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Graph theory

Graph theory
Refer to the glossary of graph theory for basic definitions in graph theory. Definitions[edit] Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph[edit] Other senses of graph stem from different conceptions of the edge set. All of these variants and others are described more fully below. The vertices belonging to an edge are called the ends, endpoints, or end vertices of the edge. V and E are usually taken to be finite, and many of the well-known results are not true (or are rather different) for infinite graphs because many of the arguments fail in the infinite case. (the number of vertices). For an edge {u, v}, graph theorists usually use the somewhat shorter notation uv. Applications[edit] The network graph formed by Wikipedia editors (edges) contributing to different Wikipedia language versions (nodes) during one month in summer 2013.[3] History[edit] The Königsberg Bridge problem "[...]

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information architecture Introduction This lesson discusses ideas associated with the phrase "information architecture" and relates them to aspects of the library- and information-science (LIS) professions. Origin of the Phrase, "Information Architecture" The phrase "information architecture" appears to have been coined, or at least brought to wide attention, by Richard Saul Wurman, a man trained as an architect but who has become also a skilled graphic designer and the author, editor, and/or publisher of numerous books that employ fine graphics in the presentation of information in a variety of fields. In the 1960s, early in his career as an architect, he became interested in matters concerning the ways in which buildings, transport, utilities, and people worked and interacted with each other in urban environments.

Tree (graph theory) The term "tree" was coined in 1857 by the British mathematician Arthur Cayley.[1] A tree is an undirected simple graph G that satisfies any of the following equivalent conditions: If G has finitely many vertices, say n of them, then the above statements are also equivalent to any of the following conditions: G is connected and has n − 1 edges.G has no simple cycles and has n − 1 edges. As elsewhere in graph theory, the order-zero graph (graph with no vertices) is generally excluded from consideration: while it is vacuously connected as a graph (any two vertices can be connected by a path), it is not 0-connected (or even (−1)-connected) in algebraic topology, unlike non-empty trees, and violates the "one more node than edges" relation.

Simple Brainstorming and Mind mapping Tool Manual Thinking is created by Luki Huber (Luzern, 1973) and Gerrit Jan Veldman (Leicester, 1983), who initially developed the tool for internal use in their product design studio situated in Barcelona. The tool has taken shape and has been tested during extensive collaborations with clients where organization, creativity and teamwork have been essential for success. In December 2009 the design studio moved to its actual location in the center of Barcelona, which has been arranged as a space where clients are invited to co-create on their projects together with the studio’s team members and other strategic guests. The Manual Thinking tool plays a central role in this process, enabling newly formed teams with participants of different backgrounds and nationalities to work with each other in an effective manner from the very minute they enter the studio!

[Omnigator] Welcome Page The Omnigator is a technology showcase and teaching aid designed to demonstrate the power of Topic Maps. It is also used extensively as a topic map debugger and prototyping tool. Now, with the introduction of RDF support, the Omnigator is evolving into a multi-purpose Semantic Web Agent. Features The Omnigator is omnivorous: It eats anything, provided it is a topic map – or can be viewed as one! Its most unique feature is that it lets you load and navigate any conforming topic map, whether its format be XTM 1.0, XTM 2.0, LTM – or even RDF.

torus interconnect Diagram of a 3-dimensional torus interconnect. It is not limited to 8 nodes but can consist of any number of nodes in a similar rectilinear array. A torus interconnect is a network topology for connecting processing nodes in a parallel computer system. It can be visualized as a mesh interconnect with nodes arranged in a rectilinear array of N = 2, 3, or more dimensions, with processors connected to their nearest neighbors, and corresponding processors on opposite edges of the array connected.[1] The lattice has the topology of an N dimensional torus and each node has 2N connections. A number of supercomputers on the TOP500 list use three-dimensional torus networks, e.g. IBM's Blue Gene/L and Blue Gene/P, and the Cray XT3.[2] IBM's Blue Gene/Q uses a five-dimensional torus network.

MATLAB - The Language of Technical Computing MATLAB® is a high-level language and interactive environment for numerical computation, visualization, and programming. Using MATLAB, you can analyze data, develop algorithms, and create models and applications. The language, tools, and built-in math functions enable you to explore multiple approaches and reach a solution faster than with spreadsheets or traditional programming languages, such as C/C++ or Java™.

Pellet Features Pellet supports a wide range of standard and novel features: Standard Reasoning Services Pellet supports reasoning with the full expressivity of OWL-DL (SHOIN(D) in Description Logic jargon) and has been extended to support the forthcoming OWL 2 specification (SROIQ(D)), which adds the following language constructs: qualified cardinality restrictions complex subproperty axioms (between a property chain and a property) local reflexivity restrictions reflexive, irreflexive, symmetric, and anti-symmetric properties disjoint properties negative property assertions vocabulary sharing (punning) between individuals, classes, and properties user-defined dataranges Pellet also provides reasoning with the following features from OWL Full: inverse functional datatype properties

Object-oriented programming Overview[edit] Rather than structure programs as code and data, an object-oriented system integrates the two using the concept of an "object". An object has state (data) and behavior (code). 50 Places You Can Learn to Code (for Free) Online If you’re curious about learning a programming language then you’re in luck: there’s no shortage of resources for learning how to code online. University-level courses, tutorials, cheat sheets, and coding communities all offer excellent ways to pick up a new language, and maybe even a new job, too. Read on, and you’ll discover 50 great places to learn how to code, for free, online. University Many big names in education including MIT and Stanford offer programming courses, absolutely free.

MIT discovers the location of memories: Individual neurons Update 12/2/15: We’ve now followed up on this story: The more we learn about memory, the weirder it gets. The original continues below. MIT researchers have shown, for the first time ever, that memories are stored in specific brain cells. By triggering a small cluster of neurons, the researchers were able to force the subject to recall a specific memory. By removing these neurons, the subject would lose that memory.

Storage options MindMup supports several storage options for your maps. They have hugely different capabilities and constraints. Once a map is modified, the toolbar and menu bar show the save button. The icon next to Save shows the currently selected storage option. Clicking on Save (blue) button directly will save to that storage. WebProtege WebProtégé The new WebProtégé with simplified editing and improved collaboration support WebProtégé is a free, open source collaborative ontology development environment for the Web. UML & SysML Toolset Models the physical deployment of software components with UML deployment diagram. In deployment diagram, hardware components (e.g., web server, mail server, application server) are presented as nodes, with the software components that run inside the hardware components presented as artifacts. User-defined notation symbol Apply your own image file as graphical representation of any notation. You may use your own avatar to replace traditional stickman shape for UML actor, if you like. Make shape appearance follow stereotype's definition Specify in stereotype the background color, font color and font weight and font settings of model element, and let the model elements that extend the stereotype follow.

ISO What is a standard? A standard is a document that provides requirements, specifications, guidelines or characteristics that can be used consistently to ensure that materials, products, processes and services are fit for their purpose. We published over 21000 International Standards that can be purchased from the ISO store or from our members.

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