A class of equations with peakon and pulson solutions (with an Appendix by Harry Braden and John Byatt-Smith)

We consider a family of integro-differential equations depending upon a parameter $b$ as well as a symmetric integral kernel $g(x)$. When $b=2$ and $g$ is the peakon kernel (i.e. $g(x)=\exp(-|x|)$ up to rescaling) the dispersionless Camassa-Holm equation results, while the Degasperis-Procesi equation is obtained from the peakon kernel with $b=3$. Although these two cases are integrable, generically the corresponding integro-PDE is non-integrable. However,for $b=2$ the family restricts to the pulson family of Fringer & Holm, which is Hamiltonian and numerically displays elastic scattering of pulses. On the other hand, for arbitrary $b$ it is still possible to construct a nonlocal Hamiltonian structure provided that $g$ is the peakon kernel or one of its degenerations: we present a proof of this fact using an associated functional equation for the skew-symmetric antiderivative of $g$. The nonlocal bracket reduces to a non-canonical Poisson bracket for the peakon dynamical system, for any value of $b\neq 1$.Comment: Contribution to volume of Journal of Nonlinear Mathematical Physics in honour of Francesco Caloger

Improving parallel program performance using critical path analysis

A programming tool that performs analysis of critical paths for parallel programs has been developed. This tool determines the critical path for the program as scheduled onto a parallel computer with P processing elements, the critical path for the program expressed as a data flow graph (when maximal parallelism can be expressed), and the minimum number of processing elements (P_opt) needed to obtain maximum program speedup. Experiments were performed using several versions of a Gaussian elimination program to examine how speedup varied with changes in granularity and critical path length. These experiments showed that when the available numer of processing elements P < P_opt, increasing granularity improved program speedup more than reducing (the data flow graph's) critical path length, whereas when P ≥ P_opt, increasing granularity degraded program speedup while reducing critical path length improved program speedup

Photometric Selection of QSO Candidates From GALEX Sources

We present a catalog of 36,120 QSO candidates from the Galaxy Evolution Explorer (GALEX) Release Two (GR2) UV catalog and the USNO-A2.0 optical catalog. The selection criteria are established using known quasars from the Sloan Digital Sky Survey (SDSS). The SDSS sample is then used to assign individual probabilities to our GALEX-USNO candidates. The mean probability is ~50%, and would rise to ~65% if better morphological information than that from USNO were available to eliminate galaxies. The sample is ~40% complete for i<=19.1. Candidates are cross-identified in 2MASS, FIRST, SDSS, and XMM-Newton Slewing Survey (XMMSL1), whenever such counterparts exist. The present catalog covers the 8000 square degrees of GR2 lying above 25 degrees Galactic latitude, but can be extended to all 24,000 square degress that satisfy this criterion as new GALEX data become available.Comment: AASTeX v5.2, 31 pages, 9 figures. Accepted for publication in ApJ. Extended tables available in the online edition of the journa

The impact of feed cost on U.S. poultry production: implications for the impact of increased ethanol production

Crop Production/Industries, Livestock Production/Industries,

When it comes to teaching and tenure it is time to walk the walk.

Institutions should value teaching and service, and not just research, when considering faculty for promotion and tenure

Residual Symmetries Applied to Neutrino Oscillations at NOν\nuA and T2K

The results previously obtained from the model-independent application of a generalized hidden horizontal $\mathbb{Z}_2$ symmetry to the neutrino mass matrix are updated using the latest global fits for the neutrino oscillation parameters. The resulting prediction for the Dirac $CP$ phase $\delta_D$ is in agreement with recent results from T2K. The distribution for the Jarlskog invariant $J_\nu$ has become sharper and appears to be approaching a particular region. The approximate effects of matter on long baseline neutrino experiments are explored, and it is shown how the weak interactions between the neutrinos and the particles that make up the Earth can help to determine the mass hierarchy. A similar strategy is employed to show how NO$\nu$A and T2K could determine the octant of $\theta_a (\equiv \theta_{23})$. Finally, the exact effects of matter are obtained numerically in order to make comparisons with the form of the approximate solutions. From this analysis there emerges some interesting features of the effective mass eigenvalues.Comment: 9 pages, 1 table, 17 figure

Determining the Mass of Kepler-78b With Nonparametric Gaussian Process Estimation

Kepler-78b is a transiting planet that is 1.2 times the radius of Earth and orbits a young, active K dwarf every 8 hours. The mass of Kepler-78b has been independently reported by two teams based on radial velocity measurements using the HIRES and HARPS-N spectrographs. Due to the active nature of the host star, a stellar activity model is required to distinguish and isolate the planetary signal in radial velocity data. Whereas previous studies tested parametric stellar activity models, we modeled this system using nonparametric Gaussian process (GP) regression. We produced a GP regression of relevant Kepler photometry. We then use the posterior parameter distribution for our photometric fit as a prior for our simultaneous GP + Keplerian orbit models of the radial velocity datasets. We tested three simple kernel functions for our GP regressions. Based on a Bayesian likelihood analysis, we selected a quasi-periodic kernel model with GP hyperparameters coupled between the two RV datasets, giving a Doppler amplitude of 1.86 $\pm$ 0.25 m s$^{-1}$ and supporting our belief that the correlated noise we are modeling is astrophysical. The corresponding mass of 1.87 $^{+0.27}_{-0.26}$ M$_{\oplus}$ is consistent with that measured in previous studies, and more robust due to our nonparametric signal estimation. Based on our mass and the radius measurement from transit photometry, Kepler-78b has a bulk density of 6.0$^{+1.9}_{-1.4}$ g cm$^{-3}$. We estimate that Kepler-78b is 32$\pm$26% iron using a two-component rock-iron model. This is consistent with an Earth-like composition, with uncertainty spanning Moon-like to Mercury-like compositions.Comment: 10 pages, 5 figures, accepted to ApJ 6/16/201

Safe Policy Synthesis in Multi-Agent POMDPs via Discrete-Time Barrier Functions

A multi-agent partially observable Markov decision process (MPOMDP) is a modeling paradigm used for high-level planning of heterogeneous autonomous agents subject to uncertainty and partial observation. Despite their modeling efficiency, MPOMDPs have not received significant attention in safety-critical settings. In this paper, we use barrier functions to design policies for MPOMDPs that ensure safety. Notably, our method does not rely on discretization of the belief space, or finite memory. To this end, we formulate sufficient and necessary conditions for the safety of a given set based on discrete-time barrier functions (DTBFs) and we demonstrate that our formulation also allows for Boolean compositions of DTBFs for representing more complicated safe sets. We show that the proposed method can be implemented online by a sequence of one-step greedy algorithms as a standalone safe controller or as a safety-filter given a nominal planning policy. We illustrate the efficiency of the proposed methodology based on DTBFs using a high-fidelity simulation of heterogeneous robots.Comment: 8 pages and 4 figure

Barrier Functions for Multiagent-POMDPs with DTL Specifications

Multi-agent partially observable Markov decision processes (MPOMDPs) provide a framework to represent heterogeneous autonomous agents subject to uncertainty and partial observation. In this paper, given a nominal policy provided by a human operator or a conventional planning method, we propose a technique based on barrier functions to design a minimally interfering safety-shield ensuring satisfaction of high-level specifications in terms of linear distribution temporal logic (LDTL). To this end, we use sufficient and necessary conditions for the invariance of a given set based on discrete-time barrier functions (DTBFs) and formulate sufficient conditions for finite time DTBF to study finite time convergence to a set. We then show that different LDTL mission/safety specifications can be cast as a set of invariance or finite time reachability problems. We demonstrate that the proposed method for safety-shield synthesis can be implemented online by a sequence of one-step greedy algorithms. We demonstrate the efficacy of the proposed method using experiments involving a team of robots