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

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

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

Sex differences in the neural control of muscle

Sex-differences in muscle strength have been linked to differences in muscle size, involved limb, and daily activities. Early work has shown that sex-differences are greater in the upper compared to lower limb, making the upper limb an ideal model to investigate the best statistical approaches for sex comparison. Large differences in the upper limb reveals how biomechanical factors may impact neural control. Since males and females are more comparable with respect to strength in the lower limb, it allows for a determination of whether potential sex-differences in neural control exist without large differences in biomechanics. Understanding sex-differences allows for prescription of rehabilitation and training modalities, taking into account potential specificities in sex-related neuromuscular and musculoskeletal factors. The overall purpose was to examine neural and biomechanical differences that would account for sex-differences in neural control of muscle. Manuscript 1 examined normalization versus an ANCOVA to assess sex-differences. Sex-differences were seen in elbow flexor strength and rate of force development (RFD). Normalization by either maximum strength or neural factors couldn’t account for all sex-differences in RFD, resulting in an ambiguous interpretation. In contrast, both variables were able to be incorporated in an ANCOVA to determine their relative contribution. Manuscript 2 examined the effect of task familiarization and the contribution of maximum strength, twitch contraction time, muscle fiber condition velocity, and rate of muscle activation to sex-differences in the RFD during dorsiflexion. There were no significant differences between the sexes in muscle properties, but there were differences in neural control. Additionally, across days females exhibited a neural adaptation leading to an improvement in the RFD. Manuscript 3 directly assessed potential sex-differences in neural control during force gradation by recording motor unit activity during maximal and submaximal contractions. Females had less force steadiness (FS), which may have resulted from neural compensation for a less optimal pennation angle or a tendency towards greater joint laxity. Higher motor unit discharge rates and incidence of doublets may increase twitch force summation leading to a reduction in FS. Thus, biomechanical, not inherent sex-differences in neural drive led to neural compensation strategies manifesting as a difference in FS