Ricci flow for homogeneous compact models of the universe

Using quaternions, we give a concise derivation of the Ricci tensor for homogeneous spaces with topology of the 3-dimensional sphere. We derive explicit and numerical solutions for the Ricci flow PDE and discuss their properties. In the collapse (or expansion) of these models, the interplay of the various components of the Ricci tensor are studied. We dedicate this paper to honor the work of Josh Goldberg.Comment: 18 pages, 2 figure

Bayesian uncertainty analysis for complex systems biology models: emulation, global parameter searches and evaluation of gene functions

Many mathematical models have now been employed across every area of systems biology. These models increasingly involve large numbers of unknown parameters, have complex structure which can result in substantial evaluation time relative to the needs of the analysis, and need to be compared to observed data of various forms. The correct analysis of such models usually requires a global parameter search, over a high dimensional parameter space, that incorporates and respects the most important sources of uncertainty. This can be an extremely difficult task, but it is essential for any meaningful inference or prediction to be made about any biological system. It hence represents a fundamental challenge for the whole of systems biology

How predation and landscape fragmentation affect vole population dynamics

Background: Microtine species in Fennoscandia display a distinct north-south gradient from regular cycles to stable populations. The gradient has often been attributed to changes in the interactions between microtines and their predators. Although the spatial structure of the environment is known to influence predator-prey dynamics of a wide range of species, it has scarcely been considered in relation to the Fennoscandian gradient. Furthermore, the length of microtine breeding season also displays a north-south gradient. However, little consideration has been given to its role in shaping or generating population cycles. Because these factors covary along the gradient it is difficult to distinguish their effects experimentally in the field. The distinction is here attempted using realistic agent-based modelling. Methodology/Principal Findings: By using a spatially explicit computer simulation model based on behavioural and ecological data from the field vole (Microtus agrestis), we generated a number of repeated time series of vole densities whose mean population size and amplitude were measured. Subsequently, these time series were subjected to statistical autoregressive modelling, to investigate the effects on vole population dynamics of making predators more specialised, of altering the breeding season, and increasing the level of habitat fragmentation. We found that fragmentation as well as the presence of specialist predators are necessary for the occurrence of population cycles. Habitat fragmentation and predator assembly jointly determined cycle length and amplitude. Length of vole breeding season had little impact on the oscillations. Significance: There is good agreement between our results and the experimental work from Fennoscandia, but our results allow distinction of causation that is hard to unravel in field experiments. We hope our results will help understand the reasons for cycle gradients observed in other areas. Our results clearly demonstrate the importance of landscape fragmentation for population cycling and we recommend that the degree of fragmentation be more fully considered in future analyses of vole dynamics

Type-Decomposition of a Pseudo-Effect Algebra

The theory of direct decomposition of a centrally orthocomplete effect algebra into direct summands of various types utilizes the notion of a type-determining (TD) set. A pseudo-effect algebra (PEA) is a (possibly) noncommutative version of an effect algebra. In this article we develop the basic theory of centrally orthocomplete PEAs, generalize the notion of a TD set to PEAs, and show that TD sets induce decompositions of centrally orthocomplete PEAs into direct summands.Comment: 18 page

Re-identification of c. 15 700 cal yr BP tephra bed at Kaipo Bog, eastern North Island: implications for dispersal of Rotorua and Puketarata tephra beds.

A 10 mm thick, c. 15 700 calendar yr BP (c. 13 100 14C yr BP) rhyolitic tephra bed in the well-studied montane Kaipo Bog sequence of eastern North Island was previously correlated with Maroa-derived Puketarata Tephra. We revise this correlation to Okataina-derived Rotorua Tephra based on new compositional data from biotite phenocrysts and glass. The new correlation limits the known dispersal of Puketarata Tephra (sensu stricto, c. 16 800 cal yr BP) and eliminates requirements to either reassess its age or to invoke dual Puketarata eruptive events. Our data show that Rotorua Tephra comprises two glass-shard types: an early-erupted low-K2O type that was dispersed mostly to the northwest, and a high-K2O type dispersed mostly to the south and southeast, contemporary with late-stage lava extrusion. Late-stage Rotorua eruptives contain biotite that is enriched in FeO compared with biotite from Puketarata pyroclastics. The occurrence of Rotorua Tephra in Kaipo Bog (100 km from the source) substantially extends its known distribution to the southeast. Our analyses demonstrate that unrecognised syn-eruption compositional and dispersal changes can cause errors in fingerprinting tephra deposits. However, the compositional complexity, once recognised, provides additional fingerprinting criteria, and also documents magmatic and dispersal processes

Pathogenic Potential to Humans of Bovine Escherichia coli O26, Scotland

Escherichia coli O26 and O157 have similar overall prevalences in cattle in Scotland, but in humans, Shiga toxin–producing E. coli O26 infections are fewer and clinically less severe than E. coli O157 infections. To investigate this discrepancy, we genotyped E. coli O26 isolates from cattle and humans in Scotland and continental Europe. The genetic background of some strains from Scotland was closely related to that of strains causing severe infections in Europe. Nonmetric multidimensional scaling found an association between hemolytic uremic syndrome (HUS) and multilocus sequence type 21 strains and confirmed the role of stx<sub>2</sub> in severe human disease. Although the prevalences of E. coli O26 and O157 on cattle farms in Scotland are equivalent, prevalence of more virulent strains is low, reducing human infection risk. However, new data on E. coli O26–associated HUS in humans highlight the need for surveillance of non-O157 enterohemorrhagic E. coli and for understanding stx<sub>2</sub> phage acquisition

Evolution equations of curvature tensors along the hyperbolic geometric flow

We consider the hyperbolic geometric flow $\frac{\partial^2}{\partial t^2}g(t)=-2Ric_{g(t)}$ introduced by Kong and Liu [KL]. When the Riemannian metric evolve, then so does its curvature. Using the techniques and ideas of S.Brendle [Br,BS], we derive evolution equations for the Levi-Civita connection and the curvature tensors along the hyperbolic geometric flow. The method and results are computed and written in global tensor form, different from the local normal coordinate method in [DKL1]. In addition, we further show that any solution to the hyperbolic geometric flow that develops a singularity in finite time has unbounded Ricci curvature.Comment: 15 page

Key drivers of cloud response to surface-active organics

This is the final version. Available on open access from Nature Research via the DOI in this recordData availability: The data used to produce Figs. 1–5 are available from the Bolin database (https://bolin.su.se/data/lowe-2019) and/or upon request from the authors. The observational data in Fig. 4 has been acquired from the EBAS database (www.ebas.nilu.no).Code availability: Plotting, data analysis and simulation setup scripts are available at https://github.com/SamJLowe/NatComms_OrgSurfaceCloudsAerosol-cloud interactions constitute the largest source of uncertainty in global radiative forcing estimates, hampering our understanding of climate evolution. Recent empirical evidence suggests surface tension depression by organic aerosol to significantly influence the formation of cloud droplets, and hence cloud optical properties. In climate models, however, surface tension of water is generally assumed when predicting cloud droplet concentrations. Here we show that the sensitivity of cloud microphysics, optical properties and shortwave radiative effects to the surface phase are dictated by an interplay between the aerosol particle size distribution, composition, water availability and atmospheric dynamics. We demonstrate that accounting for the surface phase becomes essential in clean environments in which ultrafine particle sources are present. Through detailed sensitivity analysis, quantitative constraints on the key drivers – aerosol particle number concentrations, organic fraction and fixed updraft velocity – are derived for instances of significant cloud microphysical susceptibilities to the surface phase.Knut and Alice Wallenberg foundationChemical Sciences Geosciences and Biosciences Division, Office of Basic Energy Sciences, U.S. Department of Energ

Closure between measured and modelled particle hygroscopic growth during TORCH2 implies ammonium nitrate artefact in the HTDMA measurements

International audienceMeasurements of aerosol properties were made in aged polluted and clean background air masses encountered at the North Norfolk (UK) coastline during the second field campaign of the Tropospheric ORganic CHemistry project (TORCH2) in May 2004. Hygroscopic growth factor (GF) measurements were performed at 90% relative humidity (RH) for D0=27?217 nm particles using a Hygroscopicity Tandem Differential Mobility Analyser (HTDMA), while the aerosol composition was simultaneously measured with an Aerodyne aerosol mass spectrometer (Q-AMS). During the clean background events the aerosol was characterised by little size dependence of properties with generally large GFs and inorganic sulphate being the dominant compound. In aged polluted air masses the particles were dominated by inorganic sulphate and nitrate at larger sizes, whereas organics were the largest fraction in smaller particles, thus explaining the trend of smaller GFs at smaller sizes. Organics do contribute to the hygroscopic growth, particularly at small sizes, but generally the dominant contribution to growth at 90% RH comes from inorganic salts. The ZSR mixing rule was used to predict GFs based on the chemical composition, theoretical GFs of pure inorganic salts and a "bulk" GF of ~1.20 for the organics. Good quantitative closure with HTDMA measurements as a function of both particle size and time was achieved in the absence of nitrate. However, GFs were clearly overpredicted at times when a significant fraction of nitrate was present. After careful considerations we attribute the overprediction to substantial evaporation losses of ammonium nitrate in the HTDMA instrument. If true, this implies that the ZSR predictions based on composition might be more representative of the actual "bulk" behaviour of undisturbed ambient particles than the HTDMA measurements. The simplified model approach using the ZSR rule and a constant organic growth factor made high size and time resolution possible, which has proven to be essential for a valid closure study. The ZSR mixing rule appears to be sufficiently accurate, as the GF predictions are more sensitive to the exact GFs of the inorganic compounds than to the growth factor of the moderately hygroscopic organics. Therefore a more detailed analysis and modelling of the organic fraction at the expense of time and size resolution is not worth the effort for an aged aerosol and discrepancies in either direction might even be cancelled out by averaging