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

Quasi-periodic pulsations in solar and stellar flares: re-evaluating their nature in the context of power-law flare Fourier spectra

The nature of quasi-periodic pulsations in solar and stellar flares remains debated. Recent work has shown that power-law-like Fourier power spectra, also referred to as 'red' noise processes, are an intrinsic property of solar and stellar flare signals, a property that many previous studies of this phenomenon have not accounted for. Hence a re-evaluation of the existing interpretations and assumptions regarding QPP is needed. Here we adopt a Bayesian method for investigating this phenomenon, fully considering the Fourier power law properties of flare signals. Using data from the PROBA2/LYRA, Fermi/GBM, Nobeyama Radioheliograph and Yohkoh/HXT instruments, we study a selection of flares from the literature identified as QPP events. Additionally we examine optical data from a recent stellar flare that appears to exhibit oscillatory properties. We find that, for all but one event tested, an explicit oscillation is not required in order to explain the observations. Instead, the flare signals are adequately described as a manifestation of a power law in the Fourier power spectrum, rather than a direct signature of oscillating components or structures. However, for the flare of 1998 May 8, strong evidence for the existence of an explicit oscillation with P ~ 14-16 s is found in the 17 GHz radio data and the 13-23 keV Yohkoh HXT data. We conclude that, most likely, many previously analysed events in the literature may be similarly described in terms of power laws in the flare Fourier power spectrum, without the need to invoke a narrowband, oscillatory component. As a result the prevalence of oscillatory signatures in solar and stellar flares may be less than previously believed. The physical mechanism behind the appearance of the observed power laws is discussed.Comment: 11 pages, 7 figures, 1 table. Accepted for publication in The Astrophysical Journa

They are Small Worlds After All: Revised Properties of Kepler M Dwarf Stars and their Planets

We classified the reddest ($r-J>2.2$) stars observed by the NASA $Kepler$ mission into main sequence dwarf or evolved giant stars and determined the properties of 4216 M dwarfs based on a comparison of available photometry with that of nearby calibrator stars, as well as available proper motions and spectra. We revised the properties of candidate transiting planets using the stellar parameters, high-resolution imaging to identify companion stars, and, in the case of binaries, fitting light curves to identify the likely planet host. In 49 of 54 systems we validated the primary as the host star. We inferred the intrinsic distribution of M dwarf planets using the method of iterative Monte Carlo simulation. We compared several models of planet orbital geometry and clustering and found that one where planets are exponentially distributed and almost precisely coplanar best describes the distribution of multi-planet systems. We determined that $Kepler$ M dwarfs host an average of $2.2 \pm 0.3$ planets with radii of 1-4$R_{\oplus}$ and orbital periods of 1.5-180 d. The radius distribution peaks at $\sim 1.2R_{\oplus}$ and is essentially zero at $4R_{\oplus}$, although we identify three giant planet candidates other than the previously confirmed Kepler-45b. There is suggestive but not significant evidence that the radius distribution varies with orbital period. The distribution with logarithmic orbital period is flat except for a decline for orbits less than a few days. Twelve candidate planets, including two Jupiter-size objects, experience an irradiance below the threshold level for a runaway greenhouse on an Earth-like planet and are thus in a "habitable zone".Comment: MNRAS, in press. Tables 1, 3, and 4 are available in electronic form in the "anc" director

Little Kingdoms: The Counties of Kentucky, 1850–1891

Kentucky’s counties though theoretically provinces of the state were in reality powerful semi-sovereign entities during the latter half of the 19th century. Their positive accomplishments were many. Government funds were wisely invested in internal improvements, road construction, law enforcement, tax collection, and relief of the poor. Keen competition for county offices, placed on an electoral basis by the Constitution of 1850, brought added vitality to Kentucky’s uniquely intense political life, and the official day on which the county courts met continued to be the foremost social and economic day of the month. Despite these positive facets and the good intentions of the reformers of 1849-1850, however, Kentucky’s counties retained a tradition of parochialism, corruption, and inefficiency. The establishment of elective offices eliminated few of the deficiencies of the county system. The railroads were the focus of rivalry and scandal. Prevailing lawlessness compounded the semi-anarchical condition of many of the counties. Rising crime rates rendered insecure the lives of many Kentuckians. Nineteenth-century Kentucky left no legacy of law and order. A grasp of this paradoxical situation is essential to an understanding of late 19th-century Kentucky history. In this probing study, Robert M. Ireland offers the first thorough examination of the impact of Kentucky’s counties on the state’s constitutional, political, social, and economic development during this period. Robert M. Ireland is associate professor of history at the University of Kentucky.https://uknowledge.uky.edu/upk_political_science_american_politics/1017/thumbnail.jp

Predicting and Characterising Zinc Metal Binding Sites in Proteins

Zinc is one of the most important biologically active metals. Ten per cent of the human genome is thought to encode a zinc binding protein and its uses encompass catalysis, structural stability, gene expression and immunity. Knowing whether a protein binds to zinc can offer insights into its function, and knowing precisely where it binds zinc can show the mechanism by which it carries out its intended function, as well as provide suggestions as to how pharmaceutical molecules might disrupt or enhance this function where required for medical interventions. At present, there is no specific resource devoted to identifying and presenting all currently known zinc binding sites. This PhD has resulted in the creation of ZincBind — a database of zinc binding sites (ZincBindDB), predictive models of zinc binding at the family level (ZincBindPredict) and a user-friendly, modern website frontend (ZincBindWeb). Both ZincBindDB and ZincBindPredict are also available as GraphQL APIs. The database of zinc binding sites currently contains 38,141 sites, and is automatically updated every week. The predictive models, trained using the Random Forest Machine Learning algorithm, all achieve an MCC ≥ 0.88, recall ≥0.93 and precision ≥0.91 for the structural models (mean MCC = 0.97), while the sequence models have MCC ≥ 0.64, recall ≥0.80 and pre- cision ≥0.83 (mean MCC = 0.87), outperforming competing, previous predictive models

Binary Black Holes in the Inspiral Regime: The Effect of Spins and Eccentricity on Spacetime Dynamics and Gravitational Radiation

Observations of black hole binaries via the emission of gravitational waves are one of the most exciting discoveries in physics in the past 50 years. The most generic black holes in nature are ones with spin, which may be misaligned with the orbital angular momentum of the binary, and also orbital eccentricity. This demands computationally inexpensive and accurate models of spinning binary black holes for hundreds of orbits as the binary inspirals. This dissertation is divided into two projects, both of which focus on binary black holes with spin. In the first project, I construct and present a new global, fully analytic, approximate spacetime which accurately describes the dynamics of nonprecessing, spinning black hole binaries during the inspiral phase of the relativistic merger process. This approximate solution of the vacuum Einstein\u27s equations can be obtained by asymptotically matching perturbed Kerr solutions near the two black holes to a post-Newtonian metric valid far from the two black holes. This metric is then matched to a post-Minkowskian metric even farther out in the wave zone. The procedure of asymptotic matching is generalized to be valid to all times, instead of a small group of initial hypersurfaces discussed in previous works. I then re-examine the asymptotic matching in the case of precession of the spins, allowing for generically spinning black hole binary metrics. This metric is well suited for long term dynamical simulations of spinning black hole binary spacetimes prior to merger, such as studies of circumbinary gas accretion which requires hundreds of binary orbits. In the second project, I present a method for developing and calculating the gravitational waveforms from generically spinning, black hole binaries, with significant orbital eccentricity. I use the Lagrangian formulation of the post Newtonian equations of motion in the harmonic gauge for the generation of precessing, eccentric gravitational wave signatures. The equations of motion describing the black hole binary system are important to our understanding of fundamental relativity, for both the context of supermassive black holes as well as stellar mass systems. If gravitational wave measurements are able to measure a non-negligible eccentricity from the binary, this may point to a unique formation model through relativistic 3-body interactions in dense stellar fields, which will impart occasionally significant eccentricity. This provides insight into the formation history of the binary, and explicitly the last dynamical effect the binary experienced before merging