Subject: [icnrg] Manifolds and Nature Driven Patterning

From: Sitaraman Vilayannur <[email-masked]>
Date: Sat, 29 Jun 2013 00:11:15 +0530

This is kind of long,  I hope this is ok to bounce this thought off here,
since it is a research group....
One factor with the separation of control plane from the data plane that we
would need to confront with is the tradeoff between viewspan and the
granularity of information that the controller has.  Going further, for
optimized reprovisioning and fault analysis, based on the concluding
aspects of the below, i am wondering if an applicability that can be
explored is to see if
Nature prefers, which we can look up to Topologists or Geometers, evolution
paths of topologies (characterized by say curvatures and the likes, given a
known stimuli) and if we can classify our network situation to belong to
one of these known topologies and its evolutionary behavior then we could
then exploit natures preference to be able to mask details of fine grain
and yet be able to do accurate network operations.
 This sort of a thing could be more application in Information than just
plain bits and bytes.

Now that PGM is over, i did what i was always afraid of doing, watch a
movie with popcorn in hand (hint of my status and sorry state of affairs
:-)))  The movie happened to be Russel Crowes "A Bueatiful Mind"

John Nash (and Steve Jobs per what he said at the commencement in Stanford)
perhaps didnt have the opportunity of courseera else they could have simply
attended classes they like from the worlds best profs...

Now in the Movie  (Thanks to the makers, simplifying what these
mathematicians do must be a  well, "non trivial" result WLOG :-)) Russel
Crowe says

1. "In a competitive behavior someone always looses"

   Isnt there a sort of duality here, if you make an edge characterizing
people who compete,  the expansion of the graph is inverse to the expansion
characterising the "common good"  Relate to the post i was musing about in
the post thanking this course....

2. Crowe also says "Derive and Equilibrium where prevalence is a non
singular event, where nobody losses"

The term prevalence points to probability. Now looking at this statement,
isnt is eerily close to Reiemann Hypothesis, where everybody (every root )
has a real  part 0.5 We could consider this is "nobody losses" or simply a
Max Fair allocation problem optimization where everybody has a fair share
of winning or loosing.

There were two posts on LinkedIn recently one about Steve Jobs commencement
speech at Stanford and another about how to get the job one really wants.

For both i commented that what if

a) we wake up everyday and think it is the last day for others.

b) We just do the job the organization really needs and as a result if the
jobs that we really want come to us then it is an indicator of a healthy
economy.

It appears that both the above was driven by my musings earlier (summarized
in the Thank You note) in the group related to Expander Graphs.

Several years ago my colleagues were strongly recommending me to see this
movie while working at IIT Madras, i was going thro some issues and last
thing i was interested in was looking at a Genius for contrast and never
did.   Glad i didnt and did after i took the PGM course, especially if we
go by Steve Jobs quote about connecting the dots backwards..It is more
emotionally and aesthically satisfying now.

3. Relate the above to what Crowe goes on to say...Everybody in the group
does what he does for himself and the group.

This too relates to the above.

Now, we come to an earlier posting of mine on this group regarding duality
on the domain and its transform.  The situation at Princeton with the
single Blonde "could do with some revision" now that we have taken
PGM...:-) A more likely scenario is there are many Blondes who are and find
mathematicians attractive and the converse.  The leaves out the first
argument of Crowe (which in any case assumes a strong dependency between
the two events). Now for the more likely scenario i was wondering what if
each Gentelmen Mathematican indentify (with independence assumption being
made) who each is most attracted to, and then, listen to this, also
indentifies his best male Mathematician friend (or debatedly, his fircest
male mathematician competitor) and then takes the pain to introduce him to
her (and then perhaps iterate and let the markov chain mix) Would that be
closer to the Riemannian Middle? What is the domain and the transform. Is
one (The Adam Smith version that needed alteration) more of instant
gratification and the other (what i have said here is an altered version of
Russel Crowes) delayed gratification (assuming the adage what goes around
comes around hold true :-0)  Doing good to oneself is instant gratification
and doing good for the others, hoping mother nature is fair when mixing has
been achieved, is delayed gratification. In the former it is hard to fit in
an mixing scenrio when in the latter it is more natural.

In tamil we have a song that has an approx meaning that goes like so "IF
you win a lottery it is a good day for one and and for that day"  and so on
and finally "if you have others good in your mind every day of your life is
a good life" is Riemannian hypothesis then a statement of everyone getting
the best chance of winning when your interest coincides with others
interest (both the domain and the transform together) a probabilistic
mixing gives everyone a fair chance of winning?  Eveything i have mentioned
above seem to be tied together by this hypothesis including the two comments
  made on the Linked Posts Business and Personal Life!

Interestingly also, Russel Mentions Manifold Embedding....googled (gosh i
would have never gone all the way to a library to search for books on this,
Google and such has so tremendoulsy changes academic endeavor unthinkable
during my student dates, pun intended) and it throws up this interesting
Rimeannian Manifolds. It is interesting we have a feature that we always
need in Probability all probability instances summing to one in a slightly
different perspective here.. Isometric embedded families of the manifold.
All curvatures are determined solely by distance along the path no matter
which instance of embedding you use. [The paper example in wikipedia] I
have never known what an isometric embedding was before, so would
appreciate a correction if i got the meaning wrong there from what i picked
up from wikileaks on Geometry. Probing further there is even this
osculating paraboloid concept and the curvature at the centre of a parabola
is well very eerily half.

There are various ways perhaps we can use (if not already) this fact in
probabilistic inference then and perhaps be able to use fundamental
properties these Geometers, Algebraic or otherwise., discover for us,  to
quickly go inference or learning once we assign it to a manifold class.  This
relates to an earlier posting i made about topolgies and continous
eigenvalues. So a question arises is the osculating parabola (or
paraboloid) on manifolds viewed probabilistically be considered as a
restatement of Riemanian Hypothesis.

Russel Crowes scenario about one Blonde could be applied to isolated
security threats in a network, while the other scenario could be used for
optimum resource allocation or facility location. Knowledge existing in
evolution of topology or differntial geometry could help us do  trend
analysis, and inference, learning at a much corser level and exploting the
isometric embedding property infer the changes to stimuli.

 I pray dearly my Physical Metallurgy Professor is not in the audience, and
neither is Robert Reedhill but i only vaguely rememeber Austenite
martensite, diffusonless transoformation and Shape memory alloys.  Relate
the above, markov mixing and any applications to resilient network systems
probabilistically.

Sitaraman

---

From: Hamed Haddadi <[email-masked]>
Date: Fri, 28 Jun 2013 16:36:31 -0400

I was not really able to grasp your intended outcome from this post to
two very technical and subject-specific mailing lists, perhaps you would be
better off using other online discussions communities and blogs

There has been quite some work done on evolution of topologies , including
two published in IEEE surveys and tutorials in 2008, and one by Philipa
Gill, and one by Amogh Dhamdhere, and one by us using both BGP and
traceroute data,  which may help you

Cheers

P.s. I thought, without runining any Hollywood heroes , I'd point out that,
as any game theorists would tell you, if the "blonde scenario" had
really happened, the optimal strategy for Nash would have been to send his
friends to the brunettes, and then for himself to approach the blonde. That
would have been the Nash equilibrium

==
Hamed (Currently at AT&T Research Labs, NJ)
http://www.eecs.qmul.ac.uk/~hamed/

On 28 June 2013 14:41, Sitaraman Vilayannur
<[email-masked]>wrote:

> One factor with the separation of control plane from the data plane that
> we would need to confront with is the tradeoff between viewspan and the
> Nature prefers, which we can look up to Topologists or Geometers,
> evolution paths of topologies (characterized by say curvatures and the
> likes, given a known stimuli) and if we can classify our network situation
> to belong to one of these known topologies and its evolutionary behavior
> then we could then exploit natures preference to be able to mask details of
> fine grain and yet be able to do accurate network operations.
> John Nash (and Steve Jobs per what he said at the commencement in
> Stanford) perhaps didnt have the opportunity of courseera else they could
> have simply attended classes they like from the worlds best profs...
>
> people who compete,  the expansion of the graph is inverse to the
> expansion characterising the "common good"  Relate to the post i was
> musing about in the post thanking this course....
>
> has a real  part 0.5 We could consider this is "nobody losses" or simply
> a Max Fair allocation problem optimization where everybody has a fair share
> of winning or loosing.
>
> There were two posts on LinkedIn recently one about Steve Jobs
> commencement speech at Stanford and another about how to get the job one
> really wants.
>
> It appears that both the above was driven by my musings earlier
> (summarized in the Thank You note) in the group related to Expander Graphs.
>
> comes around hold true :-0)  Doing good to oneself is instant
> gratification and doing good for the others, hoping mother nature is fair
> when mixing has been achieved, is delayed gratification. In the former it
> is hard to fit in an mixing scenrio when in the latter it is more natural.
>
> you win a lottery it is a good day for one and and for that day"  and so
> on and finally "if you have others good in your mind every day of your life
> is a good life" is Riemannian hypothesis then a statement of everyone
> getting the best chance of winning when your interest coincides with others
> mixing gives everyone a fair chance of winning?  Eveything i have
> mentioned above seem to be tied together by this hypothesis including the
> two comments  made on the Linked Posts Business and Personal Life!
>
>  I pray dearly my Physical Metallurgy Professor is not in the audience,
> and neither is Robert Reedhill but i only vaguely rememeber Austenite
> _______________________________________________
> icnrg mailing list
> [email-masked]
> https://www.irtf.org/mailman/listinfo/icnrg
>
>

---

From: Sitaraman Vilayannur <[email-masked]>
Date: Sat, 29 Jun 2013 19:09:51 +0530

Thanks much for the response and pointers Hamed, Will get hold of those
references and ramp up....
My intent was the following,
1.  To get further pointers.
2.  Both the groups Christened as a research group, i was personally
stricken by the patterns that appear common, and just like Its Saturday
Night and i dont want to save, i was looking for practical applications,
SDN and ICN seemed like good candidates. I was particularly interested in
a)Identifying and then exploring opportunities for Duality patterns.  Given
that Transforms which i kind of coarsely club into a duality pattern has
had such a wide applicability in Communication Systems, and given that
Stochastic Analysis would be a necessity going forward, i was looking for
precedents and further work on (this is related to an earlier posting i
made in the similar vein) viewing the possibile duality between
deterministicity and stochasticty as a common theme overlaid on
transform-pair domains (already to to-be identified),  That combined with
this post which proposes possibly addressing the complexity issue of
simulataneous granularity and volume in stochasitic analysis by taking
recourse to classification of the parameters onto coarser grain continuous
topologies (which, for example, fits the isometric embedding - sum of
probabilities 1 ) and therefore being able to reuse existing rigorous
characterizations in the field of Topology, Algebraic Geometry.
Data is discrete, but Information is less so, therefore i thought such an
analysis such as the above would be useful in exploiting the wider scope of
the source of routing information in SDN (which could include the data in
the most general case) along with ICN viewed in a scope broader than mere
location optimized redundant caching, could lead us to develop software for
self-organizing components of the network. This could with a Stochastic
analysis incorporate feedback loops and learning.  Also SDN/ICN would
eventually have to necessarily address Service Assurance OSS component, and
here too such analysis could come handy.
 I was also partly motivated by Steve Jobs speech at Stanford i stumbled on
LinkedIn. Going beyond  games and cartoon films, graphics and analysis
based on them i felt could propel an effort such as Pixars higher up the
value chain and the above could be an example of the same.
 3. Just a fetish with this Riemann Hypothesis, and seeing  what
probabilistic interpretations have mathematician come up with for that and
see if my thoughts are reasonable or am i just going plain crazy.
 Regarding you mention of two very technical and subject specific, i still
seem to think that one way of addressing growing complexities of todays
problem, are to take a step back, identifiy common patterns, even if
seemingly unrelated and then work on its applications to specific problems.
Perhaps i thought the quote a problem cannot be solved at the level it is
created also holds for the level of abstraction and specificity of the said
subject.
  Thanks again!  I may contact you offline later for additional pointers on
the same...in case you happen to have the time at that point.....hope that
is ok.
 Sitaraman

On Sat, Jun 29, 2013 at 2:06 AM, Hamed Haddadi <[email-masked]> wrote:

> P.s. I thought, without runining any Hollywood heroes , I'd point
> out that, as any game theorists would tell you, if the "blonde scenario"
> had really happened, the optimal strategy for Nash would have been to send
> his friends to the brunettes, and then for himself to approach the blonde.
> That would have been the Nash equilibrium
>
> ==
> On 28 June 2013 14:41, Sitaraman Vilayannur <
> [email-masked]> wrote:
>
>> b) We just do the job the organization really needs and as a result if
>> the jobs that we really want come to us then it is an indicator of a
>> healthy economy.
>>
>> did.   Glad i didnt and did after i took the PGM course, especially if
>> we go by Steve Jobs quote about connecting the dots backwards..It is more
>> Now, we come to an earlier posting of mine on this group regarding
>> duality on the domain and its transform.  The situation at Princeton
>> with the single Blonde "could do with some revision" now that we have taken

---

From: Hamed Haddadi <[email-masked]>
Date: Fri, 28 Jun 2013 15:08:04 -0400

There has been quite some work done on evolution of topologies , including
two published in IEEE surveys and tutorials in 2008 which may help you

Cheers

as any game theorist would tell you, if the "blonde scenario" had

-- 
=======
Hamed