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Morse Set Classification and Hierarchical Refinement Using Conley Index

Guoning Chen, Qingqing Deng, A. Szymczak, R. S. Laramee, E. Zhang
2012 IEEE Transactions on Visualization and Computer Graphics  
Index Terms-Morse decomposition, vector field topology, upper bound of Conley index, topology refinement, hierarchical refinement.  ...  We make use of an upper bound for the Conley index, provided by the Betti numbers of an index pair for a translation along the flow, to classify the Morse sets.  ...  This work was supported by NSF IIS-0546881 and CCF-0830808 awards, and in part, by EPSRC research grant EP/F002335/1.  ... 
doi:10.1109/tvcg.2011.107 pmid:21690641 fatcat:6srcgsrnbzawhhmgixnltbruk4

Cover1

2012 IEEE Transactions on Visualization and Computer Graphics  
Kirby ................................................................................................................................... 753 Morse Set Classification and Hierarchical Refinement Using  ...  Conley Index G.  ... 
doi:10.1109/tvcg.2012.81 fatcat:xudny3xiufaq3ng4flajyjbx3q

Robust Morse Decompositions of Piecewise Constant Vector Fields

A. Szymczak, E. Zhang
2012 IEEE Transactions on Visualization and Computer Graphics  
In addition, we describe a Morse set classification framework which we use to color code the Morse sets in order to enhance the visualization.  ...  Index Terms-Morse decomposition, vector field topology. Ç 938  ...  Laramee and Guoning Chen for data sets used in Section 7. We are also grateful to Guoning Chen and Qingqing Deng for help with Figs. 15 and 16.  ... 
doi:10.1109/tvcg.2011.88 pmid:21747131 fatcat:io7jlnj3uzab5kklmothl2jh4a

Fair morse functions for extracting the topological structure of a surface mesh

Xinlai Ni, Michael Garland, John C. Hart
2004 ACM Transactions on Graphics  
We make Morse theory on meshes more robust with teflon saddles and flat edge collapses, and devise a new "intermediate value propagation" multigrid solver for finding fair Morse functions that runs in  ...  This paper solves a relaxed form of Laplace's equation to find a "fair" Morse function with a user-controlled number and configuration of critical points.  ...  Thanks to Zoe Wood for the genus-6 Buddha model, Patrick Lacz for the manifold teapot, Jesse Hall for video production, and Rob Ghrist for introducing us to the Conley index.  ... 
doi:10.1145/1015706.1015769 fatcat:jtvm744gsvgnbjtlqlrgfsr5ua

Fair morse functions for extracting the topological structure of a surface mesh

Xinlai Ni, Michael Garland, John C. Hart
2004 ACM SIGGRAPH 2004 Papers on - SIGGRAPH '04  
We make Morse theory on meshes more robust with teflon saddles and flat edge collapses, and devise a new "intermediate value propagation" multigrid solver for finding fair Morse functions that runs in  ...  This paper solves a relaxed form of Laplace's equation to find a "fair" Morse function with a user-controlled number and configuration of critical points.  ...  Thanks to Zoe Wood for the genus-6 Buddha model, Patrick Lacz for the manifold teapot, Jesse Hall for video production, and Rob Ghrist for introducing us to the Conley index.  ... 
doi:10.1145/1186562.1015769 fatcat:6bjscxc54rg3xp2gz53ewffb4a

Salient critical points for meshes

Yu-Shen Liu, Min Liu, Daisuke Kihara, Karthik Ramani
2007 Proceedings of the 2007 ACM symposium on Solid and physical modeling - SPM '07  
We give a direct application to the hierarchical topological representation for meshes by combining the salient critical points with the Morse-Smale complex.  ...  In this paper, we use the idea of mesh saliency as a measure of regional importance for meshes.  ...  Acknowledgements This work was supported in part by the National Institute of General Medical Sciences of the National Institutes of Health (R01 GM075004) awarded to Professor Kihara and Professor Ramani  ... 
doi:10.1145/1236246.1236285 dblp:conf/sma/LiuLKR07 fatcat:hch6usjgabdnpllpfl3nl65w5q

A Hierarchy of Local Symplectic Filling Obstructions for Contact 3-Manifolds [article]

Chris Wendl
2013 arXiv   pre-print
obstructions to planarity and embeddings of partially planar domains.  ...  , and we give examples of contact manifolds that have planar k-torsion for any k > 2 but no Giroux torsion.  ...  theorem for holomorphic currents, and Janko Latschev and Patrick Massot for several useful comments on earlier versions of the paper.  ... 
arXiv:1009.2746v3 fatcat:ohxddvv2bfdlvajdc73jqv2nl4

Fourier's Method of Linear Programming and Its Dual

H. P. Williams
1986 The American mathematical monthly  
37B30 Index theory, Morse-Conley indices 37B35 Gradient-like and recurrent behavior; isolated (locally maximal) invariant sets 37B40 Topological entropy 37B45 Continua theory in dynamics 37B50  ...  It will be extremely useful for both users and classifiers to familiarize themselves with the entire classification system and thus to become aware of all the classifications of possible interest to them  ...  etc.) 83-01 Instructional exposition (textbooks, tutorial papers, etc.) 83-02 Research exposition (monographs, survey articles) 83-03 Historical (must also be assigned at least one classification number  ... 
doi:10.2307/2322281 fatcat:yvhgyh2epbcwdoqdhuaopkcrue

Dynamics of Patterns

Wolf-Jürgen Beyn, Bernold Fiedler, Björn Sandstede
2012 Oberwolfach Reports  
This workshop brought together researchers from these diverse areas to bridge existing gaps and to facilitate interaction. (2000) : 35B40, 35P05, 65M12. Mathematics Subject Classification  ...  Mathematical descriptions and analyses draw from a variety of fields such as partial differential equations of various types, differential and difference equations on networks and lattices, multi-particle  ...  Using a Poincaré compactification and the Conley index at infinity [2] , we are able to determine that projections of the Fučik eigenfunctions to infinite norm compose a subset of the equilibria at infinity  ... 
doi:10.4171/owr/2012/60 fatcat:b4zptysvy5b27peqdgddeaev74

Dynamics of Patterns

Wolf-Jürgen Beyn, Bernold Fiedler, Björn Sandstede
2008 Oberwolfach Reports  
This workshop brought together researchers from these diverse areas to bridge existing gaps and to facilitate interaction. (2000) : 35B40, 35P05, 65M12. Mathematics Subject Classification  ...  Mathematical descriptions and analyses draw from a variety of fields such as partial differential equations of various types, differential and difference equations on networks and lattices, multi-particle  ...  Using a Poincaré compactification and the Conley index at infinity [2] , we are able to determine that projections of the Fučik eigenfunctions to infinite norm compose a subset of the equilibria at infinity  ... 
doi:10.4171/owr/2008/57 fatcat:cdoyqz5rzngbdi7pgz2ixcsjly

Volunteer Meanings in the Making of Place [chapter]

Ben Amsden, Richard C. Stedman, Linda E. Kruger
2012 Place-Based Conservation  
Rather it emerges from and is refined and validated by systems of networked learners.  ...  McGuire (2007) presents the same process in a somewhat modified form for use by teams in hierarchical organizations like business and government.  ... 
doi:10.1007/978-94-007-5802-5_9 fatcat:dfxenftyrvha5lk2qsxqy74wv4

2-D blind deconvolution by partitioning into coupled 1-D problems using discrete Radon transforms

H. Ahn, A.E. Yagle
Proceedings., International Conference on Image Processing  
It proves the graph representability of the discrete energy function and optimizes it using graph cuts.  ...  CP3 Image Restoration Using Bounded Variation and Sobolev Spaces of Negative Differentiability We recover an unknown image from a blurry and noisy image f.  ...  The non-orthogonal nature of regions and substances in classification leads to the use of frames.  ... 
doi:10.1109/icip.1995.537409 dblp:conf/icip/AhnY95 fatcat:ecos74jfmfgonkuk5gsq2essp4

'Parallel Worlds' - Clusters for a Theory of Concepts of Communications: Historical Intercultural and Cultural Comparative Studies of Perspectives of National and Transnational Conditions, Values, Concepts, and Terms of 'Communication' - 'Orality' - 'Literacy' - 'Rhetoric' - 'Media'

Fee-Alexandra Haase
2008 Social Science Research Network  
It was marked by a variety of theories and classification of art styles.  ...  Conley, Thomas M. "Stasis in Rhetorical Invention." In: Conley, Thomas M. Rhetoric in the European Tradition. New York: Longman 1990. Pp. 32-33. 73 Cf. Carter, Michael.  ...  of form and meaning, and the psychology of syntax, metaphor, and diction both in your own writing and in the works of others. 1001 According to Heinle's Dictionary communication is an act of passing  ... 
doi:10.2139/ssrn.1227842 fatcat:4sffl3hstvc6ba6z5sufjopg6u

Evidence Based Practice for Information Professionals: a Handbook Biographies

Andrew Booth, Anne Brice, Andrew Booth, Anne Brice, Andrew Booth, Anne Brice, Andrew Booth, Anne Brice, Andrew Booth, Anne Brice
2003 unpublished
We, the editors, would like to invite you to examine this model with an open mind and attempt to identify its potential usefulness wthin your specific context.  ...  management, its associated skills and technologies in centre stage in the delivery of appropriate and effective care.  ...  ' We've made the first faltering toddler's steps but we are a long way from adolescence and maturity.'  ... 
fatcat:6v3b7bjpovhuzchyfuq7b2zy2u

Ends, Norms, and Representations: Why ask "Why?" in Biology?

Brandon Conley
2018
a barrier to the project of integrating biological work on Tinbergen's four questions. iii BIOGRAPHICAL SKETCH Brandon Conley attended Appalachian State University, near his home town of Wilkesboro, NC  ...  In the final chapter, I develop a historical and philosophical interpretation of Ernst Mayr's distinction between proximate and ultimate causes and its relation to Niko Tinbergen's "four questions."  ...  ACKNOWLEDGEMENTS I would like to acknowledge and thank five groups of people for their roles in the development in this dissertation.  ... 
doi:10.7298/x4zc813j fatcat:4mwhqksdi5fplkskozrqntvysy
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