Topology

Aug 06, 2014

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Topology. What the subject of topology is all about? . Which shapes are the same from my point of view? . What about these shapes?. compare. What about now?. circle. rectangle. Continuous deformations. Continuous deformations of a sphere. Continuous deformations(continued).

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orthogonal vectors
2-dimentionalrectangle
jordan theorem
jordan curve
continuous deformations
orientable surface

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Topology

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Topology What the subject of topology is all about?
Which shapes are the same from my point of view? 
What about these shapes?
compare
What about now? circle rectangle
Continuous deformations
Continuous deformations of a sphere
Continuous deformations(continued)
Other continuous deformations

Jordan Curve

Jordan Theorem
Jordan Theorem
2-dimentionalrectangle
Rectangle to cylinder
Rectangle to Mobius strip
Orientable surfaces

“orientation ” of a pair od orthogonal vectors same different
Non-orientable surface
Non-orientable surfaces

Closed surface

Topology Cleanup

MONUMENTS. LANDSCAPE. MonumentID Mnumber Name Type Datum Easting Northing Elevation LandscapeID HardscapeID BuildingID MSLINK MAPID. LandscapeID Type Easting Northing BuildingID MSLINK MAPID. There is a geometry error (undershoot) in the corner of the building. HARDSCAPE.

350 views • 1 slides

Topology

Topology. Uniformly Continuous. The field of topology is about the geometrical study of continuity. A map f from a metric space ( X , d ) to a metric space ( Y , D ) is continuous if: Given e > 0,  d > 0, If d ( x 1 , x 2 ) < d , then d (f( x 1 ), f( x 2 )) < e . Sequences.

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Ring Topology

Topology. RingIn a ring network, every device has exactly two neighbors for communication purposes. All messages travel through a ring in the same direction (effectively either "clockwise" or "counterclockwise"). A failure in any cable or device breaks the loop and can take down the entire network.

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Topology

Topology. YAN JIE (Ryan). What is topology?. Topology is t he study of properties of a shape that do not change under deformation A simple way to describe topology is as a ‘ rubber sheet geometry ’. The rule of deformation.

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GEOMETRIC TOPOLOGY

GEOMETRIC TOPOLOGY. MAIN GOAL: TO PROVE TOPOLOGICAL RESULTS ABOUT SMOOTH MANIFOLDS BY ENDOWING THEM WITH ADDITIONAL GEOMETRIC STRUCTURES Example of a geometric structure: Riemannian metric. GEOMETRIC TOPOLOGY OF LOW DIMENSIONAL MANIFOLDS. SYMPLECTIC FOUR DIMENSIONAL MANIFOLDS

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Topology

Topology. “The Topology is the geometric representation of the relationship of the links and linking devices” OR “Topology defines physical or logical arrangement of links in a Network”. Topology. Mesh. Star. Tree. Bus. Ring. Categories of Topology. Mesh Topology. Mesh.

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Network Topology

Network Topology. The WAN. Cisco 2921 Integrated Services Router. Security Embedded hardware-accelerated VPN encryption Secure collaborative communications with Group Encrypted Transport VPN, Dynamic Multipoint VPN, or Enhanced Easy VPN

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Star Topology

Star Topology. Ring Topology. Bus Topology. Mesh Topology. Tree Topology.

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Topology What is a Topology?

Topology What is a Topology?. The physical topology of a network refers to the configuration of cables,computers,and other peripherals.Physical topology should not be contused with logical topology which is the method used to pass information between workstations. Topology. Bus

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Topology Control

Topology Control. Murat Demirbas SUNY Buffalo Uses slides from Y.M. Wang and A. Arora. Why Control Communications Topology. High density deployment is common Even with minimal sensor coverage, we get a high density communication network (radio range > typical sensor range)

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Topology Mapping

Topology Mapping. Bo Sheng Sept. 15. Outline. Overview Solutions LTM ACE Problems and discussion Conclusion. Introduction. Topology mapping Mismatch between overlay and physical infrastructure Topology optimization. Introduction. Traffic problem Facts

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Topology

Topology. What are the consequences of using fewer than n 2 connections? Fewer interconnects make it practically feasible Contention likely – lower bisection bandwidth Other Topologies & worst case distances Token Ring – N (N is no of nodes) 2D torus - N Fat tree – 2logN 2D meshes 2N

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Topology

Topology. T- Mon Server. T-Mon server. T -Mon Server is developed for monitoring and managing an UPS that is connected to a computer via RS232. The minimum required equipments are: 1 PC Win 95/98 – NT or Win2000 operating system. 1 UPS 1 RS232 connection cable.

469 views • 23 slides

Review + Topology

NETWORKS. Review + Topology. Review. A computer network is a number of computers linked together to allow them to share resources. Networked computers can share hardware , software , and data .

508 views • 20 slides

Topology Control

Topology Control. What’s topology control?. What’s topology control?. When nodes are deployed, how do they organize into a network? And how do they maintain this organization over the lifetime of the system? Neighbor-discovery protocol is important.

372 views • 26 slides

Network Topology

Network Topology. Single-level Diversity Coding System (DCS) An information source is encoded by a number of encoders. There are a number of decoders, each of which can access a certain subset of the encoders. The Graph Representing the Diversity Coding System

257 views • 7 slides

Network Topology

Network Topology. LAN (Local Area Network) A group of computers and associated devices (printers, etc.) connected through a wired or wireless medium by networking devices (hubs, switches, routers) u se protocols for communication. Review : Computer Network. Objectives. Topology

481 views • 17 slides

Topology

Topology. Senior Math Presentation Nate Black. Bob Jones University 11/19/07. History. Leonard Euler Königsberg Bridge Problem. Königsberg Bridge Problem. J. J. O’Connor, A history of Topology. Königsberg Bridge Problem. C. B. D. A.

873 views • 64 slides

Topology Management

Topology Management. EE206A (Spring 2003): Lecture #10. References. Mandatory Reading Rong Zheng, Jennifer Hou, Lui Sha, “Asynchronous Wakeup for Power Management in Ad Hoc Networks,” ACM MobiHoc, June 2003. http://nesl.ee.ucla.edu/pw/ee206a/Zheng_MobiHoc03.pdf

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Topology

Topology. What is a polygon? Set operations Interior, boundary, exterior Skin, Hair, Wound, Cut, and regularization Components, holes Polygons and faces Loops A linear geometric complex. Motivation.

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Topology

Topology. Relationships between features: Polygons can share parts of boundaries Polylines can share endpoints Supposed to prevent: Gaps Slivers Overlaps http://www.esri.com/library/whitepapers/pdfs/geodatabase-topology.pdf. Topology. Wyoming. Colorado. Non-Topological. Wyoming.

518 views • 23 slides

TOPOLOGY

TOPOLOGY. DEFINITIONS: 1. The study of the properties of geometric figures or solids that are not normally affected by changes in size or shape.

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