Updated index.rst

index.rst

@@ -328,7 +328,7 @@ Yes. All these drafts revolve around the fundamental philosophical/mathematical
            1.7 People(Social and Professional Networks) - experiential and intrinsic(recursive mistake correction tree, Question-Answering in Interviews/Examinations/Contests),
            1.8 People(Social and Professional Networks) - lognormal least energy(inverse lognormal sum of education-wealth-valour,Sports Analytics-Intrinsic Performance Ratings-IPR e.g Elo ratings,Real Plus Minus, Non-perceptive Rankings in Sports, PSPACE-hardness of most games encoded as TQBF, Wealth, Research and Academics),
            1.9 People(Professional Networks)-analytics(attritions, tenure histogram set partitions - correlations, set partition analytics, analytics driven automatic recruitment of talent - an alternative to manual Interviews, Career transition score, Career Polynomials and Inner Product Spaces, Chaotic Hidden Markov Model and Weighted automata model of Tenures, Originality of a profile measured by tenure choices-equivalence of state transition automata, Novelty detection-Innovation-Patents, Fibonaccian Search of sorted unique id(s)),
-           1.10 People-Opinion Mining and election analytics(Boyer-Moore Streaming majority, Reservoir sampling-Compression of Boolean circuits, Opinion polls-Approximate Majority-Promise Majority-Certifying polynomials-Algebraic Immunity, Popular Opinion Mining from news articles, set partition Drone Voter Received Encrypted Paper Audit Trail (VREPAT) EVMs, drone electronic voting machine by autonomous delivery, voting analytics, efficient population count, pre-poll and post-poll forecast analytics, Bertrand ballot theorem, Arrow and Gibbard-Satterthwaite No-Go Theorems on Impossibilty of Fair Voting satisfying criteria for 3 or more candidates),
+           1.10 People-Opinion Mining and election analytics(Boyer-Moore Streaming majority, Reservoir sampling-Compression of Boolean circuits, Opinion polls-Approximate Majority-Promise Majority-Certifying polynomials-Algebraic Immunity, Popular Opinion Mining from news articles as multipolar votes (objective and subjective) - multipolar vote generalizes traditional vote to a triple of percentage like-dislike-neutrality voter (each news article sourced from public opinion is an aggregated vote which reflects a mix of voter sentiments) harbors towards a candidate, set partition Drone Voter Received Encrypted Paper Audit Trail (VREPAT) EVMs, drone electronic voting machine by autonomous delivery, voting analytics, efficient population count, pre-poll and post-poll forecast analytics, Bertrand ballot theorem, Arrow and Gibbard-Satterthwaite No-Go Theorems on Impossibilty of Fair Voting satisfying criteria for 3 or more candidates),
            1.11 People(Social and Professional Networks)-unique person search (similar name clustering by phonetic syllable vectorspace embedding of names - String Tensors, People profiles as Tensors, Graph Edit Distance, contextual name parsing, unique person identification from multiple datasources viz.,LinkedIn,Twitter,Facebook,PIPL.com,Emails)
            1.12 People(Social and Professional Networks,Archaeology-Civilizations)-face and handwriting recognition (textual,topological and graph theoretic handwriting and face recognition-physique recognition by dynamic time warping on physical mobility timeseries-gender recognition, fingerprint recognition for unique identification, Feasibility of Non Fungible Tokens as non-biometric unique id alternatives e.g Neuro fictitious Cryptocurrency Boost UUIDs, Archaeoastronomical dating from scriptures by astronomical algorithms, Decipherment of ancient scripts by Rebus principle topological script recognition - Chain Approximation Contour polynomials clustering/Homeomorphism/Product Homotopy/Pasting Lemma/Graph Edit Distance and Earth mover distance/Gromov-Hausdorff distance/Multiple Netrd Graph distances/Graph matching/Exact-Approximate Graph and Subgraph Isomorphisms/Trimesh-Quadmesh/Bezier-animated Mesh Deformations/Dynamic Time Warping/Common Subgraph Problem/Approximate Topological Matching between Dlib face landmark detected and segmented Image Voronoi tessellation FaceGraphs,Delaunay Triangulation graphs and Quadrilateral Mesh Graphs/Euler Characteristic of 2D and 3D Voronoi tessellations),Sentiment Analysis based Reciprocal Recommender Systems for Bipartite Social Network Graphs - Matrimonial and other Match making Services,Gale-Shapley Stable Marriage Problem,Hall's Marriage Theorem, Physique recognition by Dynamic Time Warping Timeseries similarity of trimesh-quadmesh sequences of full body video footages - claimed to be more accurate than face recognition. Decipherment of ancient writing systems is a harder problem of handwriting recognition where no prior training data are available for an AI model to decipher an unknown inscription on potsherds-painted_gray_ware into natural language and Rebus principle is often resorted to e.g Asko Parpola's Rebus decipherment of Indus script - four conditions for Rebus principle -  https://www.harappa.com/content/indus-script-6 - [Iravatam Mahadevan] - The Indus Script: Texts, Concordance and Tables - https://www.harappa.com/content/indus-script-texts-concordance-and-tables and An epigraphic perspective on the antiquity of Tamil - https://www.thehindu.com/opinion/op-ed/An-epigraphic-perspective-on-the-antiquity-of-Tamil/article16265606.ece (Antiquity of Tamil language, Tamil Brahmi which predates Ashoka Brahmi - deciphered by [KV Subramanya Iyer] in year 1924 - and similarities to Ashoka Brahmi - https://en.wikipedia.org/wiki/Tamil-Brahmi , Lectures by [Iravatam Mahadevan] - https://www.tamildigitallibrary.in/admin/assets/book/TVA_BOK_0010654_Tamil_Brahmi_Inscriptions.pdf, Status of Tamil as classical language vis-a-vis Other languages - [George L Hart - Institute for South Asia Studies-UC Berkeley] - https://southasia.berkeley.edu/statement-status-tamil-classical-language). Rebus principle topological script recognition from textgraph of ImageNet predictions of inscription imagery could extract deeplearnt meanings of individual script pictograms graph theoretically and serve as a validation of a decipherment - For example following fictitious undeciphered inscriptions:
 		Inscription1 - ABCD - ImageNet prediction Textgraph1
@@ -340,7 +340,7 @@ isolate the meanings of common pictogram B in three ways by 1) Set intersection
 	   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 (music, traffic-electronic and transport, meteorology-precipitation, medical imagery-ECG, financial-stock and commodities price fluctuations)  - Multifractal Detrended Fluctuation Analysis (MFDFA) of Music-Financial-Precipitation timeseries, Multimodal Gaussian Mixture Models(GMM) and Gaussian Ensemble Timeseries Forecast of Precipitation by choosing most probable Integer Partition (modes of GMM forecast timeseries correspond to peaks in N-Body gravity), 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]
+	   1.18 Fame-Merit Equilibrium(any Semantic Network) - applies to all previous merit measures and how they relate to perceptions. Google PageRank is a perception (Fame) ranking based on majority voting while Microsoft Bing SPTAG is an Intrinsic Merit algorithm to find nearest neighbours (URLs) of a search query and rank them by distance. 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 ). Fast factorization algorithm could speedup Fast Fourier Transform algorithm which is universally used (Example: Good-Thomas Prime Factor FFT - https://en.wikipedia.org/wiki/Prime-factor_FFT_algorithm) - in digital signal processing, music, digital image processing, telecom FDM, integer multiplication among others. Computational Geometric Parallel Planar Point Location Polylogarithmic Factorization implemented in NeuronRain is classical while fastest known classical factorization algorithms are of O(exp(logN)^1/3(loglogN)^2/3)) complexity and quantum factorization due to [Shor] is in BQP. Possibility of polynomial time factorization has been holy grail of computer science and a classical deterministic polylogarithmic time factorization implies derandomization of [Shor] quantum factorization (which in itself is a mixture of classical and quantum speedup phases) as [Grover] quantum unstructured list search has been shown to be derandomizable by amplitude amplification. Quantum networks and gates are described by registers of N-qubits operated by finite set of unitary transformations which preserve inner products. Stability of Quantum Computation is determined by decoherence a process by which a quantum N-bit register dissipates density (amplitude) of a superposed state by interference with a thermal reservoir - http://www.cs.tau.ac.il/~amnon/Classes/2003-Class-Quantum/Papers/ekert-joza-on-shor.p733_1.pdf - "... To study the typical effects of decoherence, let us consider a quantum register composed of L qubits with the selected basis states labeled as |0> and |1>. Any quantum state of the register can be described by a density operator of the form Sigma_i,j=1_to_2^L-1(rho(i,j)*|i><j|), (49) where |ui> is defined as in Sec. V, as a tensor product of the qubit basis states, |i> = |iL-1> * |iL-2> * ... * |i1> (50) The rhs is the binary decomposition of the number Sigma_l=0_to_L-1(2^l*il) .  Quantum computation derives its power from quantum interference and entanglement. The degree of the interference and entanglement in an L-qubit register is quantified by the coherences, i.e., the off-diagonal elements rij (i != j) of the density operator in the computational basis. When a quantum computer is in contact with a thermal reservoir, the resulting dissipation destroys the coherences and changes the populations (the diagonal elements). In time the density matrix will approach the diagonal form, rthermal = Sigma_i=0_to_2^l-1 (exp(-Ei/kT)/Z * |i><i|, (51) ..." - Stability concerns affect classical computations as well - an arbitrary classical bit on a RAM could be altered by cosmic ray - Decoherence of 2^L possible values of L-qubit register in superposition explained by [Unruh] - https://arxiv.org/pdf/hep-th/9406058.pdf - "... A crucial feature of the ability of quantum computers to be more efficient in certain problems involves having the computer be placed in the coherent superposition of a very large number (exponential in L) of “classical states”, and having the outputs interfere in such a way that there is a very high probability that on the appropriate reading of the output, one would obtain the required answer. One is replacing exponentiallity in time with exponentiallity in quantum coherence. This requires that the computer be able to maintain the coherence during the course of the calculation.  This paper examines this requirement, and examines the constraints placed on the ability to maintain this coherence in the face of coupling to external heat baths. ..." - and [Palma et al] - https://opg.optica.org/abstract.cfm?uri=IQEC-1996-FF4 - "... In quantum computers the superposition state of the register has a crucial role, but unfortunately it is very vulnerable to decoherence effects. We have studied the case where the decoherence appears as fluctuations in the phases of the probability amplitudes for the qubits [1], We show that due to the decoherence the superposition decays as exp[-p(L) t], where t is time and p(L) is some polynomial of the number of qubits in the register. Therefore the time to perform, for instance, Peter Shor’s factorisation algorithm [2] scales exponentially with L. Thus the advantage of this quantum algorithm over the classical factorisation algorithms is lost. ..." - Quantum Decoherence could be one of the ways to derandomize (but in the wrong way corrupting the answer) or collapse the wavefunction. NeuronRain implements sequential and parallel versions of computational geometric factorization in Rust by iterative binary search, sequential rasterization factor point location and parallel planar factor point location by Rayon parallel iterators. Rust implementation of computational geometric parallel planar point location factorization (internally based on Rayon parallel iterator - suited for HPC Supercomputers - thus in Nick's class) has been found to be upto 1000 times faster than PySpark cloud implementation (DMRC MapReduce class) for range of multiple consecutive integers but limited to 32-bits integers.  
 	4. Tiling/Filling/Packing is a generalization of Complement Functions (Exact Cover).