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Analyzed about 8 hours ago. based on code collected 1 day ago.
Nov 05, 2025 — Nov 05, 2026
Commit Message Contributor Files Modified Lines Added Lines Removed Code Location Date
Theory - Set Partition to Square Tiles Cover reduction, Factorization, Non-linear Programming Optimization
Srinivasan Kannan
More... over 7 years ago
Theory - Factorization and Sum of Four Squares Tile Cover of Rectangle
Srinivasan Kannan
More... over 7 years ago
Updated NeuronRain Usecases
Srinivasan Kannan
More... over 7 years ago
Theory - Sage Math Library - Set Partition implementation - references
Srinivasan Kannan
More... over 7 years ago
Set Partitions, Partition distance measures, Clustering - References
Srinivasan Kannan
More... over 7 years ago
(FEATURE) Histogram-Set Partition Analytics - Adjusted Mutual Information
Srinivasan Kannan
More... over 7 years ago
-------------------------------------------------------------------------------------------------------- 652. (FEATURE) Histogram-Set Partition Analytics - Adjusted Mutual Information - 3 April 2019 -------------------------------------------------------------------------------------------------------- 1.adjusted_mutual_info_score() from sklearn.metrics has been invoked in adjusted_rand_index() for comparing two set partitions. 2.Logs in testlogs/Streaming_SetPartitionAnalytics.log2.3April2019 show the difference between two measures - adjusted rand index and adjusted mutual information
Srinivasan Kannan
More... over 7 years ago
(THEORY and FEATURE) Reduction from Set Partition to Exact Square Tiles Cover of Rectangular Region, Lagrange Four Square Theorem, Complementary Sets, Computational Geometric Factorization, Space Filling, Tile Cover, Packing, Set Partition/Histogram Analytics, LSH Partitions, Separate Chaining Hashtables
Srinivasan Kannan
More... over 7 years ago
-------------------------------------------------------------------------------------------------------- 651. (THEORY and FEATURE) Reduction from Set Partition to Exact Square Tiles Cover of Rectangular Region, Lagrange Four Square Theorem, Complementary Sets, Computational Geometric Factorization, Space Filling, Tile Cover, Packing, Set Partition/Histogram Analytics, LSH Partitions, Separate Chaining Hashtables - 3 April 2019 - related to 649 and 650 -------------------------------------------------------------------------------------------------------- 1.Python implementation for Set Partition Analytics (Streaming_SetPartitionAnalytics.py) has been updated for a new function which reduces a histogram set partition to exact square tiles cover of rectangular region which has area equal to number of elements in the histogram. 2.Function setpartition_to_tilecover() loops through histogram buckets (set partition) and maps each bucket size to sum of four squares by Lagrange Four Square Theorem essentially mapping each 1-dimensional bucket to 4 2-dimensional square tiles. 3.Collection of these sets of 4 square tiles covers the rectangular region of area equal to number of elements partitioned by histogram/LSH/Separate Chaining. 4.Example logs in testlogs/Streaming_SetPartitionAnalytics.log.3April2019 demonstrate reduction of histogram buckets [11,12,13,14,15] of total number of 65 elements to tile cover of rectangular region which has composite area 13*5=65: square tiles for partition 11 : set([(0, 1, 1, 3)]) square tiles for partition 12 : set([(1, 1, 1, 3)]) square tiles for partition 13 : set([(1, 2, 2, 2)]) square tiles for partition 14 : set([(0, 1, 2, 3)]) square tiles for partition 15 : set([(1, 1, 2, 3)]) Lagrange Four Square Tiles Cover reduction of Set Partition [11, 12, 13, 14, 15] : [0, 1, 1, 9, 1, 1, 1, 9, 1, 4, 4, 4, 0, 1, 4, 9, 1, 1, 4, 9] 5.This reduction indirectly solves factorization problem (complexity depends on sum of four squares) geometrically by following square tiles cover algorithm: 5.1 Number to factorize N is partitioned arbitrarily by some integer partition and is isomorphic to a histogram 5.2 Square tiles are obtained from partition by previous Lagrange Four Square reduction 5.3 Square tiles are geometrically juxtaposed/arranged to create a tiled rectangle sides of which are factors of N
Srinivasan Kannan
More... over 7 years ago
(THEORY) Planar Graph Theoretic Circle Packing, Space Filling/Grid Filling, CSP/Linear Programming, Tile Cover and LSH/Separate Chaining Partitions
Srinivasan Kannan
More... over 7 years ago
(THEORY and FEATURE) Streaming Set Partition (Histogram) Analytics
Srinivasan Kannan
More... over 7 years ago
-------------------------------------------------------------------------------------------------------- 650. (THEORY and FEATURE) Streaming Set Partition (Histogram) Analytics - 28 March 2019 -------------------------------------------------------------------------------------------------------- 1.New Python implementation for multipurpose analytics of streamed set partitions (histograms) has been committed - Streaming_SetPartitionAnalytics.py 2.Two new bigdata sources have been defined in Streaming_AbstractGenerator.py - "TextHistogramPartition" and "DictionaryHistogramPartition" which respectively: (*) Map a list of textfiles to list of histograms by finding word frequency in the text and yield partition datastructure as iterable which is a dictionary of words to buckets in histograms (occurrences are mapped to array of 1s e.g occurence 5 for word "word" is mapped to binned bucket ('word',[1,1,1,1,1])) (*) Read a text file - Streaming_SetPartitionAnalytics.txt - containing list of dictionaries, literal_eval() it and yield the elements as iterable 3.TextHistogramPartition is a fancy datasource which facilitates an alternative measure of streaming text analytics and text similarity 4.DictionaryHistogramPartition is the conventional datasource for succinctly representing a set partition which could be anything ranging from LSH partition, Exact Cover, Balls-Bins, Separate Chained Hashtables, Electronic Voting Machines based on LSH and Separate Chaining, Business Intelligence Histograms, SMS voting histograms, Music Spectrograms etc.,. 5.adjusted_rand_index() in Streaming_SetPartitionAnalytics.py instantiates both these datasource iterators and computes Adjusted Rand Index for two consecutive partitions in the stream by SciKitLearn adjusted_rand_score() 6.Because of the fact that every set partition is set of class labels in some classifier, various other clustering performance measures - mutual information, silhouette etc., (https://scikit-learn.org/stable/modules/clustering.html#clustering-evaluation) could compare partitions too. 7.tocluster() in Streaming_SetPartitionAnalytics.py maps a partition to an array of labelled elements in scikitlearn format 8.An example streaming set partition analytics for linux kernel logs (TextHistogramPartition) and list of dictionaries (DictionaryHistogramPartition) is committed to Streaming_SetPartitionAnalytics.log.28March2019 which show how Adjusted Rand Index works for similar and dissimilar partitions. 9.For circumventing sklearn exception two compared partitions are truncated to minimum size of the two
Srinivasan Kannan
More... over 7 years ago
(THEORY) Planar Graph Theoretic Circle Packing, Space Filling/Grid Filling and CSP/Linear Programming - Integer Linear Programming - References
Srinivasan Kannan
More... over 7 years ago
(THEORY) Planar Graph Theoretic Circle Packing, Space Filling/Grid Filling and CSP/Linear Programming - References
Srinivasan Kannan
More... over 7 years ago
(THEORY) Planar Graph Theoretic Circle Packing, Space Filling/Grid Filling and CSP/Linear Programming
Srinivasan Kannan
More... over 7 years ago
(THEORY) Planar Graph Theoretic Circle Packing, Space Filling/Grid Filling and CSP/Linear Programming
Srinivasan Kannan
More... over 7 years ago
Theory - Miscellaneous Updates - Elitzur-Vaidman Bomb Tester for Bigdata, Knot Theoretic Secret Ballot for Majority Voting, Circle Packing Theorem and Space Filling
Srinivasan Kannan
More... over 7 years ago
(THEORY) Voting in Knot Theory, Gordion Knot, One-Way Functions, Hardness Amplification Lemma for Majority + VoterSAT Boolean Function Composition, Separate Chaining or LSH Partition based Theoretical EVMs
Srinivasan Kannan
More... over 7 years ago
(THEORY and FEATURE) Bounded Error Factorization (Approximate Factors), Ray Shooting Queries, Transition from Quantum to Classical Computation, Derandomization
Srinivasan Kannan
More... over 7 years ago
Theory - Complexity Analysis of Possible ways of transition from quantum world to classical computation - references
Srinivasan Kannan
More... over 7 years ago
Theory - Complementary Equations, Spectra of Numbers, Complementary Integer Sequences - References
Srinivasan Kannan
More... over 7 years ago
Theory - Complementary Equations, Spectra of Numbers, Complementary Integer Sequences - References
Srinivasan Kannan
More... over 7 years ago
Theory - Complementary Equations, Spectra of Numbers, Complementary Integer Sequences - related to 645 and all sections on Complement Functions, Complementary Sets and Diophantines
Srinivasan Kannan
More... over 7 years ago
(THEORY) Comparing Partitions - Related to 620 and all sections on Majority Voting, Theoretical EVMs, Separate Chaining Hashtable/LSH Set Partitions, Integer Partitions, Complementary Sets and Diophantines, Streaming Histogram/Dictionary Analytics, People Analytics, Software Analytics, Business Analytics
Srinivasan Kannan
More... over 7 years ago
Theory - Factorization - Possibility of Wave Function Collapse via QNC-BPNC and BPNC-NC Derandomization
Srinivasan Kannan
More... over 7 years ago
Feature - Intrinsic Merit of Audio/Music - Mel Frequency Cepstral Coefficients
Srinivasan Kannan
More... over 7 years ago
------------------------------------------------------------------------------------------------------- 644. (FEATURE) Intrinsic Merit of Audio/Music - Mel Frequency Cepstral Coefficients - 11 March 2019 ------------------------------------------------------------------------------------------------------- 1.New function for Mel Frequency Cepstral Coefficients (MFCCs) of a music audio clip (invokes librosa) has been added in this commit. 2.MFCCs are kind of spectra of spectra of an audio waveform and have been widely used for speech recognition and music genre identification. 3.logs for example MFCCs of a music file are committed to testlogs/AudioToBitMatrix.log.MFCC.11March2019
Srinivasan Kannan
More... over 7 years ago
Update - Video EventNet example visuals - tense changed because of an anachronistic simultaneous multilocation ambiguity and agitation it creates from some quarters
Srinivasan Kannan
More... over 7 years ago
(FEATURE) Merit of Audio/Music - Music Synthesizer - Music from mathematical functions
Srinivasan Kannan
More... over 7 years ago
-------------------------------------------------------------------------------------------------------- 643. (FEATURE) Merit of Audio/Music - Music Synthesizer - Music from mathematical functions - 6 March 2019 -------------------------------------------------------------------------------------------------------- 1.New clause has been added to notes_to_audio() for synthesizing music from values of any mathematical function 2.Function expression string is eval()-ed in a lambda function and applied to a list of range values of variable x by map() and a wave file function_synthesized_music.wav is written to. 3.Error in prevstates has been corrected by prevprevstates and resetting prevstates for each state transition for an alphabet. 4.Logs for this have been committed to testlogs/AudioToBitMatrix.log.MusicSynthesizer.6March2019 5.The wave files do not play any human palatable music and are representative only. 6.Infact learning the right DFA (or in general a mathematical function) for language of music is the exact opposite of the previous and is measure of merit.
Srinivasan Kannan
More... over 7 years ago