A mathematical theory of stochastic microlensing. II. Random images, shear, and the Kac-Rice formula

Continuing our development of a mathematical theory of stochastic microlensing, we study the random shear and expected number of random lensed images of different types. In particular, we characterize the first three leading terms in the asymptotic expression of the joint probability density function (pdf) of the random shear tensor due to point masses in the limit of an infinite number of stars. Up to this order, the pdf depends on the magnitude of the shear tensor, the optical depth, and the mean number of stars through a combination of radial position and the star's mass. As a consequence, the pdf's of the shear components are seen to converge, in the limit of an infinite number of stars, to shifted Cauchy distributions, which shows that the shear components have heavy tails in that limit. The asymptotic pdf of the shear magnitude in the limit of an infinite number of stars is also presented. All the results on the random microlensing shear are given for a general point in the lens plane. Extending to the general random distributions (not necessarily uniform) of the lenses, we employ the Kac-Rice formula and Morse theory to deduce general formulas for the expected total number of images and the expected number of saddle images. We further generalize these results by considering random sources defined on a countable compact covering of the light source plane. This is done to introduce the notion of global expected number of positive parity images due to a general lensing map. Applying the result to microlensing, we calculate the asymptotic global expected number of minimum images in the limit of an infinite number of stars, where the stars are uniformly distributed. This global expectation is bounded, while the global expected number of images and the global expected number of saddle images diverge as the order of the number of stars. © 2009 American Institute of Physics.

Molecular mapping of movement-associated areas in the avian brain: a motor theory for vocal learning origin.

Vocal learning is a critical behavioral substrate for spoken human language. It is a rare trait found in three distantly related groups of birds-songbirds, hummingbirds, and parrots. These avian groups have remarkably similar systems of cerebral vocal nuclei for the control of learned vocalizations that are not found in their more closely related vocal non-learning relatives. These findings led to the hypothesis that brain pathways for vocal learning in different groups evolved independently from a common ancestor but under pre-existing constraints. Here, we suggest one constraint, a pre-existing system for movement control. Using behavioral molecular mapping, we discovered that in songbirds, parrots, and hummingbirds, all cerebral vocal learning nuclei are adjacent to discrete brain areas active during limb and body movements. Similar to the relationships between vocal nuclei activation and singing, activation in the adjacent areas correlated with the amount of movement performed and was independent of auditory and visual input. These same movement-associated brain areas were also present in female songbirds that do not learn vocalizations and have atrophied cerebral vocal nuclei, and in ring doves that are vocal non-learners and do not have cerebral vocal nuclei. A compilation of previous neural tracing experiments in songbirds suggests that the movement-associated areas are connected in a network that is in parallel with the adjacent vocal learning system. This study is the first global mapping that we are aware for movement-associated areas of the avian cerebrum and it indicates that brain systems that control vocal learning in distantly related birds are directly adjacent to brain systems involved in movement control. Based upon these findings, we propose a motor theory for the origin of vocal learning, this being that the brain areas specialized for vocal learning in vocal learners evolved as a specialization of a pre-existing motor pathway that controls movement.

Small-scale Fisheries and the Global Economy: Understanding Common-pool Resource Governance in the Context of Market Pressures, Neoliberal Policies, and Transnational Institutions

The purpose of this dissertation is to contribute to a better understanding of how global seafood trade interacts with the governance of small-scale fisheries (SSFs). As global seafood trade expands, SSFs have the potential to experience significant economic, social, and political benefits from participation in export markets. At the same time, market connections that place increasing pressures on resources pose risks to both the ecological and social integrity of SSFs. This dissertation seeks to explore the factors that mediate between the potential benefits and risks of global seafood markets for SSFs, with the goal of developing hypotheses regarding these relationships.

The empirical investigation consists of a series of case studies from the Yucatan Peninsula, Mexico. This is a particularly rich context in which to study global market connections with SSFs because the SSFs in this region engage in a variety of market-oriented harvests, most notably for octopus, groupers and snappers, lobster, and sea cucumber. Variation in market forms and the institutional diversity of local-level governance arrangements allows the dissertation to explore a number of examples.

The analysis is guided primarily by common-pool resource (CPR) theory because of the insights it provides regarding the conditions that facilitate collective action and the factors that promote long-lasting resource governance arrangements. Theory from institutional economics and political ecology contribute to the elaboration of a multi-faceted conceptualization of markets for CPR theory, with the aim of facilitating the identification of mechanisms through which markets and CPR governance actually interact. This dissertation conceptualizes markets as sets of institutions that structure the exchange of property rights over fisheries resources, affect the material incentives to harvest resources, and transmit ideas and values about fisheries resources and governance.

The case studies explore four different mechanisms through which markets potentially influence resource governance: 1) Markets can contribute to costly resource governance activities by offsetting costs through profits, 2) markets can undermine resource governance by generating incentives for noncompliance and lead to overharvesting resources, 3) markets can increase the costs of resource governance, for example by augmenting monitoring and enforcement burdens, and 4) markets can alter values and norms underpinning resource governance by transmitting ideas between local resource users and a variety of market actors.

Data collected using participant observation, survey, informal and structured interviews contributed to the elaboration of the following hypotheses relevant to interactions between global seafood trade and SSFs governance. 1) Roll-back neoliberalization of fisheries policies has undermined cooperatives’ ability to achieve financial success through engagement with markets and thus their potential role as key actors in resource governance (chapter two). 2) Different relations of production influence whether local governance institutions will erode or strengthen when faced with market pressures. In particular, relations of production in which fishers own their own means of production and share the collective costs of governance are more likely to strengthen resource governance while relations of production in which a single entrepreneur controls capital and access to the fishery are more likely to contribute to the erosion of resource governance institutions in the face of market pressures (chapter three). 3) By serving as a new discursive framework within which to conceive of and talk about fisheries resources, markets can influence norms and values that shape and constitute governance arrangements.

In sum, the dissertation demonstrates that global seafood trade manifests in a diversity of local forms and effects. Whether SSFs moderate risks and take advantage of benefits depends on a variety of factors, and resource users themselves have the potential to influence the outcomes of seafood market connections through local forms of collective action.

Theory and Practice in Sustainability Science: Influence of Urban Form on the Urban Heat Island and Implications for Urban Systems

As the world population continues to grow past seven billion people and global challenges continue to persist including resource availability, biodiversity loss, climate change and human well-being, a new science is required that can address the integrated nature of these challenges and the multiple scales on which they are manifest. Sustainability science has emerged to fill this role. In the fifteen years since it was first called for in the pages of Science, it has rapidly matured, however its place in the history of science and the way it is practiced today must be continually evaluated. In Part I, two chapters address this theoretical and practical grounding. Part II transitions to the applied practice of sustainability science in addressing the urban heat island (UHI) challenge wherein the climate of urban areas are warmer than their surrounding rural environs. The UHI has become increasingly important within the study of earth sciences given the increased focus on climate change and as the balance of humans now live in urban areas.

In Chapter 2 a novel contribution to the historical context of sustainability is argued. Sustainability as a concept characterizing the relationship between humans and nature emerged in the mid to late 20th century as a response to findings used to also characterize the Anthropocene. Emerging from the human-nature relationships that came before it, evidence is provided that suggests Sustainability was enabled by technology and a reorientation of world-view and is unique in its global boundary, systematic approach and ambition for both well being and the continued availability of resources and Earth system function. Sustainability is further an ambition that has wide appeal, making it one of the first normative concepts of the Anthropocene.

Despite its widespread emergence and adoption, sustainability science continues to suffer from definitional ambiguity within the academe. In Chapter 3, a review of efforts to provide direction and structure to the science reveals a continuum of approaches anchored at either end by differing visions of how the science interfaces with practice (solutions). At one end, basic science of societally defined problems informs decisions about possible solutions and their application. At the other end, applied research directly affects the options available to decision makers. While clear from the literature, survey data further suggests that the dichotomy does not appear to be as apparent in the minds of practitioners.

In Chapter 4, the UHI is first addressed at the synoptic, mesoscale. Urban climate is the most immediate manifestation of the warming global climate for the majority of people on earth. Nearly half of those people live in small to medium sized cities, an understudied scale in urban climate research. Widespread characterization would be useful to decision makers in planning and design. Using a multi-method approach, the mesoscale UHI in the study region is characterized and the secular trend over the last sixty years evaluated. Under isolated ideal conditions the findings indicate a UHI of 5.3 ± 0.97 °C to be present in the study area, the magnitude of which is growing over time.

Although urban heat islands (UHI) are well studied, there remain no panaceas for local scale mitigation and adaptation methods, therefore continued attention to characterization of the phenomenon in urban centers of different scales around the globe is required. In Chapter 5, a local scale analysis of the canopy layer and surface UHI in a medium sized city in North Carolina, USA is conducted using multiple methods including stationary urban sensors, mobile transects and remote sensing. Focusing on the ideal conditions for UHI development during an anticyclonic summer heat event, the study observes a range of UHI intensity depending on the method of observation: 8.7 °C from the stationary urban sensors; 6.9 °C from mobile transects; and, 2.2 °C from remote sensing. Additional attention is paid to the diurnal dynamics of the UHI and its correlation with vegetation indices, dewpoint and albedo. Evapotranspiration is shown to drive dynamics in the study region.

Finally, recognizing that a bridge must be established between the physical science community studying the Urban Heat Island (UHI) effect, and the planning community and decision makers implementing urban form and development policies, Chapter 6 evaluates multiple urban form characterization methods. Methods evaluated include local climate zones (LCZ), national land cover database (NCLD) classes and urban cluster analysis (UCA) to determine their utility in describing the distribution of the UHI based on three standard observation types 1) fixed urban temperature sensors, 2) mobile transects and, 3) remote sensing. Bivariate, regression and ANOVA tests are used to conduct the analyses. Findings indicate that the NLCD classes are best correlated to the UHI intensity and distribution in the study area. Further, while the UCA method is not useful directly, the variables included in the method are predictive based on regression analysis so the potential for better model design exists. Land cover variables including albedo, impervious surface fraction and pervious surface fraction are found to dominate the distribution of the UHI in the study area regardless of observation method.

Chapter 7 provides a summary of findings, and offers a brief analysis of their implications for both the scientific discourse generally, and the study area specifically. In general, the work undertaken does not achieve the full ambition of sustainability science, additional work is required to translate findings to practice and more fully evaluate adoption. The implications for planning and development in the local region are addressed in the context of a major light-rail infrastructure project including several systems level considerations like human health and development. Finally, several avenues for future work are outlined. Within the theoretical development of sustainability science, these pathways include more robust evaluations of the theoretical and actual practice. Within the UHI context, these include development of an integrated urban form characterization model, application of study methodology in other geographic areas and at different scales, and use of novel experimental methods including distributed sensor networks and citizen science.