The bending of light in the presence of spacetime curvature follows immediately from this new law. Then general relativity immediately generates a new law from Fermat’s principle: in the presence of gravity, light rays follow the paths which extremize proper time. For instance, the Fermat principle states that, in the absence of gravity, light rays follow the paths which extremize time. This feature makes it an unprecedented heuristic machine: to uncover the effect of gravity on a given physical phenomenon, consider the old law which describes it in the absence gravity, phrase it in kinematical terms (times lapses and distance intervals), replace “time” by “proper time” and “distance” by “proper distance”, and read off the new law in the presence of gravity. Here, we use this term to intend the description of a phenomenon purely in terms of space and time. 1 1 1“Kinematics” has several, inconsistent, meanings in the physics literature. Image Anal.If general relativity is “probably the most beautiful of all existing physical theories”, it is certainly thanks of its geometric character, which reduces the dynamics of test bodies in a gravitational field to pure kinematics. Wang, G., Zhang, X., Su, Q., Shi, J., Caselli, R.J., Wang, Y.: A novel cortical thickness estimation method based on volumetric Laplace-Beltrami operator and heat kernel. Van Essen, D.C., et al.: The human connectome project: a data acquisition perspective. Tan, M., Qiu, A.: Spectral Laplace-Beltrami wavelets with applications in medical images. Smith, B., et al.: The OBO foundry: coordinated evolution of ontologies to support biomedical data integration. In: Third International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT), pp. Shen, L., Chung, M.: Large-scale modeling of parametric surfaces using spherical harmonics. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. Seo, S., Chung, M.K., Vorperian, H.K.: Heat Kernel smoothing using Laplace-Beltrami eigenfunctions. Reuter, M.: Hierarchical shape segmentation and registration via topological features of Laplace-Beltrami eigenfunctions. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. Cambridge University Press, Cambridge (2010) Olver, F.W.J., Lozier, D.W., Boisvert, R.F., Clark, C.W.: NIST Handbook of Mathematical Functions. Lyu, I., Kim, S., Woodward, N., Styner, M., Landman, B.: TRACE: a topological graph representation for automatic sulcal curve extraction. In: Advances in Neural Information Processing Systems, pp. Kim, W.H., Pachauri, D., Hatt, C., Chung, M.K., Johnson, S., Singh, V.: Wavelet based multi-scale shape features on arbitrary surfaces for cortical thickness discrimination. Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products, 7th edn. Glasser, M.F., et al.: The minimal preprocessing pipelines for the Human Connectome Project. Genovese, C.R., Lazar, N.A., Nichols, T.: Thresholding of statistical maps in functional neuroimaging using the false discovery rate. 1, 269–271 (1959)ĭouglas, D.H., Peucker, T.K.: Algorithms for the reduction of the number of points required to represent a digitized line or its caricature. 3844–3852 (2016)ĭijkstra, E.W.: A note on two problems in connexion with graphs. 467–473 (2003)ĭefferrard, M., Bresson, X., Vandergheynst, P.: Convolutional neural networks on graphs with fast localized spectral filtering. In: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. 22, 63–76 (2015)Ĭhung, M.K., Worsley, K.J., Robbins, S., Evans, A.C.: Tensor-based brain surface modeling and analysis. Imaging 22, 754–765 (2003)Ĭhung, M.K., Qiu, A., Seo, S., Vorperian, H.K.: Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images. 12, 79–93 (2001)Ĭachia, A., et al.: A primal sketch of the cortex mean curvature: a morphogenesis based approach to study the variability of the folding patterns. Andrade, A., et al.: Detection of fMRI activation using cortical surface mapping.
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