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.
Conversely, mapping the data flow between the components determines the logical topology of the network. Topology There are two basic categories of network topologies: Physical topologiesLogical topologies The shape of the cabling layout used to link devices is called the physical topology of the network. The logical topology in contrast, is the way that the signals act on the network media, or the way that the data passes through the network from one device to the next without regard to the physical interconnection of the devices. Diagram of different network topologies. The study of network topology recognizes eight basic topologies: Point-to-pointBusStarRing or circularMeshTreeHybridDaisy chain Point-to-point Mesh. Variété systeme. Network topology. Combinatorics. Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures.
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). Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, and combinatorics also has many applications in mathematical optimization, computer science, ergodic theory and statistical physics.
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.
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, a 1-sphere is the circle, which is the one-dimensional circumference of a (two-dimensional) disk in the plane, a 2-sphere is the two-dimensional surface of a (three-dimensional) ball in three-dimensional space. Spheres of dimension n > 2 are sometimes called hyperspheres, with 3-spheres sometimes known as glomes.
Description Euclidean coordinates in (n + 1)-space where c is a center point, and r is the radius. n-ball Specifically: . And , respectively. where. 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).
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. However, such examples may be hard to come by. The concept of a spherical design is due to Delsarte, Goethals, and Seidel (1977). For all positive integers d and t. See also Thomson problem References
Copula approach. Abstract.
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.
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. Combinatorial design theory can be applied to the area of design of experiments. Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including; Finite geometry, tournament scheduling, lotteries, mathematical biology, algorithm design and analysis, networking, group testing and cryptography.
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.
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 An alternative expression for Cn is which is equivalent to the expression given above because . The Catalan numbers satisfy the recurrence relation moreover, This is because since choosing n numbers from a 2n set of numbers can be uniquely divided into 2 parts: choosing i numbers out of the first n numbers and then choosing n-i numbers from the remaining n numbers.
They also satisfy: which can be a more efficient way to calculate them. Asymptotically, the Catalan numbers grow as in the sense that the quotient of the nth Catalan number and the expression on the right tends towards 1 as n → +∞. Where on are. 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).
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Graph databases employ nodes, properties, and edges. Graph database 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. Edges are the lines that connect nodes to nodes or nodes to properties and they represent the relationship between the two. Properties Graph databases are a powerful tool for graph-like queries, for example computing the shortest path between two nodes in the graph.
Graph database projects The following is a list of several well-known graph database projects: Graph database features The following table compares the features of the above graph databases. Distributed Graph Processing GPGPU Graph Processing Medusa - A framework for graph processing using Graphics Processing Units (GPUs) on both shared memory and distributed environments. See also References 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.
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. In a glimpse, a view into the key demographic data available for every member's profile.
The second poster gives you an overview of the geographic location of all members, based on a world map. The aim was to provide the management team with a visualization tool that would allow a better understanding of the community members, rather than a just a simple scan of their database. 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.