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One-Sided Instance-Based Boundary Sets [chapter]

Evgueni N. Smirnov, Ida G. Sprinkhuizen-Kuyper, H Jaap van den Herik
2004 Lecture Notes in Computer Science  
Instance retraction is a difficult problem for concept learning by version spaces. This chapter introduces a family of version-space representations called one-sided instance-based boundary sets.  ...  Compared to other representations, they are the most efficient useful 1 version-space representations for instance retraction. 1 In this chapter, the notion useful has a technical meaning defined in subsection  ...  We compared the one-sided instance-based boundary sets with other existing version-space representations that are efficient for instance retraction.  ... 
doi:10.1007/978-3-540-44497-8_14 fatcat:gcbdgmvt2jgyjpkhnho46krwxu

A Unifying Version-Space Representation

E.N. Smirnov, H.J. van den Herik, I.G. Sprinkhuizen-Kuyper
2004 Annals of Mathematics and Artificial Intelligence  
We demonstrate that this space includes the boundary-set representation and the instance-based boundary-set representation; i.e., the ABSs unify these two representations.  ...  We present a first solution to this problem, namely a new version-space representation called adaptable boundary sets (ABSs). We show that a version space can have a space of ABSs representations.  ...  section 4; thus, it is not dangerous anymore to use the boundary sets from a computational point of view; • if version-space learning is realised with instance-based boundary sets and we need to improve  ... 
doi:10.1023/b:amai.0000018576.88552.df fatcat:muzj2hro6nf37cxt7sgkdz7t74

Generalizing version spaces

Haym Hirsh
1994 Machine Learning  
The resulting learning algorithm, incremental version-space merging (IVSM), allows version spaces to contain arbitrary sets of classifiers, however generated, as long as they can be represented by boundary  ...  Although a landmark work, version spaces have proven fundamentally limited by being constrained to only consider candidate classifiers that are strictly consistent with data.  ...  Given version spaces VS 1 with boundary sets S 1 and G 1 , and VS 2 with boundary sets S 2 and G 2 , the version-space merging algorithm finds the boundary sets S 1u2 and G 1u2 for their intersection,  ... 
doi:10.1007/bf00993863 fatcat:oyiyfegjgjclldtrq75njof5bu

Computational homotopy of finite regular CW-spaces

Graham Ellis, Fintan Hegarty
2013 Journal of Homotopy and Related Structures  
We describe a computational approach to the basic homotopy theory of finite regular CW-spaces, paying particular attention to spaces arising as a union of closures of n-cells with isomorphic face posets  ...  Proposition 2.2 (i) Let X be a finite regular CW-space. Let X ⊆ X be a deformation CW-retract, and let A be a contractible CW-subspace of X . Then H k (X ; A) ∼ = H k (X , A; A), k ≥ 1.  ...  Full details of the retract can be seen by enlarging Fig. 11 in the electronic version of this article.  ... 
doi:10.1007/s40062-013-0029-4 fatcat:lbtgtlmyqnehfhey7fbot4mprq

Finding Narrow Passages with Probabilistic Roadmaps: The Small-Step Retraction Method

Mitul Saha, Jean-Claude Latombe, Yu-Chi Chang, Friedrich Prinz
2005 Autonomous Robots  
However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method -smallstep retraction -that helps PRM planners find paths through such passages.  ...  This method consists of slightly "fattening" robot's free space, constructing a roadmap in fattened free space, and finally repairing portions of this roadmap by retracting them out of collision into actual  ...  It benefited from discussions with Dr. Fabian Schwarzer and Dr. Pekka Isto. We also thank Dr. Zhongxue Gan at ABB Automation for providing us a CAD model of the IRB-2400 robot.  ... 
doi:10.1007/s10514-005-4748-1 fatcat:ev6en7x4ybealji6rxler4njsm

Decorated Teichmüller theory of bordered surfaces

R. C. Penner
2004 Communications in analysis and geometry  
This paper extends the decorated Teichmüller theory developed before for punctured surfaces to the setting of "bordered" surfaces, i.e., surfaces with boundary, and there is non-trivial new structure discovered  ...  One tool in the proof is a homeomorphism between two versions of a "decorated" moduli space for bordered surfaces.  ...  retraction of one version of decorated moduli space which is required in the sequel.  ... 
doi:10.4310/cag.2004.v12.n4.a2 fatcat:5fzvpd4oa5bcznt74sqakhyf2u

Finding narrow passages with probabilistic roadmaps: the small step retraction method

M. Saha, J.-C. Latombe
2005 2005 IEEE/RSJ International Conference on Intelligent Robots and Systems  
However, their efficiency decreases dramatically in spaces with narrow passages. This paper presents a new method -smallstep retraction -that helps PRM planners find paths through such passages.  ...  This method consists of slightly "fattening" robot's free space, constructing a roadmap in fattened free space, and finally repairing portions of this roadmap by retracting them out of collision into actual  ...  It benefited from discussions with Dr. Fabian Schwarzer and Dr. Pekka Isto. We also thank Dr. Zhongxue Gan at ABB Automation for providing us a CAD model of the IRB-2400 robot.  ... 
doi:10.1109/iros.2005.1545606 dblp:conf/iros/SahaL05 fatcat:sxwajjnp4nepjadbzg5tzfctim

Retracting Graphs to Cycles

Samuel Haney, Mehraneh Liaee, Bruce M. Maggs, Debmalya Panigrahi, Rajmohan Rajaraman, Ravi Sundaram, Michael Wagner
2019 International Colloquium on Automata, Languages and Programming  
Our first result is an O(min{k, √ n})-approximation for retracting any graph on n nodes to a cycle with k nodes.  ...  This problem has its roots in the rich theory of retraction of topological spaces, and has strong ties to well-studied metric embedding problems such as minimum bandwidth and 0-extension.  ...  It is easy to see that the distance-based lower bound has a value of 2 on this instance.  ... 
doi:10.4230/lipics.icalp.2019.70 dblp:conf/icalp/HaneyLMPRS19 fatcat:q4iq3mfvv5ekzi7wljytegp2fm

Retracting Graphs to Cycles [article]

Samuel Haney, Mehraneh Liaee, Bruce M. Maggs, Debmalya Panigrahi, Rajmohan Rajaraman, Ravi Sundaram
2019 arXiv   pre-print
Our first result is an O(mink, sqrtn)-approximation for retracting any graph on n nodes to a cycle with k nodes.  ...  This problem has its roots in the rich theory of retraction of topological spaces, and has strong ties to well-studied metric embedding problems such as minimum bandwidth and 0-extension.  ...  Given an instance φ of MAX-3SAT(5) with k-provers, we have thus constructed an instance seeking the retraction of guest graph G to the host defined by the set T with metric d T .  ... 
arXiv:1904.11946v1 fatcat:fersuyyl55fglnizy7hbpqihlu

A non-rigid registration framework that accommodates resection and retraction

Petter Risholm, Eigil Samsett, Ion-Florin Talos, William Wells
2009 Information processing in medical imaging : proceedings of the ... conference  
Resection is detected by a level set method evolving in the space where image intensities disagree.  ...  Retraction is detected at areas of the deformation field with high internal strain and the estimated retraction boundary is integrated as a diffusion boundary in the smoother to allow discontinuities to  ...  In particular, we will model resection by what we have termed a diffusion sink and retraction with a diffusion boundary.  ... 
pmid:19694284 pmcid:PMC2898517 fatcat:2xhwlkjj2bamtcmqj4d66jcrha

Retraction: Improved Approximation Schemes for Dominating Set Problems in Unit Disk Graphs [article]

Jittat Fakcharoenphol, Pattara Sukprasert
2021 arXiv   pre-print
He noted that the idea for dealing with the connected version using a constant number of extra layers in the shifting technique not only appeared Zhang et al.  ...  Abstract before retraction: We present two (exponentially) faster PTAS's for dominating set problems in unit disk graphs.  ...  Note that over all instances and cells, each point v ∈ V belongs to at most 4 expanded boundaries; thus we have PTAS for Connected MDS ** This manuscript has been retracted.  ... 
arXiv:2109.01283v3 fatcat:5eeo2q6hlnajpn6ohhqrkvsjjy

Boundaries of cocompact proper CAT(0) spaces

Ross Geoghegan, Pedro Ontaneda
2007 Topology  
For example: a compact manifold with non-empty boundary cannot be ∂ ∞ X with X cocompact.  ...  A proper CAT(0) metric space X is cocompact if it has a compact generating domain with respect to its full isometry group.  ...  Equivalently, picking a base point p ∈ X one can regard ∂ ∞ X as the set of geodesic rays starting at p endowed with the compact-open topology.  ... 
doi:10.1016/j.top.2006.12.002 fatcat:xtodve6c3fa3rosuchvspi44te

Manifolds of Preferences and Equilibria

Graciela Chichilnisky
2009 Social Science Research Network  
~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~P reface This work is concerned with the study of local and global properties of spaces of prefe rences and their applications to general equilibrium ,  ...  These structur es on spaces of preferenc es are then used to extend major • results on the regularity of equilib ria , based on Sard '. theorem and Abraham -Thom tra nsversality theory, to economie s where  ...  Let c c R~ be an open bounded set with C boundary.  ... 
doi:10.2139/ssrn.1366868 fatcat:2sgj24nbezb7dn4blwirmqqsny

Decorated Teichmüller Theory of Bordered Surfaces [article]

R. C. Penner
2003 arXiv   pre-print
This paper extends the decorated Teichm\"uller theory developed before for punctured surfaces to the setting of "bordered" surfaces, i.e., surfaces with boundary, and there is non-trivial new structure  ...  One tool in the proof is a homeomorphism between two versions of a "decorated" moduli space for bordered surfaces.  ...  retraction of one version of decorated moduli space which is required in the sequel.  ... 
arXiv:math/0210326v2 fatcat:idtsgxj5sjeirmeqzzoil2vhxa

Polyfolds: A first and second look

Oliver Fabert, Joel Fish, Roman Golovko, Katrin Wehrheim
2016 EMS Surveys in Mathematical Sciences  
It aims to systematically address the common difficulties of compactification and transversality with a new notion of smoothness on Banach spaces, new local models for differential geometry, and a nonlinear  ...  Polyfold theory was developed by Hofer-Wysocki-Zehnder by finding commonalities in the analytic framework for a variety of geometric elliptic PDEs, in particular moduli spaces of pseudoholomorphic curves  ...  For instance, the discussion that follows can be adapted to Gromov-Witten theory, various versions of Floer homology, various versions of contact homology, Symplectic Field Theory, and other moduli space  ... 
doi:10.4171/emss/16 fatcat:y76ihi4kmnanjkaftj4atmuam4
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