Michael Chrisopher Singer, Ph.D. - US grants

This conference on Kac-Moody algebras will be held December 13 - 17, 1988 at North Carolina State University. It is for experts in the field as well as researchers in related areas of mathematics and mathematical physics. The conference is partly expository in nature, with Professors Kac and Moody giving a series of lectures on the mathematical aspects of Kac-Moody algebras. In addition, David Olive will lecture on the physical application of Kac-Moody algebras, and there will be technical lectures by other participants. The theory of Kac-Moody algebras began twenty years ago with the seminal work of Kac and Moody, and has connections with diverse areas of mathematics, including number theory, combinatorics, topology, completely integral systems, and particle physics.

This grant is under the Scientific Computing Research Equipment for the Mathematical Sciences program of the Division of Mathematical Sciences. It is for the purchase of special purpose equipment dedicated to the support of research in the mathematical sciences. In general, this equipment is required by several research projects, and would be difficult to justify for one project alone. Support from the National Science Foundation is coupled with discounts and contributions from manufacturers, and with substantial cost-sharing from the institution submitting the proposal. This is an instance of university, industrial, and government cooperation in the support of basic research in the mathematical sciences. The equipment in this project will be utilized in the following projects in the mathematics department: connections between finite simple groups and nonassociative algebras; hyperbolic partial differential equations describing plastic flow; closed form solutions of differential equations; and some problems in optimization, with various applications.

A joint U.S. - France workshop entitled "Computer Algebra and Differential Equations" will be held in Grenoble, France from May 24 to May 27, 1988. The organizing committee consists of Jean Della Dora, Evelyne Tournier (both of the TIM3 Laboratory at Grenoble) and Michael F. Singer (at North Carolina State University in Raleigh, N.C.). In recent years, there have been several advances in the theory of formal solutions of differential equations. These have included deeper understanding of power series, asymptotic and closed form solutions of differential equations and difference equations. At the same time, computer algebra systems have become more and more sophisticated and offer the opportunity to automate these ideas. The present workshop is planned to allow workers in computer algebra to learn of the theoretical developments and at the same time make the researchers in theoretical areas aware of questions arising in the design of computer algebra systems. Professors B. Malgrange, J.P. Ramis and M.F. Singer will deliver a series of expository lectures on various aspects of formal solutions of differential equations and there will also be a few additional short talks. Time will be allowed for the participants to study the material presented as well as hold informal discussions. Attendance will be limited to about 50 people; 25 from France and 25 from the United States. By limiting the attendance the organizers hope to enhance the conditions leading to a fruitful exchange of ideas. Academic Press has agreed to publish the proceedings of this conference.

A principal aim of the proposal work is to understand the evolution of interactions between a herbivorous insect and several of its host plants. Although it is generally accepted that insects evolve in response to selection pressures mediated by plants, the role of insects attack as a cause of plant evolution is controversial. The P.I.'s propose to initiate a preliminary investigation of this role, using the butterfly Euphydryas editha, in which geographical variation of diet is already well documented. Studies of interpopulation variation of plant acceptability will quantify the contribution of plant variation to the observed geographical variation of insect diet. Correlations between attack rates and acceptability may suggest hypotheses about the nature and extent of plant evolutionary responses to insect attack. Within a plant population that shows variation of acceptability the investigators will estimate the correlation between acceptability and fitness in the presence and absence of insects. If there studies are successful, an experiment that simulates the evolutionary effects of insect attack by applying artificial selection to plant acceptability will be attempted.

This project centers around an analysis of the algebraic properties of the solutions of linear differential equations with polynomial coefficients and the development of algorithms based upon this analysis that can be used to construct improved interpolation schemes. In particular, the principal investigator will use the theory of galois groups to solve linear differential equations in terms of special functions. He will study also the algebraic structure of these special functions with a view to improving algorithms for integration of the differential equation in finite terms. And finally he will employ techniques from the algebraic theory of differential equations to develop improved interpolation formulas for sparse polynomials and rational functions.

Prior work has documented a change in host-plant preference over the last ten years in a population of an herbivorous butterfly. This population has incorporated a European weed into its diet. Comparing the preference of insects for plants maintained in laboratory culture for ten years will test whether the change is due to adaptation by the insect or to a change in the plant that has increased its acceptability. Similarly, the fact that different populations of this insect exhibit different preferences could be due to genetic variation in the insect (already shown) or variation in the plants, or both. The potential contribution of variation in plant acceptability to this geographic variation will be quantified. The results of this research will show how the complexity of insect diet in time and space arises from past and present insect-plant interactions. The information has implications for biological pest control as a model for insect invasions of agricultural habitats.

The principal investigators plan to develop three courses during the period of the award. The courses are designed to interest students in aspects of Scientific Computation through computer algebra, numerical bifurcation, and partial differential equations. The students holding fellowships will have various educational tasks, such as writing up clear lecture notes and assignment solutions, software testing, maintenance and consultation. They will also run a weekly tutorial for lectures and demonstrations concerning the use of software for applications in the courses. The three courses will be loosely coordinated through a weekly seminar, in which the principal investigators, and later the students, will give presentations on topics of common interest, and will lead discussion. The award recommendation is for a one-time contribution to equipment and student support for this laudable activity, consistent with the gold of High Performance Computing and Communications.

This project assembles historical measures of soil degradation and its effects on agricultural productivity in India and China, countries containing 44 percent of the population of all developing nations. Now that population growth is near the fastest rate in all history, how fast is productive land being lost to erosion, aggradation, salinity, alkalinity, and cities? How fast has the net soil loss really been? How much has it cost? The techniques developed here can become a model for solving other debates over trends in soil quality. Most estimates of soil degradation are erosion estimates. These estimates suggest enormous losses. For example, it is estimated that rivers carry 24 billion tons of sediment to the ocean each year, compared with only 9 billion tons before the introduction of agriculture, grazing and other human activities. But such studies give gross measures of soil loss, not the net measures that are closer to the productivity measures needed in order to assess the productivity effects of erosion. These measures lack information on the earlier amount and quality of soil, for comparison with water levels. Instead of a chain of snapshots over time, we are asked to judge movement from a single snapshot. In contrast, this project assembles and analyzes six main data sets on soil qualities and agricultural productivity in China from the 1930s to the 1980s and three main data sets for land quality in India from 1950 to 1984. Considerable time is spent on direct comparisons of soil data from cultivated lands within each county in China and India. The productivity consequences of land attributes will be estimated from these data. Finally a range of related hypotheses about land tenure and the role of specific policies will be rigorously tested.

Sequences of paleosols and loess units throughout the world have been interpreted as geologic records of terrestrial climate change. Of particular significance has been the discovery of a correlation between variations in the magnetic susceptibility in the Chinese loess sequence and the oxygen isotope record of the deep sea. Using an approach that combines rock magnetic measurements with a soil chemistry extraction procedure, we have obtained new data that challenges previous interpretations about the origin and nature of the magnetic susceptibility signal. In this proposal we request support for a comprehensive, interdisciplinary study of the rock magnetism and soil chemistry of paleosol/loess sequences in China and elsewhere. The goals of our study are 1) to complete our determination of the general characteristics of the magnetic susceptibility signal using a combination of rock magnetic and soil chemistry techniques, 2) to compare our rock magnetic analyses of the Chinese loess/paleosol sequence with similar analyses of loess/paleosols sequences in Alaska and New Zealand, and 3) to obtain complete soil descriptions and detailed profiles of soil chemistry and rock magnetic properties from selected loess and paleosols units. The work for this last objective will be done in close collaboration with Chinese colleagues.

9307804 Singer This project investigates the processes that cause herbivorous insects to feed on particular plants or to change those associations. One of the processes that influences insect diet is human manipulation of the landscape. This project investigates changes in diet of the butterfly Euphydryas editha, that have been brought about by two types of human activity: cattle ranching and clear-cutting of coniferous forest. In each case, human intervention has caused insects to change their preferences for egg-laying sites and incorporate new plant species into their diets. These populations are undergoing rapid diet shifts mediated by genetic changes of host preference. Diet expansion may be aided by correlations between maternal oviposition preference and offspring performance. This project will determine whether such correlations are present at the first arrival of the novel host. The project also continues long-term assessment of the extensive geographical variation in host specificity of E. editha. Comparisons between populations that differ in diet breadth will show whether this variation is mechanistically caused by variation among plants, among insects, or both. %%% Understanding patterns of plant use by herbivorous insects has been a central concern of plant-animal interactions. The PI has documented extensive temporal and spatial variation in this association of a widespread butterfly and has shown that changes in diet may be due to human influences. These diet shifts have implications for the conservation of threatened insects that live on managed land. Understanding the processes that cause herbiv ores to expand their diets will also help to elucidate the mechanisms by which non-pest insects become converted to pest status when their diets change to incorporate crop plants. s t One major focus of this proposal seems to be the PI's laboratory hybridization attempts and field work to assess ecological and sexual isolation. There is a problem, especially with sexual isolation, in that the PI has done preliminary testing with a species pair currently considered to be in different major clades and the 0 . 3 ! ! ! ! F # # < Times New Roman Symbol & Arial Dutch (scalable) " h < % e e - Laurel R. Fox Gayle Edmonds

9520600 Singer Metapopulations are collections of populations that interact through dispersal. Their persistence in the face of population extinctions relies on colonization; the establishment of new populations in unused habitat. However, mechanistic studies of colonization in natural systems are lacking, even though mechanism at this scale may strongly structure large-scale metapopulation dynamics. The goal of this research is to investigate the behavioral and ecological mechanisms that structure colonization in a metapopulation of the checkerspot butterfly. The metapopulation, located in the Sierra Nevada of California, recently suffered a set of weather-induced population extinctions, and provides unoccupied habitat patches for study. Behavioral mechanisms to be studied include habitat preference and host-plant search efficiency within habitats. The ecological mechanisms are temporal and spatial patterns in habitat quality and host-parasitoid relations between the checkerspot butterfly and a braconid wasp. Preliminary results indicate that colonization is occurring slowly, that habitat quality is highly structured temporally, and that habitat preference is not optimal, but depends instead on history of host use at the study site. This study will contribute significantly to basic understanding of the role of dispersal in maintaining metapopulation structure, and some of the mechanisms governing colonization of new habitat patches. The results will have broad application to resource management strategies and attempts to conserve biodiversity.

This project develops symbolic algorithms to determine the algebraic structure of solutions of differential equations. In particular, the research includes the following: (i) Refine and extend algorithms for computing Galois groups of linear differential equations and algorithms for solving these equations in terms of classes of special functions; (ii) Develop algorithms to decide various properties of the Galois group. For example, give an algorithm to calculate the dimension of the group; (iii) Construct linear differential equations with a given Galois group; (iv) Develop improved algorithms to factor linear equations; and (v) Find first integrals of nonlinear systems of differential equations.

9710051 Verosub Three important elements of Earth Systems History are Milankovitch forcing, Tibetan uplift and global ice volume. A terrestrial record of the interaction of these three elements can be found in the paleoclimatic record of the Chinese loess plateau. However, most studies of the Chinese loess and associated paleosols have dealt with the upper two-thirds of this 2.6 million year-long sequence. The lower one-third, known as the Wucheng Formation, has a very different physical appearance, and the data that are available suggest that its pedogenic and magnetic properties are also different from the upper two-thirds. These differences are believed to reflect the increasing influence of the Tibetan uplift as well as a shift from Milankovitch forcing dominated by obliquity and precession to one dominated by eccentricity. This proposal represents a request for support to undertake fundamental pedogenic, sedimentologic, and mineral magnetic investigations of the Wucheng Formation with the goal of deciphering its paleoclimatic history. We believe that such a study will serve as an important counterpoint to studies of the rest of the Chinese loess/paleosol sequence, that it will significantly improve our ability to interpret the paleoclimate record of the entire sequence, that it will provide new insights about the coupling between marine and terrestrial climate, and that it will lead to new opportunities to test computer models of atmospheric and oceanic circulation.

A one day meeting called the East Coast Computer Algebra Day will be held at North Carolina State University (NCSU) in Raleigh on Saturday, April 24, l999.

The purpose of this meeting is to stimulate interest in and enhance understanding of the technical aspects of computer algebra, by providing a way for those in the region who are active or interested in becoming more active in computer algebra to meet with each other in an inexpensive and easily accessible way. This meeting will be more informal than the annual ISSAC meetings, with ample time for unstructured interaction. Participation by the region's graduate students will be particularly encouraged through special invitation to contribute to the poster sessions, and through travel support. The meeting will have three invited speakers who have made outstanding contributions to the field of computer algebra. The speakers will anchor the meeting and will help attract participants. The invited talks and poster sessions contributed by the community are expected to cover the breadth of computer algebra: algorithms, software, and applications. The principle theme of the l999 meeting will be applications.

9870342
Fogg

Though stream-dominated alluvial fans comprise a large percentage of important aquifer systems, detailed three-dimensional characterizations of these deposits are notably lacking in the literature. Successful application of sequence stratigraphic concepts in petroleum research to predict subsurface facies distributions strongly suggests that, when modified for purely continental strata, sequence stratigraphy can be applied to characterize alluvial fan systems. This project involves the fusion of several disciplines, including hydrology, geology, geophysics, and soil science, to develop a sequence stratigraphic framework from which a more advanced, tractable model of heterogeneity can be produced for typical, stream-dominated alluvial fans. Significance of this research is three-fold. First, it will create some needed "order" in our understanding of heterogeneity in many alluvial fan groundwater systems through development of continental sequence stratigraphic concepts. Second, the research will provide a method to incorporate geostatistical simulation into a sequence stratigraphic framework, thus providing a detailed characterization of the aquifer system. Finally, the research will provide a large step forward in our ability to characterize and model regional groundwater flow and transport in many types of alluvial deposits. Such an advance is sorely needed for estimating long-term impacts of agricultural and urban pollution on sustainability of groundwater quality.

Central to the proposed research is the recognition of sequences, related to Quaternary climate cycles, bounded by laterally extensive, mature paleosols. These paleosols mark fan exposure during interglacial periods, and form laterally extensive aquitards in the aquifer system. Strata within the sequences represents deposition that occurred on the fan during glacial episodes, when accommodation space was made available by increased discharge and sediment supply. Within these sequences, systems tracts (e.g., linked assemblage of lithofacies deposited during one time period of the climatic cycle) have also been recognized in core, driller's logs, and geomorphic mapping of the Kings River fan. It is proposed that additional continuous core will be collected specific systems tracts (e.g., incised valley fill deposits) to examine these differences. The systems tracts will be compared through use of environmental magnetism, facies morphology, and petrographic analysis. Calibration of relatively abundant drillers logs to the core data, already successfully accomplished in other portions of the Kings River alluvial fan, will provide a means to define systems tract geometry in the subsurface. A new Markov-chain technique for geostatistical modeling of spatial distribution in sedimentary units with greater geologic rigor (Carle and Fogg, 1996a, 1997) will be used to produce stochastic simulations of textural units within the sequence stratigraphic framework.

This research addresses foundational and computational issues concerning the algebraic behavior of systems of linear difference and differential equations and allows researchers to understand aspects of the qualitative behavior of solutions of these equations. This research develops algorithms that will be of use not only to mathematicians but engineers and scientists in many fields as well. These algorithms will be the basis of code appearing in symbolic computation computer packages used in the education as well as the day-to-day work of engineers and other scientists.

In particular, this research investigates new and more efficient algorithms for the classical Picard-Vessiot theories of over determined systems of differential and difference equations, and develops new algorithms to determine elementary algebraic properties of under determined systems of linear partial differential and difference equations. It also extends the classical Picard-Vessiot theory and its algorithms to Galois theories with infinite dimensional groups, allowing applications to parameterized linear equations as well as some classes of nonlinear equations.

High Performance Symbolic Computation

The Department of Mathematics at the North Carolina State University will purchase 4 units of SUN HPC 450 (each having 4 processors) which will be dedicated to the support of research in the mathematical sciences. The equipment will be used for several research projects, including in particular:

Helminck's project: Computer Algebra and Symmetric Varieties,
Hong's project : Solving Real Algebraic Constraints,
Kaltofen's project: Computing with Black Box Objects and
Singer's project : Symbolic Computation and
Differential and Difference Equations.

9905367
Singer
Spatial patterns in plant-insect interaction may be caused by variation among plants, among insects, or both. Often, the nature of the variation may produce the appearance that insects are variable, when in fact it is the plants that vary (or vice versa). In this SGER project, this investigator will tease apart the two variables to understand the cause of an apparent example of interdemic selection acting on butterfly diet. The result will tell us if interdemic selection really does act in this system. The importance of this project is that there are still no documented examples of interdemic selection in nature, for any trait of any organisms. This plant-herbivore system will provide the best opportunity yet to address this interesting and controversial research question.

The investigators propose to use a combination of behavioral, ecological and genetic techniques to understand the development of genetic differentiation among populations of a butterfly species, Euphydryas editha. One outcome of this study will be an analysis of past and current movement patterns of these butterflies among habitats of different types. The investigators will ask whether and to what extent the movements of insects among habitats depend on the distance between those habitats, the nature of the landscape in the intervening terrain, and the adaptations of the insects to particular host plant species.

Plant-feeding insects possess sophisticated behavioral mechanisms for choosing their hosts, that is, the plants on which they feed. Understanding of the basic biology of these mechanisms is important in several contexts. It assists humans in tracking and predicting the changes of diet that insects undergo, changes that are involved in the transformation of innocuous insects to crop pests. It also helps in assessment and manipulation of the quality of habitats for endangered insect species. This is because insects that are introduced to a restored habitat will leave if they are not sufficiently attracted to the plants that are present. The proposed work includes populations that are closely related to a federally endangered sub-species, and will assess how the food preferences of these insects should influence plans for habitat restoration and conservation.

The proposed work is a sequel to a long-term study of the influence of logging on populations of Euphydryas editha butterfly in Sequoia National Forest, California. Prior work showed that logging influenced the evolution of diet in the butterflies. They acquired a novel hostplant in habitat patches that had been logged, but retained their traditional diet in undisturbed patches. Population growth was faster in the disturbed patches, but insects emigrated disproportionately from those patches, partly because they retained a preference for their traditional habitat and hostplant.

The proposed work will examine genetic differentiation both within this disturbed system and between this system and other populations of the same species within a distance of 50 km. The investigators will conduct an equivalent study on an unlogged system in Yosemite National Park and environs. These two studies will ask what genetic differentiation naturally existed among populations of this butterfly and how human activities might be affecting it. The work will also examine how much genetic differentiation among populations is associated with the distance between habitats, the nature of the landscape in the intervening terrain, and the adaptations of the insects to particular host plant species.

Human intervention in the landscape affects herbivorous insects in dramatic ways. Introduction of exotic plants alters the range of plant species available as food. Ranching and logging techniques also change the relative qualities of existing native plants. For example, in the current study system logging removed the insects' principal hostplant but incidentally provided a novel host by improving the quality (from the insects' perspective) of a native plant species. Changes in the insects' environment influence their patterns of movement among habitats and their likelihoods of successfully reproducing when they do move. These effects on movement will in turn affect the tendency for populations to differ from each other genetically. This genetic differentiation among populations is the focus of the proposed work, which will illuminate both the natural patterns that exist and the influence that human activities are having upon those patterns.

0456285
Singer

This is a U.S.- China Conference consisting of two workshops on research and education partnership in symbolic computation proposed by Dr. Michael Singer, North Carolina State University and Professor Ziming Li, Chinese Academy of Sciences, China. One workshop will be at North Carolina State University in Raleigh, NC on October 16-22, 2005, and the other at the Mathematics Mechanization Research Center, Chinese Academy of Sciences, Beijing, China, from July 31-August 6, 2006. The workshops will focus on important issues related to symbolic computation and will include one junior scientist and 7 U.S. graduate students. A long-term research partnership is expected to develop between the U.S. and Chinese researchers and graduate students. This conference will be jointly supported by the NSF and the Chinese Academy of Sciences.

Hydraulic mining in the Sierra Nevada of California displaced great volumes of sediment as a byproduct of gold extraction from placer gravels. The spatial distribution of hydraulic mining sediment reworking and deposition in flood bypasses over the last century are relevant to the fate of contaminants, flood conveyance, and the land-use in the lower Sacramento Valley of California, which is undergoing a massive program of restoration and development, and to basic research on valley floor sediment budgets and floodplain sedimentation. This research employs a suite of new techniques and data to investigate the temporal and spatial links between Central Valley floodplain sedimentation and erosion of hydraulic mining sediment in the Sierra piedmont over the last century. Recent field evidence of episodic piedmont erosion and bypass deposition calls for a new investigation of the hydraulic mining sediment delivery problem in the lower Sacramento valley over the last century. The research will track the movement of fine sediments derived from hydraulic mining tailings in the lower Sacramento Valley. The research team will link spatial and temporal patterns and processes of deposition in Sutter and Yolo Bypasses (leveed floodplains of the Central Valley) with erosion of piedmont tailings of the lower Bear, Yuba, and Feather Rivers downstream of the last major dam on each. It will track historical erosion of hydraulic mining sediments in the piedmont through a combination of photogrammetry, channel change analysis, and field surveys. The team will document history and provenance of mining sediment deposits in the Central Valley by granulometry, X-ray fluorescence spectroscopy, magnetism, and geochronology. In addition, records from a network of streamflow gauging stations will be perused for corroborative analysis of temporal correlation between piedmont erosion and Central Valley sedimentation. The project will produce quantitative, field-based estimates of volumetric sediment storage and erosion along piedmont channels and the timing of its evacuation. It will document geochemical, grain size, and magnetic properties of mining and non-mining sediment and develop appropriate mixing models for discerning the relative influence of each source downstream through the fluvial system. It will identify the spatial extent and volume of discrete sediment deposits in the bypass system, and document sedimentation rates and histories along various transects spanning Sutter and Yolo Bypasses. The research will develop quantitative links between piedmont erosion and bypass deposition that are based on historical hydrology and refined conceptual models of bypass sedimentation processes. It will provide the basis for predictive modeling of the impact of future floods on sediment movement through the Central Valley.

The project will provide a quantitative basis for future management decisions and direction in the Sacramento Valley and a set of methodologies that can be applied to other large, managed river basins. Data and interpretations from this study will be of great practical use to river and environmental management in the lower Sacramento Valley and the Delta, where our results are of utmost importance to flood conveyance, maintenance of islands, and potential toxicity of sediment. This research will create educational opportunities for a new generation of geomorphologists, including those from historically underrepresented groups. The output from this research will be made available as a project website via the World Wide Web and provide direct K-12 scientific outreach through the NASA space consortium, an educator resource center.

The Institute for Mathematics at North Carolina State University (I'm at State) will support U.S. students through their transition to graduate school in mathematics. Its goals are to increase the number of students going to graduate school and to improve the retention of graduate students in the first two years.





The programs are designed to engage students in research early and to encourage them to continue in mathematics. Research for Early Graduate Students (REG) is designed to sustain the enthusiasm for collaborative original research that attracts students to Ph.D. programs, by providing students with research experiences during the early years of graduate work. Research and enrichment experience for undergraduate students belonging to groups under-represented in mathematics (REU+) is designed to provide a supportive REU experience for students who may not usually consider an REU program. An important feature is the participation in the Institute of accomplished mentors of students from under-represented groups. These programs will develop the students' sense of belonging and enthusiasm as undergraduates and reinforce it through the early graduate school years.

Michael S. Singer, Proposal IOS-0744676

How changes in diet can enable caterpillars to overcome parasite infection

Changes in feeding behavior can enable individual animals to cure themselves of parasite infections or other physiological distress. All animals have immunological defenses that can potentially change in strength based on an individual's diet. In addition, herbivores such as caterpillars may kill their parasites by ingesting and accumulating toxic chemicals found in the plants they eat. This research project will investigate these two means of anti-parasite behavior by the woolly bear caterpillar Grammia geneura. This species is suspected from previous study to ward off natural parasites through its feeding choices. First, behavioral experiments will characterize the dietary choices of experimentally parasitized caterpillars in relation to unparasitized caterpillars. Second, to evaluate the role of specific diets in resistance against parasites, the survival of parasitized and unparasitized caterpillars on different diets will be tested. Third, physiological experiments will evaluate the effects of these diets on the caterpillar's immune response to parasites. Finally, to analyze direct effects of caterpillar diet without the immune system, the parasites will be raised on artificial diets that reflect different caterpillar diets. Caterpillars newly infected by the potentially lethal, parasitic fly Exorista mella, are expected to choose a nutritious diet to enhance their immunological resistance. This mechanism is expected to carry minimal physiological costs for the caterpillar. However, caterpillars threatened by late-stage parasitic infections are expected to choose a diet rich in natural plant toxins called pyrrolizidine alkaloids. Ingesting unusually large quantities of alkaloids is expected to be physiologically costly for the caterpillar, and thus used as a last resort.

The broader impacts of this research include training diverse students and a post-doctoral fellow in linking behavior, physiology, and ecology to animal health. Through public presentations, this project will also educate the public about the scientific link between animal health, behavior, and the environment.

This proposal aims to improve the retention of graduate students in the first two years and increase the number of students going to graduate school. We do this by incorporating students in research and the mathematical community earlier and providing support programs for pre-graduate students. The main component is a set of interconnected summer programs involving research experiences and short courses for students. These are designed to engage them and encourage them to continue in mathematics. Several parts of this proposal are directly aimed at underrepresented students. The major programs include the following. (1) Research for Early Graduate Students (REG), designed to sustain the enthusiasm for collaborative original research that attracts students to Ph.D. programs by providing them with research experiences during the early years of graduate work. (2) Research and enrichment experiences for under-represented undergraduate students (REU+), designed to provide a supportive REU experience for underrepresented students who may not usually consider an REU program. An important feature is the inclusion of established mentors of underrepresented students to work with the program and us. (3) Enhanced Research Program for Early Graduates (REG+), a one-year program for students who have graduated from college and are not quite prepared for graduate studies in mathematics. This program targets underrepresented groups. The program includes a summer research experience, a year of remedial course work and significant mentoring.


Four important groups are included: underrepresented undergraduate students, post-baccalaureate students considering returning to mathematics, under-prepared graduate students, and early graduate students. In particular, this grant features a collaborative effort between faculty at NCSU, and the Mathematics Departments of 6 Historically Black Colleges and Universities. We aim to increase the number of underrepresented students who get graduate degrees in Mathematics.

Herbivores with specialized diets can co-opt the defensive chemicals of their food-plants for their own defense. This research provides a first test of the hypothesis that grazing herbivores do the same, by regulating their intake of multiple plant chemicals to optimize defense against enemies. Alternatively, grazing among toxic plants might benefit herbivores by reducing the harmful effects of over-ingesting a single toxin associated with a particular food-plant species. These alternative hypotheses will be tested through three experiments involving a caterpillar already known to ingest one type of plant toxin as a defense against lethal parasites. First, the researcher will investigate how parasitism and the type of parasite affect the caterpillar's intake of two types of toxins (found in different food-plants). Second, she will compare caterpillar resistance against parasites when they have consumed the two toxins singly or in combination. To address toxin dilution, this experiment will also determine the effects of these diets on the survival and growth of unparasitized caterpillars. Finally, she will test whether the ratio of toxins eaten by unparasitized caterpillars confers deterrency against ubiquitous ant predators. Taken together, these results will identify how this herbivore benefits by grazing on toxic plants.

This work will connect the science of pharmacology with animal behavior and ecology. Humans, domesticated grazing herbivores, and wild grazing herbivores face the common problem of obtaining a healthy diet from a chemically diverse array of plant foods. Using grazing caterpillars as a model, this research will test and develop scientific theory that can be applied to other species, including livestock and humans. In addition, understanding the reasons for host plant selection by herbivores will inform the management and conservation of biodiversity in grasslands, which are imperiled ecosystems and home to the caterpillars, plants, predators and parasites under study.

Many of the functions of interest in mathematics and physics are defined by difference or differential equations. Understanding their algebraic properties is key to using these functions to describe physical and mathematical phenomena. The investigator will develop algorithms that will reveal these properties. In particular, he will develop algorithms to determine the algebraic and differential relations that occur among solutions of a given set of linear difference equations. In addition, he will develop theory and give algorithms to measure the algebraic behavior of solutions of parameterized linear differential equations as one varies the parameter. Finally, he proposes to attack the problem of factoring underdetermined systems of partial differential equations.

Although disparate in appearance, these problems will be attacked using techniques based on studying the underlying symmetries of the defining equations. In the past, the investigator has contributed to the development of theory and algorithms to solve differential and difference equations, in particular to the Galois theories of these equations and algorithms to solve them in closed form. The present project in part refines and extends this work but goes beyond to attack the broader problems mentioned above.

This research addresses foundational and computational issues concerning the algebraic behavior of systems of linear difference and differential equations. It allows researchers in many scientific fields to understand aspects of the qualitative behavior of solutions of these equations. The researcher will develop algorithms that that will be useful to number theorists, combinatorists and analysts. In addition, the investigator anticipates that these algorithms will form the foundation on which Maple and Mathematica code are based and so have an impact on the education and day-to-day work of engineers and other scientists.

Key components of this project are the development of human resources, the fostering of interactions with other scientific fields and the advancement of international collaborations. The investigator will continue to not only train his Ph.D. students but to further develop with his colleagues a program at NC State University to train students in a broad range of topics in Symbolic Computation. He will sponsor a postdoctoral scholar, involving this scholar in the research proposed here as well as develop the scholar's teaching skills and integrate the scholar into the scientific community. He will continue and expand his work on revising the undergraduate Abstract Algebra curriculum to include Symbolic Computation as a core topic. In addition he will continue to organize workshops aimed at students and colleagues in diverse fields to disseminate to a broad scientific community the ideas of Symbolic Computation in general and Symbolic Analysis in particular. He will continue his recent collaborations with researchers in Germany, France and China and will involve graduate students from NC State University in these projects, allowing them to integrate themselves in the international research community.

This proposal seeks support to increase the participation of US researchers to the Conference on the Foundations of Computational Mathematics (FoCM) which will be hosted by the Budapest University of Technology and Economics in Hungary between July 4-14, 2011. The conference is the seventh in a sequence of international meetings organized by the Society for the Foundations of Computational Mathematics. The meetings are held every three years and the preceding ones have been held in different countries in North and South America and Europe. The NSF funding will cover the travel costs (airfare and partial subsistence support) for 30 conference participants who are US citizens/permanent residents, or work/study at a US institution. The supported participants will be predominantly students and young researchers from the US, but the organizers expect to also cover the travel and subsistence expenses of some senior participants. NSF funding to support travel and other participant costs for approximately 30 junior researchers and graduate students. The conference organizers have been traditionally and continue to be dedicated to attracting young participants and participants from under-represented groups and providing valuable opportunities for networking with the leaders of the disciplines. The conference will facilitate the flow of ideas between the theoretical computer science, computational and core mathematics communities.


The research areas represented at the conference span a diverse array of topics on the broad interface between mathematics and contemporary computation. The agenda of the conference includes 20 workshops on a broad array of topics including Approximation theory, Computational harmonic analysis, Computational algebraic geometry, Stochastic computation, Computational dynamics, Computational number theory, Combinatorics and intractability in computation, Discrete Optimization, Continuous Optimization, Learning theory, Information-based complexity, etc.

The proposed work is an investigation of mercury (Hg) in river systems that have experienced large anthropogenic inputs of this toxic substance (e.g., by upstream mining). This interdisciplinary project will identify critical locations in river systems where the risk of Hg input to food webs increases and elucidate the processes by which this occurs. The study will focus on the longitudinal (downstream) transport and biogeochemical processing of sediment-adsorbed Hg derived from hydraulic gold mining in the Sierra Nevada and mercury mining in the Coast Ranges within and through the Yuba-Feather-Sacramento River system of Northern California, USA. It will document the primary sources (Coast Range v. Sierra Nevada) of Hg contamination to lowland ecosystems in the Sacramento Valley and Bay-Delta and the relative contribution and risks of each. We will: 1) mathematically model flood inundation in river corridors to identify areas of high potential of oxidation/reduction; 2) identify preferential zones of sedimentation through numerical modeling of event-based washload transport; 3) identify distinct contamination sources to lowlands by conducting Hg stable isotopic analysis of sediment; and 4) investigate Hg speciation in conjunction with changes in Hg species isotopic signatures, associated with redox conditions and sediment source.

In river basins beset by Hg contamination from atmospheric deposition or anthropogenic inputs from mining, there is great uncertainty about the interplay among sediment transport, deposition, and remobilization and the evolution of Hg reactivity in response to inundation regimes and ambient chemistry. These factors have important implications for bioavailability of sediment-adsorbed Hg to food webs, as it travels to sensitive downstream ecosystems where methylation potential is high. This research will address this problem and provide new understanding into the physical and biogeochemical processes that threaten sensitive lowland ecosystems. The importance of sediment deposits originating from legacy mines, especially in the Bay-Delta watershed, has recently increased due to realizations that they may contain high levels of Hg that may be available to food webs. These factors are being investigated by various government agencies and nonprofit groups responsible for river basin management. The research team has developed close contacts and relations with personnel from interested parties in the US with whom findings will be shared.

This project will investigate how ecological interactions among caterpillars, treehoppers, and ants determine the health trees. Caterpillars damage forest trees by eating leaves and treehoppers feed on trees by sucking sap. An important consequence of sap-feeding by treehoppers is their excretion of a sugary solution called honeydew. Some forest-dwelling ants depend on the honeydew for food. This relationship is called a food-for-protection mutualism because ants receive carbohydrate-rich food, while treehoppers receive protection from predators by the ants. In this project, investigators will study how this interaction between ants and treehoppers affects all participants, and how the outcome impacts forest health.

Societal benefits of this project are several-fold. First, results from the research will contribute to the scientific understanding of pest control in forests. Second, the project will contribute to education about forest ecology and entomology through the training of undergraduate research assistants, as well as through broader educational benefits to college students, public school teachers, and members of the public. Third, the investigators will partner with the Connecticut Forest and Park Association (CFPA), which offers outdoor education programs for teachers and members of the public.

More specifically, this research will experimentally test several hypothesized mechanisms for top-down trophic effects of ant-sap-feeder mutualisms in a temperate forest community. This system contains multiple species of predatory ants interacting with sap-feeding insects (mainly Membracidae). Ant-sap-feeder mutualisms may trigger top-down trophic effects on caterpillars and plants via increases in total ant abundance (the "density increase hypothesis"), changes in the behavior of individual ants (the "behavioral modification hypothesis"), or changes in ant community structure (the "community shift hypothesis"). Experiments will be used to distinguish among these hypotheses. The community scope of this study system, which currently lacks an invasive ant species, is novel and important because it offers an opportunity to test ant-community mechanisms for keystone mutualism effects as well as ant density- and ant trait-related mechanisms in a relatively intact ecosystem.

This project investigates how an animal's nutrient intake affects its interaction with its parasites. Using an experimentally tractable model system of a caterpillar and its parasitic wasp, Dr. Singer and Ms. Bernardo will conduct experiments designed to reveal how the parasitic wasp benefits by manipulating its host caterpillar's highly regulated nutrient intake. The basic scientific value of this research stems from integrating the perspectives of animal nutrition, immunology, and behavioral ecology, while also contributing to scientific knowledge used in pest control in agriculture and forestry. Public outreach impacts will happen through Elementary Schools in Middlesex County, CT, and Ms. Bernardo's position as vice-president of the Connecticut Entomological Society. The school program will highlight the natural history of insects kept in the lab, while the CT Entomological Society program will organize outreach activities for Connecticut residents of all ages and provide opportunities for other students to share their research with the community at an annual Student Symposium.

Parasitoids must battle host defenses and alter the behavior and physiology of their hosts to their own benefit. Parasitoid manipulation of host nutrient intake might be a fundamental component of such interactions, yet it has received limited study in the broader field of host-parasite interactions. This research will test alternative functional hypotheses that could explain manipulation of caterpillar host feeding behavior by a parasitoid wasp. Preliminary evidence from this host-parasitoid interaction suggests that host caterpillars exhibit altered nutrient intake when parasitized by the parasitoid wasp, and this change in host feeding behavior benefits the parasitoid. Hypothetically, altering dietary nutrients of the host can have large effects on parasitoid growth performance and host immune function. Consequently, parasitoids could manipulate host nutrient intake so as to maximize the nutrient supply to host tissues eaten by the parasitoid, or to limit nutrients required for maximal host immune function. The researchers propose to manipulate macronutrient ratios in host diets and use techniques employed in the field of ecoimmunology and insect physiology to evaluate these hypothetical mechanisms of nutrient-mediated host manipulation, and their possible interaction. Data from this project will be stored at Wesleyan University and made accessible as published.

The fragmentation of habitats in to smaller and more isolated pieces can leave animals in areas that have insufficient food resources within reach. This problem is particularly acute for those species that are dietary specialists. These specialists may then be lost from the habitats, and their loss can have cascading effects on other species that may further alter the composition of ecological communities. This project will test alternative hypotheses that have been proposed to explain declines in specialist herbivores from fragmented forests. This research is important in understanding how changes in land use or other disturbances that fragment habitats will affect biodiversity and the integrity of ecosystems. The project will focus on butterfly larvae of species with different diet requirements as model study organisms. Their dependence on particular plant species and their role as prey for birds will be studied in 40 forest sites in Connecticut where the basic ecological interactions are well known. In addition to analysis of response to past forest fragmentation, experiments protecting caterpillars from predation will help quantify the importance of food resources. The study will improve understanding of natural food webs subject to human impacts and can guide future forest management. This project will also provide research training for students in forest ecology that will strengthen the scientific workforce.

Forest fragmentation is likely to substantially modify interactions among species and a recurrent pattern is the loss of dietary specialists from food webs in small forest fragments. Focusing on a complex, tri-trophic ecological network of larval Lepidoptera, their hostplants and avian predators, the project will establish how bottom-up and top-down mechanisms alter the absolute and relative abundance of specialist herbivores in forest fragments. The project will combine extensive extant data on plant-Lepidoptera associations and regional forest fragmentation, new data on plants and caterpillars at 40 sites, field experiments, and lab analyses on caterpillar diet breadth and growth response to quantify effects of host plant availability and predation on the diet specificity of lepidopteran larvae in temperate deciduous forests. This detailed, multi-trophic approach will enhance mechanistic understanding of changes in trophic networks due to fragmentation. Four broader impacts will result from this work: 1) training future scientists, 2) recruiting underrepresented groups, 3) public outreach in science and 4) improving scientific infrastructure.

This research project will develop a suite of water-stress indicators at several scales to assess the health of riparian ecosystems in response to sustained groundwater decline. This project will address a topic of scientific and societal importance, namely how to evaluate and help prevent negative impacts of drought and human-induced water shortages on vulnerable, high-value riparian ecosystems. It will integrate advanced methods in two rapidly emerging fields, hyperspectral remote sensing and isotope dendroecology, to develop a more holistic understanding of water stress at multiple scales of resolution. The project will compare water stress indicators that vary in their timing, strength, and rates of change, and it will facilitate the evaluation of warning signs and time lags among physiological water stress, reduced growth, and dieback in individual trees as well as synoptic forest decline evident throughout a river corridor. This project has the potential to influence groundwater management practices throughout California and in water-limited, multiple-use basins elsewhere. In partnership with The Nature Conservancy and other project collaborators, the investigators will integrate project findings with statewide guidelines for protecting groundwater-dependent riparian ecosystems mandated under California's recently implemented Groundwater Sustainability Management Act. The investigators will interact with groundwater conservation and management efforts in river basins through workshops for managers and stakeholders. They will mentor early-career environmental scientists, including women in STEM fields, and they will conduct outreach activities for elementary and secondary school students to increase regional environmental awareness in the study region.

Riparian forests and woodlands are hotspots of biodiversity, and they support key functions and habitats within river corridors, but they are particularly sensitive to large changes in water supply. This project will take place in the Santa Clara River in southern California, where sustained groundwater pumping for irrigation during a severe drought has had negative impacts and allows for study of riparian woodland response to changing environmental conditions over both short and longer terms. The investigators will assess the signals and thresholds of water stress over the last decade using high-resolution aerial imagery and tree-rings to develop predictors of long-term impairment and collapse. They will capitalize on extensive groundwater well records to link water-table dynamics with changes in plant water status detected at two different scales through the use of basin-wide, high-resolution aerial imagery taken seasonally during the drought and annual growth and carbon isotope data from tree rings covering the same period.

Forests along rivers are under threat due to climate-driven changes in water availability to trees. When water in the rooting zone is limited, trees undergo physiological changes that affect their overall growth and health. This problem is particularly acute within forests in river floodplains in regions with warm, dry summers (e.g., large areas of the USA). Such forests provide a range of ecosystem services, but they are limited in area, species diversity, and are challenging to manage under a changing climate. This project aims to build new understanding of the ?ecohydrological? links between water availability and forest health by employing an interdisciplinary set of research methods. It involves extracting tree cores from floodplain trees to investigate annual growth and will further investigate the ?isotopic signatures? of source water used by trees as recorded within each annual ring. By also monitoring climate variations and collecting water from various contributing sources, the project will provide insight into variations in potential source waters to forest trees. To generalize this research, the research will employ a numerical model to assess how climate controls water access to forests under plausible scenarios of regional climate change. The project will generate: new tools and information for practitioners of forest/water/basin management, international educational opportunities for underrepresented groups in the hydrologic sciences, and a new ecohydrology course for undergraduates.
This research project combines: 1) field-based measurements of climate and hydrology and laboratory analysis of oxygen isotopes from all potential tree water sources; (2) contemporary and retrospective analysis of oxygen and carbon isotopes in annual tree-rings to investigate recent climate-driven fluctuations in tree water use and water use efficiency; (3) seasonal (intra-annual) analysis of oxygen isotopes via high-resolution ?micro-slicing? of annual tree rings to assess seasonal fluctuations in tree water source use; and 4) improvement and application of a climate-driven numerical ecohydrology model that includes dynamic water fluxes into the floodplain, isotopic fractionation/mixing, and tree water uptake. It will compare the ecohydrologic responses to climate in water availability at forest sites along a strong climatic gradient.
There is currently limited ability to link tree/forest response to decadal climate shifts. Generalizable understanding linking regional climate to water availability to water use by riparian trees across forests stands is currently lacking, which limits predictive capability of forest response to drought stress over decadal timescales. This research will enable: i) identification of signatures of water stress within riparian forests; ii) predictive capability of forest response to climate change; iii) a clearer picture of regional variations in the expression of climate within floodplain water availability; and iv) improvement of dendro-paleoclimate reconstructions by providing better constraints on water availability and use under different conditions of climatic forcing.
This research project will provide managers with a new perspective and tools for anticipating and mitigating the risks of climate change on vulnerable riparian forest resources along major rivers in temperate and Mediterranean climatic regions. The project will host a 2-day workshop to disseminate our findings to practitioners and stakeholders in in the study region. It also includes a Research Experiences for Undergraduates (REU) supplement to enable two female and/or minority students to travel to France as their first international trip to participate on the first field campaign. The REU will provide these students will an exciting international research experience, a world-class learning opportunity, and an introduction to a potential career in environmental/hydrologic sciences. Additionally, data and models from this research will be integrated into a new upper division course on dryland ecohydrology at UCSB.