A novel magnetic resonance imaging postprocessing technique for the assessment of intervertebral disc degeneration-Correlation with histological grading in a rabbit disc degeneration model.

Introduction:Estimation of intervertebral disc degeneration on magnetic resonance imaging (MRI) is challenging. Qualitative schemes used in clinical practice correlate poorly with pain and quantitative techniques have not entered widespread clinical use. Methods:As part of a prior study, 25 New Zealand white rabbits underwent annular puncture to induce disc degeneration in 50 noncontiguous lumbar discs. At 16 weeks, the animals underwent multi-echo T2 MRI scanning and were euthanized. The discs were stained and examined histologically. Quantitative T2 relaxation maps were prepared using the nonlinear least squares method. Decay Variance maps were created using a novel technique of aggregating the deviation in the intensity of each echo signal from the expected intensity based on the previous rate of decay. Results:Decay Variance maps showed a clear and well demarcated nucleus pulposus with a consistent rate of decay (low Decay Variance) in healthy discs that showed progressively more variable decay (higher Decay Variance) with increasing degeneration. Decay Variance maps required significantly less time to generate (1.0 ± 0.0 second) compared with traditional T2 relaxometry maps (5 (±0.9) to 1788.9 (±116) seconds). Histology scores correlated strongly with Decay Variance scores (r = 0.82, P < .01) and weakly with T2 signal intensity (r = 0.32, P < .01) and quantitative T2 relaxometry (r = 0.39, P < .01). Decay Variance had superior sensitivity and specificity for the detection of degenerate discs when compared to T2 signal intensity or Quantitative T2 mapping. Conclusion:Our results show that using a multi-echo T2 MRI sequence, Decay Variance can quantitatively assess disc degeneration more accurately and with less image-processing time than quantitative T2 relaxometry in a rabbit disc puncture model. The technique is a viable candidate for quantitative assessment of disc degeneration on MRI scans. Further validation on human subjects is needed

Glass Transition of the Monodisperse Gaussian Core Model

We numerically study dynamical properties of the one-component Gaussian Core Model in the supercooled states. We find that nucleation is suppressed as density increases. Concomitantly the system exhibits glassy slow dynamics characterized by the two-step and stretched exponential relaxation of the density correlation as well as drastic increase of the relaxation time. It is found that violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than typical model glass formers, implying weaker dynamic heterogeneities. Besides, agreement of simulation data with the prediction of mode-coupling theory is exceptionally good, indicating that the nature of slow dynamics of this ultra-soft particle fluid is mean-field-like. This fact may be understood as the consequences of multiple overlaps of the constituent particles at high densities.Comment: 5 pages, 4 figure

An exponential lower bound for Individualization-Refinement algorithms for Graph Isomorphism

The individualization-refinement paradigm provides a strong toolbox for testing isomorphism of two graphs and indeed, the currently fastest implementations of isomorphism solvers all follow this approach. While these solvers are fast in practice, from a theoretical point of view, no general lower bounds concerning the worst case complexity of these tools are known. In fact, it is an open question whether individualization-refinement algorithms can achieve upper bounds on the running time similar to the more theoretical techniques based on a group theoretic approach. In this work we give a negative answer to this question and construct a family of graphs on which algorithms based on the individualization-refinement paradigm require exponential time. Contrary to a previous construction of Miyazaki, that only applies to a specific implementation within the individualization-refinement framework, our construction is immune to changing the cell selector, or adding various heuristic invariants to the algorithm. Furthermore, our graphs also provide exponential lower bounds in the case when the $k$-dimensional Weisfeiler-Leman algorithm is used to replace the standard color refinement operator and the arguments even work when the entire automorphism group of the inputs is initially provided to the algorithm.Comment: 21 page

Ab initio studies of the spin-transfer torque in tunnel junctions

We calculate the spin-transfer torque in Fe/MgO/Fe tunnel junctions and compare the results to those for all-metallic junctions. We show that the spin-transfer torque is interfacial in the ferromagnetic layer to a greater degree than in all-metallic junctions. This result originates in the half metallic behavior of Fe for the $\Delta_1$ states at the Brillouin zone center; in contrast to all-metallic structures, dephasing does not play an important role. We further show that it is possible to get a component of the torque that is out of the plane of the magnetizations and that is linear in the bias. However, observation of such a torque requires highly ideal samples. In samples with typical interfacial roughness, the torque is similar to that in all-metallic multilayers, although for different reasons.Comment: 5 pages, 4 figure

Slow Dynamics of the High Density Gaussian Core Model

We numerically study crystal nucleation and glassy slow dynamics of the one-component Gaussian core model (GCM) at high densities. The nucleation rate at a fixed supersaturation is found to decrease as the density increases. At very high densities, the nucleation is not observed at all in the time window accessed by long molecular dynamics (MD) simulation. Concomitantly, the system exhibits typical slow dynamics of the supercooled fluids near the glass transition point. We compare the simulation results of the supercooled GCM with the predictions of mode-coupling theory (MCT) and find that the agreement between them is better than any other model glassformers studied numerically in the past. Furthermore, we find that a violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than canonical glassformers. Analysis of the probability distribution of the particle displacement clearly reveals that the hopping effect is strongly suppressed in the high density GCM. We conclude from these observations that the GCM is more amenable to the mean-field picture of the glass transition than other models. This is attributed to the long-ranged nature of the interaction potential of the GCM in the high density regime. Finally, the intermediate scattering function at small wavevectors is found to decay much faster than its self part, indicating that dynamics of the large-scale density fluctuations decouples with the shorter-ranged caging motion.Comment: 15 pages, 13 figure