Updated index.rst

index.rst

@@ -324,7 +324,7 @@ isolate the meanings of common pictogram B in three ways by 1) Set intersection
 	   1.14 Streaming Analytics for different types of streaming datasources - Spark streaming, many NoSQL DBs and other backends - text, audio, video, people, numeric, frequent subgraphs, A-star graph best first search for Drone motion planning, histograms for music spectrograms-set partitions-business intelligence, OS scheduler runqueue etc., - by standard streaming algorithms (LogLog counter, HyperLogLog counter, Bloom Filter, CountMinSketch, Boyer-Moore majority, CountMeanMinSketch, Approximate counting, Distinct Elements)
 	   1.15 Deep Learning Analytics for different types of datasources - text, PSUtils OS Scheduler analytics - ThoughtNet Reinforcement Learning, Recommender Systems, LSTM/GRU Recurrent Neural Networks, Convolution Networks, BackPropagation
 	   1.16 Computational Learning Theory Analytics - Complement Diophantines Learning, PAC Learning from numeric and binary encoded datasets
-	   1.17 Time Series Analysis for different types of datasources - Leaky Bucket, ARMA and ARIMA, miscellaneous statistics functions based on R and PythonR (Economic merit - Poverty alleviation example by timeseries correlation of poverty and financial deepening - https://www.researchgate.net/publication/287580802_Financial_development_and_poverty_alleviation_Time_series_evidence_from_Pakistan, Granger causality)
+	   1.17 Time Series Analysis for different types of datasources (music, traffic-electronic and transport, meteorology-precipitation, medical imagery-ECG, financial-stock and commodities price fluctuations)  - Multifractal Detrended Fluctuation Analysis, Leaky Bucket, ARMA and ARIMA, miscellaneous statistics functions based on R and PythonR (Economic merit - Poverty alleviation example by timeseries correlation of poverty and financial deepening - https://www.researchgate.net/publication/287580802_Financial_development_and_poverty_alleviation_Time_series_evidence_from_Pakistan, Granger causality)
 	   1.18 Fame-Merit Equilibrium(any Semantic Network) - applies to all previous merit measures and how they relate to perceptions. In the absence of 100% good intrinsic merit function, it is often infeasible to ascertain merit exactly. But Market Equilibrium Pricing in algorithmic economics solves this problem approximately by finding an equilibrium point between intrinsic and perceived price of a commodity. Similar Intrinsic(Merit) Versus Perceived(Fame) equilibria can be defined for every class of merit above and solution is only approximate. [Conjecture: Fame-Merit equilibrium and Converging Markov Random Walk (PageRank) rankings should coincide - Both are two facets of mistake-minimizing Nash equilibrium per Condorcet Jury Theorem for infinite jury though algorithmically different - former is a convex program and latter is a markov chain. Convex Optimization has been shown to be solved by Random Walks - https://www.mit.edu/~dbertsim/papers/Optimization/Solving%20Convex%20Programs%20by%20Random%20Walks.pdf]
 	2. Complement Functions are subset of Diophantine Equations (e.g Beatty functions). 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. Prime-Composite complementation is a special diophantine problem of finding patterns in primes which relies on non-trivial zeroes of Riemann Zeta Function (Riemann Hypothesis). ABC Conjecture can be rephrased as a complementation problem. Riemann Hypothesis has Diophantine representation by Davis-Matiyasevich-Robinson Theorem.
 	3. Factorization has a Diophantine Representation (Brahmagupta's Chakravala and Pell Equation: x^2 - y^2 = N = (x+y)(x-y)). Four major problems are solved by NeuronRain MapReduce-NC-PRAM-BSP-Multicore Computational Geometric Factorization: (*) Factorization of composites for which no polynomial time algorithms known (*) Primality Testing which is known to be O((logN)^6) by an improved version of AKS primality test - [Pomerance-Lenstra] - https://math.dartmouth.edu/~carlp/aks041411.pdf (*) Finding Square Roots - known to be O((logN)^kloglogN) by Newton-Raphson algorithm (*) Pell's equation (which so far has only a quantum polynomial time algorithm known - https://arxiv.org/abs/quant-ph/0302134 )