7,507 research outputs found
Persistent Homology in Sparse Regression and its Application to Brain Morphometry
Sparse systems are usually parameterized by a tuning parameter that
determines the sparsity of the system. How to choose the right tuning parameter
is a fundamental and difficult problem in learning the sparse system. In this
paper, by treating the the tuning parameter as an additional dimension,
persistent homological structures over the parameter space is introduced and
explored. The structures are then further exploited in speeding up the
computation using the proposed soft-thresholding technique. The topological
structures are further used as multivariate features in the tensor-based
morphometry (TBM) in characterizing white matter alterations in children who
have experienced severe early life stress and maltreatment. These analyses
reveal that stress-exposed children exhibit more diffuse anatomical
organization across the whole white matter region.Comment: submitted to IEEE Transactions on Medical Imagin
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The role of HG in the analysis of temporal iteration and interaural correlation
Persistent Magnetic Wreaths in a Rapidly Rotating Sun
When our Sun was young it rotated much more rapidly than now. Observations of
young, rapidly rotating stars indicate that many possess substantial magnetic
activity and strong axisymmetric magnetic fields. We conduct simulations of
dynamo action in rapidly rotating suns with the 3-D MHD anelastic spherical
harmonic (ASH) code to explore the complex coupling between rotation,
convection and magnetism. Here we study dynamo action realized in the bulk of
the convection zone for a system rotating at three times the current solar
rotation rate. We find that substantial organized global-scale magnetic fields
are achieved by dynamo action in this system. Striking wreaths of magnetism are
built in the midst of the convection zone, coexisting with the turbulent
convection. This is a surprise, for it has been widely believed that such
magnetic structures should be disrupted by magnetic buoyancy or turbulent
pumping. Thus, many solar dynamo theories have suggested that a tachocline of
penetration and shear at the base of the convection zone is a crucial
ingredient for organized dynamo action, whereas these simulations do not
include such tachoclines. We examine how these persistent magnetic wreaths are
maintained by dynamo processes and explore whether a classical mean-field
-effect explains the regeneration of poloidal field.Comment: 17 pages, 9 figures, 1 appendix, emulateapj format; published version
of sections 3-4, 7 and appendix from arXiv:0906.240
Self-organized dynamics and the transition to turbulence of confined active nematics
We study how confinement transforms the chaotic dynamics of bulk
microtubule-based active nematics into regular spatiotemporal patterns. For
weak confinements, multiple continuously nucleating and annihilating
topological defects self-organize into persistent circular flows of either
handedness. Increasing confinement strength leads to the emergence of distinct
dynamics, in which the slow periodic nucleation of topological defects at the
boundary is superimposed onto a fast procession of a pair of defects. A defect
pair migrates towards the confinement core over multiple rotation cycles, while
the associated nematic director field evolves from a distinct double spiral
towards a nearly circularly symmetric configuration. The collapse of the defect
orbits is punctuated by another boundary-localized nucleation event, that sets
up long-term doubly-periodic dynamics. Comparing experimental data to a
theoretical model of an active nematic, reveals that theory captures the fast
procession of a pair of defects, but not the slow spiral
transformation nor the periodic nucleation of defect pairs. Theory also fails
to predict the emergence of circular flows in the weak confinement regime. The
developed confinement methods are generalized to more complex geometries,
providing a robust microfluidic platform for rationally engineering
two-dimensional autonomous flows
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