Reflection positive doubles

Here we introduce reflection positive doubles, a general framework for reflection positivity, covering a wide variety of systems in statistical physics and quantum field theory. These systems may be bosonic, fermionic, or parafermionic in nature. Within the framework of reflection positive doubles, we give necessary and sufficient conditions for reflection positivity. We use a reflection-invariant cone to implement our construction. Our characterization allows for a direct interpretation in terms of coupling constants, making it easy to check in concrete situations. We illustrate our methods with numerous examples

Switching to nonhyperbolic cycles from codimension two bifurcations of equilibria of delay differential equations

In this paper we perform the parameter-dependent center manifold reduction near the generalized Hopf (Bautin), fold-Hopf, Hopf-Hopf and transcritical-Hopf bifurcations in delay differential equations (DDEs). This allows us to initialize the continuation of codimension one equilibria and cycle bifurcations emanating from these codimension two bifurcation points. The normal form coefficients are derived in the functional analytic perturbation framework for dual semigroups (sun-star calculus) using a normalization technique based on the Fredholm alternative. The obtained expressions give explicit formulas which have been implemented in the freely available numerical software package DDE-BifTool. While our theoretical results are proven to apply more generally, the software implementation and examples focus on DDEs with finitely many discrete delays. Together with the continuation capabilities of DDE-BifTool, this provides a powerful tool to study the dynamics near equilibria of such DDEs. The effectiveness is demonstrated on various models

On Local Bifurcations in Neural Field Models with Transmission Delays

Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay equations, among which DDE. In particular, it may be used advantageously for the investigation of stability and bifurcation of steady states. After introducing the neural field model in its basic functional analytic setting and discussing its spectral properties, we elaborate extensively an example and derive a characteristic equation. Under certain conditions the associated equilibrium may destabilise in a Hopf bifurcation. Furthermore, two Hopf curves may intersect in a double Hopf point in a two-dimensional parameter space. We provide general formulas for the corresponding critical normal form coefficients, evaluate these numerically and interpret the results

Does alpha phase modulate visual target detection? Three experiments with tACS-phase-based stimulus presentation

In recent years, the influence of alpha (7–13 Hz) phase on visual processing has received a lot of attention. Magneto‐/encephalography (M/EEG) studies showed that alpha phase indexes visual excitability and task performance. Studies with transcranial alternating current stimulation (tACS) aim to modulate oscillations and causally impact task performance. Here, we applied right occipital tACS (O2 location) to assess the functional role of alpha phase in a series of experiments. We presented visual stimuli at different pre‐determined, experimentally controlled, phases of the entraining tACS signal, hypothesizing that this should result in an oscillatory pattern of visual performance in specifically left hemifield detection tasks. In experiment 1, we applied 10 Hz tACS and used separate psychophysical staircases for six equidistant tACS‐phase conditions, obtaining contrast thresholds for detection of visual gratings in left or right hemifield. In experiments 2 and 3, tACS was at EEG‐based individual peak alpha frequency. In experiment 2, we measured detection rates for gratings with (pseudo‐)fixed contrast. In experiment 3, participants detected brief luminance changes in a custom‐built LED device, at eight equidistant alpha phases. In none of the experiments did the primary outcome measure over phase conditions consistently reflect a one‐cycle sinusoid. However, post hoc analyses of reaction times (RT) suggested that tACS alpha phase did modulate RT for specifically left hemifield targets in both experiments 1 and 2 (not measured in experiment 3). This observation requires future confirmation, but is in line with the idea that alpha phase causally gates visual inputs through cortical excitability modulation

The effects of dietary fibre type on satiety-related hormones and voluntary food intake in dogs

Depending on type and inclusion level, dietary fibre may increase and maintain satiety and postpone the onset of hunger. This 7-week study evaluated the effect of fibre fermentability on physiological satiety-related metabolites and voluntary food intake (VFI) in dogs. Sixteen healthy adult dogs were fed a low-fermentable fibre (LFF) diet containing 8·5 % cellulose or a high-fermentable fibre (HFF) diet containing 8·5 % sugarbeet pulp and 2 % inulin. Large intestinal fibre degradation was evaluated by apparent faecal digestibility of nutrients and faecal SCFA and NH3 concentrations. Postprandial blood samples were obtained to determine postprandial plasma glucose, insulin, total peptide tyrosine–tyrosine (PYY), total glucagon-like peptide-1 (GLP-1) and total ghrelin concentrations. At the end of the study, the dogs were given a single meal of a dry dog food to determine VFI. Dogs fed the HFF diet had a significantly higher large intestinal fibre degradation and production of SCFA compared with the dogs fed the LFF diet. The HFF-fed dogs tended (P = 0·058) to show a lower VFI at the end of the study. No treatment effects were found for postprandial plasma glucose, PYY, GLP-1 and ghrelin responses. The concentrations of these metabolites could not be related to the observed difference in VFI. The inclusion of fermentable fibre in canine diets may contribute to the prevention or mitigation of obesity through its effects on satiety. The underlying mechanisms require further investigatio

Age Determination of a Granite Gneiss from the Precambrian Basement of Scioto County, Ohio

Author Institution: Department of Geology and Mineralogy, The Ohio State University, Columbus, Ohio 43210 and Ohio Division of Geological Survey, Columbus, Ohio 43212Biotite and potassium feldspar from a specimen of granite gneiss from the Precambrian basement of Scioto County (Permit No. 212, Greenup Quadrangle of Green Township) have been dated by the Rb-Sr method. The model dates, calculated relative to an assumed initial 87Sr/86Sr ratio of 0.7040, are 898±40 million years (biotite) and 1242±46 million years (potassium feldspar). The dates are discordant, which suggests that the minerals gained or lost rubidium and/or strontium during an episode of metamorphism. The age of the metamorphism is estimated as 840=t42 million years, assuming that both minerals were isotopically re-equilibrated and had the same 87Sr/86Sr ratio of 0.7178± 0.0026. The model date of the biotite agrees with previous age determinations of basement rocks from Ohio and confirms the interpretation that the Grenville Province of the Canadian Precambrian Shield extends southward into Ohio

Direct current control of three magnon scattering processes in spin-valve nanocontacts

We have investigated the generation of spin waves in the free layer of an extended spin-valve structure with a nano-scaled point contact driven by both microwave and direct electric current using Brillouin light scattering microscopy. Simultaneously with the directly excited spin waves, strong nonlinear effects are observed, namely the generation of eigenmodes with integer multiple frequencies (2 \emph{f}, 3 \emph{f}, 4 \emph{f}) and modes with non-integer factors (0.5 \emph{f}, 1.5 \emph{f}) with respect to the excitation frequency \emph{f}. The origin of these nonlinear modes is traced back to three magnon scattering processes. The direct current influence on the generation of the fundamental mode at frequency \emph{f} can be related to the spin-transfer torque, while the efficiency of three-magnon-scattering processes is controlled by the Oersted field as an additional effect of the direct current