Generic bifurcation of Hamiltonian vector fields with symmetry

One of the goals of this paper is to describe explicitly the generic movement of eigenvalues through a one-to-one resonance in a linear Hamiltonian system which is equivariant with respect to a symplectic representation of a compact Lie group. We classify this movement, and hence answer the question of when the collisions are 'dangerous' in the sense of Krein by using a combination of group theory and definiteness properties of the associated quadratic Hamiltonian. For example, for systems with no symmetry or O(2) symmetry generically the eigenvalues split, whereas for systems with S1 symmetry, generically the eigenvalues may split or pass. It is in this last case that one has to use both group theory and energetics to determine the generic eigenvalue movement. The way energetics and group theory are combined is summarized in table 1. The result is to be contrasted with the bifurcation of steady states (zero eigenvalue) where one can use either group theory alone (Golubitsky and Stewart) or definiteness properties of the Hamiltonian (Cartan-Oh) to determine whether the eigenvalues split or pass on the imaginary axis

Amyloid beta dimer/trimer: a potent stimulator of neuronal amyloid beta secretion and cofilin-actin rod formation, The

2010 Fall.Includes bibliographical references.Amyloid beta (Aβ) peptides, a heterogeneous mixture of 39-43 amino acid peptides produced from β- and γ-secretase cleavage of the amyloid precursor protein (APP), are one of the causative agents of Alzheimer disease (AD). Although sensitive enzyme-linked immunosorbent assays (ELISAs) for specific rodent Aβ peptides and for total and specific human Aβ peptides have been commercially available, no commercial assay for total rodent Aβ was available when we began these studies. Such an assay is desirable to determine the effects of the human Aβ peptides on production of Aβ from cultured rodent neurons, the major model system used in AD research. Here we report an ELISA for total rodent Aβ and show that it can be used without interference from physiologically relevant concentrations of human Aβ. We then apply the assay to measure the production of Aβ in cultured dissociated rat cortical neurons and rat and mouse hippocampal organotypic slices in response to oxidative stress or treatment with human Aβ dimer/trimer (Aβd/t) obtained from culture medium of Chinese hamster ovary cell line 7PA2 expressing a mutant form of human amyloid precursor protein. Neither of the treatments leads to accumulation of intracellular Aβ peptides. Peroxide increases Aβ secretion by about 2 fold, similar to results from previous reports that used an immunoprecipitation and western blot assay. Of greater significance is that physiologically relevant concentrations (250 pM) of human Aβd/t increase rodent Aβ secretion by >3 fold over 4 days, providing support for an Aβ-mediated feed-forward model of AD progression. The over two fold increase in rodent Aβ secreted in response to human Aβd/t was nearly identical between organotypic hippocampal slices of TAU knock-out mice and TAU knock-out mice expressing the human tau transgene, demonstrating that tau plays no role in the enhanced production of Aβ. Previous studies showed oligomers of synthetic amyloid beta (Aβ1-42) induced cofilin activation and formation of cofilin-actin rods in a neuronal subpopulation of rat hippocampus primarily localized within the dentate gyrus. Here we demonstrate that Aβd/t at ~250 pM is more potent in rod induction in both dissociated hippocampal neuronal cultures and organotypic slices than is 1 μM synthetic Aβ as typically prepared oligomers, about a 4000 fold difference. Treatment of the Aβd/t fraction with an Aβ-neutralizing antibody eliminates its rod inducing activity. Traditionally prepared synthetic Aβ oligomers contain SDS-stable trimers and tetramers, but are devoid of dimers. When synthetic human Aβ was incubated under conditions that generate a tyrosine oxidized dimer, the concentration that was required to induce rods decreased dramatically. The oxidized dimer had a maximum rod-inducing activity at ~2 nM (10 ng/mL), suggesting it is the presence of the SDS-stable tyrosine oxidized Aβ dimer in a low-n state that is largely responsible for the potency of the secreted Aβd/t. Aβd/t-induced rods are highly localized to the dentate gyrus and mossy fiber pathway and form more rapidly (significant over controls by 2 h compared to 8 h for those induced by synthetic Aβ-oligomers). Aβd/t-induced rods are reversible, disappearing by 24 h after washout. Cofilin dephosphorylation in response to Aβd/t is greatest within the hippocampal regions of rod formation. Overexpression of cofilin phosphatases slingshot and chronophin increase rod formation when expressed alone and exacerbate rod formation when coupled with Aβd/t treatment both in dissociated neurons and organotypic slice cultures. Overexpression of the cofilin kinase, LIM kinase 1, inhibits Aβd/t-induced rod formation. Together these data support a mechanism through which Aβd/t produces selective synaptic dysfunction affecting learning and memory at least in part via primary effects on cofilin regulation and rod formation in sensitive hippocampal regions

Magnetic fields and differential rotation on the pre-main sequence

Maps of magnetic field topologies of rapidly rotating stars obtained over the last decade or so have provided unique insight into the operation of stellar dynamos. However, for solar-type stars many of the targets imaged to date have been lower-mass zero-age main sequence stars. We present magnetic maps and differential rotation measurements of two-higher mass pre-main sequence stars HD 106506 (~10 Myrs) and HD 141943 (~15 Myrs). These stars should evolve into mid/late F-stars with predicted high differential rotation and little magnetic activity. We investigate what effect the extended convection zones of these pre-main sequence stars has on their differential rotation and magnetic topologies. ©2009 American Institute of Physic

Platform values and democratic elections: how can the law regulate digital disinformation?

This article examines how governments can regulate the values of social media companies that themselves regulate disinformation spread on their own platforms. We use ‘disinformation’ to refer to motivated faking of news. We examine the effects that disinformation initiatives (many based on automated decision-making systems using Artificial Intelligence [AI] to cope with the scale of content being shared) have on freedom of expression, media pluralism and the exercise of democracy, from the wider lens of tackling illegal content online and concerns to request proactive (automated) measures of online intermediaries. We particularly focus on the responses of the member states and institutions of the European Union. In Section 1, we argue that the apparent significance of the threat has led many governments to legislate despite this lack of evidence, with over 40 national laws to combat disinformation chronicled by March 2019. Which types of regulation are proposed, which actors are targeted, and who is making these regulations? Regulating fake news should not fall solely on national governments or supranational bodies like the European Union. Neither should the companies be responsible for regulating themselves. Instead, we favour co-regulation. Co-regulation means that the companies develop – individually or collectively – mechanisms to regulate their own users, which in turn must be approved by democratically legitimate state regulators or legislatures, who also monitor their effectiveness. In Section 2, we explain the current EU use of Codes of Conduct. In Section 3, we then explain the relatively novel idea that social media content regulation, and specifically disinformation, can be dealt with by deploying AI at massive scale. It is necessary to deal with this technological issue in order to explain the wider content of co-regulatory policy options, which we explain and for which we argue in Section 4. In Section 5 we explain what this means for technology regulation generally, and the socio-economic calculus in this policy field

Is graphene on copper doped?

Angle-resolved photoemission spectroscopy (ARPES) and X-ray photoemission spectroscopy have been used to characterise epitaxially ordered graphene grown on copper foil by low-pressure chemical vapour deposition. A short vacuum anneal to 200 °C allows observation of ordered low energy electron diffraction patterns. High quality Dirac cones are measured in ARPES with the Dirac point at the Fermi level (undoped graphene). Annealing above 300 °C produces n-type doping in the graphene with up to 350 meV shift in Fermi level, and opens a band gap of around 100 meV. Dirac cone dispersion for graphene on Cu foil after vacuum anneals (left: 200 °C, undoped; right: 500 °C, n-doped). Centre: low energy electron diffraction from graphene on Cu foil after 200 °C anneal. Data from Antares (SOLEIL)

The constrained Liapunov-Schmidt procedure and periodic orbits

This paper develops the Liapunov-Schmidt procedure for systems with additional constraints such as having a first integral, being Hamiltonian, or being a gradient system. Similar developments for systems with symmetry, including reversibility, are well known, and the method of this paper augments and is consistent with that approach. One of the results states that the bifurcation equation for Hamiltonian systems is actually a Hamiltonian vector field. In general, we use "implicit constraints" to encode the information constraining the system. The method is applied to the Liapunov center theorem for reversible systems and systems with an integral, as well as to the Hamiltonian Hopf bifurcation and resonance bifurcations for Hamiltonian and reversible systems

Discovery of the magnetic field in the B1/B2V star sigma Lupi

The ultraviolet stellar wind lines of the photometrically periodic variable early B-type star sigma Lupi were found to behave very similarly to what has been observed in known magnetic B stars, although no periodicity could be determined. AAT spectropolarimetric measurements with SEMPOL were obtained. We detected a longitudinal magnetic field with varying strength and amplitude of about 100 G with error bars of typically 20 G. This type of variability supports an oblique magnetic rotator model. We fold the equivalent width of the 4 usable UV spectra in phase with the well-known photometric period of 3.019 days, which we identify with the rotation period of the star. The magnetic field variations are consistent with this period. Additional observations with ESPaDOnS attached to the CFHT strongly confirmed this discovery, and allowed to determine a precise magnetic period. Like in the other magnetic B stars the wind emission likely originates in the magnetic equatorial plane, with maximum emission occurring when a magnetic pole points towards the Earth. The 3.0182 d magnetic rotation period is consistent with the photometric period, with maximum light corresponding to maximum magnetic field. No helium or other chemical peculiarity is known for this object.Comment: 2 pages, 2 figures, to appear in the proceedings of IAU Symposium 272, Active OB stars - structure, evolution, mass loss, and critical limit