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

A Simple Calculus for Discrete Systems, Part B

Mathematical model for man machine development cycle

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

Cognitive network science: A review of research on cognition through the lens of network representations, processes, and dynamics

10.1155/2019/2108423Complexity2019210842

The Effects of a Stably Stratified Region with radially varying Electrical Conductivity on the Formation of Zonal Winds on Gas Planets

The outer areas of Jupiter and Saturn have multiple zonal winds, reaching the high latitudes, that penetrate deep into the planets' interiors, as suggested by gravity measurements. These characteristics are replicable in numerical simulations by including both a shallow stably stratified layer, below a convecting envelope, and increasing electrical conductivity. A dipolar magnetic field, assumed to be generated by a dynamo below our model, is imposed. We find that the winds' depth into the stratified layer depends on the local product of the squared magnetic field strength and electrical conductivity. The key for the drop-off of the zonal winds is a meridional circulation which perturbs the density structure in the stable layer. In the stable region its dynamics is governed by a balance between Coriolis and electromagnetic forces. Our models suggest that a stable layer extending into weakly conducting regions could account for the observed deep zonal wind structures.Comment: Accepted by JGR - Planet

Serum metabolic signatures of primary biliary cirrhosis and primary sclerosing cholangitis

BACKGROUND & AIMS: A greater understanding of cholestatic disease is necessary to advance diagnostic tools and therapeutic options for conditions such as primary biliary cirrhosis (PBC) and primary sclerosing cholangitis (PSC). The purpose of this study was to determine and compare the serum metabolomes of patients with PBC (n = 18) or PSC (n = 21) and healthy controls (n = 10) and to identify metabolites that may differentiate these two cholestatic diseases. METHODS AND RESULTS: Using a mass spectrometry-based, non-targeted biochemical profiling approach, we identified 420 serum metabolites, 101 that differed significantly (P ≤ 0.05) between PBC and control groups, 115 that differed significantly between PSC and control groups, and 56 that differed significantly between PSC and PBC groups. Random forest classification analysis was able to distinguish patients with PBC or PSC with 95% accuracy with selected biochemicals reflective of protein and amino acid metabolism identified as the major contributors. Metabolites related to bile acid metabolism, lipid metabolism, inflammation, and oxidative stress/lipid peroxidation were also identified as differing significantly when comparing the disease groups and controls, with some of these pathways differentially affected in the PBC and PSC groups. CONCLUSION: In this study, we identified novel metabolic changes associated with cholestatic disease that were both consistent and different between PBC and PSC. Validation studies in larger patient cohorts are required to determine the utility of these biochemical markers for diagnosis and therapeutic monitoring of patients with PBC and PSC

A quadratic stability result for singular switched systems with application to anti-windup control

In this note we consider the problem of determining necessary and sufficient conditions for the existence of a common quadratic Lyapunov function for a pair of stable linear time-invariant systems whose system matrices are of the form A, A−ghT , and where one of the matrices is singular. We then apply this result in a study of a feedback system with a saturating actuator