Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections

We prove two conjectures from [M. R. Douglas, B. Shiffman and S. Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning the expected number of critical points of random holomorphic sections of a positive line bundle. We show that, on average, the critical points of minimal Morse index are the most plentiful for holomorphic sections of {\mathcal O}(N) \to \CP^m and, in an asymptotic sense, for those of line bundles over general K\"ahler manifolds. We calculate the expected number of these critical points for the respective cases and use these to obtain growth rates and asymptotic bounds for the total expected number of critical points in these cases. This line of research was motivated by landscape problems in string theory and spin glasses.Comment: 14 pages, corrected typo

Could decision trees help improve Farm Service Agency lending decisions?

This study examines whether a statistically derived decision tree could serve as a means to improve U.S.A. Farm Service Agency lending decisions. The study is a substantial extension and reanalysis of an earlier work by Barney, Graves and Johnson, (1999). Results indicate that a decision tree could be a valuable tool for Farm Service Agency employees in their lending decisions. The decision tree provides as good or better predictive accuracy than neural networks and logistic regression models at reasonable cutoff levels of Type II to Type I costs of lending. The decision tree also meets the transparency criteria for Farm Service Agency purposes by providing logical, understandable rules for lending decisions

Seasonal modulation of mesoscale processes alters nutrient availability and plankton communities in the Red Sea

Hydrographic and atmospheric forcing set fundamental constraints on the biogeochemistry of aquatic ecosystems and manifest in the patterns of nutrient availability and recycling, species composition of communities, trophic dynamics, and ecosystem metabolism. In the Red Sea, latitudinal gradients in environmental conditions and primary production have been ascribed to fluctuations in Gulf of Aden Water inflow, upwelling/mixing, and regenerated nutrient utilization i.e. rapidly recycled nitrogen in upper layers. However, our understanding of upper layer dynamics and related changes in plankton communities, metabolism and carbon and nitrogen export is limited. We surmised that stratification and mesoscale eddies modulate the nutrient availability and taxonomic identity of plankton communities in the Red Sea. Based on remote-sensing data of sea level anomalies and high resolution in situ measurements (ScanFish) we selected stations for hydrographic CTD profiles, water sampling (nutrients, seawater oxygen stable isotopes [δ18OSW]), phytoplankton and zooplankton collections. In fall 2014, strong stratification subjected the plankton community to an overall nitrogen and phosphorus shortage. The nutrient deficiency increased numbers of heterotrophic dinoflagellates, microzooplankton, and diazotrophs (Trichodesmium, diatom-diazotroph associations [DDAs]), albeit largely decreased phytoplankton and mesozooplankton abundances. In spring 2015, mesoscale eddies increased the nutrient availability, and the thermohaline characteristics and low δ18OSW point to the interaction of eddies with Gulf of Aden Surface Water (GASW). Cyclonic eddies and, most likely, the availability of nutrients associated with the GASW, increased the abundances of autotrophs (diatoms, Prasinophytes) and supported larger numbers of zooplankton and their larvae. We demonstrate that the interplay of stratification, advection of Gulf of Aden water and mesoscale eddies are key elements to better understand changes in plankton community composition, ecosystem metabolism, and macronutrient export in the Red Sea in space and time

Genetic correlates of longevity and selected age-related phenotypes: a genome-wide association study in the Framingham Study

BACKGROUND: Family studies and heritability estimates provide evidence for a genetic contribution to variation in the human life span. METHODS:We conducted a genome wide association study (Affymetrix 100K SNP GeneChip) for longevity-related traits in a community-based sample. We report on 5 longevity and aging traits in up to 1345 Framingham Study participants from 330 families. Multivariable-adjusted residuals were computed using appropriate models (Cox proportional hazards, logistic, or linear regression) and the residuals from these models were used to test for association with qualifying SNPs (70, 987 autosomal SNPs with genotypic call rate [greater than or equal to]80%, minor allele frequency [greater than or equal to]10%, Hardy-Weinberg test p [greater than or equal to] 0.001).RESULTS:In family-based association test (FBAT) models, 8 SNPs in two regions approximately 500 kb apart on chromosome 1 (physical positions 73,091,610 and 73, 527,652) were associated with age at death (p-value < 10-5). The two sets of SNPs were in high linkage disequilibrium (minimum r2 = 0.58). The top 30 SNPs for generalized estimating equation (GEE) tests of association with age at death included rs10507486 (p = 0.0001) and rs4943794 (p = 0.0002), SNPs intronic to FOXO1A, a gene implicated in lifespan extension in animal models. FBAT models identified 7 SNPs and GEE models identified 9 SNPs associated with both age at death and morbidity-free survival at age 65 including rs2374983 near PON1. In the analysis of selected candidate genes, SNP associations (FBAT or GEE p-value < 0.01) were identified for age at death in or near the following genes: FOXO1A, GAPDH, KL, LEPR, PON1, PSEN1, SOD2, and WRN. Top ranked SNP associations in the GEE model for age at natural menopause included rs6910534 (p = 0.00003) near FOXO3a and rs3751591 (p = 0.00006) in CYP19A1. Results of all longevity phenotype-genotype associations for all autosomal SNPs are web posted at http://www.ncbi.nlm.nih.gov/projects/gap/cgi-bin/study.cgi?id=phs000007. CONCLUSION: Longevity and aging traits are associated with SNPs on the Affymetrix 100K GeneChip. None of the associations achieved genome-wide significance. These data generate hypotheses and serve as a resource for replication as more genes and biologic pathways are proposed as contributing to longevity and healthy aging

Serverification of Molecular Modeling Applications: the Rosetta Online Server that Includes Everyone (ROSIE)

The Rosetta molecular modeling software package provides experimentally tested and rapidly evolving tools for the 3D structure prediction and high-resolution design of proteins, nucleic acids, and a growing number of non-natural polymers. Despite its free availability to academic users and improving documentation, use of Rosetta has largely remained confined to developers and their immediate collaborators due to the code's difficulty of use, the requirement for large computational resources, and the unavailability of servers for most of the Rosetta applications. Here, we present a unified web framework for Rosetta applications called ROSIE (Rosetta Online Server that Includes Everyone). ROSIE provides (a) a common user interface for Rosetta protocols, (b) a stable application programming interface for developers to add additional protocols, (c) a flexible back-end to allow leveraging of computer cluster resources shared by RosettaCommons member institutions, and (d) centralized administration by the RosettaCommons to ensure continuous maintenance. This paper describes the ROSIE server infrastructure, a step-by-step 'serverification' protocol for use by Rosetta developers, and the deployment of the first nine ROSIE applications by six separate developer teams: Docking, RNA de novo, ERRASER, Antibody, Sequence Tolerance, Supercharge, Beta peptide design, NCBB design, and VIP redesign. As illustrated by the number and diversity of these applications, ROSIE offers a general and speedy paradigm for serverification of Rosetta applications that incurs negligible cost to developers and lowers barriers to Rosetta use for the broader biological community. ROSIE is available at http://rosie.rosettacommons.org