05-techno

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Topologie de réseau. Weak-strong ties. Comment nous arrive l’information ? Haptique (toucher) Network topology. A good example is a local area network (LAN): Any given node in the LAN has one or more physical links to other devices in the network; graphically mapping these links results in a geometric shape that can be used to describe the physical topology of the network.

network topology

Conversely, mapping the data flow between the components determines the logical topology of the network. Topology[edit] There are two basic categories of network topologies:[4] Mesh. Variété systeme. Network topology. Combinatorics. Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.

combinatorics

Aspects of combinatorics include counting the structures of a given kind and size (enumerative combinatorics), deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria (as in combinatorial designs and matroid theory), finding "largest", "smallest", or "optimal" objects (extremal combinatorics and combinatorial optimization), and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems (algebraic combinatorics). A mathematician who studies combinatorics is called a combinatorialist or a combinatorist. N-sphere. In mathematics, the n-sphere is the generalization of the ordinary sphere to a n-dimensional space.

n-sphere

For any natural number n, an n-sphere of radius r is defined as the set of points in (n + 1)-dimensional Euclidean space which are at distance r from a central point, where the radius r may be any positive real number. Thus, the n-sphere centred at the origin is defined by: It is an n-dimensional manifold in Euclidean (n + 1)-space. In particular: a 0-sphere is the pair of points at the ends of a (one-dimensional) line segment,

Spherical design. A spherical design, part of combinatorial design theory in mathematics, is a finite set of N points on the d-dimensional unit hypersphere Sd such that the average value of any polynomial f of degree t or less on the set equals the average value of f on the whole sphere (that is, the integral of f over Sd divided by the area or measure of Sd).

spherical design

Such a set is often called a spherical t-design to indicate the value of t, which is a fundamental parameter. Spherical t-designs for different values of N and t can be found precomputed at Spherical designs can be of value in approximation theory, in statistics for experimental design (being usable to construct rotatable designs), in combinatorics, and in geometry. The main problem is to find examples, given d and t, that are not too large. Copula approach. Abstract.

copula approach

Probability distributions of multivariate random variables are generally more complex compared to their univariate counterparts which is due to a possible nonlinear dependence between the random variables. One approach to this problem is the use of copulas, which have become popular over recent years, especially in fields like econometrics, finance, risk management, or insurance.

Since this newly emerging field includes various practices, a controversial discussion, and vast field of literature, it is difficult to get an overview. The aim of this paper is therefore to provide an brief overview of copulas for application in meteorology and climate research. We examine the advantages and disadvantages compared to alternative approaches like e.g. mixture models, summarize the current problem of goodness-of-fit (GOF) tests for copulas, and discuss the connection with multivariate extremes.

Copule. Combinatorial design. Combinatorial design theory is the part of combinatorial mathematics that deals with the existence, construction and properties of systems of finite sets whose arrangements satisfy generalized concepts of balance and/or symmetry.

combinatorial design

These concepts are not made precise so that a wide range of objects can be thought of as being under the same umbrella. At times this might involve the numerical sizes of set intersections as in block designs, while at other times it could involve the spatial arrangement of entries in an array as in Sudoku grids. Catalan number.

In combinatorial mathematics, the Catalan numbers form a sequence of natural numbers that occur in various counting problems, often involving recursively-defined objects.

Catalan number

They are named after the Belgian mathematician Eugène Charles Catalan (1814–1894). The nth Catalan number is given directly in terms of binomial coefficients by The first Catalan numbers for n = 0, 1, 2, 3, … are Properties[edit] Musical Nodes. Nankai combinatorics. Projet "sphère" Nebula. Revêtement. Réseau valué. Couleurs. Cancel Edit Delete Preview revert Text of the note (may include Wiki markup) Could not save your note (edit conflict or other problem).

couleurs

Please copy the text in the edit box below and insert it manually by editing this page. Upon submitting the note will be published multi-licensed under the terms of the CC-BY-SA-3.0 license and of the GFDL, versions 1.2, 1.3, or any later version. See our terms of use for more details. Graph database.

Structure[edit] Graph databases are based on graph theory.

graph database

Graph databases employ nodes, properties, and edges. Nodes represent entities such as people, businesses, accounts, or any other item you might want to keep track of. Properties are pertinent information that relate to nodes. A visual exploration on mapping complex networks. Data visualisation of a social network. For his final year project in information design, Felix Heinen created an amazing set of visualizations of different aspects of a social network.

Data visualisation of a social network

Two big (200 x 90 cm - 80 x 36 inches) posters show the variety and attitudes of members from an internet community like MySpace. On the first poster you can see the functions used, as well as additional information, such as age, educational background, family status, gender and how often they are logged in. Seattle Band Map. The Seattle Band Map is a project that showcases the northwest's vibrant music scene by documenting the thousands of bands who have performed throughout the decades; it also explores how these bands are interconnected through personal relationships and collaborations. This project aims to diversify the audience for and broaden the understanding of Seattle's music scene, while spotlighting unrepresented artists and musical genres. Seattle has long been known as a hotbed of musical creativity, from the thriving 60s and early 70s Soul and Funk scene, to the 90s grunge movement.

Music continues to thrive in Seattle, and the authors see the Seattle Band Map as an opportunity to keep it in the forefront of people's minds. The three bands with a highest number of connections are The Unnatural Helpers (43), Oldominion (38), and Your Heart Breaks (30), while the most popular in the map are Nirvana, The Unnatural Helpers, and Pearl Jam.

Weeplaces. Invisible Cities. Invisible Cities maps information from one realm - online social networks - to another: an immersive, three dimensional space. It displays geocoded activity from online services such as Twitter and Flickr, both in real-time and in aggregate. Real-time activity is represented as individual nodes that appear whenever a message or image is posted. Aggregate activity is reflected in the underlying terrain: over time, the landscape warps as data is accrued, creating hills and valleys representing areas with high and low densities of data. The interplay between the aggregate and the real-time recreates the kind of dynamics present within the physical world, where the city is both a vessel for and a product of human activity. Nodes are connected by narrative threads, based on themes emerging from the overlaid information.