Atmospheric Circulation of Brown Dwarfs and Jupiter and Saturn-like Planets: Zonal Jets, Long-term Variability, and QBO-type Oscillations

Brown dwarfs and directly imaged giant planets exhibit significant evidence for active atmospheric circulation, which induces a large-scale patchiness in the cloud structure that evolves significantly over time, as evidenced by infrared light curves and Doppler maps. These observations raise critical questions about the fundamental nature of the circulation, its time variability, and the overall relationship to the circulation on Jupiter and Saturn. Jupiter and Saturn themselves exhibit numerous robust zonal (east-west) jet streams at the cloud level; moreover, both planets exhibit long-term stratospheric oscillations involving perturbations of zonal wind and temperature that propagate downward over time on timescales of ~4 years (Jupiter) and ~15 years (Saturn). These oscillations, dubbed the Quasi Quadrennial Oscillation (QQO) for Jupiter and the Semi-Annual Oscillation (SAO) on Saturn, are thought to be analogous to the Quasi-Biennial Oscillation (QBO) on Earth, which is driven by upward propagation of equatorial waves from the troposphere. To investigate these issues, we here present global, three-dimensional, high-resolution numerical simulations of the flow in the stratified atmosphere--overlying the convective interior--of brown dwarfs and Jupiter-like planets. The effect of interior convection is parameterized by inducing small-scale, randomly varying perturbations in the radiative-convective boundary at the base of the model. In the simulations, the convective perturbations generate atmospheric waves and turbulence that interact with the rotation to produce numerous zonal jets. Moreover, the equatorial stratosphere exhibits stacked eastward and westward jets that migrate downward over time, exactly as occurs in the terrestrial QBO, Jovian QQO, and Saturnian SAO. This is the first demonstration of a QBO-like phenomenon in 3D numerical simulations of a giant planet.Comment: 27 pages, 15 figures, in press at ApJ; this is the revised (accepted) version, which includes a major new section providing detailed analysis of the types of wave modes present in the model, and characterizing the wave-mean-flow interactions by which they generate the QBO-like oscillation

Bayesian Nonparametrics to Model Content, User, and Latent Structure in Hawkes Processes

Communication in social networks tends to exhibit complex dynamics both in terms of the users involved and the contents exchanged. For example, email exchanges or activities on social media may exhibit reinforcing dynamics, where earlier events trigger follow-up activity through multiple structured latent factors. Such dynamics have been previously represented using models of reinforcement and reciprocation, a canonical example being the Hawkes process (HP). However, previous HP models do not fully capture the rich dynamics of real-world activity. For example, reciprocation may be impacted by the significance and receptivity of the content being communicated, and modeling the content accurately at the individual level may require identification and exploitation of the latent hierarchical structure present among users. Additionally, real-world activity may be driven by multiple latent triggering factors shared by past and future events, with the latent features themselves exhibiting temporal dependency structures. These important characteristics have been largely ignored in previous work. In this dissertation, we address these limitations via three novel Bayesian nonparametric Hawkes process models, where the synergy between Bayesian nonparametric models and Hawkes processes captures the structural and the temporal dynamics of communication in a unified framework. Empirical results demonstrate that our models outperform competing state-of-the-art methods, by more accurately capturing the rich dynamics of the interactions and influences among users and events, and by improving predictions about future event times, user clusters, and latent features in various types of communication activities

The Impact of Access to Cancer Care on Adjuvant Endocrine Therapy Use Among Breast Cancer Survivors in Appalachia.

OBJECTIVES: The Appalachia region experiences excess cancer mortality and a lack of access to cancer care resources. There is limited research examining adjuvant treatment use disparities in this region. This study aims to explore adjuvant endocrine therapy (AET) utilization in Appalachia, and delineate the effects of access to cancer on AET use. METHODS: Female breast cancer patients were identified in cancer registries from the Appalachian counties in four states (KY, NC, OH, and PA) and linked to 2006-2008 Medicare claims data. We included patients with invasive, non-metastatic, hormone-receptor-positive breast cancer and assessed the prevalence of receiving guideline-recommended AET. We then assessed AET adherence among those who received guideline-recommended AET using the Medication Possession Ratio (MPR), and determined non-persistence, defined as exceeding a 60-day medication gap. We also used survival analyses to examine the influences of AET adherence and persistence on overall survival. RESULTS: Only 450 of the 946 eligible patients (47.6%) received guideline-recommended AET, which was significantly associated with shorter travel time to receive care, dual Medicare and Medicaid eligibility, being unmarried (vs. married), and living in Pennsylvania (vs. Ohio). The non-adherence rate was about 31% and non-persistence rate was 30% over an average follow-up period of 421 days. Tamoxifen, relative to aromatase inhibitors, was associated with higher odds of adherence (Odds Ratio = 2.82, p < 0.001) and a lower risk of non-persistence (Hazard Ratio = 0.40, p < 0.001). Side effects like pain may be an important factor leading to non-adherence and early discontinuation. Non-adherence to and non-persistence with AET were associated with higher risks of all-cause mortality. CONCLUSIONS: In Appalachia, geographic and socioeconomic factors such as travel time to receive care and healthcare plan type are important elements that could contribute to disparities in access to adjuvant treatment, while treatment choice and medication-related factors may exert strong influences on AET use behaviors.PhDSocial and Administrative SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111366/1/tanxi_1.pd

Boolean function monotonicity testing requires (almost) n1/2n^{1/2} non-adaptive queries

We prove a lower bound of $\Omega(n^{1/2 - c})$, for all $c>0$, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an $n$-variable Boolean function is monotone versus constant-far from monotone. This improves a $\tilde{\Omega}(n^{1/5})$ lower bound for the same problem that was recently given in [CST14] and is very close to $\Omega(n^{1/2})$, which we conjecture is the optimal lower bound for this model

Near-optimal small-depth lower bounds for small distance connectivity

We show that any depth-$d$ circuit for determining whether an $n$-node graph has an $s$-to-$t$ path of length at most $k$ must have size $n^{\Omega(k^{1/d}/d)}$. The previous best circuit size lower bounds for this problem were $n^{k^{\exp(-O(d))}}$ (due to Beame, Impagliazzo, and Pitassi [BIP98]) and $n^{\Omega((\log k)/d)}$ (following from a recent formula size lower bound of Rossman [Ros14]). Our lower bound is quite close to optimal, since a simple construction gives depth-$d$ circuits of size $n^{O(k^{2/d})}$ for this problem (and strengthening our bound even to $n^{k^{\Omega(1/d)}}$ would require proving that undirected connectivity is not in $\mathsf{NC^1}.$) Our proof is by reduction to a new lower bound on the size of small-depth circuits computing a skewed variant of the "Sipser functions" that have played an important role in classical circuit lower bounds [Sip83, Yao85, H{\aa}s86]. A key ingredient in our proof of the required lower bound for these Sipser-like functions is the use of \emph{random projections}, an extension of random restrictions which were recently employed in [RST15]. Random projections allow us to obtain sharper quantitative bounds while employing simpler arguments, both conceptually and technically, than in the previous works [Ajt89, BPU92, BIP98, Ros14]