Algorithms for Bohemian Matrices

This thesis develops several algorithms for working with matrices whose entries are multivariate polynomials in a set of parameters. Such parametric linear systems often appear in biology and engineering applications where the parameters represent physical properties of the system. Some computations on parametric matrices, such as the rank and Jordan canonical form, are discontinuous in the parameter values. Understanding where these discontinuities occur provides a greater understanding of the underlying system. Algorithms for computing a complete case discussion of the rank, Zigzag form, and the Jordan canonical form of parametric matrices are presented. These algorithms use the theory of regular chains to provide a unified framework allowing for algebraic or semi-algebraic constraints on the parameters. Corresponding implementations for each algorithm in the Maple computer algebra system are provided. In some applications, all entries may be parameters whose values are limited to finite sets of integers. Such matrices appear in applications such as graph theory where matrix entries are limited to the sets {0, 1}, or {-1, 0, 1}. These types of parametric matrices can be explored using different techniques and exhibit many interesting properties. A family of Bohemian matrices is a set of low to moderate dimension matrices where the entries are independently sampled from a finite set of integers of bounded height. Properties of Bohemian matrices are studied including the distributions of their eigenvalues, symmetries, and integer sequences arising from properties of the families. These sequences provide connections to other areas of mathematics and have been archived in the Characteristic Polynomial Database. A study of two families of structured matrices: upper Hessenberg and upper Hessenberg Toeplitz, and properties of their characteristic polynomials are presented

Computation in Classical Mechanics

There is a growing consensus that physics majors need to learn computational skills, but many departments are still devoid of computation in their physics curriculum. Some departments may lack the resources or commitment to create a dedicated course or program in computational physics. One way around this difficulty is to include computation in a standard upper-level physics course. An intermediate classical mechanics course is particularly well suited for including computation. We discuss the ways we have used computation in our classical mechanics courses, focusing on how computational work can improve students' understanding of physics as well as their computational skills. We present examples of computational problems that serve these two purposes. In addition, we provide information about resources for instructors who would like to include computation in their courses.Comment: 6 pages, 3 figures, submitted to American Journal of Physic

Fine particle pH and the partitioning of nitric acid during winter in the northeastern United States

Particle pH is a critical but poorly constrained quantity that affects many aerosol processes and properties, including aerosol composition, concentrations, and toxicity. We assess PM1 pH as a function of geographical location and altitude, focusing on the northeastern U.S., based on aircraft measurements from the Wintertime Investigation of Transport, Emissions, and Reactivity campaign (1 February to 15 March 2015). Particle pH and water were predicted with the ISORROPIA-II thermodynamic model and validated by comparing predicted to observed partitioning of inorganic nitrate between the gas and particle phases. Good agreement was found for relative humidity (RH) above 40%; at lower RH observed particle nitrate was higher than predicted, possibly due to organic-inorganic phase separations or nitrate measurement uncertainties associated with low concentrations (nitrate \u3c 1 µg m−3). Including refractory ions in the pH calculations did not improve model predictions, suggesting they were externally mixed with PM1 sulfate, nitrate, and ammonium. Sample line volatilization artifacts were found to be minimal. Overall, particle pH for altitudes up to 5000 m ranged between −0.51 and 1.9 (10th and 90th percentiles) with a study mean of 0.77 ± 0.96, similar to those reported for the southeastern U.S. and eastern Mediterranean. This expansive aircraft data set is used to investigate causes in variability in pH and pH-dependent aerosol components, such as PM1 nitrate, over a wide range of temperatures (−21 to 19°C), RH (20 to 95%), inorganic gas, and particle concentrations and also provides further evidence that particles with low pH are ubiquitous

Assessing simulation ecosystem processes for climate variability research at Glacier National Park

Glacier National Park served as a test site for ecosystem analyses that involved a suite of integrated models embedded within a geographic information system. The goal of the exercise was to provide managers with maps that could illustrate probable shifts in vegetation, net primary production (NPP), and hydrologic responses associated with two selected climatic scenarios. The climatic scenarios were (a) a recent 12-yr record of weather data, and (b) a reconstituted set that sequentially introduced in repeated 3-yr intervals wetter–cooler, drier–warmer, and typical conditions. To extrapolate the implications of changes in ecosystem processes and resulting growth and distribution of vegetation and snowpack, the model incorporated geographic data. With underlying digital elevation maps, soil depth and texture, extrapolated climate, and current information on vegetation types and satellite-derived estimates of leaf area indices, simulations were extended to envision how the park might look after 120 yr. The predictions of change included underlying processes affecting the availability of water and nitrogen. Considerable field data were acquired to compare with model predictions under current climatic conditions. In general, the integrated landscape models of ecosystem processes had good agreement with measured NPP, snowpack, and streamflow, but the exercise revealed the difficulty and necessity of averaging point measurements across landscapes to achieve comparable results with modeled values. Under the extremely variable climate scenario significant changes in vegetation composition and growth as well as hydrologic responses were predicted across the park. In particular, a general rise in both the upper and lower limits of treeline was predicted. These shifts would probably occur along with a variety of disturbances (fire, insect, and disease outbreaks) as predictions of physiological stress (water, nutrients, light) altered competitive relations and hydrologic responses. The use of integrated landscape models applied in this exercise should provide managers with insights into the underlying processes important in maintaining community structure, and at the same time, locate where changes on the landscape are most likely to occur

Atmospheric carbon dioxide variability in the Community Earth System Model : evaluation and transient dynamics during the twentieth and twenty-first centuries

Author Posting. © American Meteorological Society, 2013. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Climate 26 (2013): 4447–4475, doi:10.1175/JCLI-D-12-00589.1.Changes in atmospheric CO2 variability during the twenty-first century may provide insight about ecosystem responses to climate change and have implications for the design of carbon monitoring programs. This paper describes changes in the three-dimensional structure of atmospheric CO2 for several representative concentration pathways (RCPs 4.5 and 8.5) using the Community Earth System Model–Biogeochemistry (CESM1-BGC). CO2 simulated for the historical period was first compared to surface, aircraft, and column observations. In a second step, the evolution of spatial and temporal gradients during the twenty-first century was examined. The mean annual cycle in atmospheric CO2 was underestimated for the historical period throughout the Northern Hemisphere, suggesting that the growing season net flux in the Community Land Model (the land component of CESM) was too weak. Consistent with weak summer drawdown in Northern Hemisphere high latitudes, simulated CO2 showed correspondingly weak north–south and vertical gradients during the summer. In the simulations of the twenty-first century, CESM predicted increases in the mean annual cycle of atmospheric CO2 and larger horizontal gradients. Not only did the mean north–south gradient increase due to fossil fuel emissions, but east–west contrasts in CO2 also strengthened because of changing patterns in fossil fuel emissions and terrestrial carbon exchange. In the RCP8.5 simulation, where CO2 increased to 1150 ppm by 2100, the CESM predicted increases in interannual variability in the Northern Hemisphere midlatitudes of up to 60% relative to present variability for time series filtered with a 2–10-yr bandpass. Such an increase in variability may impact detection of changing surface fluxes from atmospheric observations.The CESM project is supported by the National Science Foundation and the Office of Science (BER) of the U.S. Department of Energy. Computing resources were provided by the Climate Simulation Laboratory at NCAR’s Computational and Information Systems Laboratory (CISL), sponsored by the National Science Foundation and other agencies. G.K.A. acknowledges support of a NOAA Climate and Global Change postdoctoral fellowship. J.T.R., N.M.M., S.C.D., K.L., and J.K.M. acknowledge support of Collaborative Research: Improved Regional and Decadal Predictions of the Carbon Cycle (NSF AGS-1048827, AGS-1021776,AGS-1048890). TheHIPPO Programwas supported byNSF GrantsATM-0628575,ATM-0628519, and ATM-0628388 to Harvard University, University of California (San Diego), and by University Corporation for Atmospheric Research, University of Colorado/ CIRES, by the NCAR and by the NOAAEarth System Research Laboratory. Sunyoung Park, Greg Santoni, Eric Kort, and Jasna Pittman collected data during HIPPO. The ACME project was supported by the Office of Biological and Environmental Research of the U.S. Department of Energy under Contract DE-AC02- 05CH11231 as part of the Atmospheric Radiation Measurement Program (ARM), the ARM Aerial Facility, and the Terrestrial EcosystemScience Program. TCCON measurements at Eureka were made by the Canadian Network for Detection of Atmospheric Composition Change (CANDAC) with additional support from the Canadian Space Agency. The Lauder TCCON program was funded by the New Zealand Foundation for Research Science and Technology contracts CO1X0204, CO1X0703, and CO1X0406. Measurements at Darwin andWollongong were supported by Australian Research Council Grants DP0879468 and DP110103118 and were undertaken by David Griffith, Nicholas Deutscher, and Ronald Macatangay. We thank Pauli Heikkinen, Petteri Ahonen, and Esko Kyr€o of the Finnish Meteorological Institute for contributing the Sodankyl€a TCCON data. Measurements at Park Falls, Lamont, and Pasadena were supported byNASAGrant NNX11AG01G and the NASA Orbiting Carbon Observatory Program. Data at these sites were obtained by Geoff Toon, Jean- Francois Blavier, Coleen Roehl, and Debra Wunch.2014-01-0

Trial protocol OPPTIMUM : does progesterone prophylaxis for the prevention of preterm labour improve outcome?

Background Preterm birth is a global problem, with a prevalence of 8 to 12% depending on location. Several large trials and systematic reviews have shown progestogens to be effective in preventing or delaying preterm birth in selected high risk women with a singleton pregnancy (including those with a short cervix or previous preterm birth). Although an improvement in short term neonatal outcomes has been shown in some trials these have not consistently been confirmed in meta-analyses. Additionally data on longer term outcomes is limited to a single trial where no difference in outcomes was demonstrated at four years of age of the child, despite those in the “progesterone” group having a lower incidence of preterm birth. Methods/Design The OPPTIMUM study is a double blind randomized placebo controlled trial to determine whether progesterone prophylaxis to prevent preterm birth has long term neonatal or infant benefit. Specifically it will study whether, in women with singleton pregnancy and at high risk of preterm labour, prophylactic vaginal natural progesterone, 200 mg daily from 22 – 34 weeks gestation, compared to placebo, improves obstetric outcome by lengthening pregnancy thus reducing the incidence of preterm delivery (before 34 weeks), improves neonatal outcome by reducing a composite of death and major morbidity, and leads to improved childhood cognitive and neurosensory outcomes at two years of age. Recruitment began in 2009 and is scheduled to close in Spring 2013. As of May 2012, over 800 women had been randomized in 60 sites. Discussion OPPTIMUM will provide further evidence on the effectiveness of vaginal progesterone for prevention of preterm birth and improvement of neonatal outcomes in selected groups of women with singleton pregnancy at high risk of preterm birth. Additionally it will determine whether any reduction in the incidence of preterm birth is accompanied by improved childhood outcome