Optimal Focusing for Monochromatic Scalar and Electromagnetic Waves

For monochromatic solutions of D'Alembert's wave equation and Maxwell's equations, we obtain sharp bounds on the sup norm as a function of the far field energy. The extremizer in the scalar case is radial. In the case of Maxwell's equation, the electric field maximizing the value at the origin follows longitude lines on the sphere at infinity. In dimension $d=3$ the highest electric field for Maxwell's equation is smaller by a factor 2/3 than the highest corresponding scalar waves. The highest electric field densities on the balls $B_R(0)$ occur as $R\to 0$. The density dips to half max at $R$ approximately equal to one third the wavelength. The extremizing fields are identical to those that attain the maximum field intensity at the origin.Comment: 30 pages, 7 figure

Archaeal ubiquity

In the seventeenth century, Antoine von Leeuwenhook used a simple microscope to discover that we live within a previously undetected microbial world containing an enormously diverse population of creatures. The late nineteenth and early twentieth century brought advances in microbial culture techniques and in biochemistry, uncovering the roles that microbes play in all aspects of our world, from causing disease to modulating geochemical cycles. In the last 25 years, molecular biology has revealed the complexity and pervasiveness of the microbial world and its importance for understanding the interactions that maintain living systems on the planet. The paper by Preston et al. (1) in this issue of the Proceedings provides a clear illustration of the power of these molecular techniques to describe new biological relationships and to pose important questions about the mechanisms that drive evolution. The analysis of ribosomal RNA gene sequences is one molecular approach that has radically altered our view of microbial diversity. Its application can be extended and expedited by the use of PCR. The confluence of these techniques has stimulated the rapid assembly of sequence information from homologues rRNA gene regions derived from virtually all classes of organisms. The data collected thus far support the scheme first presented by Woese et al. (2), which holds that the relationships among organisms can be summarized in the form of a universal phylogenetic tree comprised of one eukaryotic and two prokaryotic domains: the Eucarya, the Bacteria, and the Archaea (Fig. 1)

When Does the Market Matter? Stock Prices and the Investsment of Equity-Dependent Firms

We use a simple model to outline the conditions under which corporate investment will be sensitive to non-fundamental movements in stock prices. The key cross-sectional prediction of the model is that stock prices will have a stronger impact on the investment of firms that are “equity dependent†– firms that need external equity to finance their marginal investments. Using an index of equity dependence based on the work of Kaplan and Zingales (1997), we find strong support for this prediction. In particular, firms that rank in the top quintile of the KZ index have investment that is almost three times as sensitive to stock prices as firms in the bottom quintile. We also verify several other predictions of the model.

When Does the Market Matter? Stock Prices and the Investment of Equity-Dependent Firms

We use a simple model of corporate investment to determine when investment will be sensitive to non-fundamental movements in stock prices. The key cross-sectional prediction of the model is that stock prices will have a stronger impact on the investment of firms that are 'equity dependent' - firms that need external equity to finance their marginal investments. Using an index of equity dependence based on the work of Kaplan and Zingales (1997), we find strong support for this prediction. In particular, firms that rank in the top quintile of the KZ index have investment that is almost three times as sensitive to stock prices as firms in the bottom quintile. We also verify several other predictions of the model.

The Neighbor's Portfolio: Word-of-Mouth Effects in the Holdings and Trade of Money Managers

A mutual-fund manager is more likely to hold (or buy, or sell) a particular stock in any quarter if other managers in the same city are holding (or buying, or selling) that same stock. This pattern shows up even when controlling for the distance between the fund manager and the stock in question, so it is distinct from a local-preference effect. It is also robust to a variety of controls for investment styles. These results can be interpreted in terms of an epidemic model in which investors spread information about stocks to one another by word of mouth.

Social Interaction and Stock-Market Participation

We investigate the idea that stock-market participation is influenced by social interaction. We build a simple model in which any given 'social' investor finds it more attractive to invest in the market when the participation rate among his peers is higher. The model predicts higher participation rates among social investors than among 'non-socials'. It also admits the possibility of multiple social equilibria. We then test the theory using data from the Health and Retirement Study. Social households - defined as those who interact with their neighbors, or who attend church - are indeed substantially more likely to invest in the stock market than non-social households, controlling for other factors like wealth, race, education and risk tolerance. Moreover, consistent with a peer-effects story, the impact of sociability is stronger in states where stock-market participation rates are higher.

The Only Game in Town: Stock-Price Consequences of Local Bias

Theory suggests that, in the presence of local bias, the price of a stock should be decreasing in the ratio of the aggregate book value of firms in its region to the aggregate risk tolerance of investors in its region. We test this proposition using data on U. S. Census regions and states, and find clear-cut support for it. Most of the variation in the ratio of interest comes from differences across regions in aggregate book value per capita. Regions with low population density—e. g. , the Deep South—are home to relatively few firms per capita, which leads to higher stock prices via an “only-game-in-town” effect. This effect is especially pronounced for smaller, less visible firms, where the impact of location on stock prices is roughly 12 percent.

Sport Fish Research in Illinois: A Look Inside Sport Fish Restoration Fund Project F-69-R

Executive Summary: For over 75 years, the Federal Aid in Sport Fish Restoration Fund has worked with state partners to conserve, protect, and enhance fish and their habitats, along with the sport fishing and recreational boating opportunities they provide. During more than a third of the existence of this important conservation program, Project F-69-R has been the cornerstone for collection and analysis of Illinois fisheries data, with a specific focus through much of its existence on understanding the interface between recreational anglers and the recreational fisheries on which they depend. F-69-R has produced a wide array of groundbreaking research findings, supported modern advancements in fisheries management, and implemented state-of-the-art technologies for fisheries data management. Most recently, this project has opened the door to connect resource users with data-driven information about Illinois fisheries through the use of emergent Internet technologies.In its first few years, Project F-69-R was tasked with developing an efficient method for conducting regular creel surveys on inland lakes in Illinois. Additionally, several research studies led to improvements in sampling design and a better understand-ing of how the efficiency of sampling gear used by fisheries managers is affected by environmental conditions. The design and implementation of creel surveys and more effective sampling was supported by what was, at the time, a cutting-edge computer-ized system for storing and analyzing fisheries data, the Fisheries Analysis System (FAS). This system became the single tool used by fisheries managers and researchers alike to tap into valuable information about sport fish populations across the state. Illinois emerged as a leader in fisheries data management through the development of FAS, serving as a model for other states to develop their own systems.From 1992 – 2009, Project F-69-R was focused on the execution of inland creel surveys, producing 334 lake and river creel surveys that have played a major role in fisheries management decisions, such as setting size and bag limits, informing supple-mental stocking strategies, and identifying needs for habitat improvement. Data from those creel surveys has been utilized by other Federal Aid Projects as well. For example, a project evaluating the effectiveness of stocking largemouth bass at certain sizes and anther project evaluating the regulation and stocking strategies designed to improve stunted bluegill populations were among the many projects that utilized creel survey data on study lakes. The combination of managing long-term fisheries data and addressing emerging research needs continues to be the corner-stone of Project F-69-R today. In the last three years, the breadth of research topics has expanded to include an evaluation of urban stream restoration on the DuPage River (p. 4–5), an in-depth investigation into largemouth bass recruitment dynamics as affected by spring angling (p. 6–7), an assessment of land-use practices and their impacts through the Fishes of Champaign County study (p. 8), and an investigation into natural reproduction of lake trout in southern Lake Michigan (p. 10). Bringing this information back to the angler has been a key component of Project F-69-R for the last 10 years through the creation of IFishIllinois.org and its social media counterparts (p. 9).A bright and exciting future is unfolding for the Sport Fish Restoration Program, and F-69-R is a central piece of that future in Illinois. Within these pages is a snapshot of the many contributions this project has made to sustaining sport fish populations in Illinois. As this project evolves to answer more complex, data-driven research questions to inform fisheries management decisions, anglers in Illinois will have access to a wide array of sustainable fisheries for generations to come.Good Fishing! Dr. Jeffrey A. Stein, Project LeaderSenior Research ScientistIllinios Natural History SurveyUS Fish and Wildlife Service/IL Department of Natural ResourcesOpe