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A sheaf-theoretic approach to pattern matching and related problems

Yellamraju V. Srinivas
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Science 112 (1993) A sheaf-theoretic approach to pattern matching and related problems Yellamraju V.  ...  ., A sheaf-theoretic approach to pattern matching and related problems, Theoretical Computer Science 112 (1993) 53-97.  ...  Concluding remarks We have given a sheaf-theoretic characterization of pattern matching. We defined an occurrence to be an arrow in a category.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(93)90239-p">doi:10.1016/0304-3975(93)90239-p</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pnofhx7rtbhhbjtcgn4typkzh4">fatcat:pnofhx7rtbhhbjtcgn4typkzh4</a> </span>
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Page 2865 of Mathematical Reviews Vol. , Issue 94e [page]

<span title="">1994</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
A sheaf-theoretic approach to pattern matching and related problems. (English summary) International Conference on Algebraic Methodology and Software Technology (AMAST 91) (Iowa City, IA, 1991).  ...  Represent- ing the geometry of the pattern via a Grothendieck topology, the extension of the matching relation for a constant target and vary- ing pattern forms a sheaf.  ... 
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Author index volume 112 (1993)

<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
The Bore1 hierarchy is infinite in the class of regular sets of trees (Note) Srinivas, Y.V., A sheaf-theoretic approach to pattern matching and related problems Sturtivant. C. and G.S.  ...  ., A theory of binding structures and applications to rewriting Teillaud, M., sre J.-D. Boissonnat Thomas, M. and P.  ... 
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Semantic Unification A sheaf theoretic approach to natural language [article]

Samson Abramsky, Mehrnoosh Sadrzadeh
<span title="2014-03-13">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Language is contextual and sheaf theory provides a high level mathematical framework to model contextuality.  ...  Within this setting, we formulate a notion of semantic unification --- gluing meanings of parts of a discourse into a coherent whole --- as a form of sheaf-theoretic gluing.  ...  fed back into the sheaf-theoretic approach, in order to combine the strengths of structural and statistical methods in natural language semantics.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1403.3351v1">arXiv:1403.3351v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fkmgt5lzovgfxnkq5dfdk72ab4">fatcat:fkmgt5lzovgfxnkq5dfdk72ab4</a> </span>
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In-Depth Motivic Analysis Based On Multiparametric Closed Pattern And Cyclic Sequence Mining

Olivier Lartillot
<span title="2014-10-27">2014</span> <i title="Zenodo"> Zenodo </i> &nbsp;
Previous approaches have shown the difficulty of the problem related to the combinatorial explosion of possible candidate patterns [2] .  ...  The thematic class related to ground-truth pattern #2, which is the first countersubject, is extracted in the same way, forming a paradigmatic sheaf.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.1418345">doi:10.5281/zenodo.1418345</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nqm26xdajrcuzmosjt74cjjsqy">fatcat:nqm26xdajrcuzmosjt74cjjsqy</a> </span>
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Editorial

Teodor Rus
<span title="">1993</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/elaf5sq7lfdxfdejhkqbtz6qoq" style="color: black;">Theoretical Computer Science</a> </i> &nbsp;
Srinivas, in the article A sheaf-theoretic approach to pattern matching and related problems, uses Grothendieck topologies to provide a unifying methodology for the development of pattern-matching algorithms  ...  The structure of the patterns in the fast pattern-matching algorithms is defined in terms of the structure provided by the pattern components.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0304-3975(93)90237-n">doi:10.1016/0304-3975(93)90237-n</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qhwqtdeb6bg4bot3qwomwbypsu">fatcat:qhwqtdeb6bg4bot3qwomwbypsu</a> </span>
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Going Beyond the Data as the Patching (Sheaving) of Local Knowledge

Steven Phillips
<span title="2018-10-09">2018</span> <i title="Frontiers Media SA"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5r5ojcju2repjbmmjeu5oyawti" style="color: black;">Frontiers in Psychology</a> </i> &nbsp;
Tracking the passage from local to global properties is the purview of sheaf theory, a branch of mathematics at the nexus of algebra and geometry/topology.  ...  Two cognitive domains are examined: (1) learning cue-target patterns that conform to an underlying algebraic rule, and (2) visual attention requiring the integration of space-based feature maps.  ...  Category theory has been used as a basis for children's difficulty with understanding and exploiting the common relations in a reasoning problem (Halford and Wilson, 1980) , and as an approach to analogy  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3389/fpsyg.2018.01926">doi:10.3389/fpsyg.2018.01926</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/30356817">pmid:30356817</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC6189483/">pmcid:PMC6189483</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4zyvhqjlbjfe5anoxv3pihurei">fatcat:4zyvhqjlbjfe5anoxv3pihurei</a> </span>
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Page 6921 of Mathematical Reviews Vol. , Issue 93m [page]

<span title="">1993</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
Srinivas, A sheaf-theoretic ap- proach to pattern matching and related problems (53-97); Carolyn Talcott, A theory of binding structures and applications to rewrit- ing (99-143); Muffy Thomas and Phil  ...  Sompolinsky, Theoretical issues in learning from examples (217-237); Kenji Yamanishi, A statistical approach to computational learning theory (238-276).  ... 
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Super-resolving star clusters with sheaves

Michael Robinson, Christopher T. Capraro
<span title="2022-03-28">2022</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hqblpsydr5emviirtqkkmctpha" style="color: black;">EURASIP Journal on Advances in Signal Processing</a> </i> &nbsp;
AbstractThis article presents an optimization-based approach for counting and localizing stars within a small cluster, based on photon counts in a focal plane array.  ...  To ensure generality of our approach, it was constructed as a special case of a general theory built upon topological signal processing using the mathematics of sheaves that is applicable to general source  ...  Acknowledgements Fig. 11 Magnitude root mean squared error (RMSE) of the sheaf, CLEAN, and Richardson-Lucy algorithms split by Test (see Table 1 ).  ... 
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Page 3796 of Psychological Abstracts Vol. 79, Issue 9 [page]

<span title="">1992</span> <i title="American Psychological Association"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_psychological-abstracts" style="color: black;">Psychological Abstracts </a> </i> &nbsp;
Speed of naming problems may be related to prob- lems in rate of processing in other domains; a deficit in a specific timing mechanism is considered. 31732. Wolf, Maryanne & a dng Mateo.  ...  Five RP Ss showed problems with PPR and short-term memory, but this was unrelated to RS. There was no evidence that visual weaknesses were related to RS.  ... 
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Light Scattering from Crystalline Superstructure in Tubular-Extruded Poly(1-butene) Films. II. Analysis of Interparticle Interference Effect Based upon a Paracrystal Model

Takeji Hashimoto, Akira Todo, Hiromichi Kawai
<span title="">1978</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/euva77sbwjfg5id7ngmlz5kyzy" style="color: black;">Polymer journal</a> </i> &nbsp;
The lamellar overgrowth from the nuclei gives a sheaflike crystalline superstructures aligned regularly along the nuclei and nearly side by side with their axes preferentially oriented perpendicular to  ...  The analyses have yielded information on (i) average size of the sheaf, (ii) average intersheaf distance and its paracrystalline disorder, and (iii) average orientation of the row nuclei.  ...  ., Oz 2 and that of the sheaf axis, i.e., Oy3 are set to be symmetric with respect to the ED (Oz1 axis) and the transverse direction (Oy1 524 axis) so that the symmetry of the system matches to that of  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1295/polymj.10.521">doi:10.1295/polymj.10.521</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vzila7mh5rhxjnwhyf2zp6eyoq">fatcat:vzila7mh5rhxjnwhyf2zp6eyoq</a> </span>
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Sheaf theoretic formulation for consciousness and qualia and relationship to the idealism of non-dual philosophies

Menas C. Kafatos, Goro C. Kato
<span title="">2017</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/r3iw4i7vsvg3baci7ij2v5osfu" style="color: black;">Progress in Biophysics and Molecular Biology</a> </i> &nbsp;
., Sheaf theoretic formulation for consciousness and qualia and relationship to the idealism of non-dual philosophies ABSTRACT Questions about the nature of reality, whether Consciousness is the fundamental  ...  We advocate instead what we consider to be an approach that is in agreement with the foundation of quantum reality, which is based on Rāmānuja's version of Vedanta philosophy and non-dual Kashmir Śaivism  ...  For a more general and updated description of the above in terms of a general t-topos theoretic sheaf theory, see Kato (2017) or Kato (2013) .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.pbiomolbio.2017.09.003">doi:10.1016/j.pbiomolbio.2017.09.003</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/28887144">pmid:28887144</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mslt5yh3uvelpcrkgwp7podqgm">fatcat:mslt5yh3uvelpcrkgwp7podqgm</a> </span>
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Toward a spectral theory of cellular sheaves

Jakob Hansen, Robert Ghrist
<span title="2019-08-30">2019</span> <i title="Springer Science and Business Media LLC"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c5jvinnaofg2pnrpaxbxvqkocq" style="color: black;">Journal of Applied and Computational Topology</a> </i> &nbsp;
By lifting the combinatorial graph Laplacian to the Hodge Laplacian on a cellular sheaf of vector spaces over a regular cell complex, one can relate spectral data to the sheaf cohomology and cell structure  ...  This paper outlines a program in what one might call spectral sheaf theory-an extension of spectral graph theory to cellular sheaves.  ...  Approaching these notions of partitioning, partial sections, and noninvertible matchings from a sheaf-theoretic perspective offers new tools and clarifies the problems in question, with potential for the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s41468-019-00038-7">doi:10.1007/s41468-019-00038-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6kpswljp2zdptlyyolyhw2vgji">fatcat:6kpswljp2zdptlyyolyhw2vgji</a> </span>
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In 1967 Errett Bishop's book ' Foundations of constructive analysis' appeared

P. Aczel
<span title="">1981</span> <i title="Cambridge University Press (CUP)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/32b3egxidndk3mhj6jkag77nvu" style="color: black;">Proceedings of the Edinburgh Mathematical Society</a> </i> &nbsp;
While this notion continues to fascinate logicians and may have interesting sheaf theoretic models Bishop showed quite convincingly that Brouwer's free choice sequences are unnecessary for analysis.  ...  To my mind we will not have to wait long before there will be a significant interaction between constructive mathematics and theoretical computer science.  ... 
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From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality [article]

G. Masse
<span title="2021-05-28">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Doing so, we argue that contextuality emerged as a discrete logical problem and developed into a quantifiable quantum resource.  ...  We present and compare the main theoretical frameworks that have been derived. Finally, we focus on the complex task of establishing experimental tests of contextuality.  ...  approach [31] • Sheaf-theoretic and Operational approach [143] • Sheaf-theoretic and CbD approach [136] The following table is conceived as a way to depict the correspondence between the different  ... 
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