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Institut für elegante Mathematik ... gruppe eM math services categorical topology / CatTop / kategorielle Topologie U.a. ist Visualisierung unser Schwerpunkt, Hauptgebiet Topologische Navigation.Wir sind topophil ... und toposoph/ we are topophil ... and toposoph: »Topologie ist Nutzen der "→rechten*) Hemisphäre" für Grundlagenforschung«. *): "→ rechte" ist hierbei sinnvollerweise mit doppelter Bedeutung anzuwenden ... Database-gurus claimed long time ago: »think in relations ...«. Since - or long time after, but due to - CatTop and / or Topoi, they know why ...  
Summary: where we have to go ... ? • better isos e.g. automation for order, optimiser for visualisation, ... • part of grid (sub spaces) • gluing together of grids (coproducts) • simplifying grids/interrelations, "portfolios" (quotients) • product of grids (products) 
our 5-point-"navigator"-program: computer assistance for • "topology" of configuration (ref. integrity) • arbitrary relation (or point/object) "on top" (extraction) • neighbourhoods stepwise visible (partial morphisms) • alternative info ("fuzzy", "nearness") • "pattern" recognition (quick reconstruction/reuse of path) In → cat top  elegant math H²
we give an brief overview of the last 20 years' applications of categorical and
topological methods in industry. Most of them have already been presented at conferences
in recent years and papers as well. In particular during the series of conferences
»North West European Category Seminar (see below, formerly called NWDKS, NDKS and/or NWEKS)«
we have shown the current "state of the art".Concrete applications are: forecasts, scheduling, optimisation, pattern recognition, data chasing, referential integrity, data integrity, time series, artificial (i.e. computer aided) smelling, hearing, visualising, manufacturing, quality checks. The disciplines are: energy industry, space technology, architecture, civil engineering, mechanical engineering, medicine, dental, animal farming, chemistry, biochemistry, climate research, weather forecast, reinsurance (derivatives). The talk was given in homage to our cat top friend Horst Herrlich, "THE CATTOPologist", dedicated to his retirement (see: → NWECS 2003, Berlin). (By coincidence the data of a.m. event has been exactly the same day and place with regard to Alexander Grothendieck's 75th birthday, born March, 28th 1928 in Berlin) In → Pretopologies for Pattern Recognition, Data Integrity Checks, Ref. Integrity, and div. other Apps. we give an overview where pattern recognition currently is applied for. Mostly engineers apply "fuzzy methods" and/or other "modern things". In particular if self learning or training is required -in particular if no further investigation w.r.t. "what physics is behind?"- the models are combined with neural networks. We will demonstrate that pretopologies (= non-idempotent hull operators) or applying a given, well defined topology stepwise, could be more efficient with respect to less computing time, and also to less memory and program code, i.e. optimal for constructing small "intelligent" machines. Concrete applications, key words and phrases (math. & comp. sciences): • pattern recognition, data chasing, referential integrity, data integrity, time series • artificial (i.e. computer aided) smelling, hearing, visualising Existing applications in other disciplines: • medicine/dental: ECG, tartar; animal farming • mechanical engineering: manufacturing and quality checks • chemistry and energy industry: errors/missings in process data, metering data, inconsistencies in forecasts, and other • climate research & weather forecast, reinsurance (derivatives): wind chill, further methods ...  Applications of Quasitopos Axioms in Optimisation → Übersichtsvortrag → International Symposium on Applications of Categorical Methods It is the purpose to offer an interdisciplinary program including the application of categorical methods in various branches of mathematics such as Algebra, Topology, Functional Analysis and Order. "Topologie versus Algebra für Gas Management Systeme": angewandte kategorielle Topologie für Netze | "topology vs algebra w.r.t. gas management systems": categorical topology applied for grids → Übersichtsvortrag → abstract / Zusammenfassung / Kurztext 
Entry-Exit Management Systems "dehydraulisation" and "detopologysation" of grids »IT-Unterstützung für Entry-Exit-Modelle« → EEMS | abstract und Agenda → pdf-Vortrag, Köln, 2006 Topological Visualisation and »Entry-Exit Management Systeme« Energiedatenmanagement, Transparenzanforderungen, Prognose → abstract, agenda and lit. ... → pdf-Vortrag, Karlsruhe, 2006 
Topologische Kategorien und Topologische Universen, um gestohlene Synergien zurückzugewinnen ... |topological categories and topological universes, ... avoid anergy ...: "IT-Systeme für Netzbetrieb und Dispatching" → ppt-Vortrag → abstract und Agenda "Unbundling und die Folgen für das Vertragsdispatching (ConCADA)" → ppt-Vortrag → abstract und Agenda "Neue Technologien" → aktuelle Version für DVGW → 2005er Version für DVGW → 2005er Version für BGW | DVGW "10 Jahre Rückschau": »Wandel in der Energiewirtschaft und Wandel in IT und Kommunikation - Geht Prognose ohne Rückschau?« → ppt-Vortrag, Agenda und abstract → abstract und Literatur TopKat Methoden und Daten Universen | topcat methods and data universes: → »Datenmanagement und Datenintegrität: Grundlage für ein optimales Bilanzkreismanagement« → abstract 
→ »Energiebedarfsprognose und Energiedatenmanagement«→ gwf-Gas/Erdgas 2/2005, 146. Jahrgang 2005, ISSN 0016-4909, Oldenbourg Industrieverlag, München, p. 89-93  → abstract, agenda u.a. CatTop-Anwendungen, Prätopologien und klassische Prognoseverfahren, EDM, SCADA & ConCADA, Sigmoide, logistische Kurve | Richards-Funktion, Prognose nur mit Vortagestemperatur, SLP | Standardlastprofile | Lastprofile ... »Windgas und Mathematik«: Prognose, Simulation und Rekonstruktion für optimierte Einspeisungen von off-spec-Gasen: → Windgas und Mathematik, Kassel, November 2013 ... → Windgas und Mathematik, Berlin, November 2012 ... Gas-, Energiedatenmanagement (EDM), elektronische Kommunikation (EDI und EAI) Ausgang und Eingang, Anfang und Ende ..., Bilanzkreismanagement, Regel- und Ausgleichsenergiemanagement ... Exit and Entry, end and existence ..., balancing regime ... → »GABi: BKM & RAM - Bilanzkreismanagement sowie Regel- und Ausgleichsenergiemanagement« → abstract → workshop: »GABi: BKM & RAM - Bilanzkreismanagement sowie Regel- und Ausgleichsenergiemanagement« → abstract → »Illustration effektiven Gasdatenmanagements für das Bilanzkreismanagement« → abstract → »Besonderheiten beim Datenmanagement Gas / Bilanzkreismanagement« → abstract → »Bilanzkreismanagement Gas im Marktgebiet - Datenkommunikation & Prozessgestaltung« → abstract → »Bilanzkreismanagement: Kommunikation und Kooperation« → abstract ;)
→ »Datenmanagement zwischen den Beteiligten«→ EDM | abstract, agenda → »Gas- und Datenmanagement« → GuDM | abstract, agenda → »Datenaustausch bei Gas – ein gro�er Unterschied zum Strom?« → EDI ... | abstract → »Datenaustausch ..., Energiedatenmanagement und Kommunikation« → EDM | EDI ... | abstract → »Bilanzkreismanagement: Energiedatenmanagement und Kommunikation« → BKM | EDM | EDI ... | abstract »elegant«: natural*) principles in natural gas *) =universal: »ad Galois, Garbe, Topos, TopCats, alles dual virtueller Punkt ...« Mathematics Applied in Energy Industry → Übersichtsvortrag → Programm, s.u. \item 10.30 -- 11.15 R. D. Brandt: Aplikovan\'a matematika v plyn\'arenskom priemysle → abstract Jasna. Newest Mathematics (CAT and TOP) Applied in Energy Industry → Übersichtsvortrag → CATOP 2000, Uni Fribourg It is the aim of this conference to discuss categorical topological methods that are likely to be mathematically important in the next century. CAT and TOP Thinking for Industrial Solutions 
→ Übersichtsvortrag→ CatMAT 2000 → abstract This conference will commemorate 25 years of categorical research and teaching at the University of Bremen and follows a long tradition of similar conferences (e.g. Mannheim 1975, Berlin 1978, Ottawa 1980, Cape Town 1981, Toledo, Ohio 1983, L'Aquila 1986, Prague 1988, Antwerp 1998). Convergence Theory, Galois Connections, categorical and topological background (english, parts in italian): 
→ Strutture Generali di Convergenza per Filtri, Connessioni di Galois e "Atomi" per Strutture Iniziali (inclusive of nearly complete representative bibliography) → pdf-version Quaderni matematici, Università di Trieste, n. 129 (1987). → abstract "Hereditary Topological Categories and Applications to Classes of Convergence Spaces", Baku, 1987 → paper - " -, Baku, 1989 (→ pdf-file - " -, Baku, 1989). → abstract "Quasitopoi for Analysis", Capri, 1988, »CARTEMI« → abstract "Quasitopoi for Topology", Sorrento, 1988 → abstract "Topos theoretical principles in optimization", Vienna, 1990 
"Application of Quasitopoi, Galois Connections, 16 years after ..."→ abstract, Ischia, 2004, »CARTEMI« → pdf-file of talk, Ischia, 2004, »CARTEMI« Info to group eM: Institute for elegant Mathematics https://www.algrotopoi.de/group eM is a world-wide active net of engineers, mathematicians, and other researchers. We are open to anybody to help solving problems and/or to find potential experts. keywords and phrases: eM Institut, gruppe eM, cat top, topologie, topology, category theory, Kategorien Theorie, topos, Galois Connections, topology editor, topology navigator, topological visualisation, euch3, algrotopoi, algrotopoide, topoide, eM, group eM, Leibniz, Leibnizianer, A.G., Alexander Grothendieck, Horst Herrlich, NWDKS, NDKS, NWEKS, NWECS, topologists, structure theorists, category theorists, measure theorists, Topologen, Strukturtheoretiker, Kategorientheoretiker, Masstheoretiker. |
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