math services categorical topology /
Mathematischer Service kategorielle Topologie
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 ... ?
cattop editors + cattop navigators = our 10-point-program => new topological features required !!!
our 5-point-"edit"-program: computer assistance for
• 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 ...
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 ...
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):