Minimal kernels of Dirac operators along maps

Let $M$ be a closed spin manifold and let $N$ be a closed manifold. For maps $f\colon M\to N$ and Riemannian metrics $g$ on $M$ and $h$ on $N$, we consider the Dirac operator $D^f_{g,h}$ of the twisted Dirac bundle $\Sigma M\otimes_{\mathbb{R}} f^*TN$. To this Dirac operator one can associate an index in $KO^{-dim(M)}(pt)$. If $M$ is $2$-dimensional, one gets a lower bound for the dimension of the kernel of $D^f_{g,h}$ out of this index. We investigate the question whether this lower bound is obtained for generic tupels $(f,g,h)$

Why genes evolve faster on secondary chromosomes in bacteria

In bacterial genomes composed of more than one chromosome, one replicon is typically larger, harbors more essential genes than the others, and is considered primary. The greater variability of secondary chromosomes among related taxa has led to the theory that they serve as an accessory genome for specific niches or conditions. By this rationale, purifying selection should be weaker on genes on secondary chromosomes because of their reduced necessity or usage. To test this hypothesis we selected bacterial genomes composed of multiple chromosomes from two genera, Burkholderia and Vibrio, and quantified the evolutionary rates (dN and dS) of all orthologs within each genus. Both evolutionary rate parameters were faster among orthologs found on secondary chromosomes than those on the primary chromosome. Further, in every bacterial genome with multiple chromosomes that we studied, genes on secondary chromosomes exhibited significantly weaker codon usage bias than those on primary chromosomes. Faster evolution and reduced codon bias could in turn result from global effects of chromosome position, as genes on secondary chromosomes experience reduced dosage and expression due to their delayed replication, or selection on specific gene attributes. These alternatives were evaluated using orthologs common to genomes with multiple chromosomes and genomes with single chromosomes. Analysis of these ortholog sets suggested that inherently fast-evolving genes tend to be sorted to secondary chromosomes when they arise; however, prolonged evolution on a secondary chromosome further accelerated substitution rates. In summary, secondary chromosomes in bacteria are evolutionary test beds where genes are weakly preserved and evolve more rapidly, likely because they are used less frequently

Machine dependence and reproducibility for coupled climate simulations: the HadGEM3-GC3.1 CMIP Preindustrial simulation

When the same weather or climate simulation is run on different high-performance computing (HPC) platforms, model outputs may not be identical for a given initial condition. While the role of HPC platforms in delivering better climate projections is to some extent discussed in the literature, attention is mainly focused on scalability and performance rather than on the impact of machine-dependent processes on the numerical solution. Here we investigate the behaviour of the Preindustrial (PI) simulation prepared by the UK Met Office for the forthcoming CMIP6 (Coupled Model Intercomparison Project Phase 6) under different computing environments. Discrepancies between the means of key climate variables were analysed at different timescales, from decadal to centennial. We found that for the two simulations to be statistically indistinguishable, a 200-year averaging period must be used for the analysis of the results. Thus, constant-forcing climate simulations using the HadGEM3-GC3.1 model are reproducible on different HPC platforms provided that a sufficiently long duration of simulation is used. In regions where El Niño–Southern Oscillation (ENSO) teleconnection patterns were detected, we found large sea surface temperature and sea ice concentration differences on centennial timescales. This indicates that a 100-year constant-forcing climate simulation may not be long enough to adequately capture the internal variability of the HadGEM3-GC3.1 model, despite this being the minimum simulation length recommended by CMIP6 protocols for many MIP (Model Intercomparison Project) experiments. On the basis of our findings, we recommend a minimum simulation length of 200 years whenever possible

On the Expansions in Spin Foam Cosmology

We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of consistency conditions would be required to control the expansion. We show that the factorisation of the amplitude originally considered is best interpreted in topological terms. We then consider the next higher term in the graph expansion. We demonstrate the tension between the truncation to small graphs and going to the homogeneous sector, and conclude that it is necessary to truncate the dynamics as well.Comment: 17 pages, 4 figures, published versio

Potential Benefits on Impairment of Endothelial Function after a High-Fat Meal of 4 Weeks of Flavonoid Supplementation

Studies with foods high in flavonoids have demonstrated improvement in endothelial function. We investigated whether 4 weeks of flavonoid supplementation would prevent an adverse impact on endothelial function of a high-fat meal. Endothelial function was measured by reactive hyperemia peripheral arterial tonometry (RH-PAT). The RH-PAT index was measured both before and 3 h after a high-fat meal, in 23 healthy volunteers. Subjects were randomized in a double-blind, cross-over design to 4 weeks of daily supplementation with OPC-3, or a matching placebo. RH-PAT index before and after the high-fat meal was measured at the beginning and end of each 4-week treatment phase. The high-fat meal caused a decline in endothelial function at baseline in the placebo (-10.71%, P = .006) and flavonoid [-9.97% (P = .077)] groups, and there was no difference in decline between arms (P = .906). The high-fat meal produced a decline after 4 weeks of placebo [-12.37% (P = .005)], but no decline after 4 weeks of flavonoid supplement [-3.16% (P = .663)], and the difference between the two responses was highly significant (P < .0001). Within-group comparisons revealed no difference in endothelial function decline in the placebo arm between baseline and 4 weeks [-10.71% versus -12.37% (P = .758)]. In the flavonoid supplement arm, the difference in endothelial function decline between baseline and 4 weeks was -9.97% versus -3.16%, but did not reach statistical significance (P = .451). These results suggest that the flavonoid supplement used in this study mitigates the impairment of endothelial function caused by a high-fat meal. Whether certain subpopulations derive greater or lesser benefit remains unclear

Permutation combinatorics of worldsheet moduli space

52 pages, 21 figures52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published version52 pages, 21 figures; minor corrections, "On the" dropped from title, matches published versio

Condensation and Polymerization Explain the Humification of Lignin Into Aliphatic and Aromatic Structures in Soil

Soil organic matter (SOM) constitutes a global reservoir of carbon that is more than twice that of either atmospheric carbon or aquatic carbon; however, the manner in which it forms from degraded plant biomass is poorly understood. Some have recently questioned whether plant biomass is involved directly in SOM formation and suggest that it is microbial carbon that constitutes the main source of stable SOM. Such a view implies that above and below ground plant biomass is rapidly decomposed and mineralized. This view contrasts significantly with traditional ones that involve the transformation of plant biomass to recalcitrant humic materials fueled mainly by lignin. One of the main observations for the new viewpoint is that lignin phenols, biomarkers for lignin in plant biomass, become depleted rapidly in SOM and are thought to indicate that lignin, carbohydrates, proteins, and other plant biopolymers are depleted at the same rate. In the current study we demonstrate that lignin plays a pivotal role in the formation of geologically stable SOM and that the new viewpoint grossly miscalculates the input of microbial biomass. Promoted by the strong oxidation of prevalent reactive oxygen species (ROS) in soil, lignin is not completely mineralized but molecularly transformed to structures not recognizable by lignin phenol biomarker studies. We employ NMR and ultrahigh resolution mass spectrometry on a series of plant biopolymers, synthesized lignin, soil, and peat samples to demonstrate the effect of ROS transformations involving mainly hydroxyl radicals

On globally non-trivial almost-commutative manifolds

Within the framework of Connes' noncommutative geometry, we define and study globally non-trivial (or topologically non-trivial) almost-commutative manifolds. In particular, we focus on those almost-commutative manifolds that lead to a description of a (classical) gauge theory on the underlying base manifold. Such an almost-commutative manifold is described in terms of a 'principal module', which we build from a principal fibre bundle and a finite spectral triple. We also define the purely algebraic notion of 'gauge modules', and show that this yields a proper subclass of the principal modules. We describe how a principal module leads to the description of a gauge theory, and we provide two basic yet illustrative examples.Comment: 34 pages, minor revision

Integrable theories and loop spaces: fundamentals, applications and new developments

We review our proposal to generalize the standard two-dimensional flatness construction of Lax-Zakharov-Shabat to relativistic field theories in d+1 dimensions. The fundamentals from the theory of connections on loop spaces are presented and clarified. These ideas are exposed using mathematical tools familiar to physicists. We exhibit recent and new results that relate the locality of the loop space curvature to the diffeomorphism invariance of the loop space holonomy. These result are used to show that the holonomy is abelian if the holonomy is diffeomorphism invariant. These results justify in part and set the limitations of the local implementations of the approach which has been worked out in the last decade. We highlight very interesting applications like the construction and the solution of an integrable four dimensional field theory with Hopf solitons, and new integrability conditions which generalize BPS equations to systems such as Skyrme theories. Applications of these ideas leading to new constructions are implemented in theories that admit volume preserving diffeomorphisms of the target space as symmetries. Applications to physically relevant systems like Yang Mills theories are summarized. We also discuss other possibilities that have not yet been explored.Comment: 64 pages, 8 figure

Homotopy Theory of Strong and Weak Topological Insulators

We use homotopy theory to extend the notion of strong and weak topological insulators to the non-stable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be "truly d-dimensional", i.e. not realizable by stacking lower-dimensional insulators, a more restrictive definition of "strong" is required. However, this does not exclude weak topological insulators from being "truly d-dimensional", which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of replacing $T^d$ by $S^d$ and $T^{d_k}\times S^{d_x}$ by $S^{d_k+d_x}$ as is common in the current literature.Comment: 11 pages, 3 figure