From U-bounds to isoperimetry with applications to H-type groups

In this paper we study applications of U-bounds to coercive and isoperimetric problems for probability measures on finite and infinite products of H-type groups.Comment: 40 pages, with addition

Quasi-periodic pulsations in solar and stellar flares: re-evaluating their nature in the context of power-law flare Fourier spectra

The nature of quasi-periodic pulsations in solar and stellar flares remains debated. Recent work has shown that power-law-like Fourier power spectra, also referred to as 'red' noise processes, are an intrinsic property of solar and stellar flare signals, a property that many previous studies of this phenomenon have not accounted for. Hence a re-evaluation of the existing interpretations and assumptions regarding QPP is needed. Here we adopt a Bayesian method for investigating this phenomenon, fully considering the Fourier power law properties of flare signals. Using data from the PROBA2/LYRA, Fermi/GBM, Nobeyama Radioheliograph and Yohkoh/HXT instruments, we study a selection of flares from the literature identified as QPP events. Additionally we examine optical data from a recent stellar flare that appears to exhibit oscillatory properties. We find that, for all but one event tested, an explicit oscillation is not required in order to explain the observations. Instead, the flare signals are adequately described as a manifestation of a power law in the Fourier power spectrum, rather than a direct signature of oscillating components or structures. However, for the flare of 1998 May 8, strong evidence for the existence of an explicit oscillation with P ~ 14-16 s is found in the 17 GHz radio data and the 13-23 keV Yohkoh HXT data. We conclude that, most likely, many previously analysed events in the literature may be similarly described in terms of power laws in the flare Fourier power spectrum, without the need to invoke a narrowband, oscillatory component. As a result the prevalence of oscillatory signatures in solar and stellar flares may be less than previously believed. The physical mechanism behind the appearance of the observed power laws is discussed.Comment: 11 pages, 7 figures, 1 table. Accepted for publication in The Astrophysical Journa

Electroshock protection circuit

Circuit was developed to prevent accidental shock through electrodes used to test subjects as part of Skylab program. This circuit is placed between electrical apparatus and electrode that is attached to patient's body. Thus, patient is effectively protected from dangerous electrical shock that might be caused by failure in electrical apparatus

Indirect observation of phase conjugate magnons from non-degenerate four-wave mixing

A phase conjugate mirror utilising four-wave mixing in a magnetic system is experimentally realised for the first time. Indirect evidence of continuous-wave phase conjugation has been observed experimentally and is supported by simulations. The experiment utilizes a pump-probe method to excite a four-wave mixing process. Two antennae are used to pump a region of a thin-film yttrium iron garnet waveguide with magnons of frequency $f_{1}$ to create a spatio-temporally periodic potential. As the probe magnons of $f_{\mathrm{p}}$ impinge on the pumped region, a signal with frequency $f_{\mathrm{c}} = 2f_{1}-f_{\mathrm{p}}$ is observed. The amplitude of the nonlinear signal was highly dependent on the applied magnetic field $H$. Width modes of the probe magnons and standing wave modes of the pump magnons were shown to affect the amplitude of the signal at $f_{\mathrm{c}}$. Experimental data is compared with simulations and theory to suggest that $f_{\mathrm{c}}$ is a phase conjugate of $f_{\mathrm{p}}$.Comment: 6 pages, 6 figure

Particle systems with a singular mean-field self-excitation. Application to neuronal networks

We discuss the construction and approximation of solutions to a nonlinear McKean-Vlasov equation driven by a singular self-excitatory interaction of the mean-field type. Such an equation is intended to describe an infinite population of neurons which interact with one another. Each time a proportion of neurons 'spike', the whole network instantaneously receives an excitatory kick. The instantaneous nature of the excitation makes the system singular and prevents the application of standard results from the literature. Making use of the Skorohod M1 topology, we prove that, for the right notion of a 'physical' solution, the nonlinear equation can be approximated either by a finite particle system or by a delayed equation. As a by-product, we obtain the existence of 'synchronized' solutions, for which a macroscopic proportion of neurons may spike at the same time

A general framework for stochastic traveling waves and patterns, with application to neural field equations

In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular the framework can incorporate versions of the stochastic neural field equation that may exhibit traveling fronts, pulses or stationary patterns. To do this, we first formulate a local SDE that describes the position of the stochastic wave up until a discontinuity time, at which point the position of the wave may jump. We then study the local stability of this stochastic front, obtaining a result that recovers a well-known deterministic result in the small-noise limit. We finish with a study of the long-time behavior of the stochastic wave.Comment: 43 pages, 3 figure

Displaying 3D images: algorithms for single-image random-dot

A new, simple, and symmetric algorithm can be implemented that results in higher levels of detail in solid objects than previously possible with autostereograms. In a stereoscope, an optical instrument similar to binoculars, each eye views a different picture and thereby receives the specific image that would have arisen naturally. An early suggestion for a color stereo computer display involved a rotating filter wheel held in front of the eyes. In contrast, this article describes a method for viewing on paper or on an ordinary computer screen without special equipment, although it is limited to the display of 3D monochromatic objects. (The image can be colored, say, for artistic reasons, but the method we describe does not allow colors to be allocated in a way that corresponds to an arbitrary coloring of the solid object depicted.) The image can easily be constructed by computer from any 3D scene or solid object description