Towards Verifying Nonlinear Integer Arithmetic

We eliminate a key roadblock to efficient verification of nonlinear integer arithmetic using CDCL SAT solvers, by showing how to construct short resolution proofs for many properties of the most widely used multiplier circuits. Such short proofs were conjectured not to exist. More precisely, we give n^{O(1)} size regular resolution proofs for arbitrary degree 2 identities on array, diagonal, and Booth multipliers and quasipolynomial- n^{O(\log n)} size proofs for these identities on Wallace tree multipliers.Comment: Expanded and simplified with improved result

Quantum whistling in superfluid 4He

Fundamental considerations predict that macroscopic quantum systems such as superfluids and the electrons in superconductors will exhibit oscillatory motion when pushed through a small constriction. Here we report the observation of these oscillations between two reservoirs of superfluid 4He partitioned by an array of nanometer-sized apertures. They obey the Josephson frequency equation and are coherent amongst all the apertures. This discovery at the relatively high temperature of 2K (2000 times higher than related phenomena in 3He) may pave the way for a new class of practical rotation sensors of unprecedented precision.Comment: 6 pages, 3 figures, to be published in Natur

Factors controlling tropospheric O3, OH, NOx, and SO2 over the tropical Pacific during PEM-Tropics B

Observations over the tropical Pacific during the Pacific Exploratory Mission (PEM)-Tropics B experiment (March-April 1999) are analyzed. Concentrations of CO and long-lived nonmethane hydrocarbons in the region are significantly enhanced due to transport of pollutants from northern industrial continents. This pollutant import also enhances moderately O3 concentrations but not NOx concentrations. It therefore tends to depress OH concentrations over the tropical Pacific. These effects contrast to the large enhancements of O3 and NOx concentrations and the moderate increase of OH concentrations due to biomass burning outflow during the PEM-Tropics A experiment (September-October 1996). Observed CH3I concentrations, as in PEM-Tropics A, indicate that convective mass outflux in the middle and upper troposphere is largely independent of altitude over the tropical Pacific. Constraining a one-dimensiohal model with CH3I observations yields a 10-day timescale for convective turnover of the free troposphere, a factor of 2 faster than during PEM-Tropics A. Model simulated HO2, CH2O, H2O2, and CH3OOH concentrations are generally in agreement with observations. However, simulated OH concentrations are lower (∼25%) than observations above 6 km. Whereas models tend to overestimate previous field measurements, simulated HNO3 concentrations during PEM-Tropics B are too low (a factor of 2-4 below 6 km) compared to observations. Budget analyses indicate that chemical production of O3 accounts for only 50% of chemical loss; significant transport of O3 into the region appears to take place within the tropics. Convective transport of CH3OOH enhances the production of HOx and O3 in the upper troposphere, but this effect is offset by HOx loss due to the scavenging of H2O2. Convective transport and scavenging of reactive nitrogen species imply a necessary source of 0.4-1 Tg yr-1 of NOx in the free troposphere (above 4 km) over the tropics. A large fraction of the source could be from marine lightning. Oxidation of DMS transported by convection from the boundary layer could explain the observed free tropospheric SO2 concentrations over the tropical Pacific. This source of DMS due to convection, however, would imply in the model free tropospheric concentrations much higher than observed. The model overestimate cannot be reconciled using recent kinetics measurements of the DMS-OH adduct reaction at low pressures and temperatures and may reflect enhanced OH oxidation of DMS during convection. Copyright 2001 by the American Geophysical Union

Seasonal differences in the photochemistry of the South Pacific: A comparison of observations and model results from PEM-Tropics A and B

A time-dependent photochemical box model is used to examine the photochemistry of the equatorial and southern subtropical Pacific troposphere with aircraft data obtained during two distinct seasons: the Pacific Exploratory Mission-Tropics A (PEM-Tropics A) field campaign in September and October of 1996 and the Pacific Exploratory Mission-Tropics B (PEM-Tropics B) campaign in March and April of 1999. Model-predicted values were compared to observations for selected species (e.g., NO2, OH, HO2) with generally good agreement. Predicted values of HO2 were larger than those observed in the upper troposphere, in contrast to previous studies which show a general underprediction of HO2 at upper altitudes. Some characteristics of the budgets of HOx, NOx, and peroxides are discussed. The integrated net tendency for O3 is negative over the remote Pacific during both seasons, with gross formation equal to no more than half of the gross destruction. This suggests that a continual supply of O3 into the Pacific region throughout the year must exist in order to maintain O3 levels. Integrated net tendencies for equatorial O3 showed a seasonality, with a net loss of 1.06×1011 molecules cm-2 s-1 during PEM-Tropics B (March) increasing by 50% to 1.60×1011 molecules cm-2 s-1 during PEM-Tropics A (September). The seasonality over the southern subtropical Pacific was somewhat lower, with losses of 1.21×1011 molecules cm-2 s-1 during PEM-Tropics B (March) increasing by 25% to 1.51×1011 molecules cm-2 s-1 during PEM-Tropics A (September). While the larger net losses during PEM-Tropics A were primarily driven by higher concentrations of O3, the ability of the subtropical atmosphere to destroy O3 was ∼30% less effective during the PEM-Tropics A (September) campaign due to a drier atmosphere and higher overhead O3 column amounts. Copyright 2001 by the American Geophysical Union

Evaluating Active U: an Internet-mediated physical activity program.

Background: Engaging in regular physical activity can be challenging, particularly during the winter months. To promote physical activity at the University of Michigan during the winter months, an eight-week Internet-mediated program (Active U) was developed providing participants with an online physical activity log, goal setting, motivational emails, and optional team participation and competition. Methods: This study is a program evaluation of Active U. Approximately 47,000 faculty, staff, and graduate students were invited to participate in the online Active U intervention in the winter of 2007. Participants were assigned a physical activity goal and were asked to record each physical activity episode into the activity log for eight weeks. Statistics for program reach, effectiveness, adoption, and implementation were calculated using the Re-Aim framework. Multilevel regression analyses were used to assess the decline in rates of data entry and goal attainment during the program, to assess the likelihood of joining a team by demographic characteristics, to test the association between various predictors and the number of weeks an individual met his or her goal, and to analyze server load. Results: Overall, 7,483 individuals registered with the Active U website (≈16% of eligible), and 79% participated in the program by logging valid data at least once. Staff members, older participants, and those with a BMI < 25 were more likely to meet their weekly physical activity goals, and average rate of meeting goals was higher among participants who joined a competitive team compared to those who participated individually (IRR = 1.28, P < .001). Conclusion: Internet-mediated physical activity interventions that focus on physical activity logging and goal setting while incorporating team competition may help a significant percentage of the target population maintain their physical activity during the winter months

An assessment of western North Pacific ozone photochemistry based on springtime observations from NASA's PEM-West B (1994) and TRACE-P (2001) field studies

The current study provides a comparison of the photochemical environments for two NASA field studies focused on the western North Pacific (PEM-West-B (PWB) and TRACE-P (TP)). These two studies were separated in calendar time by approximately 7 years. Both studies were carried out under springtime conditions, with PWB being launched in 1994 and TP being deployed in 2001 (i.e., 23 February - 15 March 1994 and 10 March-15 April 2001, respectively). Because of the 7-year time separation, these two studies presented a unique scientific opportunity to assess whether evidence could be found to support the Department of Energy\u27s projections in 1997 that increases in anthropogenic emissions from East Asia could reach 5%/yr. Such projections would lead one to the conclusion that a significant shift in the atmospheric photochemical properties of the western North Pacific would occur. To the contrary, the findings from this study support the most recent emission inventory data [Streets et al., 2003] in that they show no significant systematic trend involving increases in any O3 precursor species and no evidence for a significant shift in the level of photochemical activity over the western North Pacific. This conclusion was reached in spite of there being real differences in the concentration levels of some species as well as differences in photochemical activity between PWB and TP. However, nearly all of these differences were shown to be a result of a near 3-week shift in TP\u27s sampling window relative to PWB, thus placing it later in the spring season. The photochemical enhancements seen during TP were most noticeable for latitudes in the range of 25-45°N. Most important among these were increases in J(O1D), OH, and HO2 and values for photochemical ozone formation and destruction, all of which were typically two times larger than those calculated for PWB. A comparison of these airborne results with ozonesonde data from four Japanese stations provided further evidence showing that the 3-week shift in the respective sampling windows of PWB and TP was a likely cause for the differences seen in O3 levels and in photochemical activity between the two airborne studies. Copyright 2003 by the American Geophysical Union

Low Resistance Polycrystalline Diamond Thin Films Deposited by Hot Filament Chemical Vapour Deposition

Polycrystalline diamond thin films with outgrowing diamond (OGD) grains were deposited onto silicon wafers using a hydrocarbon gas (CH4) highly diluted with H2 at low pressure in a hot filament chemical vapour deposition (HFCVD) reactor with a range of gas flow rates. X-ray diffraction (XRD) and SEM showed polycrystalline diamond structure with a random orientation. Polycrystalline diamond films with various textures were grown and (111) facets were dominant with sharp grain boundaries. Outgrowth was observed in flowerish character at high gas flow rates. Isolated single crystals with little openings appeared at various stages at low gas flow rates. Thus, changing gas flow rates had a beneficial influence on the grain size, growth rate and electrical resistivity. CVD diamond films gave an excellent performance for medium film thickness with relatively low electrical resistivity and making them potentially useful in many industrial applications

Assessment of ozone photochemistry in the western North Pacific as inferred from PEM-West A observations during the fall 1991

This study examines the influence of photochemical processes on ozone distributions in the western North Pacific. The analysis is based on data generated during NASA's western Pacific Exploratory Mission (PEM-West A) during the fall of 1991. Ozone trends were best described in terms of two geographical domains: the western North Pacific rim (WNPR) and the western tropical North Pacific (WTNP). For both geographical regions, ozone photochemical destruction, D(O3), decreased more rapidly with altitude than did photochemical formation, F(O3). Thus the ozone tendency, P(O3), was typically found to be negative for z &lt;6 km and positive for z &gt; 6-8 km. For nearly all altitudes and latitudes, observed nonmethane hydrocarbon (NMHC) levels were shown to be of minor importance as ozone precursor species. Air parcel types producing the largest positive values of P(O3) included fresh continental boundary layer (BL) air and high-altitude (z &gt; 7 km) parcels influenced by deep convection/lightning. Significant negative P(O3) values were found when encountering clean marine BL air or relatively clean lower free-tropospheric air. Photochemical destruction and formation fluxes for the Pacific rim region were found to exceed average values cited for marine dry deposition and stratospheric injection in the northern hemisphere by nearly a factor of 6. This region was also found to be in near balance with respect to column-integrated O3 photochemical production and destruction. By contrast, for the tropical regime column-integrated O3 showed photochemical destruction exceeding production by nearly 80%. Both transport of O3 rich midlatitude air into the tropics as well as very high-altitude (10-17 km) photochemical O3 production were proposed as possible additional sources that might explain this estimated deficit. Results from this study further suggest that during the fall time period, deep convection over Asia and Malaysia/Indonesia provided a significant source of high-altitude NOx to the western Pacific. Given that the high-altitude NOx lifetime is estimated at between 3 and 9 days, one would predict that this source added significantly to high altitude photochemical O3 formation over large areas of the western Pacific. When viewed in terms of strong seasonal westerly flow, its influence would potentially span a large part of the Pacific. Copyright 1996 by the American Geophysical Union

Patient perspectives of managing fatigue in ankylosing spondylitis, and views on potential interventions: a qualitative study

&lt;p&gt;Background: Fatigue is a major component of living with ankylosing spondylitis (AS), though it has been largely over-looked, and currently there are no specific agreed management strategies.&lt;/p&gt; &lt;p&gt;Methods: This qualitative exploratory study involved participants who are members of an existing population-based ankylosing spondylitis (PAS) cohort. Participants residing in South West Wales were invited to participate in a focus group to discuss; (1) effects of fatigue, (2) self-management strategies and (3) potential future interventions. The focus groups were audio-recorded and the transcripts were analysed using thematic analysis.&lt;/p&gt; &lt;p&gt;Results: Participants consisted of 3 males/4 females (group 1) and 4 males/3 females (group 2), aged between 35 and 73 years (mean age 53 years). Three main themes were identified: (1) The effects of fatigue were multi-dimensional with participants expressing feelings of being ‘drained’ (physical), ‘upset’ (emotional) and experiencing ‘low-mood’ (psychological); (2) The most commonly reported self-management strategy for fatigue was a balanced combination of activity (exercise) and rest. Medication was reluctantly taken due to side-effects and worries over dependency; (3) Participants expressed a preference for psychological therapies rather than pharmacological for managing fatigue. Information on Mindfulness-Based Stress Reduction (MBSR) was received with interest, with recommendations for delivery in a group format with the option of distance-based delivery for people who were not able to attend a group course.&lt;/p&gt; &lt;p&gt;Conclusions: Patients frequently try and manage their fatigue without any formal guidance or support. Our research indicates there is a need for future research to focus on psychological interventions to address the multi-faceted aspects of fatigue in AS.&lt;/p&gt