Julia: A Fresh Approach to Numerical Computing

Bezanson, Jeff; Edelman, Alan; Karpinski, Stefan; Shah, Viral B.

doi:10.48550/arxiv.1411.1607

Cited by 60 publications

(68 citation statements)

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“…The model has been calibrated using a range of summary statistics of the observed Kepler planet population, including (but not limited to) the observed distributions of multiplicities, orbital periods and period ratios, transit depths and depth ratios, and transit durations. SysSim is implemented in the Julia programming language (Bezanson et al 2014) within the Exoplan-etsSysSim.jl package. Both the core SysSim code (https://github.com/ExoJulia/ExoplanetsSysSim.jl) and the specific forward models explored in this study (https://github.com/ExoJulia/SysSimExClusters) are publicly available.…”

Section: Simulations: Syssim Planet Populationsmentioning

confidence: 99%

Evidence for a Non-Dichotomous Solution to the Kepler Dichotomy: Mutual Inclinations of Kepler Planetary Systems from Transit Duration Variations

Millholland,

He,

Ford

et al. 2021

Preprint

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Early analyses of exoplanet statistics from the Kepler Mission revealed that a model population of multiple-planet systems with low mutual inclinations (∼ 1 • − 2 • ) adequately describes the multipletransiting systems but underpredicts the number of single-transiting systems. This so-called "Kepler dichotomy" signals the existence of a sub-population of multi-planet systems possessing larger mutual inclinations. However, the details of these inclinations remain uncertain. In this work, we derive constraints on the intrinsic mutual inclination distribution by statistically exploiting Transit Duration Variations (TDVs) of the Kepler planet population. When planetary orbits are mutually inclined, planet-planet interactions cause orbital precession, which can lead to detectable long-term changes in transit durations. These TDV signals are inclination-sensitive and have been detected for roughly two dozen Kepler planets. We compare the properties of the Kepler observed TDV detections to TDV detections of simulated planetary systems constructed from two population models with differing assumptions about the mutual inclination distribution. We find strong evidence for a continuous distribution of relatively low mutual inclinations that is well-characterized by a power law relationship between the median mutual inclination (μ i,n ) and the intrinsic multiplicity (n): μi,n = μi,5 (n/5) α , where μi,5 = 1.10 +0.15 −0.11 and α = −1.73 +0.09 −0.08 . These results suggest that late-stage planet assembly and possibly stellar oblateness are the dominant physical origins for the excitation of Kepler planet mutual inclinations.

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Section: Simulations: Syssim Planet Populationsmentioning

confidence: 99%

Evidence for a Non-Dichotomous Solution to the Kepler Dichotomy: Mutual Inclinations of Kepler Planetary Systems from Transit Duration Variations

Millholland,

He,

Ford

et al. 2021

Preprint

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“…Note that the small deviations from the figures reported in Englert and Kieser (2013) originate from the fact that we did not need to restrict possible assignments by specifying a minimal or maximal conditional power in order to render the optimization feasible. All computations were conducted in the programming language Julia (Bezanson et al, 2014) using its interface (Lubin and Dunning, 2015) to the commercial Gurobi solver (Gurobi Optimization, Inc., 2015). Graphics were produced using R (R Core Team, 2015) and the ggplot2 package (Wickham, 2009).…”

Section: Resultsmentioning

confidence: 99%

Optimal adaptive two-stage designs for single-arm trial with binary endpoint

Kunzmann¹,

Kieser²

2016

Preprint

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Minimizing the number of patients exposed to potentially harmful drugs in early oncological trials is a major concern during planning. Adaptive designs account for the inherent uncertainty about the true effect size by determining the final sample size within an ongoing trial after an interim look at the data. We formulate the problem of finding adaptive designs which minimize expected sample size under the null hypothesis for single-arm trials with binary outcome as an integer linear program. This representation can be used to identify optimal adaptive designs which improve previous designs in two ways: Firstly, designs can be found exhibiting lower expected sample size under the null hypothesis than those provided by previous algorithms. Secondly, we explain how integer programming techniques can be exploited to remove pathologies of the optimal and previous solutions arising from the discrete nature of the underlying statistics. The resulting designs are both efficient in terms of expected sample size under the null hypothesis and well interpretable.

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“…The details about the numerical implementation of this strategy are summarized in the appendix A. Our numerical code is implemented in the programming language Julia [36].…”

Section: The Holographic Modelmentioning

confidence: 99%

Is the Chiral Magnetic Effect fast enough?

Ghosh,

Grieninger,

Landsteiner

et al. 2021

Preprint

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It depends: While we find within holography that the lifetime of the magnetic field for collider energies like the ones achieved at RHIC is long enough to build up the chiral magnetic current, the lifetime of the magnetic field at LHC seems to be too short.We study the real time evolution of the chiral magnetic effect out-of-equilibrium in strongly coupled holographic gauge theories. We consider the backreaction of the magnetic field onto the geometry and monitor pressure and chiral magnetic current. Our findings show that generically at small magnetic field the pressure builds up faster than the chiral magnetic current whereas at strong magnetic field the opposite is true. At large charge we also find that equilibration is delayed significantly due to long lived oscillations. We also match the parameters of our model to QCD parameters and draw lessons of possible relevance to the realization of the chiral magnetic effect in heavy ion collisions. In particular, we find an equilibration time of about ∼ 0.35 fm/c in presence of the chiral anomaly for plasma temperatures of order T ∼ 300 − 400 MeV. CONTENTSB. Simulations for µ 5 = 100MeV. 12 References 13

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Julia: A Fresh Approach to Numerical Computing

Cited by 60 publications

References 0 publications

Evidence for a Non-Dichotomous Solution to the Kepler Dichotomy: Mutual Inclinations of Kepler Planetary Systems from Transit Duration Variations

Evidence for a Non-Dichotomous Solution to the Kepler Dichotomy: Mutual Inclinations of Kepler Planetary Systems from Transit Duration Variations

Optimal adaptive two-stage designs for single-arm trial with binary endpoint

Is the Chiral Magnetic Effect fast enough?

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