Monotonicity Formulas for Diffusion Operators on Manifolds and Carnot Groups, Heat Kernel Asymptotics and Wiener\u27s Criterion on Heisenberg-type Groups

The contents of this thesis are an assortment of results in analysis and subRiemannian geometry, with a special focus on the Heisenberg group Hn, Heisenbergtype (H-type) groups, and Carnot groups. As we wish for this thesis to be relatively self-contained, the main definitions and background are covered in Chapter 1. This includes basic information about Carnot groups, Hn, H-type groups, diffusion operators, and the curvature dimension inequality. Chapter 2 incorporates excerpts from a paper by N. Garofalo and the author, [42]. In it, we propose a generalization of Almgren’s frequency function N : (0, 1) → R for solutions to the sub-elliptic Laplace equation ΔHu = 0 in the unit ball of a Carnot group of arbitrary step. If the function u has vanishing discrepancy, then the frequency is monotonically non-decreasing, and we are able to prove a form of strong unique continuation for such functions. Chapter 3 grew out of the author seeking parabolic montonicity formulas in the same vein as Almgren’s frequency. These include two types of monotonicity formulas, those of Struwe- and Poon-type [72], [67]. If a diffusion operator L on a complete manifold M satisfies the curvature dimension inequality CD(ρ, n), then we are able to prove that for solutions to L u = ut in M × (0, T), Struwe’s energy monotonicity holds, at least for time values close enough to T. We introduce a new condition, C(ω) where ω ∈ C1(0, T), related to the Hessian of the heat kernel, and are able to prove a Poon-type frequency monotonicity formula when taking into account a weighting factor depending on ω. We also give examples of manifolds satisfying C(ω), the most interesting of which includes the Ornstein-Uhlenbeck operator. Monotonicity of the weighted frequency also implies a form of strong-unique continuation. In Chapter 4, we derive asymptotics for the heat kernel on H-type groups and generalize a gradient bound from a paper of Garofalo and Segala [43] to these groups. This gradient bound in turn implies a strong Harnack inequality and Wiener criterion similar to those found in [31] and [43]

Nitrogen–climate interactions in US agriculture

Agriculture in the United States (US) cycles large quantities of nitrogen (N) to produce food, fuel, and fiber and is a major source of excess reactive nitrogen (Nr) in the environment. Nitrogen lost from cropping systems and animal operations moves to waterways, groundwater, and the atmosphere. Changes in climate and climate variability may further affect the ability of agricultural systems to conserve N. The N that escapes affects climate directly through the emissions of nitrous oxide (N2O), and indirectly through the loss of nitrate (NO3-), nitrogen oxides (NOx) and ammonia to downstream and downwind ecosystems that then emit some of the N received as N2O and NOx. Emissions of NOx lead to the formation of tropospheric ozone, a greenhouse gas that can also harm crops directly. There are many opportunities to mitigate the impact of agricultural N on climate and the impact of climate on agricultural N. Some are available today; many need further research; and all await effective incentives to become adopted. Research needs can be grouped into four major categories: (1) an improved understanding of agriculturalNcycle responses to changing climate; (2) a systems-level understanding of important crop and animal systems sufficient to identify key interactions and feedbacks; (3) the further development and testing of quantitative models capable of predicting N-climate interactions with confidence across a wide variety of crop-soil-climate combinations; and (4) socioecological research to better understand the incentives necessary to achieve meaningful deployment of realistic solutions

Tradeoffs in the quest for climate smart agricultural intensification in Mato Grosso, Brazil.

Low productivity cattle ranching, with its linkages to rural poverty, deforestation and greenhouse gas (GHG) emissions, remains one of the largest sustainability challenges in Brazil and has impacts worldwide. There is a nearly universal call to intensify extensive beef cattle production systems to spare land for crop production and nature and to meet Brazil?s Intended Nationally Determined Contribution to reducing global climate change. However, different interventions aimed at the intensification of livestock systems in Brazil may involve substantial social and environmental tradeoffs. Here we examine these tradeoffs using a whole-farm model calibrated for the Brazilian agricultural frontier state ofMato Grosso, one of the largest soybean and beef cattle production regions in the world. Specifically, we compare the costs and benefits of a typical extensive, continuously grazed cattle system relative to a specialized soybean production system and two improved cattle management strategies (rotational grazing and integrated soybean-cattle) under different climate scenarios.We found clear tradeoffs in GHG and nitrogen emissions, climate resilience, and water and energy use across these systems. Relative to continuously grazed or rotationally grazed cattle systems, the integreated soybean-cattle system showed higher food production and lower GHG emissions per unit of human digestible protein, as well as increased resilience under climate change (both in terms of productivity and financial returns). All systems suffered productivity and profitability losses under severe climate change, highlighting the need for climate smart agricultural development strategies in the region. By underscoring the economic feasibility of improving the performance of cattle systems, and by quantifying the tradeoffs of each option, our results are useful for directing agricultural and climate policy

Syndromic Surveillance and Bioterrorism-related Epidemics

To facilitate rapid detection of a future bioterrorist attack, an increasing number of public health departments are investing in new surveillance systems that target the early manifestations of bioterrorism-related disease. Whether this approach is likely to detect an epidemic sooner than reporting by alert clinicians remains unknown. The detection of a bioterrorism-related epidemic will depend on population characteristics, availability and use of health services, the nature of an attack, epidemiologic features of individual diseases, surveillance methods, and the capacity of health departments to respond to alerts. Predicting how these factors will combine in a bioterrorism attack may be impossible. Nevertheless, understanding their likely effect on epidemic detection should help define the usefulness of syndromic surveillance and identify approaches to increasing the likelihood that clinicians recognize and report an epidemic

iNOS activity is critical for the clearance of Burkholderia mallei from infected RAW 264.7 murine macrophages

Burkholderia mallei is a facultative intracellular pathogen that can cause fatal disease in animals and humans. To better understand the role of phagocytic cells in the control of infections caused by this organism, studies were initiated to examine the interactions of B. mallei with RAW 264.7 murine macrophages. Utilizing modified kanamycin-protection assays, B. mallei was shown to survive and replicate in RAW 264.7 cells infected at multiplicities of infection (moi) of ≤ 1. In contrast, the organism was efficiently cleared by the macrophages when infected at an moi of 10. Interestingly, studies demonstrated that the monolayers only produced high levels of TNF-α, IL-6, IL-10, GM-CSF, RANTES and IFN-β when infected at an moi of 10. In addition, nitric oxide assays and inducible nitric oxide synthase (iNOS) immunoblot analyses revealed a strong correlation between iNOS activity and clearance of B. mallei from RAW 264.7 cells. Furthermore, treatment of activated macrophages with the iNOS inhibitor, aminoguanidine, inhibited clearance of B. mallei from infected monolayers. Based upon these results, it appears that moi significantly influence the outcome of interactions between B. mallei and murine macrophages and that iNOS activity is critical for the clearance of B. mallei from activated RAW 264.7 cells

Global Research Alliance N2O chamber methodology guidelines : Summary of modeling approaches

Acknowledgements Funding for this publication was provided by the New Zealand Government to support the objectives of the Livestock Research Group of the Global Research Alliance on Agricultural Greenhouse Gases. Individual authors work contribute to the following projects for which support has been received: Climate smart use of Norwegian organic soils (MYR, 2017-2022) project funded by the Research Council of Norway (decision no. 281109); Scottish Government's Strategic Research Programme, SuperG (under EU Horizon 2020 programme); DEVIL (NE/M021327/1), Soils-R-GRREAT (NE/P019455/1) and the EU H2020 project under Grant Agreement 774378—Coordination of International Research Cooperation on Soil Carbon Sequestration in Agriculture (CIRCASA); to project J-001793, Science and Technology Branch, Agriculture and Agri-Food Canada; and New Zealand Ministry of Business, Innovation and Employment (MBIE) core funding. Thanks to Alasdair Noble and the anonymous reviewers for helpful comments on a draft of this paper and to Anne Austin for editing services.Peer reviewedPublisher PD

Endemic, Notifiable Bioterrorism-Related Diseases, United States, 1992–1999

Little information is available in the United States regarding the incidence and distribution of diseases caused by critical microbiologic agents with the potential for use in acts of terrorism. We describe disease-specific, demographic, geographic, and seasonal distribution of selected bioterrorism-related conditions (anthrax, botulism, brucellosis, cholera, plague, tularemia, and viral encephalitides) reported to the National Notifiable Diseases Surveillance System in 1992–1999. Tularemia and brucellosis were the most frequently reported diseases. Anthrax, plague, western equine encephalitis, and eastern equine encephalitis were rare. Higher incidence rates for cholera and plague were noted in the western United States and for tularemia in the central United States. Overall, the incidence of conditions caused by these critical agents in the United States is low. Individual case reports should be considered sentinel events. For potential bioterrorism-related conditions that are endemic and have low incidence, the use of nontraditional surveillance methods and complementary data sources may enhance our ability to rapidly detect changes in disease incidence