the faint signal from the planet itself to be investigated. Next-generation stellar interferometers are increasingly incorporating photonic technologies due to the increase in fidelity of the data generated. Here, we report the design, construction and commissioning of a new high contrast imager; the integrated pupil-remapping interferometer; an instrument we expect will find application in the detection of young faint companions in the nearest star-forming regions. The laboratory characterisation of the instrument demonstrated high visibility fringes on all interferometer baselines in addition to stable closure phase signals. We also report the first successful on-sky experiments with the prototype instrument at the 3.9-m Anglo-Australian Telescope. Performance metrics recovered were consistent with ideal device behaviour after accounting for expected levels of decoherence and signal loss from the uncompensated seeing. The prospect of complete Fourier-coverage coupled with the current performance metrics means that this photonically-enhanced instrument is well positioned to contribute to the science of high contrast companions.Comment: 10 pages, 7 figures, accepted to Mon. Not. of Roy. Ast. Soc., 201

bRing: An observatory dedicated to monitoring the β\beta Pictoris b Hill sphere transit

Aims. We describe the design and first light observations from the $\beta$ Pictoris b Ring ("bRing") project. The primary goal is to detect photometric variability from the young star $\beta$ Pictoris due to circumplanetary material surrounding the directly imaged young extrasolar gas giant planet \bpb. Methods. Over a nine month period centred on September 2017, the Hill sphere of the planet will cross in front of the star, providing a unique opportunity to directly probe the circumplanetary environment of a directly imaged planet through photometric and spectroscopic variations. We have built and installed the first of two bRing monitoring stations (one in South Africa and the other in Australia) that will measure the flux of $\beta$ Pictoris, with a photometric precision of $0.5\%$ over 5 minutes. Each station uses two wide field cameras to cover the declination of the star at all elevations. Detection of photometric fluctuations will trigger spectroscopic observations with large aperture telescopes in order to determine the gas and dust composition in a system at the end of the planet-forming era. Results. The first three months of operation demonstrate that bRing can obtain better than 0.5\% photometry on $\beta$ Pictoris in five minutes and is sensitive to nightly trends enabling the detection of any transiting material within the Hill sphere of the exoplanet

Properties of dense partially random graphs

We study the properties of random graphs where for each vertex a {\it neighbourhood} has been previously defined. The probability of an edge joining two vertices depends on whether the vertices are neighbours or not, as happens in Small World Graphs (SWGs). But we consider the case where the average degree of each node is of order of the size of the graph (unlike SWGs, which are sparse). This allows us to calculate the mean distance and clustering, that are qualitatively similar (although not in such a dramatic scale range) to the case of SWGs. We also obtain analytically the distribution of eigenvalues of the corresponding adjacency matrices. This distribution is discrete for large eigenvalues and continuous for small eigenvalues. The continuous part of the distribution follows a semicircle law, whose width is proportional to the "disorder" of the graph, whereas the discrete part is simply a rescaling of the spectrum of the substrate. We apply our results to the calculation of the mixing rate and the synchronizability threshold.Comment: 14 pages. To be published in Physical Review