Borel complexity of sets of normal numbers via generic points in subshifts with specification

We study the Borel complexity of sets of normal numbers in several numeration systems. Taking a dynamical point of view, we offer a unified treatment for continued fraction expansions and base $r$ expansions, and their various generalisations: generalised L\"uroth series expansions and $\beta$-expansions. In fact, we consider subshifts over a countable alphabet generated by all possible expansions of numbers in $[0,1)$. Then normal numbers correspond to generic points of shift-invariant measures. It turns out that for these subshifts the set of generic points for a shift-invariant probability measure is precisely at the third level of the Borel hierarchy (it is a $\Pi^0_3$-complete set, meaning that it is a countable intersection of $F_\sigma$-sets, but it is not possible to write it as a countable union of $G_\delta$-sets). We also solve a problem of Sharkovsky--Sivak on the Borel complexity of the basin of statistical attraction. The crucial dynamical feature we need is a feeble form of specification. All expansions named above generate subshifts with this property. Hence the sets of normal numbers under consideration are $\Pi^0_3$-complete.Comment: A talk explaining this paper may be found at https://www.youtube.com/watch?v=g9va0ZzVIj

Deconstructing Superconductivity

We present a dimensionally deconstructed model of an s-wave holographic superconductor. The 2+1 dimensional model includes multiple charged Cooper pair fields and neutral exciton fields that have interactions governed by hidden local symmetries. We derive AdS/CFT-like relations for the current and charge density in the model, and we analyze properties of the Cooper pair condensates and the complex conductivity.Comment: 24 pages, 10 eps figures. v2: Sign conventions clarified, references adde

Tracking icebergs with time-lapse photography and sparse optical flow, LeConte Bay, Alaska, 2016–2017

We present a workflow to track icebergs in proglacial fjords using oblique time-lapse photos and the Lucas-Kanade optical flow algorithm. We employ the workflow at LeConte Bay, Alaska, where we ran five time-lapse cameras between April 2016 and September 2017, capturing more than 400 000 photos at frame rates of 0.5–4.0 min−1. Hourly to daily average velocity fields in map coordinates illustrate dynamic currents in the bay, with dominant downfjord velocities (exceeding 0.5 m s−1 intermittently) and several eddies. Comparisons with simultaneous Acoustic Doppler Current Profiler (ADCP) measurements yield best agreement for the uppermost ADCP levels (∼ 12 m and above), in line with prevalent small icebergs that trace near-surface currents. Tracking results from multiple cameras compare favorably, although cameras with lower frame rates (0.5 min−1) tend to underestimate high flow speeds. Tests to determine requisite temporal and spatial image resolution confirm the importance of high image frame rates, while spatial resolution is of secondary importance. Application of our procedure to other fjords will be successful if iceberg concentrations are high enough and if the camera frame rates are sufficiently rapid (at least 1 min−1 for conditions similar to LeConte Bay).This work was funded by the U.S. National Science Foundation (OPP-1503910, OPP-1504288, OPP-1504521 and OPP-1504191).Ye

Rapid Start-up and Loading of an Attached Growth, Simultaneous Nitrification/Denitrification Membrane Aerated Bioreactor

Membrane aerated bioreactors (MABR) are attached-growth biological systems used for simultaneous nitrification and denitrification to reclaim water from waste. This design is an innovative approach to common terrestrial wastewater treatments for nitrogen and carbon removal and implementing a biologically-based water treatment system for long-duration human exploration is an attractive, low energy alternative to physiochemical processes. Two obstacles to implementing such a system are (1) the "start-up" duration from inoculation to steady-state operations and (2) the amount of surface area needed for the biological activity to occur. The Advanced Water Recovery Systems (AWRS) team at JSC explored these two issues through two tests; a rapid inoculation study and a wastewater loading study. Results from these tests demonstrate that the duration from inoculation to steady state can be reduced to under two weeks, and that despite low ammonium removal rates, the MABRs are oversized

Results of the Alternative Water Processor Test, A Novel Technology for Exploration Wastewater Remediation

Biologically-based water recovery systems are a regenerative, low energy alternative to physiochemical processes to reclaim water from wastewater. This report summarizes the results of the Alternative Water Processor (AWP) Integrated Test, conducted from June 2013 until April 2014. The system was comprised of four (4) membrane aerated bioreactors (MABRs) to remove carbon and nitrogen from an exploration mission wastewater and a coupled forward and reverse osmosis system to remove large organic and inorganic salts from the biological system effluent. The system exceeded the overall objectives of the test by recovering 90% of the influent wastewater processed into a near potable state and a 64% reduction of consumables from the current state of the art water recovery system on the International Space Station (ISS). However, the biological system fell short of its test goals, failing to remove 75% and 90% of the influent ammonium and organic carbon, respectively. Despite not meeting its test goals, the BWP demonstrated the feasibility of an attached-growth biological system for simultaneous nitrification and denitrification, an innovative, volume- and consumable-saving design that does not require toxic pretreatment

Associations Between Anabolic-Androgenic Steroid Use and Sexual Health Behaviors Among Adolescent Boys: Results From the 2019 Youth Risk Behavior Survey.

The aim of this study was to determine the association between lifetime anabolic-androgenic steroid (AAS) use and seven indicators of sexual health behaviors among a nationally representative sample of adolescent boys in the United States. Multiple modified Poisson regression analyses were conducted to determine the associations between any lifetime AAS use and seven indicators of sexual health behaviors among 2,095 sexually active adolescent boys from the 2019 National Youth Risk Behavior Survey. Sexually active boys who reported lifetime AAS use were at greater risk of having sexual intercourse before the age of 13 years (adjusted risk ratio [aRR] = 2.73, 95% confidence interval [CI] = [1.44, 5.17]), reporting ≥4 sexual partners in their lifetime (aRR = 1.96, 95% CI = [1.34, 2.89]) and in the past 3 months (aRR = 6.77, 95% CI = [3.19, 14.37]), having been tested for HIV in their lifetime (aRR = 2.49, 95% CI = [1.13, 4.73]), and having been tested for any sexually transmitted infection in the past 12 months (aRR = 3.14, 95% CI = [1.63, 6.03]). These findings align with prior research among adult men and have implications for public health and health care prevention efforts to reduce the use of AAS, as well as support the engagement in safe sexual health behaviors among adolescent boys

Performance-Enhancing Substance Use and Sexual Risk Behaviors among U.S. Men: Results from a Prospective Cohort Study.

Performance-enhancing substance (PES) use is common among young men and prior research has documented cross-sectional associations between anabolic-androgenic steroid (AAS) use and sexual risk behaviors. However, this relationship remains understudied among a longitudinal cohort of young adult men, and research on prospective associations between legal PES (e.g., creatine) use and sexual risk behaviors is lacking. The current study addressed these oversights using data from the National Longitudinal Study of Adolescent to Adult Health (N = 5,451). AAS use and legal PES use were assessed at Wave III (ages 18-26) and 10 indicators of sexual risk behavior were assessed at seven-year follow up (Wave IV; ages 24-32). Linear and logistic regression analyses were conducted adjusting for demographic and behavioral confounders. Participants who reported AAS use and legal PES use had significantly higher number of one-time sexual partners and higher odds of multiple sex partners around the same time in the past 12 months. Participants who reported AAS use had higher odds of any STI in the past 12 months. These results extend prior research on the risk behaviors and adverse effects of PES use. Health care professionals should assess for PES use among young adult men and provide guidance on healthful sexual behaviors