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Nov 05, 2025 — Nov 05, 2026
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Section 1312 updated
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+----------------------------------------------------------------------------------------------------------------------------- +1312. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Polya Urn Urban Growth Model - Urban sprawl area computation - 22 September 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301,1304 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Gridded Population Estimators (SEDAC GPW4 and GHSL convex hull estimators), DBSCAN and Neural Network Urban Extent Learners, Computational Geometry, Intrinsic Merit Rankings, R Ricker Population Estimation, Community detection, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing, Computational Geometry and Polygonal packing by Voronoi Tessellation, Four color theorem, Economic Merit, Computational Economics - GDP estimation from Urban sprawl demographics, electricity consumption, Poverty alleviation, MARA (Multiple Agent Resource Allocation) Facegraph walk coloring DNFSAT algorithm, Preferential Attachment, Fixed Parameter Tractability-Kernelization +------------------------------------------------------------------------------------------------------------------------------
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----------------------------------------------------------------------------------------------------------------------------- 1312. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Polya Urn Urban Growth Model - Urban sprawl area computation - 22 September 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301,1304 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Gridded Population Estimators (SEDAC GPW4 and GHSL convex hull estimators), DBSCAN and Neural Network Urban Extent Learners, Computational Geometry, Intrinsic Merit Rankings, R Ricker Population Estimation, Community detection, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing, Computational Geometry and Polygonal packing by Voronoi Tessellation, Four color theorem, Economic Merit, Computational Economics - GDP estimation from Urban sprawl demographics, electricity consumption, Poverty alleviation, MARA (Multiple Agent Resource Allocation) Facegraph walk coloring DNFSAT algorithm, Preferential Attachment, Fixed Parameter Tractability-Kernelization ------------------------------------------------------------------------------------------------------------------------------ 1312.1 python-src/image_pattern_mining/ImageNet/GISUrbanSprawlAnalytics.py has been updated to compute total area of urban sprawl before and after Polya Urn UGM expansion simulation by sum of contour areas (cv2.contourArea()). Area computation reflects percentage growth of urban sprawl better than number of contour segments. 1312.2 Poly Urn contents are now tuples of the form (<colored_segment>,<contour_area>) for facilitating area computation. 1312.3 Function urban_sprawl_from_raster(79.07,12.41,80.3,13.19,"testlogs/RemoteSensingGIS/GHS_SMOD_POP2015_GLOBE_R2019A_54009_1K_V2_0.tif",dt="Degree of Urbanization") has been invoked for computing Degree of Urbanization of Chennai Metropolitan Area for R2019A dataset from R2019A GHS-SMOD DEGURBA GeoTIFF raster testlogs/RemoteSensingGIS/GHS_SMOD_POP2015_GLOBE_R2019A_54009_1K_V2_0.tif. There is no visual explorer available for R2019A GHS-SMOD as datasets have been replaced by R2022A and Polya Urn UGM has to be populated from settlement classes of the raster pixels instead of contour segments (classes listed in 1312.7). Following are some examples of classes printed from raster for bounding box coordinates: Degree of Urbanization from raster: [array([30], dtype=int16)] Degree of Urbanization from raster: [array([30], dtype=int16)] Degree of Urbanization from raster: [array([10], dtype=int16)] Degree of Urbanization from raster: [array([12], dtype=int16)] Degree of Urbanization from raster: [array([12], dtype=int16)] Degree of Urbanization from raster: [array([23], dtype=int16)] Degree of Urbanization from raster: [array([21], dtype=int16)] Degree of Urbanization from raster: [array([21], dtype=int16)] Degree of Urbanization from raster: [array([13], dtype=int16)] Degree of Urbanization from raster: [array([13], dtype=int16)] Degree of Urbanization from raster: [array([12], dtype=int16)] Degree of Urbanization from raster: [array([11], dtype=int16)] 1312.4 Dimensions of the longitude-latitude bounding box have been expanded to match R2022A GHS-SMOD Degree of Urbanization imagery. 1312.5 Following are Polya Urn UGM projections for Chennai Metropolitan Area (difference in projections with and without learnt replacement matrix is noticeable): ----------------------------------------------------------------------------------- R2019A (future projection based on 2019 data - without learnt replacement matrix): ----------------------------------------------------------------------------------- Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model (in terms of segments): 24.668275030156817 Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model (in terms of total area): 4.0728209942696205 ----------------------------------------------------------------------------------- R2022A (future projection based on 2022 data - without learnt replacement matrix): ----------------------------------------------------------------------------------- Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model (in terms of segments): 95.9780621572212 Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model (in terms of total area): 43.19988994359609 -------------------------------------------------------------------------------- R2022A (future projection based on 2022 data - with learnt Replacement matrix): -------------------------------------------------------------------------------- Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model (in terms of segments): 90.67325509573811 Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model (in terms of total area): 112.80220836963039 (<- 112% growth projected by learning contour segment replacement - replication weights - from 3 years trend between 2019-2022 as against 43% without learning in previous trial)
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1311. (THEORY and FEATURE) Intrinsic Merit of Music - Deep Learnt Automata and Music Synthesis - a Boolean Composition and Learning Theory perspective - 21 September 2022 - related to 3,110,1223,1224,1257,1258,1261,1305,1306,1307,1308,1309,1310 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, Additive Synthesis, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants,Computational Learning Theory, Boolean Function Composition
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1310. (THEORY and FEATURE) Intrinsic Merit of Music - Virtual Piano Implementation - Carnatic Music Synthesis from 12-notes octave - 20 September 2022 - related to 3,110,1223,1224,1257,1258,1261,1305,1306,1307,1308,1309 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, Additive Synthesis, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants
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------------------------------------------------------------------------------------------------------------------------------- 1310. (THEORY and FEATURE) Intrinsic Merit of Music - Virtual Piano Implementation - Carnatic Music Synthesis from 12-notes octave - 20 September 2022 - related to 3,110,1223,1224,1257,1258,1261,1305,1306,1307,1308,1309 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, Additive Synthesis, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants ------------------------------------------------------------------------------------------------------------------------------ 1310.1 Carnatic music svara(s) have been integrated into Piano Notes Frequencies and piano_notes is stored in a dictionary of dictionaries of the form genre-note-frequency (including svara subdivisions - frequencies for Gandhara-3,Nishadha-1 and 3,Dhaivadha-3 could be slightly off): piano_notes={"WesternClassical":{'A':440,'B':493.89,'C':261.63,'D':293.67,'E':329.63,'F':349.23,'G':392,'a':466.17,'c':227.18,'d':311.13,'f':370,'g':415.31},"Carnatic":{'S':240, 'R₁':254.27, 'R₂':269.39, 'R₃':275,'G₁':285.41, 'G₂':302.38, 'G₃':311, 'M₁':320.36, 'M₂':339.41, 'P':359.60, 'D₁':380.98, 'D₂':403.63, 'D₃':415, 'N₁':425,'N₂':453.06, 'N₃':480}} 1310.2 Function all_12notes_melodies(iterations=10,number_of_notes=10,keynotes=88,tempo=0.25,musicgenre="WesternClassical") has been changed to add music genre as parameter("WesternClassical" or "Carnatic") and if genre is Carnatic, notes basis is a concatenation of 72 melakarta notes from librosa.mela_to_svara() which is randomly sampled to synthesize music. As number of possible melodies in Carnatic are limited to 72000 (Janya or derivatives of 72), synthesis of Carnatic music must be a mathematical function of 72000 derived raaga(s). Existing state-of-the-art in music synthesis is centered around Deep Learning Convolution Neual Networks of huge parameter set and multiple convolution-maxpooling-perceptron layers. An alternative automata theoretic view of music envisages set of notes as language accepted by a finite state automaton. Ramifications of music as automata are enormous - synthesis of new music could be reduced to closure operators of Finite State Machines - Union, Intersection, Difference, Concatenation, Kleene Closure, Reversal, Homomorphism, Inverse Homomorphism - or new music is obtained from operand music FSMs through closures. 1310.3 Function get_piano_frequencies(virtual_piano_notes,genre="WesternClassical") has been changed to add genre of music as parameter. 1310.4 Function music_synthesis(training_music=None,dur=5,samplerate=44100,polynomial_interpolation=True,polyfeatures=False,virtual_piano_notes=None,tempo=1,amplitude=4096,musicgenre="WesternClassical") has been changed to include music genre as parameter to obtain piano frequencies for Western classical or Carnatic. 1310.5 Function all_12notes_melodies(iterations=5,number_of_notes=100,keynotes=12,tempo=0.5,musicgenre="Carnatic") has been invoked for synthesizing randomly sampled music (of 100 notes length) from Carnatic notes for 5 iterations (written to python-src/music_pattern_mining/virtual_piano_music.wav).
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1309. (THEORY and FEATURE) Intrinsic Merit of Music - Virtual Piano Implementation and Music Synthesis from 12-notes octave - Correction to Frequencies - 19 September 2022 - related to 3,110,1223,1224,1257,1258,1261,1305,1306,1307,1308 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, Additive Synthesis, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants
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---------------------------------------------------------------------------------------------------------------------------------------- 1309. (THEORY and FEATURE) Intrinsic Merit of Music - Virtual Piano Implementation and Music Synthesis from 12-notes octave - Correction to Frequencies - 19 September 2022 - related to 3,110,1223,1224,1257,1258,1261,1305,1306,1307,1308 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, Additive Synthesis, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants ---------------------------------------------------------------------------------------------------------------------------------------- 1309.1 New dictionary piano_notes mapping 12-note octave to frequencies has been introduced to correct the signal synthesis by tone() so that it matches Piano music: piano_notes={'A':440,'B':493.89,'C':261.63,'D':293.67,'E':329.63,'F':349.23,'G':392,'a':466.17,'c':227.18,'d':311.13,'f':370,'g':415.31} 1309.2 Function all_12notes_melodies(iterations=10,number_of_notes=10,keynotes=88,tempo=0.25) has been changed to add clauses and parameters - keynotes and tempo - which respectively define number of keys (88 or 12) to form octave basis and tempo of music synthesized (duration per note). 1309.3 New function get_piano_frequencies(virtual_piano_notes) returns the array of frequencies for piano notes sequence passed on to it by lookup of piano_notes dictionary earlier. 1309.4 Function music_synthesis(training_music=None,dur=5,samplerate=44100,polynomial_interpolation=True,polyfeatures=False,virtual_piano_notes=None,tempo=1,amplitude=4096) has been changed to include amplitude as parameter set to 4096 as default, tempo as parameter for librosa.tone() and replace note_to_hz() by get_piano_frequencies() as note_to_hz() produces different values simulating a drumbeat. 1309.5 Following notes for "Twinkle Twinkle Little Star" have been synthesized in Virtual Piano and written to virtual_piano_music.wav : music_synthesis(virtual_piano_notes=['C','C','G','G','A','A','G','F','F','E','E','D','D','C','G','G','F','F','E','E','D','G','G','F','F','E','E','D','C','C','G','G','A','A','G','F','F','E','E','D','D','C','C','C','G','G','A','A','G','F','F','E','E','D','D','C','G','G','F','F','E','E','D','G','G','F','F','E','E','D','C','C','G','G','A','A','G','F','F','E','E','D','D','C'],tempo=1)
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Section 1308 updated
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Updated Requirements.txt
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1308. (THEORY and FEATURE) Intrinsic Merit of Music - Virtual Piano Implementation and Music Synthesis from 12-notes octave - 16 September 2022 - related to 3,110,1223,1224,1257,1258,1261,1305,1306,1307 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, Additive Synthesis, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants
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---------------------------------------------------------------------------------------------------------------------------- 1308. (THEORY and FEATURE) Intrinsic Merit of Music - Virtual Piano Implementation and Music Synthesis from 12-notes octave - 16 September 2022 - related to 3,110,1223,1224,1257,1258,1261,1305,1306,1307 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, Additive Synthesis, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants ---------------------------------------------------------------------------------------------------------------------------- 1308.1 AudioToBitMatrix.py has been updated to import IPython.display, mir_eval.sonify and playsound python3.7 packages. Function music_synthesis(training_music=None,dur=5,samplerate=44100,polynomial_interpolation=True,polyfeatures=False,virtual_piano_notes=None) has been updated to implement a new clause for Virtual Piano Music Synthesizer implementation based on notes passed on to it through virtual_piano_notes. Notes based synthesis is more human than polynomial interpolation and strings of notes alphabets could be programmatically churned out. 1308.2 Notes from virtual_piano_notes in usual CDEFGABC 12-note Piano notation [C, C-Sharp (D-Flat), D, D-sharp (E-Flat), E, F, F-Sharp (G-Flat), G, G-Sharp (A-Flat), A, A-Sharp (B-Flat), and B] are converted to frequency domain by note_to_hz() and signals are synthesized from them iteratively by librosa.tone(). Synthesized music is written to separate WAV file virtual_piano_music.wav and plotted as waveform by waveshow() - commented at present. Invocation of mir_eval.sonify.pitch_contour(librosa.times_like(freq),freq,samplerate,amplitudes=amps) has also been commented which is a music synthesizer similar to librosa.tone(). 1308.3 New function all_12notes_melodies() randomly and iteratively chooses a set of notes from concatenation of 12 notes in C-major,A-minor,... (totalling 60 notes) formats by numpy.random.choice() and music_synthesis() is invoked on those to synthesize piano music - For Example following set of notes are programmatically created and synthesizer earlier is a DFA state machine over notes alphabet: virtual piano notes: ['F♯' 'E' 'F' 'D♯' 'F♯' 'A𝄫' 'G' 'C♯' 'D' 'F' 'F𝄪' 'A♯' 'E' 'G' 'G' 'D' 'G♯' 'B' 'B♯' 'E♯' 'A♯' 'G' 'A♯' 'D' 'F♯' 'D' 'D' 'A' 'F♯' 'D' 'A♯' 'B' 'F♯' 'A♯' 'B' 'F♯' 'G♯' 'C' 'E♯' 'B' 'A' 'A♯' 'C' 'G♯' 'E' 'E♭' 'A♯' 'G♯' 'A♯' 'C' 'D' 'F♯' 'E' 'D♯' 'D♯' 'D♯' 'G♯' 'D♯' 'B' 'A♯' 'C♯' 'D♯' 'A♯' 'E' 'E' 'D♯' 'A♯' 'E♭' 'D' 'F' 'A♯' 'C♭' 'B' 'B𝄫' 'G' 'E♯' 'E' 'G' 'C♯' 'G♯' 'G♯' 'G' 'D' 'D♯' 'C♯' 'A' 'D' 'E' 'D♯' 'C♯' 'D' 'D' 'G♯' 'G♯' 'C♯' 'F' 'A♯' 'A' 'B' 'E'] 1308.4 Logs testlogs/AudioToBitMatrix.log.16September2022 capture following invocations: all_12notes_melodies(iterations=2,number_of_notes=100) music_synthesis(virtual_piano_notes=['A','a','B','B','b','b','C','D','E','B','C','E','E','e','F','f','C','d','d','d','g','g','g']) 1308.5 Function all_12notes_melodies() essentially captures the notion of "Music discovery" or "No music is new" enshrined in 68-billion melodies algorithm of 1223.13. For earlier 100 notes (based on 60 repetitive notes) long synthesis possible melodies are 60^100.
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Updated Requirements.txt
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1307. (THEORY and FEATURE) Intrinsic Merit of Music - AI Music Synthesis from Polynomials Learnt from training data - PolyFeatures and Carnatic-Hindustani notes support - related to 3,110,1223,1224,1257,1258,1261,1305,1306 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants - 15 September 2022
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----------------------------------------------------------------------------------------------------------------------------- 1307. (THEORY and FEATURE) Intrinsic Merit of Music - AI Music Synthesis from Polynomials Learnt from training data - PolyFeatures and Carnatic-Hindustani notes support - related to 3,110,1223,1224,1257,1258,1261,1305,1306 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, Waveshaping, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants - 15 September 2022 ----------------------------------------------------------------------------------------------------------------------------- 1307.1 AudioToBitMatrix.py has been updated to import librosa.display and librosa has been upgraded to 0.9.2. Function audio_to_notes() has been enhanced to set default duration and print Carnatic and Hindustani notes of a music waveform based on newly added support for Hindustani and Carnatic music in Librosa 0.9.2 through hz_to_svara_c() and hz_to_svara_h() API based on argument "music" set to default "Carnatic" - Index of mela has been hardcoded to 66. 1307.2 Function music_synthesis(training_music,dur=5,samplerate=44100,polynomial_interpolation=True,polyfeatures=False) has been changed to exploit poly_features() API of Librosa which fits the spectrogram of a waveform to n-th order polynomial. If boolean flag polyfeatures is set to True, poly_features() of order-5 is invoked on stft() of the waveform to interpolate the spectrogram to degree-5 polynomial. Spectrogram Interpolation and music waveform are plotted as graphics and order-5 interpolation is chosen by polyfit() of timepoints versus degree-5 interpolation points. Use of polyfeatures refines the structural analysis of music waveform. If polyfeatures is False, behaviour is limited to usual polyfit() earlier. Synthesis by polynomial interpolation is a Waveshaping technique for turning simple sounds to complex sounds. 1307.3 Periodicity has been increased to 100 in notes_to_audio(function=synth_poly_string[:len(synth_poly_string)-1], fractal=False, periodicity=100). Librosa tone() synthesis has been further refined by abs() cast of frequencies. 1307.4 Logs testlogs/AudioToBitMatrix.log.15September2022 capture following invocations: music_synthesis(["testlogs/JSBach_Musicological_Offering.mp4","testlogs/Bach_Flute_Sonata_EFlat.mp4"],dur=10) audio_to_notes("testlogs/JSBach_Musicological_Offering.mp4", dur=10, music="Carnatic")
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Section 1301 updated
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Sections 1301,1306 updated
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1306. (THEORY and FEATURE) Intrinsic Merit of Music - AI Music Synthesis from Polynomials Learnt from training data - related to 3,110,1223,1224,1257,1258,1261,1305 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants - 12 September 2022
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---------------------------------------------------------------------------------------------------------------------------- 1306. (THEORY and FEATURE) Intrinsic Merit of Music - AI Music Synthesis from Polynomials Learnt from training data - related to 3,110,1223,1224,1257,1258,1261,1305 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants - 12 September 2022 ---------------------------------------------------------------------------------------------------------------------------- 1306.1 AudioToBitMatrix.py has been updated to implement new function music_synthesis(training_music,dur=5,samplerate=44100,polynomial_interpolation=True) which learns music (based on a boolean flag polynomial_interpolation) from training music waveforms by (*) interpolating training music to polynomials by polyfit() and computing a function over interpolated polynomials which is passed on to notes_to_audio() for synthesizing new music by tone() (*) or mapping training music waveforms to array of notes in CDEFGABC notation by hertz-to-notes and synthesizing signal frequencies (by random sampling) from training music notes collated to new music waveform by notes-to-hertz and tone() 1306.2 Invocation of SciPy barycentric_interpolate() which is a recent advance in Lagrange interpolation and could be better than polyfit() has been commented due to slowdown. Function computed over polynomial interpolation of music waveforms is simple summation at present and could be arbitrary. Synthesis by random sampling of notes from training music waveforms is discrete version of continuous polynomial interpolation and randomness could be replaced by a predictable sampling function. Synthesized music earlier (random notes sampling especially) could be one of the 68 billion 12-note melodies (Section 1223.14) 1306.3 Following are logs and synthesized music files from 2 compositions of JS Bach for both the clauses of synthesis - polynomial interpolation and randomly sampled notes: python-src/music_pattern_mining/function_synthesized_music.wav python-src/music_pattern_mining/testlogs/AudioToBitMatrix.log.MusicSynthesizer.12September2022 python-src/music_pattern_mining/testlogs/AudioToBitMatrix.log2.MusicSynthesizer.12September2022 python-src/music_pattern_mining/testlogs/function_synthesized_music.interpolation.wav.xz python-src/music_pattern_mining/testlogs/function_synthesized_music.random.wav.xz
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1305. (THEORY and FEATURE) Intrinsic Merit of Music - AI Music Synthesis from Sum of Sinusoids - Signal synthesis from librosa tone() - related to 110,1223,1224,1257,1258,1261 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants - 9 September 2022
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------------------------------------------------------------------------------------------------------------------------------- 1305. (THEORY and FEATURE) Intrinsic Merit of Music - AI Music Synthesis from Sum of Sinusoids - Signal synthesis from librosa tone() - related to 110,1223,1224,1257,1258,1261 and all sections on Music search-Music discovery, Intrinsic Merit of Music, MIR(Music Information Retrieval), Music Similarity and Clustering, AI Music Synthesis from summation of damped sinusoids, fMRI connectomes - OpenNeuro - Psychology of music, Weighted automata, Chaos, Deep Learning, Dynamic Time Warping-Music Timeseries analysis, Music Evoked Autobiographical Memories, ThoughtNet, Majority Voting (Enjoyable music) Vs Intrinsic (Quality music) - Condorcet Jury Theorem variants - 9 September 2022 ------------------------------------------------------------------------------------------------------------------------------- 1305.1 Updated notes_to_audio(automaton=False, function=None, deterministic=True, samplerate=44100, fractal=True, periodicity=100) in AudioToBitMatrix.py to add new parameter periodicity for length of music waveform synthesized and replace existing synthesis code to compute signal waveform from librosa.tone() which produces far superior music rivalling manual composition by keyboard or piano. 1305.2 Lambda function passed on to notes_to_audio() is eval()-ed for each point in range determined by periodicity and resultant function values are deemed as frequencies of signal synthesized by librosa.tone() for duration of 0.25 seconds. 1305.3 Signals synthesized for all points of the function in periodicity range are concatenated and written to WAV file. 1305.4 Following are affected logs and function synthesized waveform files for notes_to_audio(function='(np.iinfo(np.int16).max*math.sin(2*3.1428*720*x) + np.iinfo(np.int16).max*math.sin(2*3.1428*1240*x) + np.iinfo(np.int16).max*math.sin(2*3.1428*2400*x))', fractal=False, periodicity=35) which is a sum of damped sinusoids of 3 fourier frequencies: function_synthesized_music.wav testlogs/AudioToBitMatrix.log.9September2022 1305.5 Synthesized waveform function_synthesized_music.wav can be loaded in Audacity for spectral analysis and playing. 1305.6 Human compositions could be simulated in earlier AI function synthesis by learning polynomial interpolations from manually composed music waveforms as training data (e.g SciPy interpolate() - https://docs.scipy.org/doc/scipy/reference/interpolate.html) and use a function of learnt interpolation polynomials as baseline for librosa.tone() signal synthesis.
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Section 1302 updated
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Updated Section 1303 and 1304
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1304. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Polya Urn Urban Growth Model - Weights Learnt - 8 September 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Gridded Population Estimators (SEDAC GPW4 and GHSL convex hull estimators), DBSCAN and Neural Network Urban Extent Learners, Computational Geometry, Intrinsic Merit Rankings, R Ricker Population Estimation, Community detection, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing, Computational Geometry and Polygonal packing by Voronoi Tessellation, Four color theorem, Economic Merit, Computational Economics - GDP estimation from Urban sprawl demographics, electricity consumption, Poverty alleviation, MARA (Multiple Agent Resource Allocation) Facegraph walk coloring DNFSAT algorithm, Preferential Attachment
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------------------------------------------------------------------------------------------------------------------------------- 1304. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Polya Urn Urban Growth Model - Weights Learnt - 8 September 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301 and all sections on GIS Urban Sprawl Analytics, Merit of Large Scale Visuals, Gridded Population Estimators (SEDAC GPW4 and GHSL convex hull estimators), DBSCAN and Neural Network Urban Extent Learners, Computational Geometry, Intrinsic Merit Rankings, R Ricker Population Estimation, Community detection, Social Network Analytics, Space filling by Curves, Unequal Circle and Polynomial packing, Computational Geometry and Polygonal packing by Voronoi Tessellation, Four color theorem, Economic Merit, Computational Economics - GDP estimation from Urban sprawl demographics, electricity consumption, Poverty alleviation, MARA (Multiple Agent Resource Allocation) Facegraph walk coloring DNFSAT algorithm, Preferential Attachment ------------------------------------------------------------------------------------------------------------------------------ 1304.1 GISUrbanSprawlAnalytics.py has been updated to learn replication weights of Polya Urn Urban Growth Model sampling which chooses a random colored segment and replicates it while replacing, through function learn_polya_urn_growth_weights(). 1304.2 Function learn_polya_urn_growth_weights(ncolorsegments_date1,ncolorsegments_date2) takes as arguments two n-colored segments of date1(earlier) and date2(later) computed from an urban sprawl segmentation by function polya_urn_urban_growth_model() and returns dictionary of replication weights per color as ratio of lengths of corresponding colored bins within Polya Urns of date2 and date1. 1304.3 Function polya_urn_urban_growth_model(image,ncoloredsegments,segmentedgis,iterations=1000,replicationweights=None) additionally takes an optional argument replicationweights which is the dictionary of color-to-weights learnt by learn_polya_urn_growth_weights(). Polya Urn Growth routine has been rewritten, if learnt replicationweights are supplied, to replicate a randomly sampled contour color segment as many times as the color's weight lookedup within replicationweights which makes the Polya Urn Growth a Randomized Controlled Trial or a predictable randomization learnt from the past - contours of different colors grow at different rates based on past historical growth (typical preferential attachment or Rich-get-richer - a trend which may not be disrupted unless a radical new masterplan is drafted). 1304.4 Percentage Growth of an Urban Sprawl after Polya Urn UGM process is printed as ratio of total number of segments (all colors) before and after Urn growth. Replication weights are learnt from two GHSL GIS Imagery separated by 3 years for Chennai Metropolitan Area Sprawl - testlogs/GHSL_GIS_ChennaiMetropolitanArea.jpg (R2019A) and testlogs/RemoteSensingGIS/ChennaiMetropolitanArea_GHSL_R2022A_GHS_SMOD_DegreeOfUrbanisation.jpg (R2022A) - and learnt weights are applied to project future growth after 2022 on R2022A testlogs/RemoteSensingGIS/ChennaiMetropolitanArea_GHSL_R2022A_GHS_SMOD_DegreeOfUrbanisation.jpg (Assumption: Same color coding is used across R2019A and R2022A and images approximately have similar scales) 1304.5 Following are 3 trials of Polya Urn Urban Growth Model projections (1000 iterations each) for Chennai Metropolitan Area without and with learnt replication weights quoted from testlogs/GISUrbanSprawlAnalytics.log.8September2022: -------------------- Trial 1 -------------------- (random - no weights learning) R2019A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 24.4270205066345 (random - no weights learning) R2022A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 101.09689213893967 (predictably random - after weights learning based on 3 years growth) R2022A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 95.7498482088646 -------------------- Trial 2 -------------------- (random - no weights learning) R2019A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 25.03015681544029 (random - no weights learning) R2022A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 101.64533820840951 (predictably random - after weights learning based on 3 years growth) R2022A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 76.72727272727273 ------------------- Trial 3 ------------------- (random - no weights learning) R2019A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 23.70325693606755 (random - no weights learning) R2022A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 103.47349177330896 (predictably random - after weights learning based on 3 years growth) R2022A - Percentage growth of urban sprawl simulated by Polya Urn Urban Growth Model: 85.66265060240964 1304.6 On an average earlier weights-learnt Polya Urn Growth predicts 76-95% growth of contour segments in Chennai Metropolitan Area based on 3 years growth trend (2019-2022) implying proportional future growth of Urban city center and Urban metro cluster - From 1174.8.4.3 expanded jurisdiction of Chennai Metropolitan Area in 2018 - 8848 sqkm - might witness urban cluster growth of 76-95% to 17253 sqkms and GHSL (R2019A) city administrative area of Chennai from 1196.4 and 1253.12 - 940 sqkm - might witness urban center growth of 76-95% to 1833 sqkms (rough estimate assuming equal area contours). 1304.7 Allocating new segments projected by weights-learnt Polya Urn Model along periphery of Facegraph of the Urban sprawl described in 1234.6 adhering to DNFSAT Facegraph walk arithmetic progression coloring MARA algorithm in 1177 is a sustainable Urban Growth Model assuring equitable growth.
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Section 1301 updated
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1303. (THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.10.4 upgrade - 2232 and 67 bits Quadcore Benchmarks and MATLAB-Pari/GP-FLINT performance numbers comparison - related to 1259 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP - 7 September 2022
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-------------------------------------------------------------------------------------------------------------------------------------------- 1303. (THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.10.4 upgrade - 2232 and 67 bits Quadcore Benchmarks and MATLAB-Pari/GP-FLINT performance numbers comparison - related to 1259 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP - 7 September 2022 -------------------------------------------------------------------------------------------------------------------------------------------- 1303.1 DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py has been upgraded to Python 3.10.4 from Python 3.7-3.8 for performance and two random integers 93928329389239283919 (67 bits) and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bits) have been factorized by DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py on Spark 3.0.1+Python 3.10.4 1303.2 Following are excerpts of benchmark numbers from: testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log.7September2022 testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log2.7September2022 -------------------------------------------------------------------------------------------------------------- 93928329389239283919 - 67 bits - time to first factor -------------------------------------------------------------------------------------------------------------- xl + intervalmidpoint = 35223123520964731470 xl = 31309443129746427973 yl = 3 Factor point verification: (xl + intervalmidpoint)*yl == number_to_factorize = False Factor point verification: xl*yl == number_to_factorize = True ('Factors are: (', 3, ',', 31309443129746427973, ') (at ', 'Wed, 07 Sep 2022 07:05:39 GMT', ')') nanoseconds elapsed so far in finding all factors: 4552969670 (4.55 seconds) ------------------------------------------------------------------------------------------------------------------------------------------- 918289829182891892818298192891893791937177127197279719277127172971271729719279172791727192791771783717391737972974747974927947297497297492794792749729749273927429794797274927947297492794774749279427497927492749747979274979749729797497294797497294729794774297492749274972947972974927497294792749279247927947294792749749792749279742974972974927492749729479274927497297472947927947927947927497297242799274972947297497297494274972974297492797372378273872387827372873872378723872372738728378273728732773872836826386263623628638628368268368263862836826386826386283628368268368263826638263826863826386283682632863826826386238628368623826382638623862863826386283682638263227479247 - 2232 bits - time to first factor ------------------------------------------------------------------------------------------------------------------------------------------- xl + intervalmidpoint = 13705818346013311833108928252117817790107121301451936108613838402556294473422077205846674519280175876378981163775742507088476825335780559593952130592981332446678056638765297432049216310369772377304888028768548503701183208652981041753690967126825294474548870111832078730939521984700410407384966407152954148467086458951489444019100641417507088470041040738496640708914887655939223103402207873093988698496641387273096974589466790641407425265632423556326453549662281699587742147348846846692213040727354833922937707257666024308039229377139824833773683975922781884830274153259227818308033788460654125168413173624833236214719979527889907856457292893475579498302741531914376529541 xl = 13705818346013311833108928252117817790107121301451936108613838402556294473422077205846674519280175876378981163775742507088476825335780559593952130592981332446678056638765297432049216310369772377304888028768548503701183208652981041753690967126825294474548870111832078730939521984700410407384966407152954148467086458951489444019100641417507088470041040738496640708914887655939223103402207873093988698496641387273096974589466790641407425265632423556326453549662281699587742147348846846692213040727354833922937707257666024308039229377139824833773683975922781884830274153259227818308033788460654125168413173624833236214719979527889907856457292893475579498302741531914376529539 yl = 67 Factor point verification: (xl + intervalmidpoint)*yl == number_to_factorize = True Factor point verification: xl*yl == number_to_factorize = False ('Factors are: (', 67, ',', 13705818346013311833108928252117817790107121301451936108613838402556294473422077205846674519280175876378981163775742507088476825335780559593952130592981332446678056638765297432049216310369772377304888028768548503701183208652981041753690967126825294474548870111832078730939521984700410407384966407152954148467086458951489444019100641417507088470041040738496640708914887655939223103402207873093988698496641387273096974589466790641407425265632423556326453549662281699587742147348846846692213040727354833922937707257666024308039229377139824833773683975922781884830274153259227818308033788460654125168413173624833236214719979527889907856457292893475579498302741531914376529541, ') (at ', 'Wed, 07 Sep 2022 06:54:05 GMT', ')') nanoseconds elapsed so far in finding all factors: 12204434562 (12.204 seconds) 1303.3 Earlier numbers can be contrasted with FLINT (Fast library for Number Theory)-Mathematica-Pari/GP factorization benchmarks quoted from https://www.flintlib.org/benchmarks.html (which are implementations of some special case optimized factoring algorithms) from 16 bits to 64 bits on Highend Octacore-Tencore Intel Xeon E5-2650, 2.00 GHz CPU - https://www.intel.in/content/www/in/en/products/sku/64590/intel-xeon-processor-e52650-20m-cache-2-00-ghz-8-00-gts-intel-qpi/specifications.html - 384 GB RAM 16-Hyperthreaded configuration: n-bits Mathematica 9.0 Pari/GP 2.5.4 FLINT 2.4 (time in seconds) 16 0.0720 0.0160 0.00476 24 0.108 0.0560 0.0192 32 0.272 0.233 0.0812 40 0.960 0.608 0.199 48 1.87 1.17 0.430 56 2.76 2.28 1.19 64 4.60 4.21 3.86 ------------------------------------------------------------------------------------------- NeuronRain Computational Geometric Factorization (all factors) on Quadcore 2.00 GHZ 4 GB RAM configuration which is trivial compared to Xeon ES-2650 Octacore (time to first factor): ------------------------------------------------------------------------------------------- 67 bits - 4.55 seconds 2232 bits - 12.204 seconds
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Section 1283 updated
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Updated Requirements.txt
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