Reconstruction of the Human Hand Functional Structure Based On a Magnetomyogram

The new method of magnetomyography data analysis is proposed. The method is based on the Fourier transform of prolonged time series and on the massive solution of the inverse problem for all spectral components. For the method testing the following experiment was proposed. The subject clenched and relaxed the hand for five minutes, holding the handle, fixed on the table. Magnetomyograms were registered near the hand using the 7-channel SQUID-magnetometer based on the axial second-order gradiometers. The subject and experimental setup were placed inside a thick-walled aluminum camera, designed for shielding from an alternating electromagnetic field. No shielding from static magnetic field was used. Magnetomyograms with amplitude 20 picoTesla were registered in broad frequency band (up to 500 Hz), signal to noise ratio was more than 20. After filtering and extracting of clench/relax periods two synthetic 135 seconds myograms were formed. The multichannel spectra were calculated, and the functional tomograms were estimated. In case of the relaxed hand, no significant object was reconstructed. In case of the clenched hand, the 3D-object was extracted, representing the functional structure of the muscles, tensed in this experiment. The method can be used for diagnostics and study of the human muscle system.

RECOVERY OF GAUGE INVARIANCE IN STRONG-COUPLING QED

Under a novel ansatz for the vertex function, the Schwinger- Dyson equation for the fermion propagator in the cutoff QED is solved in the arbitrary gauge, taking account of the vacuum polarization in the photon propagator. For any ultraviolet cutoff Λ, there exists a bifurcation point ec(Λ) of the bare coupling constant above which the trivial fermion-mass function for massless QED bifurcates to another, nontrivial massive solution. With a proper choice of the transverse vertex function and the longitudinal vertex that respects the Ward-Takahashi identity, the critical point ec(∞) and the critical scaling behavior in the vicinity of the critical point are shown to be gauge-independent. In the arbitrary gauge, it is shown that the quenched, planar QED obeys Miransky’s scaling of the essential-singularity type and that the unquenched QED exhibits the mean-field critical behavior with classical critical exponents.