Covering collections and a challenge problem of Serre

We answer a challenge of Serre by showing that every rational point on the projective curve X$^4$ + Y$^4$ = 17 Z$^4$ is of the form ($\pm$1, $\pm$2, 1) or ($\pm$2, $\pm$1, 1). Our approach builds on recent ideas from both Nils Bruin and the authors on the application of covering collections and Chabauty arguments to curves of high rank. This is the only value of c$\le$81 for which the Fermat quartic X$^4$ + Y$^4$ = c Z$^4$ cannot be solved trivially, either by local considerations or maps to elliptic curves of rank 0, and it seems likely that our approach should give a method of attack for other nontrivial values of c

Finding rational points on bielliptic genus 2 curves

We discuss a technique for trying to find all rational points on curves of the form $Y^2 = f_3 X^6 + f_2 X^4 + f_1 X^2 + f_0$, where the sextic has nonzero discriminant. This is a bielliptic curve of genus 2. When the rank of the Jacobian is 0 or 1, Chabauty's Theorem may be applied. However, we shall concentrate on the situation when the rank is at least 2. In this case, we shall derive an associated family of elliptic curves, defined over a number field Q(a). If each of these elliptic curves has rank less than the degree of Q(a) : Q, then we shall describe a Chabauty-like technique which may be applied to try to find all the points (x,y) defined over Q(a) on the elliptic curves, for which x is in Q. This in turn allows us to find all Q-rational points on the original genus 2 curve. We apply this to give a solution to a problem of Diophantus (where the sextic in X is irreducible over Q), which simplifies the recent solution of Wetherell. We also present two examples where the sextic in X is reducible over Q

Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves

This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six quantities is the size of the Shafarevich-Tate group. Unable to compute that, we computed the five other quantities and solved for the last one. In all 32 cases, the result is very close to an integer that is a power of 2. In addition, this power of 2 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute

GIS data and tools available at SGS-LTER

The SGS-LTER research site was established in 1980 by researchers at Colorado State University as part of a network of long-term research sites within the US LTER Network, supported by the National Science Foundation. Scientists within the Natural Resource Ecology Lab, Department of Forest and Rangeland Stewardship, Department of Soil and Crop Sciences, and Biology Department at CSU, California State Fullerton, USDA Agricultural Research Service, University of Northern Colorado, and the University of Wyoming, among others, have contributed to our understanding of the structure and functions of the shortgrass steppe and other diverse ecosystems across the network while maintaining a common mission and sharing expertise, data and infrastructure.Poster presented at the 7th Shortgrass Steppe Symposium held in Fort Collins, Colorado on 1/14/05

Characterization of in band stray light in SBUV/2 instruments

Significant in-band stray light (IBSL) error at solar zenith angle (SZA) values larger than 77° near sunset in 4 SBUV/2 (Solar Backscattered Ultraviolet) instruments, on board the NOAA-14, 17, 18 and 19 satellites, has been characterized. The IBSL error is caused by large surface reflection and scattering of the air-gapped depolarizer in front of the instrument's monochromator aperture. The source of the IBSL error is direct solar illumination of instrument components near the aperture rather than from earth shine. The IBSL contamination at 273 nm can reach 40% of earth radiance near sunset, which results in as much as a 50% error in the retrieved ozone from the upper stratosphere. We have analyzed SBUV/2 albedo measurements on both the dayside and nightside to develop an empirical model for the IBSL error. This error has been corrected in the V8.6 SBUV/2 ozone retrieval

Differences in reactivation of tuberculosis induced from anti-tnf treatments are based on bioavailability in granulomatous tissue

The immune response to Mycobacterium tuberculosis (Mtb) infection is complex. Experimental evidence has revealed that tumor necrosis factor (TNF) plays a major role in host defense against Mtb in both active and latent phases of infection. TNF-neutralizing drugs used to treat inflammatory disorders have been reported to increase the risk of tuberculosis (TB), in accordance with animal studies. The present study takes a computational approach toward characterizing the role of TNF in protection against the tubercle bacillus in both active and latent infection. We extend our previous mathematical models to investigate the roles and production of soluble (sTNF) and transmembrane TNF (tmTNF). We analyze effects of anti-TNF therapy in virtual clinical trials (VCTs) by simulating two of the most commonly used therapies, anti-TNF antibody and TNF receptor fusion, predicting mechanisms that explain observed differences in TB reactivation rates. The major findings from this study are that bioavailability of TNF following anti-TNF therapy is the primary factor for causing reactivation of latent infection and that sTNF-even at very low levels-is essential for control of infection. Using a mathematical model, it is possible to distinguish mechanisms of action of the anti-TNF treatments and gain insights into the role of TNF in TB control and pathology. Our study suggests that a TNF-modulating agent could be developed that could balance the requirement for reduction of inflammation with the necessity to maintain resistance to infection and microbial diseases. Alternatively, the dose and timing of anti-TNF therapy could be modified. Anti-TNF therapy will likely lead to numerous incidents of primary TB if used in areas where exposure is likely. © 2007 Marino et al

TOBIAS CENTER FOR LEADERSHIP EXCELLENCE

poster abstractThe Randall L. Tobias Center for Leadership Excellence was established in 2004. The vision is for it to become one of the top 3 or 4 internationally recognized Centers on Leadership Excellence. The Tobias Center is explicitly cross-disciplinary in its study of leadership and was created as a collaboration of the Kelley School of Business, the School of Public and Environmental Affairs (SPEA) and the School of Education and the Center on Philanthropy. The Tobias Center is an Indiana University center and is housed in the Kelley School in Indianapolis. The programs of the Center fall into three major areas: research, community outreach and education, and teaching. The poster will highlight each of the Center’s programs in each of the three areas. For Research, it will describe the Center’s Faculty Fellows, Doctoral Fellows and Leadership Laboratories. The Center’s community outreach and education programs include the Hoosier Fellows Program, the three lecture programs, and its annual conference. Teaching initiatives of the Tobias Center include the Urban Leadership Education Institute, the Undergraduate Leadership Academy and School of Medicine Leadership course

Celecoxib concentration predicts decrease in prostaglandin E\u3csub\u3e2\u3c/sub\u3e concentrations in nipple aspirate fluid from high risk women

BACKGROUND: Epidemiologic studies suggest that long term low dose celecoxib use significantly lowers breast cancer risk. We previously demonstrated that 400 mg celecoxib taken twice daily for 2 weeks lowered circulating plasma and breast nipple aspirate fluid (NAF) prostaglandin (PG)E2 concentrations in post- but not premenopausal high risk women. We hypothesized that circulating concentrations of celecoxib influenced PGE2 response, and that plasma levels of the drug are influenced by menopausal status. To address these hypotheses, the aims of the study were to determine: 1) if circulating plasma concentrations of celecoxib correlated with the change in plasma or NAF PGE2 concentrations from baseline to end of treatment, and 2) whether menopausal status influenced circulating levels of celecoxib. METHODS: Matched NAF and plasma were collected from 46 high risk women who were administered celecoxib twice daily for two weeks, 20 subjects receiving 200 mg and 26 subjects 400 mg of the agent. NAF and plasma samples were collected before and 2 weeks after taking celecoxib. RESULTS: In women taking 400 mg bid celecoxib, plasma concentrations of the agent correlated inversely with the change in NAF PGE2 levels from pre- to posttreatment. Nonsignificant trends toward higher celecoxib levels were observed in post- compared to premenopausal women. There was a significant decrease in NAF but not plasma PGE2 concentrations in postmenopausal women who took 400 mg celecoxib (p = 0.03). CONCLUSION: In high risk women taking 400 mg celecoxib twice daily, plasma concentrations of celecoxib correlated with downregulation of PGE2 production by breast tissue. Strategies synergistic with celecoxib to downregulate PGE2 are of interest, in order to minimize the celecoxib dose required to have an effect

Conventional clear-sky aerosol retrievals: Do they work for cloudy days?

This presentation highlights different approaches to determine the aerosol properties between clouds and covers a broad range of related topics, including the passive aerosol remote sensing from space, in situ observations of aerosol aloft and at surface and numerical modeling of aerosol and cloud properties. Some of these approaches, which are still in research phase, can reduce substantially the impact of cloud-induced contamination on the cloudy-sky aerosol retrievals, while other can reduce uncertainties associated with aerosol hygroscopicity and enhanced relative humidity near cloud edges. The combination of these approaches for addressing outstanding issues of the cloudy-sky aerosol retrievals is also discussed