GILP: An Interactive Tool for Visualizing the Simplex Algorithm

The Simplex algorithm for solving linear programs-one of Computing in Science & Engineering's top 10 most influential algorithms of the 20th century-is an important topic in many algorithms courses. While the Simplex algorithm relies on intuitive geometric ideas, the computationally-involved mechanics of the algorithm can obfuscate a geometric understanding. In this paper, we present gilp, an easy-to-use Simplex algorithm visualization tool designed to explicitly connect the mechanical steps of the algorithm with their geometric interpretation. We provide an extensive library with example visualizations, and our tool allows an instructor to quickly produce custom interactive HTML files for students to experiment with the algorithm (without requiring students to install anything!). The tool can also be used for interactive assignments in Jupyter notebooks, and has been incorporated into a forthcoming Data Science and Decision Making interactive textbook. In this paper, we first describe how the tool fits into the existing literature on algorithm visualizations: how it was designed to facilitate student engagement and instructor adoption, and how it substantially extends existing algorithm visualization tools for Simplex. We then describe the development and usage of the tool, and report feedback from its use in a course with roughly 100 students. Student feedback was overwhelmingly positive, with students finding the tool easy to use: it effectively helped them link the algebraic and geometrical views of the Simplex algorithm and understand its nuances. Finally, gilp is open-source, includes an extension to visualizing linear programming-based branch and bound, and is readily amenable to further extensions.Comment: ACM SIGCSE 2023 Manuscript, 13 pages, 5 figure

Optimization of inhomogeneous electron correlation factors in periodic solids

A method is presented for the optimization of one-body and inhomogeneous two-body terms in correlated electronic wave functions of Jastrow-Slater type. The most general form of inhomogeneous correlation term which is compatible with crystal symmetry is used and the energy is minimized with respect to all parameters using a rapidly convergent iterative approach, based on Monte Carlo sampling of the energy and fitting energy fluctuations. The energy minimization is performed exactly within statistical sampling error for the energy derivatives and the resulting one- and two-body terms of the wave function are found to be well-determined. The largest calculations performed require the optimization of over 3000 parameters. The inhomogeneous two-electron correlation terms are calculated for diamond and rhombohedral graphite. The optimal terms in diamond are found to be approximately homogeneous and isotropic over all ranges of electron separation, but exhibit some inhomogeneity at short- and intermediate-range, whereas those in graphite are found to be homogeneous at short-range, but inhomogeneous and anisotropic at intermediate- and long-range electron separation.Comment: 23 pages, 15 figures, 1 table, REVTeX4, submitted to PR

Local and global pyrogeographic evidence that indigenous fire management creates pyrodiversity

Despite the challenges wildland fire poses to contemporary resource management, many fire-prone ecosystems have adapted over centuries to millennia to intentional landscape burning by people to maintain resources. We combine fieldwork, modeling, and a literature survey to examine the extent and mechanism by which anthropogenic burning alters the spatial grain of habitat mosaics in fire-prone ecosystems. We survey the distribution of Callitris intratropica, a conifer requiring long fire-free intervals for establishment, as an indicator of long-unburned habitat availability under Aboriginal burning in the savannas of Arnhem Land. We then use cellular automata to simulate the effects of burning identical proportions of the landscape under different fire sizes on the emergent patterns of habitat heterogeneity. Finally, we examine the global extent of intentional burning and diversity of objectives using the scientific literature. The current distribution of Callitris across multiple field sites suggested long-unburnt patches are common and occur at fine scales (<0.5 ha), while modeling revealed smaller, patchy disturbances maximize patch age diversity, creating a favorable habitat matrix for Callitris. The literature search provided evidence for intentional landscape burning across multiple ecosystems on six continents, with the number of identified objectives ranging from two to thirteen per study. The fieldwork and modeling results imply that the occurrence of long-unburnt habitat in fire-prone ecosystems may be an emergent property of patch scaling under fire regimes dominated by smaller fires. These findings provide a model for understanding how anthropogenic burning alters spatial and temporal aspects of habitat heterogeneity, which, as the literature survey strongly suggests, warrant consideration across a diversity of geographies and cultures. Our results clarify how traditional fire management shapes fire-prone ecosystems, which despite diverse objectives, has allowed human societies to cope with fire as a recurrent disturbance

Detecting the Companions and Ellipsoidal Variations of RS CVn Primaries: II. omicron Draconis, a Candidate for Recent Low-Mass Companion Ingestion

To measure the stellar and orbital properties of the metal-poor RS CVn binary o Draconis (o Dra), we directly detect the companion using interferometric observations obtained with the Michigan InfraRed Combiner at Georgia State University's Center for High Angular Resolution Astronomy (CHARA) Array. The H-band flux ratio between the primary and secondary stars is the highest confirmed flux ratio (370 +/- 40) observed with long-baseline optical interferometry. These detections are combined with radial velocity data of both the primary and secondary stars, including new data obtained with the Tillinghast Reflector Echelle Spectrograph on the Tillinghast Reflector at the Fred Lawrence Whipple Observatory and the 2-m Tennessee State University Automated Spectroscopic Telescope at Fairborn Observatory. We determine an orbit from which we find model-independent masses and ages of the components (M_A = 1.35 +\- 0.05 M_Sun, M_B = 0.99 +\- 0.02 M_Sun, system age = 3.0 -\+ 0.5 Gyr). An average of a 23-year light curve of o Dra from the Tennessee State University Automated Photometric Telescope folded over the orbital period newly reveals eclipses and the quasi-sinusoidal signature of ellipsoidal variations. The modeled light curve for our system's stellar and orbital parameters confirm these ellipsoidal variations due to the primary star partially filling its Roche lobe potential, suggesting most of the photometric variations are not due to stellar activity (starspots). Measuring gravity darkening from the average light curve gives a best-fit of beta = 0.07 +\- 0.03, a value consistent with conventional theory for convective envelope stars. The primary star also exhibits an anomalously short rotation period, which, when taken with other system parameters, suggests the star likely engulfed a low-mass companion that had recently spun-up the star.Comment: 14 pages, 13 figures, Accepted to Ap

Multifrequency Observations of Radio Pulse Broadening and Constraints on Interstellar Electron Density Microstructure

We have made observations of 98 low-Galactic-latitude pulsars to measure pulse broadening caused by multipath propagation through the interstellar medium. Data were collected with the 305-m Arecibo telescope at four radio frequencies between 430 and 2380 MHz. We used a CLEAN-based algorithm to deconvolve interstellar pulse broadening from the measured pulse shapes. We employed two distinct pulse broadening functions (PBFs): PBF$_1$ is appropriate for a thin screen of scattering material between the Earth and a pulsar, while PBF$_2$ is appropriate for scattering material uniformly distributed along the line of sight from the Earth to a pulsar. We found that some observations were better fit by PBF$_1$ and some by PBF$_2$. Pulse broadening times ($\tau_d$) are derived from fits of PBFs to the data, and are compared with the predictions of a smoothed model of the Galactic electron distribution. Several lines of sight show excess broadening, which we model as clumps of high density scattering material. A global analysis of all available data finds that the pulse broadening scales with frequency, $\nu$, as \taud \propto\nu^{-\alpha} where $\alpha\sim 3.9\pm 0.2$. This is somewhat shallower than the value $\alpha=4.4$ expected from a Kolmogorov medium, but could arise if the spectrum of turbulence has an inner cutoff at $\sim$300--800 km. A few objects follow particularly shallow scaling laws (the mean scaling index \meanalpha \sim 3.1 \pm 0.1 and $\sim 3.8 \pm 0.2$ respectively for the case of PBF$_1$ and PBF$_2$), which may arise from large scale refraction or from the truncation of scattering screens transverse to the Earth--pulsar line of sight.Comment: Accepted for publication in the Astrophysical Journal; 32 pages, 11 figure

Optical to near-infrared transmission spectrum of the warm sub-Saturn HAT-P-12b

We present the transmission spectrum of HAT-P-12b through a joint analysis of data obtained from the Hubble Space Telescope Space Telescope Imaging Spectrograph (STIS) and Wide Field Camera 3 (WFC3) and Spitzer, covering the wavelength range 0.3-5.0 $\mu$m. We detect a muted water vapor absorption feature at 1.4 $\mu$m attenuated by clouds, as well as a Rayleigh scattering slope in the optical indicative of small particles. We interpret the transmission spectrum using both the state-of-the-art atmospheric retrieval code SCARLET and the aerosol microphysics model CARMA. These models indicate that the atmosphere of HAT-P-12b is consistent with a broad range of metallicities between several tens to a few hundred times solar, a roughly solar C/O ratio, and moderately efficient vertical mixing. Cloud models that include condensate clouds do not readily generate the sub-micron particles necessary to reproduce the observed Rayleigh scattering slope, while models that incorporate photochemical hazes composed of soot or tholins are able to match the full transmission spectrum. From a complementary analysis of secondary eclipses by Spitzer, we obtain measured depths of $0.042\%\pm0.013\%$ and $0.045\%\pm0.018\%$ at 3.6 and 4.5 $\mu$m, respectively, which are consistent with a blackbody temperature of $890^{+60}_{-70}$ K and indicate efficient day-night heat recirculation. HAT-P-12b joins the growing number of well-characterized warm planets that underscore the importance of clouds and hazes in our understanding of exoplanet atmospheres.Comment: 25 pages, 19 figures, accepted for publication in AJ, updated with proof correction

A Precise Water Abundance Measurement for the Hot Jupiter WASP-43b

The water abundance in a planetary atmosphere provides a key constraint on the planet's primordial origins because water ice is expected to play an important role in the core accretion model of planet formation. However, the water content of the Solar System giant planets is not well known because water is sequestered in clouds deep in their atmospheres. By contrast, short-period exoplanets have such high temperatures that their atmospheres have water in the gas phase, making it possible to measure the water abundance for these objects. We present a precise determination of the water abundance in the atmosphere of the 2 $M_\mathrm{Jup}$ short-period exoplanet WASP-43b based on thermal emission and transmission spectroscopy measurements obtained with the Hubble Space Telescope. We find the water content is consistent with the value expected in a solar composition gas at planetary temperatures (0.4-3.5x solar at 1 $\sigma$ confidence). The metallicity of WASP-43b's atmosphere suggested by this result extends the trend observed in the Solar System of lower metal enrichment for higher planet masses.Comment: Accepted to ApJL; this version contains three supplemental figures that are not included in the published paper. See also our companion paper "Thermal structure of an exoplanet atmosphere from phase-resolved emission spectroscopy" by Stevenson et a

How Reasoning Aims at Truth

Many hold that theoretical reasoning aims at truth. In this paper, I ask what it is for reasoning to be thus aim-directed. Standard answers to this question explain reasoning’s aim-directedness in terms of intentions, dispositions, or rule-following. I argue that, while these views contain important insights, they are not satisfactory. As an alternative, I introduce and defend a novel account: reasoning aims at truth in virtue of being the exercise of a distinctive kind of cognitive power, one that, unlike ordinary dispositions, is capable of fully explaining its own exercises. I argue that this account is able to avoid the difficulties plaguing standard accounts of the relevant sort of mental teleology

Detecting the Companions and Ellipsoidal Variations of RS CVn Primaries: I. sigma Geminorum

To measure the properties of both components of the RS CVn binary sigma Geminorum (sigma Gem), we directly detect the faint companion, measure the orbit, obtain model-independent masses and evolutionary histories, detect ellipsoidal variations of the primary caused by the gravity of the companion, and measure gravity darkening. We detect the companion with interferometric observations obtained with the Michigan InfraRed Combiner (MIRC) at Georgia State University's Center for High Angular Resolution Astronomy (CHARA) Array with a primary-to-secondary H-band flux ratio of 270+/-70. A radial velocity curve of the companion was obtained with spectra from the Tillinghast Reflector Echelle Spectrograph (TRES) on the 1.5-m Tillinghast Reflector at Fred Lawrence Whipple Observatory (FLWO). We additionally use new observations from the Tennessee State University Automated Spectroscopic and Photometric Telescopes (AST and APT, respectively). From our orbit, we determine model-independent masses of the components (M_1 = 1.28 +/- 0.07 M_Sun, M_2 = 0.73 +/- 0.03 M_Sun), and estimate a system age of 5 -/+ 1 Gyr. An average of the 27-year APT light curve of sigma Gem folded over the orbital period (P = 19.6027 +/- 0.0005 days) reveals a quasi-sinusoidal signature, which has previously been attributed to active longitudes 180 deg apart on the surface of sigma Gem. With the component masses, diameters, and orbit, we find that the predicted light curve for ellipsoidal variations due to the primary star partially filling its Roche lobe potential matches well with the observed average light curve, offering a compelling alternative explanation to the active longitudes hypothesis. Measuring gravity darkening from the light curve gives beta < 0.1, a value slightly lower than that expected from recent theory.Comment: Accepted to ApJ, 11 pages, 6 figures, 8 table