Transition from rotating waves to modulated rotating waves on the sphere

We study non-resonant and resonant Hopf bifurcation of a rotating wave in SO(3)-equivariant reaction-diffusion systems on a sphere. We obtained reduced differential equations on so(3), the characterization of modulated rotating waves obtained by Hopf bifurcation of a rotating wave, as well as results regarding the resonant case. Our main tools are the equivariant center manifold reduction and the theory of Lie groups and Lie algebras, especially for the group SO(3) of all rigid rotations on a sphere

Bifurcation from relative periodic solutions

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Short oestrous cycles in sheep during anoestrus involve defects in progesterone biosynthesis and luteal neovascularisation

Anoestrous ewes can be induced to ovulate by the socio-sexual, 'ram effect'. However, in some ewes the induced ovulation is followed by an abnormally short luteal phase causing a so called, "short cycle". The defect responsible for this luteal dysfunction has not been identified. In this experiment we investigated ovarian and uterine factors implicated in male-induced short cycles in anoestrus ewes using a combined endocrine and molecular strategy. Prior to ovulation, we were able to detect a moderate loss of thecal expression of steroid acute regulatory protein (STAR) in ewes that had not received progesterone priming (which prevents short cycles). At and following ovulation we were able to identify significant loss of expression of genes coding key proteins involved in the biosynthesis of progesterone (STAR, CYP11A1, HSD3B) as well as genes coding proteins critical for vascular development during early luteal development (VEGFA, VEGFR2) suggesting dysfunction in at least two pathways critical for normal luteal function. Furthermore, these changes were associated with a significant reduction of progesterone production and luteal weight. Additionally, we cast doubt on the proposed uterine-mediated effect of prostaglandin F2α as a cause of short cycles by demonstrating both the dysregulation of luteal expression of the PGF receptor, which mediates the luteal effects of PGF2α, and by finding no significant changes in the circulating concentrations of PGFM, the principal metabolite of PGF2α in ewes with short cycles. This study is the first of its kind to examine concurrently, the endocrine and molecular events in the follicular and early luteal stages of the short cycle

A novel method for evaluating the critical nucleus and the surface tension in systems with first order phase transition

We introduce a novel method for calculating the size of the critical nucleus and the value of the surface tension in systems with first order phase transition. The method is based on classical nucleation theory, and it consists in studying the thermodynamics of a sphere of given radius embedded in a frozen metastable surrounding. The frozen configuration creates a pinning field on the surface of the free sphere. The pinning field forces the sphere to stay in the metastable phase as long as its size is smaller than the critical nucleus. We test our method in two first-order systems, both on a two-dimensional lattice: a system where the parameter tuning the transition is the magnetic field, and a second system where the tuning parameter is the temperature. In both cases the results are satisfying. Unlike previous techniques, our method does not require an infinite volume limit to compute the surface tension, and it therefore gives reliable estimates even by using relatively small systems. However, our method cannot be used at, or close to, the critical point, i.e. at coexistence, where the critical nucleus becomes infinitely large.Comment: 12 pages, 15 figure

Riverine transport of biogenic elements to the Baltic Sea ? past and possible future perspectives

International audienceThe paper reviews critical processes for the land-sea fluxes of biogenic elements (C, N, P, Si) in the Baltic Sea catchment and discusses possible future scenarios as a consequence of improved sewage treatment, agricultural practices and increased hydropower demand (for N, P and Si) and of global warming, i.e., changes in hydrological patterns (for C). These most significant drivers will not only change the total amount of nutrient inputs and fluxes of organic and inorganic forms of carbon to the Baltic Sea, their ratio (C:N:P:Si) will alter as well with consequences for phytoplankton species composition in the Baltic Sea. In summary, we propose that N fluxes may increase due to higher livestock densities in those countries recently acceded to the EU, whereas P and Si fluxes may decrease due to an improved sewage treatment in these new EU member states and with further damming and still eutrophic states of many lakes in the entire Baltic Sea catchment. This might eventually decrease cyanobacteria blooms in the Baltic but increase the potential for other nuisance blooms. Dinoflagellates could eventually substitute diatoms that even today grow below their optimal growth conditions due to low Si concentrations in some regions of the Baltic Sea. C fluxes will probably increase from the boreal part of the Baltic Sea catchment due to the expected higher temperatures and heavier rainfall. However, it is not clear whether dissolved organic carbon and alkalinity, which have opposite feedbacks to global warming, will increase in similar amounts, because the spring flow peak will be smoothed out in time due to higher temperatures that cause less snow cover and deeper soil infiltration

Xanthomonas campestris pv. campestris race 1 is the main causal agent of black rot of Brassicas in Southern Mozambique

Severe outbreaks of bacterial black rot caused by Xanthomonas campestris pv. campestris (Xcc) were observed in Brassica production fields of Southern Mozambique. The causal agent of the disease in the Mahotas and Chòkwé districts was identified and characterised. In total, 83 Xanthomonas-like strains were isolated from seed samples and leaves of cabbage and tronchuda cole with typical symptoms of the disease. Forty-six out of the 83 strains were found to be putative Xcc in at least one of the tests used: Classical biochemical assays, enzyme-linked immunosorbent assay (ELISA) with monoclonal antibodies, Biolog identification system, polymerase chain reaction (PCR) with specific primers and pathogenicity tests. The ELISA tests were positive for 43 strains. Biolog identified 43 strains as Xanthomonas, but only 32 as Xcc. PCR tests with primers targeting a fragment of the hrpF gene were positive for all 46 strains tested. Three strains were not pathogenic or weakly pathogenic and all other strains caused typical black rot symptoms in brassicas. Race type differentiation tests revealed the Xcc strains from Mozambique as members of race 1. The prevalence of this pathogenic race of the Xcc pathogen in Mozambique should be considered when black rot resistant cultivars are evaluated or introduced into the production regions of this country

Forced Symmetry Breaking from SO(3) to SO(2) for Rotating Waves on the Sphere

We consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating wave on the sphere that persists to a normally hyperbolic SO(2)-invariant manifold $M(\epsilon)$. We investigate the effects of this forced symmetry breaking by studying the perturbed dynamics induced on $M(\epsilon)$ by the above reaction-diffusion system. We prove that depending on the frequency vectors of the rotating waves that form the relative equilibrium SO(3)u_{0}, these rotating waves will give SO(2)-orbits of rotating waves or SO(2)-orbits of modulated rotating waves (if some transversality conditions hold). The orbital stability of these solutions is established as well. Our main tools are the orbit space reduction, Poincare map and implicit function theorem

KCa3.1 inhibition switches the phenotype of glioma-infiltrating microglia/macrophages

Among the strategies adopted by glioma to successfully invade the brain parenchyma is turning the infiltrating microglia/macrophages (M/MΦ) into allies, by shifting them toward an anti-inflammatory, pro-tumor phenotype. Both glioma and infiltrating M/MΦ cells express the Ca(2+)-activated K(+) channel (KCa3.1), and the inhibition of KCa3.1 activity on glioma cells reduces tumor infiltration in the healthy brain parenchyma. We wondered whether KCa3.1 inhibition could prevent the acquisition of a pro-tumor phenotype by M/MΦ cells, thus contributing to reduce glioma development. With this aim, we studied microglia cultured in glioma-conditioned medium or treated with IL-4, as well as M/MΦ cells acutely isolated from glioma-bearing mice and from human glioma biopsies. Under these different conditions, M/MΦ were always polarized toward an anti-inflammatory state, and preventing KCa3.1 activation by 1-[(2-Chlorophenyl)diphenylmethyl]-1H-pyrazole (TRAM-34), we observed a switch toward a pro-inflammatory, antitumor phenotype. We identified FAK and PI3K/AKT as the molecular mechanisms involved in this phenotype switch, activated in sequence after KCa3.1. Anti-inflammatory M/MΦ have higher expression levels of KCa3.1 mRNA (kcnn4) that are reduced by KCa3.1 inhibition. In line with these findings, TRAM-34 treatment, in vivo, significantly reduced the size of tumors in glioma-bearing mice. Our data indicate that KCa3.1 channels are involved in the inhibitory effects exerted by the glioma microenvironment on infiltrating M/MΦ, suggesting a possible role as therapeutic targets in glioma

Feasibility of Establishing Small Livestock Slaughter Plants in North Dakota

Agribusiness,