SUMMARY / RELATED TOPICS

French football league system

The French football league system is a series of interconnected leagues for club football in France and Monaco, includes one Spanish side. At the top two levels of the system is the Ligue de Football Professionnel, which consists of two professional national divisions, Ligue 1 and Ligue 2. Below that are a number of leagues run by the Fédération Française de Football. At level 3 is the semi-professional Championnat National. Below, the amateur Championnat National 2, divided into four parallel regional divisions, followed by the Championnat National 3, divided into 12 parallel regional divisions. Underneath that are many more regional and departmental leagues and divisions. Clubs finishing the season at or near the top of their division may be eligible for promotion to a higher division. Clubs finishing at or near the bottom of their division may be relegated to a lower division. Starting in 2017–18 there were changes at Levels 3 and 4 and Level 5. For the 2017–18 season, this was the structure of the regional leagues, operating directly below the national leagues.

For the 2017–18 season, this was the structure of the departmental leagues, operating at various levels below the regional leagues. There are no district divisions in Corsica Clubs in the arrondissements of Paris are divided between the three surrounding suburban districts; the District of Hauts-de-Seine includes 6th, 7th, 8th, 14th, 15th, 16th and 17th, the District of Seine-Saint-Denis has the 9th, 10th, 11th, 18th, 19th, 20th and the District of Val-de-Marne includes 1st, 2nd, 3rd, 4th, 5th, 12th and 13th. FFF Regional Leagues FFF Districts League321.com - French football league tables, records & statistics database

Lattice Miner

Lattice Miner is a formal concept analysis software tool for the construction and manipulation of concept lattices. It allows the generation of formal concepts and association rules as well as the transformation of formal contexts via apposition, subposition and object/attribute generalization, the manipulation of concept lattices via approximation and selection. Lattice Miner allows the drawing of nested line diagrams. Formal concept analysis is a branch of applied mathematics based on the formalization of concept and concept hierarchy and used as a framework for conceptual clustering and rule mining. Over the last two decades, a collection of tools have emerged to help FCA users visualize and analyze concept lattices, they range from the earliest DOS-based implementations to more recent implementations in Java like ToscanaJ, ConExp and Coron. A main issue in the development of FCA tools is to visualize large concept lattices and provide efficient mechanisms to highlight patterns that could be relevant to the user.

The initial objective of the FCA tool called Lattice Miner was to focus on visualization mechanisms for the representation of concept lattices, including nested line diagrams. On, many other interesting features were integrated into the tool. Lattice Miner is a Java-based platform; the Lattice Miner core provides all low-level operations and structures for the representation and manipulation of contexts and association rules. The core of Lattice Miner consists of three modules: context and association rule modules; the user interface offers a context editor and concept lattice manipulator to assist the user in a set of tasks. The architecture of Lattice Miner is open and modular enough to allow the integration of new features and facilities in each one of its components; the context module offers all the basic operations and structures to manipulate binary and valued contexts as well as context decomposition to produce nested line diagrams. Basic context operations include apposition, generalization, reduction as well as the complementary context computation.

The module provides the arrow relations. The tool has an input LMB format and recognizes the binary format SLF found in Galicia and the format CEX produced by ConExp; the main function of the concept module is to generate the concepts of the current binary context and construct the corresponding lattice and nested structure. It provides the user with basic operators such as projection and exact search as well as advanced features like pair approximation; some known algorithms are included in this module such as Bordat’s procedure, Godin’s algorithm and NextClosure algorithm. The approximation feature implemented in Lattice Miner is based on the following idea: given a pair where X ⊆ G, Y ⊆ M, is there a set of formal concepts which are “close to”? To answer this question, The tool starts to identify the type of couple, it can be a protoconcept, a semiconcept or a preconcept. In the last case, the approximation is highlighted in the line diagram; this module includes procedures for computing the Guigues–Duquenne base using NextClosure algorithm, as well as the generic and informative bases.

Implications with negation can be obtained using the apposition of its complementary. This module embeds procedures for the computation of a non-redundant family C of implications and the closure of a set Y of attributes for the given implication set C; the initial objective of Lattice Miner was to focus on lattice drawing and visualization either as a flat or nested structure by taking into account the cognitive process of human beings and known principles for lattice drawing. Some well-known visualization techniques were implemented such as context and fisheye view; the basic idea behind focus & context visualization paradigm is to allow a viewer to see key objects in full detail in the foreground while at the same time an overview of all the surrounding information remains available in the background. Lattice Miner translates the focus & context paradigm into clear and blurred elements while the size of nodes and the intensity of their color were used to indicate their importance. Various forms of highlighting and animation are provided.

In order to better handle the display of large lattices, nested line diagrams are offered in the tool. Figure 3 shows the third level of the nested line diagram corresponding to the binary context of Figure 1 where three levels of nesting are defined; each one of the inner nodes of this diagram represents a combination of attributes from the previous two levels. Real inner concepts are identified by colored nodes; each node of levels 1 and 2 can be expanded to exhibit its internal line diagram. Both flat and nested diagrams can be saved as an image. Simple lattices can be saved as an XML format file. Http://www.upriss.org.uk/fca/fca.html http://w3.uqo.ca/icfca10/ http://sourceforge.net/projects/lattice-miner/

Jean-Fran├žois Quint

Jean-François Quint is a French mathematician, specializing in dynamical systems theory for homogeneous spaces. He studied at the École normale supérieure de Lyon and received his Ph. D. from École Normale Supérieure in Paris under Yves Benoist with Thèse de Doctorat: Sous-groupes discrets des groupes de Lie semi-simples réels et p-adiques. In 2002 he joined the faculty of the Institut Camille Jordan as Chargé de recherche of the Centre national de la recherche scientifique. In 2005 he joined the staff working on "Ergodic theory and dynamics systems" of Laboratoire Analyse, Géométrie et Applications at the Institut Galilée of the University of Paris 13. Since 2012 he has worked as CNRS Directeur de recherche at the University of Bordeaux. In 2011, Yves Benoist and Jean-François Quint received the Clay Research Award for their collaborative research. According to the citations and Quint were honored "for their spectacular work on stationary measures and orbit closures for actions of nonabelian groups on homogeneous spaces.

This work is related areas of mathematics. In particular and Quint proved the following conjecture of Furstenberg: Let H be a Zariski dense semisimple subgroup of a Lie group which acts by left translations on the quotient of G by a discrete subgroup with finite covolume. Consider a probability m measure on H whose support generates H. Any m-stationary probability measure for such an action is H-invariant." Mesures de Patterson-Sullivan en rang supérieur. Geom. Funct. Anal. 12, no. 4, 776–809. Doi:10.1007/s00039-002-8266-4 with Benoist: Mesures stationnaires et fermés invariants des espaces homogènes, Parts 1,2, Comptes Rendus Mathématiques, vol. 347, 2009, pp. vol. 349, 2011, pp. 341–345. 174, 2011, pp. 1111–1162 doi:10.4007/annals.2011.174.2.8 with Benoist: Random walks on finite volume homogeneous spaces, Inventiones Mathematicae, vol. 187, 2012, pp. 37–59 doi:10.1007/s00222-011-0328-5 with Benoist: Stationary measures and invariant subsets of homogeneous spaces. J. Amer. Math. Soc. 26, no. 3, 659–734.

MR3037785 with Benoist: Stationary measures and invariant subsets of homogeneous spaces. Ann. of Math. 178, no. 3, 1017–1059. MR3092475 with Benoist: Random Walks on Reductive Groups. Springer. 2016. Jean-François Quint - Institut de Mathématiques de Bordeaux website Jean-François Quint - 1/6 Mesures stationnaires et fermés invariants des espaces homogènes, YouTube Jean-François Quint - 2/6 Mesures stationnaires et fermés invariants des espaces homogènes Jean-François Quint - 3/6 Mesures stationnaires et fermés invariants des espaces homogènes Jean-François Quint - 4/6 Mesures stationnaires et fermés invariants des espaces homogènes Jean-François Quint - 5/6 Mesures stationnaires et fermés invariants des espaces homogènes Jean-François Quint - 6/6 Mesures stationnaires et fermés invariants des espaces homogènes