Analytic-domain lens design with proximate ray tracing.

We have developed an alternative approach to optical design which operates in the analytical domain so that an optical designer works directly with rays as analytical functions of system parameters rather than as discretely sampled polylines. This is made possible by a generalization of the proximate ray tracing technique which obtains the analytical dependence of the rays at the image surface (and ray path lengths at the exit pupil) on each system parameter. The resulting method provides an alternative direction from which to approach system optimization and supplies information which is not typically available to the system designer. In addition, we have further expanded the procedure to allow asymmetric systems and arbitrary order of approximation, and have illustrated the performance of the method through three lens design examples.

Analytic expressions for the constitutive parameters of magnetoelectric metamaterials

Electromagnetic metamaterials are artificially structured media typically composed of arrays of resonant electromagnetic circuits, the dimension and spacing of which are considerably smaller than the free-space wavelengths of operation. The constitutive parameters for metamaterials, which can be obtained using full-wave simulations in conjunction with numerical retrieval algorithms, exhibit artifacts related to the finite size of the metamaterial cell relative to the wavelength. Liu showed that the complicated, frequency-dependent forms of the constitutive parameters can be described by a set of relatively simple analytical expressions. These expressions provide useful insight and can serve as the basis for more intelligent interpolation or optimization schemes. Here, we show that the same analytical expressions can be obtained using a transfer-matrix formalism applied to a one-dimensional periodic array of thin, resonant, dielectric, or magnetic sheets. The transfer-matrix formalism breaks down, however, when both electric and magnetic responses are present in the same unit cell, as it neglects the magnetoelectric coupling between unit cells. We show that an alternative analytical approach based on the same physical model must be applied for such structures. Furthermore, in addition to the intercell coupling, electric and magnetic resonators within a unit cell may also exhibit magnetoelectric coupling. For such cells, we find an analytical expression for the effective index, which displays markedly characteristic dispersion features that depend on the strength of the coupling coefficient. We illustrate the applicability of the derived expressions by comparing to full-wave simulations on magnetoelectric unit cells. We conclude that the design of metamaterials with tailored simultaneous electric and magnetic response-such as negative index materials-will generally be complicated by potentially unwanted magnetoelectric coupling. © 2010 The American Physical Society.

Global fire emissions and the contribution of deforestation, savanna, forest, agricultural, and peat fires (1997-2009)

New burned area datasets and top-down constraints from atmospheric concentration measurements of pyrogenic gases have decreased the large uncertainty in fire emissions estimates. However, significant gaps remain in our understanding of the contribution of deforestation, savanna, forest, agricultural waste, and peat fires to total global fire emissions. Here we used a revised version of the Carnegie-Ames-Stanford-Approach (CASA) biogeochemical model and improved satellite-derived estimates of area burned, fire activity, and plant productivity to calculate fire emissions for the 1997-2009 period on a 0.5° spatial resolution with a monthly time step. For November 2000 onwards, estimates were based on burned area, active fire detections, and plant productivity from the MODerate resolution Imaging Spectroradiometer (MODIS) sensor. For the partitioning we focused on the MODIS era. We used maps of burned area derived from the Tropical Rainfall Measuring Mission (TRMM) Visible and Infrared Scanner (VIRS) and Along-Track Scanning Radiometer (ATSR) active fire data prior to MODIS (1997-2000) and estimates of plant productivity derived from Advanced Very High Resolution Radiometer (AVHRR) observations during the same period. Average global fire carbon emissions according to this version 3 of the Global Fire Emissions Database (GFED3) were 2.0 PgC year-1 with significant interannual variability during 1997-2001 (2.8 Pg Cyear-1 in 1998 and 1.6 PgC year-1 in 2001). Globally, emissions during 2002-2007 were rela-tively constant (around 2.1 Pg C year-1) before declining in 2008 (1.7 Pg Cyear-1) and 2009 (1.5 PgC year-1) partly due to lower deforestation fire emissions in South America and tropical Asia. On a regional basis, emissions were highly variable during 2002-2007 (e.g., boreal Asia, South America, and Indonesia), but these regional differences canceled out at a global level. During the MODIS era (2001-2009), most carbon emissions were from fires in grasslands and savannas (44%) with smaller contributions from tropical deforestation and degradation fires (20%), woodland fires (mostly confined to the tropics, 16%), forest fires (mostly in the extratropics, 15%), agricultural waste burning (3%), and tropical peat fires (3%). The contribution from agricultural waste fires was likely a lower bound because our approach for measuring burned area could not detect all of these relatively small fires. Total carbon emissions were on average 13% lower than in our previous (GFED2) work. For reduced trace gases such as CO and CH4, deforestation, degradation, and peat fires were more important contributors because of higher emissions of reduced trace gases per unit carbon combusted compared to savanna fires. Carbon emissions from tropical deforestation, degradation, and peatland fires were on average 0.5 PgC year-1. The carbon emissions from these fires may not be balanced by regrowth following fire. Our results provide the first global assessment of the contribution of different sources to total global fire emissions for the past decade, and supply the community with an improved 13-year fire emissions time series. © 2010 Author(s).

BAYESIAN MODEL SEARCH AND MULTILEVEL INFERENCE FOR SNP ASSOCIATION STUDIES.

Technological advances in genotyping have given rise to hypothesis-based association studies of increasing scope. As a result, the scientific hypotheses addressed by these studies have become more complex and more difficult to address using existing analytic methodologies. Obstacles to analysis include inference in the face of multiple comparisons, complications arising from correlations among the SNPs (single nucleotide polymorphisms), choice of their genetic parametrization and missing data. In this paper we present an efficient Bayesian model search strategy that searches over the space of genetic markers and their genetic parametrization. The resulting method for Multilevel Inference of SNP Associations, MISA, allows computation of multilevel posterior probabilities and Bayes factors at the global, gene and SNP level, with the prior distribution on SNP inclusion in the model providing an intrinsic multiplicity correction. We use simulated data sets to characterize MISA's statistical power, and show that MISA has higher power to detect association than standard procedures. Using data from the North Carolina Ovarian Cancer Study (NCOCS), MISA identifies variants that were not identified by standard methods and have been externally "validated" in independent studies. We examine sensitivity of the NCOCS results to prior choice and method for imputing missing data. MISA is available in an R package on CRAN.

Antibiotic resistance-the need for global solutions.

The causes of antibiotic resistance are complex and include human behaviour at many levels of society; the consequences affect everybody in the world. Similarities with climate change are evident. Many efforts have been made to describe the many different facets of antibiotic resistance and the interventions needed to meet the challenge. However, coordinated action is largely absent, especially at the political level, both nationally and internationally. Antibiotics paved the way for unprecedented medical and societal developments, and are today indispensible in all health systems. Achievements in modern medicine, such as major surgery, organ transplantation, treatment of preterm babies, and cancer chemotherapy, which we today take for granted, would not be possible without access to effective treatment for bacterial infections. Within just a few years, we might be faced with dire setbacks, medically, socially, and economically, unless real and unprecedented global coordinated actions are immediately taken. Here, we describe the global situation of antibiotic resistance, its major causes and consequences, and identify key areas in which action is urgently needed.

The Justice Gap in Global Forest Governance

Claims of injustice in global forest governance are prolific: assertions of colonization, marginalization and disenfranchisement of forest-dependent people, and privatization of common resources are some of the most severe allegations of injustice resulting from globally-driven forest conservation initiatives. At its core, the debate over the future of the world's forests is fraught with ethical concerns. Policy makers are not only deciding how forests should be governed, but also who will be winners, losers, and who should have a voice in the decision-making processes. For 30 years, policy makers have sought to redress the concerns of the world's 1.6 billion forest-dependent poor by introducing rights-based and participatory approaches to conservation. Despite these efforts, however, claims of injustice persist. This research examines possible explanations for continued claims of injustice by asking: What are the barriers to delivering justice to forest-dependent communities? Using data collected through surveys, interviews, and collaborative event ethnography in Laos and at the Tenth Conference of Parties to the Convention on Biological Diversity, this dissertation examines the pursuit of justice in global forest governance across multiple scales of governance. The findings reveal that particular conceptualizations of justice have become a central part of the metanormative fabric of global environmental governance, inhibiting institutional evolution and therewith perpetuating the justice gap in global forest governance.

Gold mining in the Peruvian Amazon: global prices, deforestation, and mercury imports.

Many factors such as poverty, ineffective institutions and environmental regulations may prevent developing countries from managing how natural resources are extracted to meet a strong market demand. Extraction for some resources has reached such proportions that evidence is measurable from space. We present recent evidence of the global demand for a single commodity and the ecosystem destruction resulting from commodity extraction, recorded by satellites for one of the most biodiverse areas of the world. We find that since 2003, recent mining deforestation in Madre de Dios, Peru is increasing nonlinearly alongside a constant annual rate of increase in international gold price (∼18%/yr). We detect that the new pattern of mining deforestation (1915 ha/year, 2006-2009) is outpacing that of nearby settlement deforestation. We show that gold price is linked with exponential increases in Peruvian national mercury imports over time (R(2) = 0.93, p = 0.04, 2003-2009). Given the past rates of increase we predict that mercury imports may more than double for 2011 (∼500 t/year). Virtually all of Peru's mercury imports are used in artisanal gold mining. Much of the mining increase is unregulated/artisanal in nature, lacking environmental impact analysis or miner education. As a result, large quantities of mercury are being released into the atmosphere, sediments and waterways. Other developing countries endowed with gold deposits are likely experiencing similar environmental destruction in response to recent record high gold prices. The increasing availability of satellite imagery ought to evoke further studies linking economic variables with land use and cover changes on the ground.

Tectonic and magmatic segmentation of the Global Ocean Ridge System: A synthesis of observations

© 2016 The Author(s).Mid-ocean ridges display tectonic segmentation defined by discontinuities of the axial zone, and geophysical and geochemical observations suggest segmentation of the underlying magmatic plumbing system. Here, observations of tectonic and magmatic segmentation at ridges spreading from fast to ultraslow rates are reviewed in light of influential concepts of ridge segmentation, including the notion of hierarchical segmentation, spreading cells and centralized v. multiple supply of mantle melts. The observations support the concept of quasi-regularly spaced principal magmatic segments, which are 30-50 km long on average at fast- to slow-spreading ridges and fed by melt accumulations in the shallow asthenosphere. Changes in ridge properties approaching or crossing transform faults are often comparable with those observed at smaller offsets, and even very small discontinuities can be major boundaries in ridge properties. Thus, hierarchical segmentation models that suggest large-scale transform fault-bounded segmentation arises from deeper level processes in the asthenosphere than the finer-scale segmentation are not generally supported. The boundaries between some but not all principal magmatic segments defined by ridge axis geophysical properties coincide with geochemical boundaries reflecting changes in source composition or melting processes. Where geochemical boundaries occur, they can coincide with discontinuities of a wide range of scales.

A theory of hypoellipticity and unique ergodicity for semilinear stochastic PDEs

We present a theory of hypoellipticity and unique ergodicity for semilinear parabolic stochastic PDEs with "polynomial" nonlinearities and additive noise, considered as abstract evolution equations in some Hilbert space. It is shown that if Hörmander's bracket condition holds at every point of this Hilbert space, then a lower bound on the Malliavin covariance operatorμt can be obtained. Informally, this bound can be read as "Fix any finite-dimensional projection on a subspace of sufficiently regular functions. Then the eigenfunctions of μt with small eigenvalues have only a very small component in the image of Π." We also show how to use a priori bounds on the solutions to the equation to obtain good control on the dependency of the bounds on the Malliavin matrix on the initial condition. These bounds are sufficient in many cases to obtain the asymptotic strong Feller property introduced in [HM06]. One of the main novel technical tools is an almost sure bound from below on the size of "Wiener polynomials," where the coefficients are possibly non-adapted stochastic processes satisfying a Lips chitz condition. By exploiting the polynomial structure of the equations, this result can be used to replace Norris' lemma, which is unavailable in the present context. We conclude by showing that the two-dimensional stochastic Navier-Stokes equations and a large class of reaction-diffusion equations fit the framework of our theory.

Comparing the model-simulated global warming signal to observations using empirical estimates of unforced noise.

The comparison of observed global mean surface air temperature (GMT) change to the mean change simulated by climate models has received much public and scientific attention. For a given global warming signal produced by a climate model ensemble, there exists an envelope of GMT values representing the range of possible unforced states of the climate system (the Envelope of Unforced Noise; EUN). Typically, the EUN is derived from climate models themselves, but climate models might not accurately simulate the correct characteristics of unforced GMT variability. Here, we simulate a new, empirical, EUN that is based on instrumental and reconstructed surface temperature records. We compare the forced GMT signal produced by climate models to observations while noting the range of GMT values provided by the empirical EUN. We find that the empirical EUN is wide enough so that the interdecadal variability in the rate of global warming over the 20(th) century does not necessarily require corresponding variability in the rate-of-increase of the forced signal. The empirical EUN also indicates that the reduced GMT warming over the past decade or so is still consistent with a middle emission scenario's forced signal, but is likely inconsistent with the steepest emission scenario's forced signal.

Hostile attributional bias and aggressive behavior in global context.

We tested a model that children's tendency to attribute hostile intent to others in response to provocation is a key psychological process that statistically accounts for individual differences in reactive aggressive behavior and that this mechanism contributes to global group differences in children's chronic aggressive behavior problems. Participants were 1,299 children (mean age at year 1 = 8.3 y; 51% girls) from 12 diverse ecological-context groups in nine countries worldwide, followed across 4 y. In year 3, each child was presented with each of 10 hypothetical vignettes depicting an ambiguous provocation toward the child and was asked to attribute the likely intent of the provocateur (coded as benign or hostile) and to predict his or her own behavioral response (coded as nonaggression or reactive aggression). Mothers and children independently rated the child's chronic aggressive behavior problems in years 2, 3, and 4. In every ecological group, in those situations in which a child attributed hostile intent to a peer, that child was more likely to report that he or she would respond with reactive aggression than in situations when that same child attributed benign intent. Across children, hostile attributional bias scores predicted higher mother- and child-rated chronic aggressive behavior problems, even controlling for prior aggression. Ecological group differences in the tendency for children to attribute hostile intent statistically accounted for a significant portion of group differences in chronic aggressive behavior problems. The findings suggest a psychological mechanism for group differences in aggressive behavior and point to potential interventions to reduce aggressive behavior.

Global Rates of Free Hydrogen (H2) Production by Serpentinization and other Abiogenic Processes within Young Ocean Crust

The main conclusion of this dissertation is that global H2 production within young ocean crust (<10 Mya) is higher than currently recognized, in part because current estimates of H2 production accompanying the serpentinization of peridotite may be too low (Chapter 2) and in part because a number of abiogenic H2-producing processes have heretofore gone unquantified (Chapter 3). The importance of free H2 to a range of geochemical processes makes the quantitative understanding of H2 production advanced in this dissertation pertinent to an array of open research questions across the geosciences (e.g. the origin and evolution of life and the oxidation of the Earth’s atmosphere and oceans).

The first component of this dissertation (Chapter 2) examines H2 produced within young ocean crust [e.g. near the mid-ocean ridge (MOR)] by serpentinization. In the presence of water, olivine-rich rocks (peridotites) undergo serpentinization (hydration) at temperatures of up to ~500°C but only produce H2 at temperatures up to ~350°C. A simple analytical model is presented that mechanistically ties the process to seafloor spreading and explicitly accounts for the importance of temperature in H2 formation. The model suggests that H2 production increases with the rate of seafloor spreading and the net thickness of serpentinized peridotite (S-P) in a column of lithosphere. The model is applied globally to the MOR using conservative estimates for the net thickness of lithospheric S-P, our least certain model input. Despite the large uncertainties surrounding the amount of serpentinized peridotite within oceanic crust, conservative model parameters suggest a magnitude of H2 production (~1012 moles H2/y) that is larger than the most widely cited previous estimates (~1011 although previous estimates range from 1010-1012 moles H2/y). Certain model relationships are also consistent with what has been established through field studies, for example that the highest H2 fluxes (moles H2/km2 seafloor) are produced near slower-spreading ridges (<20 mm/y). Other modeled relationships are new and represent testable predictions. Principal among these is that about half of the H2 produced globally is produced off-axis beneath faster-spreading seafloor (>20 mm/y), a region where only one measurement of H2 has been made thus far and is ripe for future investigation.

In the second part of this dissertation (Chapter 3), I construct the first budget for free H2 in young ocean crust that quantifies and compares all currently recognized H2 sources and H2 sinks. First global estimates of budget components are proposed in instances where previous estimate(s) could not be located provided that the literature on that specific budget component was not too sparse to do so. Results suggest that the nine known H2 sources, listed in order of quantitative importance, are: Crystallization (6x1012 moles H2/y or 61% of total H2 production), serpentinization (2x1012 moles H2/y or 21%), magmatic degassing (7x1011 moles H2/y or 7%), lava-seawater interaction (5x1011 moles H2/y or 5%), low-temperature alteration of basalt (5x1011 moles H2/y or 5%), high-temperature alteration of basalt (3x1010 moles H2/y or <1%), catalysis (3x108 moles H2/y or <<1%), radiolysis (2x108 moles H2/y or <<1%), and pyrite formation (3x106 moles H2/y or <<1%). Next we consider two well-known H2 sinks, H2 lost to the ocean and H2 occluded within rock minerals, and our analysis suggests that both are of similar size (both are 6x1011 moles H2/y). Budgeting results suggest a large difference between H2 sources (total production = 1x1013 moles H2/y) and H2 sinks (total losses = 1x1011 moles H2/y). Assuming this large difference represents H2 consumed by microbes (total consumption = 9x1011 moles H2/y), we explore rates of primary production by the chemosynthetic, sub-seafloor biosphere. Although the numbers presented require further examination and future modifications, the analysis suggests that the sub-seafloor H2 budget is similar to the sub-seafloor CH4 budget in the sense that globally significant quantities of both of these reduced gases are produced beneath the seafloor but never escape the seafloor due to microbial consumption.

The third and final component of this dissertation (Chapter 4) explores the self-organization of barchan sand dune fields. In nature, barchan dunes typically exist as members of larger dune fields that display striking, enigmatic structures that cannot be readily explained by examining the dynamics at the scale of single dunes, or by appealing to patterns in external forcing. To explore the possibility that observed structures emerge spontaneously as a collective result of many dunes interacting with each other, we built a numerical model that treats barchans as discrete entities that interact with one another according to simplified rules derived from theoretical and numerical work, and from field observations: Dunes exchange sand through the fluxes that leak from the downwind side of each dune and are captured on their upstream sides; when dunes become sufficiently large, small dunes are born on their downwind sides (“calving”); and when dunes collide directly enough, they merge. Results show that these relatively simple interactions provide potential explanations for a range of field-scale phenomena including isolated patches of dunes and heterogeneous arrangements of similarly sized dunes in denser fields. The results also suggest that (1) dune field characteristics depend on the sand flux fed into the upwind boundary, although (2) moving downwind, the system approaches a common attracting state in which the memory of the upwind conditions vanishes. This work supports the hypothesis that calving exerts a first order control on field-scale phenomena; it prevents individual dunes from growing without bound, as single-dune analyses suggest, and allows the formation of roughly realistic, persistent dune field patterns.