Updated index.rst

index.rst

@@ -343,7 +343,7 @@ Yes. All these drafts revolve around the fundamental philosophical/mathematical
            1.1 Alphanumeric Text(WordNet, ConceptNet, compressed sensing and vowelless string complexity, text restoration, Numeric compression by unique integer factorization, text summarization, topic detection and tracking, citation graph maxflow, syllabification and TeX hyphenation, fliplr memoryview O(1) Mirroring and Reversing primitives of string and binary matrices, String Factorization - factorization of strings as consonant and vowel matrix multiplication - Vowelless text compression as a consonant-vowel vectors Matrix product, Generative AI-Markov k-order Model of languages, Mildly Context Sensitive Tree Adjoining Grammar Parsers for natural languages, language independent phonetic syllable vector embedding of strings - String tensors, Array intersection-text and visuals, recursive gloss overlap,recursive lambda function growth, Question-Answering[Interview algorithm,LTFs,PTFs,Cognitive automata-Switching circuits with background intelligence], Answer-Questioning and learning LTFs, Reduction between Question-Answering and Boolean and Non-Boolean Query complexity measures (certifcate complexity, decision trees, polynomial degree, block sensitivity - classical and quantum), Coh-Metrix, Berlekamp-Welch error correction, Polynomial text encoding, Named Entity Recognition, Sentiment Analysis, Graph Mining, Graph Edit Distance between Text graphs, Locality Sensitive Hashing, Unsorted search, Set Partition Analytics, FP Growth frequent itemset mining, Machine translation, Originality by Word2Vec embedding,Bibliometrics-merit of academic publications by Meaning Representation in first order logic and Beta reduction of Lambda calculus,Novelty detection and Patent search,Multilingual strings-code switching) - Note on String mirroring vis-a-vis reversal: Mirroring topologically inverts the string or mirrors the string image than just reversing the symbols of the string - realworld example: Mirror instantaneously inverts the objects irrespective of size of object,a paradox by nature,simulating O(1) fliplr memoryview mirroring 
            1.2 Alphanumeric Text(String Analytics - Longest Repeated Substring-SuffixArray-LongestCommonPrefix, BioPython/ClustalOmega Multiple Sequence Alignment, Sequence Mining, Minimum Description Length, Entropy, Support Vector Machines, Knuth-Morris-Pratt string match, String reversal by XOR swap algorithm implemented in Go (Gochannels and Goroutines), Needleman-Wunsch alignment, Longest common substring, KNN clustering, KMeans clustering, Decision Tree, Bayes, Edit Distance, Earth Mover Distance, Linear Complexity Relaxed Word Mover Distance, PrefixSpan - astronomical,binary,numeric and generic encoded string datasets - astronomical datasets and algorithmic usecases include (*) USGS Earthquakes and NOAA HURDAT2 datasets (*) Cosmology - Deep Field Space Telescope Visuals - Hubble and WMAP imagery - AstroPy-AstroQuery interface of JPL Horizon Ephemeris service and AstroML astronomical machine learning algorithms integration (*) SkyField-AstroPy JPL Ephemeris queries for positions of celestial bodies (*) Maitreya 8t - encoded strings of celestial bodies obtained from ephemeris corresponding to various extreme weather events (*) Ephemeris Search for astronomical events in SkyField-AstroPy (*) correlation of terrestrial climate events and gravitational influence of solar system N-body orbit choreographies-Syzygies,Conjunctions,Quadratures - implementation of N-Body equation solver to gauge gravitational accelerations of solar system bodies on Earth-Moon barycenter on days of extreme weather events (*) correlation of extreme weather events and celestial bodies by Sequence mining of historic (Hurricane and Earthquake) astronomical datasets to get Class Association Rules (*) prediction of extreme weather and seismic events from N-Body angular separation and gravitational acceleration computed from Sequence Mined Class Association Rules),
            1.3 Audio-speech(Speech-to-Text and recursive lambda function growth,Graph Edit Distance),
-           1.4 Audio-music(Music Information Retrieval-MIR, mel frequency cepstral coefficients, Learning weighted automata from music notes waveform, Graph Edit Distance between weighted automata, Equivalence of Weighted automata by Table filling, Kullback-Leibler and Jensen-Shannon divergence, Novelty detection and Originality of a score by waveform distance, AI music synthesis by functions-automata-fractals and polynomial interpolations of training music waveforms, AI music synthesis by Virtual Piano from random 12-notes string by Numpy random choice() (which is combinations) and Fisher-Yates-Knuth shuffle (which is NeuronRain implementation of permutations) of all non-repetitive notes sequences, Deep Learnt Automata, Dynamic Time Warping distance similarity between music timeseries, Music synthesis from sum of damped sinusoids, Weierstrass Function - Fractal Fourier summation, Music evoked autobiographical memories, Normalized Compression Distance-Kolmogorov Complexity, Contours of Functional MRI medical imageing for music stimuli - https://openneuro.org/datasets/ds000171/versions/00001) - AI Music Synthesizer from mathematical functions is the converse of Learning weighted automata from music notes wherein innate fractal self-similar structure of music is exploited by machine learning to churn out music - JS Bach + Fractals = New Music - https://www.nytimes.com/1991/04/16/science/j-s-bach-fractals-new-music.html, https://link.springer.com/chapter/10.1007/978-3-642-78097-4_3. Learning a polynomial from music waveform as against weighted automaton learning (graph structure of music) could extract algebraic structure of music - NeuronRain implements a Degree 5 (Quintic) polynomial learner for music waveforms - Unsolvability of Quintic polynomial (Degree >= 5) by Abel-Ruffini Theorem intuitively means roots of polynomial learnt from music waveform could not be expressed as formulae on radicals - tough nut to crack and could be irreducible. Earth Mover Distance Triple Sequence from moves of Towers of Hanoi Single Bin Sorted LIFO histogram exhibits a Collatz-like Chaotic structure suitable for Music and Financial Timeseries modelling ending always in (0,0,0) for 3 buckets.
+           1.4 Audio-music(Music Information Retrieval-MIR, mel frequency cepstral coefficients, Learning weighted automata from music notes waveform, Graph Edit Distance between weighted automata, Equivalence of Weighted automata by Table filling, Kullback-Leibler and Jensen-Shannon divergence, Novelty detection and Originality of a score by waveform distance, AI music synthesis by functions-automata-fractals and polynomial interpolations of training music waveforms, AI music synthesis by Virtual Piano from random 12-notes string by Numpy random choice() (which is combinations) and Fisher-Yates-Knuth shuffle (which is NeuronRain implementation of permutations) of all non-repetitive notes sequences, Deep Learnt Automata, Dynamic Time Warping distance similarity between music timeseries, Music synthesis from sum of damped sinusoids, Weierstrass Function - Fractal Fourier summation, Music evoked autobiographical memories, Normalized Compression Distance-Kolmogorov Complexity, Contours of Functional MRI medical imageing for music stimuli - https://openneuro.org/datasets/ds000171/versions/00001) - AI Music Synthesizer from mathematical functions is the converse of Learning weighted automata from music notes wherein innate fractal self-similar structure of music is exploited by machine learning to churn out music - JS Bach + Fractals = New Music - https://www.nytimes.com/1991/04/16/science/j-s-bach-fractals-new-music.html, https://link.springer.com/chapter/10.1007/978-3-642-78097-4_3. Learning a polynomial from music waveform as against weighted automaton learning (graph structure of music) could extract algebraic structure of music - NeuronRain implements a Degree 5 (Quintic) polynomial learner for music waveforms - Unsolvability of Quintic polynomial (Degree >= 5) by Abel-Ruffini Theorem intuitively means roots of polynomial learnt from music waveform could not be expressed as formulae on radicals - tough nut to crack and could be irreducible. Earth Mover Distance Triple Sequence from moves of Towers of Hanoi Single Bin Sorted LIFO histogram exhibits a Collatz-like Chaotic structure suitable for Music and Financial Timeseries modelling ending always in (0,0,0) for 3 buckets. NeuronRain Music Synthesizer is more inclined towards colored sequence representation of music notes than just AI synsthesis - for 12-note octave, every music notes sequence is 12-colored and by Van Der Waerden theorem, arithmetic progression of similar notes inevitably emerge even in random note sequence (or) Sufficiently long (or notes sequence of length equal to Van Der Waerden number) random noise is also a music with order in it. New music notes sequences could be synthesized by pumping lemma and from closure operations on weighted automata learnt from training music waveforms - Weighted automata (On the Definition of a Family of Automata - [Schutzenberger] - https://core.ac.uk/reader/82727930 , Weighted Automata - Kleene-Schutzenberger Theorem - Rational semiring series are recognizable - https://www.cmi.ac.in/~madhavan/courses/qath-2015/reading/droste-kuske-weighted-automata.pdf ) have been studied a lot in Natural Language Processing and Image Compression (Hasse Diagram of Weighted Automata variants - https://en.wikipedia.org/wiki/Weighted_automaton ). An example usage of weights in music weighted automata: If there is a transition from state s1 to state s2 for note C with weight 0.5, it might imply the tempo of note C to be 0.5 (and there could be many other interpretations). 
            1.5 Visuals-images(Compressed Sensing,ImageNet ImageGraph algorithm, Graph Edit Distance between FaceGraphs of segmented images, GIS Remote Sensing Analytics, Weather analytics, Climate analytics, Clustering Analytics of celestial bodies in sky imagery from planetarium software and their correlation to extreme weather events - visual analogue of textual astronomical datasets, Modularity-Community Detection, Urban planning analytics (3D UGM - Digital Elevation Models from GHSL BUILT-H,BUILT-V and BUILT-S datasets - Mapping and 3D modelling using quadrotor drone and GIS software - https://journalofbigdata.springeropen.com/articles/10.1186/s40537-021-00436-8, 2D UGM - Dynamic Facegraph, Cellular Automata and Polya Urn Urban Growth [by Learnt Replacement matrix] Models), Four colored morphological settlement zone classification from GHSL BUILT-C, Standard of Life metrics-Liveability, Automatic Delineation of Urban Growth Boundaries-from (*) VIIRS NightsLights contour segmentation - high night lights points to urbanization - example city comparison by nightlights: https://worldbank.github.io/OpenNightLights/tutorials/mod5_4_comparing_cities.html - NeuronRain supports Google Earth Engine VIIRS Radiance rankings of urban sprawls (*) Isochrones or polygon created by drive time  radius in all directions - https://developer.nvidia.com/blog/interactively-visualizing-a-drivetime-radius-from-any-point-in-the-us/ - NeuronRain isochrone implementation is based on OSMnx road network graph (*) Suburban Commuting patterns - live realtime traffic (e.g Sensors, Google Maps traffic busy markers gathered from velocity of mobile devices transmitting GPS info, OpenStreetMap GPS Traces, Suburban-Metro rail traffic) is proportional to urbanization - bottlenecks in live traffic classification (slow to fast) should in principle correspond to betweenness centrality or a minimum cut computed from transportation network graph - an example of betweenness centrality based mincut estimation as an alternative to augmenting path mincut - http://bit.kuas.edu.tw/~jihmsp/2015/vol6/JIH-MSP-2015-05-016.pdf - NeuronRain implements Maxflow-Mincut bottleneck measure alongwith betweenness centrality of OSMnx road network graph and a TypeScript ViteJS webserver GUI for Google Maps Live Traffic Layer - a longitude-latitude configurable variant of Google Maps documentation example (*) OSMnx OpenStreetMap Road Density analytics - Road density and Road gravity increase proportional to urbanization (*) 3D UGM Digital Elevation Models of Built-up surface - skyscrapers indicate Central Business District and urbanization, Gini Coefficient of Inequality, Moran's I measure of Urban Sprawl Dispersion-Diffusion Factor, Canny Edge Detection-Transportation Network Lattice Grid, Ocean Floor Bathymetry GIS, Machine Learning models of Urban Extent-NASA SEDAC GPW,Facebook HRSL,European Union GHSL R2019A-R2022A-R2023A BUILT_S-BUILT_V-BUILT_C datasets and NASA VIIRS NightLights, USGS LandSat9 TIRS-2/OLI-2 imagery, Population Estimation Models from GIS imagery - Verhulste and Ricker, Voronoi Tessellation, Delaunay Triangulation, GMSH Trimesh-Quadmesh, Preferential attachment, Face and Handwriting Recognition, Neural network clustering, DBSCAN Clustering, DICOM-Medical imageing-ECG-MRI-fMRI-EEG-CTSCAN-PET-Doppler-XRay, Convex Hull, Patches Extraction-RGB and 2-D, Segmentation, Random forests, Autonomous Driving-LIDAR point cloud data, Flood vulnerability detection from GIS and LiDAR DEM, Drone Aerial Imagery Analytics, Astronomy-Cosmology Datasets-Deep Field Visuals from Space Telescopes) - GHSL rasters are mosaics created from Symbolic Machine Learning which is quite akin to Multiple Sequence Alignment and Class Association Rules based learning implemented for Astronomical Pattern Mining in NeuronRain. GDP and other socioeconomic indicators can be estimated from GIS Imagery analytics - Examples: (1) Electricity consumption for Residential-Industrial-Commercial purposes can be estimated from VIIRS NightLights (2) Infrastructure (Built-up volume and surface) can be estimated from GHSL rasters and OSMnx Road network density statistics (3) Foodgrain production can be estimated from radiance of waterbodies and vegetation - a linear regression-logit for GDP might be: GDP per square bounding box = [weight1*number_of_bright_pixels(Metro areas) + weight2*number_of_dim_pixels(Urban-Semiurban areas) + weight3*number_of_ndvi_pixels(Vegetation-Agrarian-Waterbodies) + weight4*road_density + weight5*number_of_unlit_pixels(Rural) + bias] / area of the bounding box - Some more regressions based on VIIRS radiances and Vegetation Indices could be found in https://learn.geo4.dev/RemoteSensingTutorial.html , https://learn.geo4.dev/Radiance%20Calibrated%20Nighttime%20Lights.html and Radiance calibrated night data analysis of subway transit network of cities in - [Gonzalez-Navarro and Turner - 2018] - Subways and Urban Growth: Evidence from Earth - http://eprints.lse.ac.uk/66535/1/__lse.ac.uk_storage_LIBRARY_Secondary_libfile_shared_repository_Content_LSE%20Spatial%20Economic%20Research%20Centre_Discussion%20Papers_2016_April_sercdp0195.pdf e.g City centrality regression - "... ln yi = A + Bln xi + ϵi to create these centrality measures, where yi is the mean light intensity within an area, xi is the radius of the associated area, and B is the rate at which light decays when increasing the distance from the city center ..."
            1.6 Visuals-videos(ImageNet VideoGraph EventNet Tensor products algorithm for measuring Tensor Rank connectivity merits of movies,youtube videos and Large Scale Visuals, Graph Edit Distance between Video EventNet, Sentiment analysis of predictions textgraphs for youtube and movie videos by Empath-MarkovRandomFields Recursive Gloss Overlap Belief Propagation-SentiWordNet, Topological Sort for video summary, Digital watermarking, Drone Aerial Video Streaming Analytics, GIS Imagery Contour graphs for A-Star motion planning and Road Geometry Airspace Drone obstacle avoidance),
            1.7 People(Social and Professional Networks) - experiential and intrinsic(recursive mistake correction tree, Question-Answering in Interviews/Examinations/Contests),