Abdi, H. 2007. The RV Coefficient and the Congruence Coefficient. Sage.Google Scholar

Achanta, R., Shaji, A., Smith, K., Lucchi, A., Fua, P., and Süsstrunk, S. 2012. SLIC superpixels compared to state-of-the-art superpixel methods. IEEE Transactions on Pattern Analysis and Machine Intelligence, 34, 2274–2282.Google Scholar

Achard, S., and Bullmore, E. 2007. Efficiency and cost of economical brain functional networks. PLoS Computational Biology, 3(2), e17.Google Scholar

Achard, S., Salvador, R., Whitcher, B., Suckling, J., and Bullmore, E.D. 2006. A resilient, low-frequency, small-world human brain functional network with highly connected association cortical hubs. Journal of Neuroscience, 26, 63–72.Google Scholar

Adamic, L.A. 1999. The small world web. Pages 443–452 of: Proceedings of ECDL, vol. 99. Springer.Google Scholar

Adams, H., Tausz, A., and Vejdemo-Johansson, M. 2014. javaPlex: A research software package for persistent (Co) homology. Pages 129–136 of: Mathematical Software– ICMS 2014. Springer.Google Scholar

Adler, R.J. 1981. The Geometry of Random Fields. John Wiley & Sons.Google Scholar

Adler, R.J. 1990. An Introduction to Continuity, Extrema, and Related Topics for General Gaussian Processes. IMS.CrossRefGoogle Scholar

Adler, R.J. 2000. On excursion sets, tube formulas and maxima of random fields. Annals of Applied Probability, 10, 1–74.Google Scholar

Adler, R.J., and Taylor, J.E. 2007. Random Fields and Geometry. Springer Verlag.Google Scholar

Adler, R.J., Bobrowski, O., Borman, M.S., Subag, E., and Weinberger, S. 2010. Persistent homology for random fields and complexes. Pages 124–143 of: Borrowing Strength: Theory Powering Applications: A Festschrift for Lawrence D. Brown. Institute of Mathematical Statistics.Google Scholar

Allen, E.A., Damaraju, E., Plis, S.M., Erhardt, E.B., Eichele, T., and Calhoun, V.D. 2014. Tracking whole-brain connectivity dynamics in the resting state. Cerebral Cortex, 24, 663–676.Google Scholar

Anderson, T.W. 1984. An Introduction to Multivariate Statistical Analysis. 2nd edn. Wiley.Google Scholar

Andrade, A., Kherif, F., Mangin, J., et al. J-B. 2001. Detection of fMRI activation using cortical surface mapping. Human Brain Mapping, 12, 79–93.Google Scholar

Anirudh, R., Thiagarajan, J.J., Kim, I., and Polonik, W. 2016. Autism spectrum disorder classification using graph kernels on multidimensional time series. arXiv preprint arXiv:1611.09897.Google Scholar

Antoine, J.-P., Roşca, D., and Vandergheynst, P. 2010. Wavelet transform on manifolds: old and new approaches. Applied and Computational Harmonic Analysis, 28, 189–202.Google Scholar

Antoine, J.B., Petra, A., and Max, A. 1996. Evaluation of ridge seeking operators for multimodality medical image matching. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18, 353–365.Google Scholar

Arai, K., and Barakbah, A.R. 2007. Hierarchical K-means: an algorithm for centroids initialization for K-means. Reports of the Faculty of Science and Engineering, 36, 25–31.Google Scholar

Arfken, G.B. 2000. Mathematical Methods for Physicists. 5th edn. Academic Press.Google Scholar

Arsigny, V., Fillard, P., Pennec, X., and Ayache, N. 2005. Fast and simple calculus on tensors in the Log-Euclidean framework. Lecture Notes in Computer Science, 3749, 115–122.Google Scholar

Arsigny, V., Fillard, P., Pennec, X., and Ayache, N. 2006. Log-Euclidean metrics for fast and simple calculus on diffusion tensors. Magnetic Resonance in Medicine, 56, 411–421.Google Scholar

Arsigny, V., Fillard, P., Pennec, X., and Ayache, N. 2007. Geometric means in a novel vector space structure on symmetric positive-definite matrices. SIAM Journal on Matrix Analysis and Applications, 29, 328–347.Google Scholar

Ashburner, J., and Friston, K. 2000. Voxel-based morphometry – the methods. NeuroImage, 11, 805–821.Google Scholar

Ashburner, J, Good, C., and Friston, , K.J. 2000. Tensor based morphometry. NeuroImage, 11S, 465.Google Scholar

Avants, B.B., Cook, P.A., Ungar, L., Gee, J.C., and Grossman, M. 2010. Dementia induces correlated reductions in white matter integrity and cortical thickness: a multivariate neuroimaging study with sparse canonical correlation analysis. NeuroImage, 50, 1004–1016.Google Scholar

Aylward, E.H., Minshew, , N.J, Goldstein, G., et al. 1999. MRI volumes of amygdala and hippocampus in nonmentally retarded autistic adolescents and adults. Neurology, 53, 2145–2150.CrossRefGoogle ScholarPubMed

Babuška, I., Tempone, R., and Zouraris, G.E. 2004. Galerkin finite element approximations of stochastic elliptic partial differential equations. Siam Journal of Numerical Analysis, 42, 800–825.Google Scholar

Bagarinao, E., Nakai, T., and Tanaka, Y. 2006. Real-time functional MRI: development and emerging applications. Magnetic Resonance in Medical Sciences, 5, 157–165.Google Scholar

Banerjee, O., Ghaoui, L.E., d’Aspremont, A., and Natsoulis, G. 2006. Convex optimization techniques for fitting sparse Gaussian graphical models. Page 96 of: Proceedings of the 23rd International Conference on Machine Learning.Google Scholar

Banerjee, O., El Ghaoui, L., and d’Aspremont, A. 2008. Model selection through sparse maximum likelihood estimation for multivariate Gaussian or binary data. Journal of Machine Learning Research, 9, 485–516.Google Scholar

Banks, D., and Carley, K. 1994. Metric inference for social networks. Journal of Classification, 11, 121–149.Google Scholar

Banuelos, R., and Burdzy, K. 1999. On the hot spots conjecture of J Rauch. Journal of Functional Analysis, 164, 1–33.Google Scholar

Basser, P.J., and Pierpaoli, C. 1996. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. Journal of Magnetic Resonance, Series B, 111, 209–219.Google Scholar

Basser, P.J., Mattiello, J., and LeBihan, D. 1994. MR diffusion tensor spectroscopy and imaging. Biophysical Journal, 66, 259–267.Google Scholar

Basser, P.J., Pajevic, S., Pierpaoli, C., Duda, J., and Aldroubi, A. 2000. In vivo tractography using DT-MRI data. Magnetic Resonance in Medicine, 44, 625–632.Google Scholar

Bassett, D.S. 2006. Small-world brain networks. The Neuroscientist, 12, 512–523.Google Scholar

Batchelor, P.G., Hill, D.L.G., Calamante, F., and Atkinson, D. 2001. Study of connectivity in the brain using the full diffusion tensor from MRI. Lecture Notes in Computer Science, 2082, 121–133. Springer.Google Scholar

Batchelor, P.G., Calamante, F., Tournier, J.D., Atkinson, D., Hill, D.L., and Connelly, A. 2006. Quantification of the shape of fiber tracts. Magnetic Resonance in Medicine, 55, 894–903.Google Scholar

Behrens, T.E.J., Berg, H.J., Jbabdi, S., Rushworth, M.F.S., and Woolrich, M.W. 2007. Probabilistic diffusion tractography with multiple fibre orientations: what can we gain? NeuroImage, 34, 144–155.Google Scholar

Belkin, M., Niyogi, P., and Sindhwani, V. 2006. Manifold regularization: a geometric framework for learning from labeled and unlabeled examples. Journal of Machine Learning Research, 7, 2399–2434.Google Scholar

Benjamini, Y., and Hochberg, Y. 1995. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of Royal Statistical Society, Series. B, 57, 289–300.Google Scholar

Benjamini, Y., and Yekutieli, D. 2001. The control of the false discovery rate in multiple testing under dependency. Annals of Statistics, 29, 1165–1188.Google Scholar

Berge, A., Jensen, A.C., and Solberg, A.H.S. 2007. Sparse inverse covariance estimates for hyperspectral image classification. IEEE Transactions on Geoscience and Remote Sensing, 45, 1399.Google Scholar

Bernal-Rusiel, J., Atienza, M., and Cantero, J. 2008. Detection of focal changes in human cortical thickness: spherical wavelets versus Gaussian smoothing. NeuroImage, 41, 1278–1292.Google Scholar

Betounes, D. 1998. Partial Differential Equations for Computational Science: With Maple and Vector Analysis. Springer.CrossRefGoogle Scholar

Betzel, R.F., and Bassett, D.S. 2017. Multi-scale brain networks. NeuroImage, 160, 73–83.Google Scholar

Bickel, P.J., and Levina, E. 2008. Regularized estimation of large covariance matrices. Annals of Statistics, 36, 199–227.Google Scholar

Bien, J., and Tibshirani, R. 2011. Hierarchical clustering with prototypes via minimax linkage. Journal of American Statistical Association, 106, 1075–1084.CrossRefGoogle ScholarPubMed

Billingsley, P. 1995. Convergence of Probability Measures. 3rd edn. John Wiley & Sons.Google Scholar

Blakley, B.R., Quiñones, M.A., Crawford, M.S., and Jago, I. 1994. The validity of isometric strength tests. Personnel Psychology, 47, 247–274.Google Scholar

Bocher, M. 1906. Introduction to the theory of Fourier’s series. Annals of Mathematics, 7, 81–152.Google Scholar

Böhm, W., and Hornik, K. 2010. A Kolmogorov–Smirnov test for r samples. Institute for Statistics and Mathematics, Research Report Series, Report 105.Google Scholar

Boothby, W.M. 1986. An Introduction to Differential Manifolds and Riemannian Geometry. 2nd edn. Academic Press.Google Scholar

Boubela, R.N., Kalcher, K., Huf, W., Našel, C., and Moser, E. 2016. Big data approaches for the analysis of large-scale fMRI data using Apache Spark and GPU processing: a demonstration on resting-state fMRI data from the Human Connectome Project. Frontiers in Neuroscience, 9, 492.Google Scholar

Brezinski, C. 2004. Extrapolation algorithms for filtering series of functions, and treating the Gibbs phenomenon. Numerical Algorithms, 36, 309–329.CrossRefGoogle Scholar

Bronstein, M.M., and Kokkinos, I. 2010. Scale-invariant heat kernel signatures for non-rigid shape recognition. Pages 1704–1711 of: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), IEEE.Google Scholar

Bubenik, P. 2015. Statistical topological data analysis using persistence landscapes. Journal of Machine Learning Research, 16, 77–102.Google Scholar

Bubenik, P., and Kim, P.T. 2007. A statistical approach to persistent homology. Homology Homotopy and Applications, 9, 337–362.Google Scholar

Bullmore, E., and Sporns, O. 2009. Complex brain networks: graph theoretical analysis of structural and functional systems. Nature Review Neuroscience, 10, 186–198.Google Scholar

Bulow, T. 2004. Spherical diffusion for 3D surface smoothing. IEEE Transactions on Pattern Analysis and Machine Intelligence, 26, 1650–1654.Google Scholar

Cachia, A., Mangin, J.-F., Riviére, D., et al. 2003a. A generic framework for parcellation of the cortical surface into gyri using geodesic Voronoï diagrams. Image Analysis, 7, 403–416.Google Scholar

Cachia, A., Mangin, J.-F., Riviére, D., et al. 2003b. A primal sketch of the cortex mean curvature: a morphogenesis based approach to study the variability of the folding patterns. IEEE Transactions on Medical Imaging, 22, 754–765.Google Scholar

Cao, J., and Worsley, K.J. 1999a. The detection of local shape changes via the geometry of Hotelling’s T2 fields. Annals of Statistics, 27, 925–942.Google Scholar

Cao, J., and Worsley, K.J. 1999b. The geometry of correlation fields with an application to functional connectivity of the brain. Annals of Applied Probability, 9, 1021–1057.Google Scholar

Cao, J., and Worsley, K.J. 2001. Applications of random fields in human brain mapping. Spatial Statistics: Methodological Aspects and Applications, 159, 170–182.Google Scholar

Carlsson, G., and Memoli, F. 2008. Persistent clustering and a theorem of J. Kleinberg. arXiv preprint arXiv:0808.2241.Google Scholar

Carlsson, G., and Mémoli, F. 2010. Characterization, stability and convergence of hierarchical clustering methods. Journal of Machine Learning Research, 11, 1425–1470.Google Scholar

Carlsson, G., Ishkhanov, T., De Silva, V., and Zomorodian, A. 2008. On the local behavior of spaces of natural images. International Journal of Computer Vision, 76, 1–12.Google Scholar

Cassidy, B., Rae, C., and Solo, V. 2015. Brain activity: conditional dissimilarity and persistent homology. Pages 1356–1359 of: IEEE 12th International Symposium on Biomedical Imaging (ISBI), IEEE.Google Scholar

Castillo, R., Castillo, E., Guerra, R., Johnson, V.E., et al. 2009. A framework for evaluation of deformable image registration spatial accuracy using large landmark point sets. Physics in Medicine and Biology, 54, 1849–1870.CrossRefGoogle ScholarPubMed

Catani, M., Howard, R.J., Pajevic, S., and Jones, D.K. 2002. Virtual in vivo interactive dissection of white matter fasciculi in the human brain. NeuroImage, 17, 77–94.Google Scholar

Chaiken, S., and Kleitman, D.J. 1978. Matrix tree theorems. Journal of Combinatorial Theory, Series A, 24, 377–381.Google Scholar

Chan, G., and Wood, A.T.A. 1997. Algorithm AS 312: an algorithm for simulating stationary Gaussian random fields. Journal of the Royal Statistical Society: Series C, 46, 171–181.Google Scholar

Chan, T.F., Golub, G.H., and LeVeque, R.J. 1983. Algorithms for computing the sample variance: analysis and recommendations. The American Statistician, 37, 242–247.Google Scholar

Chen, X., Zhang, H., Gao, Y., Wee, C.-Y., Li, G., and Shen, D. 2016. High-order resting-state functional connectivity network for MCI classification. Human Brain Mapping, 37, 3282–3296.Google Scholar

Cheng, L., De, J., Zhang, X., Lin, F., and Li, H. 2014. Tracing retinal blood vessels by matrix-forest theorem of directed graphs. Pages 626–633 of: International Conference on Medical Image Computing and Computer Assisted Intervention. Springer.Google Scholar

Christakis, N.A., and Fowler, J.H. 2007. The spread of obesity in a large social network over 32 years. New England Journal of Medicine, 2007, 370–379.Google Scholar

Chung, F.R.K., and Yau, S.T. 1997. Eigenvalue inequalities for graphs and convex subgraphs. Communications in Analysis and Geometry, 5, 575–624.Google Scholar

Chung, M.K. 2001. Statistical Morphometry in Neuroanatomy. Ph.D. thesis, McGill University. www.stat.wisc.edu/^∼mchung/papers/thesis.pdf.Google Scholar

Chung, M.K. 2006. Heat kernel smoothing on unit sphere. Pages 467–473 of: Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI), vol. I. IEEE.Google Scholar

Chung, M.K. 2007. Correlation Coefficient. Sage Publications.Google Scholar

Chung, M.K. 2012. Computational Neuroanatomy: The Methods. World Scientific.Google Scholar

Chung, M.K. 2013. Statistical and Computational Methods in Brain Image Analysis. CRC Press.CrossRefGoogle Scholar

Chung, M.K. 2018. Statistical challenges of big brain network data. Statistics and Probability Letter, 136, 79–82.CrossRefGoogle ScholarPubMed

Chung, M.K., and Taylor, J. 2004. Diffusion smoothing on brain surface via finite element method. Pages 432–435 of: Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI), vol. 1.Google Scholar

Chung, M.K., Worsley, K.J., Taylor, J., Ramsay, J., Robbins, S., and Evans, A.C. 2001a. Diffusion smoothing on the cortical surface. NeuroImage, 13, S95.Google Scholar

Chung, M.K., Worsley, K.J., Paus, T., et al. 2001b. A unified statistical approach to deformation-based morphometry. NeuroImage, 14, 595–606.CrossRefGoogle ScholarPubMed

Chung, M.K., Worsley, K.J., Robbins, S., et al. 2003a. Deformation-based surface morphometry applied to gray matter deformation. NeuroImage, 18, 198–213.Google Scholar

Chung, M.K., Lazar, M., Alexander, A.L., Lu, Y., and Davidson, R.J. 2003b. Probabilistic connectivity measure in diffusion tensor imaging via anisotropic kernel smoothing. University of Wisconsin, Department of Statistics, Technical Report, 1081.Google Scholar

Chung, M.K., Worsley, K.J., Robbins, S., and Evans, A.C. 2003c. Tensor-based brain surface modeling and analysis. Pages 467–473 of: IEEE Conference on Computer Vision and Pattern Recognition (CVPR), vol. I.Google Scholar

Chung, M.K., Robbins, S., Dalton, K.M., Davidson, R.J., Alexander, A.L., and Evans, A.C. 2005a. Cortical thickness analysis in autism with heat kernel smoothing. NeuroImage, 25, 1256–1265.CrossRefGoogle ScholarPubMed

Chung, M.K., Robbins, S., and Evans, A.C. 2005b. Unified statistical approach to cortical thickness analysis. Information Processing in Medical Imaging (IPMI), Lecture Notes in Computer Science, 3565, 627–638.Google Scholar

Chung, M.K., Dalton, K.M., Shen, L., Evans, A.C., and Davidson, R.J. 2007. Weighted Fourier representation and its application to quantifying the amount of gray matter. IEEE Transactions on Medical Imaging, 26, 566–581.Google Scholar

Chung, M.K., Hartley, R., Dalton, K.M., and Davidson, R.J. 2008a. Encoding cortical surface by spherical harmonics. Statistica Sinica, 18, 1269–1291.Google Scholar

Chung, M.K., Dalton, K.M., and Davidson, R.J. 2008b. Tensor-based cortical surface morphometry via weighted spherical harmonic representation. IEEE Transactions on Medical Imaging, 27, 1143–1151.Google Scholar

Chung, M.K., Bubenik, P., and Kim, P.T. 2009a. Persistence diagrams of cortical surface data. Proceedings of the 21st International Conference on Information Processing in Medical Imaging (IPMI), Lecture Notes in Computer Science (LNCS), 5636, 386–397.Google Scholar

Chung, M.K., Singh, V., Kim, P.T., Dalton, K.M., and Davidson, R.J. 2009b. Topological characterization of signal in brain images using min–max diagrams. MICCAI, Lecture Notes in Computer Science (LNCS), 5762, 158–166.Google Scholar

Chung, M.K., Adluru, N., Lee, J.E., Lazar, M., Lainhart, J.E., and Alexander, A.L. 2010a. Cosine series representation of 3D curves and its application to white matter fiber bundles in diffusion tensor imaging. Statistics and Its Interface, 3, 69–80. www.stat.wisc.edu/∼mchung/papers/chung.2010.SII.pdf.Google Scholar

Chung, M.K., Worsley, K.J., Brendon, M.N., Dalton, K.M., and Davidson, R.J. 2010b. General multivariate linear modeling of surface shapes using SurfStat. NeuroImage, 53, 491–505.Google Scholar

Chung, M.K., Hanson, J.L., Avants, B., Gee, J., Davidson, R.J., and Pollak, S.D. 2010c. Structural connectivity mapping via the tensor-based morphometry. Page 481 of: 16th Annual Meeting of the Organization for Human Brain Mapping.Google Scholar

Chung, M.K., Hanson, J.L., Davidson, R.J., and Pollak, S.D. 2011a. Effect of family income on hippocampus growth: longitudinal study. Page 2697 of: 17th Annual Meeting of the Organization for Human Brain Mapping.Google Scholar

Chung, M.K., Seo, S., Adluru, N., and Vorperian, H.K. 2011b. Hot spots conjecture and its application to modeling tubular structures. Pages 225–232 of: International Workshop on Machine Learning in Medical Imaging, vol. 7009.Google Scholar

Chung, M.K., Adluru, N., Dalton, K.M., Alexander, A.L., and Davidson, R.J. 2011c. Scalable brain network construction on white matter fibers. Page 79624G of: Proceedings of SPIE, vol. 7962.Google Scholar

Chung, M.K., Hanson, J.L., Lee, H., et al. 2013. Persistent homological sparse network approach to detecting white matter abnormality in maltreated children: MRI and DTI multimodal study. MICCAI, Lecture Notes in Computer Science (LNCS), 8149, 300–307.Google Scholar

Chung, M.K., Kim, S.-G., Schaefer, S.M., et al. 2014. Improved statistical power with a sparse shape model in detecting an aging effect in the hippocampus and amygdala. Page 90340Y of: Medical Imaging 2014: Image Processing, vol. 9034.Google Scholar

Chung, M.K., Hanson, J.L., Ye, J., Davidson, R.J., and Pollak, S.D. 2015a. Persistent homology in sparse regression and its application to brain morphometry. IEEE Transactions on Medical Imaging, 34, 1928–1939.Google Scholar

Chung, M.K., Qiu, A., Seo, S., and Vorperian, H.K. 2015b. Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images. Medical Image Analysis, 22, 63–76.Google Scholar

Chung, M.K., Vilalta-Gil, V., Lee, H., Rathouz, P.J., Lahey, B.B., and Zald, D.H. 2017a. Exact topological inference for paired brain networks via persistent homology. Information Processing in Medical Imaging (IPMI), Lecture Notes in Computer Science (LNCS), 10265, 299–310.Google Scholar

Chung, M.K., Hanson, J.L., Adluru, L., Alexander, A.L., Davidson, R.J., and Pollak, S.D. 2017b. Integrative structural brain network analysis in diffusion tensor imaging. Brain Connectivity, 7, 331–346.Google Scholar

Chung, M.K., Chuang, Y.J., and Vorperian, H.K. 2017c. Online statistical inference for large-scale binary images. MICCAI, Lecture Notes in Computer Science (LNCS), 10434, 729–736.Google Scholar

Chung, M.K., Lee, H., Solo, V., Davidson, R.J., and Pollak, S.D. 2017d. Topological distances between brain networks. Pages 161–170 of: International Workshop on Connectomics in Neuroimaging, Lecture Notes in Computer Science.Google Scholar

Chung, M.K., Wang, Y., and Wu, G. 2018a. Heat kernel smoothing in irregular image domains. Pages 5101–5104 of: International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).Google Scholar

Chung, M.K., Luo, Z., Adluru, A., Alexander, A.L., Richard, D.J., and Goldsmith, H.H. 2018b. Heritability of hierarchical structural brain network. Pages 554–557 of: International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC).Google Scholar

Clayden, J.D., Storkey, A.J., and Bastin, M.E. 2007. A probabilistic model-based approach to consistent white matter tract segmentation. IEEE Transactions on Medical Imaging, 11, 1555–1561.Google Scholar

Cohen-Steiner, D., Edelsbrunner, H., and Harer, J. 2007. Stability of persistence diagrams. Discrete and Computational Geometry, 37, 103–120.Google Scholar

Collins, D.L., Paus, T., Zijdenbos, A., et al. 1998. Age related changes in the shape of temporal and frontal lobes: an MRI study of children and adolescents. Society of Neuroscience Abstracts, 24, 304.Google Scholar

Conturo, T.E., Lori, N.F., Cull, T.S., Akbudak, E., et al. 1999. Tracking neuronal fiber pathways in the living human brain. National Academy of Sciences USA, 96, 10422–10427.Google Scholar

Conway, J.B. 1990. A Course in Functional Analysis. Springer.Google Scholar

Cook, P.A., Bai, Y., Nedjati-Gilani, S., et al. 2006. Camino: open-source diffusion– MRI reconstruction and processing. Page 2759 in: 14th Scientific Meeting of the International Society for Magnetic Resonance in Medicine.Google Scholar

Cootes, T.F., Hill, A., Taylor, C.J., and Haslam, J. 1993. The use of active shape models for locating structures in medical images. Lecture Notes in Computer Science, 687, 33–33.Google Scholar

Corey, D.M., Dunlap, W.P., and Burke, M.J. 1998. Averaging correlations: expected values and bias in combined Pearson rs and Fisher’s z transformations. Journal of General Psychology, 125, 245–261.Google Scholar

Corouge, I., Gouttard, S., and Gerig, G. 2004. Towards a shape model of white matter fiber bundles using diffusion tensor MRI. Pages 344–347 of: IEEE International Symposium on Biomedical Imaging: Nano to Macro.Google Scholar

Courant, R., and Hilbert, D. 1953. Methods of Mathematical Physics. English edn. Interscience.Google Scholar

Craddock, R.C., James, G.A., Holtzheimer, P.E., Hu, X.P., and Mayberg, H.S. 2012. A whole brain fMRI atlas generated via spatially constrained spectral clustering. Human Brain Mapping, 33, 1914–1928.Google Scholar

David, O., Kiebel, S.J., Harrison, L.M., Mattout, J., Kilner, J.M., and Friston, K.J. 2006. Dynamic causal modeling of evoked responses in EEG and MEG. NeuroImage, 30, 1255–1272.Google Scholar

de Goes, F., Goldenstein, S., and Velho, L. 2008. A hierarchical segmentation of articulated bodies. Computer Graphics Forum, 27, 1349–1356.Google Scholar

de Silva, V., and Ghrist, R. 2007. Homological sensor networks. Notices of the American Mathematical Society, 54, 10–17.Google Scholar

Deng, C.Y. 2011. A generalization of the Sherman–Morrison–Woodbury formula. Applied Mathematics Letters, 24, 1561–1564.CrossRefGoogle Scholar

Desikan, R.S., Ségonne, F., Fischl, B., et al. 2006. An automated labeling system for subdividing the human cerebral cortex on MRI scans into gyral based regions of interest. NeuroImage, 31, 968–980.CrossRefGoogle ScholarPubMed

Ding, C., and He, X. 2004. K-means clustering via principal component analysis. Page 29 of: Proceedings of the Twenty-First International Conference on Machine Learning. ACM.Google Scholar

do Carmo, M.P. 1992. Riemannian Geometry. Prentice Hall, Inc.Google Scholar

Dobra, A., Hans, C., Jones, B., Nevins, J.R., Yao, G., and West, M. 2004. Sparse graphical models for exploring gene expression data. Journal of Multivariate Analysis, 90, 196–212.Google Scholar

Dong, S., Bremer, P.T., Garland, M., Pascucci, V., and Hart, J.C. 2006. Spectral surface quadrangulation. Pages 1057–1066 of: ACM SIGGRAPH 2006 Papers. ACM.Google Scholar

Donoho, D.L., and Tsaig, Y. 2006. Fast Solution of l₁-Norm Minimization Problems When the Solution May Be Sparse. Citeseer.Google Scholar

Donoho, D.L., Johnstone, I.M., Kerkyacharian, G., and Picard, D. 1995. Wavelet shrinkage: asymptopia? Journal of the Royal Statistical Society. Series B (Method-ological), 57, 301–369.Google Scholar

Dougherty, E.R. 1999. Random Processes for Image and Signal Processing. IEEE Press.Google Scholar

Doyle, P.G., and Snell, J.L. 1984. Random Walks and Electric Networks. Mathematical Association of America.Google Scholar

Edelsbrunner, H., and Harer, J. 2008. Persistent homology: a survey. Contemporary Mathematics, 453, 257–282.Google Scholar

Edelsbrunner, H., and Harer, J. 2010. Computational Topology: An Introduction. American Mathematical Society.Google Scholar

Edelsbrunner, H., Letscher, D., and Zomorodian, A. 2002. Topological persistence and simplification. Discrete and Computational Geometry, 28, 511–533.Google Scholar

Efron, B. 1982. The Jackknife, the Bootstrap and Other Resampling Plans, vol. 38. SIAM.Google Scholar

Eguíluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., and Apkarian, A.V. 2005. Scale-free brain functional networks. Physical Review Letters, 94(1), 018102.Google Scholar

Embrechts, P., Resnick, S.I., and Samorodnitsky, G. 1999. Extreme value theory as a risk management tool. North American Actuarial Journal, 3, 30–41.Google Scholar

Erdös, P., and Rényi, A. 1961. On the evolution of random graphs. Bulletin of the International Statistical Institute, 38, 343–347.Google Scholar

Fan, J., Han, F., and Liu, H. 2014. Challenges of big data analysis. National Science Review, 1, 293–314.Google Scholar

Fiedler, M. 1973. Algebraic connectivity of graphs. Czechoslovak Mathematical Journal, 23, 298–305.CrossRefGoogle Scholar

Finch, T. 2009. Incremental calculation of weighted mean and variance. University of Cambridge, 4, 11–5.Google Scholar

Fischl, B., and Dale, A.M. 2000. Measuring the thickness of the human cerebral cortex from magnetic resonance images. Proceedings of the National Academy of Sciences (PNAS), 97, 11050–11055.Google Scholar

Fisher, R.A. 1915. Frequency distribution of the values of the correlation coefficient in samples of an indefinitely large population. Biometrika, 10, 507–521.Google Scholar

Fisher, R.A. 1966. The Design of Experiements. 8 edn. Hafner.Google Scholar

Fletcher, P.T., Lu, C., Pizer, S.M., and Joshi, S. 2004. Principal geodesic analysis for the study of nonlinear statistics of shape. IEEE Transactions on Medical Imaging, 23, 995–1005.Google Scholar

Flury, B. 1997. A First Course in Multivariate Statistics. Springer.Google Scholar

Fornito, A., Zalesky, A., and Bullmore, E.T. 2010. Network scaling effects in graph analytic studies of human resting-state fMRI data. Frontiers in Systems Neuroscience, 4, 1–16.Google Scholar

Fornito, A., Zalesky, A., and Bullmore, E. 2016. Fundamentals of Brain Network Analysis. Academic Press.Google Scholar

Foster, J., and Richards, F.B. 1991. The Gibbs phenomenon for piecewise-linear approximation. American Mathematical Monthly, 98.Google Scholar

Fox, J. 2002. An R and S-Plus Companion to Applied Regression. Sage Publications, Inc.Google Scholar

Fox, J., Friendly, M., and Monette, G. 2009. Visualizing hypothesis tests in multivariate linear models: the heplots package for R. Computational Statistics, 24, 233–246.Google Scholar

Frangi, A.F., Niessen, W.J., Vincken, K.L., and Viergever, M.A. 1998. Multiscale vessel enhancement filtering. Pages 130–137 of: International Conference on Medical Image Computing and Computer-Assisted Intervention, vol. 1496.Google Scholar

Freeman, L.C. 1977. A set of measures of centrality based on betweenness. Sociometry, 40, 35–41.Google Scholar

Friedman, J., Hastie, T., and Tibshirani, R. 2008. Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9, 432.Google Scholar

Frigge, M., Hoaglin, D.C., and Iglewicz, B. 1989. Some implementations of the boxplot. American Statistician, 50–54.Google Scholar

Friston, K.J. 1994. Functional and effective connectivity in neuroimaging: A synthesis. Human Brain Mapping, 2, 56–78.Google Scholar

Friston., K.J. 2002. A short history of statistical parametric mapping in functional neuroimaging. Technical report. Wellcome Department of Imaging Neuroscience, ION, UCL.Google Scholar

Friston, K.J., Frith, C.D., Liddle, P.F., and Frackowiak, R.S.J. 1993a. Functional connectivity: the principal-component analysis of large (PET) data sets. Journal of Cerebral Blood Flow and Metabolism, 13, 5–14.Google Scholar

Friston, K.J., Frith, C.D., and Frackowiak, R.S.J. 1993b. Time-dependent changes in effective connectivity measured with PET. Human Brain Mapping, 1, 69–79.CrossRefGoogle Scholar

Friston, K.J., Holmes, A.P., Worsley, K.J., Poline, J.-P., Frith, C.D., and Frackowiak, R.S.J. 1995. Statistical parametric maps in functional imaging: A general linear approach. Human Brain Mapping, 2, 189–210.CrossRefGoogle Scholar

Friston, K.J., Harrison, L., and Penny, W. 2003. Dynamic causal modelling. NeuroImage, 19, 1273–1302.Google Scholar

Fukunaga, K., and Koontz, W.L.G. 1970. Application of the Karhunen–Loeve expansion to feature selection and ordering. IEEE Transactions on Computers, 100, 311–318.Google Scholar

Gaser, C., Volz, H.-P., Kiebel, S., Riehemann, S., and Sauer, H. 1999. Detecting structural changes in whole brain based on nonlinear deformations: application to schizophrenia research. NeuroImage, 10, 107–113.Google Scholar

Genovese, C.R., Lazar, N.A., and Nichols, T. 2002. Thresholding of statistical maps in functional neuroimaging using the false discovery rate. NeuroImage, 15, 870–878.CrossRefGoogle ScholarPubMed

Gerig, G., Styner, M., Jones, D., Weinberger, D., and Lieberman, J. 2001. Shape analysis of brain ventricles using SPHARM. Pages 171–178 of: MMBIA.Google Scholar

Ghrist, R. 2008. Barcodes: the persistent topology of data. Bulletin of the American Mathematical Society, 45, 61–75.Google Scholar

Gibbons, J. D., and Chakraborti, S. 2011. Nonparametric Statistical Inference. Chapman & Hall/CRC Press.Google Scholar

Gibbs, J.W. 1898. Fourier’s series. Nature, 59, 200.CrossRefGoogle Scholar

Girvan, M., and Newman, M.E.J. 2002. Community structure in social and biological networks. Proceedings of the National Academy of Sciences, 99, 7821.Google Scholar

Gladwell, G.M.L., and Zhu, H. 2002. Courant’s nodal line theorem and its discrete counterparts. Quarterly Journal of Mechanics and Applied Mathematics, 55, 1–15.Google Scholar

Goldsmith, J., Crainiceanu, C.M., Caffo, B.S., and Reich, D.S. 2011. Penalized functional regression analysis of white-matter tract profiles in multiple sclerosis. NeuroImage, 57, 431–439.Google Scholar

Goldsmith, J., Crainiceanu, C.M., Caffo, B., and Reich, D. 2012. Longitudinal penalized functional regression for cognitive outcomes on neuronal tract measurements. Journal of the Royal Statistical Society: Series C (Applied Statistics), 61 453–469.Google Scholar

Gong, G., He, Y., Concha, L., et al. 2009. Mapping anatomical connectivity patterns of human cerebral cortex using in vivo diffusion tensor imaging tractography. Cerebral Cortex, 19, 524–536.Google Scholar

Gottlieb, D., and Shu, C.-W. 1997. On the Gibbs phenomenon and its resolution. SIAM Review, 39, 644–668.Google Scholar

Gower, J. C., and Ross, G. J. S. 1969. Minimum spanning trees and single linkage cluster analysis. Journal of the Royal Statistical Society, Series C (Applied statistics), 18, 54–64.Google Scholar

Greicius, M.D., Srivastava, G., Reiss, A.L., and Menon, V. 2004 . Default-mode network activity distinguishes Alzheimer’s disease from healthy aging: evidence from functional MRI. Proceedings of the National Academy of Sciences, 101, 4637–4642.Google Scholar

Grigoryan, A. 1999. Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds. Bulletin of the American Mathematical Society, 36, 135–249.CrossRefGoogle Scholar

Gritsenko, A., Lindquist, M.A., Kirk, G.R., and Chung, M.K. 2018. Hill climbing optimized twin classification using resting-state functional MRI. arXiv, 1807.00244.Google Scholar

Gritsenko, A, Kirk, G.R., and Chung, M.K. 2018. Resting-state fMRI segmentation in spatio-temporal domain using supervoxels. Page 2595, of: Organization for Human Brain Meeting Annual Meeting.Google Scholar

Gruen, A., and Akca, D. 2005. Least squares 3D surface and curve matching. ISPRS Journal of Photogrammetry and Remote Sensing, 59, 151–174.Google Scholar

Gu, X., Wang, Y.L., Chan, T.F., Thompson, T.M., and Yau, S.T. 2004. Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Transactions on Medical Imaging, 23, 1–10.Google Scholar

Gueziec, A., Pennec, X., and Ayache, N. 1997. Medical image registration using geometeric hashing. IEEE Computational Science and Engineering, 4, 29–41.CrossRefGoogle Scholar

Haff, L.R., Kim, P.T., Koo, J.-Y., and Richards, D.S.P. 2011. Minimax estimation for mixtures of Wishart distributions. Annals of Statistics, 39, 3417–3440.Google Scholar

Hagmann, P., Thiran, J.P., Vandergheynst, P., Clarke, S., Meuli, R., and Lausanne, S. 2000. Statistical fiber tracking on DT-MRI data as a potential tool for morphological brain studies. Page 216 in: ISMRM Workshop on Diffusion MRI: Biophysical Issues.Google Scholar

Hagmann, P., Kurant, M., Gigandet, X., et al. 2007. Mapping human whole-brain structural networks with diffusion MRI. PLoS One, 2(7), e597.Google Scholar

Hagmann, P., Cammoun, L., Gigandet, X., et al. 2008. Mapping the structural core of human cerebral cortex. PLoS Biolology, 6(7), e159.Google Scholar

Hair, J.F., Tatham, R.L, Anderson, R.E., and Black, W.C. 1998. Multivariate Data Analysis. Prentice Hall, Inc.Google Scholar

Hall, K.M. 1970. An r-dimensional quadratic placement algorithm. Management Science, 17, 219–229.Google Scholar

Ham, J., Lee, D.D., Mika, S., and Schölkopf, B. 2004. A kernel view of the dimensionality reduction of manifolds. Page 47 of: Proceedings of the Twenty-First International Conference on Machine Learning.CrossRefGoogle Scholar

Ham, J., Lee, D., and Saul, L. 2005. Semisupervised alignment of manifolds. Pages 120–127 of: Proceedings of the Annual Conference on Uncertainty in Artificial Intelligence, vol. 10.Google Scholar

Hammond, D.K., Vandergheynst, P., and Gribonval, R. 2011. Wavelets on graphs via spectral graph theory. Applied and Computational Harmonic Analysis, 30, 129–150.Google Scholar

Han, X., Jovicich, J., Salat, D., et al. 2006. Reliability of MRI-derived measurements of human cerebral cortical thickness: the effects of field strength, scanner upgrade and manufacturer. NeuroImage, 32, 180–194.Google Scholar

Hanson, J.L., Adluru, N., Chung, M.K., Alexander, A.L., Davidson, R.J., and Pollak, S.D. 2013. Early neglect is associated with alterations in white matter integrity and cognitive functioning. Child Development, 84, 1566–1578.Google Scholar

Hart, J.C. 1999. Computational topology for shape modeling. Pages 36–43 of: Proceedings of the International Conference on Shape Modeling and Applications.CrossRefGoogle Scholar

Harville, D.A. 1997. Matrix Algebra from a Statistician’s Perspective. Springer Verlag.CrossRefGoogle Scholar

Hayasaka, S., Peiffer, A.M., Hugenschmidt, C.E., and Laurienti, P.J. 2007. Power and sample size calculation for neuroimaging studies by non-central random field theory. NeuroImage, 37, 721–730.Google Scholar

He, Y., Chen, Z.J., and Evans, A.C. 2007. Small-world anatomical networks in the human brain revealed by cortical thickness from MRI. Cerebral Cortex, 17, 2407–2419.Google Scholar

He, Y., Chen, Z., and Evans, A. 2008. Structural insights into aberrant topological patterns of large-scale cortical networks in Alzheimer’s disease. Journal of Neuroscience, 28, 4756.Google Scholar

Heo, G., Gamble, J., and Kim, P.T. 2012. Topological analysis of variance and the maxillary complex. Journal of the American Statistical Association, 107, 477–492.Google Scholar

Histed, M.H., Bonin, V., and Reid, R.C. 2009. Direct activation of sparse, distributed populations of cortical neurons by electrical microstimulation. Neuron, 63, 508–522.Google Scholar

Holzrichter, M., and Oliveira, S. 1999. A graph based method for generating the Fiedler vector of irregular problems. Parallel and Distributed Processing, Lecture Notes in Computer Science (LNCS), 1586, 978–985.Google Scholar

Horak, D., Maletić, S., and Rajković, M. 2009. Persistent homology of complex networks. Journal of Statistical Mechanics: Theory and Experiment, 2009, P03034.Google Scholar

Hsieh, C.-J., Sustik, M.A., Dhillon, I.S., Ravikumar, P.K., and Poldrack, R. 2013. BIG & QUIC: sparse inverse covariance estimation for a million variables. Pages 3165–3173 of: Advances in Neural Information Processing Systems.Google Scholar

Huang, S., Li, J., Sun, L., et al. 2009. Learning brain connectivity of Alzheimer’s disease from neuroimaging data. Pages 808–816 of: Advances in Neural Information Processing Systems.Google Scholar

Huang, S., Li, J., Sun, L., et al. 2010. Learning brain connectivity of Alzheimer’s disease by sparse inverse covariance estimation. NeuroImage, 50, 935–949.Google Scholar

Hutchinson, J.E. 1981. Fractals and self-similarity. Indiana University Mathematics Journal, 30, 713–747.Google Scholar

James, A.T. 1968. Calculation of zonal polynomial coefficients by use of the Laplace–Beltrami operator. Annals of Mathematical Statistics, 39, 1711–1718.Google Scholar

Jbabdi, S., Bellec, P., Toro, R., Daunizeau, J., Pélégrini-Issac, M., and Benali, H. 2008. Accurate anisotropic fast marching for diffusion-based geodesic tractography. International Journal of Biomedical Imaging, 2008, 1–12.CrossRefGoogle ScholarPubMed

Jerri, A.J. 1998. The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approximations. Springer.Google Scholar

Jezzard, P., and Clare, S. 1999. Sources of distortion in functional MRI data. Human Brain Mapping, 8, 80–85.Google Scholar

Jolliffe, I.T., Trendafilov, N.T., and Uddin, M. 2003. A modified principal component technique based on the LASSO. Journal of Computational and Graphical Statistics, 12, 531–547.Google Scholar

Jones, S.E., Buchbinder, B.R., and Aharon, I. 2000. Three-dimensional mapping of cortical thickness using Laplace’s equation. Human Brain Mapping, 11, 12–32.Google Scholar

Joshi, A.A., Shattuck, D. W., Thompson, P. M., and Leahy, R. M. 2009. A parameterization-based numerical method for isotropic and anisotropic diffusion smoothing on non-flat Surfaces. IEEE Transactions on Image Processing, 18, 1358–1365.Google Scholar

Joshi, S.C. 1998. Large Deformation Diffeomorphisms and Gaussian Random Fields for Statistical Characterization of Brain Sub-Manifolds. Ph.D. thesis, Washington University, St. Louis.Google Scholar

Joshi, S.C., Wang, J., Miller, M.I., Van Essen, D.C., and Grenander, U. 1995. Differential geometry of the cortical surface. Pages 304–311 of: Vision Geometry IV, Vol. 2573, Proceedings of the SPIE 1995 International Symposium on Optical Science, Engineering and Instrumentation.Google Scholar

Joshi, S.C., Davis, B., Jomier, M., and Gerig, G. 2004. Unbiased diffeomorphic atlas construction for computational anatomy. NeuroImage, 23, 151–160.Google Scholar

Kazi-Aoual, F., Hitier, S., Sabatier, R., and Lebreton, J.D. 1995. Refined approximations to permutation tests for multivariate inference. Computational Statistics and Data Analysis, 20, 643–656.Google Scholar

Khalid, A., Kim, B.S., Chung, M.K., Ye, J.C., and Jeon, D. 2014. Tracing the evolution of multi-scale functional networks in a mouse model of depression using persistent brain network homology. NeuroImage, 101, 351–363.Google Scholar

Kiebel, S.J., Poline, J.-P., Friston, K.J., Holmes, A.P., and Worsley, K.J. 1999. Robust smoothness estimation in statistical parametric maps using standardized residuals from the general linear model. NeuroImage, 10, 756–766.Google Scholar

Kim, S.-G., Chung, M.K., Hanson, J.L., et al. 2011. Structural connectivity via the tensor-based morphometry. Pages 808–811 of: The Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI).Google Scholar

Kim, S.-G., Lee, H.K., Chung, M.K., et al. 2012a. Agreement between the white matter connectivity based on the tensor-based morphometry and the volumetric white matter parcellations based on diffusion tensor imaging. Pages 42–45 of: The Proceedings of IEEE International Symposium on Biomedical Imaging (ISBI).CrossRefGoogle Scholar

Kim, W.H., Pachauri, D., Hatt, C., Chung, M.K., Johnson, S., and Singh, V. 2012b. Wavelet based multi-scale shape features on arbitrary surfaces for cortical thickness discrimination. Pages 1250–1258 of: Advances in Neural Information Processing Systems.Google Scholar

Kim, W.H., Adluru, N., Chung, M.K., et al. 2015. Multi-resolution statistical analysis of brain connectivity graphs in preclinical Alzheimer’s disease. NeuroImage, 118, 103–117.Google Scholar

Kirby, M. 2000. Geometric Data Analysis: An Empirical Approach to Dimensionality Reduction and the Study of Patterns. John Wiley & Sons, Inc.Google Scholar

Kishon, E., Hastie, T., and Wolfson, H. 1990. 3D curve matching using splines. Pages 589–591 of: Proceedings of the European Conference on Computer Vision.Google Scholar

Knuth, D. 1981. The Art of Computing, Volume 2: Seminumerical Algorithms. Addison-Wesley.Google Scholar

Koch, M.A., Norris, D.G., and Hund-Georgiadis, M. 2002. An investigation of functional and anatomical connectivity using magnetic resonance imaging. NeuroImage, 16, 241–250.CrossRefGoogle ScholarPubMed

Kondor, R., Howard, A., and Jebara, T. 2007. Multi-object tracking with representations of the symmetric group. Page 5 of: International Conference on Artificial Intelligence and Statistics (AISTATS), vol. 1.Google Scholar

Koren, Y., and Harel, D. 2002. A multi-scale algorithm for the linear arrangement problem. 2573, 296–309.Google Scholar

Korfiatis, P.D., Kalogeropoulou, C., Karahaliou, A.N., Kazantzi, A.D., and Costaridou, L.I. 2011. Vessel tree segmentation in presence of interstitial lung disease in MDCT. IEEE Transactions on Information Technology in Biomedicine, 15, 214–220.Google Scholar

Kreyszig, E. 1959. Differential Geometry. University of Toronto Press.Google Scholar

Kwapien, S., and Woyczynski, W.A. 1992. Random Series and Stochastic Integrals: Single and Multiple. Birkhauser.Google Scholar

Lazar, M., Weinstein, D.M., Tsuruda, J.S., et al. 2003. White matter tractography using tensor deflection. Human Brain Mapping, 18, 306–321.Google Scholar

Lee, H., Chung, M.K., Kang, H., and Lee, D.S. 2014. 2014. Hole detection in metabolic connectivity of Alzheimer’s disease using k-Laplacian. Pages 297–304 of: International Conference on Medical Image Computing and Computer-Assisted Intervention, Lecture Notes in Computer Science.Google Scholar

Lee, H., Chung, M.K., Kang, H., Kim, B.-N., and Lee, D.S. 2011a. Computing the shape of brain networks using graph filtration and Gromov–Hausdorff metric. MICCAI, Lecture Notes in Computer Science, 6892, 302–309.Google Scholar

Lee, H., Chung, M.K., Kang, H., Kim, B.-N., and Lee, D.S. 2011b. Discriminative persistent homology of brain networks. Pages 841–844 of: IEEE International Symposium on Biomedical Imaging (ISBI).Google Scholar

Lee, H., Lee, D.S.., Kang, H., Kim, B.-N., and Chung, M.K. 2011c. Sparse brain network recovery under compressed sensing. IEEE Transactions on Medical Imaging, 30, 1154–1165.Google Scholar

Lee, H., Kang, H., Chung, M.K., Kim, B.-N., and Lee, D.S. 2012. Persistent brain network homology from the perspective of dendrogram. IEEE Transactions on Medical Imaging, 31, 2267–2277.Google Scholar

Lee, H., Kang, H., Chung, M.K., Lim, S., Kim, B.-N., and Lee, D.S. 2017. Integrated multimodal network approach to PET and MRI based on multidimensional persistent homology. Human Brain Mapping, 38, 1387–1402.Google Scholar

Lee, H., Chung, M.K., Kang, H., Choi, H., Kim, Y.K., and Lee, D.S. 2018a. Abnormal hole detection in brain connectivity by kernel density of persistence diagram and Hodge Laplacian. Pages 20–23 of: IEEE International Symposium on Biomedical Imaging (ISBI).Google Scholar

Lee, M.-H., Kim, D.-Y., Chung, M.K., Alexander, A.L., and Davidson, R.J. 2018b. Topological properties of the brain network constructed using the epsilon-neighbor method. IEEE Transactions on Biomedical Engineering, 65, 2323–2333.Google Scholar

Leemans, A., Sijbers, J., Backer, S. De, Vandervliet, E., and Parizel, P. 2006. Multiscale white matter fiber tract coregistration: a new feature-based approach to align diffusion tensor data. Magnetic Resonance in Medicine, 55, 1414–1423.Google Scholar

Lehoucq, R.B., and Sorensen, D.C. 1996. Deflation techniques for an implicitly restarted Arnoldi iteration. SIAM Journal on Matrix Analysis and Applications, 17, 789–821.Google Scholar

Lepore, N., Brun, C.A., Chiang, M.C., et al. 2006. Multivariate statistics of the Jacobian matrices in tensor based morphometry and their application to HIV/AIDS. Lecture Notes in Computer Science, 4190, 191–198.Google Scholar

Lerch, J.P., Worsley, K., Shaw, W.P., et al. 2006. Mapping anatomical correlations across cerebral cortex (MACACC) using cortical thickness from MRI. NeuroImage, 31, 993–1003.Google Scholar

Lévy, B. 2006. Laplace–Beltrami eigenfunctions towards an algorithm that “understands” geometry. Page 13 of: IEEE International Conference on Shape Modeling and Applications.Google Scholar

Li, Y., Liu, Y., Li, J., et al. 2009. Brain anatomical network and intelligence. PLoS Computational Biology, 5(5), e1000395.Google Scholar

Lindvere, L., Janik, R., Dorr, A., et al. 2013. Cerebral microvascular network geometry changes in response to functional stimulation. Neuroimage, 71, 248–259.Google Scholar

Luscombe, N.M., Babu, M.M., Yu, H., Snyder, M., Teichmann, S.A., and Gerstein, M. 2004. Genomic analysis of regulatory network dynamics reveals large topological changes. Nature, 431, 308–312.Google Scholar

Maass, H. 1955. Die Bestimmung der Dirichletreihen mit Grössencharakteren zu den Modulformen n-ten Grades. Journal of Indian Mathematical Society, 19, 1–23.Google Scholar

MacDonald, J.D., Kabani, N., Avis, D., and Evans, A.C. 2000. Automated 3-D extraction of inner and outer surfaces of cerebral cortex from MRI. NeuroImage, 12, 340–356.Google Scholar

Mahadevan, S., and Maggioni, M. 2006. Value function approximation with diffusion wavelets and Laplacian eigenfunctions. Advances in Neural Information Processing Systems, 18, 843.Google Scholar

Malladi, R, and Ravve, I. 2002. Fast difference schemes for edge enhancing Beltrami flow. Pages 343–357 of: Proceedings of Computer Vision–ECCV, Lecture Notes in Computer Science (LNCS), vol. 2350.Google Scholar

Mandelbrot, B.B. 1982. The Fractal Geometry of Nature. Freeman.Google Scholar

Marrelec, G., Krainik, A., Duffau, H., et al. 2006. Partial correlation for functional brain interactivity investigation in functional MRI. NeuroImage, 32, 228–237.Google Scholar

Marrelec, G., Kim, J., Doyon, J., and Horwitz, B. 2009. Large-scale neural model validation of partial correlation analysis for effective connectivity investigation in functional MRI. Human Brain Mapping, 30, 941–950.Google Scholar

Marsden, J.E., and Hughes, T.J.R. 1983. Mathematical Foundations of Elasticity. Dover Publications, Inc.Google Scholar

Mather, M., Canli, T., English, T., et al. 2004. Amygdala responses to emotionally valanced stimuli in older and younger adults. Psychological Science, 15, 259–263.Google Scholar

Mazumder, R., and Hastie, T. 2012. Exact covariance thresholding into connected components for large-scale graphical LASSO. Journal of Machine Learning Research, 13, 781–794.Google Scholar

McIntosh, A.R., and Lobaugh, N.J. 2004. Partial least squares analysis of neuroimaging data: applications and advances. NeuroImage, 23, 250–263.Google Scholar

McIntosh, A.R., Bookstein, F.L., Haxby, J.V., and Grady, C.L. 1996. Spatial pattern analysis of functional brain images using partial least squares. NeuroImage, 3, 143–157.Google Scholar

Mclntosh, A.R., and Gonzalez-Lima, F. 1994. Structural equation modeling and its application to network analysis in functional brain imaging. Human Brain Mapping, 2, 2–22.Google Scholar

Mémoli, F. 2008. Gromov–Hausdorff distances in Euclidean Spaces. Pages 1–8 of: Workshop on Non-Rigid Shape Analysis and Deformable Image Alignment (CVPR Workshop, NORDIA’08).Google Scholar

Miller, M.I., Banerjee, A., Christensen, G.E., et al. 1997. Statistical methods in computational anatomy. Statistical Methods in Medical Research, 6, 267–299.Google Scholar

Milliken, J.K., and Edland, S.D. 2000. Mixed effect models of longitudinal Alzheimer’s disease data: a cautionary note. Statistics in Medicine, 19, 1617–1629.Google Scholar

Milnor, J. 1973. Morse Theory. Princeton University Press.Google Scholar

Moakher, M. 2005. A differential geometric approach to the geometric mean of symmetric positive-definite matrices. SIAM Journal on Matrix Analysis and Applications, 26, 735–747.Google Scholar

Moakher, M., and Zéraï, M. 2011. The Riemannian geometry of the space of positive-definite matrices and its application to the regularization of positive-definite matrix-valued data. Journal of Mathematical Imaging and Vision, 40, 171–187.Google Scholar

Mori, S., and van Zijl, P.C.M. 2002. Fiber tracking: principles and strategies – a technical review. NMR in Biomedicine, 15, 468–480.Google Scholar

Mori, S., Crain, B.J., Chacko, V.P., and van Zijl, P.C. 1999. Three-dimensional tracking of axonal projections in the brain by magnetic resonance imaging. Annals of Neurology, 45, 256–269.Google Scholar

Mori, S., Oishi, K., Jiang, H., et al. 2008. Stereotaxic white matter atlas based on diffusion tensor imaging in an ICBM template. NeuroImage, 40, 570–582.Google Scholar

Morozov, D. 2008. Homological Illusions of Persistence and Stability. Ph.D. thesis, Duke University.Google Scholar

Naiman, D.Q. 1990. Volumes for tubular neighborhoods of spherical polyhedra and statistical inference. Annals of Statistics, 18, 685–716.Google Scholar

Nain, D., Styner, M., Niethammer, M., et al. 2007. Statistical shape analysis of brain structures using spherical wavelets. Pages 209–212 in: IEEE Symposium on Biomedical Imaging ISBI.Google Scholar

Newman, M.E.J. 2003. The structure and function of complex networks. SIAM Review, 45, 167.Google Scholar

Newman, M.E.J., and Watts, D.J. 1999. Scaling and percolation in the small-world network model. Physical Review E, 60, 7332–7342.CrossRefGoogle ScholarPubMed

Newman, M.E.J., Strogatz, S.H., and Watts, D.J. 2001. Random graphs with arbitrary degree distributions and their applications. Physical Review E, 64, 26118.Google Scholar

Newman, M.E.J., Barabasi, A.L., and Watts, D.J. 2006. The Structure and Dynamics of Networks. Princeton University Press.Google Scholar

Neykov, M., Lu, J., and Liu, H. 2016. Combinatorial inference for graphical models. arXiv preprint arXiv:1608.03045.Google Scholar

Nichols, T., and Hayasaka, S. 2003. Controlling the familywise error rate in functional neuroimaging: a comparative review. Statistical Methods in Medical Research, 12, 419–446.Google Scholar

Nichols, T.E., and Holmes, A.P. 2002. Nonparametric permutation tests for functional neuroimaging: a primer with examples. Human Brain Mapping, 15, 1–25.Google Scholar

Nilsson, J., Sha, F., and Jordan, M.I. 2007. Regression on manifolds using kernel dimension reduction. Pages 697–704 of: Proceedings of the 24th International Conference on Machine Learning. ACM.Google Scholar

O’Donnell, L.J., and Westin, C.F. 2007. Automatic tractography segmentation using a high-dimensional white matter atlas. IEEE Transactions on Medical Imaging, 26, 1562–1575.Google Scholar

O’Donnell, L.J., Kubicki, M., Shenton, M.E., Dreusicke, M.H., Grimson, W.E., and Westin, C.F. 2006. A method for clustering white matter fiber tracts. American Journal of Neuroradiology, 27, 1032–1036.Google Scholar

Øksendal, B. 2010. Stochastic Differential Equations: An Introduction with Applications. Springer.Google Scholar

Ombao, H., and Van Bellegem, S. 2008. Evolutionary coherence of nonstationary signals. IEEE Transactions on Signal Processing, 56, 2259–2266.Google Scholar

Ombao, H., Von Sachs, R., and Guo, W. 2005. SLEX analysis of multivariate nonstationary time series. Journal of the American Statistical Association, 100, 519–531.Google Scholar

Ombao, H., Fiecas, M., Ting, C.-M., and Low, Y. F. 2017. Statistical models for brain signals with properties that evolve across trials. NeuroImage, 180, 609–618.Google Scholar

Osborne, M.R., Presnell, B., and Turlach, B.A. 2000. A new approach to variable selection in least squares problems. IMA Journal of Numerical Analysis, 20, 389–404.Google Scholar

Osher, S., and Fedkiw, R.P. 2003. Level Set Methods and Dynamic Implicit Surfaces. Springer Verlag.Google Scholar

Palande, S., Jose, V., Zielinski, B., Anderson, J., Fletcher, P.T., and Wang, B. 2017. Revisiting abnormalities in brain network architecture underlying autism using topology-inspired statistical inference. Pages 98–107 of: International Workshop on Connectomics in Neuroimaging.Google Scholar

Parker, G.J.M., Wheeler-Kingshott, C.A.M., and Barker, G.J. 2002. Estimating distributed anatomical connectivity using fast marching methods and diffusion tensor imaging. IEEE Transactions on Medical Imaging, 21, 505–512.Google Scholar

Paul, W., and Baschnagel, J. 1999. Stochastic Processes from Physics to Finance. Berlin: Springer Verlag.Google Scholar

Peng, J., Wang, P., Zhou, N., and Zhu, J. 2009. Partial correlation estimation by joint sparse regression models. Journal of the American Statistical Association, 104, 735–746.Google Scholar

Penny, W.D., Stephan, K.E., Mechelli, A., and Friston, K.J. 2004. Comparing dynamic causal models. NeuroImage, 22, 1157–1172.Google Scholar

Pepe, A., Auzias, G., De Guio, F., et al. 2015. Spectral clustering based parcellation of fetal brain MRI. Pages 152–155 of: IEEE International Symposium on Biomedical Imaging (ISBI).Google Scholar

Perona, P., and Malik, J. 1990. Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12, 629–639.Google Scholar

Persoon, E., and Fu, K.S. 1977. Shape discrimination using Fourier descriptors. IEEE Transactions on Systems, Man and Cybernetics, 7, 170–179.Google Scholar

Petri, G., Expert, P., Turkheimer, F., et al. 2014. Homological scaffolds of brain functional networks. Journal of the Royal Society Interface, 11, 20140873.Google Scholar

Pinehiro, J.C., and Bates, D.M. 2002. Mixed Effects Models in S and S-Plus. 3rd edn. Springer.Google Scholar

Plumbley, M.D. 2005. Geometry and homotopy for l₁ sparse representations. Proceedings of SPARS, 5, 206–213.Google Scholar

Pothen, A., and Fan, C.J. 1990. Computing the block triangular form of a sparse matrix. ACM Transactions on Mathematical Software (TOMS), 16, 324.Google Scholar

Prabhu, P., and Anbazhagan, N. 2011. Improving the performance of k-means clustering for high dimensional data set. International Journal on Computer Science and Engineering, 3, 2317–2322.Google Scholar

Qiu, A., Bitouk, D., and Miller, M.I. 2006. Smooth functional and structural maps on the neocortex via orthonormal bases of the Laplace–Beltrami operator. IEEE Transactions on Medical Imaging, 25, 1296–1396.Google Scholar

Qiu, A., Lee, A., Tan, M., and Chung, M.K. 2015. Manifold learning on brain functional networks in aging. Medical Image Analysis, 20, 52–60.Google Scholar

Raftery, A.E., Newton, M.A., Satagopan, J.M., and Krivitsky, P.N. 2006. Estimating the integrated likelihood via posterior simulation using the harmonic mean identity. Memorial Sloan Kettering Cancer Center, Dept. of Epidemiology and Biostatistics Working Paper Series. Working Paper 6.Google Scholar

Ramsay, J.O., and Silverman, B.W. 1997. Functional Data Analysis. Springer Verlag.Google Scholar

Reid, M., and Szendròi, B. 2005. Geometry and Topology. Cambridge University Press.Google Scholar

Reuter, M. 2010. Hierarchical shape segmentation and registration via topological features of Laplace–Beltrami eigenfunctions. International Journal of Computer Vision, 89, 287–308.Google Scholar

Reuter, M., Wolter, F.-E., Shenton, M., and Niethammer, M. 2009. Laplace–Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis. Computer-Aided Design, 41, 739–755.Google Scholar

Richards, D.S.P. 1985. Applications of invariant differential operators to multivariate distribution theory. SIAM Journal on Applied Mathematics, 45, 280–288.Google Scholar

Richards, D.S.P. 2011. High-dimensional random matrices from the classical matrix groups, and generalized hypergeometric functions of matrix argument. Symmetry, 3, 600–610.Google Scholar

Robert, P., and Escoufier, Y. 1976. A unifying tool for linear multivariate statistical methods: the RV-coefficient. Journal of the Royal Statistical Society. Series C (Applied Statistics), 25, 257–265.Google Scholar

Roy, S.N. 1953. On a heuristic method of test construction and its use in multivariate analysis. Annals of Mathematics and Statistics, 24, 220–238.Google Scholar

Rubinov, M., and Sporns, O. 2010. Complex network measures of brain connectivity: uses and interpretations. NeuroImage, 52, 1059–1069.Google Scholar

Rubinov, M., Knock, S. A., Stam, C. J., et al. 2009. Small-world properties of nonlinear brain activity in schizophrenia. Human Brain Mapping, 30, 403–416.Google Scholar

Salmond, CH, Ashburner, J., Vargha-Khadem, F., Connelly, A., Gadian, DG, and Friston, KJ. 2002. Distributional assumptions in voxel-based morphometry. NeuroImage, 17, 1027–1030.Google Scholar

Salvador, R., Suckling, J., Coleman, M. R., Pickard, J. D., Menon, D., and Bullmore, E. 2005. Neurophysiological architecture of functional magnetic resonance images of human brain. Cerebral Cortex, 15, 1332–1342.Google Scholar

Sato, Y., Nakajima, S., Shiraga, N., et al. 1998. Three-dimensional multi-scale line filter for segmentation and visualization of curvilinear structures in medical images. Medical Image Analysis, 2, 143–168.Google Scholar

Schäfer, J., and Strimmer, K. 2005. A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4, 32.Google Scholar

Schmidt, V., and Spodarev, E. 2005. Joint estimators for the specific intrinsic volumes of stationary random sets. Stochastic Processes and Their Applications, 115, 959–981.Google Scholar

Schölkopf, B., and Smola, A.J. 2002. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press.Google Scholar

Seo, S., Chung, M.K., and Vorperian, H.K. 2010. Heat kernel smoothing using Laplace–Beltrami eigenfunctions. Pages 505–512 of: Medical Image Computing and Computer-Assisted Intervention – MICCAI 2010. Lecture Notes in Computer Science, vol. 6363.Google Scholar

Shang, Y., Deklerck, R., Nyssen, E., et al. 2011. Vascular active contour for vessel tree segmentation. IEEE Transactions on Biomedical Engineering, 58, 1023–1032.Google Scholar

Shattuck, D.W., Mirza, M., Adisetiyo, V., et al. 2008. Construction of a 3D probabilistic atlas of human cortical structures. NeuroImage, 39, 1064–1080.Google Scholar

Shawe-Taylor, J., and Cristianini, N. 2004. Kernel Methods for Pattern Analysis. Cambridge University Press.Google Scholar

Shen, L., and Chung, M.K. 2006. Large-scale modeling of parametric surfaces using spherical harmonics. Pages 294–301 in: Third International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT).Google Scholar

Shen, L., Ford, J., Makedon, F., and Saykin, A. 2004. Surface-based approach for classification of 3D neuroanatomical structures. Intelligent Data Analysis, 8, 519–542.Google Scholar

Shen, X., Papademetris, X., and Constable, R.T. 2010. Graph-theory based parcellation of functional subunits in the brain from resting-state fMRI data. NeuroImage, 50, 1027–1035.Google Scholar

Shinkareva, S.V., Ombao, H.C., Sutton, B.P., Mohanty, A., and Miller, G.A. 2006. Classification of functional brain images with a spatio-temporal dissimilarity map. NeuroImage, 33, 63–71.Google Scholar

Siegmund, D.O., and Worsley, K.J. 1996. Testing for a signal with unknown location and scale in a stationary Gaussian random field. Annals of Statistics, 23, 608–639.Google Scholar

Silver, N.C., and Hollingsworth, S.C. 1989. A FORTRAN 77 program for averaging correlation coefficients. Behavior Research Methods, 21, 647–650.Google Scholar

Smirnov, N.V. 1939. Estimate of deviation between empirical distribution functions in two independent samples. Bulletin of Moscow University, 2, 3–16.Google Scholar

Smith, R.L. 1989. Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone. Statistical Science, 4, 367–377.Google Scholar

Sochen, N., Kimmel, R., and Malladi, R. 1998. A general framework for low level vision. IEEE Transactions on Image Processing, 7, 310–318.Google Scholar

Song, C., Havlin, S., and Makse, H.A. 2005. Self-similarity of complex networks. Nature, 433, 392–395.Google Scholar

Sporns, O., and Zwi, J.D. 2004. The small world of the cerebral cortex. Neuroinformatics, 2, 145–162.Google Scholar

Sporns, O., Tononi, G., and Edelman, GM. 2000. Theoretical neuroanatomy: relating anatomical and functional connectivity in graphs and cortical connection matrices. Cerebral Cortex, 10, 127.Google Scholar

Staempfli, P., Jaermann, T., Crelier, G.R., Kollias, S., Valavanis, A., and Boesiger, P. 2006. Resolving fiber crossing using advanced fast marching tractography based on diffusion tensor imaging. NeuroImage, 30, 110–120.Google Scholar

Staib, L.H., and Duncan, J.S. 1992. Boundary finding with parametrically deformable models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 14, 1061–1075.Google Scholar

Stam, C.J., Tewarie, P., Van Dellen, E., van Straaten, E.C.W., and Hillebrand, A. 2014. The trees and the forest: characterization of complex brain networks with minimum spanning trees. International Journal of Psychophysiology, 92, 129–138.Google Scholar

Steinke, F., and Hein, M. 2008. Non-parametric regression between manifolds. Advances in Neural Information Processing Systems, 21, 1561–1568.Google Scholar

Stevens, C.F. 1995. The Six Core Theories of Modern Physics. MIT Press.Google Scholar

Stroup, W.W. 2012. Generalized Linear Mixed Models: Modern Concepts, Methods and Applications. CRC Press.Google Scholar

Subasi, A., and Ercelebi, E. 2005. Classification of EEG signals using neural network and logistic regression. Computer Methods and Programs in Biomedicine, 78, 87–99.Google Scholar

Sun, J., Ovsjanikov, M., and Guibas, L. J. 2009. A concise and provably informative multi-scale signature based on heat diffusion. Computer Graphics Forum, 28, 1383–1392.Google Scholar

Supekar, K., Menon, V., Rubin, D., Musen, M., and Greicius, M.D. 2008. Network analysis of intrinsic functional brain connectivity in Alzheimer’s disease. PLoS Computational Biology, 4(6), e1000100.Google Scholar

Talairach, J., and Tournoux, P. 1988. Co-Planar Stereotactic Atlas of the Human Brain: 3-Dimensional Proportional system: An Approach to Cerebral Imaging. Thieme, Stuttgart.Google Scholar

Tan, M., and Qiu, A. 2015. Spectral Laplace–Beltrami wavelets with applications in medical images. IEEE Transactions on Medical Imaging, 34, 1005–1017.Google Scholar

Tang, B., Sapiro, G., and Caselles, V. 1999. Direction diffusion. Pages 2:1245–1252 of: The Proceedings of the Seventh IEEE International Conference on Computer Vision.Google Scholar

Taubin, G. 2000. Geometric signal processing on polygonal meshes. EURO-GRAPHICS.Google Scholar

Taylor, J.E., and Worsley, K.J. 2007. Detecting sparse signals in random fields, with an application to brain mapping. Journal of the American Statistical Association, 102, 913–928.Google Scholar

Taylor, J.E., and Worsley, K.J. 2008. Random fields of multivariate test statistics, with applications to shape analysis. Annals of Statistics, 36, 1–27.Google Scholar

Taylor, P.N., Wang, Y., and Kaiser, M. 2017. Within brain area tractography suggests local modularity using high resolution connectomics. Scientific Reports, 7, 39859.Google Scholar

Tench, C.R., Morgan, P.S., Blumhardt, L.D., and Constantinescu, C. 2002. Improved white matter fiber tracking using stochastic labeling. Magnetic Resonance in Medicine, 48, 677–683.Google Scholar

Tenenbaum, J.B., De Silva, V., and Langford, J.C. 2000. A global geometric framework for nonlinear dimensionality reduction. Science, 290, 2319–2323.Google Scholar

Thirion, B., Varoquaux, G., Dohmatob, E., and Poline, J.-B. 2014. Which fMRI clustering gives good brain parcellations? Frontiers in Neuroscience, 8, 167.Google Scholar

Thompson, P.M., MacDonald, D., Mega, M.S., Holmes, C.J., Evans, A.C., and Toga, A.W. 1997. Detection and mapping of abnormal brain structure with a probabilistic atlas of cortical surfaces. Journal of Computer Assisted Tomography, 21, 567–581.Google Scholar

Thompson, P.M., Cannon, T.D., Narr, K.L., et al. 2001. Genetic influences on brain structure. Nature Neuroscience, 4, 1253–1258.Google Scholar

Thottakara, P., Lazar, M., Johnson, S.C., and Alexander, A.L. 2006. Probabilistic connectivity and segmentation of white matter using tractography and cortical templates. NeuroImage, 29, 868–878.Google Scholar

Tibshirani, R. 1996. Regression shrinkage and selection via the LASSO. Journal of the Royal Statistical Society. Series B (Methodological), 58, 267–288.CrossRefGoogle Scholar

Timm, N.H., and Mieczkowski, T.A. 1997. Univariate and Multivariate General Linear Models: Theory and Applications Using SAS Software. SAS Publishing.Google Scholar

Ting, C.-M., Ombao, H., Samdin, S.B., and Salleh, S.-H. 2018. Estimating dynamic connectivity states in fMRI using regime-switching factor models. IEEE Transactions on Medical Imaging, 37, 1011–1023.Google Scholar

Tlusty, T. 2007. A relation between the multiplicity of the second eigenvalue of a graph Laplacian, Courants nodal line theorem and the substantial dimension of tight polyhedral surfaces. Electronic Journal of Linear Algebra, 16, 315–24.Google Scholar

Topaz, C.M., Ziegelmeier, L., and Halverson, T. 2015. Topological data analysis of biological aggregation models. PLoS One, e0126383.Google Scholar

Tuzhilin, A.A. 2016. Who invented the Gromov–Hausdorff distance? arXiv preprint arXiv:1612.00728.Google Scholar

Tzourio-Mazoyer, N., Landeau, B., Papathanassiou, D., et al. 2002. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. NeuroImage, 15, 273–289.Google Scholar

Uddin, L.Q., Kelly, A.M.C., Biswal, B.B., et al. 2008. Network homogeneity reveals decreased integrity of default-mode network in ADHD. Journal of Neuroscience Methods, 169, 249–254.Google Scholar

Valdés-Sosa, P.A., Sánchez-Bornot, J.M., Lage-Castellanos, A., et al. 2005. Estimating brain functional connectivity with sparse multivariate autoregression. Philosophical Transactions of the Royal Society B: Biological Sciences, 360, 969–981.Google Scholar

Vallet, B., and Lévy, B. 2008. Spectral geometry processing with manifold harmonics. Computer Graphics Forum, 27, 251–260.Google Scholar

Van Dijk, K.R.A., Sabuncu, M.R., and Buckner, R.L. 2012. The influence of head motion on intrinsic functional connectivity MRI. NeuroImage, 59, 431–438.Google Scholar

Van Essen, D.C., Ugurbil, K., Auerbach, E., et al. 2012. The Human Connectome Project: a data acquisition perspective. NeuroImage, 62, 2222–2231.Google Scholar

Vilanova, A., Berenschot, G., and van Pul, C. 2004. DTI visualization with stream-surfaces and evenly-spaced volume seeding. Pages 173–182 of: VisSym04 Joint Eurographics-IEEETCVG Symposium on Visualization, Conference Proceedings.Google Scholar

Wang, Y., Kang, J., Kemmer, P.B., and Guo, Y. 2016a. An efficient and reliable statistical method for estimating functional connectivity in large scale brain networks using partial correlation. Frontiers in Neuroscience, 10, 123.Google Scholar

Wang, Y., Ting, C.-M., and Ombao, H. 2016b. Modeling effective connectivity in high-dimensional cortical source signals. IEEE Journal of Selected Topics in Signal Processing, 10, 1315–1325.Google Scholar

Wang, Y., Chung, M.K., Dentico, D., Lutz, A., and Davidson, R.J. 2017. Topological network analysis of electroencephalographic power maps. Pages 134–142 of: International Workshop on Connectomics in NeuroImaging, Lecture Notes in Computer Science (LNCS), vol. 10511.Google Scholar

Wang, Y., Ombao, H., and Chung, M.K. 2018. Topological data analysis of single-trial electroencephalographic signals. Annals of Applied Statistics, 12, 1506–1534.Google Scholar

Watts, D.J., and Strogatz, S.H. 1998. Collective dynamics of small-world networks. Nature, 393(6684), 440–442.Google Scholar

Wijk, B. C. M., Stam, C. J., and Daffertshofer, A. 2010. Comparing brain networks of different size and connectivity density using graph theory. PloS One, 5, e13701.Google Scholar

Wilbraham, H. 1848. On a certain periodic function. Cambridge and Dublin Mathematical Journal, 3, 198–201.Google Scholar

Wilk, M.B., and Gnanadesikan, R. 1968. Probability plotting methods for the analysis of data. Biometrika, 55, 1.Google Scholar

Witten, D.M. Friedman, J.H., and Simon, N. 2011. New insights and faster computations for the graphical LASSO. Journal of Computational and Graphical Statistics, 20, 892–900.Google Scholar

Wong, E., Palande, S., Wang, B., Zielinski, B., Anderson, J., and Fletcher, P.T. 2016. Kernel partial least squares regression for relating functional brain network topology to clinical measures of behavior. Pages 1303–1306 of: IEEE International Symposium on Biomedical Imaging (ISBI).Google Scholar

Worsley, K.J. 1994. Local maxima and the expected Euler characteristic of excursion sets of χ², F and t fields. Advances in Applied Probability, 26, 13–42.Google Scholar

Worsley, K.J. 2003. Detecting activation in fMRI data. Statistical Methods in Medical Research., 12, 401–418.Google Scholar

Worsley, K.J., Evans, A.C., Marrett, S., and Neelin, P. 1992. A three-dimensional statistical analysis for CBF activation studies in human brain. Journal of Cerebral Blood Flow and Metabolism, 12, 900–918.Google Scholar

Worsley, K.J., Poline, J-B., Vandal, A.C., and Friston, K.J. 1995. Test for distributed, non-focal brain activations. NeuroImage, 2, 173–181.Google Scholar

Worsley, K.J., Marrett, S., Neelin, P., and Evans, A.C. 1996a. Searching scale space for activation in PET images. Human Brain Mapping, 4, 74–90.Google Scholar

Worsley, K.J., Marrett, S., Neelin, P., Vandal, A.C., Friston, K.J., and Evans, A.C. 1996b. A unified statistical approach for determining significant signals in images of cerebral activation. Human Brain Mapping, 4, 58–73.Google Scholar

Worsley, K.J., Cao, J., Paus, T., Petrides, M., and Evans, A.C. 1998. Applications of random field theory to functional connectivity. Human Brain Mapping, 6, 364–7.Google Scholar