Merge branch 'master' of https://github.com/shrinivaasanka/Krishna_iR…

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index.rst

@@ -183,7 +183,7 @@ Yes. All these drafts revolve around the fundamental philosophical/mathematical
 
 Following are the conceptual relations between various draft publications in a nutshell creating a connected graph:
 	1. Intrinsic Merit is a Non-majority Social Choice Function
-	2. Complement Functions are subset of Diophantine Equations. Polynomial Reconstruction Problem/List decoding/Interpolation which retrieve a polynomial (exact or approximate) for set of message points is indeed a Diophantine Representation/Diophantine Approximation problem for the complementary sets (e.g. approximating Real Pi by Rational Continued Fractions).
+	2. Complement Functions are subset of Diophantine Equations. Polynomial Reconstruction Problem/List decoding/Interpolation which retrieve a polynomial (exact or approximate) for set of message points is indeed a Diophantine Representation/Diophantine Approximation problem for the complementary sets (e.g. approximating Real Pi by Rational Continued Fractions). Undecidability of Complement Diophantine Representation follows from MRDP theorem and Post's Correspondence Problem.
 	3. Factorization has a Diophantine Representation (Pell Equation)
 	4. Tiling/Filling/Packing is a generalization of Complement Functions (Exact Cover)
 	5. Majority Function has a Tabulation Hashing definition (e.g Electronic Voting Machines) i.e Hash table of candidates as keys and votes per candidate as chained buckets 
@@ -202,7 +202,7 @@ Following are the conceptual relations between various draft publications in a n
 	18. Money Changing Problem/Coin Problem/Combinatorial Schur Theorem for Partitions and Tabulation Hashing are equivalent i.e expressing an integer as a linear combination of products, which defines distribution of buckets in a hash table.
 	19. ThoughtNet/EventNet are theoretical reinforcement learning simulations of Cognitive Evocation, Cause-Effect ordering and events involving actors in Clouds. ThoughtNet is a contextual multiarmed bandit Hypergraph which evokes thought/knowledge of maximum potential. Potential of thoughts/knowledge in Hypergraph is proportional to their intrinsic merit.
 	20. Neuro Electronic Currency is an experimental fictitious currency for modelling Intrinsic Merit in economic networks. EventNet is an economic network for Money Flow Markets/Trade. Intrinsic merit in economic network is the economic influence of each vertex in trade.
-	21. Text sentences are Ramsey colored by Part-of-Speech tags and alphabet positions. Similarly graph representation of texts are Ramsey edge-colored by relations (e.g WordNet, ConceptNet relations). Text-graph complement to convert cliques to independent sets and vice-versa is a special application of Complement Functions.
+	21. Text sentences are Ramsey colored by Part-of-Speech tags and alphabet positions. Similarly graph representation of texts are Ramsey edge-colored by relations (e.g WordNet, ConceptNet relations). Text-graph complement to convert cliques to independent sets and vice-versa is a special application of Complement Functions. Coloring texts by vowel-consonant and alphabets creates 2-coloring and 255 coloring respectively and imply existence of monochromatic APs in texts. Vowel-consonant 2-coloring and vowelless string complexity are equivalent to Compressed Sensing sketches i.e extracted APs are sketches compressing text.
 	22. Shell Turing Machines are experimental novelty in definition of Turing computability which introduce dimension of truth as an additional parameter in addition to tapes, alphabets, head of tape etc., to simulate hierarchy of truths across dimensions E.g 2-D Turing Machine has no knowledge about concept of Volume which is defined only in a 3-D Turing Machine. This has similarities to Tarski Truth Undefinability - Object language versus Meta Language and parallels Goedel Incompleteness. Shell Turing machines have applications in intrinsic merit definitions in the context of word2vec embeddings of words in vector spaces.
 	23. Pseudorandomness and Random Close Packing are equivalent - a random close packing is generated by a pseudorandom generator e.g shaking a container of balls shuffles the centroids of balls at random. Cellular Automaton algorithm uses Parallel PRGs to simulate Filling of Space by random strewing of solids/liquids.
 	24. A random integer partition can be generated by a Pseudorandom generator. This extends the Partition-HashTable isomorphism to PRG-Partition-Hashtable transitive equivalence: PRG produces random partitions of integer, random partitions map to random buckets in tabulation hashing.