Orientation dependent transverse relaxation in human brain white matter: The magic angle effect on a cylindrical helix

Purpose: To overcome limitations of prior orientation-dependent R2 and R2* formalisms in white matter (WM) with a novel framework based on magic angle effect. Methods: A cylindrical helix model was developed embracing both anisotropic rotational and translational diffusions of ordered water in WM, with the former characterized by an axially symmetric system. Both R2 and R2* were divided into isotropic (R2i) and anisotropic parts, R2a*f(ε-ε0,α), with α denoting a funnel opening angle and ε0 an orientation (ε) offset relative to DTI-derived primary diffusivity direction. The proposed framework (Fit A) was compared with prior model without ε0 (Fit B) and applied to published R2 and R2* in WM of underdeveloped, healthy, and diseased conditions. Goodness of fit was characterized by root-mean-square error (RMSE). F-test and Pearson correlation coefficient (PCC) were used with statistical significance set to P ≤ .05. Results: Fit A significantly outperformed Fit B as demonstrated by reduced RMSEs in myelin water (i.e., 0.349 vs. 0.724). The fitted ε0 was in good agreement with the calculated ε0 from DTI directional diffusivities. Significant positive (R2i) and negative (α and R2a) correlations were found with aging (demyelination) in adults while ε0 showed a weak positive correction (PCC=0.11, P= .28). Compared to those from healthy adult WM, the fits of R2i, R2a, and α from neonates were considerably reduced but ε0 increased, consistent with limited myelination. Conclusion: The developed framework can better characterize anisotropic transverse relaxation in WM, shedding new light on myelin microstructural alterations at the molecular level.

APPLICATION OF RULED SURFACES IN FREEFORM AND GEAR METROLOGY

An application of two ruled surfaces (i.e., surfaces generated by a motion of a straight line), a surface of hyperbolic paraboloid and a tangent surface of a cylindrical helix in freeform and gear metrology is introduced in this paper. Both surfaces have been implemented as the main functional figures in several artefacts – metrological calibration standards intended for testing the freeform capabilities of various measuring technologies (e.g., tactile point-to-point measurement and tactile scanning on coordinate measuring machine, optical scanning, computer tomography). Geometrical and mathematical properties of the surface used are summarised, CAD models of all the developed standards are presented and photos of the manufactured standards are shown.

Super-Elastic Double-Helix Model of Photon. Huygens-de Broglie Particle on the Helical Path Guided by the Newton-Bohm Entangled Helical Evolute. Quantum of Magnetic Flux Based on the Mathematical Beauty of Newton, Lorentz, Einstein, Dirac, Gell-Mann, Schw

In our approach we have combined knowledge of Old Masters (working in this field before the year 1905), New Masters (working in this field after the year 1905) and Dissidents under the guidance of Louis de Broglie and David Bohm. In our model the photon is represented as the Huygens-de Broglie’s particle on the helical path (full wave) guided by the Newton-Bohm entangled evolute (empty wave). We have formulated the concept of the Super-Elastic Photon WAVE based on the Great Works of Weber, Abbe, Voigt and Einstein. This model works with the longitudinal elasticity of that WAVE that was already very well tested experimentally. Newly, we propose to test the elastic amplitude of this WAVE for the case of the Doppler’s redshift, the Doppler’s blueshift, and the Zwicky’s redshift. We have newly used the concept of the Lorentz’ force for the description of the photon acting force and the fermion reacting force. In this model the Lorentz’ factors γ and γ3 do not describe the “transverse mass of fermions” and longitudinal mass of fermions” but the “reacting transverse force of fermions” and the “reacting longitudinal force of fermions”. (The mass of photons and fermions does not change with their speed). It is very well-known that the cylindrical helix observed from different angles forms shadows in the Plato’s Cave as circle, sine, cosine, trochoid, cochleoid, hyperbolic spiral. Therefore, the resulting shape depends on the observer position in the Plato’s Cave-this is the famous Rashomon effect between observers. Based on the Newton-Bohm helical evolute and the Huygens-de Broglie helical path of the particle we have derived interesting formula known as the quantum of the magnetic flux. When we work further with this concept based on the Mathematical Beauty developed by Dirac, Gell-Mann, Schwinger, Polchinski, Witten and many others, we will obtain possible properties of the magnetic monopole. This photon quantum of the magnetic flux can be experimentally evaluated in the known tests with superconductors and micro-WAVES and infrared-WAVES. Can it be that Nature cleverly works with the magnetic monopole hidden in plain sight? We want to pass this concept into the hands of Readers of this Journal better educated in the Mathematics and Physics.

Harmonic curvatures of the strip in Minkowski space

This study aimed to give definitions and relations between strip theory and harmonic curvatures of the strip in Minkowski space. Previously, the same was done in Euclidean Space (see [F. Ertem Kaya, Y. Yayli and H. H. Hacısalihoglu, A characterization of cylindrical helix strip, Commun. Fac. Sci. Univ. Ank. Ser. A1 59(2) (2010) 37–51]). The present paper gives for the first time a generic characterization of the harmonic curvatures of the strip, helix strip and inclined strip in Minkowski space.