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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
+--------------------------------------------------------------------------------------------------------------------------------------------- +1162. (THEORY and FEATURE) Merit of Large Scale Visuals - GIS and Urban Sprawl Analytics, CoronaVirus 2019 Analyzer, Histogram Partition +Distance Similarity of images - implementation - related to 1159 and all sections on GIS and Urban Sprawl Analytics, Earth Mover Distance, +CoronaVirus 2019 Analyzer, Large Scale Visual Recognition, Social Network Analytics - 3,4 September 2021 +---------------------------------------------------------------------------------------------------------------------------------------------
Krishna iResearch - NeuronRain - K.Srinivasan
More... about 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1162. (THEORY and FEATURE) Merit of Large Scale Visuals - GIS and Urban Sprawl Analytics, CoronaVirus 2019 Analyzer, Histogram Partition Distance Similarity of images - implementation - related to 1159 and all sections on GIS and Urban Sprawl Analytics, Earth Mover Distance, CoronaVirus 2019 Analyzer, Large Scale Visual Recognition, Social Network Analytics - 3,4 September 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1162.1 In this update new function histogram_partition_distance_similarity() has been defined which computes histogram partition distance similarity between pixel histograms of two images which is by default Earth Mover Distance though other partition distances could be defined as clauses later (e.g SymPy Partition distance). 1162.2 By CoronaVirus 2019 analyzer usecase mentioned in 1159, following GIS images of Population Density and COVID19 hotspots are compared for histogram Earth Mover Distance similarity (from SEDAC,GHSL and JHU datasources) and their Voronoi facegraphs are computed from image_segmentation() - color coding has been ignored, images might have to be converted to grayscale: 1162.2.1 SEDAC GPW4 Population Density GIS for India - SEDAC_PopulationDensity_India_2021-09-04-10-49-24_segmented.jpg - https://sedac.ciesin.columbia.edu/mapping/popest/gpw-v4/ 1162.2.2 SEDAC COVID19 Hotspots GIS - SEDAC_COVID19_Hotspots_GIS_2021-09-04-10-51-29_segmented.jpg - https://sedac.ciesin.columbia.edu/mapping/popest/covid-19/ and https://ghsl.jrc.ec.europa.eu/visualisation.php (Global Human Settlements Layer) 1162.2.3 JHU COVID19 Hotspots GIS - JHU_COVID19_Hotspots_GIS_2021-09-04-11-02-11_segmented.jpg - https://coronavirus.jhu.edu/map.html 1162.3 image_segmentation() has been changed to write the Facets Graph of each segmented image in labelled DOT files in testlogs/RemoteSensingGIS/ which could be separately read and instantiated as FaceGraph by NeuronRain Graph Analytics (GraphMining_GSpan.py) per segmented image. 1162.4 Logs for this update are at testlogs/ImageGraph_Keras_Theano.HistogramDistance.log.4September2021 1162.5 tosig() function used for preprocessing in CompressedSensing.py alphabet vector space embedding EMD has been changed as tosig3d() for transforming 3 Dimensional Keras image pixel ndarray to two dimensional OpenCV2 UMat format.
Srinivasan Kannan
More... about 5 years ago
Updated Requirements.txt
Krishna iResearch - NeuronRain - K.Srinivasan
More... about 5 years ago
1161 updated
Krishna iResearch - NeuronRain - K.Srinivasan
More... about 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1161. (THEORY and FEATURE) Set Partition Analytics - Set Partition to Lagrangian Sun of Squares tile cover reduction - Integer Linear Programming Exact Solution - 29,30 August 2021 - related to all sections on Set Partitions and Histogram analytics, Space filling by tile cover, Integer Factorization by Equidepth histograms, Drone Set Partition Electronic Voting Machines, Integer Linear Programming --------------------------------------------------------------------------------------------------------------------------------------------- 1161.1 Streaming_SetPartitionAnalytics.py has been updated to compute exact Integer Linear Programming solution for sides of the rectangle to which a set partition is reduced, by CVXOPT GLPK ilp() mixed integer linear programming function. 1161.2 ILP function has been imported from CVXOPT GLPK module. 1161.3 setpartition_to_tilecover() function has been changed to take additional argument "solution" which defaults to "ILP". 1161.4 Two linear programs in equationsA matrix are made different by random permutation. 1161.5 Error condition has been handled while populating equationsB matrix. 1161.6 New if-else clause has been introduced which chooses between exact CVXOPT Integer Linear Programming solution (NP-Hard) and approximate least squares solutions including LSMR (polynomial time) 1161.7 cvxopt.glpk.ilp() function is invoked by suitably passing arguments C,G,H,A,B,I which are interpreted as below: 1161.7.1 C - constraints matrix which is all 1s for variables (number of tiles per square tile side) 1161.7.2 G - mask matrix which has 1 row per variable and each row has one 1 at the variable index 1161.7.3 H - Array of all 0s which has size equal to number of variables 1161.7.4 A - EquationsA matrix 1161.7.5 B - EquationsB matrix 1161.7.6 I - Array of variable indices 1161.8 Sides of the rectangle are printed as addition of sides of square tiles computed by CVXOPT GLPK ILP Simplex which are exact for ILP and approximate for Least squares. 1161.9 As an example following is a reduction from Set partition to Rectangular region by NeuronRain computational geometric factorization - Factors 7 and 77 of 539 (Rectangular periphery) are expressed in terms of sides of square tiles from Lagrange sum of squares of a set partition by CVXOPT GLPK ILP simplex:
Krishna iResearch - NeuronRain - K.Srinivasan
More... about 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1161. (THEORY and FEATURE) Set Partition Analytics - Set Partition to Lagrangian Sun of Squares tile cover reduction - Integer Linear Programming Exact Solution - 29,30 August 2021 - related to all sections on Set Partitions and Histogram analytics, Space filling by tile cover, Integer Factorization by Equidepth histograms, Drone Set Partition Electronic Voting Machines, Integer Linear Programming --------------------------------------------------------------------------------------------------------------------------------------------- 1161.1 Streaming_SetPartitionAnalytics.py has been updated to compute exact Integer Linear Programming solution for sides of the rectangle to which a set partition is reduced, by CVXOPT GLPK ilp() mixed integer linear programming function. 1161.2 ILP function has been imported from CVXOPT GLPK module. 1161.3 setpartition_to_tilecover() function has been changed to take additional argument "solution" which defaults to "ILP". 1161.4 Two linear programs in equationsA matrix are made different by random permutation. 1161.5 Error condition has been handled while populating equationsB matrix. 1161.6 New if-else clause has been introduced which chooses between exact CVXOPT Integer Linear Programming solution (NP-Hard) and approximate least squares solutions including LSMR (polynomial time) 1161.7 cvxopt.glpk.ilp() function is invoked by suitably passing arguments C,G,H,A,B,I which are interpreted as below: 1161.7.1 C - constraints matrix which is all 1s for variables (number of tiles per square tile side) 1161.7.2 G - mask matrix which has 1 row per variable and each row has one 1 at the variable index 1161.7.3 H - Array of all 0s which has size equal to number of variables 1161.7.4 A - EquationsA matrix 1161.7.5 B - EquationsB matrix 1161.7.6 I - Array of variable indices 1161.8 Sides of the rectangle are printed as addition of sides of square tiles computed by CVXOPT GLPK ILP Simplex which are exact for ILP and approximate for Least squares. 1161.9 As an example following is a reduction from Set partition to Rectangular region by NeuronRain computational geometric factorization - Factors 7 and 77 of 539 (Rectangular periphery) are expressed in terms of sides of square tiles from Lagrange sum of squares of a set partition by CVXOPT GLPK ILP simplex:
Srinivasan Kannan
More... about 5 years ago
1160. (THEORY and FEATURE) Set Partition Analytics - Set Partition to Lagrangian Sum of Squares tile cover reduction - Python 3.9.0 upgrade + and some code changes - 27 August 2021 - related to all sections on Set Partitions and Histogram analytics, Space filling by tile cover, Integer Factorization by Equidepth histograms, Drone Set Partition Electronic Voting Machines, Diophantines and Complement Functions
Srinivasan Kannan
More... about 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1160. (THEORY and FEATURE) Set Partition Analytics - Set Partition to Lagrangian Sum of Squares tile cover reduction - Python 3.9.0 upgrade and some code changes - 27 August 2021 - related to all sections on Set Partitions and Histogram analytics, Space filling by tile cover, Integer Factorization by Equidepth histograms, Drone Set Partition Electronic Voting Machines, Diophantines and Complement Functions --------------------------------------------------------------------------------------------------------------------------------------------- 1160.1 Streaming_SetPartitionAnalytics.py implementation has been upgraded to Python 3.9.0 and package imports have been changed to suit Python 3.9.0 (SymPy Diophantine SOS solvers) 1160.2 Subprocess call to computational geometric factorization has been upgraded to Spark 3.0.1 1160.3 NumPy ndarray has been cast to float by astype() 1160.4 Randomized rounding after LSMR least square AX=B solver approximation has been changed to Python round() 1160.5 Rectangular Periphery - Sides of Square tiles - approximated from LSMR rounding are computed from equationsA matrix to preserve order. 1160.6 complement.py has been upgraded to python 3.9.0 and imports of SymPy Diophantine Sum of Squares (SOS) solver have been changed. 1160.7 testlogs/Streaming_SetPartitionAnalytics.Python3.9Upgrade.log.27August2021 and DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.factors contain the logs for this update.
Srinivasan Kannan
More... about 5 years ago
Section 1159 updated for Topological Face recognition
Srinivasan Kannan
More... about 5 years ago
+--------------------------------------------------------------------------------------------------------------------------------------------- +1159. (THEORY and FEATURE) Computational Geometric Factorization - Python 3.9.0 + Spark 3.0.1 - 20437 bits integer benchmarks, Equidepth +and Equiheight histograms, Partition distance and SETH, Comparison and Merit of Large Scale Visuals, Urban Sprawl GIS Analytics, CoronaVirus +2019 GIS Geospatial usecase - related to 1158 and all sections on Set Partition and Histogram analytics, Integer Factorization, SETH - +25,26 August 2021 +---------------------------------------------------------------------------------------------------------------------------------------------
Srinivasan Kannan
More... about 5 years ago
1159. (THEORY and FEATURE) Computational Geometric Factorization - Python 3.9.0 + Spark 3.0.1 - 20437 bits integer benchmarks, Equidepth and Equiheight histograms, Partition distance and SETH, Comparison and Merit of Large Scale Visuals, Urban Sprawl GIS Analytics, CoronaVirus 2019 GIS Geospatial usecase - related to 1158 and all sections on Set Partition and Histogram analytics, Integer Factorization, SETH - 25,26 August 2021
Srinivasan Kannan
More... about 5 years ago
--------------------------------------------------------------------------------------------------------------------------------------------- 1158. (THEORY and FEATURE) Computational Geometric Factorization - 18000+ bits quadcore singlenode cluster benchmarks - Python 3.9.0 + Spark 3.0.1, Earth Mover Distance, SETH, Equivalence of Factorization and Set Partition - related to 575,651,728,1142 and all sections on Integer Factorization, Lagrangian Sum of squares covering of space and Histogram Set Partitions, Multiplicative Partitions --------------------------------------------------------------------------------------------------------------------------------------------- 1158.1 Two Huge integers of 18000+ bits have been factorized by Computational Geometric Factorization implementation DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py (largest factorized by NeuronRain thus far) which is a nonuniform logdepth circuit of depth 1284 or PRAM time O((logN)^1284). 1158.2 Integer1 - 18178 bits - first 2 factors printed in 5+ minutes - 1 huge and 1 small - ('factors of ', 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'(', 18177.59042325476, ' bits integer) are:'): ================================================= xl + intervalmidpoint = 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xl = 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yl = 289 Factor point verification: (xl + intervalmidpoint)*yl == number_to_factorize = True Factor point verification: xl*yl == number_to_factorize = False ('Factors are: (', 289, ',', 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') (at ', 'Sun, 01 Aug 2021 09:01:11 GMT', ')') ================================================= 1158.3 Integer2 - 18181 bits - first 2 factors are printed in 11+ minutes - 1 small and 1 huge - ('factors of ', 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'(', 18180.912351349645, ' bits integer) are:'): ================================================= xl + intervalmidpoint = 909020356448265539174580993008372099281190218109445720992809930820853853902810993720034803620762084793889762480671161157935216612480702157034797611670752157029885338525703388520761661248067157034798520794298852067157124798852979442985257035206711624843079306624884306621620658166349074907489935308439362180267117216621802671167208035712662712029384757127117627117207635389444480357176208543899439076298543893907629903480362089448089452985299852944480893621658116711803629854384762945299445294448089448089438536203543907629853571271180299903481671753089358084399902581579883980658066253066167026170338853438853385390762998375636363636363636363636363630266630026720853821729944571900267200846291263902810944836657291190210993720280935749020911264475536630082084627539172937209927483998480267180258021720763481672571266218021180844490754393574580930820821729936390084565748263900354811837120362034816711802883793380661984288428844289343798434702610793470751988437984347026107934707525611701162471565366621167181120293839302112029384748448265482082172993655367200935472081992810083710893562081075380852079339884430661252980352035207942976247944298033852570344294347943897620670657935216206702488934430752579843075257935216617021127175307543983999025817207571271180357126626711671753490749025802671120293847566574839302180254756474448102710893562089257174390744801656473829208930211202938475672572165748393021120357388536203475664657483927636292720125242413839493021120272029395353138333302929944298525703520671162484307930662488430662162065816634907490748993530843936218026711721662180267116720803571266271202938475712711762711720763538944448035717620854389943907629854389390762990348036208944808945298529985294448089362165811671180362985438476294529944529444808944808943853620354390762985357127118029990348167175308935808439990258157988398065806625306616702617033885343885338539076299837563636363636363636363636363026663002672085382172994457190026720084629126390281094483665729119021099372028093574902091126447553663008208462753917293720992748399848026718025802172076348167257126621802118084449075439357458093082082172993639008456574826390035481183712036203481671180288379338066198428842884428934379843470261079347075217025798430793398435211580657935215703389434793089362180218021720803571208945299438994389452994389448076298538998475665748439984489984448036266217175308444893581662671180357127116663490263075308936217536218025802712567175362089438538943907635712711203567257217256717536217536216580893081663490258084399845302717620894448036208535712717530885261125338533898033889429889761158071158065811803572564836363636363636363636363635753935729944812654900267184462753992811901853663008367210938456391748372099300820847629363853720280935735481190026644566448265475672575299445298529444803620894529853894529390811721802712084730820354809445720911735729302099117308208456439308930754398453015652065338925701570157156207107116197533806619802489753071158066125707938853385207942976116707520362089452945294448076298481672572166267116725721662175349025811725748393021167257217257175308993489902581172166308935398453084399843936217535802581663490263490753075439839902634816711266216634908439983930839984489983990263490263489308165808936217530811672572575444893621720763481262985444803612533852611261170761162157162488430798430793084530845292109090909090909090909090908481208457217539927627539911735481265539174580935735639938211183664475644826573548120356636580993008208462753917299371839175538202945302572172571256717530893621802581167256663538994529984812003547627536718448184463002029371844580935729166581658027125725742924792611650237865568778492295829649331022866105710248106616617016616525692478334783478965296511057152843519842893437851943288055783301702561661079347026107934714743297420692511601160160251160697420692478832974206515692511560660156974206515966923287061102561173907448083538927117439016634663472480166011519661016610657258165816580844399348453089358026307530893580258117126621753621120293848036208536208116726298535389448085299452990348167207634802998538994389452998538998543894390762035389984530749025802712720763475672036208536203538998538998529445294452998538944480362089390812572580843998448993490811672089452945294448076298481672572166267116725721662175349025811725748393021167257217257175308993489902581172166308935398453084399843936217535802581663490263490753075439839902634816711266216634908439983930839984489983990263490263489308165808936217530811672572575444893621720763481262985444803572581658165808443993484530893580263075308935802581171266217536211202938480362085362081167262985353894480852994529903481672076348029985389943894529985389985438943907620353899845307490258027127207634756720362085362035389985389985294452944529985389445299445294448089448089438536203543907629853571271180299903481671753089358084399902581579883980658066253066167026170338853438853385390762998375636363636363636363636363630266630026720853821729944571900267200846291263902810944836657291190210993720280935749020911264475536630082084627539172937209927483998480267180258021725721725671753621753621658089308166349025808439984530271762089444803620853571271753088526112533853389803388942988976312585349853081353990439930902580267175308989408994390909090909090897868126727271900267200846291263902810944836657291190210993720280935749020911264475536630082084627539172937209927483998480267180258021720763481666353984530811672572172076353894519753380252889343793519884379843067 xl = 90902035644826553917458099300837209928119021810944572099280993082085385390281099372003480362076208479388976248067116115793521661248070215703479761167075215702988533852570338852076166124806715703479852079429885206715712479885297944298525703520671162484307930662488430662162065816634907490748993530843936218026711721662180267116720803571266271202938475712711762711720763538944448035717620854389943907629854389390762990348036208944808945298529985294448089362165811671180362985438476294529944529444808944808943853620354390762985357127118029990348167175308935808439990258157988398065806625306616702617033885343885338539076299837563636363636363636363636363026663002672085382172994457190026720084629126390281094483665729119021099372028093574902091126447553663008208462753917293720992748399848026718025802172076348167257126621802118084449075439357458093082082172993639008456574826390035481183712036203481671180288379338066198428842884428934379843470261079347075198843798434702610793470752561170116247156536662116718112029383930211202938474844826548208217299365536720093547208199281008371089356208107538085207933988443066125298035203520794297624794429803385257034429434794389762067065793521620670248893443075257984307525793521661702112717530754398399902581720757127118035712662671167175349074902580267112029384756657483930218025475647444810271089356208925717439074480165647382920893021120293847567257216574839302112035738853620347566465748392763629272012524241383949302112027202939535313833330292994429852570352067116248430793066248843066216206581663490749074899353084393621802671172166218026711672080357126627120293847571271176271172076353894444803571762085438994390762985438939076299034803620894480894529852998529444808936216581167118036298543847629452994452944480894480894385362035439076298535712711802999034816717530893580843999025815798839806580662530661670261703388534388533853907629983756363636363636363636363636302666300267208538217299445719002672008462912639028109448366572911902109937202809357490209112644755366300820846275391729372099274839984802671802580217207634816725712662180211808444907543935745809308208217299363900845657482639003548118371203620348167118028837933806619842884288442893437984347026107934707521702579843079339843521158065793521570338943479308936218021802172080357120894529943899438945299438944807629853899847566574843998448998444803626621717530844489358166267118035712711666349026307530893621753621802580271256717536208943853894390763571271120356725721725671753621753621658089308166349025808439984530271762089444803620853571271753088526112533853389803388942988976115807115806581180357256483636363636363636363636363575393572994481265490026718446275399281190185366300836721093845639174837209930082084762936385372028093573548119002664456644826547567257529944529852944480362089452985389452939081172180271208473082035480944572091173572930209911730820845643930893075439845301565206533892570157015715620710711619753380661980248975307115806612570793885338520794297611670752036208945294529444807629848167257216626711672572166217534902581172574839302116725721725717530899348990258117216630893539845308439984393621753580258166349026349075307543983990263481671126621663490843998393083998448998399026349026348930816580893621753081167257257544489362172076348126298544480361253385261126117076116215716248843079843079308453084529210909090909090909090909090848120845721753992762753991173548126553917458093573563993821118366447564482657354812035663658099300820846275391729937183917553820294530257217257125671753089362180258116725666353899452998481200354762753671844818446300202937184458093572916658165802712572574292479261165023786556877849229582964933102286610571024810661661701661652569247833478347896529651105715284351984289343785194328805578330170256166107934702610793471474329742069251160116016025116069742069247883297420651569251156066015697420651596692328706110256117390744808353892711743901663466347248016601151966101661065725816581658084439934845308935802630753089358025811712662175362112029384803620853620811672629853538944808529945299034816720763480299853899438945299853899854389439076203538998453074902580271272076347567203620853620353899853899852944529445299853894448036208939081257258084399844899349081167208945294529444807629848167257216626711672572166217534902581172574839302116725721725717530899348990258117216630893539845308439984393621753580258166349026349075307543983990263481671126621663490843998393083998448998399026349026348930816580893621753081167257257544489362172076348126298544480357258165816580844399348453089358026307530893580258117126621753621120293848036208536208116726298535389448085299452990348167207634802998538994389452998538998543894390762035389984530749025802712720763475672036208536203538998538998529445294452998538944529944529444808944808943853620354390762985357127118029990348167175308935808439990258157988398065806625306616702617033885343885338539076299837563636363636363636363636363026663002672085382172994457190026720084629126390281094483665729119021099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yl = 11 Factor point verification: (xl + intervalmidpoint)*yl == number_to_factorize = True Factor point verification: xl*yl == number_to_factorize = False ('Factors are: (', 11, ',', 909020356448265539174580993008372099281190218109445720992809930820853853902810993720034803620762084793889762480671161157935216612480702157034797611670752157029885338525703388520761661248067157034798520794298852067157124798852979442985257035206711624843079306624884306621620658166349074907489935308439362180267117216621802671167208035712662712029384757127117627117207635389444480357176208543899439076298543893907629903480362089448089452985299852944480893621658116711803629854384762945299445294448089448089438536203543907629853571271180299903481671753089358084399902581579883980658066253066167026170338853438853385390762998375636363636363636363636363630266630026720853821729944571900267200846291263902810944836657291190210993720280935749020911264475536630082084627539172937209927483998480267180258021720763481672571266218021180844490754393574580930820821729936390084565748263900354811837120362034816711802883793380661984288428844289343798434702610793470751988437984347026107934707525611701162471565366621167181120293839302112029384748448265482082172993655367200935472081992810083710893562081075380852079339884430661252980352035207942976247944298033852570344294347943897620670657935216206702488934430752579843075257935216617021127175307543983999025817207571271180357126626711671753490749025802671120293847566574839302180254756474448102710893562089257174390744801656473829208930211202938475672572165748393021120357388536203475664657483927636292720125242413839493021120272029395353138333302929944298525703520671162484307930662488430662162065816634907490748993530843936218026711721662180267116720803571266271202938475712711762711720763538944448035717620854389943907629854389390762990348036208944808945298529985294448089362165811671180362985438476294529944529444808944808943853620354390762985357127118029990348167175308935808439990258157988398065806625306616702617033885343885338539076299837563636363636363636363636363026663002672085382172994457190026720084629126390281094483665729119021099372028093574902091126447553663008208462753917293720992748399848026718025802172076348167257126621802118084449075439357458093082082172993639008456574826390035481183712036203481671180288379338066198428842884428934379843470261079347075217025798430793398435211580657935215703389434793089362180218021720803571208945299438994389452994389448076298538998475665748439984489984448036266217175308444893581662671180357127116663490263075308936217536218025802712567175362089438538943907635712711203567257217256717536217536216580893081663490258084399845302717620894448036208535712717530885261125338533898033889429889761158071158065811803572564836363636363636363636363635753935729944812654900267184462753992811901853663008367210938456391748372099300820847629363853720280935735481190026644566448265475672575299445298529444803620894529853894529390811721802712084730820354809445720911735729302099117308208456439308930754398453015652065338925701570157156207107116197533806619802489753071158066125707938853385207942976116707520362089452945294448076298481672572166267116725721662175349025811725748393021167257217257175308993489902581172166308935398453084399843936217535802581663490263490753075439839902634816711266216634908439983930839984489983990263490263489308165808936217530811672572575444893621720763481262985444803612533852611261170761162157162488430798430793084530845292109090909090909090909090908481208457217539927627539911735481265539174580935735639938211183664475644826573548120356636580993008208462753917299371839175538202945302572172571256717530893621802581167256663538994529984812003547627536718448184463002029371844580935729166581658027125725742924792611650237865568778492295829649331022866105710248106616617016616525692478334783478965296511057152843519842893437851943288055783301702561661079347026107934714743297420692511601160160251160697420692478832974206515692511560660156974206515966923287061102561173907448083538927117439016634663472480166011519661016610657258165816580844399348453089358026307530893580258117126621753621120293848036208536208116726298535389448085299452990348167207634802998538994389452998538998543894390762035389984530749025802712720763475672036208536203538998538998529445294452998538944480362089390812572580843998448993490811672089452945294448076298481672572166267116725721662175349025811725748393021167257217257175308993489902581172166308935398453084399843936217535802581663490263490753075439839902634816711266216634908439983930839984489983990263490263489308165808936217530811672572575444893621720763481262985444803572581658165808443993484530893580263075308935802581171266217536211202938480362085362081167262985353894480852994529903481672076348029985389943894529985389985438943907620353899845307490258027127207634756720362085362035389985389985294452944529985389445299445294448089448089438536203543907629853571271180299903481671753089358084399902581579883980658066253066167026170338853438853385390762998375636363636363636363636363630266630026720853821729944571900267200846291263902810944836657291190210993720280935749020911264475536630082084627539172937209927483998480267180258021725721725671753621753621658089308166349025808439984530271762089444803620853571271753088526112533853389803388942988976312585349853081353990439930902580267175308989408994390909090909090897868126727271900267200846291263902810944836657291190210993720280935749020911264475536630082084627539172937209927483998480267180258021720763481666353984530811672572172076353894519753380252889343793519884379843067, ') (at ', 'Sun, 01 Aug 2021 09:53:18 GMT', ')') ================================================= 1158.4 Every rectangular region could be thought of as histogram union of equal sized buckets which makes Factorization (or multiplicative partition) a special case of set partitions. 1158.5 Example Schematic equivalence between a histogram H1 of unequal sized buckets and factorization histogram H2 of equal sized buckets - both of total size N: Histogram H1 Histogram H2 ------------ ------------ h1b1 ################## h2b ########### h1b2 ####### h2b ########### h1b3 ########## h2b ########### h1b4 ############# h2b ########### h1b5 #### h2b ########### => h1b1 + h1b2 + ... + h1b5 = N = h2b + h2b + ... + h2b 1158.6 Finding the exact Earth Mover Distance between H1 and H2 solves integer factorization indirectly. LC-ACT Earth Mover Distance between arbitrary unequal size bucket histogram H1 and equal size bucket histogram H2 could be written as optimization program: => h1b1 + h1b2 + ... + h1b5 = N = h2b + h2b + ... + h2b = (h1b1 +/- a1c1) + (h1b2 +/- a2c2) + ... + (h1bn +/- ancn) for any integral value of ai and ci. a1c1 + a2c2 + ... + ancn = function_of(EMD) and solving for ai and ci finds factors of N. 1158.6 Linguistically, every string made of one alphabet and arbitrary length is equivalent to factorization (ASCII or Unicode integer value replaces the alphabet) - Example: "aaaaa" is a string of length 5 which maps to a string histogram of 5 equal sized buckets (size of each bucket equals the ASCII or Unicode value v('a') of the alphabet 'a') => N = length_of_the_string * v(alphabet) 1158.7 Recursion limit has been increased in DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py for stack overrun issues while recursing binary search point location for large integers. 1158.8 Disclaimer: All benchmarks for NeuronRain computational geometric factorization so far have been performed as Nick's Class proof-of-concept only on single node Python-Spark cluster quadcore for randomly chosen non-RSA moduli or semiprime integers (high omega, easy, smooth and hard). Factorizing RSA moduli and semiprimes could be significantly harder and expensive practically and requires enterprise cloud. An optimal PRAM implementation of Planar Point Location by Sorting/WaveletTrees/SegmentTrees/IntervalTrees might have to be plugged-in for accurate Parallel RAM results (e.g https://github.com/jlabeit/wavelet-suffix-fm-index). Previous Benchmark numbers might scale exponentially on a production-grade BSP cloud of huge multicores if communication complexity is negligible (e.g 1 second on single node quadcore might scale to nanosecond on BSP cloud of 10^9 multicores subject to Amdahl and Brent speedup theorems).
Krishna iResearch - NeuronRain - K.Srinivasan
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1158. (THEORY and FEATURE) Computational Geometric Factorization - 18000+ bits quadcore singlenode cluster benchmarks - Python 3.9.0 + Spark 3.0.1, Earth Mover Distance, SETH, Equivalence of Factorization and Set Partition - related to 575,651,728,1142 and all sections on Integer Fa ctorization, Lagrangian Sum of squares covering of space and Histogram Set Partitions, Multiplicative Partitions
Krishna iResearch - NeuronRain - K.Srinivasan
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Section 1156 updated
Krishna iResearch - NeuronRain - K.Srinivasan
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1157. (THEORY and FEATURE) Computational Geometric Factorization - Python 3.9.0 + Spark 3.0.1 Single node cluster - cast to Decimal() - 4960 bits integer quadcore Benchmarks - related to all sections on Integer Factorization, Derandomization of BQP, Numeric Compression by Prime Factorization,Set Partition to Exact Square Tile Cover Space Filling Reduction of Rectangular Region, Lagranges Four Square Theorem - 9 August 2021
Krishna iResearch - NeuronRain - K.Srinivasan
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--------------------------------------------------------------------------------------------------------------------------------------------- 1157. (THEORY and FEATURE) Computational Geometric Factorization - Python 3.9.0 + Spark 3.0.1 Single node cluster - cast to Decimal() - 4960 bits integer quadcore Benchmarks - related to all sections on Integer Factorization, Derandomization of BQP, Numeric Compression by Prime Factorization,Set Partition to Exact Square Tile Cover Space Filling Reduction of Rectangular Region, Lagranges Four Square Theorem - 9 August 2021 --------------------------------------------------------------------------------------------------------------------------------------------- 1157.1 Huge 4960 bits integer (each digit of the integer has been randomly chosen - i.i.d) has been factorized by NeuronRain Computational Geometric Factorization (Python 3.9.0 + Spark 3.0.1) which is by far the largest integer factorized by NeuronRain by a non-uniform logdepth circuit of depth 402 which is theoretically O((logN)^402) PRAM time and requires O(2^4960/4960^402) PRAMs or multicores : 1157.2 First 4 factors of 4960 bits integer are printed in 8 seconds and 22 seconds - 2 small and 2 huge - commandline: spark-3.0.1-bin-hadoop3.2/bin/spark-submit DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py 99992239209309209309203909230920930920930923992039029309209092390293923929309209309203828398283829327327873872873827727372873827372877237273827737283782737273287387237827372737283782737287387273827837287372873727387283727873827738728378273872738278732738723728737273728378272398298398239823892883928329839829382893828398293828392883928392898323232323283982938982892839892838892839289382939828938298392839828329839289382839829839289839828382983823892898298382392838298399283982323923982938982389289839289838238982389829839283892839829832989382983892839829389283989283973787237872387287837278372878737273878273872392983929821319999999999999999999999999329329302939293920390293902909029392093092039029309203932032302030923209309230902932392300239092309029309029309029309023093092023239832829389828382389283982983982839283982329892893982983293203902390290390293002909302232309029039029302083239823829838298317217271872818271727172871827817827817287187281782718728178278172871872817827817287127871872190328328389923232322323232323232322329309203029039029302090392102901929019209109208198291828918291893728727387287372737827838723872873727387273872783723782737872378273828738273772372873782737273782787382783782738278372873827872323989283829838239892839892832839829839283928938283892883982392838293823232323232323232323239828023212189291298198291829818289182981928182212121212982323232323232323982938232323232323239312738982382323112323232039992199213776665522344232323229923233488845216663322293731 201 False 2> testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.Python3.9Upgrade.4960bits.9August2021 ('Spark Python version:', '3.9.0 (default, Nov 4 2020, 21:28:32) \n[GCC 7.4.0]') ('factors of ', 99992239209309209309203909230920930920930923992039029309209092390293923929309209309203828398283829327327873872873827727372873827372877237273827737283782737273287387237827372737283782737287387273827837287372873727387283727873827738728378273872738278732738723728737273728378272398298398239823892883928329839829382893828398293828392883928392898323232323283982938982892839892838892839289382939828938298392839828329839289382839829839289839828382983823892898298382392838298399283982323923982938982389289839289838238982389829839283892839829832989382983892839829389283989283973787237872387287837278372878737273878273872392983929821319999999999999999999999999329329302939293920390293902909029392093092039029309203932032302030923209309230902932392300239092309029309029309029309023093092023239832829389828382389283982983982839283982329892893982983293203902390290390293002909302232309029039029302083239823829838298317217271872818271727172871827817827817287187281782718728178278172871872817827817287127871872190328328389923232322323232323232322329309203029039029302090392102901929019209109208198291828918291893728727387287372737827838723872873727387273872783723782737872378273828738273772372873782737273782787382783782738278372873827872323989283829838239892839892832839829839283928938283892883982392838293823232323232323232323239828023212189291298198291829818289182981928182212121212982323232323232323982938232323232323239312738982382323112323232039992199213776665522344232323229923233488845216663322293731, '(', 4959.638533697945, ' bits integer) are:') ================================================= ('Factors are: (', 3, ',', 33330746403103069769734636410306976973643641330679676436403030796764641309769736436401276132761276442442624624291275909124291275790959079091275912427927579091095795745942457579094594245762462424609279095790957909129094575957942579576126091290912759577579574576245757909459424132766132746607964294642776613276460964609466097942797627976130966107744107761327646327630946630946297613096460979942979432797613276109946429794279943279763279942794327941297632766127464279432799761327441307994312994129763279763279412994129943279761297613276610996460994630946609796427996427991262412624129095945759457626245757959424624130994643273773333333333333333333333333109776434313097973463431300969676464031030679676436401310677434010307736436410300977464100079697436343103009769676436341031030674413277609796609460796427994327994279761327443297631327661097734634130096796764334303100744103009679676434027746607943279432772405757290939423909057623942605942605762395760594239576059426057623957605942605762375957290730109442796641077440774410774410774109769734343013009767363464034300643006403036402732763942972763964576242462429124245942612907957624575795757957594574594245957459424609579424590790957927579091260929127594594246092790957942624107996427943279413297613297610946609946427976312761297627994130946097941077441077441077441079942674404063097099399430609939429727660642727404040404327441077441077441327646077441077441079770912994127441037441077346664066404592221840781410774409974411162948405554440764577, ') (at ', 'Mon, 02 Aug 2021 18:47:16 GMT', ')') ================================================= ('Factors are: (', 13, ',', 7691710708408400716092608402378533147763917230156848408400699414637994148408400716092602184483371486717528759451832902105605679028682864405679056714137133636406722095217490210560290979791337482602141329797913363645175671374909826056029097990210636825595286440672097979106020953715261403063376375686794603063798684140646022602184067994491761409479409483383302998684064607141453295329952533832995253722526140640756868414064602295329987679106383371068684484490953295253723021844794147998687614029945372253064479921722294603021837910756140999183306453295371491483383791074906710605568252910559874836825944144482605568691071524716923076923076923076923076871486869456868763106945684839156107084084003002254554148617869386994093023786992533260946172237869925331463793002254540237930155633833294568448337106867998691075603021844794607145690998714861838645406953099461762254017869925310694561698710755679218330639785943990216790132859451679062909832099014406290978363706021397913220985986755175932913220937717563722301787101717171717171717102254554079156848407853107084838609924554546862169099371455253222594517491329797902909833747990221055952867220983363367902913259867217595251828644067214056713367906721752598672175259451832913255691483371526018453295376371756909987637225302944914837229414833714909479409479409479409479986771016322253176784483986909099167921686783247086247152486402486402486460226017871017871018408672229414024854794094772307092247213589655564940947940763325652988093589486330287, ') (at ', 'Mon, 02 Aug 2021 18:47:30 GMT', ')') 1157.3 Tiles computation in DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py has been updated to cast the polylog to decimal.Decimal() datatype which removes overflow, Python C Size and floating point errors. By this integers of arbitrary bits length can be factorized by optimally choosing circuit depth in commandline. Exponentiation operator has been reinstated.
Krishna iResearch - NeuronRain - K.Srinivasan
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Section 1156 updated - conversion of quantum gates to PRAMs
Krishna iResearch - NeuronRain - K.Srinivasan
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1155 updated - References
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1155 updated - References
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Section 1156 updated
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1156 - reference updated - non boolean social choice and sharp thresholds
Krishna iResearch - NeuronRain - K.Srinivasan
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1156. (THEORY and FEATURE) Majority Voting by NC^BQP Oracle Turing Machine, Derandomization of BQP, Integer Factorization in BQP and PRAM-NC-BSP - 4 August 2021 - related to 1152,1154 and all sections on Majority Voting, Communication complexity, KRW Conjecture, Boolean Function Composition and Integer Factorization
Krishna iResearch - NeuronRain - K.Srinivasan
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Updated BestPractices.txt
Krishna iResearch - NeuronRain - K.Srinivasan
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1155. (THEORY and FEATURE) Computational Geometric Factorization - Python 3.9.0 + Spark 3.0.1 - 2061 bits integer quadcore Benchmarks - related to all sections on Integer Factorization, Derandomization of BQP, Numeric Compression by Prime Factorization,Set Partition to Exact Square Tile Cover Space Filling Reduction of Rectangular Region, Lagranges Four Square Theorem - 1 August 2021
Krishna iResearch - NeuronRain - K.Srinivasan
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1155. (THEORY and FEATURE) Computational Geometric Factorization - Python 3.9.0 + Spark 3.0.1 - 2061 bits integer quaadcore Benchmarks - related to all sections on Integer Factorization, Derandomization of BQP, Numeric Compression by Prime Factorization,Set Partition to Exact Square Tile Cover Space Filling Reduction of Rectangular Region, Lagranges Four Square Theorem - 1 August 2021
Krishna iResearch - NeuronRain - K.Srinivasan
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Section 1154 - references updated
Krishna iResearch - NeuronRain - K.Srinivasan
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Section 166 updated - references
Krishna iResearch - NeuronRain - K.Srinivasan
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1154. (THEORY and FEATURE) Conflicts between Derandomization of Shor Factorization in BQP by Majority-VoterSAT boolean composition or BQP^BQP oracle machine and PRAM-NC-BSP computational geometric factorization, Gamma approximation of sum of hyperbolic tiles in average case polynomial time sequential computational geometric factorization and Quantum NC computational geometric factorization - related to 562, 668, 670, 712, 1152 and all sections on Majority Voting, Condorcet Jury Theorem and Integer Factorization - 27,28 July 2021
Krishna iResearch - NeuronRain - K.Srinivasan
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Updated Section 1184 - Hub-Spokes
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Section 1142 updated for biway reduction between ED and EMD
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