A Cantor set of tori with monodromy near a focus-focus singularity

We write down an asymptotic expression for action coordinates in an integrable Hamiltonian system with a focus-focus equilibrium. From the singularity in the actions we deduce that the Arnol'd determinant grows infinitely large near the pinched torus. Moreover, we prove that it is possible to globally parametrise the Liouville tori by their frequencies. If one perturbs this integrable system, then the KAM tori form a Whitney smooth family: they can be smoothly interpolated by a torus bundle that is diffeomorphic to the bundle of Liouville tori of the unperturbed integrable system. As is well-known, this bundle of Liouville tori is not trivial. Our result implies that the KAM tori have monodromy. In semi-classical quantum mechanics, quantisation rules select sequences of KAM tori that correspond to quantum levels. Hence a global labeling of quantum levels by two quantum numbers is not possible.Comment: 11 pages, 2 figure

Oak forest carbon and water simulations:Model intercomparisons and evaluations against independent data

Models represent our primary method for integration of small-scale, process-level phenomena into a comprehensive description of forest-stand or ecosystem function. They also represent a key method for testing hypotheses about the response of forest ecosystems to multiple changing environmental conditions. This paper describes the evaluation of 13 stand-level models varying in their spatial, mechanistic, and temporal complexity for their ability to capture intra- and interannual components of the water and carbon cycle for an upland, oak-dominated forest of eastern Tennessee. Comparisons between model simulations and observations were conducted for hourly, daily, and annual time steps. Data for the comparisons were obtained from a wide range of methods including: eddy covariance, sapflow, chamber-based soil respiration, biometric estimates of stand-level net primary production and growth, and soil water content by time or frequency domain reflectometry. Response surfaces of carbon and water flux as a function of environmental drivers, and a variety of goodness-of-fit statistics (bias, absolute bias, and model efficiency) were used to judge model performance. A single model did not consistently perform the best at all time steps or for all variables considered. Intermodel comparisons showed good agreement for water cycle fluxes, but considerable disagreement among models for predicted carbon fluxes. The mean of all model outputs, however, was nearly always the best fit to the observations. Not surprisingly, models missing key forest components or processes, such as roots or modeled soil water content, were unable to provide accurate predictions of ecosystem responses to short-term drought phenomenon. Nevertheless, an inability to correctly capture short-term physiological processes under drought was not necessarily an indicator of poor annual water and carbon budget simulations. This is possible because droughts in the subject ecosystem were of short duration and therefore had a small cumulative impact. Models using hourly time steps and detailed mechanistic processes, and having a realistic spatial representation of the forest ecosystem provided the best predictions of observed data. Predictive ability of all models deteriorated under drought conditions, suggesting that further work is needed to evaluate and improve ecosystem model performance under unusual conditions, such as drought, that are a common focus of environmental change discussions

The Non-Trapping Degree of Scattering

We consider classical potential scattering. If no orbit is trapped at energy E, the Hamiltonian dynamics defines an integer-valued topological degree. This can be calculated explicitly and be used for symbolic dynamics of multi-obstacle scattering. If the potential is bounded, then in the non-trapping case the boundary of Hill's Region is empty or homeomorphic to a sphere. We consider classical potential scattering. If at energy E no orbit is trapped, the Hamiltonian dynamics defines an integer-valued topological degree deg(E) < 2. This is calculated explicitly for all potentials, and exactly the integers < 2 are shown to occur for suitable potentials. The non-trapping condition is restrictive in the sense that for a bounded potential it is shown to imply that the boundary of Hill's Region in configuration space is either empty or homeomorphic to a sphere. However, in many situations one can decompose a potential into a sum of non-trapping potentials with non-trivial degree and embed symbolic dynamics of multi-obstacle scattering. This comprises a large number of earlier results, obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more detailed proofs and remark

Non-integrability of the mixmaster universe

We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case irrespective of the value, $I$, of the generating Hamiltonian which is a constant of motion. For $I < 0$ we find numerous closed orbits with two unstable eigenvalues strongly indicating that there cannot exist two additional first integrals apart from the Hamiltonian and thus that the system, at least for this case, is very likely not integrable. In addition, we present numerical evidence that the average Lyapunov exponent nevertheless vanishes. The model is thus a very interesting example of a Hamiltonian dynamical system, which is likely non-integrable yet passes the reduced Painlev\'{e} test.Comment: 11 pages LaTeX in J.Phys.A style (ioplppt.sty) + 6 PostScript figures compressed and uuencoded with uufiles. Revised version to appear in J Phys.

Maslov Indices and Monodromy

We prove that for a Hamiltonian system on a cotangent bundle that is Liouville-integrable and has monodromy the vector of Maslov indices is an eigenvector of the monodromy matrix with eigenvalue 1. As a corollary the resulting restrictions on the monodromy matrix are derived.Comment: 6 page

Peptides with Potential Cardioprotective Effects Derived from Dry-Cured Ham Byproducts

"This document is the unedited Author s version of a Submitted Work that was subsequently accepted for publication in Journal of Agricultural and Food Chemistry, copyright © American Chemical Society after peer review. To access the final edited and published work see https://pubs.acs.org/doi/10.1021/acs.jafc.8b05888"[EN] The interest in using food byproducts as a source of bioactive peptides has increased significantly in the recent years. The goal of this work was to determine the presence and stability of peptides showing angiotensin I-converting enzyme (ACE-I), endothelin-converting enzyme (ECE), dipeptidyl peptidase-IV (DPP-IV), and platelet-activating factor-acetylhydrolase (PAF-AH) inhibitory activity derived from dry-cured ham bones, which could exert cardiovascular health benefits. ACE-I and DPP-IV inhibitory peptides were stable against heating typically used in Mediterranean household cooking methods and also to in vitro digestion. PAF-AH inhibitory activity significantly increased following simulated gastrointestinal digestion whereas ECE inhibitory significantly decreased (P < 0.05). The mass spectrometry analysis revealed a notable degradation of hemoglobin-derived peptides after simulated digestion, and the release of a large number of dipeptides that may have contributed to the observed bioactivities. These results suggest that natural peptides from Spanish dry-cured ham bones could contribute to a positive impact on cardiovascular health.This study was funded by the Emerging Research Group Grant from Generalitat Valenciana in Spain (GV/2015/138). A Ramon y Cajal postdoctoral contract to L.M. is acknowledged. Proteomic analysis was performed in the proteomics facility of SCSIE University of Valencia that belongs to ProteoRed, PRB2-ISCIII, supported by grant PT13/0001.Gallego-Ibáñez, M.; Mora Soler, L.; Hayes, M.; Reig Riera, MM.; Toldrá Vilardell, F. (2019). Peptides with Potential Cardioprotective Effects Derived from Dry-Cured Ham Byproducts. Journal of Agricultural and Food Chemistry. 67(4):1115-1126. https://doi.org/10.1021/acs.jafc.8b05888S1115112667

PHYSIOLOGY AND ENDOCRINOLOGY SYMPOSIUM: How single nucleotide polymorphism chips will advance our knowledge of factors controlling puberty and aid in selecting replacement beef females

The promise of genomic selection is accurate prediction of the genetic potential of animals from their genotypes. Simple DNA tests might replace low-accuracy predictions for expensive or lowly heritable measures of puberty and fertility based on performance and pedigree. Knowing with some certainty which DNA variants (e.g., SNP) affect puberty and fertility is the best way to fulfill the promise. Several SNP from the BovineSNP50 assay have tentatively been associated with reproductive traits including age at puberty, antral follicle count, and pregnancy observed on different sets of heifers. However, sample sizes are too small and SNP density is too sparse to definitively determine genomic regions harboring causal variants affecting reproductive success. Additionally, associations between individual SNP and similar phenotypes are inconsistent across data sets, and genomic predictions do not appear to be globally applicable to cattle of different breeds. Discrepancies may be a result of different QTL segregating in the sampled populations, differences in linkage disequilibrium (LD) patterns such that the same SNP are not correlated with the same QTL, and spurious correlations with phenotype. Several approaches can be used independently or in combination to improve detection of genomic factors affecting heifer puberty and fertility. Larger samples and denser SNP will increase power to detect real associations with SNP having more consistent LD with underlying QTL. Meta- analysis combining results from different studies can also be used to effectively increase sample size. High-density genotyping with heifers pooled by pregnancy status or early and late puberty can be a cost-effective means to sample large numbers. Networks of genes, implicated by associations with multiple traits correlated with puberty and fertility, could provide insight into the complex nature of these traits, especially if corroborated by functional annotation, established gene interaction pathways, and transcript expression. Example analyses are provided to demonstrate how integrating information about gene function and regulation with statistical associations from whole-genome SNP genotyping assays might enhance knowledge of genomic mechanisms affecting puberty and fertility, enabling reliable DNA tests to guide heifer selection decisions

Retrospective model-based inference guides model-free credit assignment

An extensive reinforcement learning literature shows that organisms assign credit efficiently, even under conditions of state uncertainty. However, little is known about credit-assignment when state uncertainty is subsequently resolved. Here, we address this problem within the framework of an interaction between model-free (MF) and model-based (MB) control systems. We present and support experimentally a theory of MB retrospective-inference. Within this framework, a MB system resolves uncertainty that prevailed when actions were taken thus guiding an MF credit-assignment. Using a task in which there was initial uncertainty about the lotteries that were chosen, we found that when participants’ momentary uncertainty about which lottery had generated an outcome was resolved by provision of subsequent information, participants preferentially assigned credit within a MF system to the lottery they retrospectively inferred was responsible for this outcome. These findings extend our knowledge about the range of MB functions and the scope of system interactions

Low-threshold analysis of CDMS shallow-site data

Data taken during the final shallow-site run of the first tower of the Cryogenic Dark Matter Search (CDMS II) detectors have been reanalyzed with improved sensitivity to small energy depositions. Four ~224 g germanium and two ~105 g silicon detectors were operated at the Stanford Underground Facility (SUF) between December 2001 and June 2002, yielding 118 live days of raw exposure. Three of the germanium and both silicon detectors were analyzed with a new low-threshold technique, making it possible to lower the germanium and silicon analysis thresholds down to the actual trigger thresholds of ~1 keV and ~2 keV, respectively. Limits on the spin-independent cross section for weakly interacting massive particles (WIMPs) to elastically scatter from nuclei based on these data exclude interesting parameter space for WIMPs with masses below 9 GeV/c^2. Under standard halo assumptions, these data partially exclude parameter space favored by interpretations of the DAMA/LIBRA and CoGeNT experiments' data as WIMP signals, and exclude new parameter space for WIMP masses between 3 GeV/c^2 and 4 GeV/c^2.Comment: 18 pages, 12 figures, 5 table

Analysis of the low-energy electron-recoil spectrum of the CDMS experiment

We report on the analysis of the low-energy electron-recoil spectrum from the CDMS II experiment using data with an exposure of 443.2 kg-days. The analysis provides details on the observed counting rate and possible background sources in the energy range of 2 - 8.5 keV. We find no significant excess in the counting rate above background, and compare this observation to the recent DAMA results. In the framework of a conversion of a dark matter particle into electromagnetic energy, our 90% confidence level upper limit of 0.246 events/kg/day at 3.15 keV is lower than the total rate above background observed by DAMA by 8.9$\sigma$. In absence of any specific particle physics model to provide the scaling in cross section between NaI and Ge, we assume a Z^2 scaling. With this assumption the observed rate in DAMA differs from the upper limit in CDMS by 6.8$\sigma$. Under the conservative assumption that the modulation amplitude is 6% of the total rate we obtain upper limits on the modulation amplitude a factor of ~2 less than observed by DAMA, constraining some possible interpretations of this modulation.Comment: 4 pages, 3 figure