Error analysis of QR algorithms for computing Lyapunov exponents

Lyapunov exponents give valuable information about long term dynamics. The discrete and continuous QR algorithms are widely used numerical techniques for computing approximate Lyapunov exponents, although they are not yet supported by a general error analysis. Here, a rigorous convergence theory is developed for both the discrete and continuous QR algorithm applied to a constant coefficient linear system with real distinct eigenvalues. For the discrete QR algorithm, the problem essentially reduces to one of linear algebra for which the timestepping and linear algebra errors uncouple and precise convergence rates are obtained. For the continuous QR algorithm, the stability, rather than the local accuracy, of the timestepping algorithm is relevant, and hence the overall convergence rate is independent of the stepsize. In this case it is vital to use a timestepping method that preserves orthogonality in the ODE system. We give numerical results to illustrate the analysis. Further numerical experiments and a heuristic argument suggest that the convergence properties carry through to the case of complex conjugate eigenvalue pairs

The Acoustic Peak in the Lyman Alpha Forest

We present the first simulation of the signature of baryonic acoustic oscillations (BAO) in Lyman alpha forest data containing 180,000 mock quasar sight-lines. We use eight large dark-matter only simulations onto which we paint the Lyman alpha field using the fluctuating Gunn-Peterson approximation. We argue that this approach should be sufficient for the mean signature on the scales of interest. Our results indicate that Lyman alpha flux provides a good tracer of the underlying dark matter field on large scales and that redshift space distortions are well described by a simple linear theory prescription. We compare Fourier and configuration space approaches to describing the signal and argue that configuration space statistics provide useful data compression. We also investigate the effect of a fluctuating photo-ionizing background using a simplified model and find that such fluctuations do add smooth power on large scales. The acoustic peak position is, however, unaffected for small amplitude fluctuations (<10%). Larger amplitude fluctuations make the recovery of the BAO signal more difficult and may degrade the achievable significance of the measurement.Comment: 10 pages, 8 figures; v2: minor revision matching version accepted by JCAP (new references, better figures, clarifications

Vegetation classification in a floristically complex area: the Agulhas Plain

The vegetation of the Agulhas Plain was classified and described using Campbell’s (1985) approach. Data collected included a subset of Campbell’s structural and higher taxon characters, as well as dominant (10% cover) species, which would enable the recognition of communities to at least the sub-series level in his hierarchy. The classification was produced using the Braun–Blanquet method of table sorting. Nine zonal communities, at various hierarchical levels, were recognized and mapped. Non-fynbos communities included Forest & Thicket, and Renoster Shrubland. Fynbos communities, which covered most of the study area, were Mesotrophic Asteraceous Fynbos, Dune Asteraceous Fynbos, Dry Restioid Fynbos, Protea repens Proteoid Fynbos, Protea obtusifolia–Leucadendron meridianum/P. susannae–L. coniferum Proteoid Fynbos, L. platyspermum–P. compacta–L. xanthoconus Proteoid Fynbos and Mesic Ericaceous Fynbos. It was not possible to classify Forest & Thicket below the group level while a new concept (Dune Asteraceous Fynbos) was developed at the sub-series level. In all other respects the largely lowland vegetation of the Agulhas Plain could be integrated with Campbell’s Fynbos Biome mountain vegetation concepts. This study therefore demolished any justification for retaining a lowland fynbos vegetation concept. Since we utilized the skills of a number of trained botanists in collecting easily recognizable structural, and limited floristic data, the entire study was completed in under 18months. The mapped communities are adequate for conservation planning and comprise an essential descriptive basis for future studies on the evolution and maintenance of species diversity on the Agulhas Plain. The efficiency and effectiveness of our approach makes it suitable as a model for rapid vegetation classification of the much-threatened vegetation of the fynbos biome lowlands

Distribution function approach to redshift space distortions. Part IV: perturbation theory applied to dark matter

We develop a perturbative approach to redshift space distortions (RSD) using the phase space distribution function approach and apply it to the dark matter redshift space power spectrum and its moments. RSD can be written as a sum over density weighted velocity moments correlators, with the lowest order being density, momentum density and stress energy density. We use standard and extended perturbation theory (PT) to determine their auto and cross correlators, comparing them to N-body simulations. We show which of the terms can be modeled well with the standard PT and which need additional terms that include higher order corrections which cannot be modeled in PT. Most of these additional terms are related to the small scale velocity dispersion effects, the so called finger of god (FoG) effects, which affect some, but not all, of the terms in this expansion, and which can be approximately modeled using a simple physically motivated ansatz such as the halo model. We point out that there are several velocity dispersions that enter into the detailed RSD analysis with very different amplitudes, which can be approximately predicted by the halo model. In contrast to previous models our approach systematically includes all of the terms at a given order in PT and provides a physical interpretation for the small scale dispersion values. We investigate RSD power spectrum as a function of \mu, the cosine of the angle between the Fourier mode and line of sight, focusing on the lowest order powers of \mu and multipole moments which dominate the observable RSD power spectrum. Overall we find considerable success in modeling many, but not all, of the terms in this expansion.Comment: 37 pages, 13 figures, published in JCA

Higgs bosons near 125 GeV in the NMSSM with constraints at the GUT scale

We study the NMSSM with universal Susy breaking terms (besides the Higgs sector) at the GUT scale. Within this constrained parameter space, it is not difficult to find a Higgs boson with a mass of about 125 GeV and an enhanced cross section in the diphoton channel. An additional lighter Higgs boson with reduced couplings and a mass <123 GeV is potentially observable at the LHC. The NMSSM-specific Yukawa couplings lambda and kappa are relatively large and tan(beta) is small, such that lambda, kappa and the top Yukawa coupling are of order 1 at the GUT scale. The lightest stop can be as light as 105 GeV, and the fine-tuning is modest. WMAP constraints can be satisfied by a dominantly higgsino-like LSP with substantial bino, wino and singlino admixtures and a mass of ~60-90 GeV, which would potentially be detectable by XENON100.Comment: 20 pages, 14 figure

Observations on the pollination of Pelargonium tricolor, section Campylia (Geraniaceae)

A group of four species of Pelargonium L’Hérit. in the section Campylia (Sweet) DC. have embossed ‘warty areas’ at the bases of the posterior petals of the zygomorphic flowers. In Pelargonium tricolor Curt, these embossed areas are most distinctive. The significance of these embossed areas in the attraction of insect pollinators is discussed. From repeated observations of P. tricolor it is concluded that these areas are false nectaries and that they are effective in attracting dipteran pollinators. Megapalpus capensis Wiedemann (Diptera: Bombyliidae), in particular, exhibits strong association with these false nectaries. It is further predicted that the embossed areas on the petals of the remaining three species in the group, namely P. capillare (Cav.) Willd., P. ocellatum J.J.A. van der Walt and P. incarnatum (L’Hérit.) Moench have similar value for attracting anthophilous insects

Using chemical, microbial and fluorescence techniques to understand contaminant sources and pathways to wetlands in a conservation site

Nutrients and faecal contaminants can enter wetland systems in a number of ways, with both biological and potentially human-health implications. In this study we used a combination of inorganic chemistry, dissolved organic matter (DOM) fluorescence and Escherichia coli and total coliform (TC) count techniques to study the sources and multiple pathways of contamination affecting a designated sand dune site of international conservation importance, surrounded by agricultural land. Analysis of stream samples, groundwater and dune slack wetlands revealed multiple input pathways. These included riverbank seepage, runoff events and percolation of nutrients from adjacent pasture into the groundwater, as well as some on-site sources. The combined techniques showed that off-site nutrient inputs into the sand dune system were primarily from fertilisers, revealed by high nitrate concentrations, and relatively low tryptophan-like fulvic-like ratios < 0.4 Raman units (R.U.). The E. coli and TC counts recorded across the site confirm a relatively minor source of bacterial and nutrient inputs from on-site grazers. Attenuation of the nutrient concentrations in streams, in groundwater and in run-off inputs occurs within the site, restoring healthier groundwater nutrient concentrations showing that contaminant filtration by the sand dunes provides a valuable ecosystem service. However, previous studies show that this input of nutrients has a clear adverse ecological impact

Post-weaning and whole-of-life performance of pigs is determined by live weight at weaning and the complexity of the diet fed after weaning

The production performance and financial outcomes associated with weaner diet complexity for pigs of different weight classes at weaning were examined in this experiment. A total of 720 weaner pigs (360 entire males and 360 females) were selected at weaning (27 ± 3 d) and allocated to pens of 10 based on individual weaning weight (light weaning weight: pigs below 6.5 kg; medium weaning weight: 6.5 to 8 kg; heavy weaning weight: above 8.5 kg). Pens were then allocated in a 3 × 2 × 2 factorial arrangement of treatments with the respective factors being weaning weight (heavy, medium and light; H, M and L, respectively), weaner diet complexity (high complexity/cost, HC; low complexity/cost, LC), and gender (male and female). Common diets were fed to both treatment groups during the final 4 weeks of the weaner period (a period of 39 days). In the first 6 d after weaning, pigs offered the HC diets gained weight faster and used feed more efficiently than those offered the LC diets (P = 0.031). Pigs fed a HC diet after weaning tended to be heavier at the sale live weight of 123 d of age compared with pigs fed the LC diet (P = 0.056). There were no other main effects of the feeding program on growth performance through to slaughter. Weaning weight had a profound influence on lifetime growth performance and weight at 123 d of age, with H pigs at weaning increasing their weight advantage over the M and L pigs (101.3, 97.1, 89.6 kg respectively, P < 0.001). Cost-benefit analyses suggested there was a minimal benefit in terms of cost per unit live weight gain over lifetime when pigs were offered a HC feeding program to L, with a lower feed cost/kg gain. The results from this investigation confirm the impact of weaning weight on lifetime growth performance, and suggest that a HC feeding program should be focused on L weaner pigs (i.e., weaning weight less than 6.5 kg at 27 d of age) in order to maximise financial returns

Increasing viscosity of the intestinal contents alters small intestinal structure and intestinal growth, and stimulates proliferation of enterotoxigenic Escherichia coli in newly-weaned pigs

Sources of viscous soluble fibre, such as barley and oats, have often been included in the weaning diet of the pig to accelerate development of the large intestine. Inclusion of a non-fermentable, viscous compound, sodium carboxymethylcellulose (CMC), in a low-fibre weaning diet was tested to assess the influence of digesta viscosity on the gut in the absence of increased fermentation. Two CMC sources, of low and high viscosity, were added to cooked rice-based diet at 40 g/kg total diet. A third control rice diet did not contain any CMC. Diets were fed for 13 d following weaning at 3 weeks of age. Addition of CMC to the diet significantly increased the intestinal viscosity of digesta within the small (P<0.001) and large (P<0.05) intestine. No simple association was found between increases in intestinal viscosity and effects on intestinal morphology and whole-body growth. The average empty-body-weight gain and the small intestinal villus height increased with low-viscosity CMC, but decreased with the high-viscosity CMC group. The full large intestinal weight increased in all pigs fed CMC. Dietary CMC (both low- and high-viscosity) increased the percentage moisture of digesta and faeces, and was associated with increased faecal shedding of enterotoxigenic haemolytic Escherichia coli. Feed ingredients in weaning diets that excessively increase the viscosity of the intestinal digesta may be detrimental to pig health and production

Distribution function approach to redshift space distortions. Part II: N-body simulations

Measurement of redshift-space distortions (RSD) offers an attractive method to directly probe the cosmic growth history of density perturbations. A distribution function approach where RSD can be written as a sum over density weighted velocity moment correlators has recently been developed. We use Nbody simulations to investigate the individual contributions and convergence of this expansion for dark matter. If the series is expanded as a function of powers of mu, cosine of the angle between the Fourier mode and line of sight, there are a finite number of terms contributing at each order. We present these terms and investigate their contribution to the total as a function of wavevector k. For mu^2 the correlation between density and momentum dominates on large scales. Higher order corrections, which act as a Finger-of-God (FoG) term, contribute 1% at k~0.015h/Mpc, 10% at k~0.05h/Mpc at z=0, while for k>0.15h/Mpc they dominate and make the total negative. These higher order terms are dominated by density-energy density correlations which contribute negatively to the power, while the contribution from vorticity part of momentum density auto-correlation is an order of magnitude lower. For mu^4 term the dominant term on large scales is the scalar part of momentum density auto-correlation, while higher order terms dominate for k>0.15h/Mpc. For mu^6 and mu^8 we find it has very little power for k<0.15h/Mpc. We also compare the expansion to the full 2D P^ss(k,mu) as well as to their multipoles. For these statistics an infinite number of terms contribute and we find that the expansion achieves percent level accuracy for kmu<0.15h/Mpc at 6th order, but breaks down on smaller scales because the series is no longer perturbative. We explore resummation of the terms into FoG kernels, which extend the convergence up to a factor of 2 in scale. We find that the FoG kernels are approximately Lorentzian.Comment: 21 pages, 9 figures, published in JCA