Tropical polar cones, hypergraph transversals, and mean payoff games

We discuss the tropical analogues of several basic questions of convex duality. In particular, the polar of a tropical polyhedral cone represents the set of linear inequalities that its elements satisfy. We characterize the extreme rays of the polar in terms of certain minimal set covers which may be thought of as weighted generalizations of minimal transversals in hypergraphs. We also give a tropical analogue of Farkas lemma, which allows one to check whether a linear inequality is implied by a finite family of linear inequalities. Here, the certificate is a strategy of a mean payoff game. We discuss examples, showing that the number of extreme rays of the polar of the tropical cyclic polyhedral cone is polynomially bounded, and that there is no unique minimal system of inequalities defining a given tropical polyhedral cone.Comment: 27 pages, 6 figures, revised versio

The Literacy of America's College Students

Measures the literacy of 1,827 graduating college and university students from eighty institutions. Looks at the ability to perform prose tasks such as read and use texts; search and comprehend forms; and conduct quantitative, computational tasks

Critical ingredients of supernova Ia radiative-transfer modeling

We explore the physics of SN Ia light curves and spectra using the 1-D non-LTE time-dependent radiative-transfer code CMFGEN. Rather than adjusting ejecta properties to match observations, we select as input one "standard" 1-D Chandrasekhar-mass delayed-detonation hydrodynamical model, and then explore the sensitivity of radiation and gas properties on radiative-transfer modeling assumptions. The correct computation of SN Ia radiation is not exclusively a solution to an "opacity problem", characterized by the treatment of a large number of lines. It is also key to treat important atomic processes consistently. Besides handling line blanketing in non-LTE, we show that including forbidden line transitions of metals is increasingly important for the temperature and ionization of the gas beyond maximum light. Non-thermal ionization and excitation are also critical since they affect the color evolution and the Delta-M15 of our model. While impacting little the bolometric luminosity, a more complete treatment of decay routes leads to enhanced line blanketing, e.g., associated with 48Ti in the U and B bands. Overall, we find that SN Ia radiation properties are influenced in a complicated way by the atomic data we employ, so that obtaining converged results is a challenge. We nonetheless obtain a good match to the golden standard type Ia SN 2005cf in the optical and near-IR, from 5 to 60d after explosion, suggesting that assuming spherical symmetry is not detrimental to SN Ia radiative-transfer modeling at these times. Multi-D effects no doubt matter, but they are perhaps less important than accurately treating non-LTE processes [abridged].Comment: Accepted to MNRA

Constraints on the explosion mechanism and progenitors of type Ia supernovae

Observations of SN 2011fe at early times reveal an evolution analogous to a fireball model of constant color. In contrast, our unmixed delayed detonations of Chandrasekhar-mass white dwarfs (DDC series) exhibit a faster brightening concomitant with a shift in color to the blue. In this paper, we study the origin of these discrepancies. We find that strong chemical mixing largely resolves the photometric mismatch at early times, but it leads to an enhanced line broadening that contrasts, for example, with the markedly narrow SiII6355A line of SN 2011fe. We also explore an alternative configuration with pulsational-delayed detonations (PDDEL model series). Because of the pulsation, PDDEL models retain more unburnt carbon, have little mass at high velocity, and have a much hotter outer ejecta after the explosion. The pulsation does not influence the inner ejecta, so PDDEL and DDC models exhibit similar radiative properties beyond maximum. However, at early times, PDDEL models show bluer optical colors and a higher luminosity, even for weak mixing. Their early-time radiation is derived primarily from the initial shock-deposited energy in the outer ejecta rather than radioactive decay heating. Furthermore, PDDEL models show short-lived CII lines, reminiscent of SN 2013dy. They typically exhibit lines that are weaker, narrower, and of near-constant width, reminiscent of SN 2011fe. In addition to multi-dimensional effects, varying configurations for such ``pulsations" offer a source of spectral diversity amongst SNe Ia. PDDEL and DDC models also provide one explanation for low- and high-velocity gradient SNe Ia.Comment: Accepted to MNRA

Neutron-powered precursors of kilonovae

The merger of binary neutron stars (NSs) ejects a small quantity of neutron rich matter, the radioactive decay of which powers a day to week long thermal transient known as a kilonova. Most of the ejecta remains sufficiently dense during its expansion that all neutrons are captured into nuclei during the r-process. However, recent general relativistic merger simulations by Bauswein and collaborators show that a small fraction of the ejected mass (a few per cent, or ~1e-4 Msun) expands sufficiently rapidly for most neutrons to avoid capture. This matter originates from the shocked-heated interface between the merging NSs. Here we show that the beta-decay of these free neutrons in the outermost ejecta powers a `precursor' to the main kilonova emission, which peaks on a timescale of a few hours following merger at U-band magnitude ~22 (for an assumed distance of 200 Mpc). The high luminosity and blue colors of the neutron precursor render it a potentially important counterpart to the gravitational wave source, that may encode valuable information on the properties of the merging binary (e.g. NS-NS versus NS-black hole) and the NS equation of state. Future work is necessary to assess the robustness of the fast moving ejecta and the survival of free neutrons in the face of neutrino absorptions, although the precursor properties are robust to a moderate amount of leptonization. Our results provide additional motivation for short latency gravitational wave triggers and rapid follow-up searches with sensitive ground based telescopes.Comment: 6 pages, 5 figures, accepted to MNRAS main journa

[CoIII] versus NaID in type Ia supernova spectra

The high metal content and fast expansion of supernova (SN) Ia ejecta lead to considerable line overlap in their optical spectra. Uncertainties in composition and ionization further complicate the process of line identification. In this paper, we focus on the 5900A emission feature seen in SN Ia spectra after bolometric maximum, a line which in the last two decades has been associated with [CoIII]5888A or NaID. Using non-LTE time-dependent radiative-transfer calculations based on Chandrasekhar-mass delayed-detonation models, we find that NaID line emission is extremely weak at all post-maximum epochs. Instead, we predict the presence of [CoIII]5888A after maximum in all our SN Ia models, which cover a range from 0.12 to 0.87Msun of 56Ni. We also find that the [CoIII]5888A forbidden line is present within days of bolometric maximum, and strengthens steadily for weeks thereafter. Both predictions are confirmed by observations. Rather than trivial taxonomy, these findings confirm that it is necessary to include forbidden-line transitions in radiative-transfer simulations of SNe Ia, both to obtain the correct ejecta cooling rate and to match observed optical spectra.Comment: Accepted to MNRA

Sub-Inertial Gravity Modes in the B8V Star KIC 7760680 Reveal Moderate Core Overshooting and Low Vertical Diffusive Mixing

KIC 7760680 is so far the richest slowly pulsating B star, by exhibiting 36 consecutive dipole ($\ell=1$) gravity (g-) modes. The monotonically decreasing period spacing of the series, in addition to the local dips in the pattern confirm that KIC 7760680 is a moderate rotator, with clear mode trapping in chemically inhomogeneous layers. We employ the traditional approximation of rotation to incorporate rotational effects on g-mode frequencies. Our detailed forward asteroseismic modelling of this g-mode series reveals that KIC 7760680 is a moderately rotating B star with mass $\sim3.25$ M$_\odot$. By simultaneously matching the slope of the period spacing, and the number of modes in the observed frequency range, we deduce that the equatorial rotation frequency of KIC 7760680 is 0.4805 day$^{-1}$, which is 26\% of its Roche break up frequency. The relative deviation of the model frequencies and those observed is less than one percent. We succeed to tightly constrain the exponentially-decaying convective core overshooting parameter to $f_{\rm ov}\approx0.024\pm0.001$. This means that convective core overshooting can coexist with moderate rotation. Moreover, models with exponentially-decaying overshoot from the core outperform those with the classical step-function overshoot. The best value for extra diffusive mixing in the radiatively stable envelope is confined to $\log D_{\rm ext}\approx0.75\pm0.25$ (with $D_{\rm ext}$ in cm$^2$ sec$^{-1}$), which is notably smaller than theoretical predictions.Comment: 12 Figures, 2 Tables, all data publicly available for download; accepted for publication in Astrophysical Journa

Analysis of Model-Aided Navigation of Unmanned Aerial Vehicles

To overcome the rapid and unbounded error growth of low-cost Inertial Navigation Systems (INS), aircraft localization methods commonly compensate for Inertial Measurement Unit (IMU) sensor errors by integrating them with Global Positioning System (GPS) measurements via a Kalman Filter. However, over the past decade, the potential of GPS jamming or even spoofing GPS signals has forced the research community to focus on the development of GPS-denied navigation technologies. Among the GPS-denied techniques, one approach that has been considered is the use of a Vehicle Dynamic Models (VDM) to reduce the rate at which an INS becomes unusable. As such, this Master\u27s thesis considers the use of different aerodynamic modeling approaches to aid in compensation of IMU errors of a fixed-wing Unmanned Aerial Vehicle (UAV). The goals of this research are to evaluate the sensitivity of the performance of dynamic model aided navigation in the context of low-cost platforms where performance benefit must be weighed against the complexity that is required to develop the dynamic model. To do this, first, in simulation, the sensitivity to the required modeling accuracy is shown by perturbing the model coefficients with errors. In addition, different sensors and sensor grades are evaluated, and three different model-aided navigation architectures are discussed and evaluated. To conduct this work, a UAV simulation is developed within which a UAV trajectory is driven by ``truth\u27\u27 dynamic model and then IMU measurements are derived and errors are added to them using standard stochastic models for IMU sensors. Finally, the algorithm performance is then evaluated using actual UAV flight testing data from a low cost testbed equipped with GPS and IMU sensors. The testbed used and modeled is a 2.4 m span fixed wing UAV designed and instrumented at WVU

How can allocative inefficiency reveal risk preference? An empirical investigation on French wheat farms

We focus on a simple framework on wheat producer behaviour in a context of price output uncertainty. More precisely, we establish a relationship between ex post output price level and allocative inefficiency that allows to characterize farmers’ risk preferences. Given this analysis, the connection between risk aversion and other socioeconomic variables (such as degree of output specialisation, total asset, debts, farmer’s age…) can furthermore empirically be explored. This relationship is empirically tested on an unbalanced panel including about 650 wheat producers located in the French Department of Meuse over 1992- 2003.Producer behaviour, allocative inefficiency, risk aversion, Crop Production/Industries, Risk and Uncertainty,

Measurements of total scattering spectra from bocaccio (Sebastes paucispinis)

Marine sportfishing in southern California is a huge industry with annual revenues totaling many billions of dollars. However, the stocks of lingcod and six rockfish species have been declared overfished by the Pacific Fisheries Management Council. As part of a multifaceted fisheries management plan, marine conservation areas, covering many million square nautical miles, have been mandated. To monitor the recovery of the rockfish stocks in these areas, scientists are faced with the following challenges: 1) multiple species of rockfish exist in these areas; 2) the species reside near or on the bottom at depths of 80 to 300 m; and 3) they are low in numerical density. To meet these challenges, multifrequency echosounders, multibeam sonar, and cameras mounted on remotely operated vehicles are frequently used (Reynolds et al., 2001). The accuracy and precision of these echosounder results are largely dependent upon the accuracy of the species classification and target strength estimation (MacLennan and Simmonds, 1992)