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We use neutron scattering to show that the low-temperature, short-range ordered spin configuration in the geometrically frustrated magnet SrCr 9p Ga12−9p O19 (p = 0.92(5)) is composed of small groups of spins whose dipole moments cancel. The local magnetic fluctuation spectrum, χ (ω), vanishes approximately in proportion to ω for hω < 0.5 meV, distinguishing this magnet from conventional spin glasses which display a featureless continuum of excited states. We argue that this behavior results from the absence of local, low-energy excitations in the zero-spin clusters from which the frozen spin configuration is composed.
Jacobian (detJ) from surface registration. Statistical analyses were conducted with two measurement methods: In method M1, maximal changes of the surface shape descriptors between the EOI and EOE (end-ofexhalation) were calculated and indicated as Vt ratio and detJ ratio ; In method M2, the vertex-wise Pearson's correlation between tumor shape descriptor detJ and lung volume from all respiration phases was performed. Surface vertices showing significant correlations were then extracted and the corresponding correlation coefficients were averaged (R detJ). Group-wise comparisons between lung AC and SCC tumors were conducted using metrics derived from both M1 and M2 using two-tailed student t-tests. Results: For method M1, mean surface measurement ratios (detJ ratio) for AC tumor were greater than 1 (expansion of tumor surfaces from EOI to EOE) while the same measurements for SCC tumors were less than 1 (contraction of tumor surfaces from EOI to EOE). The differences of detJ ratio between AC and SCC groups were statistically significant (pZ 0.0419). In contrast, traditional measurements based on Vt detected no statistical significance (pZ 0.8942). Using method M2, AC tumor surface descriptors showed mean negative correlation to lung volumes (i.e. tumor expands when lung contracts). However, SCC tumors surface descriptors showed mean positive correlation to the lung volume. The differences of R detJ between AC and SCC were also statistically significant (pZ0.0001). Conclusion: Based on 4D-CT, we developed a tumor surface morphology tracking pipeline to characterize ventilation induced tumor deformation, and the derived shape measurements successfully detected significant differences in deformation patterns between lung AC and SCC.
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