Doing Real Work with FHE: The Case of Logistic Regression

We describe our recent experience, building a system that uses fully-homomorphic encryption (FHE) to approximate the coefficients of a logistic-regression model, built from genomic data. The aim of this project was to examine the feasibility of a solution that operates deep within the bootstrapping regime, solving a problem that appears too hard to be addressed just with somewhat-homomorphic encryption. As part of this project, we implemented optimized versions of many bread and butter FHE tools. These tools include binary arithmetic, comparisons, partial sorting, and low-precision approximation of complicated functions such as reciprocals and logarithms. Our eventual solution can handle thousands of records and hundreds of fields, and it takes a few hours to run. To achieve this performance we had to be extremely frugal with expensive bootstrapping and data-movement operations. We believe that our experience in this project could server as a guide for what is or is not currently feasible to do with fully-homomorphic encryption

It Pays to Be Bumpy: Drag Reducing Armor in The Pacific Spiny Lumpsucker, \u3cem\u3eEumicrotremus Orbis\u3c/em\u3e

Armor is a multipurpose set of structures that has evolved independently at least 30 times in fishes. In addition to providing protection, armor can manipulate flow, increase camouflage, and be sexually dimorphic. There are potential tradeoffs in armor function: increased impact resistance may come at the cost of maneuvering ability; and ornate armor may offer visual or protective advantages, but could incur excess drag. Pacific spiny lumpsuckers (Eumicrotremus orbis) are covered in rows of odontic, cone-shaped armor whorls, protecting the fish from wave driven impacts and the threat of predation. We are interested in measuring the effects of lumpsucker armor on the hydrodynamic forces on the fish. Bigger lumpsuckers have larger and more complex armor which may incur a greater hydrodynamic cost. In addition to their protective armor, lumpsuckers have evolved a ventral adhesive disc, allowing them to remain stationary in their environment. We hypothesize a tradeoff between the armor and adhesion: little fish prioritize suction while big fish prioritize protection. Using micro-CT we compared armor volume to disc area over lumpsucker development and built 3D models to measure changes in drag over ontogeny. We found that drag and drag coefficients decrease with greater armor coverage and vary consistently with orientation. Adhesive disc area is isometric but safety factor increases with size, allowing larger fish to remain attached in higher flows than smaller fish

Characterization of soluble bromide measurements and a case study of BrO observations during ARCTAS

A focus of the Arctic Research of the Composition of the Troposphere from Aircraft and Satellites (ARCTAS) mission was examination of bromine photochemistry in the spring time high latitude troposphere based on aircraft and satellite measurements of bromine oxide (BrO) and related species. The NASA DC-8 aircraft utilized a chemical ionization mass spectrometer (CIMS) to measure BrO and a mist chamber (MC) to measure soluble bromide. We have determined that the MC detection efficiency to molecular bromine (Br2), hypobromous acid (HOBr), bromine oxide (BrO), and hydrogen bromide (HBr) as soluble bromide (Br−) was 0.9±0.1, 1.06+0.30/−0.35, 0.4±0.1, and 0.95±0.1, respectively. These efficiency factors were used to estimate soluble bromide levels along the DC-8 flight track of 17 April 2008 from photochemical calculations constrained to in situ BrO measured by CIMS. During this flight, the highest levels of soluble bromide and BrO were observed and atmospheric conditions were ideal for the space-borne observation of BrO. The good agreement (R2 = 0.76; slope = 0.95; intercept = −3.4 pmol mol−1) between modeled and observed soluble bromide, when BrO was above detection limit (\u3e2 pmol mol−1) under unpolluted conditions (NOmol−1), indicates that the CIMS BrO measurements were consistent with the MC soluble bromide and that a well characterized MC can be used to derive mixing ratios of some reactive bromine compounds. Tropospheric BrO vertical column densities (BrOVCD) derived from CIMS BrO observations compare well with BrOTROPVCD from OMI on 17 April 2008

An analysis of fast photochemistry over high northern latitudes during spring and summer using in-situ observations from ARCTAS and TOPSE

Observations of chemical constituents and meteorological quantities obtained during the two Arctic phases of the airborne campaign ARCTAS (Arctic Research of the Composition of the Troposphere from Aircraft and Satellites) are analyzed using an observationally constrained steady state box model. Measurements of OH and HO2 from the Penn State ATHOS instrument are compared to model predictions. Forty percent of OH measurements below 2 km are at the limit of detection during the spring phase (ARCTAS-A). While the median observed-to-calculated ratio is near one, both the scatter of observations and the model uncertainty for OH are at the magnitude of ambient values. During the summer phase (ARCTAS-B), model predictions of OH are biased low relative to observations and demonstrate a high sensitivity to the level of uncertainty in NO observations. Predictions of HO2 using observed CH2O and H2O2 as model constraints are up to a factor of two larger than observed. A temperature-dependent terminal loss rate of HO2 to aerosol recently proposed in the literature is shown to be insufficient to reconcile these differences. A comparison of ARCTAS-A to the high latitude springtime portion of the 2000 TOPSE campaign (Tropospheric Ozone Production about the Spring Equinox) shows similar meteorological and chemical environments with the exception of peroxides; observations of H2O2 during ARCTAS-A were 2.5 to 3 times larger than those during TOPSE. The cause of this difference in peroxides remains unresolved and has important implications for the Arctic HOx budget. Unconstrained model predictions for both phases indicate photochemistry alone is unable to simultaneously sustain observed levels of CH2O and H2O2; however when the model is constrained with observed CH2O, H2O2 predictions from a range of rainout parameterizations bracket its observations. A mechanism suitable to explain observed concentrations of CH2O is uncertain. Free tropospheric observations of acetaldehyde (CH3CHO) are 2–3 times larger than its predictions, though constraint of the model to those observations is sufficient to account for less than half of the deficit in predicted CH2O. The box model calculates gross O3 formation during spring to maximize from 1–4 km at 0.8 ppbv d−1, in agreement with estimates from TOPSE, and a gross production of 2–4 ppbv d−1 in the boundary layer and upper troposphere during summer. Use of the lower observed levels of HO2 in place of model predictions decreases the gross production by 25–50%. Net O3 production is near zero throughout the ARCTAS-A troposphere, and is 1–2 ppbv in the boundary layer and upper altitudes during ARCTAS-B

Atmospheric sampling of Supertyphoon Mireille with NASA DC-8 aircraft on September 27,1991, during PEM-West A

The DC-8 mission of September 27, 1991, was designed to sample air flowing into Typhoon Mireille in the boundary layer, air in the upper tropospheric eye region, and air emerging from the typhoon and ahead of the system, also in the upper troposphere. The objective was to find how a typhoon redistributes trace constituents in the West Pacific region and whether any such redistribution is important on the global scale. The boundary layer air (300 m), in a region to the SE of the eye, contained low mixing ratios of the tracer species O3, CO, C2H6, C2H2, C3H8, C6H6and CS2 but high values of dimethylsulfide (DMS). The eye region relative to the boundary layer, showed somewhat elevated levels of CO, substantially increased levels of O3, CS2 and all nonmethane hydrocarbons (NMHCs), and somewhat reduced levels of DMS. Ahead of the eye, CO and the NMHCs remained unchanged, O3 and CS2 showed a modest decrease, and DMS showed a substantial decrease. There was no evidence from lidar cross sections of ozone for the downward entrainment of stratospheric air into the eye region; these sections show that low ozone values were measured in the troposphere. The DMS data suggest substantial entrainment of boundary layer air into the system, particularly into the eye wall region. Estimates of the DMS sulphur flux between the boundary layer and the free troposphere, based on computations of velocity potential and divergent winds, gave values of about 69 μg S m−2 d−1 averaged over a 17.5° grid square encompassing the typhoon. A few hours after sampling with the DC-8, Mireille passed over Oki Island, just to the north of Japan, producing surface values of ozone of 5.5 ppbv. These O3 levels are consistent with the low tropospheric values found by lidar and are more typical of equatorial regions. We suggest that the central eye region may act like a Taylor column which has moved poleward from low latitudes. The high-altitude photochemical environment within Typhoon Mireille was found to be quite active as evidenced by significant levels of measured gas phase H2O2 and CH3OOH and model-computed levels of OH

Waiting times for radiotherapy: variation over time and between cancer networks in southeast England

The aim of this study was to investigate variations in the length of time that patients with cancer wait from diagnosis to treatment with radiotherapy. A total of 57 426 men and 71 018 women diagnosed with cancer between 1992 and 2001 and receiving radiotherapy within 6 months of diagnosis were identified from the Thames Cancer Registry database. In total, 12 sites were identified for which a substantial number or proportion of patients received radiotherapy: head and neck, oesophagus, colon, rectum, lung, nonmelanoma skin cancer, breast, uterus, prostate, bladder, brain and non-Hodgkin's lymphoma. Median waiting times from diagnosis to radiotherapy were calculated, together with the proportion of patients who received radiotherapy within 60 days of diagnosis, and analysed by year of diagnosis, cancer site, deprivation quintile, age at diagnosis, sex and cancer network of either residence or treatment. Logistic regression was used to adjust the proportion receiving treatment within 60 days for the effects of the other factors. There were significant differences in the proportions receiving radiotherapy within 60 days between different networks and different cancer sites, which remained after adjustment. Median waiting times varied from 42 to 65 days across networks of residence, with the adjusted proportion treated within 60 days ranging from 44 to 71%. There was no difference between male and female patients after adjustment for the other factors, particularly site. There was a highly significant trend over time: the median wait increased from 45 days in 1992 to 76 days in 2001, while the adjusted proportion being treated within 60 days declined by almost a half, from 64 to 35%, over the same period

The X-ray Properties of Nearby Abell Clusters from the ROSAT All-Sky Survey: The Sample and Correlations with Optical Properties

We present an analysis of the X-ray emission for a complete sample of 288 Abell clusters spanning the redshift range 0.016<= z <= 0.09 from the ROSAT All-Sky Survey. This sample is based on our 20cm VLA survey of nearby Abell clusters. We find an X-ray detection rate of 83%. We report cluster X-ray fluxes and luminosities and two different flux ratios indicative of the concentration and extent of the emission. We examine correlations between the X-ray luminosity, Abell Richness, and Bautz-Morgan and Rood-Sastry cluster morphologies. We find a strong correlation between Lx and cluster richness coupled to a dependence on the optical morphological type. These results are consistent with the observed scatter between X-ray luminosity and temperature and a large fraction of cooling flows. For each cluster field we also report the positions, peak X-ray fluxes, and flux-ratios of all X-ray peaks above 3-sigma significance within a box of 2x2 Mpc centered on Abell's position.Comment: 59 pages including 3 tables, + 10 figures. To appear in AJ, Dec 200

A new interpretation of total column BrO during Arctic spring

Emission of bromine from sea-salt aerosol, frost flowers, ice leads, and snow results in the nearly complete removal of surface ozone during Arctic spring. Regions of enhanced total column BrO observed by satellites have traditionally been associated with these emissions. However, airborne measurements of BrO and O3 within the convective boundary layer (CBL) during the ARCTAS and ARCPAC field campaigns at times bear little relation to enhanced column BrO. We show that the locations of numerous satellite BrO “hotspots” during Arctic spring are consistent with observations of total column ozone and tropopause height, suggesting a stratospheric origin to these regions of elevated BrO. Tropospheric enhancements of BrO large enough to affect the column abundance are also observed, with important contributions originating from above the CBL. Closure of the budget for total column BrO, albeit with significant uncertainty, is achieved by summing observed tropospheric partial columns with calculated stratospheric partial columns provided that natural, short-lived biogenic bromocarbons supply between 5 and 10 ppt of bromine to the Arctic lowermost stratosphere. Proper understanding of bromine and its effects on atmospheric composition requires accurate treatment of geographic variations in column BrO originating from both the stratosphere and troposphere

Chemical Data Assimilation Estimates of Continental US Ozone and Nitrogen Budgets during INTEX-A

Global ozone analyses, based on assimilation of stratospheric profile and ozone column measurements, and NOy predictions from the Real-time Air Quality Modeling System (RAQMS) are used to estimate the ozone and NOy budget over the Continental US during the July-August 2004 Intercontinental Chemical Transport Experiment-North America (INTEX-A). Comparison with aircraft, satellite, surface, and ozonesonde measurements collected during the INTEX-A show that RAQMS captures the main features of the global and Continental US distribution of tropospheric ozone, carbon monoxide, and NOy with reasonable fidelity. Assimilation of stratospheric profile and column ozone measurements is shown to have a positive impact on the RAQMS upper tropospheric/lower stratosphere ozone analyses, particularly during the period when SAGE III limb scattering measurements were available. Eulerian ozone and NOy budgets during INTEX-A show that the majority of the Continental US export occurs in the upper troposphere/lower stratosphere poleward of the tropopause break, a consequence of convergence of tropospheric and stratospheric air in this region. Continental US photochemically produced ozone was found to be a minor component of the total ozone export, which was dominated by stratospheric ozone during INTEX-A. The unusually low photochemical ozone export is attributed to anomalously cold surface temperatures during the latter half of the INTEX-A mission, which resulted in net ozone loss during the first 2 weeks of August. Eulerian NOy budgets are shown to be very consistent with previously published estimates. The NOy export efficiency was estimated to be 24 percent, with NOx+PAN accounting for 54 percent of the total NOy export during INTEX-A

Direct Measurements of the Convective Recycling of the Upper Troposphere

We present a statistical representation of the aggregate effects of deep convection on the chemistry and dynamics of the Upper Troposphere (UT) based on direct aircraft observations of the chemical composition of the UT over the Eastern United States and Canada during summer. These measurements provide new and unique observational constraints on the chemistry occurring downwind of convection and the rate at which air in the UT is recycled, previously only the province of model analyses. These results provide quantitative measures that can be used to evaluate global climate and chemistry models