81. Towards Exploiting Link Evolution It describes how to compute incrementally PageRank when Web graph's link topology changes. PS format http://www.almaden.ibm.com/cs/people/siva/papers/linkevol.ps

82. The Geometry Junkyard: Geometric Topology Numerous links in the Geometry Junkyard.Category Science Math topology Geometric topology......The Geometry Junkyard. Geometric topology. This area bottles. ConstructingBoy's surface out of paper and tape. Crystallographic topology. C http://www.ics.uci.edu/~eppstein/junkyard/topo.html

Geometric Topology This area of mathematics is about the assignment of geometric structures to topological spaces, so that they "look like" geometric spaces. For instance, compact two dimensional surfaces can have a local geometry based on the sphere (the sphere itself, and the projective plane), based on the Euclidean plane (the torus and the Klein bottle), or based on the hyperbolic plane (all other surfaces). Similar questions in three dimensions have more complicated answers; Thurston showed that there are eight possible geometries, and conjectured that all 3-manifolds can be split into pieces having these geometries. Computer solution of these questions by programs like SnapPea has proved very useful in the study of knot theory and other topological problems. Acme Klein Bottle . A topologist's delight, handcrafted in glass. Are most manifolds hyperbolic? From Dave Rusin's known math pages. Boy's surface , visualized with Mathematica and GeomView by Amy Hawthorne and Jenny Posson-Brown. See also the Geometry Center Boy's Surface exhibit Paul Bourke's Boy's Surface images , Tore Nordstrand's Boy Surface ray-tracing and explanation an asymmetric animated gif from the Harvard zoo Michael Wittman's CS284 project to develop polygonal and spline-based Boy's surfaces , and A. Fomenko's constructions of Boy's surface from dissected Klein bottles

83. Programming Symbolic Computation Team Research Of The University Of La Rioja Department of Mathematics and Computer Science, University of La Rioja, Logro±o, Spain. Research has been focused on the design, specification and construction of symbolic computation systems for Algebraic topology. http://www.unirioja.es/dptos/dmc/psycotrip

P rogramming and Sy mbolic Co mputation T eam O f U niversidad de La R ioja http://www.unirioja.es/ We are the Programming and Symbolic Computation Team, at the Department of Mathematics and Computer Science of the University of La Rioja Symbolic computation systems are an important tool for the scientific calculation and discovery. Apart from well-known commercial products (Mathematica, Maple, ), there exists a great variety of systems developed in the academic context, without many connections with the current trends in Software Engineering. Our previous experience has been focused on the design, specification and construction of symbolic computation systems for Algebraic Topology. In particular, our main research area has been the formal analysis of one of these tools, namely, the EAT system. At this moment, we are involved in a more holistic approach, one that deals with software verification, conceptual modelling and Internet-based services; that is, to devise algebraic manipulation systems in the Software Engineering framework. Our objective is then to make progress towards a methodology for the analysis, specification, development, verification and maintenance of symbolic computation systems. Research Areas Members Last Papers

84. The Math Forum - Math Library - Topology study of mathematics. This page contains sites relating to topology. Browseand Search the Library Home Math Topics topology. http://mathforum.org/library/topics/topology/

Browse and Search the Library Home Math Topics : Topology Library Home Search Full Table of Contents Suggest a Link ... Library Help Subcategories (see also All Sites in this category Algebraic Topology Knot Theory Topological Groups/Lie Groups Selected Sites (see also All Sites in this category GN General Topology (Front for the Mathematics ArXiv) - Univ. of California, Davis General Topology preprints, from the U.C. Davis front end for the xxx.lanl.gov e-Print archive, a major site for mathematics preprints that has incorporated many formerly independent specialist archives. Search by keyword or browse by topic. more>> Investigating Patterns: R-U-B-B-E-R Geometry (Topology) - Jill Britton Selected web pages for educators, each leading to recreation-oriented learning experiences for middle school students. Topics include: Topology / Anamorphic Art; Jordan Curves / Mazes / Networks / Map Coloring; Math-e-Magic / Mobius Strip; Flexagons.  more>> The Topological Zoo - The Geometry Center For mathematicians and educators: a visual dictionary of surfaces and other mathematical objects, consisting primarily of movies, still images and interactive pictures. Can be used to complement classroom presentations, research papers and talks. Each object is accompanied by a short description that provides background information and interconnections among the objects in the zoo. Where appropriate, the equations that describe the objects are included. Primarily a reference, not an introduction to topology or other branches of mathematics. An ongoing project at the Geometry Center, the work of graduate students from the the University of Minnesota and undergraduates who participate in the Summer Institute at the Geometry Center.

85. Math Forum: Leonard Euler And The Bridges Of Konigsberg The Beginnings of topology A Math Forum Project topology is one ofthe newest branches of mathematics. A simple way to describe http://mathforum.org/isaac/problems/bridges1.html

The Beginnings of Topology... A Math Forum Project Table of Contents: Famous Problems Home The Bridges of Konigsberg The Value of Pi Prime Numbers ... Links Topology is one of the newest branches of mathematics. A simple way to describe topology is as a 'rubber sheet geometry' - topologists study those properties of shapes that remain the same when the shapes are stretched or compressed. The 'Euler number' of a 'network' like the ones presented later in this discussion is an example of a property that does not change when the network is stretched or compressed. The foundations of topology are often not part of high school math curricula, and thus for many it sounds strange and intimidating. However, there are some readily graspable ideas at the base of topology that are interesting, fun, and highly applicable to all sorts of situations. One of these areas is the topology of networks, first developed by Leonard Euler in 1735. His work in this field was inspired by the following problem: The Seven Bridges of Konigsberg In Konigsberg, Germany, a river ran through the city such that in its center was an island, and after passing the island, the river broke into two parts. Seven bridges were built so that the people of the city could get from one part to another. A crude map of the center of Konigsberg might look like this:

86. Visualizing Internet Topology At A Macroscopic Scale - CAIDA : ANALYSIS : Topolo location ANALYSIS topology as_core_network Visualizing Internettopology at a Macroscopic Scale, When the Internet was in its http://www.caida.org/analysis/topology/as_core_network/

ANALYSIS topology Visualizing Internet Topology at a Macroscopic Scale When the Internet was in its infancy, monitoring traffic was relatively simple. However, after experiencing phenomonal growth in the 1990's, tracking connectivity has become a daunting task. Recently, CAIDA researchers have attempted to strip away lesser connected autonomous systems (or `ASes') in order to find out how Internet connectivity is distributed among ISPs. About current AS Internet graph Available posters Previous versions Visualizing the AS Core We describe a visualization that shows a macroscopic snapshot of the Internet core taken from data collected during a two week period from April 1-16, 2002. Input Data The graph reflects 1,224,733 IP addresses and 2,093,194 IP links, (immediately adjacent addresses in a traceroute-like path) of skitter data from 21 monitors probing approximately 932,000 destinations spread across over 75,000 (70%) of globally routable network prefixes. We then aggregate this view of the network into a topology of Autonomous Systems (ASes), each of which approximately maps to an Internet Service Provider (ISP) (Some ISPs administer more than one AS but it is not typical). We map each IP address to the AS responsible for routing it, i.e., the origin (end-of-path) AS for the best match IP prefix of this address in Border Gateway Protocol (BGP) routing tables collected by the University of Oregon's RouteViews project (http://www.antc.uoregon.edu/route-views/)

87. Mahdavi SUNY Potsdam, NY, USA; 2006 June 2003. http://www2.potsdam.edu/mahdavk/Conf.htm

Math. Dept. Registration Financial Support SUNY Potsdam ... Map of Parking Lots Interactions between Representation Theories, Knot Theory, Topology, Quantum Field Theory, Category Theory, and Mathematical Physics. SUNY Potsdam June 2-6, 2003 Speakers SCHEDULES ABSTRACTS This workshop investigates the interactions between Representation Theories, Knot Theory, Topology, quantum Field Theory, Category Theory, and Mathematical Physics. This conference will be of great benefit to the researchers, recent Ph.Ds, and graduate students. Some financial support is available for graduate students, recent Ph.Ds, and others who are qualified. REGISTRATION Total cost of room and board, on Campus, is $206.5 Participants who choose to stay on campus will be housed in (SUNY Potsdam Map) Off Campus housing Hotel listing (you need to make your own reservation) a block of rooms has been reserved at Clarkson Inn. For reservation please call 1 800 790 6970, before May 15, 2003($89.00 for single, and$99.00 for double, per night). you need to mention SUNY Potsdam math. conference.

88. AS Internet Graph - CAIDA : ANALYSIS : Topology : As_core_network Page URL http//www.caida.org/analysis/topology/as_core_network/AS_Network.xmlLast updated Fri Jun 14 090658 PDT 2002 Maintained by Bradley Huffaker. http://www.caida.org/analysis/topology/as_core_network/AS_Network.xml

ANALYSIS topology : AS_Network.xml AS Internet graph The AS Internet graph: A Macroscopic Visualisation of the Internet April 1 - April 16, 2002. The option to preview and purchase the new 24"x32" AS Internet graph poster is available thanks to the cooperation of About current AS Internet graph Available posters Previous versions Cooperative Association for Internet Data Analysis (CAIDA) Page URL: http://www.caida.org/analysis/topology/as_core_network/AS_Network.xml Last updated: Fri Jun 14 09:06:58 PDT 2002 Maintained by: Bradley Huffaker

89. Lehigh Geometry/Topology Conference Held each summer at Lehigh University. 1416 June 2001. http://www.lehigh.edu/dlj0/public/www-data/geotop.html

Lehigh University Geometry and Topology Conference Dates: June 12-14, 2003 The conference will start at 11:00 am on Thursday, June 12. The first talk will be at 1:30 Thursday, and the last talk will end at 3:25 Saturday, June 14. Principal Speakers Jeff Cheeger, Courant Institute, NYU Ruth Lawrence, Hebrew University Doug Ravenel, University of Rochester Vladimir Voevodsky, Institute for Advanced Study TBA, Previous Principal Speakers All principal talks will be in Neville Hall, Auditorium II. In addition, there will be parallel sessions of 40-minute contributed talks, divided roughly into Differential and Complex Geometry, Algebraic Topology, and Geometric Topology. These talks will take place in the Seely G. Mudd building, next to Neville. Breakfast will be provided Friday and Saturday mornings, and lunch will be provided Thursday, Friday and Saturday noons. Dinner will be the only meal not provided gratis. On Thursday, expeditions to nearby restaurants will be arranged, followed by a party. On Friday there will be a Chinese banquet at a cost of $30. More information will be available at this site as it becomes available. Please check back from time to time.

90. Ideas, Concepts And Definitions topology. topology is the mathematical study of surfaces. Sometimes Themathematical study of knots is a branch of topology. The http://www.c3.lanl.gov/mega-math/gloss/topo/topo.html

Topology Topology is the mathematical study of surfaces . Sometimes it is called ``rubber sheet geometry" because topologists consider geometric figures as though they were drawn on infinitely stretchable rubber sheets. In two dimensions, topologists imagine figures that can be stretched and pulled as though they were drawn on an infinitely thin, infinitely stretchable material that can be deformed in any way (not including tearing, perforating, or gluing). Some properties that are important in Euclidean geometry such as distance, measurement of angles, or straightness are don't hold. Other properties, such as whether lines intersect or whether figures are closed (like the letter "O" ) or open (like the letter "U") remain important. In two dimensions, a triangle, a square, and a circle are all topologiclaly equivalent. So are the upper case letters "T", "F" and "E". In 3 dimensions, the surface of a cube, a pyramid, and a sphere are topologically equivalent. A stretchable "skin" that covers any one of them can be restretched to cover any of the others. The surface of a donut and a coffee cup are topologically equivalent each is a three-dimensional object with a hole in it. This is an unusual (but valid) way to think about the world.

91. Pushpa Publishing House, Allahabad, Uttar Pradesh India (Pushpa) Table of contents and abstracts from vol.1 (2001). http://www.pphmj.com/jpgtjournals.htm

JP Journal of Geometry and Topology (ISSN 0972 - 415X) The JP Journal of Geometry and Topology is devoted to the publication of articles of current interest in any branch of Geometry and Topology The journal will be published in three issues per volume annually appearing in March, July and November. A volume is expected to comprise of 300 pages and consist of duly refereed original research papers and c ritical survey articles. Current Volumes: Content Subscription Principal Editor: Professor K. K. Azad (University of Allahabad, INDIA) Editorial Board Information to Authors Abstracted/indexed/Reviewed: Mathematical Reviews Zentralblatt fur Mathematik.

92. [hep-th/9907119] Topological Quantum Field Theories -- A Meeting Ground For Phys Topological quantum field theories can be used as a powerful tool to probe geometry and topology in low dimensions. ChernSimons theories, which are examples of such field theories, provide a field theoretic framework for the study of knots and links in three dimensions. http://xxx.lanl.gov/abs/hep-th/9907119

High Energy Physics - Theory, abstract hep-th/9907119 Topological Quantum Field Theories A Meeting Ground for Physicists and Mathematicians Author: R.K. Kaul Comments: Latex, 27 eps figures Subj-class: High Energy Physics - Theory; Mathematical Physics Full-text: PostScript PDF , or Other formats References and citations for this submission: SLAC-SPIRES HEP (refers to , cited by , arXiv reformatted); CiteBase (autonomous citation navigation and analysis) Links to: arXiv hep-th find abs

93. Nathan Dunfield Harvard University. 3dimensional topology, geometry, and related topics. http://www.math.harvard.edu/~nathand/

Nathan Dunfield Benjamin Peirce Assistant Professor of Mathematics My research interests are 3-dimensional topology, geometry, and related topics. I got my Ph.D from the University of Chicago in June 1999 under Peter Shalen and Mel Rothenberg. My time at Harvard is drawing to a close, and I will be applying for a more permanent, tenure-track, job this fall. If you might be interested in hiring me, you can find my CV below, together with my research and teaching statements. Vita: PDF or Postscript Research Statement: PDF or Postscript Teaching Statement: PDF or Postscript Publications, Preprints, and Slides. Data on the Virtual Haken Conjecture. Program to compute the boundary slopes of a 2-bridge or Montesinos knot. Additions to SnapPea, and some related tables An interesting relationship between the Jones polynomial and hyperbolic volume. Miscellaneous software Some interesting links: The pictures on this page are from Knot Plot. Mark Brittenham's Low-dimensional topology links , including a list of home pages. CompuTop: Links for computation in low-dimensional topology.

94. Topology - Webopedia.com topology IETF Physical topology Working Group Charter Describes the IETF physicaltopology working group and includes contact and mailing list information. http://www.webopedia.com/TERM/E/topology.html

You are in the: Small Business Channel Jump to Website ECommerce Guide Small Business Computing Webopedia Enter a keyword... ...or choose a category. choose one... All Categories Communications Computer Industry Companies Computer Science Data Graphics Hardware Internet and Online Services Mobile Computing Multimedia Networks Open Source Operating Systems Programming Software Standards Types of Computers Wireless Computing World Wide Web Home Term of the Day New Terms New Links ... Be a Commerce Partner topology Last modified: Monday, August 05, 2002 The shape of a local-area network (LAN) or other communications system. Topologies are either physical or logical There are four principal topologies used in LANs. bus topology: All devices are connected to a central cable, called the bus or backbone . Bus networks are relatively inexpensive and easy to install for small networks. Ethernet systems use a bus topology. ring topology All devices are connected to one another in the shape of a closed loop, so that each device is connected directly to two other devices, one on either side of it. Ring topologies are relatively expensive and difficult to install, but they offer high bandwidth and can span large distances. star topology: All devices are connected to a central hub . Star networks are relatively easy to install and manage, but bottlenecks can occur because all

95. Free Software: Jun For Smalltalk Free Software 3D Graphics Library with topology and geometry. OpenGL graphics layer for Smalltalk. http://www.sra.co.jp/people/aoki/Jun/Main_e.htm

Japanese English 21 March 2003 / Author: AOKI Atsushi Free Software: Jun for Smalltalk A 3D Graphic Multi-Media Library that supports Topology and Geometry Jun for Smalltalk ) has been released. (2003/03/21) Jun498.zip (sources) Jun498pcl.zip (parcel for VisualWorks 7.x) Jun498pcl5i.zip (parcel for VisualWorks 5i.x) Jun498pcl30.zip (parcel for VisualWorks 3.x) Jun498WinQT.zip (dynamic link library for QuickTime on Windows) Textbook about Jun for Smalltalk is available. Original version HTML version You can download the manuals Takenoko for Smalltalk ) has been released. (2002/08/25) Jun for Java ) has been released. (2002/12/25) JGCL has been released. (2000/12/26) Free Software: Kjo is available. Slides: Smalltalk Solutions 2001 @ Chicago An interface for OpenGL and QuickTime have been written for VisualWorks (Smalltalk) and incorporated into Jun. This package is being published as free software under the terms of " GNU General Public License ". Copyleft by AOKI Atsushi, ODA Tomohiro, HOSHI Takanori, NISHINAKA Yoshiyuki, YAMADA Ryousuke, WATANABE Katsuhiro, Ankur J. Chavda, NISHIHARA Satoshi, MATSUDA Ryouichi, MATSUO Minoru, Brent N. Reeves, ASAOKA Hiroko and TANAKA Shinichi. The functions of OpenGL and QuickTime have been made available for use with VisualWorks, providing high-speed rendering and multi-media handling under Smalltalk. The necessary software components are listed below.

96. Visualizing The Global Topology Of The MBone Visualizing the Global topology of the MBone. Abstract. We present a casestudy of visualizing the global topology of the Internet MBone. http://graphics.stanford.edu/papers/mbone/

Visualizing the Global Topology of the MBone Tamara Munzner and Eric Hoffman and K. Claffy and Bill Fenner Proceedings of the 1996 IEEE Symposium on Information Visualization , pp. 85-92, October 28-29 1996, San Francisco, CA, 1996. Abstract We present a case study of visualizing the global topology of the Internet MBone. The MBone is the Internet's multicast backbone. Multicast is the most efficient way of distributing data from one sender to multiple receivers with minimal packet duplication. Developed and initially deployed by researchers within the Internet community, the MBone has been extremely popular for efficient transmission across the Internet of real-time video and audio streams such as conferences, meetings, congressional sessions, and NASA shuttle launches. The MBone, like the Internet itself, grew exponentially with no central authority. The resulting suboptimal topology is of growing concern to network providers and the multicast research community. We create a geographic representation of the tunnel structure as arcs on a globe by resolving the latitude and longitude of MBone routers. The interactive 3D maps permit an immediate understanding of the global structure unavailable from the data in its original form as lines of text with only hostnames and IP addresses. Data visualization techniques such as grouping and thresholding allow further analysis of specific aspects of the MBone topology. We distribute the interactive 3D maps through the World-Wide Web using the VRML file format, thus allowing network maintainers throughout the world to analyze the structure more effectively than would be possible with still pictures or pre-made videos.

97. An Atlas Of Cyberspaces - Topology Maps topology Maps of Elements of Cyberspace (page 1). A screenshot of atAT T Research. Go to topology maps page 2 for more examples. http://www.geog.ucl.ac.uk/casa/martin/atlas/topology.html

Introduction Whats New Conceptual Artistic ... Historical Topology Maps of Elements of Cyberspace (page 1) A screenshot of a 3D model of the vBNS network which connects universities and laboratories in the USA. The model was created by Jeff Brown, a researcher at MOAT, National Laboratory for Applied Network Research (NLANR), USA, using his Cichlid data visualisation software . The model is animated to show how traffic flows over the links. More information on their work can be found in the paper "Network Performance Visualization: Insight Through Animation" by J.A. Brown, McGregor A.J and H-W Braun. These striking images are 3D hyperbolic graphs of Internet topology. They are created using the Walrus visualisation tool developed by Young Hyun at the Cooperative Association for Internet Data Analysis ( CAIDA The underlying data on the topological structure of the Internet is gathered by skitter , a CAIDA tool for large-scale collection and analysis of Internet traffic path data.

98. Agt Abstracts of all volumes.Category Science Math topology General topology......Editorsin-Chief Salvador Romaguera, Manuel Sanchis. ISSN 1576-9402 EditorialBoard. Aims and Scope. Technical Editors. Instructions for Authors. Abstracts http://www.upv.es/agt/

Editors-in-Chief: Salvador Romaguera, Manuel Sanchis. ISSN: 1576-9402 Editorial Board Aims and Scope Technical Editors Instructions for Authors Abstracts: Volume 1, no.1 Volume 2, no.1 Volume 2, no.2 Volume 3, no.1 Volume 3, no.2

99. Jose Ferreira Alves' WWW Page Xth Oporto Meeting. Oporto, Portugal; 2024 September 2001. http://www.fc.up.pt/mp/actividades/om.html

Please wait a moment to be transferred to the new URL http://www.math.ist.utl.pt/~jmourao/om/omxii

100. Topology In Matsue 2002 --Top-- Joint with the Second MexicoJapan topology Symposium. Shimane University, Matsue City, Japan; 2428 Category Science Math topology Events Past Events...... Shimane University and the Mathematical Society of Japan are organizingthe international conference topology in Matsue . This http://www.math.shimane-u.ac.jp/~top2002/

The second announcement Japanese / TeX file ( English Japanese Dear participants We have recently sent the final announcement to ALL PARTICIPANTS in our list. If you did not receive our mail, please contact to us, now!: hattori@math.shimane-u.ac.jp or top2002@math.shimane-u.ac.jp TIM2002 and JAMEX II Shimane University and the Mathematical Society of Japan are organizing the international conference "Topology in Matsue". This conference, held jointly with the Second Japan-Mexico Topology Symposium, will take place at Shimane University in Matsue City, Japan, on June 24-28, 2002. Scientific Program: The Scientific program will begin in the morning on Monday, June 24. Particular areas of interest of the conference will be included: General Topology, Geometric Topology, Homotopy Theory, Knot Theory, Set-Theoretic Topology, Set theory and Applications The conference will have several sessions; General/Set-theoretic Topology and Set Theory, Geometric Topology, Homotopy Theory and Knot Theory

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