Google Groups no longer supports new Usenet posts or subscriptions. Historical content remains viewable.

Dismiss

54 views

Skip to first unread message

Dec 20, 2014, 11:04:22 AM12/20/14

to

I'd like to draw your attention to

http://pavel.gik.kit.edu/

which contains a result from a project of former times when I used to

work as a researcher.

I am mainly interested in comments from practicioners if they see any

potential practical application of my results. I think of databases for

geo-information, CAD-data, or, in general, applications that must handle

topological data with arbitrary topologies.

A brief description:

During my work I have realized an interesting link between Relational

Algebra and Topology:

(1) Every finite topological space has a simple and efficient

relational representation.

(2) Every Relational Algebra operator has a corresponding topological

construction. This yields a complete query language for spaces.

So the idea was to extend the relational model in the following way:

(i) Given a database table $X$ add a relational representation of

a topology $T_X$ for $X$ such that the pair $(X,T_X)$ becomes

a topological space. The records in $X$ constitute the pointset

and a binary relation $R$ on $X$ represents the topology.

(ii) Provide a version for each database query operator that takes

/spaces/ as input and produces result spaces:

First act as usual on the pointsets.

Then each result set of such query has a uniquely determined

result topology, (see http://en.wikipedia.org/wiki/Final_topology

and http://en.wikipedia.org/wiki/Initial_topology) which yields

a query result space.

(iii) Do this in Lisp because Lisp is fun.

(iv) I wanted to use (and extend) CLSQL first but then decided to

change from SQL (after finding the word "madness" in the

grammar file of PostgreSQL) to Relational Algebra of which I

defined a Lispy syntax.

The web-page describes everything in more detail, contains the sources,

and has a running instance of the experimental database server. The

server is just meant as proof-of-concept and, of course, still far far

away from parcatical usefullness.

I am interested in a discussion here, because it seemed that reviewers

tended to frown on my (any my co-workers) work because, for example:

(1) The applied mathematics is too challenging for the average

audience at scientific conferences (that was an actual remark)

(2) Why should we need database systems particularly designed for

mathematicians?

(3) Arbitrary topological dimension leads to an "combinatorial

explosion of complexity" (another actual remark. Funny, because

obviously wrong)

http://pavel.gik.kit.edu/

which contains a result from a project of former times when I used to

work as a researcher.

I am mainly interested in comments from practicioners if they see any

potential practical application of my results. I think of databases for

geo-information, CAD-data, or, in general, applications that must handle

topological data with arbitrary topologies.

A brief description:

During my work I have realized an interesting link between Relational

Algebra and Topology:

(1) Every finite topological space has a simple and efficient

relational representation.

(2) Every Relational Algebra operator has a corresponding topological

construction. This yields a complete query language for spaces.

So the idea was to extend the relational model in the following way:

(i) Given a database table $X$ add a relational representation of

a topology $T_X$ for $X$ such that the pair $(X,T_X)$ becomes

a topological space. The records in $X$ constitute the pointset

and a binary relation $R$ on $X$ represents the topology.

(ii) Provide a version for each database query operator that takes

/spaces/ as input and produces result spaces:

First act as usual on the pointsets.

Then each result set of such query has a uniquely determined

result topology, (see http://en.wikipedia.org/wiki/Final_topology

and http://en.wikipedia.org/wiki/Initial_topology) which yields

a query result space.

(iii) Do this in Lisp because Lisp is fun.

(iv) I wanted to use (and extend) CLSQL first but then decided to

change from SQL (after finding the word "madness" in the

grammar file of PostgreSQL) to Relational Algebra of which I

defined a Lispy syntax.

The web-page describes everything in more detail, contains the sources,

and has a running instance of the experimental database server. The

server is just meant as proof-of-concept and, of course, still far far

away from parcatical usefullness.

I am interested in a discussion here, because it seemed that reviewers

tended to frown on my (any my co-workers) work because, for example:

(1) The applied mathematics is too challenging for the average

audience at scientific conferences (that was an actual remark)

(2) Why should we need database systems particularly designed for

mathematicians?

(3) Arbitrary topological dimension leads to an "combinatorial

explosion of complexity" (another actual remark. Funny, because

obviously wrong)

Feb 3, 2017, 5:34:42 PM2/3/17

to

Hi,

I think I noticed the same thing the other week - topologies are

defined by their binary distance relations (apologize for my poor use

of notation, I have a bachelors but I'm no academic). Googled

"relational algebra topology" and found this post but the link to the

article seems to be broken.

So why shouldn't relational databases take advantage of this fact? I

understand it might be difficult for complex structures, but I really

like the idea of "querying" based on the actual structure of data (e.g.

colors in a wheel) instead of just throwing everything in a table and

acting like it's all unrelated data points (and then analyzing it

stochastically). I've seen tables where parent and child relations are

used to represent hierarchies but usually it's all transactional (so

the data points in a row are just related by definition)

I was actually thinking about speech analytics when I made the

connection. For instance, the phrase "red and blue" seems to have a

topological structure in terms of the words: (red, and) (and, blue) are

distance relations but (red, blue) definitely isn't. However, the

phrase "red blue" would correspond to (red, blue) but intuitively this

seems more like purple.

This is an overly simple example but just wanted to start up a

conversation. Looking forward to your reply.

*as a side note this makes the whole "non relational DBMS" movement

seem like an oxymoron

I think I noticed the same thing the other week - topologies are

defined by their binary distance relations (apologize for my poor use

of notation, I have a bachelors but I'm no academic). Googled

"relational algebra topology" and found this post but the link to the

article seems to be broken.

So why shouldn't relational databases take advantage of this fact? I

understand it might be difficult for complex structures, but I really

like the idea of "querying" based on the actual structure of data (e.g.

colors in a wheel) instead of just throwing everything in a table and

acting like it's all unrelated data points (and then analyzing it

stochastically). I've seen tables where parent and child relations are

used to represent hierarchies but usually it's all transactional (so

the data points in a row are just related by definition)

I was actually thinking about speech analytics when I made the

connection. For instance, the phrase "red and blue" seems to have a

topological structure in terms of the words: (red, and) (and, blue) are

distance relations but (red, blue) definitely isn't. However, the

phrase "red blue" would correspond to (red, blue) but intuitively this

seems more like purple.

This is an overly simple example but just wanted to start up a

conversation. Looking forward to your reply.

*as a side note this makes the whole "non relational DBMS" movement

seem like an oxymoron

0 new messages

Search

Clear search

Close search

Google apps

Main menu