Numerical bifurcation analysis of homoclinic orbits embedded in one-dimensional manifolds of maps

We describe new methods for initializing the computation of homoclinic orbits for maps in a state space with arbitrary dimension and for detecting their bifurcations. The initialization methods build on known and improved methods for computing one-dimensional stable and unstable manifolds. The methods are implemented in MatContM, a freely available toolbox in Matlab for numerical analysis of bifurcations of fixed points, periodic orbits, and connecting orbits of smooth nonlinear maps. The bifurcation analysis of homoclinic connections under variation of one parameter is based on continuation methods and allows us to detect all known codimension 1 and 2 bifurcations in three-dimensional (3D) maps, including tangencies and generalized tangencies. MatContM provides a graphical user interface, enabling interactive control for all computations. As the prime new feature, we discuss an algorithm for initializing connecting orbits in the important special case where either the stable or unstable manifold is one-dimensional, allowing us to compute all homoclinic orbits to saddle points in 3D maps. We illustrate this algorithm in the study of the adaptive control map, a 3D map introduced in 1991 by Frouzakis, Adomaitis, and Kevrekidis, to obtain a rather complete bifurcation diagram of the resonance horn in a 1:5 Neimark-Sacker bifurcation point, revealing new features

Estimated glomerular filtration rate is a poor predictor of the concentration of middle molecular weight uremic solutes in chronic kidney disease

Background: Uremic solute concentration increases as Glomerular Filtration Rate (GFR) declines. Weak associations were demonstrated between estimated GFR (eGFR) and the concentrations of several small water-soluble and protein-bound uremic solutes (MW500Da). Materials and Methods: In 95 CKD-patients (CKD-stage 2-5 not on dialysis), associations between different eGFR-formulae (creatinine, CystatinC-based or both) and the natural logarithm of the concentration of several LMWP's were analyzed: i.e. parathyroid hormone (PTH), Cystatin C (CystC), interleukin-6 (IL-6), tumor necrosis factor-alpha (TNF-alpha), leptin, retinol binding protein (RbP), immunoglobin light chains kappa and lambda (Ig-kappa and Ig-lambda), beta-2-microglobulin (beta M-2), myoglobin and fibroblast growth factor-23 (FGF-23)). Results: The regression coefficients (R-2) between eGFR, based on the CKD-EPI-Crea-CystC-formula as reference, and the examined LMWP's could be divided into three groups. Most of the LMWP's associated weakly (R-2 0.7). Almost identical R-2-values were found per LMWP for all eGFR-formulae, with exception of CystC and beta M-2 which showed weaker associations with creatinine-based than with CystC-based eGFR. Conclusion: The association between eGFR and the concentration of several LMWP's is inconsistent, with in general low R-2-values. Thus, the use of eGFR to evaluate kidney function does not reflect the concentration of several LMWP's with proven toxic impact in CKD

No impact of tropospheric ozone on the gross primary productivity of a Belgian pine forest

Imbalance-P paper. Contact with Lore Verryckt: [email protected] stomatal ozone (O3) uptake has been shown to negatively affect crop yields and the growth of tree seedlings. However, little is known about the effect of O3 on the carbon uptake by mature forest trees. This study investigated the effect of high O3 events on gross primary productivity (GPP) for a Scots pine stand near Antwerp, Belgium over the period 1998-2013. Stomatal O3 fluxes were modelled using in situ O3 mixing ratio measurements and a multiplicative stomatal model, which was parameterised and validated for this Scots pine stand. Ozone-induced GPP reduction is most likely to occur during or shortly after days with high stomatal O3 uptake. Therefore, a GPP model within an artificial neural network was parameterised for days with low stomatal O3 uptake rates and used to simulate GPP during periods of high stomatal O3 uptake. Possible negative effects of high stomatal O3 uptake on GPP would then result in an overestimation of GPP by the model during or after high stomatal O3 uptake events. The O3 effects on GPP were linked to AOT40 and POD1. Although the critical levels for both indices were exceeded in every single year, no significant negative effects of O3 on GPP were found, and no correlations between GPP residuals and AOT40 and POD1 were found. Overall, we conclude that no O3 effects were detected on the carbon uptake by this Scots pine stand

Simulation and Analyses of Stage Separation Two-Stage Reusable Launch Vehicles

NASA has initiated the development of methodologies, techniques and tools needed for analysis and simulation of stage separation of next generation reusable launch vehicles. As a part of this activity, ConSep simulation tool is being developed which is a MATLAB-based front-and-back-end to the commercially available ADAMS(registered Trademark) solver, an industry standard package for solving multi-body dynamic problems. This paper discusses the application of ConSep to the simulation and analysis of staging maneuvers of two-stage-to-orbit (TSTO) Bimese reusable launch vehicles, one staging at Mach 3 and the other at Mach 6. The proximity and isolated aerodynamic database were assembled using the data from wind tunnel tests conducted at NASA Langley Research Center. The effects of parametric variations in mass, inertia, flight path angle, altitude from their nominal values at staging were evaluated. Monte Carlo runs were performed for Mach 3 staging to evaluate the sensitivity to uncertainties in aerodynamic coefficients

Simulation and Analyses of Stage Separation of Two-Stage Reusable Launch Vehicles

NASA has initiated the development of methodologies, techniques and tools needed for analysis and simulation of stage separation of next generation reusable launch vehicles. As a part of this activity, ConSep simulation tool is being developed which is a MATLAB-based front-and-back-end to the commercially available ADAMS(Registerd TradeMark) solver, an industry standard package for solving multi-body dynamic problems. This paper discusses the application of ConSep to the simulation and analysis of staging maneuvers of two-stage-to-orbit (TSTO) Bimese reusable launch vehicles, one staging at Mach 3 and the other at Mach 6. The proximity and isolated aerodynamic database were assembled using the data from wind tunnel tests conducted at NASA Langley Research Center. The effects of parametric variations in mass, inertia, flight path angle, altitude from their nominal values at staging were evaluated. Monte Carlo runs were performed for Mach 3 staging to evaluate the sensitivity to uncertainties in aerodynamic coefficients

Impact of pollen on throughfall biochemistry in European temperate and boreal forests

Pollen is known to affect forest throughfall biochemistry, but underlying mechanisms are not fully understood. We used generalized additive mixed modelling to study the relationship between long-term series of measured throughfall fluxes in spring (April–June) at forest plots and corresponding airborne pollen concentrations (Seasonal Pollen Integral, SPIn) from nearby aerobiological monitoring stations. The forest plots were part of the intensive long term monitoring (Level II) network of the UNECE International Co-operative Programme on Assessment and Monitoring of Air Pollution Effects on Forests (ICP Forests) with dominant tree genera Fagus, Quercus, Pinus and Picea, and were distributed all across Europe. We also conducted a 7-day laboratory dissolution experiment with bud scales and flower stalks of European beech (Fagus sylvatica L.), pollen of beech, common oak (Quercus robur L.), silver birch (Betula pendula L.), Scots pine (Pinus sylvestris L.), Corsican pine (Pinus nigra Arnold ssp. laricio (Poiret) Maire), Norway spruce (Picea abies (L.) Karst.) and sterilized pollen of silver birch in a nitrate (NO3--N) solution (11.3 mg N L-1). Throughfall fluxes of potassium (K+), ammonium (NH4+-N), dissolved organic carbon (DOC) and dissolved organic nitrogen (DON) showed a positive relationship with SPIn whereas NO3--N fluxes showed a negative relationship with SPIn. In years with massive seed production of beech and oak SPIn and throughfall fluxes of K+ and DOC were higher, but fluxes of NO3--N were lower. The experiment broadly confirmed the findings based on field data. Within two hours, pollen released large quantities of K+, phosphate, DOC and DON, and lesser amounts of sulphate, sodium and calcium. After 24-48 hours, NO3--N started to disappear, predominantly in the treatments with broadleaved pollen, while concentrations of nitrite and NH4+-N increased. At the end of the experiment, the inorganic nitrogen (DIN) was reduced, presumably because it was lost as gaseous nitric oxide (NO). There was no difference for sterilized pollen, indicating that the involvement of microbial activity was limited in above N transformations. Our results show that pollen dispersal might be an overlooked factor in forest nutrient cycling and might induce complex canopy N transformations, although the net-impact on N throughfall fluxes is rather lo

Matrix Protein 2 Vaccination and Protection against Influenza Viruses, Including Subtype H5N1

Vaccination of mice with influenza matrix protein 2 induced cross-reactive antibody responses

Carbon-nitrogen interactions in European forests and semi-natural vegetation - Part 2: Untangling climatic, edaphic, management and nitrogen deposition effects on carbon sequestration potentials

The effects of atmospheric nitrogen deposition (N$_{dep}$) on carbon (C) sequestration in forests have often been assessed by relating differences in productivity to spatial variations of N$_{dep}$ across a large geographic domain. These correlations generally suffer from covariation of other confounding variables related to climate and other growth-limiting factors, as well as large uncertainties in total (dry+wet) reactive nitrogen (N$_{r}$) deposition.We propose a methodology for untangling the effects of N$_{dep}$ from those of meteorological variables, soil water retention capacity and stand age, using a mechanistic forest growth model in combination with eddy covariance CO$_{2}$ exchange fluxes from a Europe-wide network of 22 forest flux towers. Total N$_{r}$ deposition rates were estimated from local measurements as far as possible. The forest data were compared with data from natural or semi-natural, non-woody vegetation sites. The response of forest net ecosystem productivity to nitrogen deposition (dNEP= dN$_{dep}$) was estimated after accounting for the effects on gross primary productivity (GPP) of the co-correlates by means of a meta-modelling standardization procedure, which resulted in a reduction by a factor of about 2 of the uncorrected, apparent dGPP/dN$_{dep}$ value. This model-enhanced analysis of the C and N$_{dep}$ flux observations at the scale of the European network suggests a mean overall dNEP/dN$_{dep}$ response of forest lifetime C sequestration to N$_{dep}$ of the order of 40–50 g C per g N, which is slightly larger but not significantly different from the range of estimates published in the most recent reviews. Importantly, patterns of gross primary and net ecosystem productivity versus N$_{dep}$ were non-linear, with no further growth responses at high N$_{dep}$ levels (N$_{dep}$ >2.5–3 gNm$^{-2}$ yr$^{-1}$) but accompanied by increasingly large ecosystem N losses by leaching and gaseous emissions. The reduced increase in productivity per unit N deposited at high N$_{dep}$ levels implies that the forecast increased N$_{r}$ emissions and increased Ndep levels in large areas of Asia may not positively impact the continent’s forest CO$_{2}$ sink. The large level of unexplained variability in observed carbon sequestration efficiency (CSE) across sites further adds to the uncertainty in the dC/dN response

Carbon-nitrogen interactions in European forests and semi-natural vegetation - Part 1: Fluxes and budgets of carbon, nitrogen and greenhouse gases from ecosystem monitoring and modelling

The impact of atmospheric reactive nitrogen (N$_{r}$) deposition on carbon (C) sequestration in soils and biomass of unfertilized, natural, semi-natural and forest ecosystems has been much debated. Many previous results of this dC/dN response were based on changes in carbon stocks from periodical soil and ecosystem inventories, associated with estimates of N$_{r}$ deposition obtained from large-scale chemical transport models. This study and a companion paper (Flechard et al., 2020) strive to reduce uncertainties of N effects on C sequestration by linking multi-annual gross and net ecosystem productivity estimates from 40 eddy covariance flux towers across Europe to local measurement-based estimates of dry and wet N$_{r}$ deposition from a dedicated collocated monitoring network. To identify possible ecological drivers and processes affecting the interplay between C and N$_{r}$ inputs and losses, these data were also combined with in situ flux measurements of NO, N$_{2}$O and CH$_{4}$ fluxes; soil NO$_{3}$̅ leaching sampling; and results of soil incubation experiments for N and greenhouse gas (GHG) emissions, as well as surveys of available data from online databases and from the literature, together with forest ecosystem (BASFOR) modelling. Multi-year averages of net ecosystem productivity (NEP) in forests ranged from -70 to 826 gCm$^{-2}$ yr$^{-1}$ at total wet+dry inorganic N$_{r}$ deposition rates (N$_{dep}$) of 0.3 to 4.3 gNm$^{-2}$ yr$^{-1}$ and from -4 to 361 g Cm$^{-2}$ yr$^{-1}$ at N$_{dep}$ rates of 0.1 to 3.1 gNm$^{-2}$ yr$^{-1}$ in short semi-natural vegetation (moorlands, wetlands and unfertilized extensively managed grasslands). The GHG budgets of the forests were strongly dominated by CO$_{2}$ exchange, while CH$_{4}$ and N$_{2}$O exchange comprised a larger proportion of the GHG balance in short semi-natural vegetation. Uncertainties in elemental budgets were much larger for nitrogen than carbon, especially at sites with elevated N$_{dep}$ where N$_{r}$ leaching losses were also very large, and compounded by the lack of reliable data on organic nitrogen and N$_{2}$ losses by denitrification. Nitrogen losses in the form of NO, N$_{2}$O and especially NO$_{3}$̅ were on average 27%(range 6 %–54 %) of N$_{dep}$ at sites with N$_{dep}$ 3 gNm$^{-2}$ yr$^{-1}$. Such large levels of N$_{r}$ loss likely indicate that different stages of N saturation occurred at a number of sites. The joint analysis of the C and N budgets provided further hints that N saturation could be detected in altered patterns of forest growth. Net ecosystem productivity increased with N$_{r}$ deposition up to 2–2.5 gNm$^{-2}$ yr$^{-1}$, with large scatter associated with a wide range in carbon sequestration efficiency (CSE, defined as the NEP = GPP ratio). At elevated N$_{dep}$ levels (> 2.5 gNm$^{-2}$ yr$^{-1}$), where inorganic N$_{r}$ losses were also increasingly large, NEP levelled off and then decreased. The apparent increase in NEP at low to intermediate N$_{dep}$ levels was partly the result of geographical cross-correlations between N$_{dep}$ and climate, indicating that the actual mean dC/dN response at individual sites was significantly lower than would be suggested by a simple, straightforward regression of NEP vs. N$_{dep}$