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Topic: Topology structure

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Topology glossary

product topology

closure topology

completeness topology

Zariski topology

base topology

continuity topology

differential topology

weak topology

general topology

neighborhood topology

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	[No title]
		Topology Glossary Mainly extracted from (a) UC Davis Math:Profile Glossary (http://www.math.ucdavis.edu/profiles/glossary.html) by Greg Kuperberg (http://www.math.ucdavis.edu/profiles/kuperberg.html), and (b) Topology Atlas Glossary (http://www.achilles.net/~mtalbot/TopoGloss.html).
		An early result in topology states that every closed 3-manifold (closed meaning that the manifold is finite and connected but has no boundary) has a Heegaard splitting and a resulting description in terms of a Heegaard diagram, which describes how the two handlebodies are glued together.
		Such a hyperbolic structure is determined by a conformal structure at the wounds of the cut (ends).
	www.ornl.gov /sci/ortep/topology/defs.txt (5717 words)

	Mathematical structure - Wikipedia, the free encyclopedia
		In mathematics, a structure on a set, or more generally a type, consists of additional mathematical objects that in some manner attach to the set, making it easier to visualize or work with, or endowing the collection with meaning or significance.
		As another example, if a set both has a topology and is a group, and the two structures are related in a certain way, the set becomes a topological group.
		Its algebraic structure and topology make it into a Lie group, a type of topological group.
	en.wikipedia.org /wiki/Mathematical_structure (285 words)

	[No title]
		Topology is a math discipline who treats of the research of invariants in a geometry cleared of all idea of measurement or of distance.
		Topology is a branch of pure mathematics, deals with the fundamental properties of abstract spaces.
		Topology is also concerned with the ways in which one manifold may be embedded within another, such as the ways a knotted circle may be embedded in three-dimensional space.
	www.chez.com /alcochet/toposi.htm (1679 words)

	DNA Structure and Topology
		This was before the discovery of the double-helical structure of DNA, and it is explained by the further demonstration that the pairing of bases is not random, but rather follows the rule that an A pairs with a T and a G pairs with a C.
		Structural variation of these grooves is one mechanism by which reactivity of DNA is modulated.
		Topology is the branch of mathematics that studies properties of objects that are invariant to continuous deformations of the object.
	www.rpi.edu /dept/bcbp/molbiochem/BiochSci/sbello/new_page_1.htm (5090 words)

	Topology
		The second, geometric topology, focuses on the connectivity properties of topological spaces and provides the core results from general topology that serve as background for subsequent courses in geometry and algebraic topology.
		General Topology’s value as a reference work is enhanced by a collection of historical notes for each section, an extensive bibliography, and an index.
		In classical topology, this relation is simple and clear: "An open set is a neighborhood of a point if and only if this point belongs to this open set." In early period of fuzzy topology, "membership relation" was similarly defined.
	www.wordtrade.com /science/mathematics/topology.htm (2132 words)

	Brainstorms: Dynamic Best Practices Topology
		Within this space-time structure are defined entities or systems with the ability to perform a type of information processing labeled biological information processing (accept or record input from the environment external to the entity, process the information as defined by a processing algorithm, and generate output into the external environment).
		The topology defined, it is suggested, provides a logical mathematical structure which can be used for formulating useful predictive scientific models and hypotheses addressing the operation of life forms and systems with information processing behavior similar to that of life forms.
		The criteria for determining the acceptability of mathematical structures or topologies are 1)logical soundness/logical consistency and 2)usefulness.
	www.iscid.org /boards/ubb-get_topic-f-6-t-000350.html (4865 words)

	List of Commands
		Structure information is generated at the end of every segment command.
		Patches make small modifications to the structure of residues such as converting one to a terminus, changing the protonation state, or creating disulphide bonds between a pair of residues.
		The O field is set to 1 for atoms with known coordinates, 0 for atoms with guessed coordinates, and -1 for atoms with no coordinate data available (coordinates are set to 0 for these atoms).
	www.ks.uiuc.edu /Research/namd/2.5b3/ug/node21.html (926 words)

	Understanding Topology and Shapefiles
		This structure can represent complex structures, such as polygons, that contain "islands." The vertices of a ring maintain a consistent, clockwise order so that the area to the right, as one "walks" along the ring boundary, is inside the polygon, and the area to the left is outside the polygon.
		The first step in enforcing planar topology in a shapefile is to remove twisted or self-intersecting polygon rings and to ensure that the "inside" of the polygon is on the correct side of the polygon boundary.
		Though the advantages previously attributed to topological data structures have become less clear, in large part because of improvements in computer performance, the bottom line is that GIS users need to adequately understand the data structures and use them appropriately.
	www.esri.com /news/arcuser/0401/topo.html (1912 words)

	rube(TM) - Documentation and Tutorial
		The first step to setting up the model structure is specifying the model and topology types.
		This is represented in MXL using the "model" and "topology" elements as follows.
		Each FBM node has the same structure, they are all of type "function" and each contains a script element which describes it's functionality.
	www.cise.ufl.edu /~kdamkjer/rube/hw2_tutorial_01.htm (388 words)

	[No title] (Site not responding. Last check: 2007-10-26)
		However, the internal topology of a Site is extremely important to the management and operation of the Site so the ESD structure provides for a rich set of organizational alternatives with different cost-benefit tradeoffs.
		The simplest structure to imagine is a Site using all Mode-0 ESDs with all the systems connected in a single Private Topology Partition (i.e., all the ESDs carry the same PTP value which is assigned by the local network administration).
		This structure will be mirrored by the actual machinery for distributing Routing Goop to the Sites as will be discussed a bit later, but this mental image of the prefixes "flowing" from the anchoring Large Structures is critical to understanding fundamental self-organizing abilities in the 8+8 model.
	psg.com /gse/draft-odell-8+8-00.txt (6953 words)

	Grain structure and topology
		It is worthwhile to mention that the interplanetary dust particles have a structure similar to that of the laboratory analogs, the PCA (Rietmeijer and Nuth [
		In addition to these two extreme cases of the chemical dust structure, we consider a model of “multishell'' grains, where each particle includes all constituents distributed within concentric spherical shells.
		To study the influence of the porosity on the extincting properties of dust grains, we fill composite and multishell spherical particles with vacuum.
	mpia-hd.mpg.de /homes/henning/Dust_opacities/Opacities/op/node5.html (431 words)

	Glasgow TOPS Structure Comparison
		The structure is converted to a simplified, TOPS representation and then compared against a non-redundant subset of all known structures.
		The compression is 1 for a pair of identical structures and 0 for two structures with no common features.
		Each pattern in the 'library' is given an attempt to match the uploaded structure and those patterns that successfully match are returned as a list.
	balabio.dcs.gla.ac.uk /tops/compare.html (268 words)

	OMNeT++ - The NED language
		The word topology will be used thoughout this paper to mean the fixed elements (nodes, resources etc.) and their interconnection structure.
		In case (a), one is forced to prepare an unnecessarily large topology description that is difficult to maintain.
		Nodes of the binary tree are mapped to module vector indices like in the heap data structure: node[0] is the root element and node[i]'s children are node[2i+1] and node[2i+2].
	www.ewh.ieee.org /soc/es/Nov1999/18/ned.htm (3261 words)

	[No title]
		Some details with respect to loading this geometry and topology in Oracle 10g topology are given in chapter 4, while chapter 5 does the same for the ESRI Geodatabase environment.
		Cadastral Data Selection and Preparation As topology structure in Oracle 10g requires a clean data set without topology errors, first the different cadastral offices were analyzed with respect to these errors.
		Preparation of Oracle topology The Dutch cadastral data used as input for the project is already topologically structured, in principle it should not be too hard to convert this into Oracle (and ArcGIS) topology.
	www.gdmc.nl /oosterom/ESRItopol_final_v3.doc (6546 words)

	A Simple Approach to Membrane Protein Secondary Structure and Topology based on NMR Spectroscopy -- Marassi 80 (2): 994 ...
		structure and its degree of tilt in the lipid bilayer membrane
		Orientational constraints as three-dimensional structural constraints from chemical shift anisotropy: the polypeptide backbone of gramicidin A in a lipid bilayer.
		Structures of the M2 channel-lining segments from nicotinic acetylcholine and NMDA receptors by NMR spectroscopy.
	www.biophysj.org /cgi/content/full/80/2/994 (4377 words)

	Structure and Topology of Microbial Communities in the Major Gut Compartments of Melolontha melolontha Larvae ...
		Structure and Topology of Microbial Communities in the Major Gut Compartments of Melolontha melolontha Larvae (Coleoptera: Scarabaeidae) -- Egert et al.
		Structure and Topology of Microbial Communities in the Major Gut Compartments of Melolontha melolontha Larvae (Coleoptera: Scarabaeidae)
		chitin structures characteristic of the hindguts of scarabaeid
	aem.asm.org /cgi/content/full/71/8/4556 (5154 words)

	Multiple four-stranded conformations of human telomere sequence d(CCCTAA) in solution -- Kanaori et al. 29 (3): 831 -- ...
		affects the folding topology and stability of the i-motif.
		For one anti-parallel duplex, the bases are in gray, and the sugar–phosphate backbones are colored depending on the residue: yellow for cytidine, blue for thymidine and red for adenosine.
		18 Smith,F.W. and Feigon,J. (1992) Quadruplex structure of Oxytricha telomeric DNA oligonucleotides.
	nar.oxfordjournals.org /cgi/content/full/29/3/831 (5440 words)

	The structure and topology of the Brjuno numbers by Eileen F. Lee (Site not responding. Last check: 2007-10-26)
		The structure and topology of the Brjuno numbers by Eileen F. Lee
		The structure and topology of the Brjuno numbers
		We construct a naturally occurring planar straight brush associated with the set of highly irrational numbers known as the Brjuno numbers, which are important in dynamical systems.
	at.yorku.ca /b/a/a/j/93.htm (105 words)

	Local structure and topology of a model amorphous metal
		The purpose of this study is to clarify the relationship between these two types of methods of describing the local structure of amorphous solids.
		It has been shown that the topology of the local structure represented by the Voronoi polyhedra is related to the local stresses and symmetry only through the coordination number.
		It is concluded, therefore, that the topological description based upon the polyhedral statistics does not provide an unambiguous microscopic basis for relating the local structure of the dense random packing model to its physical properties and could even be misleading.
	stacks.iop.org /0305-4608/11/2209 (321 words)

	Evaluation of several prediction methods of membrane protein structure and topology
		Since present prediction methods of membrane protein structure and topology made use of mixed data sets both from experiments and prediction as training and test sets, the reliability and accuracy of their prediction is still under debate.
		To benchmark the performance of these methods, this paper uses a test set of membrane proteins created by EBI with either available 3-D structure or experimentally confirmed transmembrane regions.
		Based upon recent advances in membrane protein, possible means to improve topology prediction accuracy are discussed.
	www.bioinfo.de /isb/gcb01/talks/li/main.html (138 words)

	Nucleic Acid Topology Bibliography from Ned Seeman's Laboratory.
		Chen, Y. Zhang, T.-J. Fu, X. Li, X. Yang, Y. Wang, J. Qi, B. Liu and F. Liu, Control of Structure and Topology in DNA Nanotechnology.
		Wang, R.J. Di Gate and N.C. Seeman, E. coli DNA The Construction of an RNA Knot and its Role in Demonstrating that Topoisomerase III is an RNA Topoisomerase.
		Structure, Motion, Interaction and Expression of Biological Macromolecules, ed by R.H. Sarma and M.H. Sarma, Adenine Press, New York, pp.
	seemanlab4.chem.nyu.edu /topobib.html (854 words)

	Protein structure: geometry, topology and classification
		The structural principals of proteins are reviewed and analysed from a geometric perspective with a view to revealing the underlying regularities in their construction.
		Computer methods for the automatic comparison and classification of these structures are then reviewed with an analysis of the statistical significance of comparing different shapes.
		Following an analysis of the current state of the classification of proteins, more abstract geometric and topological representations are explored, including the occurrence of knotted topologies.
	stacks.iop.org /0034-4885/64/517 (275 words)

	Workshop on DNA Topology and Structure
		Many important biological events are modulated by the topological state of the domain involved, including the initiation of gene expression and of DNA replication.
		This workshop will focus on the topological aspects of DNA structure and function that are of greatest biological importance.
		Dynamical, statistical and mechanical approaches to the analysis of topologically constrained DNA structures will be presented.
	dimacs.rutgers.edu /Workshops/Topology/announcement.html (225 words)

	List KWIC PACS and MSC+ZDM E-N lexical connection
		topologies) # several topologies on one set (change of topology, comparison of topologies, lattices of
		topology of surfaces (Donaldson polynomials, Seiberg - Witten invariants)
		topology of the line # foundations: limits and generalizations, elementary
	www.math.unipd.it /~biblio/kwic/msc-pacs/pml_11_095.htm (937 words)

	The Basic Picture, a structure for topology (ResearchIndex) (Site not responding. Last check: 2007-10-26)
		We also begin to show what kind of topology it is. Therefore we start from the following simple de nition of what we call basic pairs.
		We keep them as our principal object of study in this paper and as the ground structures in the whole series: De nition 2.1 A basic pair is a structure X = (X; ; S) where X and S are sets, and is a binary relation from X to S (Update)
		3 formal topologies (context) - topologies - 2001
	citeseer.ist.psu.edu /628748.html (376 words)

	Find in a Library: Topology and Borel structure; descriptive topology and set theory with applications to functional ...
		Find in a Library: Topology and Borel structure; descriptive topology and set theory with applications to functional analysis and measure theory
		Topology and Borel structure; descriptive topology and set theory with applications to functional analysis and measure theory
		WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
	www.worldcatlibraries.org /wcpa/ow/aa973f42adcee37d.html (73 words)

	Lecture 16: Internet Topology and Structure
		The Internet in the USA has always used a backbone topology, with the National Science Foundation Network (NSFNET) providing the original backbone network.
		In 1995, this structure was privatised, with a variety of commercial organisations (National Service Providers (NSPs)) taking over the backbone functionality.
		One difference between DSL services and other types is that, due to the way commercial access to telephone exchange DSL equipment is structured, ISPs can charge a single monthly fee including both "Basic Access" and Internet charges.
	ironbark.bendigo.latrobe.edu.au /subjects/CN/lectures/l16.d/Lect16.html (1487 words)

	On the structure topology of simplex spaces., Alan Gleit
		On the structure topology of simplex spaces., Alan Gleit
		[6] E. Effros, and A. Gleit, Structure in simplexes III, Trans.
		[9] G. Mackey, Borel structures in groups and their duals, Trans.
	projecteuclid.org /getRecord?id=euclid.pjm/1102976434 (105 words)

	[No title]
		X X parameters: alcalc - pointer to structure containing allocation size X parameters.
		X X/* X Xfunction: app_obj() X Xdescription: appends the object in the source data structure to the destination X data structure in core.
		X Xinputs: srcobj -- pointer to object structure to append to dstobj.
	www.netlib.org /poly2/dickson (1610 words)

	ExPASy - Tools (Site not responding. Last check: 2007-10-26)
		- Predict possible oligosaccharide structures that occur on proteins from their experimentally determined masses (can be used for free or derivatized oligosaccharides and for glycopeptides)
		HMMTOP - Prediction of transmembrane helices and topology of proteins (Hungarian Academy of Sciences)
		LOOPP - Sequence to sequence, sequence to structure, and structure to structure alignment
	us.expasy.org /tools (2152 words)

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