A Differentially Private Weighted Empirical Risk Minimization Procedure and its Application to Outcome Weighted Learning

It is commonplace to use data containing personal information to build predictive models in the framework of empirical risk minimization (ERM). While these models can be highly accurate in prediction, results obtained from these models with the use of sensitive data may be susceptible to privacy attacks. Differential privacy (DP) is an appealing framework for addressing such data privacy issues by providing mathematically provable bounds on the privacy loss incurred when releasing information from sensitive data. Previous work has primarily concentrated on applying DP to unweighted ERM. We consider an important generalization to weighted ERM (wERM). In wERM, each individual's contribution to the objective function can be assigned varying weights. In this context, we propose the first differentially private wERM algorithm, backed by a rigorous theoretical proof of its DP guarantees under mild regularity conditions. Extending the existing DP-ERM procedures to wERM paves a path to deriving privacy-preserving learning methods for individualized treatment rules, including the popular outcome weighted learning (OWL). We evaluate the performance of the DP-wERM application to OWL in a simulation study and in a real clinical trial of melatonin for sleep health. All empirical results demonstrate the viability of training OWL models via wERM with DP guarantees while maintaining sufficiently useful model performance. Therefore, we recommend practitioners consider implementing the proposed privacy-preserving OWL procedure in real-world scenarios involving sensitive data.Comment: 24 pages and 2 figures for the main manuscript, 5 pages and 2 figures for the supplementary material

Observation of enhanced X-ray emission from the CTTS AA Tau during a transit of an accretion funnel

AA Tau was observed for about 5h per XMM orbit (2 days) over 8 successive orbits, which covers two optical eclipse periods (8.2 days). The XMM optical/UV monitor simultaneously provided UV photometry with a ~15 min sampling rate. Some V-band photometry was also obtained from the ground during this period in order to determine the dates of the eclipses. Two X-ray and UV measurements were secured close to the center of the eclipse. The UV flux is the highest just before the eclipse starts and the lowest towards the end of it. We model the UV flux variations with a weekly modulation (inner disk eclipse), plus a daily modulation, which suggests a non-steady accretion. No eclipses are detected in X-rays. For one measurement, the X-ray count rate was nearly 50 times stronger than the minimum observed level, and the plasma temperature reached 60 MK, i.e., a factor of 2-3 higher than in the other observations. This X-ray event, observed close to the center of the optical eclipse, is interpreted as an X-ray flare. We identify the variable column density with the low-density accretion funnel flows blanketing the magnetosphere. The lack of X-ray eclipses indicates that X-ray emitting regions are located at high latitudes. Furthermore, the occurrence of a strong X-ray flare near the center of the optical eclipse suggests that the magnetically active areas are closely associated with the base of the high-density accretion funnel flow. We speculate that the impact of this free falling accretion flow onto the strong magnetic field of the stellar corona may boost the X-ray emission (abridged).Comment: 17 pages and 9 Figures. Accepted by A&

Enhanced Perturbative Continuous Unitary Transformations

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary transformation (pCUT) among others. So far, this approach required an equidistant unperturbed spectrum. Here, we pursue two goals: First, we extend its applicability to non-equidistant spectra with the particular focus on an efficient derivation of the differential flow equations, which define the enhanced perturbative continuous unitary transformation (epCUT). Second, we show that the numerical integration of the flow equations yields a robust scheme to extract data from the epCUT. The method is illustrated by the perturbation of the harmonic oscillator with a quartic term and of the two-leg spin ladders in the strong-rung-coupling limit for uniform and alternating rung couplings. The latter case provides an example of perturbation around a non-equidistant spectrum.Comment: 27 pages, 18 figures; separated methodological background from introduction, added perturbed harmonic oscillator for additional illustration, added explicit solution of deepCUT equation

A Transiting Planet of a Sun-like Star

A planet transits an 11th magnitude, G1V star in the constellation Corona Borealis. We designate the planet XO-1b, and the star, XO-1, also known as GSC 02041-01657. XO-1 lacks a trigonometric distance; we estimate it to be 200+-20 pc. Of the ten stars currently known to host extrasolar transiting planets, the star XO-1 is the most similar to the Sun in its physical characteristics: its radius is 1.0+-0.08 R_Sun, its mass is 1.0+-0.03 M_Sun, V sini < 3 km/s, and its metallicity [Fe/H] is 0.015+-0.04. The orbital period of the planet XO-1b is 3.941534+-0.000027 days, one of the longer ones known. The planetary mass is 0.90+-0.07 M_Jupiter, which is marginally larger than that of other transiting planets with periods between 3 and 4 days. Both the planetary radius and the inclination are functions of the spectroscopically determined stellar radius. If the stellar radius is 1.0+-0.08 R_Sun, then the planetary radius is 1.30+-0.11 R_Jupiter and the inclination of the orbit is 87.7+-1.2 degrees. We have demonstrated a productive international collaboration between professional and amateur astronomers that was important to distinguishing this planet from many other similar candidates.Comment: 31 pages, 9 figures, accepted for part 1 of Ap

Follow-Up Observations of PTFO 8-8695: A 3 MYr Old T-Tauri Star Hosting a Jupiter-mass Planetary Candidate

We present Spitzer 4.5\micron\ light curve observations, Keck NIRSPEC radial velocity observations, and LCOGT optical light curve observations of PTFO~8-8695, which may host a Jupiter-sized planet in a very short orbital period (0.45 days). Previous work by \citet{vaneyken12} and \citet{barnes13} predicts that the stellar rotation axis and the planetary orbital plane should precess with a period of $300 - 600$ days. As a consequence, the observed transits should change shape and depth, disappear, and reappear with the precession. Our observations indicate the long-term presence of the transit events ($>3$ years), and that the transits indeed do change depth, disappear and reappear. The Spitzer observations and the NIRSPEC radial velocity observations (with contemporaneous LCOGT optical light curve data) are consistent with the predicted transit times and depths for the $M_\star = 0.34\ M_\odot$ precession model and demonstrate the disappearance of the transits. An LCOGT optical light curve shows that the transits do reappear approximately 1 year later. The observed transits occur at the times predicted by a straight-forward propagation of the transit ephemeris. The precession model correctly predicts the depth and time of the Spitzer transit and the lack of a transit at the time of the NIRSPEC radial velocity observations. However, the precession model predicts the return of the transits approximately 1 month later than observed by LCOGT. Overall, the data are suggestive that the planetary interpretation of the observed transit events may indeed be correct, but the precession model and data are currently insufficient to confirm firmly the planetary status of PTFO~8-8695b.Comment: Accepted for publication in The Astrophysical Journa

On detectability of Zeeman broadening in optical spectra of F- and G-dwarfs

We investigate the detectability of Zeeman broadening in optical Stokes I spectra of slowly rotating sun-like stars. To this end, we apply the LTE spectral line inversion package SPINOR to very-high quality CES data and explore how fit quality depends on the average magnetic field, Bf . One-component (OC) and two-component (TC) models are adopted. In OC models, the entire surface is assumed to be magnetic. Under this assumption, we determine formal 3{\sigma} upper limits on the average magnetic field of 200 G for the Sun, and 150 G for 61 Vir (G6V). Evidence for an average magnetic field of ~ 500 G is found for 59 Vir (G0V), and of ~ 1000 G for HD 68456 (F6V). A distinction between magnetic and non-magnetic regions is made in TC models, while assuming a homogeneous distribution of both components. In our TC inversions of 59 Vir, we investigate three cases: both components have equal temperatures; warm magnetic regions; cool magnetic regions. Our TC model with equal temperatures does not yield significant improvement over OC inversions for 59 Vir. The resulting Bf values are consistent for both. Fit quality is significantly improved, however, by using two components of different temperatures. The inversions for 59 Vir that assume different temperatures for the two components yield results consistent with 0 - 450 G at the formal 3{\sigma} confidence level. We thus find a model dependence of our analysis and demonstrate that the influence of an additional temperature component can dominate over the Zeeman broadening signature, at least in optical data. Previous comparable analyses that neglected effects due to multiple temperature components may be prone to the same ambiguities.Comment: 18 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

XO-5b: A Transiting Jupiter-sized Planet With A Four Day Period

The star XO-5 (GSC 02959-00729, V=12.1, G8V) hosts a Jupiter-sized, Rp=1.15+/-0.12 Rjup, transiting extrasolar planet, XO-5b, with an orbital period of P=4.187732+/-0.00002 days. The planet mass (Mp=1.15+/-0.08 Mjup) and surface gravity (gp=22+/-5 m/s^2) are significantly larger than expected by empirical Mp-P and Mp-P-[Fe/H] relationships. However, the deviation from the Mp-P relationship for XO-5b is not large enough to suggest a distinct type of planet as is suggested for GJ 436b, HAT-P-2b, and XO-3b. By coincidence XO-5 overlies the extreme H I plume that emanates from the interacting galaxy pair NGC 2444/NGC 2445 (Arp 143).Comment: 10 pages, 9 Figures, Submitted to Ap

Delivering impact via the ebb-and-flow of a research team: reflection on a long-term program of research into a global societal challenge*

In this paper, we draw insights from a 15-year qualitative research program exploring catastrophe insurance and gaps in insurance protection as risks escalate within a world impacted by a climate emergency. We suggest that the ebb-and-flow of our research team's composition and activities through time was inextricably linked with our ability to have a sustained impact on such a large-scale societal issue. The essay situates itself within the research impact and team literature, narrates the trajectory of our research program and team development, and develops a framework for effectively managing impact-oriented qualitative research teams over time. Our framework illustrates key aspects of this process including team (re)forming, building team and individual stickability, performing, and managing team flux. We also present 10 practical takeaways for how these aspects can be managed effectively to produce long-term impact work to address grand challenges

Delivering impact via the ebb-and-flow of a research team: Reflection on a long-term program of research into a global societal challenge

In this paper, we draw insights from a fifteen-year qualitative research program exploring catastrophe insurance and gaps in insurance protection as risks escalate within a world impacted by a climate emergency. We suggest that the ebb-and-flow of our research team's composition and activities through time was inextricably linked with our ability to have a sustained impact on such a large-scale societal issue. The essay situates itself within the research impact and team literature, narrates the trajectory of our research program and team development, and develops a framework for effectively managing impact-oriented qualitative research teams over time. Our framework illustrates key aspects of this process including team (re)forming, building team and individual stickability, performing, and managing team flux. We also present 10 practical takeaways for how these aspects can be managed effectively to produce long-term impact work to address grand challenges