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

Observable Effects of Dust Formation in Dynamic Atmospheres of M-type Mira Variables

The formation of dust with temperature-dependent non-grey opacity is considered in a series of self-consistent model atmospheres at different phases of an O-rich Mira variable of mass 1.2 $M_\odot$. Photometric and interferometric properties of these models are predicted under different physical assumptions regarding the dust formation. The iron content of the initial silicate that forms and the availability of grain nuclei are found to be critical parameters that affect the observable properties. In particular, parameters were found where dust would form at 2-3 times the average continuum photospheric radius. This work provides a consistent physical explanation for the larger apparent size of Mira variables at wavelengths shorter than 1 $\mu$m than that predicted by dust free fundamental-mode pulsation models.Comment: Accepted for MNRAS; 9 pages, 5 figure

Entanglement of arbitrary superpositions of modes within two-dimensional orbital angular momentum state spaces

We use spatial light modulators (SLMs) to measure correlations between arbitrary superpositions of orbital angular momentum (OAM) states generated by spontaneous parametric down-conversion. Our technique allows us to fully access a two-dimensional OAM subspace described by a Bloch sphere, within the higher-dimensional OAM Hilbert space. We quantify the entanglement through violations of a Bell-type inequality for pairs of modal superpositions that lie on equatorial, polar, and arbitrary great circles of the Bloch sphere. Our work shows that SLMs can be used to measure arbitrary spatial states with a fidelity sufficient for appropriate quantum information processing systems

The Glasgow outcome at discharge scale: an inpatient assessment of disability after brain injury

This study assesses the validity and reliability of the Glasgow Outcome at Discharge Scale (GODS), which is a tool that is designed to assess disability after brain injury in an inpatient setting. It is derived from the Glasgow Outcome Scale-Extended (GOS-E), which assesses disability in the community after brain injury. Inter-rater reliability on the GODS is high (quadratic-weighted kappa 0.982; 95% confidence interval [CI] 0.968, 0.996) as is concurrent validity with the Disability Rating Scale (DRS) (Spearman correlation −0.728; 95% CI −0.819, −0.601). The GODS is significantly associated with physical and fatigue subscales of the short form (SF)-36 in hospital. In terms of predictive validity the GODS is highly associated with the GOS-E after discharge (Spearman correlation 0.512; 95% CI 0.281, 0.687), with the DRS, and with physical, fatigue, and social subscales of the SF-36. The GODS is recommended as an assessment tool for disability after brain injury pre-discharge and can be used in conjunction with the GOS-E to monitor disability between hospital and the community

Practical beam transport for PFI

The Planet Formation Imager (PFI) is a future kilometric-baseline infrared interferometer to image the complex physical processes of planet formation. Technologies that could be used to transport starlight to a central beam-combining laboratory in PFI include free-space propagation in air or vacuum, and optical fibres. This paper addresses the design and cost issues associated with free-space propagation in vacuum pipes. The signal losses due to diffraction over long differential paths are evaluated, and conceptual beam transport designs employing pupil management to ameliorate these losses are presented and discussed.This is the author accepted manuscript. The final version is available from SPIE via http://dx.doi.org/10.1117/12.223238

Kaon Photoproduction and the Λ\Lambda Decay Parameter α−\alpha_-

The weak decay parameter $\alpha_-$ of the $\Lambda$ is an important quantity for the extraction of polarization observables in various experiments. Moreover, in combination with $\alpha_+$ from $\bar\Lambda$ decay it provides a measure for matter-antimatter asymmetry. The weak decay parameter also affects the decay parameters of the $\Xi$ and $\Omega$ baryons and, in general, any quantity in which the polarization of the $\Lambda$ is relevant. The recently reported value by the BESIII collaboration of $0.750(9)(4)$ is significantly larger than the previous PDG value of $0.642(13)$ that had been accepted and used for over 40 years. In this work we make an independent estimate of $\alpha_-$, using an extensive set of polarization data measured in kaon photoproduction in the baryon resonance region and constraints set by spin algebra. The obtained value is 0.721(6)(5). The result is corroborated by multiple statistical tests as well as a modern phenomenological model, showing that our new value yields the best description of the data in question. Our analysis supports the new BESIII finding that $\alpha_-$ is significantly larger than the previous PDG value. Any experimental quantity relying on the value of $\alpha_-$ should therefore be re-considered.Comment: 6 pages, 1 figure