David JACOBS - US grants

This award will support travel of 7 U.S. participants to a U.S.-Sweden workshop in computer algebra in Stockholm, Sweden, June 7-9, 1995. The co-organizers are David P. Jacobs and Brian Malloy of Clemson University and Torsten Ekedahl of Stockholm University. The purpose of the workshop is to discuss the use of world wide web and other networks for sharing mathematical software systems with the scientific and educational community. The workshop addresses issues concerning the development of common standards and codes, multimedia approaches, and appropriate software development tools for building interfaces. Many specialized mathematical software systems are emerging to perform such diverse computations as solving systems of equations, constructing algebraic structures, examining properties of geometric objects, and visualizing abstract mathematical systems. These systems are not easily transported because of different formats and varied conventions for the interchange of data. The emergence of world wide web now offers an opportunity for sharing different systems through remote access to software programs. The workshop takes advantage of interaction with Swedish computer algebra specialists and other Europeans through POSSO (Polynomial Systems Solver) group.

0110718
Hartenstein

It is proposed to analyze early neural development in embryos of the flatworm species Macrostomum sp. And Neochildia fusca that can be raised in the lab so that embryos of all stages can be obtained in sufficient numbers year round. Flatworms are generally believed to have retained several primitive features of the common bilaterian ancestor and therefore represent a highly relevant system to study basic developmental processes, such as establishment of the body axes and early neurogenesis. Given the basal phylogenetic position of flatworms the proposed experiments will contribute to our understanding of neural development and the evolution of molecular networks controlling this process.

Our first aim is to reconstruct normal neurogenesis. Questions are the origin and pattern of neural progenitors, their proliferation and migration, and the pattern of axon tracts that emerges as neurons differentiate. These studies will provide a framework of data in which to interpret the expression pattern of genes that will be identified as part of the following aims. Aim 2 is the generation of a cDNA library for both species, which will greatly facilitate the screen for genes involved in neurogenesis. Aim 3 proposes to use a combined PCI and library screen approach to identify cognates of the following highly conserved genes that play fundamental roles in neural development in vertebrates and invertebrate systems: the regionalization genes vnd, ind, msh, Otx/otd, Tailless, lab and cad; the proneural genes ato and ASC, and the neural fate specifying genes of the POU/Homeodomain and LIM/Homeodomain family. Obtaining probes for these genes will serve two purposes. It will furnish early markers for neural precursors used to analyze normal neurogenesis at a satisfactory level of detail. Secondly, the expression pattern of these conserved genes is expected to provide valuable insight into how they function during neural patterning in flatworms. This in turn will aid in reconstructing how the relationship between specific molecular networks and morphogenetic events in neurogenesis arose during evolution.

Fault tolerant protocols are essential for providing various services (routing, group communication, broadcasting, multi-casting, etc.) in large, dynamic, distributed systems, where both processors and communication links can malfunction intermittently. For example, in mobile and ad hoc networks, the communication links are unreliable and some nodes may be unreachable for certain amounts of time. Such networks, consisting of mobile hosts that communicate via wireless radio channels, are being increasingly used for local area networks, law enforcement, military operations and a myriad of other applications.

The traditional approach in designing fault tolerant protocols assumes an upper bound on the number of faults and involves a worst case design by fault masking. While this approach
provides 100% system availability under assumed conditions, the implementation becomes very expensive. At the same time there are numerous applications for which the lack of system availability for very short periods is acceptable. Self-stabilization is an ``optimistic'' model to design
distributed fault tolerant systems; no upper bound on the number of faults is necessary, systems always reach a legitimate global state starting from any arbitrary (possibly illegitimate) state, and no central control is needed. However, system availability is not guaranteed during the convergence period.

This research addresses the design and analysis of fault tolerant self-stabilizing protocols for global communication primitives for dynamic distributed systems, especially suitable for mobile ad hoc networks. The research focuses on several aspects:

-- Create paradigms and guiding principles for designing self-stabilizing distributed algorithms;
-- Explore methodologies for translating a conventional algorithm into a self-stabilizing analog;
-- Discover and analyze self-stabilizing protocols for global communication primitives (resource center location, leader election, etc.) in a network;
-- Explore fractional (rational) valued self-stabilizing algorithms as a way to obtain improved approximate solutions to otherwise NP-hard problems;
-- Measure the degree to which self-stabilizing algorithms can contain a single fault.

The research takes a combined theoretical and experimental approach, and applies its results to emerging distributed applications for ad hoc networks.

Computer algebra (also known as symbolic computation) is an area of research involving both mathematics and the computer sciences. Computer algebra systems are widely used in many areas for research, education and practical problem solving. Research in computer algebra is the driving force for technological advances in commercially available computer algebra software. Its major goal is the development of highly efficient algorithms and automated software systems that can solve a wide variety of mathematical problems symbolically, numerically, or in a hybrid way.

The East Coast Computer Algebra Day (ECCAD) is one-day regional conference on computer algebra, its applications and related technological developments. Since 1994, ECCAD has been held annually at various North American locations on the East Coast. This meeting in the series is being held on Saturday, April 5, 2003, at Clemson University, Clemson, South Carolina. Three internationally recognized invited speakers will make featured presentations. There will be contributed poster/software demo sessions, covering many aspects of computer algebra.

Is there a connection between forms of social organization and the propensity to use capital punishment? Probably no other current legal sanction in any advanced society is as harsh, but there is little research on the conditions that influence executions. In part because public officials decide the criminal codes, sentences, and appeals, many theorists view punishment as an intrinsically political phenomenon. The many studies of the individual attributes that lead to death sentences have been extremely useful, but the influence of political conditions and the social divisions that influence these legal proceedings should be given more attention. For example, the state and federal appeals process has been largely ignored, but these procedures clearly are the most important explanation for execution rates. Almost entirely due to successful appeals only less than 10% of all state offenders given a death sentence ultimately are executed. Because so few capital offenders are punished in this manner and because these offenders spend such diverse amounts of time on death row, we propose to use survival analysis to assess the contextual and individual determinants that shape execution probabilities. Those states in which the death penalty is legal differ sharply in their willingness to use this extreme sanction. In many states that are reluctant to execute, as death sentences accumulate and the number of prisoners given this sentence grows, the amount of time these prisoners spend on death row becomes longer and longer, but other states execute far more quickly. This study proposes to analyze death row inmate survival rates in the US from 1973 to 2000 to detect the social conditions and the individual offender characteristics that jointly affect differences in execution probabilities over time and across the U.S. states. Such a research design is particularly appropriate for at least two reasons. First, this process is best modeled with survival techniques due to the long delay in the legal procedures that lead to an execution and due to the small minority of death row offenders who ultimately are executed. Second, one can combine aggregate time-varying covariates that measure the social and political environment with the characteristics of individual offenders in survival models to find out how these factors affect the timing and the probability of executions. It follows that analyses conducted with event history procedures that gauge both the individual and environmental determinants that should alter execution probabilities ought to add to our theoretical knowledge about the use of this lethal punishment. For example, this approach can be used to see if minority death row offenders are more or less likely to be executed or if states with larger minority populations are more likely to use this penalty. With these procedures we can see if minority capital offenders have a worse hazard rate due to the appeals process in comparatively conservative jurisdictions. The broader impacts of this study include the following. The research will be of interest to scholars and policymakers interested in understanding the factors that lead to inequalities associated with executions of US prisoners. The research we propose can throw light on some critical theoretical issues about the death penalty at a time when this severe and irreversible punishment is again starting to be questioned by the US public and policymakers.

What factors determine labor unions' ability to build membership with workplace recognition elections? Certification elections determine whether a workplace will be organized. Victory in these elections is the primary way that unions gain new members. The frequency of such elections, however, has fallen sharply. Analysts interested in the decline of union membership often emphasize shifting economic arrangements, globalization, employer resistance, and shortcomings in union organizing strategies. What is commonly overlooked, however, is the influence of national politics on labor's fortunes. For this reason and because political opportunities often are a crucial determinant of social movement success, this study fills a void in the literature by using a time-series analysis to isolate the factors that help unions' obtain these elections. The findings address how politics influence labor's capacity to build their membership. They also extend theories about how business, labor, and the government interact under different historical conditions. The results will offer new insights about the relationships between social movements and democratic states and thereby provide additional knowledge about the effects of political opportunities on social movements. This research is important for the average citizen because it sheds light on factors that contribute to the decline of organizations that provide workplace protections for workers. The new data (that come from the National Labor Relations Board and from government publications) will be made available to other scholars and thus should enhance research in this area. This research will be conducted at Ohio State University and the findings will be presented at professional conferences and in scientific journals.

Saliency-Guided Graphics and Visualization

Visual data is growing at an incredible rate due to advances in acquisition, modeling, and simulation technologies. This is posing significant challenges in its processing, display, and comprehension. Current graphics and visualization systems effectively assume a default; that every piece of data is equally important. As the data and displays get larger, visually finding useful information is becoming ever more challenging amidst the visual clutter. This research improves on the default uniform importance by associating every geometric primitive with a salience, an indication of its visual importance, and uses it to design and guide the rendering process. This research draws upon prior work in visual perception, vision, graphics, and scientific visualization and not only addresses how to present data but also what parts of the data to present for effective and compelling visual communication. This research involves advances in algorithms, tools, and techniques to generate effective visual content to facilitate comprehension and efficient rendering.

This research centers on defining and using saliency in graphics and visualization and involves developing a suite of methods for computing and assigning saliency to visual data. The investigators study how saliency can guide the rendering process to generate compelling visual content and to allocate computational and rendering resources where they have the most visual impact. The research involves rigorously validating saliency models through user studies using eye tracking and comparing them to human salience judgments. These tasks are in the driving application domains of computational biology and high-energy physics. Compelling scientific visual content has the potential to impact science education besides enhancing the accessibility of science to the common public.