Academic literature on the topic 'Compactness'

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Journal articles on the topic "Compactness"

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MALYKHIN, VIACHESLAV I., and MICHAEL V. MATVEEV. "Inverse Compactness Versus Compactness." Annals of the New York Academy of Sciences 767, no. 1 Papers on Gen (September 1995): 153–60. http://dx.doi.org/10.1111/j.1749-6632.1995.tb55902.x.

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Bella, Angelo, and Peter Nyikos. "Sequential compactness vs. countable compactness." Colloquium Mathematicum 120, no. 2 (2010): 165–89. http://dx.doi.org/10.4064/cm120-2-1.

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Kanovei, V. G., and V. A. Lyubetsky. "Effective compactness and sigma-compactness." Mathematical Notes 91, no. 5-6 (May 2012): 789–99. http://dx.doi.org/10.1134/s0001434612050252.

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Costantini, Camillo, Sandro Levi, and Jan Pelant. "Compactness and local compactness in hyperspaces." Topology and its Applications 123, no. 3 (September 2002): 573–608. http://dx.doi.org/10.1016/s0166-8641(01)00222-x.

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Kirk, W. A. "Compactness and countable compactness in weak topologies." Studia Mathematica 112, no. 3 (1995): 243–50. http://dx.doi.org/10.4064/sm-112-3-243-250.

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Rudin, Mary Ellen, Ian S. Stares, and Jerry E. Vaughan. "From countable compactness to absolute countable compactness." Proceedings of the American Mathematical Society 125, no. 3 (1997): 927–34. http://dx.doi.org/10.1090/s0002-9939-97-04030-6.

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Lipparini, Paolo. "Ordinal compactness." Filomat 34, no. 4 (2020): 1117–45. http://dx.doi.org/10.2298/fil2004117l.

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We introduce a new covering property, defined in terms of order types of sequences of open sets, rather than in terms of cardinalities. The most general form depends on two ordinal parameters. Ordinal compactness turns out to be a much more varied notion than cardinal compactness. We prove many nontrivial results of the form ?every [?,?]-compact topological space is [?',?']-compact?, for ordinals ?,?, ?'and ?' while only trivial results of the above form hold, if we restrict to regular cardinals. Counterexamples are provided showing that many results are optimal. Many spaces satisfy the very same cardinal compactness properties, but have a broad range of distinct behaviors, as far as ordinal compactness is concerned. A much more refined theory is obtained for T1 spaces, in comparison with arbitrary topological spaces. The notion of ordinal compactness becomes partly trivial for spaces of small cardinality.
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Bahmani, Zargham. "Lipschitz Compactness." Mathematical Sciences Letters 3, no. 2 (May 1, 2014): 131–32. http://dx.doi.org/10.12785/msl/030209.

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Khurana, Surjit Singh. "Eberlein compactness." Rocky Mountain Journal of Mathematics 44, no. 1 (February 2014): 179–87. http://dx.doi.org/10.1216/rmj-2014-44-1-179.

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Lyu, Jun. "Edit compactness." Nature Plants 6, no. 3 (March 2020): 180. http://dx.doi.org/10.1038/s41477-020-0623-5.

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Dissertations / Theses on the topic "Compactness"

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Morgan, Frank. "Compactness." Pontificia Universidad Católica del Perú, 2014. http://repositorio.pucp.edu.pe/index/handle/123456789/96708.

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In my opinion, compactness is the most important concept in mathematics. We 'll track it from the one-dimensional real line in calculus to infinite dimensional spaces of functions and surfaces and see what it can do.
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Davis, Brian L. "Generalized compactness and applications /." Full text available from ProQuest UM Digital Dissertations, 2006. http://0-proquest.umi.com.umiss.lib.olemiss.edu/pqdweb?index=0&did=1283960471&SrchMode=1&sid=2&Fmt=2&VInst=PROD&VType=PQD&RQT=309&VName=PQD&TS=1193421049&clientId=22256.

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Potter, M. D. "Separators, coseparators and compactness." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355770.

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Diener, Hannes. "Compactness Under Constructive Scrutiny." Thesis, University of Canterbury. Mathematics and Statistics, 2008. http://hdl.handle.net/10092/1823.

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The aim of this thesis is to understand the constructive scope of compactness. We show that it is possible to define, constructively, a meaningful notion of compactness in a more general setting than the uniform/metric space one. Furthermore, we show that it is not possible to define compactness constructively in a topological space. We investigate exactly what principles are necessary and sufficient to prove classically true theorems about compactness, as well as their antitheses. We develop beginnings of a constructive theory of differentiable manifolds.
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Devlin, Barry-Patrick. "Codensity, compactness and ultrafilters." Thesis, University of Edinburgh, 2016. http://hdl.handle.net/1842/19476.

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Codensity monads are ubiquitous, as are various different notions of compactness and finiteness. Two such examples of "compact" spaces are compact Hausdorff Spaces and Linearly Compact Vector Spaces. Compact Hausdorff Spaces are the algebras of the codensity monad induced by the inclusion of finite sets in the category of sets. Similarly linearly compact vector spaces are the algebras of the codensity monad induced by the inclusion of finite dimensional vector spaces in the category of vector spaces. So in these two examples the notions of finiteness, compactness and codensity are intertwined. In this thesis we generalise these results. To do this we generalise the notion of ultrafilter, and follow the intuition of the compact Hausdorff case. We give definitions of general notions of "finiteness" and "compactness" and show that the algebras for the codensity monad induced by the "finite" objects are exactly the "compact" objects.
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Wolf, Robert G. "Compactness of Isoresonant Potentials." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/45.

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Bruning considered sets of isospectral Schrodinger operators with smooth real potentials on a compact manifold of dimension three. He showed the set of potentials associated to an isospectral set is compact in the topology of smooth functions by relating the spectrum to the trace of the heat semi-group. Similarly, we can consider the resonances of Schrodinger operators with real valued potentials on Euclidean space of whose support lies inside a ball of fixed radius that generate the same resonances as some fixed Schrodinger operator, an ``isoresonant" set of potentials. This isoresonant set of potentials is also compact in the topology of smooth functions for dimensions one and three. The basis of the result stems from the relation of a regularized wave trace to the resonances via the Poisson formula (also known as the Melrose trace formula). The second link is the small-t asymptotic expansion of the regularized wave trace whose coefficients are integrals of the potential function and its derivatives. For an isoresonant set these coefficients are equal due to the Poisson formula. The equivalence of coefficients allows us to uniformly bound the potential functions and their derivatives with respect to the isoresonant set. Finally, taking a sequence of functions in the isoresonant set we use the uniform bounds to construct a convergent subsequence using the Arzela-Ascoli theorem.
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Masuret, Jacques. "Closure and compactness in frames." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4108.

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Thesis (MSc (Mathematics))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: As an introduction to point-free topology, we will explicitly show the connection between topology and frames (locales) and introduce an abstract notion, which in the point-free setting, can be thought of as a subspace of a topological space. In this setting, we refer to this notion as a sublocale and we will show that there are at least four ways to represent sublocales. By using the language of category theory, we proceed by investigating closure in the point-free setting by way of operators. We de ne what we mean by a coclosure operator in an abstract context and give two seemingly di erent examples of co-closure operators of Frm. These two examples are then proven to be the same. Compactness is one of the most important notions in classical topology and therefore one will nd a great number of results obtained on the subject. We will undertake a study into the interrelationship between three weaker compact notions, i.e. feeble compactness, pseudocompactness and countable compactness. This relationship has been established and is well understood in topology, but (to a degree) the same cannot be said for the point-free setting. We will give the frame interpretation of these weaker compact notions and establish a point-free connection. A potentially promising result will also be mentioned.
AFRIKAANSE OPSOMMING: As 'n inleiding tot punt-vrye topologie, sal ons eksplisiet die uiteensetting van hierdie benadering tot topologie weergee. Ons de nieer 'n abstrakte konsep wat, in die punt-vrye konteks, ooreenstem met 'n subruimte van 'n topologiese ruimte. Daar sal verder vier voorstellings van hierdie konsep gegee word. Afsluiting, deur middel van operatore, word in die puntvrye konteks ondersoek met behulp van kategorie teorie as taalmedium. Ons sal 'n spesi eke operator in 'n abstrakte konteks de nieer en twee o enskynlik verskillende voorbeelde van hierdie operator verskaf. Daar word dan bewys dat hierdie twee operatore dieselfde is. Kompaktheid is een van die mees belangrikste konsepte in klassieke topologie en as gevolg daarvan geniet dit groot belangstelling onder wiskundiges. 'n Studie in die verwantskap tussen drie swakker forme van kompaktheid word onderneem. Hierdie verwantskap is al in topologie bevestig en goed begryp onder wiskundiges. Dieselfde kan egter, tot 'n mate, nie van die puntvrye konteks ges^e word nie. Ons sal die puntvrye formulering van hierdie swakker konsepte van kompaktheid en hul verbintenis, weergee. 'n Resultaat wat moontlik belowend kan wees, sal ook genoem word.
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Marcus, Nizar. "E-compactness in pointfree topology." Doctoral thesis, University of Cape Town, 1998. http://hdl.handle.net/11427/9572.

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Bibliography: leaves 100-107.
The main purpose of this thesis is to develop a point-free notion of E-compactness. Our approach follows that of Banascheski and Gilmour in [17]. Any regular frame E has a fine nearness and hence induces a nearness on an E-regular frame L. We show that the frame L is complete with respect this nearness iff L is a closed quotient of a copower of E. This resembles the classical definition, but it is not a conservative definition: There are spaces that may be embedded as closed subspaces of powers of a space E, but their frame of opens are not closed quotients of copowers of the frame of opens of E. A conservative definition of E-compactness is obtained by considering Cauchy completeness with respect to this nearness. Another central notion in the thesis is that of K-Lindelöf frames, a generalisation of Lindelöf frames introduced by J.J. Madden [59]. In the last chapter we investigate the interesting relationship between the completely regular K-Lindelöf frames and the K-compact frames.
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Mabula, Mokhwetha Daniel. "Compactness in asymmetrically normed lattices." Doctoral thesis, University of Cape Town, 2012. http://hdl.handle.net/11427/11707.

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Includes abstract.
Includes bibliographical references.
The aim of the thesis is to investigate aspects of the theory of such spaces, concentrating mainly, but not exclusively, on nite dimensional spaces. One of the main aims of this thesis is to investigate compactness in the setting of asymmetrically normed lattices. In order to do this, it was necessary to study convergence of sequences and left-K-sequential completeness and precompactness of subsets of such spaces.
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Kudri, Soraya Rosana Torres. "L-fuzzy compactness and related concepts." Thesis, City University London, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.283158.

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Books on the topic "Compactness"

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Vrabie, I. I. Compactness methods for nonlinear evolutions. 2nd ed. Harlow, Essex, England: Longman, 1995.

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Ursul, Mihail. Topological Rings Satisfying Compactness Conditions. Dordrecht: Springer Netherlands, 2002.

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Ursul, Mihail. Topological Rings Satisfying Compactness Conditions. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-010-0249-3.

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Ursul, M. I. Topological rings satisfying compactness conditions. Dordrecht: Kluwer Academic Publishers, 2002.

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Horn, David L. District compactness: Theory and application. Wooster, Ohio: College of Wooster, 1993.

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Vrabie, I. I. Compactness methods for nonlinear evolutions. Harlow, Essex, England: Longman Scientific & Technical, 1987.

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Topological rings satisfying compactness conditions. Dordrecht: Kluwer Academic Publishers, 2002.

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Pratt, R. C. J. Urban compactness, social labour and planning. Birmingham: Faculty of the Built Environment, University of Central England in Birmingham, 1996.

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1969-, Schlag Wilhelm, ed. Concentration compactness for critical wave maps. Zürich, Switzerland: European Mathematical Society, 2012.

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Karl-Heinz, Fieseler, ed. Concentration compactness: Functional-analytic grounds and applications. London: Imperial College Press, 2007.

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Book chapters on the topic "Compactness"

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Katzourakis, Nikos, and Eugen Vărvărucă. "Compactness and sequential compactness." In An Illustrative Introduction to Modern Analysis, 119–50. Boca Raton : CRC Press, 2018.: Chapman and Hall/CRC, 2018. http://dx.doi.org/10.1201/9781315195865-5.

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Picado, Jorge, and Aleš Pultr. "Compactness and Local Compactness." In Frames and Locales, 125–44. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0154-6_7.

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Pansu, Pierre. "Compactness." In Progress in Mathematics, 233–49. Basel: Birkhäuser Basel, 1994. http://dx.doi.org/10.1007/978-3-0348-8508-9_9.

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Wendl, Chris. "Compactness." In Lecture Notes in Mathematics, 99–115. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-91371-1_4.

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Searcóid, Mícheál Ó. "Compactness." In Springer Undergraduate Mathematics Series, 231–44. London: Springer London, 2002. http://dx.doi.org/10.1007/978-1-4471-0179-6_11.

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Shakarchi, Rami. "Compactness." In Problems and Solutions for Undergraduate Analysis, 125–31. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4612-1738-1_9.

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Light, W. A. "Compactness." In An Introduction to Abstract Analysis, 71–82. Boston, MA: Springer US, 1990. http://dx.doi.org/10.1007/978-1-4899-7254-5_6.

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Lang, Serge. "Compactness." In Undergraduate Analysis, 193–205. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/978-1-4757-2698-5_9.

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Singh, Tej Bahadur. "Compactness." In Introduction to Topology, 95–124. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-6954-4_5.

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Waldmann, Stefan. "Compactness." In Topology, 73–86. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-09680-3_5.

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Conference papers on the topic "Compactness"

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Guofang Zhang. "From relative views see countable compactness and compactness." In 2011 2nd International Conference on Artificial Intelligence, Management Science and Electronic Commerce (AIMSEC). IEEE, 2011. http://dx.doi.org/10.1109/aimsec.2011.6010210.

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Martinez-Ortiz, Carlos, and Richard Everson. "Minkowski compactness measure." In 2013 13th UK Workshop on Computational Intelligence (UKCI). IEEE, 2013. http://dx.doi.org/10.1109/ukci.2013.6651288.

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Mucuk, Osman, and Hüseyin Çakallı. "G-compactness and local G-compactness of topological groups with operations." In FOURTH INTERNATIONAL CONFERENCE OF MATHEMATICAL SCIENCES (ICMS 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0042236.

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Idczak, Dariusz, and Stanislaw Walczak. "Compactness of fractional imbeddings." In 2012 17th International Conference on Methods & Models in Automation & Robotics (MMAR). IEEE, 2012. http://dx.doi.org/10.1109/mmar.2012.6347820.

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Li, Hong-Yan. "Measures of near compactness." In 2010 Seventh International Conference on Fuzzy Systems and Knowledge Discovery (FSKD). IEEE, 2010. http://dx.doi.org/10.1109/fskd.2010.5569692.

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Loranca, B., Aguirre Vara, and Zamora Alcocer. "Compactness Classification for Geographic Zones." In 2006 3rd International Conference on Electrical and Electronics Engineering. IEEE, 2006. http://dx.doi.org/10.1109/iceee.2006.251931.

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Zunic, Jovisa, Kaoru Hirota, and Carlos Martinez-Ortiz. "Compactness measure for 3D shapes." In 2012 International Conference on Informatics, Electronics & Vision (ICIEV). IEEE, 2012. http://dx.doi.org/10.1109/iciev.2012.6317466.

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Plet, Sullivan, Gerard Bouisse, and Michel Campovecchio. "Improvement of LDMOS MMICs compactness." In 2016 IEEE Topical Conference on Power Amplifiers for Wireless and Radio Applications (PAWR). IEEE, 2016. http://dx.doi.org/10.1109/pawr.2016.7440157.

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Zheng, Qi, Peng Zhang, and Xinge You. "Saliency Detection by Compactness Diffusion." In British Machine Vision Conference 2017. British Machine Vision Association, 2017. http://dx.doi.org/10.5244/c.31.68.

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Song, Yuqing. "Class compactness for data clustering." In Integration (2010 IRI). IEEE, 2010. http://dx.doi.org/10.1109/iri.2010.5558958.

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Reports on the topic "Compactness"

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Freyberger, Joachim, and Matthew Masten. Compactness of infinite dimensional parameter spaces. Institute for Fiscal Studies, January 2016. http://dx.doi.org/10.1920/wp.cem.2016.0116.

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Fryer, Roland, and Richard Holden. Measuring the Compactness of Political Districting Plans. Cambridge, MA: National Bureau of Economic Research, October 2007. http://dx.doi.org/10.3386/w13456.

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Weinberger, Hans, and George R. Sell. Metastability and Compensated Compactness in Continuum Theories. Fort Belvoir, VA: Defense Technical Information Center, January 1986. http://dx.doi.org/10.21236/ada164634.

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Karlsen, Kenneth H., Michel Rascle, and Eitan Tadmor. On the Existence and Compactness of a Two-Dimensional Resonant System of Conservation Laws. Fort Belvoir, VA: Defense Technical Information Center, October 2006. http://dx.doi.org/10.21236/ada457740.

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Hubmann, Christian, Frank Beste, Hubert Friedl, and Wolfgang Schoffmann. Single Cylinder 25kW Range Extender as Alternative to a Rotary Engine Maintaining High Compactness and NVH Performance. Warrendale, PA: SAE International, October 2013. http://dx.doi.org/10.4271/2013-32-9132.

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Ohad, Nir, and Robert Fischer. Regulation of plant development by polycomb group proteins. United States Department of Agriculture, January 2008. http://dx.doi.org/10.32747/2008.7695858.bard.

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Our genetic and molecular studies have indicated that FIE a WD-repeat Polycomb group (PcG) protein takes part in multi-component protein complexes. We have shown that FIE PcG protein represses inappropriate programs of development during the reproductive and vegetative phases of the Arabidopsis life cycle. Moreover, we have shown that FIE represses the expression of key regulatory genes that promote flowering (AG and LFY), embryogenesis (LEC1), and shoot formation (KNAT1). These results suggest that the FIE PcG protein participates in the formation of distinct PcG complexes that repress inappropriate gene expression at different stages of plant development. PcG complexes modulate chromatin compactness by modifying histones and thereby regulate gene expression and imprinting. The main goals of our original project were to elucidate the biological functions of PcG proteins, and to understand the molecular mechanisms used by FIE PcG complexes to repress the expression of its gene targets. Our results show that the PcG complex acts within the central cell of the female gametophyte to maintain silencing of MEA paternal allele. Further more we uncovered a novel example of self-imprinting mechanism by the PgG complex. Based on results obtained in the cures of our research program we extended our proposed goals and elucidated the role of DME in regulating plant gene imprinting. We discovered that in addition to MEA,DME also imprints two other genes, FWA and FIS2. Activation of FWA and FIS2 coincides with a reduction in 5-methylcytosine in their respective promoters. Since endosperm is a terminally differentiated tissue, the methylation status in the FWA and FIS2 promoters does not need to be reestablished in the following generation. We proposed a “One-Way Control” model to highlight differences between plant and animal genomic imprinting. Thus we conclude that DEMETER is a master regulator of plant gene imprinting. Future studies of DME function will elucidate its role in processes and disease where DNA methylation has a key regulatory role both in plants and animals. Such information will provide valuable insight into developing novel strategies to control and improve agricultural traits and overcome particular human diseases.
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