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Analyzed about 4 hours ago. based on code collected 1 day ago.
Nov 05, 2025 — Nov 05, 2026
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-------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1324. (JIRA,THEORY and FEATURE) Computational Geometric Integer Factorization - Python 3.10.4,Python 3.7.5,Spark 3.0.1,Spark 3.3.0 Quadcore Benchmarks - Numba JIT enabled for joblib parallelized tiles creation - Semiprimes,Cunningham's Number - related to 498,601,1226,1259,1303,1319,1321,1323 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization - 13 October 2022 -------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1324.1 python-src/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py b/python-src/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py has been updated to import joblib Parallel processing framework. 1324.2 Factors accumulator Spark Global variable has been updated within each clause of factor criteria which was printing wrong factors earlier though factors were correctly computed. 1324.3 New function parallel_tile_segments() has been defined and Numba JIT decorated for computing tile segments in parallel which is computed sequentially at present. 1324.4 Function SearchTiles_and_Factorize(n, k, Parallel_for="False") has been changed to add a boolean flag Parallel_for to choose between parallel version and sequential version of for loop. If Parallel_for is set to False tiles computation for loop is sequential. 1324.5 If Parallel_for is set to True following commented sequential for-loop code block is replaced by joblib Parallel() processing which parallelly invokes parallel_tile_segments() by setting n_jobs=<number of multicores> followed by Spark parallelize() of the 2D array which is flattened to 1D array by flatMap() and foreach() is invoked in the end - parallel version of a doubly nested for loop. This triply speeds-up the hyperbolic arc bow segmentation by combining Spark Parallelize() + Numba JIT + Joblib Parallel(). Caveat: Tile segments computed are stored in a huge 2D array in-memory and number of jobs in joblib have to be set to N/(logN)^k equal to number of multicores-PRAMs in NC-DMRC-MapReduce cloud to prevent out of memory errors - requires a Supercomputing or Large cloud infrastructure of massive multicores-PRAMs - for huge integers normal desktop configurations might not work: #((logN)^k sequential binary or interpolation searches of logN or loglogN time each on N/(logN)^k PRAMS-Multicores #for x in range(int(polylog_n)): # print("tiles_start:", tiles_start) # print("tiles_end:", tiles_end) # tiles = list(range(tiles_start, tiles_end)) # print(("len(tiles):", len(tiles))) # spcon.parallelize(tiles).foreach( # tilesearch_nonpersistent) # tiles_start = tiles_end # tiles_end += tiles_per_PRAM # if len(factors_accum.value) > maxfactors: # break #Earlier sequential for loop is parallelized by joblib to obtain a 2D array of set of tile segments followed by another nested parallelize() for each tile segment 1D array tile_segments=Parallel(n_jobs=4)(delayed(parallel_tile_segments)(tiles_per_PRAM,x) for x in range(int(polylog_n))) print("tile_segments:",tile_segments) spcon.parallelize(tile_segments).flatMap(lambda x: x).foreach(tilesearch_nonpersistent) 1324.6 Parallel_for is passed on as boolean argument (True of False) from factorization commandline. 1324.7 Following integers of varied categories have been factorized captured in respective logs - some of the benchmarks use upgraded Spark 3.3.0: 1324.7.1 testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log1.12October2022 - Python 3.10.4 + Spark 3.0.1 - Numba JIT Parallel for enabled - ('factors of ', 99999, '(', 16.609626047414267, ' bits integer) =', {1, 3, 33333, 99999}) 1324.7.2 testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log2.12October2022 - Python 3.10.4 + Spark 3.0.1 - Numba JIT Parallel for disabled - ('factors of ', 99999, '(', 16.609626047414267, ' bits integer) =', {1, 3, 813, 271, 369, 33333, 123, 99999}) 1324.7.3 testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log3.12October2022 - Python 3.10.4 + Spark 3.0.1 - Numba JIT Parallel for disabled - ('factors of ', 2137458620009, '(', 40.959033629156515, ' bits integer) =', {1462001, 2137458620009, 1462009, 1}) - Reference 1324.9 1324.7.4 testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log4.12October2022 - Python 3.10.4 + Spark 3.0.1 - Numba JIT Parallel for disabled - random 2070 bits integer - ('factors of ', 99832839829839289382939239728378871872172871827817287187281728718271872817827182781728718271872871287182781721792819898198298298291829189389829892891839018098908918398293918989083981983989182983918283928139829389283989038190809028989108390891839028090283098120938183908192839809180923092039029309203920390293203920392093092302382838182381289839829839823892839829839288392893829839829839829839283982198392819812080989238193891823908983918319898398989898982983989189289382983928928398293892898938981983921898391382198391898198319283982382839839130923090302939230293029039029309203902839289382983828382938982938283982983291909, '(', 2069.5587894854657, ' bits integer) are:') ('Factors are: (', 7, ',', 14261834261405612768991319961196981696024695975402469598183104102610267545403883254532674038838981612454683103113259985456899756898832741341404270413119859728415559771184845569869140283427026140559754846877118484183427005455829861284158341555977004012897585445848311986884691401311560441719861329886274341470457702913156156043197548311768755691404262831984691404262755484699118548547119975691326283171198974258868712748313413117701283416902842628427128426140569884184197569132704056899127556991283140560271198768885484556885474183426054691405590131870043277032899004148432758457700405612768997689768991283276897711854755987, ') (at ', 'Wed, 12 Oct 2022 08:27:50 GMT', ')') 1324.7.5 testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log5.12October2022 - Python 3.7.5 + Spark 3.3.0 - Numba JIT Parallel for disabled - (12^151 - 1)/11 - 534 bits Cunningham's number - 82219620528659701952660120743076100427390924357073396551677033937335320430502358024273032756332005408066894606696792219545093967127330845624462896060630268212317 - ('Factors are: (', 3, ',', 27406540176219900650886706914358700142463641452357798850559011312445106810167452674757677585444001802688964868898930739848364655709110281874820965353543422737439, ') (at ', 'Wed, 12 Oct 2022 10:05:57 GMT', ')') - Reference 1324.11 1324.7.6 testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.log6.12October2022 - Python 3.7.5 + Spark 3.3.0 - Numba JIT Parallel for enabled - Mersenne Semiprime - 8388607 = (2^23 - 1) - ('Factors are: (', 47, ',', 178481, ') (at ', 'Wed, 12 Oct 2022 10:35:48 GMT', ')') - Reference 1324.8
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1323.(THEORY and FEATURE) GIS Urban Sprawl Analytics - R2022A - 3D Urban Sprawl Growth Model from BUILT-V and BUILT-S datasets - Commercial segment (Central Business District) Delineation by average building height - Chennai Metropolitan Area Sprawl Example - 11 October 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301,1304,1312,1313,1320 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, Automatic Delineation of Urban Sprawls, Cellular Automata-SLEUTH-Polya Urn-Dynamic Facegraph Urban Growth Models
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----------------------------------------------------------------------------------------------------------------------------- 1323.(THEORY and FEATURE) GIS Urban Sprawl Analytics - R2022A - 3D Urban Sprawl Growth Model from BUILT-V and BUILT-S datasets - Commercial segment (Central Business District) Delineation by average building height - Chennai Metropolitan Area Sprawl Example - 11 October 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301,1304,1312,1313,1320 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, Automatic Delineation of Urban Sprawls, Cellular Automata-SLEUTH-Polya Urn-Dynamic Facegraph Urban Growth Models ----------------------------------------------------------------------------------------------------------------------------- 1323.1 GISUrbanSprawlAnalytics.py has been updated to define new function three_dimensional_urban_growth_model(rasterdata_2d,rasterdata_3d) for computing third dimension (height) from two histograms for 2D raster and 3D raster for any datatype. This function takes as input the data for 2 rasters of 2D (Surface) and 3D (Volume) from urban_sprawl_from_raster(), populates 2 defaultdict() histogram dictionaries from them, sorts the 2 histograms by values of the pixels and computes the third dimension (height) by fraction of maximum elements in the two histograms (Volume/Surface) which is an estimate of the height. GHSL Data Package 2022 report has more on definitions of ANBHx (Building height), BUVOL (Building volume) and BUSURF (Building surface) in Reference 1323.6. 1323.2 Two rasters testlogs/RemoteSensingGIS/GHS_BUILT_S_P2030LIN_GLOBE_R2022A_54009_100_V1_0_R8_C26.tif (R2022A BUILT-S - 2D surface) and testlogs/RemoteSensingGIS/GHS_BUILT_V_P2030LIN_GLOBE_R2022A_54009_100_V1_0_R8_C26.tif (R2022A BUILT-V - 3D Volume) are analyzed by three_dimensional_urban_growth_model() to find estimated building height in Chennai Metropolitan Area Sprawl Longitude-Latitude Bounding Box (of size ~130 km * ~130 km = ~16000 sqkm approximately) delineated by expanse of suburban rail-bus network (Reference 1320.6): r2ddata=urban_sprawl_from_raster(79.271851,12.439259,80.351257,13.568572,"testlogs/RemoteSensingGIS/GHS_BUILT_S_P2030LIN_GLOBE_R2022A_54009_100_V1_0_R8_C26.tif",dt="BUILT_S R2022A") r3ddata=urban_sprawl_from_raster(79.271851,12.439259,80.351257,13.568572,"testlogs/RemoteSensingGIS/GHS_BUILT_V_P2030LIN_GLOBE_R2022A_54009_100_V1_0_R8_C26.tif",dt="BUILT_V R2022A") three_dimensional_urban_growth_model(r2ddata,r3ddata) 1323.4 Vertical expansion is defined and analyzed in section 1234 and Reference 1234.8 which delineates based on DBSCAN clustering, has found the ratio of vertical land to surface to be approximately 3.0 as far as European cities (Spain) are concerned. Commercial Central Business District (CBD) of a city typically consists of highrises and CBD could be delineated with in an urban sprawl GIS by aggregating the pixels of high building height values and high NightLights from VIIRS. 1323.5 From testlogs/GISUrbanSprawlAnalytics.log.11October2022 and testlogs/GISUrbanSprawlAnalytics.log2.11October2022 building height ANBHx has been determined as (in meters): three_dimensional_urban_growth_model(): maximum building height = 18.16121440338903
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Section 1320 updated
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Updated section 1174
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Sections 1285 and 1322 updated
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----------------------------------------------------------------------------------------------------------------------------- 1322. (JIRA,THEORY and FEATURE) Computational Geometric Integer Factorization - Multiple Integers - Python 3.10.4 upgrade + Spark 3.0.1 Quadcore Benchmarks 4 - Factorization-SquareRoot-Primality of Consecutive integers from 50000 to 50100 and 9 to 200 - related to 498,601,1226,1259,1303,1319,1321 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes,Almost-Square Bounding Boxes in Large Scale Visual Recognition,Pell's Equation,Brahmagupta's Chakravala,Approximate Factoring by Newton-Raphson Rayshooting queries,Algebraic Geometry of Computational Geometric Factorization - 10 October 2022 ----------------------------------------------------------------------------------------------------------------------------- 1322.1 This commit resolves JIRA issue https://krishnairesearch.atlassian.net/browse/NEUR-1 concerning problem within python-src/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py in finding square roots,a very important special case of factorization. It is worth noting that Newton-Raphson square root algorithm is polylogarithmic - O((logN)^k*loglogN) - which is used for approximate factor rayshooting queries in algorithm of https://kuja27.blogspot.com/2018/04/grafit-course-material-newton-raphson.html - and Computational Geometric Factorization implies general cases of primality testing and factorization are polylogarithmic (O((logN)^kloglogN) if interpolation search is employed) as well which includes almost-squares (integer squareroots). Principal Ideal Algebraic Geometry and Differential Calculus involved in computation of arithmetic progression hyperbolic arc rasterization (rectification) are quite similar to Newton-Raphson algorithm: tile_segment of length delta (from first derivative - tangent - of hyperbolic arc at x) = N/x - N/(x+delta) = N *[delta/x(x+delta)] or N/(x(x+1)) for delta=1 1322.2 New clause has been added to handle when intervalmidpoint of binary search is 0 and tile x and y ordinates are equal. 1322.3 Multiple Consecutive integers from 50000 to 50100 have been factorized and following primes have been captured in python-src/testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.log.10October2022 (spikes in runtimes): 50021,50023,50033,50047,50051,50053,50069,50077,50087,50093 1322.4 Multiple Consecutive integers from 9 to 200 have been factorized and following square roots have been captured in python-src/testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.log2.10October2022 : ('Square root is: ', 3, ' (at ', 'Mon, 10 Oct 2022 09:50:34 GMT', ')') ('Square root is: ', 4, ' (at ', 'Mon, 10 Oct 2022 09:54:10 GMT', ')') ('Square root is: ', 5, ' (at ', 'Mon, 10 Oct 2022 09:57:36 GMT', ')') ('Square root is: ', 6, ' (at ', 'Mon, 10 Oct 2022 10:01:51 GMT', ')') ('Square root is: ', 7, ' (at ', 'Mon, 10 Oct 2022 10:06:55 GMT', ')') ('Square root is: ', 8, ' (at ', 'Mon, 10 Oct 2022 10:12:35 GMT', ')') ('Square root is: ', 9, ' (at ', 'Mon, 10 Oct 2022 10:19:03 GMT', ')') ('Square root is: ', 10, ' (at ', 'Mon, 10 Oct 2022 10:26:08 GMT', ')') ('Square root is: ', 11, ' (at ', 'Mon, 10 Oct 2022 10:34:12 GMT', ')') ('Square root is: ', 12, ' (at ', 'Mon, 10 Oct 2022 10:42:57 GMT', ')') ('Square root is: ', 13, ' (at ', 'Mon, 10 Oct 2022 10:52:47 GMT', ')') ('Square root is: ', 14, ' (at ', 'Mon, 10 Oct 2022 11:03:30 GMT', ')') 1322.5 Runtime plot for factoring integers from 9 to 208 has been captured in python-src/testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.jpg and spikes correspond to primes - actual runtimes are far upperbounded by theoretical plot for O(logN*logN).
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----------------------------------------------------------------------------------------------------------------------------- 1321. (JIRA,THEORY and FEATURE) Computational Geometric Integer Factorization - Multiple Integers - Python 3.10.4 upgrade + Spark 3.0.1 Quadcore Benchmarks 3 - Numba JIT optimization - Configurable number of factors - Factorization-Primality of Consecutive integers from 999 to 1874 - related to 1259,1303,1319 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes - 7 October 2022 ----------------------------------------------------------------------------------------------------------------------------- 1321.1 Logs for factorization of 875 consecutive integers from 999 to 1874 have been committed at testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.log.7October2022 1321.2 Following example awk script can be used to grep the logs for potential prime integers corresponding to spikes in runtimes (> 100): grep "in time deltas" testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.log.7October2022 |awk '{if ($15 > 100) print $5}' 1193, 1229, 1249, 1277, 1279, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1369, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1681, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1849, 1861, 1867, 1871, 1873 1321.3 JIRA issue for factorization of squares - https://krishnairesearch.atlassian.net/browse/NEUR-1 has been opened for erroneous flagging of squares as primes earlier (1369=37*37,1681=41*41)
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Logs for multiple integers factorization - from 1000 to 1875 - includes primality tests (spikes in runtimes)
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1320. (THEORY and FEATURE) GIS Urban Sprawl Analytics - R2019A and R2022A - Comparison of Raster Data Bounding Boxes for Chennai Metropolitan Area Sprawl - 7 October 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301,1304,1312,1313 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, Automatic Delineation of Urban Sprawls, Cellular Automata-SLEUTH-Polya Urn-Dynamic Facegraph Urban Growth Models
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------------------------------------------------------------------------------------------------------------------------------ 1320. (THEORY and FEATURE) GIS Urban Sprawl Analytics - R2019A and R2022A - Comparison of Raster Data Bounding Boxes for Chennai Metropolitan Area Sprawl - 7 October 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301,1304,1312,1313 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, Automatic Delineation of Urban Sprawls, Cellular Automata-SLEUTH-Polya Urn-Dynamic Facegraph Urban Growth Models ------------------------------------------------------------------------------------------------------------------------------ 1320.1 Exponential 2634% periurbanization-expansion of Chennai Metropolitan Area Sprawl deduced in 1313 from 2019 to 2022 has been re-analyzed by comparing another pair of GHSL SMOD R2019A and R2022A raster datasets. 1320.2 GISUrbanSprawlAnalytics.py has been updated to compare following pair of rasters from GHSL SMOD Degree of Urbanization - R2019A and R2022A - testlogs/RemoteSensingGIS/GHS_SMOD_POP2015_GLOBE_R2019A_54009_1K_V2_0.tif (R2019A) and testlogs/RemoteSensingGIS/GHS_SMOD_P2030_GLOBE_R2022A_54009_1000_V1_0_R8_C26.tif (Row 8 - Column 26 of R2022A GHSL SMOD dataset obtained from tiled R2022A GUI) after a new bounding box delineation based on extent of industrial base and suburban transport in Northern,Western and Southern directions of Chennai Metropolitan Area Sprawl - Bounding box is manually obtained from GUI of http://bboxfinder.com/#12.439259,79.271851,13.568572,80.351257 and committed to testlogs/GISUrbanSprawlAnalytics.ChennaiMetropolitanAreaSprawlBoundingBox.7October2022.pdf: r1data=urban_sprawl_from_raster(79.271851,12.439259,80.351257,13.568572,"testlogs/RemoteSensingGIS/GHS_SMOD_POP2015_GLOBE_R2019A_54009_1K_V2_0.tif",dt="Degree of Urbanization R2019A") r2data=urban_sprawl_from_raster(79.271851,12.439259,80.351257,13.568572,"testlogs/RemoteSensingGIS/GHS_SMOD_P2030_GLOBE_R2022A_54009_1000_V1_0_R8_C26.tif",dt="Degree of Urbanization R2022A") compare_raster_data(r1data,r2data) 1320.3 Following are the expansion and contraction percentages in 3 years between R2019A-R2022A for GHSL pixel classes within the bounding box from testlogs/GISUrbanSprawlAnalytics.log.7October2022 corroborating the trend in 1313 (except class 22 which shows 700% expansion versus 160% in 1313): compare_raster_data(): raster1hist = defaultdict(<class 'int'>, {11: 5542, 13: 1615, 12: 2544, 30: 1020, 21: 178, 23: 303, 22: 9, 10: 993}) compare_raster_data(): raster2hist = defaultdict(<class 'int'>, {21: 4370, 12: 2405, 11: 2382, 30: 1498, 22: 72, 13: 79, 23: 338, 10: 1060}) Percentage change in 11 : 57.01912666907254 (57% contraction of Very Low density rural regions versus 68% in 1313) Percentage change in 13 : 95.10835913312692 (95% contraction of rural cluster versus 99% in 1313) Percentage change in 12 : 5.463836477987422 (5% contraction of Low density rural regions versus 14% in 1313) Percentage change in 30 : -46.86274509803921 (46% expansion of Urban centre - City versus 44% in 1313) Percentage change in 21 : -2355.056179775281 (2355% massive expansion of suburban or periurban centre versus 2634% in 1313) Percentage change in 23 : -11.55115511551155 (11% expansion of Dense Urban cluster - Metro versus 7% in 1313) Percentage change in 22 : -700.0 (700% massive expansion of Semi Dense Urban cluster - Metro versus 160% in 1313) Percentage change in 10 : -6.747230614300101 (6% expansion of waterbodies versus 7% in 1313) 1320.4 Raster comparison and growth trends earlier could be used as guiding principles in Urban sprawl delineation, DNFMAXSAT Urban sprawl facegraph MARA and weights learning in Polya Urn UGM: 1320.4.1 Heavy expansion of Urban centre, Dense-Semidense Urban clusters and Periurban Pixel classes - 21,23,22 - imply an urban sprawl extension qualifying them for inclusion in metropolitan jurisdiction. In earlier example massive expansion of 2355% in suburban (class 21) and 700% in semidense urban cluster-metro (class 22) pixels show a sudden spurt in urbanization in 3 years along peripheries. 1320.4.2 Heavy contraction of rural clusters and waterbodies implies depletion of greenery and natural resources. Disproportionate growth percentages between settlements and waterbodies might require corrections.
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Section 1285 updated
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+1319. (THEORY and FEATURE) Computational Geometric Integer Factorization - Multiple Integers - Python 3.10.4 upgrade + Spark 3.0.1 Quadcore Benchmarks 2 - Numba JIT optimization - Configurable number of factors - related to 1259,1303,1317 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes - 6 October 2022
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--------------------------------------------------------------------------------------------------------------------------- 1319. (THEORY and FEATURE) Computational Geometric Integer Factorization - Multiple Integers - Python 3.10.4 upgrade + Spark 3.0.1 Quadcore Benchmarks 2 - Numba JIT optimization - Configurable number of factors - related to 1259,1303,1317 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing,RSA Semiprimes - 6 October 2022 --------------------------------------------------------------------------------------------------------------------------- 1319.1 Updated python-src/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py to import numba JIT (Just In Time) python compiler that achieves upto 20X speedup on Numeric Python-Scientific Python and Loops computation. 1319.2 Maximum number of factors found per integer has been made configurable by maxfactors. DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized.py is a Parallel Planar Point Location Factoring implementation on MapReduce that is inherently capable of finding all factors by parallel invocation of local sequential binary or interpolation search ((logN)^k sequential binary or interpolation searches of logN or loglogN time each on N/(logN)^k PRAMS-Multicores which is NC(k) contained in DMRC(k-1)) while traditional factorization is mostly limited to finding one factor alone (all factors of N can be recursively found by applying same algorithm - whether it is Quadratic Sieve,Dixon,Pollard-Rho or CADO-NFS - on N/f(prev) where f(prev) is the last factor found). 1319.3 Restricting the number of factors per integer is necessary for accurate benchmarking as different integers have different number of factors and number of factors has to be same across the board. 1319.4 Function tilesearch_nonpersistent(y,numfactors=maxfactors) and binary_search_interval_nonpersistent(xl, yl, xr, yr, numfactors=3) have been updated to pass on maxfactors as parameters which is checked by an inequality clause on length of _value field of factors Spark accumulator. 1319.5 All functions have been decorated by @jit(parallel=True) directive of Numba for enabling parallelism but commented due to compile errors per caveats in Numba documentation - https://numba.pydata.org/numba-doc/latest/reference/pysupported.html#pysupported. 1319.6 101 consecutive 22-bits integers from 3203023 have been factorized by restricting the maximum number of factors per integer to 3 and their actual and theoretical (O(logN)^2 for BigO constant 1) runtimes have been plotted in python-src/testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.jpg: python3.10 DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.py 3203023 100 2 1 2 > testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.log.6October2022 1319.7 Theoretical and Actual runtime curves in python-src/testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.jpg match except spikes caused by Spark Executor while doing a futile search for non-trivial factors in following integers which are primes (independently verified by Google Prime Search e.g https://www.google.com/search?q=3203117+prime) - 3203041,3203047,3203059,3203063,3203071,3203093,3203099,3203107,3203111,3203117. It is worth observing to note that spikes for primes in actual runtime curve touch the theoretical curve for upperbound of O(logN*logN).
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Updated BestPractices.txt
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Section 1318 updated
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1318. (THEORY and FEATURE) GIS Weather Analytics and Climate Analytics - 3 October 2022 - related to 148,445,446,463,1165,1171,1176,1266,1289,1316 and all sections on Correlation between gravitational effects of Mined Celestial N-Body Patterns and terrestrial extreme weather events (or Gravitational effects on climate change), Drone natural obstacle avoidance, Drone autonomous online shopping delivery, Drone Electronic Voting Machine, Large Scale Visuals Recognition, Artificial Intelligence models for Climate Change, Astronomical algorithms
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---------------------------------------------------------------------------------------------------------------------------- 1318. (THEORY and FEATURE) GIS Weather Analytics and Climate Analytics - 3 October 2022 - related to 148,445,446,463,1165,1171,1176,1266,1289,1316 and all sections on Correlation between gravitational effects of Mined Celestial N-Body Patterns and terrestrial extreme weather events (or Gravitational effects on climate change), Drone natural obstacle avoidance, Drone autonomous online shopping delivery, Drone Electronic Voting Machine, Large Scale Visuals Recognition, Artificial Intelligence models for Climate Change, Astronomical algorithms ----------------------------------------------------------------------------------------------------------------------------- 1318.1 GISWeatherAnalytics.py has been updated to integrate N-Body Gravitational Acceleration computation for Solar System bodies implemented in EphemerisSearch.py to correlate climate events and gravitational pull of Solar system N-Body celestial choreographies on Earth and Ocean surface (especially role of Syzygies of solar system bodies). While Sun-Earth-Moon Syzygy has been widely studied and found to have high correlation to storm intensification (Sections 1266,1289,1316), gravitational influence of rest of Solar system planets on Earth has been less studied in literature. 1318.2 Function climate_analytics(datasource,date="",time="") has been changed to include a clause for "n-body-analytics" datasource which accepts an array of extreme weather event dates, instantiate Ephemeris object (NASA JPL DE421 Ephemeris) and invoke extreme_weather_events_n_body_analytics() on those dates to compute gravitational pull and pairwise angular separation of solar system bodies. 1318.3 Function climate_analytics(datasource="n-body-analytics",date=datesofstorms) is invoked for following formation dates of storms: 1318.3.1 North Atlantic Hurricanes - Harvey (Category 4 - 17 August 2017), Irma (Category 5 - 30 August 2017), Ian (Category 4 - 23 September 2022) 1318.3.2 Bay of Bengal - Very Severe Cyclonic Storms - Amphan (20 May 2020),Gaja (10 November 2018),Vardah (6 December 2016),Thane (25 December 2011),Ockhi (29 November 2017) 1318.4 Following are excerpts of angular separations for Sun-Moon and Venus-Mercury from testlogs/GISWeatherAnalytics.log.3October2022 for earlier storms: Angular separations for Venus-Mercury : [<Angle 51deg 49' 11.5">, <Angle 26deg 43' 05.0">, <Angle 09deg 23' 44.3">, <Angle 04deg 59' 58.7">, <Angle 44deg 15' 04.4">, <Angle 23deg 56' 21.0">, <Angle 54deg 10' 52.4">, <Angle 31deg 00' 20.5">] Angular separations for Sun-Moon : [<Angle 63deg 35' 41.0">, <Angle 97deg 36' 37.7">, <Angle 33deg 52' 36.9">, <Angle 30deg 22' 33.5">, <Angle 28deg 39' 00.4">, <Angle 73deg 45' 38.6">, <Angle 04deg 17' 26.3">, <Angle 117deg 39' 43.0">] 1318.5 Angular separations of Venus-Mercury range from 9 to 54 degrees for all storms which could perhaps be anecdotal evidences for 1266.18 indicating a synergy of Venus and Mercury and not just Venus. Correlation between lowest pressure (millibar) of the storm and angular separations of solar system bodies earlier could be of importance.
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+1317. (THEORY and FEATURE) Computational Geometric Integer Factorization - Multiple Integers - Python 3.10.4 upgrade + Spark 3.0.1 Quadcore Benchmarks - related to 1259,1303 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing - 29 September 2022
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----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1317. (THEORY and FEATURE) Computational Geometric Integer Factorization - Multiple Integers - Python 3.10.4 upgrade + Spark 3.0.1 Quadcore Benchmarks - related to 1259,1303 and all sections on Integer Factorization,Computational Geometry,Set Partitions-to-Tile Cover reduction by Lagranges Four Square Theorem and ILP,Primality Testing - 29 September 2022 ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- 1317.1 python-src/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.py has been upgraded to Python 3.10.4 and 51 consecutive integers from 1000 to 1050, 101 consecutive integers from 10000 to 10100 and 101 integers from 20000 to 20100 have been factorized by Computational Geometric Factorization (253 integers in total). 1317.2 Benchmark runtime numbers for factoring 10000 to 10100 have been plotted as observed curve against a theoretical curve for k*logN*logN for k=1 (testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.jpg). Factors are captured in testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.log.29September2022 (1000 to 1050), testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.log2.29September2022 (10000 to 10100) and testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.log3.29September2022 (20000 to 20100). Earlier consecutive integers factorization includes primes. 1317.3 Actual versus theoretical runtime curves of testlogs/DiscreteHyperbolicFactorizationUpperbound_TileSearch_Optimized_MultipleIntegers.jpg are in concurrence and the few spikes could be latencies due to Python Virtual Machine Garbage collection, CPU and Spark scheduling vagaries.
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Section 1313 updated
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PDF and txt versions of ComplementOfAFunction_GoogleGroupsThread_2003.html
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1316.(THEORY and FEATURE) Astronomy and Cosmology Datasets Analytics - Solar system N-Body Pairwise angular separations computed for NOAA HURDAT2 (1851-2012) North Atlantic Hurricanes Datasets - 28 September 2022 - related to 17,137,148,445,731,1176,1206,1236,1255,1266,1267,1268,1270,1271,1272,1273,1289 and all sections on Astronomical Dataset Mining, Archaeoastronomical Dating, Sequence Mining, String analytics, Sequence Alignment, Visual Planetarium Search, Archaeology, Climate and Extreme Weather Event Analytics, Computational Astrophysics, N-Body problem, Merit of Large Scale Visuals, Astronomical algorithms, Histogram analytics
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------------------------------------------------------------------------------------------------------------------------------ 1316.(THEORY and FEATURE) Astronomy and Cosmology Datasets Analytics - Solar system N-Body Pairwise angular separations computed for NOAA HURDAT2 (1851-2012) North Atlantic Hurricanes Datasets - 28 September 2022 - related to 17,137,148,445,731,1176,1206,1236,1255,1266,1267,1268,1270,1271,1272,1273,1289 and all sections on Astronomical Dataset Mining, Archaeoastronomical Dating, Sequence Mining, String analytics, Sequence Alignment, Visual Planetarium Search, Archaeology, Climate and Extreme Weather Event Analytics, Computational Astrophysics, N-Body problem, Merit of Large Scale Visuals, Astronomical algorithms, Histogram analytics ------------------------------------------------------------------------------------------------------------------------------ 1316.1 python-src/EphemerisSearch.py has been updated to increase maxiterations in extreme_weather_events_n_body_analytics(self,datesofEWEs=None,loc="@earth-moon",angularsep=False,maxiterations=200) to 200. 1316.2 Dates of extreme weather events are read in reverse order by readlines() and reverse() (recent dates are analyzed first) as skyfield supports dates between 1899 and 2053 only and extreme weather events have increased in frequency in later half of 20th century and early 21st century. 1316.3 Pairwise angular separations between solar system bodies on extreme weather event dates after 1899 and before 2053 are computed by skyfield.separation_from() for NOAA North atlantic Hurricanes (HURDAT2) dataset. ephem.extreme_weather_events_n_body_analytics(datesofEWEs="Hurricanes",angularsep=True) 1316.4 Following are Sun-Moon and Mercury-Venus angular separations for some Hurricane formation dates on September-October 2012 showing syzygies and almost-syzygies of Sun-Moon-Earth and ~60 degree separation of Venus-Mercury (from testlogs/EphemerisSearch.log.28September2022) in almost all dates. Gravitational Forces are computed for all solar system bodies including Mercury which mysteriously shows high gravity similar to earlier data: Angular separations for Sun-Moon : [<Angle 142deg 21' 28.5">, <Angle 139deg 28' 30.8">, <Angle 136deg 34' 47.7">, <Angle 133deg 40' 17.8">, <Angle 130deg 44' 59.4">, <Angle 127deg 48' 50.7">, <Angle 124deg 51' 49.9">, <Angle 121deg 53' 54.9">, <Angle 118deg 55' 03.9">, <Angle 115deg 55' 14.6">, <Angle 112deg 54' 25.1">, <Angle 109deg 52' 33.2">, <Angle 106deg 49' 36.8">, <Angle 103deg 45' 33.9">, <Angle 100deg 40' 22.5">, <Angle 97deg 34' 00.7">, <Angle 94deg 26' 26.8">, <Angle 91deg 17' 39.3">, <Angle 88deg 07' 36.7">, <Angle 84deg 56' 18.1">, <Angle 161deg 45' 59.6">, <Angle 164deg 28' 26.6">, <Angle 167deg 10' 48.0">, <Angle 169deg 52' 47.6">, <Angle 172deg 33' 42.9">, <Angle 175deg 11' 13.6">, <Angle 177deg 32' 40.6">, <Angle 177deg 42' 05.9">, <Angle 178deg 13' 52.5">, <Angle 177deg 59' 38.1">, <Angle 175deg 50' 42.4">, <Angle 173deg 13' 39.3">, <Angle 170deg 30' 54.9">, <Angle 167deg 45' 55.8">, <Angle 164deg 59' 38.6">, <Angle 162deg 12' 24.6">, <Angle 159deg 24' 22.9">, <Angle 156deg 35' 37.6">, <Angle 153deg 46' 10.7">, <Angle 150deg 56' 02.6">, <Angle 148deg 05' 13.4">, <Angle 145deg 13' 42.4">, <Angle 142deg 21' 28.5">, <Angle 139deg 28' 30.8">, <Angle 136deg 34' 47.7">, <Angle 133deg 40' 17.8">, <Angle 130deg 44' 59.4">, <Angle 129deg 17' 01.4">, <Angle 127deg 48' 50.7">, <Angle 127deg 31' 40.4">, <Angle 124deg 51' 49.9">, <Angle 122deg 23' 37.9">, <Angle 121deg 53' 54.9">, <Angle 118deg 55' 03.9">, <Angle 115deg 55' 14.6">, <Angle 112deg 54' 25.1">, <Angle 109deg 52' 33.2">, <Angle 106deg 49' 36.8">, <Angle 103deg 45' 33.9">, <Angle 100deg 40' 22.5">, <Angle 97deg 34' 00.7">, <Angle 94deg 26' 26.8">, <Angle 91deg 17' 39.3">, <Angle 88deg 07' 36.7">, <Angle 84deg 56' 18.1">, <Angle 142deg 21' 28.5">, ... Angular separations for Mercury-Venus :[<Angle 59deg 59' 56.5">, <Angle 60deg 02' 40.0">, <Angle 60deg 05' 12.9">, <Angle 60deg 07' 35.7">, <Angle 60deg 09' 48.3">, <Angle 60deg 11' 51.3">, <Angle 60deg 13' 44.7">, <Angle 60deg 15' 28.7">, <Angle 60deg 17' 03.7">, <Angle 60deg 18' 29.8">, <Angle 60deg 19' 47.2">, <Angle 60deg 20' 56.1">, <Angle 60deg 21' 56.8">, <Angle 60deg 22' 49.3">, <Angle 60deg 23' 33.9">, <Angle 60deg 24' 10.8">, <Angle 60deg 24' 40.0">, <Angle 60deg 25' 01.9">, <Angle 60deg 25' 16.5">, <Angle 60deg 25' 23.9">, <Angle 58deg 20' 46.9">, <Angle 58deg 28' 08.3">, <Angle 58deg 35' 12.0">, <Angle 58deg 41' 58.7">, <Angle 58deg 48' 28.6">, <Angle 58deg 54' 42.3">, <Angle 59deg 00' 40.2">, <Angle 59deg 01' 09.3">, <Angle 59deg 03' 33.3">, <Angle 59deg 06' 22.6">, <Angle 59deg 11' 49.9">, <Angle 59deg 17' 02.7">, <Angle 59deg 22' 01.1">, <Angle 59deg 26' 45.7">, <Angle 59deg 31' 16.7">, <Angle 59deg 35' 34.5">, <Angle 59deg 39' 39.5">, <Angle 59deg 43' 31.9">, <Angle 59deg 47' 12.0">, <Angle 59deg 50' 40.3">, <Angle 59deg 53' 56.9">, <Angle 59deg 57' 02.2">, <Angle 59deg 59' 56.5">, <Angle 60deg 02' 40.0">, <Angle 60deg 05' 12.9">, <Angle 60deg 07' 35.7">, <Angle 60deg 09' 48.3">, <Angle 60deg 10' 51.0">, <Angle 60deg 11' 51.3">, <Angle 60deg 12' 02.7">, <Angle 60deg 13' 44.7">, <Angle 60deg 15' 12.0">, ...
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+1315.(THEORY and FEATURE) Intrinsic Merit of Music - Synthesized Bach from training music waveforms - 27 September 2022 - related to 3,110,134,298,1223,1224,1257,1258,1261,1305,1306,1307,1308,1309,1310,1311 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, Longest Common Subsequence, Suffix Trees - Longest Repeated Substring
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----------------------------------------------------------------------------------------------------------------------------- 1315.(THEORY and FEATURE) Intrinsic Merit of Music - Synthesized Bach from training music waveforms - 27 September 2022 - related to 3,110,134,298,1223,1224,1257,1258,1261,1305,1306,1307,1308,1309,1310,1311 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, Longest Common Subsequence, Suffix Trees - Longest Repeated Substring ----------------------------------------------------------------------------------------------------------------------------- 1315.1 AudioToBitMatrix.py has been updated to change sharp notes notation in piano_notes for WesternClassical as: 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}} 1315.2 get_piano_frequencies() has been changed to tokenize subdivisions of notes which range from 1 to 15 to suit 12-note piano_notes dictionary lookup earlier - notes of the form <note>-<subdivision_index> are truncated to <note>. 1315.3 Random sampling synthesis clause within Function music_synthesis() has been changed to read training music waveforms into synth_notes_freq dictionary and iterate through its contents and synthesize new music waveform by chronologically concatenating random time slices from each training waveform. Size of the slice (synthslice) is a function of total duration of clip synthesized. 1315.4 Two music waveforms of JS Bach are passed on as training data to music_synthesis() and synthesized derivative music waveform in piano is written to virtual_piano_music.wav: music_synthesis(["testlogs/JSBach_Musicological_Offering.mp4","testlogs/Bach_Flute_Sonata_EFlat.mp4"],musicgenre="WesternClassical",dur=60,polynomial_interpolation=False, tempo=0.25) 1315.5 Synthesized Bach music in virtual_piano_music.wav reasonably simulates a human playing an instrument and derives the patterns in the training Bach music waveforms. 1315.6 NeuronRain has implementations of Longest Common Subsequence (LCS) in C++ (cpp-src/asferlongestcommonsubstring.cpp) and LongestRepeatedSubstring SuffixArray in Python (python-src/StringSearch_LongestRepeatedSubstring.py) which are other possible algorithms for mining common patterns in notes sequences of music waveforms - Longest Common notes sequence among multiple training music waveforms and Longest Repeated notes sequence within a music waveform are candidates for synthesized music.
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+1314. (THEORY and FEATURE) Complement Diophantines - Lagrange and Barycentric interpolations - 26 September 2022 - related to 323,345,471,735,1160 and all sections on Complement Diophantines, Complement Functions, Complementary Sets, Quadratic Forms, Riemann Zeta Function, Patterns in Primes, Polynomial Reconstruction Problem, Error correcting codes, Computational Learning Theory - Multivariate Polynomial Reconstruction over Finite Fields, Lagrange-Taylor-Barycentric interpolation, Jones-Sato-Wada-Wiens Theorem, Prime-Composite Complementation, Prime Number Theorem, Ulam Spiral, Ramsey 2-coloring of integers, Hilbert Tenth Problem, Unique Factorization , Matiyasevich-Robinson-Davis-Putnam Theorem, Post's Correspondence Problem, Question-Answering
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---------------------------------------------------------------------------------------------------------------------------- 1314. (THEORY and FEATURE) Complement Diophantines - Lagrange and Barycentric interpolations - 26 September 2022 - related to 323,345,471,735,1160 and all sections on Complement Diophantines, Complement Functions, Complementary Sets, Quadratic Forms, Riemann Zeta Function, Patterns in Primes, Polynomial Reconstruction Problem, Error correcting codes, Computational Learning Theory - Multivariate Polynomial Reconstruction over Finite Fields, Lagrange-Taylor-Barycentric interpolation, Jones-Sato-Wada-Wiens Theorem, Prime-Composite Complementation, Prime Number Theorem, Ulam Spiral, Ramsey 2-coloring of integers, Hilbert Tenth Problem, Unique Factorization , Matiyasevich-Robinson-Davis-Putnam Theorem, Post's Correspondence Problem, Question-Answering --------------------------------------------------------------------------------------------------------------------------- 1314.1 complement.py has been changed to import barycentric_interpolate(), lagrange() interpolators in SciPy and to plot the complement polynomial in matplotlib. 1314.2 Function complement_diophantine(enumerableset, interpol_algorithm="barycentric") has been changed to add parameter "interpolation_algorithm" and clauses to fit the elements of a complementary set to a polynomial by polyfit, barycentric interpolation or Lagrange interpolation based on values to interpol_algorithm={'polyfit','barycentric','lagrange'}. 1314.3 Lagrange interpolated polynomial (Section 3.3.3 - algorithm 1 - Decidability of Existence and Construction of a Complement of a given function - https://arxiv.org/abs/1106.4102v1) interpolated earlier is of arbitrary degree and plotted as a graph in matplotlib written as JPEG in testlogs/complement.jpg. 1314.4 There is a Taylor series interpolation variant which approximates a function at pre-defined point in terms of existence of derivatives at that point. This was mentioned in Google Groups post by author (in ID [email protected] deleted by Yahoo because of cybercrime per author's request) in 2003 which mooted the question of Complement of a Function - https://groups.google.com/g/sci.math/c/RqsDNc6SBdk/m/Lgc0wLiFhTMJ - contents of the thread have been saved and committed to python-src/testlogs/ComplementOfAFunction_GoogleGroupsThread_2003.html 1314.5 Polynomial interpolations could serve as tools to quantify Question-Answering as polynomials where set of ordered pairs (question(i),score_for_answer_to_question(i)) are interpolated. Section 864.63 of NeuronRain Design - https://neuronrain-documentation.readthedocs.io/en/latest/ - delves into learning theory and complexity lower bounds aspects of Question-Answering in multiple choice and boolean setting. Complementation has nice implications for Question-Answering in boolean setting E.g. For 10 Questions of Binary Yes-No answers, if all 10 questions are answered correctly in the form of a vector [1,0,0,1,0,1,1,1,0] and interpolated by a polynomial over GF[2], its complement polynomial over GF[2] represents "all wrong answers" defined by complement vector [0,1,1,0,1,0,0,0,1].
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1313. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Comparison of Raster Data Bounding Boxes between 2 dates - 23 September 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301,1304,1312 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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------------------------------------------------------------------------------------------------------------------------------ 1313. (THEORY and FEATURE) GIS Urban Sprawl Analytics - Comparison of Raster Data Bounding Boxes between 2 dates - 23 September 2022 - related to 1174,1175,1177,1179,1194,1211,1234,1290,1291,1292,1295,1296,1297,1301,1304,1312 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 ------------------------------------------------------------------------------------------------------------------------------ 1313.1 New function compare_raster_data(raster1data,raster2data) computes dictionary histograms from longitude-latitude rectangle bounding boxes data returned by urban_sprawl_from_raster() for 2 GeoTIFF Rasters of 2 time points belonging to same genre. Two Rasters of same datatype (e.g Degree of Urbanization - R2019A and R2022A) are separated by time duration which could be in years. This kind of comparison has no assumption on scale of imagery as same longitude-latitudes are taken into account. 1313.2 Contents of 2 Dictionary histograms are iterated and percentage change of each bin is printed (as 100*(earlierdate - laterdate)/earlierdate) - Negative percentages imply expansion and Positive percentages imply contraction. Following 2 rasters from GHSL SMOD R2019A and R2022A are compared for change in urbanization between Chennai Metropolitan Sprawl Bounding Boxes of same dimensions and ordinates separated by 3 years: r1data=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 R2019A") r2data=urban_sprawl_from_raster(79.07,12.41,80.3,13.19,"testlogs/RemoteSensingGIS/GHS_SMOD_P2030_GLOBE_R2022A_54009_1000_V1_0.tif",dt="Degree of Urbanization R2022A") compare_raster_data(r1data,r2data) 1313.3 Findings of compare_raster_data() from python-src/image_pattern_mining/ImageNet/testlogs/GISUrbanSprawlAnalytics.log.23September2022 for R2019A and R2022A earlier in a nutshell (changes of class pixels as per 1312.7 in percentages - negative percentages imply expansion of the class pixels): urbansprawl_gini_coefficient(): Gini Index of the dataset = 0.1731406144601959 urbansprawl_gini_coefficient(): Gini Index of the dataset = 0.1922834751670601 compare_raster_data(): raster1hist = defaultdict(<class 'int'>, {13: 1454, 11: 3896, 23: 241, 12: 2353, 30: 1040, 21: 148, 22: 5, 10: 535}) compare_raster_data(): raster2hist = defaultdict(<class 'int'>, {21: 4047, 11: 1238, 12: 2023, 30: 1504, 23: 260, 10: 573, 13: 14, 22: 13}) Percentage change in 13 : 99.03713892709766 Percentage change in 11 : 68.22381930184805 Percentage change in 23 : -7.883817427385892 Percentage change in 12 : 14.024649383765405 Percentage change in 30 : -44.61538461538462 Percentage change in 21 : -2634.459459459459 Percentage change in 22 : -160.0 Percentage change in 10 : -7.102803738317758 1313.4 Gini coefficient of inequality has increased from 0.17 to 0.19 in 3 years. Following urban and water classes have undergone expansion between 2019 and 2022 for same Chennai Metropolitan Area bounding box sprawl (by negative percentages earlier coinciding with or even bettering Image Facegraph Polya Urn UGM projections): — Class 30: “Urban Centre grid cell”, if the cell belongs to an Urban Centre spatial entity; (44% expansion in City area) — Class 23: “Dense Urban Cluster grid cell”, if the cell belongs to a Dense Urban Cluster spatial entity; (7% expansion in dense metro area) — Class 22: “Semi-dense Urban Cluster grid cell”, if the cell belongs to a Semi-dense Urban Cluster (160% expansion in semi-dense metro area) — Class 21: “Suburban or per-urban grid cell”, if the cell belongs to an Urban Cluster cells at first (Massive 2634% expansion implying suburban fringe has witnessed an abnormal boom) — Class 10: “Water grid cell”, if the cell has 0.5 share covered by permanent surface water and is not (7% expansion of waterbodies) 1313.5 Following rural classes have contracted between 2019 and 2022 (by positive percentages): — Class 13: “Rural cluster grid cell”, if the cell belongs to a Rural Cluster spatial entity; (99% decrease in rural clusters) — Class 12: “Low Density Rural grid cell”, if the cell is classified as Rural grid cells at first hierarchical level, has more than 50 inhabitant and is not part of a Rural Cluster; (14% decrease in low density rural regions) — Class 11: “Very low density rural grid cell”, if the cell is classified as Rural grid cells at first hierarchical (68% decrease in very low density rural regions)
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