By Prof GANGAN PRATHAP (Kerala Technological University, Thiruvananthapuram), presented at the Panel Discussion on “Shaping Smart Cities: Challenges and Opportunities” in conjunction with the 5th IEEE International Conference on Advances in Computing and Communications on 5th Septemeber 2015 at Rajagiri School of Engineering & Technology, Kochi

1. The Smart Citizen and the
Fourth Paradigm
GANGAN PRATHAP
Vidya Academy of Science and Technology, Thrissur
and
Kerala Technological University, Thiruvananthapuram

2. The Natural World
vs
the World of Many Acts
of Judgement

3. The Natural World
The Four Forces:
Gravitation
Electro-magnetic
Weak Nuclear Forces
Strong Nuclear Forces

4. The Natural World
The Four Paradigms:
Experiment
Theory
Computation and Simulation
Big Data Analytics

5. The World of Many Acts
of Judgement
Intelligence is coded as DNA

6. The moral universe
Can a moral universe be invented using
reason and evidence alone?
Yes, said the Buddha.
Buddha: The Moral Universe must be governed by the same rules
as the Natural Universe. Hence the rules of reason and evidence
must apply.

7. From the Scientometricians, White and
McCain: the World of Many Acts of
Judgement –
i.e. from many acts of judgement, not raw
natural fact.
Or why scientometrics is so
difficult!

8. A social network
Members
Chitra
David
Karan
Kalam
Mariam
Rachita
Rahul
Susan

9. Gregariousness
Dumb
analysis

10. Recursive iteration
Assume that instead of giving 1 point to
each link irrespective of its standing, points
are weighted acknowledging the quality of
the giver or recipient.
But, this cannot be known beforehand.
Smart
analysis

12. Recursive iteration
But such a problem appears frequently in physics and
engineering. In a vibration problem, the deflections depend on
the forces and the forces depend on the deflections.
Engineers and physicists have been routinely solving such
problems for two centuries. Such recursive computations can
be set up as what is called an eigenvalue problem. The idea
of using such an approach to do tournament ranking in sports
is due to Kendall and Wei [1, 2], more than 50 years ago.
(http://www.math.utsc.utoronto.ca/b24/KendallWei.pdf).
[1] T.H. Wei, The algebraic foundations of ranking theory, Cambridge University Press, London, 1952.
[2] M.G. Kendall, Further contributions to the theory of paired comparisons, Biometrics 11 (1955), p. 43.

13. Recursive iteration:
Solution depends on the solution.
[A]{x} = λ{x}

15. Ranking Raw KW
Karan 22 21.51
Kalam 18 18.98
Chitra 18 17.56
Mariam 14 15.49
Rachita 14 12.85
Susan 12 10.88
Rahul 10 9.07
David 4 5.66
KW Weighted Score Rankings of Popularity

16. There is a slightly more
sophisticated and subtle way of
looking at the paired-comparison
problem.
This is because the arguments
about rankings in a paired-
comparison exercise do not end
with Kendall-Wei's protocol.

17. A half-century ago, an Indian mathematician named
Ramanujacharyulu pointed out that there is yet
another way to look at a paired-comparison problem.
The Kendall-Wei method tries to find which is the
most strong among the strong teams.
Mathematically, this looks at the matrix formulation
of the problem in a row wise manner.
Ramanujacharyulu suggested that given the same
paired-comparison matrix, we can also try to find out
which was the least weak among the weak teams.
C. Ramanujacharyulu, Analysis of preferential experiments,
Psychometrika, 3 (1964), pp. 257-261

18. The mathematical protocol now handles the
same matrix formulation of the problem in a
column wise manner.
Implementing this is no more difficult than
the Kendall-Wei approach and can be done
with a few iterations on an Excel spread
sheet.

22. Ranking Raw R
Karan 6 6.99
Chitra 10 9.28
Kalam 10 10.94
Rachita 14 12.99
Susan 16 14.89
Mariam 14 15.82
Rahul 18 16.72
David 24 24.37
R Weighted Score Rankings of Gregariousness

23. Thus, if recursive algorithms are seen as being more
rigorous than simple raw counts, we have the
intellectually unsatisfying situation where the two
schemes can produce different rankings.
There is a simple way out of this dilemma using an
elegant solution proposed by Ramanujacharyulu. The
"most-balanced" point of view is obtained by trying to
find out
- who can combine the greatest ability to win with
the least susceptibility to lose.
- who can combine the greatest popularity with
the least gregariousness.

24. In Ramanujacharyulu's own words, "in tournaments
one may be interested in locating the really talented man
(sic) in the sense that he has
-won over the largest number of opponents but
simultaneously he has been defeated by only a few
opponents.
-won over the largest number of friends but
simultaneously has made few of his own.

25. Power-Weakness Ratio
Ranking P-W Ratio
Karan 3.08
Chitra 1.89
Kalam 1.74
Rachita 0.99
Mariam 0.98
Susan 0.73
Rahul 0.54
David 0.23

26. The 4th
Paradigm - Big Data Analytics
Google’s PageRank – billions of pages; links and their
connections
Scientometrics/Bibliometrics – 50 million documents;
15 million authors, etc.
Facebook, etc.

27. Some
interesting
applications

28. Nature
Science
PLOS
PNAS
Curr Sci
Journals ranking

31. Journals Raw Weighted
Power-Weakness
ratio
KW-Raw R-Raw KW-Wt R-Wt Raw Weighted
Nature 125 102 134.70 93.97 1.23 1.43
Science 140 144 157.42 159.27 0.97 0.99
PLOS 123 112 132.87 117.58 1.10 1.13
PNAS 88 120 65.59 119.79 0.73 0.55
Curr Sci 72 70 57.42 57.40 1.03 1.00
548.00 548.00 548.00 548.00 5.06 5.10
Power-Weakness Ratio

32. http://www.ctl.ua.edu/math103/voting/methodpc.htm
The MLA of Aruvikkara is being chosen in an
election.
The four candidates are:
Rajagopal
NOTA
Vijayakumar
Sabarinadhan
Elections ranking

33. 500 registered voters cast their votes in a
first-past-the-post system:
Rajagopal 130 votes
NOTA 0 votes
Vijayakumar 150 votes
Sabarinadhan 220 votes
Dumb
analysis

34. 500 registered voters cast their preference
ballots. The results are summarized in the
preference schedule below.
Place 130 120 100 150
1st Rajagopal Sabarinadhan Sabarinadhan Vijayakumar
2nd NOTA NOTA NOTA NOTA
3rd Vijayakumar Vijayakumar Rajagopal Rajagopal
4th Sabarinadhan Rajagopal Vijayakumar Sabarinadhan
Smart
analysis

35. http://www.ctl.ua.edu/math103/voting/methodpc.htm
We shall use the Method of Pairwise Comparisons.
The completed head-to-head matchup table is shown below.
Rajagopal NOTA Vijayakumar Sabarinadhan
Rajagopal ---------- NOTA Vijayakumar Rajagopal
NOTA ---------- ---------- NOTA NOTA
Vijayakumar ---------- ---------- ---------- Vijayakumar
Sabarinadhan ---------- ---------- ---------- ----------
NOTA gets 3 points
Vijayakumar gets 2 points
Rajagopal gets 1 point
Sabarinadhan gets 0 points

36. Smart
analysis

37. Aruvikkara Raw Weighted
Power-Weakness
ratio
KW-Raw R-Raw KW-Wt R-Wt Raw Weighted
Rajagopal 640 860 658.12 825.69 0.74 0.80
NOTA 1000 500 940.73 559.90 2.00 1.68
Vijayakumar 700 800 705.22 781.39 0.88 0.90
Sabarinadhan 660 840 695.93 833.03 0.79 0.84
3000.00 3000.00 3000.00 3000.00 4.40 4.22
Smart
analysis

39. Smart Cities
need
Smart Citizens!
Smart Citizens
need the
Fourth Paradigm!