Modeling water waves beyond perturbations

In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many variables as possible, and imposing some suitable subordinate constraints. This approach allows the construction of approximations without necessarily relying on a small parameter. This is illustrated via simple examples, namely the Serre equations in shallow water, a generalization of the Klein-Gordon equation in deep water and how to unify these equations in arbitrary depth. The chapter ends with a discussion and caution on how this approach should be used in practice.Comment: 15 pages, 1 figure, 39 references. This document is a contributed chapter to an upcoming volume to be published by Springer in Lecture Notes in Physics Series. Other author's papers can be downloaded at http://www.denys-dutykh.com

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

High biomass, low export regimes in the Southern Ocean

Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 54 (2007): 601-638, doi:10.1016/j.dsr2.2007.01.013.This paper investigates ballasting and remineralization controls of carbon sedimentation in the twilight zone (100-1000 m) of the Southern Ocean. Size-fractionated (<1 μm, 1-51 μm, >51 μm) suspended particulate matter was collected by large volume in-situ filtration from the upper 1000 m in the Subantarctic (55°S, 172°W) and Antarctic (66°S, 172°W) zones of the Southern Ocean during the Southern Ocean Iron Experiment (SOFeX) in January-February 2002. Particles were analyzed for major chemical constituents (POC, P, biogenic Si, CaCO3), and digital and SEM image analyses of particles were used to aid in the interpretation of the chemical profiles. Twilight zone waters at 66°S in the Antarctic had a steeper decrease in POC with depth than at 55°S in the Subantarctic, with lower POC concentrations in all size fractions at 66°S than at 55°S, despite up to an order of magnitude higher POC in surface waters at 66°S. The decay length scale of >51 μm POC was significantly shorter in the upper twilight zone at 66°S (δe=26 m) compared to 55°S (δe=81 m). Particles in the carbonate-producing 55°S did not have higher excess densities than particles from the diatom-dominated 66°S, indicating that there was no direct ballast effect that accounted for deeper POC penetration at 55°S. An indirect ballast effect due to differences in particle packaging and porosities cannot be ruled out, however, as aggregate porosities were high (~97%) and variable. Image analyses point to the importance of particle loss rates from zooplankton grazing and remineralization as determining factors for the difference in twilight zone POC concentrations at 55°S and 66°S, with stronger and more focused shallow remineralization at 66°S. At 66°S, an abundance of large (several mm long) fecal pellets from the surface to 150 m, and almost total removal of large aggregates by 200 m, reflected the actions of a single or few zooplankton species capable of grazing diatoms in the euphotic zone, coupled with a more diverse particle feeding zooplankton community immediately below. Surface waters with high biomass levels and high proportion of biomass in the large size fraction were associated with low particle loading at depth, with all indications implying conditions of low export. The 66°S region exhibits this “High Biomass, Low Export” (HBLE) condition, with very high >51 μm POC concentrations at the surface (~2.1 μM POC), but low concentrations below 200 m (<0.07 μM POC). The 66°S region remained HBLE after iron fertilization. Iron addition at 55°S caused a ten fold increase in >51 μm biomass concentrations in the euphotic zone, bringing surface POC concentrations to levels found at 66°S (~3.8 μM), and a concurrent decrease in POC concentrations below 200 m. The 55°S region, which began with moderate levels of biomass and stronger particle export, transitioned to being HBLE after iron fertilization. We propose that iron addition to already HBLE waters will not cause mass sedimentation events. The stability of an iron-induced HBLE condition is unknown. Better understanding of biological pump processes in non-HBLE Subantarctic waters is needed.This work was supported by the DOE Office of Science, Biological and Environmental Research Program. Shiptime for SOFeX was funded by NSF

Compact pairwise models for epidemics with multiple infectious stages on degree heterogeneous and clustered networks

This paper presents a compact pairwise model that describes the spread of multi-stage epidemics on networks. The multi-stage model corresponds to a gamma-distributed infectious period which interpolates between the classical Markovian models with exponentially distributed infectious period and epidemics with a constant infectious period. We show how the compact approach leads to a system of equations whose size is independent of the range of node degrees, thus significantly reducing the complexity of the model. Network clustering is incorporated into the model to provide a more accurate representation of realistic contact networks, and the accuracy of proposed closures is analysed for different levels of clustering and number of infection stages. Our results support recent findings that standard closure techniques are likely to perform better when the infectious period is constant

Emerging role of insulin with incretin therapies for management of type 2 diabetes

Type 2 diabetes mellitus (T2DM) is a progressive disease warranting intensification of treatment, as beta-cell function declines over time. Current treatment algorithms recommend metformin as the first-line agent, while advocating the addition of either basal-bolus or premixed insulin as the final level of intervention. Incretin therapy, including incretin mimetics or enhancers, are the latest group of drugs available for treatment of T2DM. These agents act through the incretin axis, are currently recommended as add-on agents either as second-or third-line treatment, without concurrent use of insulin. Given the novel role of incretin therapy in terms of reducing postprandial hyperglycemia, and favorable effects on weight with reduced incidence of hypoglycemia, we explore alternative options for incretin therapy in T2DM management. Furthermore, as some evidence alludes to incretins potentially increasing betacell mass and altering disease progression, we propose introducing these agents earlier in the treatment algorithm. In addition, we suggest the concurrent use of incretins with insulin, given the favorable effects especially in relation to weight gain

Light-Ion-Induced Multifragmentation: The ISiS Project

An extensive study of GeV light-ion-induced multifragmentation and its possible interpretation in terms of a nuclear liquid-gas phase transition has been performed with the Indiana Silicon Sphere (ISiS)4 pi detector array. Measurements were performed with 5-15 GeV/c p, pbar, and pion beams incident on $^{197}$Au and 2-5 GeV $^3$He incident on $^{nat}$Ag and $^{197}$Au targets. Both the reaction dynamics and the subsequent decay of the heavy residues have been explored. The data provide evidence for a dramatic change in the reaction observables near an excitation energy of E*/A = 4-5 MeV per residue nucleon. In this region, fragment multiplicities and energy spectra indicate emission from an expanded/dilute source on a very short time scale (20-50 fm/c). These properties, along with caloric curve and scaling-law behavior, yield a pattern that is consistent with a nuclear liquid-gas phase transition.Comment: 67 pages, 44 figures, all included in tar fil

Parental origin of sequence variants associated with complex diseases

To access publisher full text version of this article. Please click on the hyperlink in Additional Links fieldEffects of susceptibility variants may depend on from which parent they are inherited. Although many associations between sequence variants and human traits have been discovered through genome-wide associations, the impact of parental origin has largely been ignored. Here we show that for 38,167 Icelanders genotyped using single nucleotide polymorphism (SNP) chips, the parental origin of most alleles can be determined. For this we used a combination of genealogy and long-range phasing. We then focused on SNPs that associate with diseases and are within 500 kilobases of known imprinted genes. Seven independent SNP associations were examined. Five-one with breast cancer, one with basal-cell carcinoma and three with type 2 diabetes-have parental-origin-specific associations. These variants are located in two genomic regions, 11p15 and 7q32, each harbouring a cluster of imprinted genes. Furthermore, we observed a novel association between the SNP rs2334499 at 11p15 and type 2 diabetes. Here the allele that confers risk when paternally inherited is protective when maternally transmitted. We identified a differentially methylated CTCF-binding site at 11p15 and demonstrated correlation of rs2334499 with decreased methylation of that site.info:eu-repo/grantAgreement/EC/FP7/21807