R2 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0101 0011 1111 1111 0000 0000 1110 0101 1111 1111 1111 1111 0101 1010 0000 0000 R1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1100 1100 1111 1111 1111 1111 0101 0011 1111 1111 1001 0101 0000 0000 G2 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1010 1011 0000 1010 1111 1111 0011 0010 1111 1111 1111 1111 1111 0011 1001 0100 R2 000 01001100 01010011 11100101 01011010 R1 000 00110100 11001100 01010011 10010101 G1 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 1111 R 2.2 2 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1010 1011 0000 1010 1111 1100 0011 0010 0100 1111 1111 1111 1111 0011 1001 0100 B2 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1111 1111 0000 0000 1001 0110 0000 0000 1111 1111 1111 0101 1010 1001 0010 0100 2.4 2.5 2.0: 01010011 2.3: 11100101 2.6: 01011010 R1 2.2 2.3 2.5 2.1: 11001100 2.4: 01010011 2.6: 10010101 B1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 G2 G1 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1010 0111 1000 0101 1111 1111 0000 0000 0100 1101 0101 1010 1001 1001 0110 0001 G2 0 G1 0 2.2 100 2.2 To AND G2 with B2 for example, 2.4 2.4 2.5 2.4 (since it is a common pure1) 00101100 2.5 2.0: 10101011 2.0: 11001100 2.0: 10101011 (since 2.0 is pure1 in B2) 2.1: 00001010 10101011 00001010 00110010 11110011 10010100 2.4: 01010011 2.2: 10010110 (since 2.2 is pure1 in G2) 2.3: 00110010 2.6: 10010101 100 2.5: 11110101 (since 2.5 is pure1 in G2) 2.6: 11110011 2.7: 10010100 2.6: 11110011 (mixed in G2) 00110100 11001100 01010011 10010101 B2 000 10001000 10010110 11110101 10101001 00100100 B1 000 10101001 (mixed in B2) 2.7: 10100001 10010100 (mixed in G2) B2 2.0 B1 2.2 00100100 (mixed in B2) 2.4 2.0: 10100111 00000100 2.2: 10010110 2.1: 10000101 2.5: 11110101 2.6: 10101001 2.7: 00100100 00100000 10100111 10000101 01001101 01011010 10101001 01100001 2.4: 2.5: 2.6: 2.7: 01001101 01011010 10011001 01100001
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Convergent, Dense Sub-Corpuses: CDSC(w=0%, d=10%, DS0=doc1) DS0 = {doc1} WS1=Voc(DS0)={words in > 0% of DS0} WORD 35SSS 07OMH 35SSS 50LJH 07OMH 13RRS 35SSS 50LJH 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 4 0 1 0 0 1 1 0 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 1 1 1 0 1 0 1 0 8 0 0 0 0 0 0 0 0 9 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 0 1 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 1 0 1 0 0 0 1 0 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 1 0 1 0 0 0 1 0 4 0 1 0 0 1 0 0 0 5 1 0 1 1 0 0 1 1 6 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 8 1 0 1 0 0 0 1 0 9 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 1 0 1 0 0 0 1 0 4 1 0 1 0 0 0 1 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 1 0 1 0 0 0 1 0 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 4 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 0 1 0 0 1 0 0 0 3 1 0 1 0 0 0 1 0 4 0 1 0 0 1 0 0 0 5 1 0 1 1 0 0 1 1 6 0 0 0 0 0 0 0 0 7 0 0 0 1 0 1 0 1 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 5 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 3 0 0 0 1 0 0 0 1 4 0 0 0 0 0 1 0 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 07OMH 13RRS 21LAU 35SSS 50LJH 10JAJ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 DS1={docs with > 15% of WS1} CDSC(w=0,d=10, DS0=35SSS) conv to DS4={7,10,13,21,35,50}, WS4={4,7,9,10,12,13,14,17,19,23,24,25,26,28,32,33,34,37,40,42,43,44,45,47,50,51,53,54 ED=41/28*6=24.4%. Lowering the DS%ofVocab from 15% to 10% decreases ED (Because it increases DSSize from 3 to 6?). WS2=Voc(DS1)={words in >0% of DS1} DS2={docs with > 15% of WS2} ... 10% of 13 = 1.3 D bbc O a r l C keo e at dh 11 707 1 000 2 000 3 000 4 000 5 000 6 000 7 110 8 000 9 000 10 0 0 0 1 001 2 000 3 000 4 000 5 000 6 000 7 000 8 000 21 0 1 0 2 000 3 000 5 000 6 000 7 000 8 000 9 000 30 0 0 0 2 000 3 000 5 111 6 000 7 001 8 000 9 000 41 0 0 0 2 100 3 000 4 000 5 000 6 000 7 000 8 000 9 000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ef hk auoi t l un l s g e 2233 5834 0000 0000 0000 1000 0001 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0100 0000 0000 0000 0000 1111 0010 0000 0000 0000 0001 0000 0000 0000 0000 1000 0000 0000 0000 mmn a oo i ns de e y 344 703 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 000 000 000 000 000 000 000 000 000 111 000 000 010 000 000 000 000 000 000 000 000 100 000 10% of 21 = 2.1 ps i i e n g 45 50 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 11 00 00 00 10 00 00 00 00 00 00 00 00 00 bbbbbc aaor ul ckye yo ke a t d h 111 479037 000000 000000 000000 000000 000000 000000 110110 000000 000000 000000 000001 000000 100010 000000 000000 000000 000000 000000 000100 000000 100000 000000 000000 000000 001000 000000 000000 000000 000010 010101 000000 000001 000000 001000 000000 010000 000000 000000 000010 000000 000000 000000 000000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 de f h oa uo gt l u l s e 2223 4583 0000 0000 0000 0100 0000 0000 1000 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0111 0001 0000 0000 0000 0000 0000 1000 0000 0000 0100 0000 0000 0000 k i n g 3 4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 10% of 23 = 2.3 m m mn a o oo i n ts d e he y er 3 4 44 7 0 23 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 10 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 01 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 10 0 0 00 0 0 00 0 0 00 1 1 01 0 0 00 0 0 00 0 1 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 00 1 0 00 0 0 00 opps l i i i de un mg 4445 4570 0000 0000 0000 0000 0000 0000 1000 0000 0000 1000 1000 1000 0010 0000 0001 0000 0000 0000 0010 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0101 0000 0000 0000 0100 1000 0000 0000 0000 0000 0000 0000 0000 0000 t h u m b 5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bbbbbc aa or ul ckye yo ke a t d h 111 479037 000000 000000 000000 000000 000000 000000 110110 000000 000000 000000 000001 000000 100010 000000 000000 000000 000000 000000 000100 000000 100000 000000 000000 000000 001000 000000 000000 000000 000010 010101 000000 000001 000000 001000 000000 010000 000000 000000 000010 000000 000000 000000 000000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 de f h oa uo gt l u l s e 2223 4583 0000 0000 0000 0100 0000 0000 1000 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0111 0001 0000 0000 0000 0000 0000 1000 0000 0000 0100 0000 0000 0000 10% of 26 = 2.6 k i n g 3 4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 m m mn a o oo i n t s de he y er 34 44 70 23 00 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 10 00 00 00 10 00 00 00 00 00 00 11 01 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 00 10 00 00 00 o l d 4 4 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 pps s t t i i i oho e u n nuw m g mn b 4 4 5 555 5 7 0 134 0 0 0 000 0 0 0 000 0 0 0 100 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 1 0 101 0 0 0 000 0 0 1 000 0 0 0 000 0 0 0 000 0 0 0 000 0 1 0 001 0 0 0 010 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 1 0 1 000 0 0 0 000 0 0 0 000 0 0 0 000 1 0 0 000 0 0 0 000 0 0 0 000 0 0 0 001 0 0 0 000 0 0 0 000 0 0 0 100 0 0 0 000 0 0 0 000 0 0 0 000 bbbbbc aa or ul ckye yo ke a t d h 111 479037 000000 000000 000000 000000 000000 000000 110110 000000 000000 000000 000001 000000 100010 000000 000000 000000 000000 000000 000100 000000 100000 000000 000000 000000 001000 000000 000000 000000 000010 010101 000000 000001 000000 001000 000000 010000 000000 000000 000010 000000 000000 000000 000000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 de f h oa uo gt l u l s e 2223 4583 0000 0000 0000 0100 0000 0000 1000 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0111 0001 0000 0000 0000 0000 0000 1000 0000 0000 0100 0000 0000 0000 k i n g 3 4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 m m mn a o oo i n t s de he y er 34 44 70 23 00 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 10 00 00 00 10 00 00 00 00 00 00 11 01 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 00 10 00 00 00 opps l i i i de un mg 4445 4570 0000 0000 0000 0000 0000 0000 1000 0000 0000 1000 1000 1000 0010 0000 0001 0000 0000 0000 0010 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0101 0000 0000 0000 0100 1000 0000 0000 0000 0000 0000 0000 0000 0000 s t t b cc o h o r ar n u w o ko mn w e w n n b 5 5 5 1 11 1 3 4 2 49 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 1 01 0 0 0 0 00 0 0 0 0 00 1 0 1 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 1 1 11 0 1 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 10 0 0 1 0 00 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 f h ai l l l l 23 62 00 00 00 00 10 00 00 00 00 11 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00
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WORD 35SSS 07OMH 35SSS 50LJH 07OMH 13RRS 35SSS 50LJH 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 4 0 1 0 0 1 1 0 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 1 1 1 0 1 0 1 0 8 0 0 0 0 0 0 0 0 9 0 0 0 1 0 0 0 1 1 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 0 1 0 0 1 1 0 0 4 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 1 0 1 0 0 0 1 0 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 1 0 1 0 0 0 1 0 4 0 1 0 0 1 0 0 0 5 1 0 1 1 0 0 1 1 6 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 8 1 0 1 0 0 0 1 0 9 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 3 1 0 1 0 0 0 1 0 4 1 0 1 0 0 0 1 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 1 0 1 0 0 0 1 0 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 4 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 0 0 0 2 0 1 0 0 1 0 0 0 3 1 0 1 0 0 0 1 0 4 0 1 0 0 1 0 0 0 5 1 0 1 1 0 0 1 1 6 0 0 0 0 0 0 0 0 7 0 0 0 1 0 1 0 1 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 5 0 1 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 3 0 0 0 1 0 0 0 1 4 0 0 0 0 0 1 0 0 5 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 07OMH 13RRS 21LAU 35SSS 50LJH 10JAJ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Second alg: DocSet1={doc1} Vocab1 =Vocab(DocSet1) DocSet2 =all docs with 10% of Vocab1 Vocab2 =Vocab(DocSet2) DocSet3 =all docs with 10% of Vocab2 ... So it converges to the 6 document set, {7,13,21,35,50} with Vocabulary = the 28words, {4,7,9,10,12,13,14,17,19,23,24,25,26,28,32,33,34,37,40,42,43,44,45,47,50,51,53,54} EdgeDensity is 41/28*6 = 41/360 = 24.4% 10% of 13 = 1.3 D bbc O a r l C keo e at dh 11 707 1 000 2 000 3 000 4 000 5 000 6 000 7 110 8 000 9 000 10 0 0 0 1 001 2 000 3 000 4 000 5 000 6 000 7 000 8 000 21 0 1 0 2 000 3 000 5 000 6 000 7 000 8 000 9 000 30 0 0 0 2 000 3 000 5 111 6 000 7 001 8 000 9 000 41 0 0 0 2 100 3 000 4 000 5 000 6 000 7 000 8 000 9 000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ef hk auoi t l un l s g e 2233 5834 0000 0000 0000 1000 0001 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0100 0000 0000 0000 0000 1111 0010 0000 0000 0000 0001 0000 0000 0000 0000 1000 0000 0000 0000 mmn a oo i ns de e y 344 703 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 000 000 000 000 000 000 000 000 000 111 000 000 010 000 000 000 000 000 000 000 000 100 000 10% of 21 = 2.1 ps i i e n g 45 50 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 11 00 00 00 10 00 00 00 00 00 00 00 00 00 bbbbbc aaor ul ckye yo ke a t d h 111 479037 000000 000000 000000 000000 000000 000000 110110 000000 000000 000000 000001 000000 100010 000000 000000 000000 000000 000000 000100 000000 100000 000000 000000 000000 001000 000000 000000 000000 000010 010101 000000 000001 000000 001000 000000 010000 000000 000000 000010 000000 000000 000000 000000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 de f h oa uo gt l u l s e 2223 4583 0000 0000 0000 0100 0000 0000 1000 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0111 0001 0000 0000 0000 0000 0000 1000 0000 0000 0100 0000 0000 0000 k i n g 3 4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 10% of 23 = 2.3 m m mn a o oo i n ts d e he y er 3 4 44 7 0 23 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 10 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 01 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 10 0 0 00 0 0 00 0 0 00 1 1 01 0 0 00 0 0 00 0 1 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 00 1 0 00 0 0 00 opps l i i i de un mg 4445 4570 0000 0000 0000 0000 0000 0000 1000 0000 0000 1000 1000 1000 0010 0000 0001 0000 0000 0000 0010 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0101 0000 0000 0000 0100 1000 0000 0000 0000 0000 0000 0000 0000 0000 t h u m b 5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 bbbbbc aa or ul ckye yo ke a t d h 111 479037 000000 000000 000000 000000 000000 000000 110110 000000 000000 000000 000001 000000 100010 000000 000000 000000 000000 000000 000100 000000 100000 000000 000000 000000 001000 000000 000000 000000 000010 010101 000000 000001 000000 001000 000000 010000 000000 000000 000010 000000 000000 000000 000000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 de f h oa uo gt l u l s e 2223 4583 0000 0000 0000 0100 0000 0000 1000 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0111 0001 0000 0000 0000 0000 0000 1000 0000 0000 0100 0000 0000 0000 10% of 26 = 2.6 k i n g 3 4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 m m mn a o oo i n t s de he y er 34 44 70 23 00 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 10 00 00 00 10 00 00 00 00 00 00 11 01 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 00 10 00 00 00 o l d 4 4 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 pps s t t i i i oho e u n nuw m g mn b 4 4 5 555 5 7 0 134 0 0 0 000 0 0 0 000 0 0 0 100 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 1 0 101 0 0 0 000 0 0 1 000 0 0 0 000 0 0 0 000 0 0 0 000 0 1 0 001 0 0 0 010 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 1 0 1 000 0 0 0 000 0 0 0 000 0 0 0 000 1 0 0 000 0 0 0 000 0 0 0 000 0 0 0 001 0 0 0 000 0 0 0 000 0 0 0 100 0 0 0 000 0 0 0 000 0 0 0 000 bbbbbc aa or ul ckye yo ke a t d h 111 479037 000000 000000 000000 000000 000000 000000 110110 000000 000000 000000 000001 000000 100010 000000 000000 000000 000000 000000 000100 000000 100000 000000 000000 000000 001000 000000 000000 000000 000010 010101 000000 000001 000000 001000 000000 010000 000000 000000 000010 000000 000000 000000 000000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 de f h oa uo gt l u l s e 2223 4583 0000 0000 0000 0100 0000 0000 1000 0100 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0000 1000 0000 0000 0111 0001 0000 0000 0000 0000 0000 1000 0000 0000 0100 0000 0000 0000 k i n g 3 4 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 m m mn a o oo i n t s de he y er 34 44 70 23 00 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 10 00 00 00 10 00 00 00 00 00 00 11 01 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 00 10 00 00 00 opps l i i i de un mg 4445 4570 0000 0000 0000 0000 0000 0000 1000 0000 0000 1000 1000 1000 0010 0000 0001 0000 0000 0000 0010 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0101 0000 0000 0000 0100 1000 0000 0000 0000 0000 0000 0000 0000 0000 s t t b cc o h o r ar n u w o ko mn w e w n n b 5 5 5 1 11 1 3 4 2 49 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 1 01 0 0 0 0 00 0 0 0 0 00 1 0 1 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 1 1 11 0 1 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 10 0 0 1 0 00 0 0 0 0 00 0 0 0 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 f h ai l l l l 23 62 00 00 00 00 10 00 00 00 00 11 00 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00
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1 2 3 4 5 6 WORD 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 DS0 26SBS 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 DS1 08JSC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 09HBD 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12OWF 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 26SBS 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 27CBC 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 28BBB 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 29LFW 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 38YLS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 39LCS 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 45BBB 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 07OMH 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 08JSC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 09HBD 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 DS2 0 0 12OWF 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 26SBS 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 27CBC 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 28BBB 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 29LFW 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 35SSS 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 38YLS 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 39LCS 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 41OKC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 45BBB 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 46TTP 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 50LJH 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 DS307OMH 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 26SBS 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 DS428BBB 30HDD 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 35SSS 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 39LCS 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 41OKC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 46TTP 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 50LJH 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 Convergent, Dense Sub-Corpuses: CDSC(w=0%, d=15%, DS0={26}) then CDSC(w=0%, d=10%,DS0=26) Using 10%, it converges to DS4{7,26,28,30,35,39,41,46,50} with a 39 word Vocab and an EdgeDensity of 58/39*9 = 58/351 = 16.5%. So far EdgeDens*DSSize: 55.6*2=111.2 39.7*3=119 24.4*6=146 16.5*9=149 6.3*44=277. DSSizes 2,3,6,9,44 The 4 Deltas from DSS=2 are 1,4,7,42. Multiplied by 8; 8, 32, 56, 336. Subtracting these 8*Delta values from ED*DSS, we get scores of 111, 111, 114, 93, -59. 10% of 7=.7 Vocab(DS1) D O C u m e nt 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 21 2 3 5 6 7 8 9 30 2 3 5 6 7 8 9 41 2 3 4 5 6 7 8 9 ab c c g l a hl r wb i e e ay l a e y dnn s 113 13 5 6 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 0 01 0 0 0 00 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 11 1 1 1 01 0 0 0 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 1 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 l w ao mo bl 36 60 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 11 00 01 00 00 00 00 00 00 00 10 00 00 00 00 00 00 00 00 00 00 10% of 26=2.6 Vocab(DocSet2) a ab l wa wa b a yy y s 123 000 000 000 010 000 000 000 000 001 000 000 000 000 000 000 000 000 000 000 000 000 000 101 001 000 110 010 000 000 000 000 000 000 010 000 000 000 000 001 010 000 000 000 b b b bc a e o uh g d y yi l d 11 6 8 9 35 0 0 0 00 0 0 0 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 10 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 00 1 0 1 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 1 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 10 0 0 0 00 0 1 0 00 0 0 0 00 0 0 0 00 c l e a n 1 6 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c o c k 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 c e f gl r a ura y t l ed l ey n 2 2 2 33 0 5 8 05 0 0 0 00 0 0 0 00 0 0 0 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 0 00 0 0 0 01 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 10 1 0 0 00 1 0 1 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 1 00 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 00 1 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 l mm m o a eool mr n t d b r e h y y er 3 34 4 4 6 90 2 4 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 1 1 0 00 0 0 0 00 1 0 0 00 0 1 0 00 0 1 0 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 1 00 0 0 0 00 1 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 00 0 0 0 00 0 0 1 01 0 0 0 10 0 0 0 10 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 p t t ww w i hr i oo e r e f mo e e ea l e n 4 5 5 55 6 5 2 5 89 0 0 1 0 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 10 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 01 0 0 0 0 00 0 0 0 1 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 1 0 00 0 0 0 0 01 0 0 0 0 00 1 0 0 0 00 0 0 1 0 00 1 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 1 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 1 0 1 00 0 0 1 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 0 0 00 0 0 1 0 00 0 0 0 0 00 0 Additions: 10% of 43=4.3 Vocab(DocSet3-DocSet2) bb aa ck ke 47 00 00 00 00 00 00 11 00 00 00 00 00 10 00 00 00 00 00 00 00 10 00 00 00 00 00 00 00 00 01 00 00 00 00 00 01 00 00 00 00 00 00 00 b r e a d 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 c l o t h 1 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 df hk oi oi gdun ds g le e 2233 4734 0000 0000 0000 0000 0001 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1100 0100 0000 0011 0010 0000 0000 0000 0101 0000 1000 0000 0000 0000 0000 0000 0000 mn e o ns e 34 83 00 00 00 00 10 00 00 00 00 00 10 00 00 10 00 00 10 00 00 01 00 00 00 00 00 00 00 10 00 01 10 00 00 00 00 00 00 00 00 00 00 00 00 ppr s i i ui gunn m g 4445 6790 0010 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0100 0000 0001 0000 0010 0000 0100 0000 0000 0000 0000 0000 0000 0000 0010 0000 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0000 1010 0000 0000 0000 s t oh nu m b 55 13 00 00 10 00 00 00 00 00 00 00 00 00 10 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00 Additions: 10% of 39=3.9 Vocab(DocSet4) D a a b O l wa C wa b u a yy m y e s nt 1 2 3 1 000 2 000 3 000 4 010 5 000 6 000 7 000 8 000 9 001 10 0 0 0 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 21 0 0 0 2 000 3 000 5 000 6 101 7 001 8 000 9 110 30 0 1 0 2 000 3 000 5 000 6 000 7 000 8 000 9 010 41 0 0 0 2 000 3 000 4 000 5 001 6 010 7 000 8 000 9 000 b b b bc a e o uh g d y yi l d 11 6 8 9 35 0 0 0 00 0 0 0 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 10 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 00 1 0 1 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 1 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 10 0 0 0 00 0 1 0 00 0 0 0 00 0 0 0 00 c l e a n 1 6 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 c o c k 1 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 c e f gl r a ura y t l ed l ey n 2 2 2 33 0 5 8 05 0 0 0 00 0 0 0 00 0 0 0 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 0 00 0 0 0 01 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 10 1 0 0 00 1 0 1 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 1 00 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 00 1 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 l mm m o a eool mr n t d b r e h y y er 3 34 4 4 6 90 2 4 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 1 1 0 00 0 0 0 00 1 0 0 00 0 1 0 00 0 1 0 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 1 00 0 0 0 00 1 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 0 00 0 0 0 00 0 0 1 01 0 0 0 10 0 0 0 10 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 p t t ww w b b i hr i ooaa e r e f mo c k e e ea l ke e n 4 5 5 55 6 5 2 5 89 047 0 1 0 10 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 011 0 0 0 10 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 01 000 0 0 0 00 010 0 0 1 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 1 0 00 010 0 0 0 01 000 0 0 0 00 100 0 0 0 00 000 0 1 0 00 100 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 1 0 0 00 001 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 1 0 1 00 000 0 1 0 00 000 0 0 0 00 001 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 0 0 00 000 0 1 0 00 000 0 0 0 00 000 b r e a d 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 c l o t h 1 7 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 df hk oi oi gdun ds g le e 2233 4734 0000 0000 0000 0000 0001 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 1100 0100 0000 0011 0010 0000 0000 0000 0101 0000 1000 0000 0000 0000 0000 0000 0000 mn e o ns e 34 83 00 00 00 00 10 00 00 00 00 00 10 00 00 10 00 00 10 00 00 01 00 00 00 00 00 00 00 10 00 01 10 00 00 00 00 00 00 00 00 00 00 00 00 ppr s i i ui gunn m g 4445 6790 0010 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0100 0000 0001 0000 0010 0000 0100 0000 0000 0000 0000 0000 0000 0000 0010 0000 0000 0001 0000 0000 0000 0000 0000 0000 0000 0000 0000 1010 0000 0000 0000 s t oh nu m b 55 13 00 00 10 00 00 00 00 00 00 00 00 00 10 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 10 00 00 00
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86 As the table grows: 41 11 11 10 09 31 14 08 06 07 10 10 04 4331 3233 2341 4113 1223 2211 1222 1423 1423 22 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 11 89 41 11 11 10 09 31 17 08 06 07 10 10 07 4331 3233 2341 4113 1223 2211 1222 1423 1423 223 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 94 41 11 11 10 09 31 22 08 06 07 10 10 11 01 4331 3233 2341 4113 1223 2211 1222 1423 1423 2234 1 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 01 95 41 11 11 10 09 31 23 08 06 07 10 10 11 02 4331 3233 2341 4113 1223 2211 1222 1423 1423 2234 11 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 000
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From the discussion on the previous slide, it seem practical to have the same fanout through out the tree?. Otherwise it is very difficult to even identify inodes (e.g., what does 2.2 mean). global_fanout= 4 for images, 8 for solids, 64 for sparse numeric non-spatial data cols?, 1024 for very sparse numeric data columns and for high cardinality bitmapped categorical columns????? On the other hand, maybe a database_global_fanout so that the processing code is simpler??? global_fanout=5: 86 69 17 17 17 11 11 13 17 53333 42443 31331 43121 32152 34334 11111 01110 11001 00111 10101 10111 10010 11011 11110 10011 11100 00100 11100 10011 00100 11011 11001 01000 01 010 00010 01011 00110 01000 11111 10010 11100 10111 10110 01110 11011 global_fanout=4: 86 41 11 11 10 09 04 31 14 08 06 07 10 10 4331 3233 2341 4113 1223 2211 1222 1423 1423 22 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 11 As the table grows: 86 41 11 11 10 09 31 14 08 06 07 10 10 04 4331 3233 2341 4113 1223 2211 1222 1423 1423 22 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 11 89 41 11 11 10 09 31 17 08 06 07 10 10 07 4331 3233 2341 4113 1223 2211 1222 1423 1423 223 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 94 41 11 11 10 09 31 22 08 06 07 10 10 11 01 4331 3233 2341 4113 1223 2211 1222 1423 1423 2234 1 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 01
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1 119 31 36 As the table continues to grow: 11 08 06 07 10 10 11 07 08 10 01 4113 1223 2211 1222 1423 1423 2234 1141 3230 4420 1 10 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 0001 1111 0001 1110 0011 1101 0000 1111 1111 0101 0000 1000 1 125 31 36 17 08 06 07 10 10 11 07 08 10 06 01 4113 1223 2211 1222 1423 1423 2234 1141 3230 4420 1041 1 10 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 0001 1111 0001 1110 0011 1101 0000 1111 1111 0101 0000 1000 0000 1111 0100 0001 1 131 31 36 23 08 06 07 10 10 11 07 08 10 06 05 02 4113 1223 2211 1222 1423 1423 2234 1141 3230 4420 1041 1040 2 010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 0001 1111 0001 1110 0011 1101 0000 1111 1111 0101 0000 1000 0000 1111 0100 0001 0000 1111 0000 0110 1 132 131 31 01 36 08 06 07 10 23 01 10 11 07 08 10 06 05 02 4113 1223 2211 1222 1423 1423 2234 01 1141 3230 4420 1041 1040 2000 1 010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 0001 1111 0001 1110 0011 1101 0000 1111 1111 0101 0000 1000 0000 1111 0100 0001 0000 1111 0000 0110 0000 0000 0000 0100
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95 As the table continues to grow:11 41 11 10 09 31 23 08 06 07 10 10 11 02 4331 3233 2341 4113 1223 2211 1222 1423 1423 2234 11 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 0001 103 41 11 11 10 09 31 31 08 06 07 10 10 11 07 03 4331 3233 2341 4113 1223 2211 1222 1423 1423 2234 1141 3 0 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 0001 1111 0001 1110 108 41 11 11 10 09 31 36 08 06 07 10 10 11 07 08 4331 3233 2341 4113 1223 2211 1222 1423 1423 2234 1141 3230 44 0 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 0001 1111 0001 1110 0011 1101 0000 1111 1111 119 41 11 11 10 09 31 36 08 06 07 10 11 10 11 07 08 10 01 4331 3233 2341 4113 1223 2211 1222 1423 1423 2234 1141 3230 4420 1 0 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 1100 1011 1111 0100 0001 1111 0001 1110 0011 1101 0000 1111 1111 0101 0000 1000
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set 51 35 14 00010 set 49 30 14 00010 set 47 32 13 00010 set 46 31 15 00010 set 50 36 14 00010 set 54 39 17 00100 set 46 34 14 00011 set 50 34 15 00010 set 44 29 14 00010 set 49 31 15 00001 set 54 37 15 00010 set 48 34 16 00010 set 48 30 14 00001 set 43 30 11 00001 set 58 40 12 00010 set 57 44 15 00100 set 54 39 13 00100 set 51 35 14 00011 set 57 38 17 00011 set 51 38 15 00011 set 54 34 17 00010 set 51 37 15 00100 set 46 36 10 00010 set 51 33 17 00101 set 48 34 19 00010 set 50 30 16 00010 set 50 34 16 00100 set 52 35 15 00010 set 52 34 14 00010 set 47 32 16 00010 set 48 31 16 00010 set 54 34 15 00100 set 52 41 15 00001 ver 56 42 30 14 45 set 55 001 011 01 ver 58 31 27 15 41 set 49 001 0010 ver 62 32 22 12 45 set 50 001 011 01 ver 56 35 25 13 39 set 55 001 00 11 01 ver 59 31 32 15 48 set 49 01 00010 ver 61 30 28 13 40 set 44 001 0101 ver 63 34 25 15 49 set 51 001 011 01 ver 61 35 28 13 47 set 50 001 010 10 ver 64 23 29 13 43 set 45 001 010 11 ver 66 32 30 13 44 set 44 001 011 00 ver 68 35 28 16 48 set 50 00111 00 ver 67 38 30 19 50 set 51 01 00 1001 ver 60 30 29 14 45 set 48 001 0111 57 38 35 ver 58 26 16 40 set 51 00001 010 111 0000 55 32 24 14 38 ver 50 23 33 set 46 00001 010 101 0110 55 37 24 15 37 ver 56 27 42 set 53 00001 010 111 0001 58 33 27 14 39 ver 57 30 42 set 50 ID PL PW SL DPP 2 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1s1 1 151 0 35 0 14 2 60 0 1 1 1 100 2 0 1 1 0 0 0 1 0 1 1 1 1 0 0 0 0 1s2 1 149 0 30 0 14 2 59 0 1 1 1 011 2 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 1s3 1 047 1 32 0 13 2 60 0 1 1 1 100 2 0 1 0 1 1 1 0 0 1 1 1 1 1 0 0 0 1s4 1 146 1 31 0 15 2 58 0 1 1 1 010 2 0 1 1 0 0 1 0 1 0 0 1 0 0 0 0 0 1s5 1 150 0 36 0 14 2 60 0 1 1 1 100 4 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0s6 0 054 1 39 0 17 4 58 0 1 1 1 010 3 0 1 0 1 1 1 0 1 0 0 0 1 0 0 0 0 1s7 1 146 0 34 0 14 3 60 0 1 1 1 100 2 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 0 1s8 1 150 1 34 0 15 2 59 0 1 1 1 011 2 0 1 0 1 1 0 0 0 1 1 1 0 1 0 0 0 1s9 1 144 0 29 0 14 2 59 0 1 1 1 011 1 0 1 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1s10 1 149 1 31 0 15 1 58 0 1 1 1 010 2 0 1 1 0 1 1 0 1 0 0 1 0 1 0 0 0 1s11 1 154 1 37 0 15 2 60 0 1 1 1 100 2 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0s12 0 048 0 34 0 16 2 58 0 1 1 1 010 1 0 1 1 0 0 0 0 0 1 1 1 1 0 0 0 0 1s13 1 148 0 30 0 14 1 59 0 1 1 1 011 1 0 1 0 1 0 1 1 0 1 1 1 1 0 0 0 0 1s14 0 143 1 30 0 11 1 62 0 1 1 1 110 2 0 1 1 1 0 1 0 1 0 1 0 0 0 0 0 0 1s15 1 058 0 40 0 12 2 63 0 1 1 1 111 4 0 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1s16 1 157 1 44 0 15 4 61 0 1 1 1 101 4 0 1 1 0 1 1 0 1 0 0 1 1 1 0 0 0 1s17 1 054 1 39 0 13 4 61 0 1 1 1 101 3 0 1 1 0 0 1 1 1 0 0 0 1 1 0 0 0 1s18 1 151 0 35 0 14 3 60 0 1 1 1 100 3 0 1 1 1 0 0 1 1 0 0 1 1 0 0 0 1 0s19 0 057 1 38 0 17 3 58 0 1 1 1 010 3 0 1 1 0 0 1 1 1 0 0 1 1 0 0 0 0 1s20 1 151 1 38 0 15 3 60 0 1 1 1 100 2 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 1 0s21 0 054 1 34 0 17 2 57 0 1 1 1 001 4 0 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 1s22 1 151 1 37 0 15 4 59 0 1 1 1 011 2 0 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 1s23 0 146 0 36 0 10 2 64 1 0 0 0 000 5 0 1 1 0 0 1 1 1 0 0 0 0 1 0 0 1 0s24 0 051 1 33 0 17 5 56 0 1 1 1 000 2 0 1 1 0 0 0 0 1 0 0 0 1 0 0 0 1 0s25 0 148 1 34 0 19 2 56 0 1 1 1 000 2 0 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 0s26 0 050 0 30 0 16 2 57 0 1 1 1 001 4 0 1 1 0 0 1 0 1 0 0 0 1 0 0 0 1 0s27 0 050 0 34 0 16 4 57 0 1 1 1 001 2 0 1 1 0 1 0 0 1 0 0 0 1 1 0 0 0 1s28 1 152 1 35 0 15 2 59 0 1 1 1 011 2 0 1 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1s29 1 152 0 34 0 14 2 60 0 1 1 1 100 2 0 1 0 1 1 1 1 1 0 0 0 0 0 0 0 1 0s30 0 047 0 32 0 16 2 58 0 1 1 1 010 2 0 1 1 0 0 0 0 0 1 1 1 1 1 0 0 1 0s31 0 048 0 31 0 16 2 57 0 1 1 1 001 4 0 1 1 0 1 1 0 1 0 0 0 1 0 0 0 0 1s32 1 154 1 34 0 15 4 58 0 1 1 1 010 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 0 0 1s33 1 152 1 41 0 15 1 61 0 1 1 1 101 15 1111055 2 00111101101010 100111011100 0001001s34 01 42 0 14 2 62 0 1 1 1 110 10 1101049 1 00111101000110 001111101111 0001001s35 11 31 0 15 1 58 0 1 1 1 010 15 1110050 2 00111101011100 100100010100 0001001s36 01 32 0 12 2 61 0 1 1 1 101 11 0110155 2 00111101101010 100101001011 0001001s37 11 35 0 13 2 61 0 1 1 1 101 18 0101049 1 00111101000111 011010101010 0001011s38 10 31 0 15 1 58 0 1 1 1 e26 66 01 0 1 30 44 14 27 0 0 1 001 13 0 0 2 00110111110001 001111111000 00010011 s39 1 44 1 30 0 2 60 e27 28 13 48 14 230010111 11 01 068 1 34 15 0 0 2 00111101011111 100101001001 00010110 s40 1 1 51 1 0 15 2 59 e28 30 50 17 210010111 0 1 167 100 1 35 12 1 1 3 00111101011001 100101011010 00010010 s41 1 50 1 0 3 61 e29 29 13 45 15 260010111 1 0 160 13 1 23 3 01100010100010 001101111011 00010011 s42 100145 10 0 13 3 57 e30 57 26 35 10 360011101 00 10 100 14 1 2 01100010100100 100101010100 00010010 s43 1 44 1 32 0 13 2 60 e31 24 38 11 320011101 1 0 055 000 0 35 14 6 01101000011000 100101011010 00011100 s44 0 50 0 0 6 57 e32 24 16 37 10 330011101 0 0 155 17 151 0 38 4 01101000001111 100101111100 00011100 s45 0010 11 0 19 4 56 e33 58 27 39 12 320011101 00 00 0 0 15 1 1 1 3 00111101010000 001111111001 00010010 s46 1 1 48 0 30 0 14 3 58 e34 27 51 16 200010111 0 1 060 1 0 0 10 010 1 100101101100 00011000 1 1 12 1 0 2 001111010011 s47 0 0 51 0 38 0 2 59 e35 30 16 45 15 270010111 0 11 154 11 11100 1 100100 101 001 001 0 00010011 11046 0 32 10 010 2 0011011010 s48 01 0 14 2 59 e36 60 34 45 16 270010111 01 11 0 1 10 010 100 110 1 1001011001 011 0 00010011 0 1 0 13 0 2 00111101 s49 1 1 53 1 37 0 15 2 60 e37 31 47 15 240010111 1 00 067 101 0 10010101 00110 1 00010011 010 11150 1 33 12 2 001111010010 s50 00 0 14 2 60 0 1 1 1 IRIS(SL,SW,PL,PW)  DPPMinVec,MaxVEC vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 00 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 00 vir 00 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 01 vir 63 33 60 1001 58 27 51 0011 71 30 59 0101 63 29 56 0010 65 30 58 0110 76 30 66 0101 49 25 45 0001 73 29 63 0010 67 25 58 0010 72 36 61 1001 65 32 51 0100 64 27 53 0011 68 30 55 0101 57 25 50 0100 58 28 51 1000 64 32 53 0111 65 30 55 0010 77 38 67 0110 77 26 69 0111 60 22 50 1111 69 32 57 0111 56 28 49 0100 77 28 67 0100 63 27 49 0010 67 33 57 0101 72 32 60 0010 62 28 48 0010 61 30 49 0010 64 28 56 0101 72 30 58 0000 74 28 61 0011 79 38 64 0100 64 28 56 0110 63 28 51 1111 61 26 56 1110 77 30 61 0111 63 34 56 1000 64 31 55 0010 60 30 18 0010 69 31 54 0101 67 31 56 1000 69 31 51 0111 58 27 51 0011 68 32 59 25 19 21 18 22 21 17 18 18 25 20 19 21 20 24 23 18 22 23 15 23 20 20 18 21 18 18 18 21 16 19 20 22 15 14 23 24 18 18 21 24 23 19 23 0 0 1 0 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 0 1 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 0 0 1 1 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1 0 1 0 0 0 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 0 1 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 0 0 1 0 1 1 1 1 0 1 1 0 1 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 1 0 1 0 1 0 1 1 1 0 1 1 1 0 1 0 0 1 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 1 1 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 0 0 0 1 1 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 1 0 1 0 0 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 1 1 1 0 0 0 1 1 1 1 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 0 0 1 0 1 0 1 0 0 1 1 1 1 1 1 1 1 1 0 1 1 0 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 1 1 0 1 1 1 1 1 1 0 1 1 1 1 1 1 i1 1 163 00 33 60 25 10 0 0 0 1010 1 i2 0 058 11 27 51 19 19 0 0 1 0011 1 i3 1 071 11 30 59 21 11 0 0 0 1011 1 i4 1 063 00 29 56 18 15 0 0 0 1111 1 i5 1 065 10 30 58 22 12 0 0 0 1100 0 i6 0 076 10 30 66 21 5 0 0 0 0101 0 i7 1 149 01 25 45 17 24 0 0 1 1000 1 i8 1 173 11 29 63 18 8 0 0 0 1000 1 i9 1 067 10 25 58 18 12 0 0 0 1100 1 i10 1 172 0 136 61 25 10 0 0 01010 1 i11 0 065 1 132 51 20 19 0 0 10011 1 i12 0 164 0 127 53 19 16 0 0 10000 1 i13 0 168 1 130 55 21 15 0 0 01111 1 i14 0 057 1 025 50 20 19 0 0 10011 1 i15 0 058 1 128 51 24 17 0 0 10001 1 i16 0 164 0 132 53 23 17 0 0 10001 1 i17 0 165 1 130 55 18 16 0 0 10000 0 i18 0 077 1 138 67 22 6 0 0 0 0110 0 i19 0 177 0 126 69 23 0 0 0 0 0000 1 e50 001 57028 41 13 30 0 0 11110 1 i1 1 063 01 33 60 25 10 0 0 0 1010 1 i2 0 058 01 27 51 19 19 0 0 1 0011 0 i3 0 071 11 30 59 21 11 0 0 0 1011 1 i4 0 063 01 29 56 18 15 0 0 0 1111 1 i5 1 065 01 30 58 22 12 0 0 0 1100 1 i6 1 176 00 30 66 21 5 0 0 0 0101 1 i7 0 049 00 25 45 17 24 0 0 1 1000 1 i8 0 073 01 29 63 18 8 0 0 0 1000 1 i9 1 067 00 25 58 18 12 0 0 0 1100 1 i10 1 072 1 036 61 25 10 0 0 01010 1 i11 1 165 0 132 51 20 19 0 0 10011 0 i12 0 064 0 027 53 19 16 0 0 10000 1 i13 1 068 0 030 55 21 15 0 0 01111 1 i14 0 057 1 125 50 20 19 0 0 10011 1 i15 1 058 0 028 51 24 17 0 0 10001 1 i16 1 164 0 132 53 23 17 0 0 10001 1 i17 1 065 0 030 55 18 16 0 0 10000 1 i18 0 177 1 138 67 22 6 0 0 0 0110 1 i19 0 077 1 026 69 23 0 0 0 0 0000 1 i40 0 169 1 031 54 21 16 0 0 10000 1 i41 1 067 0 031 56 24 13 0 0 01101 1 i42 0 069 1 131 51 23 18 0 0 10010 1 i43 0 058 1 127 51 19 19 0 0 10011 1 i44 1 068 1 132 59 23 11 0 0
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HOB-CDSC DS0 Start with densest doc (35SSS). Then always choose using highest count (except when doing so results in a singleton, in which case include 2nd high count also). DS1 DS2 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ef hk auoi t l un l s g e 2233 5834 0000 0000 0000 1000 0001 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0100 0000 0000 0000 0000 1111 0010 0000 0000 0000 0001 0000 0000 0000 0000 1000 0000 0000 0000 2 0 0 0 0 3 0 0 0 0 4 0 1 0 0 5 0 0 0 0 6 0 0 0 0 7 1 1 1 0 8 0 0 0 0 9 0 0 0 1 1 0 1 1 1 0 1 0 0 0 0 2 0 0 0 0 3 0 1 0 0 4 0 0 0 0 5 0 0 0 0 6 0 0 0 0 7 1 0 1 0 8 0 0 0 0 9 0 0 0 0 2 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 1 0 1 0 4 0 1 0 0 5 1 0 1 1 6 0 0 0 0 7 0 0 0 0 8 1 0 1 0 9 0 0 0 0 3 0 0 0 0 0 1 0 0 0 0 2 0 0 0 0 3 1 0 1 0 4 1 0 1 0 5 0 0 0 0 6 0 0 0 0 7 1 0 1 0 8 0 0 0 0 9 0 0 0 0 4 0 1 0 1 0 1 0 0 0 0 2 0 1 0 0 3 1 0 1 0 4 0 1 0 0 5 1 0 1 1 6 0 0 0 0 7 0 0 0 1 8 0 0 0 0 9 0 0 0 0 5 0 1 0 1 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 1 4 0 0 0 0 5 0 0 0 0 6 0 0 0 0 7 0 0 0 0 8 0 0 0 0 9 0 0 0 0 6 0 0 0 0 0 07OMH 07OMH 13RRS 35SSS 45BBB 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 0 0 0 1 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 50LJH 35SSS 39LCS 50LJH 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Starting with 07OMH, the alg converges to Sub-Corpus DS={7,13,35,45} WS={4,7,10,13,42) with EdgeDensity=11/4*5=11/20= 55%. DS0 DS1 DS2 Starting with 50LJH, the alg converges to Sub-Corpus DS={35,39,50} WS={9,25,45) with EdgeDensity=7/3*3=7/9= 77.8%. WS2 mmn a oo i ns de e y 344 703 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 000 000 000 000 000 000 000 000 000 111 000 000 010 000 000 000 000 000 000 000 000 100 000 1 0 0 0 0 Starting with 35SSS, the alg converges to Sub-Corpus DS={7,35,50} WS={7,10,25,45) with an EdgeDensity= 8/3*4 = 8/12 = 66.7%. DS0 DS1 DS2 WS1 D bbc O a r l C keo e at dh 11 707 1 000 2 000 3 000 4 000 5 000 6 000 7 110 8 000 9 000 10 0 0 0 1 001 2 000 3 000 4 000 5 000 6 000 7 000 8 000 21 0 1 0 2 000 3 000 5 000 6 000 7 000 8 000 9 000 30 0 0 0 2 000 3 000 5 111 6 000 7 001 8 000 9 000 41 0 0 0 2 100 3 000 4 000 5 000 6 000 7 000 8 000 9 000 WORD 35SSS 07OMH 35SSS 50LJH ps i i e n g 45 50 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 11 00 00 00 10 00 00 00 00 00 00 00 00 00 bb e ar a ke t ea d 12 70 5 00 0 00 0 00 0 00 1 00 0 00 0 11 0 00 1 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 01 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 11 1 00 0 00 0 00 0 00 0 00 0 10 0 00 0 00 0 00 0 00 1 00 0 00 0 00 0 p i e 4 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 WS1 bb b aa r ck e ke a d 1 47 0 00 0 00 0 00 0 00 0 00 0 00 0 11 1 00 0 00 0 00 0 00 0 00 0 10 0 00 0 00 0 00 0 00 0 00 0 00 1 00 0 10 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 01 1 00 0 00 0 00 0 00 0 00 0 01 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 b d mo uool ygt d h er 1244 3424 0000 0000 0000 0000 0000 0000 1111 0000 0010 0001 0001 0001 1000 0000 0000 0000 0000 0000 0000 0000 0000 0001 0000 0010 0000 0010 0100 0000 1000 0000 0000 0000 0000 0000 0001 0000 0100 0000 1010 0000 0000 0000 0000 WS2 bb aa ck ke 47 00 00 00 00 00 00 11 00 00 00 00 00 10 00 00 00 00 00 00 00 10 00 00 00 00 00 00 00 00 01 00 00 00 00 00 01 00 00 00 00 00 00 00 b r e a d 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 WS1 b m be u o oa y t yt h er 1 4 2 3 2 95 0 0 00 0 0 00 0 0 00 0 0 01 0 0 00 0 0 00 1 1 00 0 0 01 0 1 00 0 0 00 0 0 00 0 0 00 1 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 1 00 0 0 10 0 1 00 0 0 00 0 0 00 1 0 00 0 0 01 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 00 0 0 00 0 0 00 1 1 00 0 0 01 0 0 00 0 0 00 0 0 00 ppt i i h e uu mm b 445 573 000 000 000 000 000 000 000 000 000 000 000 000 010 000 000 000 000 000 010 001 000 000 000 000 000 000 000 000 000 100 000 000 000 100 000 000 000 000 000 000 000 000 000 WS2 be p oa i yt e 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 5 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 4 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0
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Convergent, Dense Sub-Corpuses: 1 2 3 WORD 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 07OMH 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35SSS 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 4 0 1 2 3 4 5 6 7 8 9 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 5 0 1 2 3 4 5 6 7 8 9 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 6 0 0 0 CDSC(w=0%, d=10%, DS0={7,35}) DS0 = {7,35} WS1=Voc(DS0)={words in > 0% of DS0} DS1={docs with > 15% of WS1} WS2=Voc(DS1)={words in >0% of DS1} DS2={docs with > 15% of WS2} ... CDSC(w=0%,d=10%,DS0={7,35} converges to DS0={7,35} WS1={4,7,10,13,17,23,24,25,28,33,34,37,40,42,43,44,47,50}. ED=20/18*2=55.6% So far, ED*DSSizes = 55.6*2=111.2; 39.7*3=119; 24.4*6=146; 6.3*44=277; DSS progression 2,3,6,44; ED*DSS progression 111, 119, 146, 277; DSSs=1,4,42; *8 8,32,336. Subtract from ED*DSS; 111, 111, 114, -59. Using this (highly adjusted and odd) invariant, the 3 sub-corpuses measure out about the same and higher than the MG corpus Note: ED of a single document with its vocabulary is 100%. Lower bound DocCount or at least give DocCount along with the density (or maybe DocCount*EdgeDensity)? It is not yet clear what x%Vocab Document qualification gives us and what convergence under that condition gives us. Would it be best to start by finding large DSs with high ED and work downward using some downward closure condition? 15% of 18= 2.7 D bbb O aa o C cky ke 47 1 00 2 00 3 00 4 00 5 00 6 00 7 11 8 00 9 00 10 0 0 1 00 2 00 3 10 4 00 5 00 6 00 7 00 8 00 21 0 0 2 00 3 10 5 00 6 00 7 00 8 00 9 00 30 0 0 2 00 3 00 5 01 6 00 7 00 8 00 9 00 41 0 0 2 01 3 00 4 00 5 00 6 00 7 00 8 00 9 00 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 b r e a d 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 bc dd ul i o yos g t h h 1122 3734 0000 0000 0000 0000 0000 0000 1001 0000 0000 0000 0100 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0011 0000 1000 0110 0000 0100 0000 0000 0000 0000 0001 0000 1000 0000 0000 0000 0000 e f hk a uoi t l un l s g e 2233 5834 0000 0000 0000 1000 0001 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0100 0000 0000 0000 0000 1111 0010 0000 0000 0000 0001 0000 0000 0000 0000 1000 0000 0000 0000 m m mn a o oo i n ts d e he y er 3 4 44 7 0 23 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 10 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 01 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 10 0 0 00 0 0 00 0 0 00 1 1 01 0 0 00 0 0 00 0 1 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 00 1 0 00 0 0 00 opps l i i i de un mg 4445 4570 0000 0000 0000 0000 0000 0000 1000 0000 0000 1000 1000 1000 0010 0000 0001 0000 0000 0000 0010 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0101 0000 0000 0000 0100 1000 0000 0000 0000 0000 0000 0000 0000 0000 t h u m b 5 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
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partition requiring incidence count 2 (DS0 excepted of course). 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0 0 01 0 0 00 0 0 00 0 1 10 0 0 01 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 10 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 1 11 1 0 00 0 0 00 0 0 00 0 0 00 1 0 00 0 1 00 0 0 00 0 0 00 0 0 00 0 0 01 0 0 00 0 0 00 0 0 00 0 0 01 1 WS1WS3 b bbbm bbps t bbpb t b b m b l a a r uo aui o o aui r o a u o a a c ke yt cyun w c y ue w b y t b d k e a h k m n k ma n y h y y er d er d 1 14 145 5 1 41 5 1 4 3 4 7 0 32 4371 4 43 70 4 3 3 2 3 5 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 0 0 0 00 0001 0 00 00 0 0 0 0 0 0 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 1 1 1 11 1100 0 11 01 0 0 1 1 0 0 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 0 0 0 01 0000 0 00 00 0 1 0 1 1 1 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 0 0 0 00 0000 0 00 00 0 0 0 0 0 0 1 0 0 10 1111 1 11 10 1 0 1 0 0 0 0 0 0 00 0000 0 00 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0 0 0 00 0010 0 00 10 0 0 0 0 0 0 m b m bb c c p t bc p t o a o r r ar i o r r i o t b t e o ko u w oo u w h y h awe wmn wwmn er er dn n nn 4 4 11 11 4 5 11 4 5 2 3 2 02 49 7 4 29 7 4 b c m b m bc f hp a r o a o rr ai i b y t b t oo l l e y h y h wwl l er er nn 2 4 4 11 234 3 0 2 3 2 29 625 bc be p pt be p rr oai i h oai oo yt e uu yt e ww mm nn b 11 24 45 24 29 955 73 955 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 00 0 00 0 00 0 00 0 00 0 00 0 00 1 00 0 10 1 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 10 0 11 1 01 0 00 1 00 0 00 0 00 0 00 0 00 0 00 0 01 0 00 0 00 0 00 0 00 0 00 0 10 1 01 0 00 0 00 0 00 0 00 0 00 00 00 00 00 00 00 00 00 11 00 00 00 00 00 00 00 00 11 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 11 00 00 00 00 00 00 00 00 00 00 00 00 00 10 11 00 01 00 00 00 00 00 00 00 00 00 00 00 00 11 00 00 00 00 00 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 10 00 0 0 00 00 0 0 00 00 0 0 01 01 0 0 00 00 0 0 00 00 0 0 00 00 1 1 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 11 11 1 1 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 10 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 10 0 0 00 00 0 1 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 0 0 00 00 1 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 11 0 0 00 0 0 00 0 0 00 1 1 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 11 1 1 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 1 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 1 0 00 00 00 00 00 00 01 00 11 00 00 00 00 00 00 00 00 00 00 00 00 00 10 11 00 01 00 00 00 00 00 00 00 00 00 00 00 00 11 00 00 00 00 00 00 000 00 000 00 000 00 000 00 100 00 000 00 000 00 000 00 000 11 110 00 000 00 000 00 000 00 100 00 000 00 000 00 000 00 000 11 000 00 000 00 000 00 000 00 000 00 000 00 000 00 000 00 000 00 000 00 000 00 001 00 000 00 000 00 000 00 001 00 000 00 000 00 000 00 010 00 000 00 000 00 000 00 000 00 000 00 001 000 00 000 000 00 000 000 00 000 010 00 010 000 00 000 000 00 000 000 00 000 010 00 010 000 00 000 000 00 000 000 00 000 000 00 000 000 10 000 000 00 000 000 00 000 000 00 000 000 00 000 000 00 000 000 10 000 000 01 000 000 00 000 000 00 000 000 00 000 000 00 000 100 00 100 000 00 000 000 00 000 000 00 000 000 00 000 011 00 011 000 00 000 000 00 000 000 00 000 101 00 101 000 00 000 000 00 000 000 00 000 000 00 000 000 00 000 010 00 010 000 00 000 000 00 000 000 00 000 111 11 111 D35SSS D07OMH D13RRS D45BBB D09HBD D21LAU D27CBC D10JAJ D50LJH D39LCS {07OMH {07OMH {07OMH {07OMH {09HBD {10JAJ 35SSS 13BBS 13RRS 09HBD 27CBC 13BBS 50LJH} 35SSS 45BBB} 21LAU} 27CBC 45BBB} 45BBB} 21LAU} {09HBD 27CBC 45BBB} {10JAJ 21LAU} {35SSS 39LCS 50LJH} is {39LCS 50LJH} bake bread eat pie back bake bread buy mother back bread buy plum town baby buy mother baby mother brown crown plum town baby mother brown crown boy eat pie boy pie (details 2 slides ahead)
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MIPS • 32 bit signed numbers: 0000 0000 0000 0000 0000 0000 0000 0000two = 0ten 0000 0000 0000 0000 0000 0000 0000 0001two = + 1ten 0000 0000 0000 0000 0000 0000 0000 0010two = + 2ten ... 0111 1111 1111 1111 1111 1111 1111 1110two = + 2,147,483,646ten 0111 1111 1111 1111 1111 1111 1111 1111two = + 2,147,483,647ten 1000 0000 0000 0000 0000 0000 0000 0000two = – 2,147,483,648ten 1000 0000 0000 0000 0000 0000 0000 0001two = – 2,147,483,647ten 1000 0000 0000 0000 0000 0000 0000 0010two = – 2,147,483,646ten ... 1111 1111 1111 1111 1111 1111 1111 1101two = – 3ten 1111 1111 1111 1111 1111 1111 1111 1110two = – 2ten 1111 1111 1111 1111 1111 1111 1111 1111two = – 1ten • Converting n bit numbers into numbers with more than n bits: max min – MIPS 16 bit immediate gets converted to 32 bits for arithmetic – copy the most significant bit (the sign bit) into the other bits 0010 -> 0000 0010 1010 -> 1111 1010 – "sign extension" (lbu vs. lb) CSE 45432 SUNY New Paltz 3
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BINARY CODES BCD DECIMAL 8421 0 0000 1 0001 2 0010 3 0011 4 0100 5 0101 6 0110 7 0111 8 1000 9 1001 10 0001 0001 11 0001 0010 .... 98 1001 1000 99 1001 1001 BINARY 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100010 1100011 4 Bit BCD CODES 7421 0000 0001 0010 0011 0100 0101 0110 1000 1001 1010 Introduction to Microprocessors Number Systems and Conversions 6311 5421 0000 0000 0001 0001 0011 0010 0100 0011 0101 0100 0111 1000 1000 1001 1001 1010 1011 1011 1100 1100 5311 0000 0000 0011 0100 0101 1000 1001 1011 1100 1101 5211 0000 0001 0011 0101 0111 1000 1001 1011 1101 1111 No. 1-6 9/6/00
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1 2 3 4 5 6 WORD 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 DS1 35SSS 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 DS2 Use WS1Cbit 3DS={35} 01TBM 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 1 0 Voc(DS) ={7,10,17, 23,25,28,33, 07OMH 0 0 0 1 0 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 34,37 40, 43,45,50}) ED= 100% 10JAJ 13RRS 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0 0 0 0 0 14ASO 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 17FEC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 DS2=WS1Cbit3| 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 2(=WS1Cbit2)={1,7,10,13,14,1 21LAU 26SBS 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 28BBB 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 7,21,26,28,29, 29LFW 1 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 30HDD 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 30,35,37,39,41,44,46,47,50} 35SSS 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 1 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 37MBB 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 WS2=vocabDS2=all but 5,22, 39LCS 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 41OKC 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 29,59 ED=105/(19*56)=10% Instead take 44HLH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 46TTP 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 WS2=DS2bit2={2,49} ED=9/ 47CCM 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 50LJH 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 (19*2)= 24% DS2C: 2 4 1 2 0 1 2 2 3 3 1 2 2 1 1 1 2 3 2 2 2 0 2 2 3 2 2 2 0 2 1 2 1 2 1 1 1 2 2 1 2 2 1 3 3 1 3 1 4 1 2 3 1 2 2 1 2 1 0 2 DS2b2:0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 CDSC(HOB) WS1=CDCbit2={2,3,13,2 0,22, 25,38,42,44,49,52} DS2=WS1Cb2={46} ED=4/(11*1)= 36.3% WS1=CDCbit2={2,3,13,20,2 2, 25,38,42,44,49,52} DS2=WS1Cbit 2|1 ={1,4,7,9,11, 17,27,28,29,30,32,41,45,46} ED=14/(14*11)= 9% CDC CDCb2 CDCb1 CDCb0 46TTP 2 0 1 0 0 5 1 0 1 1 4 1 0 0 0 3 0 1 1 0 2 0 1 0 0 2 0 1 0 0 3 0 1 1 0 3 0 1 1 0 3 0 1 1 0 3 0 1 1 0 2 0 1 0 0 2 0 1 0 0 4 1 0 0 0 2 0 1 0 0 2 0 1 0 0 2 0 1 0 0 3 0 1 1 0 3 0 1 1 0 2 0 1 0 0 4 1 0 0 1 2 0 1 0 0 4 1 0 0 0 2 0 1 0 0 3 0 1 1 0 5 1 0 1 1 1 0 0 1 0 0 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 1 1 1 1 0 1 0 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 0 1 1 1 0 1 1 0 0 0 0 1 0 0 1 0 WS1=Voc(DS1) D bbc O a r l C keo e at dh 11 707 1 000 2 000 3 000 4 000 5 000 6 000 7 110 8 000 9 000 10 0 0 0 1 001 2 000 3 000 4 000 5 000 6 000 7 000 8 000 21 0 1 0 2 000 3 000 5 000 6 000 7 000 8 000 9 000 30 0 0 0 2 000 3 000 5 111 6 000 7 001 8 000 9 000 41 0 0 0 2 100 3 000 4 000 5 000 6 000 7 000 8 000 9 000 d i s h 2 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 ef hk auoi t l un l s g e 2233 5834 0000 0000 0000 1000 0001 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0100 0000 0000 0000 0000 1111 0010 0000 0000 0000 0001 0000 0000 0000 0000 1000 0000 0000 0000 mmn a oo i ns de e y 344 703 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 000 000 000 000 000 000 000 000 000 111 000 000 010 000 000 000 000 000 000 000 000 100 000 ps i i e n g 45 50 00 00 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 11 00 00 00 10 00 00 00 00 00 00 00 00 00 WS1C 4 2 2 2 3 2 7 3 3 5 3 3 5 4 3 2 4 2 6 2 2 2 7 3 6 4 5 3 3 13 2 4 3 7 5 2 2 4 3 6 4 3 2 WS1Cbit3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 WS1Cbit2 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 0 1 0 1 0 0 0 1 0 1 1 1 0 0 1 0 1 0 1 1 0 0 1 0 1 1 0 0 a r wu a n y 4 29 01 00 00 10 00 00 00 00 00 00 00 00 00 00 00 00 01 00 00 00 00 00 00 00 00 10 11 00 00 00 00 00 00 10 00 00 00 00 00 11 00 00 00 a bbc d wa u r a a byyy yy 122 23302 00000 00000 00000 10000 00000 00001 00100 00000 01000 00000 00000 00000 00100 00000 00001 00000 00000 00001 00000 00000 00000 00000 01000 01010 00010 10000 10000 00001 00100 00000 00000 00000 00010 10000 00000 00000 00000 00000 01100 10010 00000 00000 00000 e mm o r a eol u t nt d n h er 2 34 4 4 5 82 4 9 0 00 0 1 0 00 0 0 0 00 0 0 1 00 0 0 0 10 0 0 0 00 0 0 0 01 1 0 1 00 0 0 0 01 0 0 0 00 1 0 0 10 1 0 0 00 1 0 0 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 10 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 01 0 0 0 00 0 0 0 01 0 0 0 00 0 1 0 10 0 0 0 00 0 0 1 00 0 0 0 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 01 0 0 1 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 t h r e e 5 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 w s 1 c 20 00 00 20 10 10 30 10 20 10 20 10 10 10 10 00 20 10 00 00 10 10 10 30 20 20 20 20 10 10 10 00 10 10 20 00 00 00 30 40 00 10 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 0 1 1 0 3 0 1 1 0 2 0 1 0 0 2 0 1 0 0 2 0 1 0 0 2 0 1 0 0 2 0 1 0 0 2 0 1 0 0 3 0 1 1 0 2 0 1 0 0 2 0 1 0 0 2 0 1 0 0 6 1 1 0 0 2 0 1 0 0 2 0 1 0 0 2 0 1 0 0 5 1 0 1 0 2 0 1 0 0 6 1 1 0 0 3 0 1 1 0 2 0 1 0 1 3 0 1 1 0 3 0 1 1 0 4 1 0 0 1 2 0 1 0 0 3 0 1 1 1 5 1 0 1 0 2 0 1 0 0 3 0 1 1 0 2 0 1 0 0 2 0 1 0 0 3 0 1 1 0 2 0 1 0 0 2 0 1 0 0 2 0 1 0 0
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Chapter 5 - Languages and the Machine 5-8 Assembled Code ld [x], %r1 1100 0010 0000 0000 0010 1000 0001 0100 ld [y], %r2 1100 0100 0000 0000 0010 1000 0001 1000 addcc %r1,%r2,%r3 1000 0110 1000 0000 0100 0000 0000 0010 st %r3, [z] 1100 0110 0010 0000 0010 1000 0001 1100 jmpl %r15+4, %r0 1000 0001 1100 0011 1110 0000 0000 0100 15 0000 0000 0000 0000 0000 0000 0000 1111 9 0000 0000 0000 0000 0000 0000 0000 1001 0 0000 0000 0000 0000 0000 0000 0000 0000 Department of Information Technology, Radford University ITEC 352 Computer Organization
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word-node label dc2 first WORD 39LCS 41OKC 35SSS 38YLS 37MBB 47CCM 22HLH 35SSS 07OMH 10JAJ 11OMM 12OWF 25WOW 41OKC 02TLP 46TTP 13RRS 21LAU 50LJH 16PPG 33BFP 37MBB 15PCD 35SSS 03DDD 13RRS 46TTP 01TBM 23MTB 28BBB 41OKC 48OTB 22HLH 50LJH 14ASO 39LCS 17FEC 48OTB 01TBM 08JSC 26SBS 28BBB D mmm mwn O e o o oa o C r n r ry s r enn e yy 3 4 4 45 4 9 0 1 17 3 o owp p pt r l loi i io o d dmg u uw u a m mn n n d 4 45 4 4 45 4 4 49 6 7 74 8 s s t t t t ww i o h h r wi o n n r ue0 f o g e me e l eb 5 5 5555 5 6 0 1 2356 8 0 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 9 000 10 0 0 0 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 21 0 0 0 2 000 3 000 5 000 6 000 7 000 8 000 9 000 30 0 0 0 2 000 3 000 5 010 6 000 7 001 8 010 9 100 41 1 0 0 2 000 3 000 4 000 5 000 6 000 7 001 8 000 9 000 0 000 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 1 10 0 0 0 00 0 0 0 00 0 0 1 10 0 0 1 10 0 0 1 11 0 0 0 00 0 1 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 0 00 0 0 0 00 0 0 1 11 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 1 10 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 1 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 01 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 1 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 1 00 0 11 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 11 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 11 0 00 0 00 0 00 1 00 0 00 0 11 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 0 00 1 00 0 00 0 00 1 00 0 00 0 00 0 00 0 01 0 00 0 00 0 00 0 00 0 00 0 00 0 10 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 0010 0000 0000 0001 0000 0000 0100 1000 0000 0000 0000 1000 0000 0000 0000 0000 0000 0000 0000 0000 0010 1000 0000 0000 0000 0000 0000 0000 1001 0000 0100 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 7 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 WC= 1always WC= 2away 25eat 49run WC= 3baby 42mother WC= 4back 13buy WC= 5bad WC= 6bag WC= 7bake 10bread WC= 8bed WC= 9boy 45pie WC=11bright WC=12brown 19crown WC=14cake WC=15child WC=16clean WC=17cloth WC=18cock WC=20cry WC=21cut WC=22day WC=23dish WC=24dog WC=26fall 38men WC=27fiddle WC=28full WC=29girl WC=30green WC=31high WC=32hill WC=33house WC=34high WC=35lady WC=36lamb WC=37maid 7 0 0 1 0 1 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 6 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 7 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 8 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 26SBS 29LFW 4LMM 30HDD 46TTP 9HBD 27CBC 45BBB 7OMH 13RRS 6SPP 49WLG 16PPG 28BBB 7OMH 35SSS 3DDD 29LFW 47CCM 39LCS 50LJH 18HTP 44HLH 10JAJ 21LAU 21LAU 42BBC 12OWF 26SBS 8JSC 26SBS 11OMM 35SSS 37MBB 17FEC 39LCS 47CCM 27CBC 28BBB 38YLS 46TTP 1TBM 14ASU 6SPP 15PCD 18MTP 32JGF 30HDD 35SSS 7OMH 30HDD 43HHD 5HDS 14ASO 30HDD 32JGF 41OKC 28BBB 35SSS 33BFP 49WLG 26SBS 39LCS 15PCD 44HLH 10JAJ 44HLH 35SSS 36LTT 5HDS 35SSS 41OKC 9HBD 44HCL 26SBS 38YLS 35SSS 48OTB 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 1 1 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 WC=39merry WC=40money WC=41morn WC=43nose WC=44old WC=46pig WC=47plum WC=48round WC=50sing WC=51son WC=52three WC=53thumb WC=55tree WC=56two WC=58wife WC=60wool 7 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 9 1 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 4 0 0 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 57way 59woman 54town 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 4 0 1 0 0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 5 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 8 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 39LCS 35SSS 37MBB 22HLH 12OWF 2TLP 13RRS 16PPG 15PCD 3DDD 1TBM 22HLH 14ASO 17FEC 1TBM 26SBS 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 1 0 0 0 5 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 1 1 0 0 1 3 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 0 0 0 0 7 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 9 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 1 41OKC 38YLS 47CCM 35SSS 25WOW 45TTP 21LAU 33BFP 37MBB 35SSS 13RRS 46TTP 23MTB 28BBB 41OKC 48OTB 50LJH 39LCS 48OTB 8JSC 28BBB
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MORE 4-BIT BCD CODES Decimal 0 1 2 3 4 5 6 7 8 9 4221 0000 0001 0010 0011 1000 0111 1100 1101 1110 1111 3321 0000 0001 0010 0011 0101 1010 1100 1101 1110 1111 Introduction to Microprocessors Number Systems and Conversions 2421 0000 0001 0010 0011 0100 1011 1100 1101 1110 1111 84/2/1 0000 0111 0110 0101 0100 1011 1010 1001 1000 1111 74/2/1 0000 0111 0110 0101 0100 1010 1001 1000 1111 1110 The / is subtract weight No. 1-7 9/6/00
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bond 1.00% 0.99% 0.95% 0.89% 0.81% 0.71% 0.59% 0.45% 0.31% 0.16% 0.00% s&p500 0.00% 0.16% 0.31% 0.45% 0.59% 0.71% 0.81% 0.89% 0.95% 0.99% 1.00% 100.511 100.931 100.000 100.253 100.625 100.402 100.458 112.560 104.676 120.472 111.264 100.462 101.745 100.557 101.014 100.000 100.176 100.481 100.330 100.364 112.188 104.607 117.156 109.198 100.442 101.654 100.592 101.162 100.000 100.112 100.330 100.260 100.276 111.464 104.427 113.237 106.905 100.480 101.546 100.561 101.393 100.000 100.062 100.170 100.168 100.190 110.313 104.131 108.851 104.490 100.536 101.422 100.392 101.578 100.000 100.017 100.005 100.045 100.093 108.717 103.743 104.476 102.268 100.524 101.277 100.328 101.471 100.012 100.079 100.000 100.073 100.105 106.990 103.500 101.517 101.107 100.512 101.239 100.636 101.218 100.000 100.390 100.411 100.524 100.441 105.665 103.734 102.748 102.429 100.644 101.479 100.674 100.912 100.000 100.859 101.066 101.155 101.006 104.578 104.064 110.842 106.870 100.639 101.836 100.076 100.534 100.000 101.284 101.439 101.407 101.385 104.130 103.176 121.875 112.237 100.183 102.002 100.601 100.815 101.616 101.368 101.574 101.333 101.520 110.939 101.852 123.302 114.554 100.000 101.743 100.498 101.415 101.151 100.000 100.297 100.245 100.081 114.037 107.580 109.876 107.572 100.197 102.290 EXP-SM MA(20) MA(100) DCC-IMA (recursive) DCC-MR (recursive) DCC-ASY (recursive) DCC-RANK (recursive) OGARCH1 (recursive) OGARCH2 (recursive) FIXED (sample 1-1000) FIXED (daily update) DCC-ASY-GEN (recursive) DCC-GEN (recursive) Average 100.238 100.874 100.000 100.165 100.328 100.287 100.285 108.954 103.868 111.942 106.909 100.165 101.400 Table 158: sample variance of minimum variance portfolios subject to a required return of 1 (sample: 1001-end) 42
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Comparing the signed number systems • • • • • Here are all the 4-bit numbers in the different systems. Positive numbers are the same in all three representations. Signed magnitude and one’s complement have two ways of representing 0. This makes things more complicated. Two’s complement has asymmetric ranges; there is one more negative number than positive number. Here, you can represent -8 but not +8. However, two’s complement is preferred because it has only one 0, and its addition algorithm is the simplest. 03/21/19 Decimal S.M. 1’s comp. 2’s comp. 7 6 5 4 3 2 1 0 -0 -1 -2 -3 -4 -5 -6 -7 -8 0111 0110 0101 0100 0011 0010 0001 0000 1000 1001 1010 1011 1100 1101 1110 1111 — 0111 0110 0101 0100 0011 0010 0001 0000 1111 1110 1101 1100 1011 1010 1001 1000 — 0111 0110 0101 0100 0011 0010 0001 0000 — 1111 1110 1101 1100 1011 1010 1001 1000 Arithmetic-logic units 7
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Comparing the signed number systems • • • • • Here are all the 4-bit numbers in the different systems. Positive numbers are the same in all three representations. Signed magnitude and one’s complement have two ways of representing 0. This makes things more complicated. Two’s complement has asymmetric ranges; there is one more negative number than positive number. Here, you can represent -8 but not +8. However, two’s complement is preferred because it has only one 0, and its addition algorithm is the simplest. 03/21/19 Decimal S.M. 1’s comp. 2’s comp. 7 6 5 4 3 2 1 0 -0 -1 -2 -3 -4 -5 -6 -7 -8 0111 0110 0101 0100 0011 0010 0001 0000 1000 1001 1010 1011 1100 1101 1110 1111 — 0111 0110 0101 0100 0011 0010 0001 0000 1111 1110 1101 1100 1011 1010 1001 1000 — 0111 0110 0101 0100 0011 0010 0001 0000 — 1111 1110 1101 1100 1011 1010 1001 1000 Subtraction 14
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Summary of methods for representing signed ints. signedMag 1sComp 2 sComp excess 8 N n  n  n  n  n n 0 1 0000 0001 1000 1001 1111 1110 0000 1111 1000 0111 1000 1001 2 0010 1010 1101 1110 0110 1010 3 4 0011 0100 1011 1100 1100 1011 1101 1100 0101 0100 1011 1100 5 0101 1101 1010 1011 0011 1101 6 7 0110 0111 1110 1111 1001 1000 1010 1001 0010 0001 1110 1111 1000=-8| 0000 unused
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Bipartite Graph cTrees (If there are only 2PARTs. Multipartite and Hyperpartite collapse to the same thing. A B C D E F G H I J K L M N A A A A A AA A B C D E F GH I B B B B BBB B A C D E FGH I C C CC C E F GH I D D DDDD C E FGHI E E EE F G HI FF FF EG HI GG HI HH GI I H J J JJ F G HL K KKK K K F GHI J L LLLL FGHI M M MMMMM G H IJKLN N N NN N N N G H IJ K L M 1 2 3 4 5 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 01 1 1 1 0 1 1 11 0 0 0 0 0 0 00 0 0 1 1 1 1 11 0 0 0 0 0 0 00 0 1 1 1 1 101 1 1 1 0 1 111 0 0 1 1 1 111 1 0 0 0 0 000 0 0 0 0 0 000 0 1 1 01 1 1 1 11 0 1 1 11 1 1 1 11 0 1 0 10 0 1 1 1011 0 0 0000 1 1 1111 1 1 1110 1 1 0100 1 0 11 1 1 10 1 1 11 1 1 10 0 1 00 10 11 11 10 11 11 11 10 00 00 00 10 11 10 00 01 10 11 10 00 1 0 1 0 0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0000 0000 0000 0000 0000 0 0 00000 0 0 00000 0 0 00000 0 0 00000 0 0 00000 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 6 7 8 9 a 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 0 0 000 0 1 1 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0000 0 0 0000 0 0 0000 0 0 0000 0 0 0000 1 0 10 1 1 10 0 0 00 0 1 11 0 0 00 10 10 11 10 00 00 00 11 00 00 00 10 00 11 11 00 10 01 11 11 0 0 1 1 1 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0 000 0 0 0000 0000 0000 0000 0111 0 0 00000 0 0 00000 0 0 00000 0 0 00000 0 0 00000 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 b v d e f 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0000 0 0 0000 0 0 0000 0 0 0000 0 0 0000 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 00 00 00 00 00 00 00 01 00 00 00 00 11 01 10 01 01 11 00 10 1 1 1 0 0 0 0 11 0 0 11 0 1 11 1 1 01 0 1 11 0 000 0 0 0 000 0 0 0 000 0 0 1 101 1 1 0 110 1 1 0011 0011 0111 1101 0110 0 0 00000 0 1 11011 1 1 11011 1 0 11111 0 0 00000 0 0 00 0 0 0 0 1 11 0 1 1 1 1 11 0 1 1 1 0 11 1 1 1 0 0 00 0 0 0 g 0 0 0 0 0 0 0 1 1 0 0 0 0 0 h 0 0 0 0 0 0 0 0 1 0 1 0 0 0 i 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 0 0 000 0 0 0 00 0 0 0 00 0 0 0 00 0 0 0 0000 0 0 0000 0 0 0000 0 0 00 0 0 00 0 0 00 00 00 00 00 00 00 00 00 00 01 00 00 1 0 0 0 0 00 0 0 00 0 0 00 0 000 0 0 0 001 0 0 0 001 0 0 0000 0000 0000 0 0 00000 0 0 00000 0 0 00000 0 0 00 0 0 0 0 0 00 0 0 0 0 0 00 0 0 0 3 3 6 4 8 8 a e c 5 4 6 3 3 2 3 2 3 3 23 1 2 3 2 3 323 2 6 5 44 2 4 4 3332 6 6 73 64 74 85 89 9 1 3 45 1 213 2 2 1455 2 2 33133 2 2 33 1 3 3 This bipartite graph clique TreeSet has NUMpTree on top and LETpTree at bottom (e.g., Nums=Investors, Lets=Socks): It is closed under AND (call it aa). The OR of 2 cTrees with a substantial AND might reveal interesting communities. It is closed under OR-AND (called oa) and AND-OR (called ao). Max Base CLQs (MBCLQs). Thms: Every MCLQ is generated, using oa, from the base CLQs, YES! Every MCLQ is generated, using oa, from the maximized base CLQs (1st round only)? oa applied to two MBCLQs gives a MCLQ. No.. Counterexample?. Find all MCLQ(A)? There doesn’t seem to be an algebraic method. Probably it will have to be a POSET method? (BCS.oa) generates (CLQ,oa) Commutative monoids (lack inverses) (CLQ,oa) (CLQ,ao) (CLQ,aa). BCS={32 base cliques}; ops, and-and (aa), or-and (oa), and-or (ao), each forming a comm. Monoid. 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 a 11 12 b 13 14 v 15 d 16 17 18 19 20 e f g h i 21 22 23 24 A 25 B C 26 D 27 E 28 29 30 F G 31 H 32 I 33 J 34 35 K C# L CL M N A B C D E F G H I J K L M N 1 2 3 4 5 6 7 8 9 a b c d e f g h i 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 1 1 0 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 1 1 0 1 1 0 1 1 0 1 0 0 1 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 1 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 8 1 7 1 8 1 7 1 4 1 4 1 4 1 3 1 4 1 4 1 4 1 6 1 7 1 8 1 5 1 2 1 2 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 3 1 3 1 6 1 4 1 8 1 8 1 a 1 e 1 c 1 5 1 4 1 6 1 3 1 3 1 Usually, the ops, XOR, AND make {0,1) into a field (the Galois Field GF(2) ). It’d be useful if we could make the cTreeSet into a field (with an XOR and AND operation). However, on cTrees, the op, XOR over AND (xa) has ID=01 and a cTree, xy, has XOR inverse of x but no AND inverse. 1 MBCLQ(X) 2 X =? 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17,18 1-ABCDEFHI 2-ABCEFGH 3-BCDEFGHI 4-ACDEFGH 345-CDEG 12346-CEFH 2347-EFGH 78-EFG 359-EGHI (10,13)-GHIL (11,12,13)-HIJL (12,13)-HIJLMN 13-GHIJLMN 14-FGIJKLMN 15-GHJKL (1,3,8,9,10,11,12,13,16)-HI (14,17,18)-IK MBCLQ(X) 124-ACEFH 123-BCEFH 123456-CE 1345-CDE 12345679-E (1234678,14)-F (234579,10,13,14,15)-G (12346789.10,11,12,13,15,16)-H (1389.10,11,12,13,14,16,17,18)-I (11,12,13,14,15)-JL (14.15.17.18)-K (10,11,12,13,14,15)-L (12,13,14)-MIJLN X =? A B C D E F G H I J K L M N 124-ACEFH 12-ABCEFH 14-ACDEFH 24-ACEFGH 1-ACEFHI
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At this point, I see no reason that rough pTree, e.g., node 2.2 truth value, should be the truth of its child but should instead be the truth of the leaf-segment it strides. So for global_fanout=4 and gt50: 1 1 1 1 1 1 0 1 1 0 1 1 1 1 1110 1111 1110 1001 0111 1100 0111 0111 0111 11 1111 1011 1011 0010 0111 1010 1101 1110 0101 1011 1111 0100 1111 1000 0100 1110 0100 1100 1001 1011 1100 1010 0001 0100 0010 0101 1001 10 01 0001 1111 1001 0111 0010 1111 0110 0111 0110 11
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A data table, R(A1..An), containing horizontal structures (records) is processed vertically (vertical scans) Vertical basic binary Predicate-tree (P-tree): vertically partition table; compress each vertical bit slice into a basic binary P-tree as follows then process using multi-operand logical ANDs. R( A1 A2 A3 A4) Horizontal structures (records) Scanned vertically 010 011 010 010 101 010 111 111 111 111 110 111 010 010 000 000 110 110 101 101 001 001 001 001 001 000 001 111 100 101 100 100 R[A1] R[A2] R[A3] R[A4] R11 0 0 0 0 1 0 1 1 The basic binary P-tree, P1,1, for R11 is built topdown by record truth of predicate pure1 recursively on halves, until purity. 1. Whole file is not pure1 0 2. 1st half is not pure1  0 3. 2nd half is not pure1  0 4. 1st half of 2nd half not  0 5. 2nd half of 2nd half is  1 6. 1st half of 1st of 2nd is  1 But it is pure (pure0) so this 7. 2nd half of 1st of 2nd not 0 branch ends 010 011 010 010 101 010 111 111 0 0 0 01 1 10 111 111 110 111 010 010 000 000 110 110 101 101 001 001 001 001 001 000 001 111 100 101 100 100 R11 R12 R13 R21 R22 R23 R31 R32 R33 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 P11 P12 P13 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 P21 P22 P23 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 R41 R42 R43 0 0 1 1 1 1 1 1 P31 P32 P33 0 0 0 0 0 0 0 0 0 1 0 1 0 0 01 0 0 0 1 0 10 10 01 0001 01 01 01 10 01 10 0 0 0 0 1 1 1 1 1 0 P11^P12^P13^P’21^P’22^P’23^P’31^P’32^P33^P41^P’42^P’43 = 1 0 1 1 0 1 0 0 P41 P42 P43 0 0 0 1 10 01 Eg, Count number of occurences of 111 000 001 100 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 01 01 0100 01 01 10 01 0 23-level 0 0 22-level =2 01 21-level
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Find all MCLQ(A) Depth First Bipartite Max Clique Mine on G9 A B C D E F G H I J K L M N A A A A A AA AAAA A A B B B B B BB B B BB B B CC CCCC B C D E F GH IJKL M N A C D E F GH I J KL M N EF GHIL D D D D D D D D D E E EE F F F F C E F G H I J K L F G HI E G H I GG HH I J J J J J J J K K K K KKK K K L L L L L L M M M MMMMM H I G I H C E F G H I L C D E F G H I J L C E F G H I A-F G H I J K L N 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 01 1000 0 0 1 1 0 1 1 11 0000 0 0 0 0 0 0 0 00 0000 0 0 0 1 1 1 1 11 0000 0 0 0 0 0 0 0 00 0000 0 0 1 1 1 1 1 01 1 0 00 0 0 1 1 0 1 1 11 0 0 00 0 0 0 1 1 1 1 11 1 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 11 0110 11 1100 11 1110 11 1100 10 1000 11 1 0 1 1 0 0 0 00 0 0 0 0 0 0 0 11 1 1 1 1 0 0 0 11 1 1 1 0 0 0 0 11 0 1 0 0 0 0 0 1 0 11 1 1 10 1 1 11 1 1 10 0 1 00 10 11 11 10 11 11 11 10 00 00 00 10 11 10 00 01 10 11 10 00 1 0 1 0 0 00 000 0 0 00 000 0 0 00 000 0 0 00 000 0 0 00 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 000000 000000 000000 000000 000000 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 11 0000 00 0000 00 0000 00 0000 00 0000 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 10 1 1 10 0 0 00 0 1 11 0 0 00 10 10 11 10 00 11 00 00 00 00 00 10 00 11 11 00 10 01 11 11 0 0 1 1 1 00 000 0 0 00 000 0 0 00 000 0 0 00 000 0 0 00 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 000000 000000 000000 000000 000111 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0000 00 0000 00 0000 00 0000 00 0000 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 00 00 00 00 00 00 00 01 00 00 00 00 11 01 10 01 01 11 00 10 1 1 1 0 0 00 001 1 1 00 001 1 1 00 011 1 1 00 110 1 1 00 011 0 1 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 1 101 1 1 0 0 0 0 110 1 1 000011 000011 000111 001101 000110 00 0 0 0 0 0 0 00 1 1 1 0 1 1 01 1 1 1 0 1 1 01 0 1 1 1 1 1 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 1 1 1 0 1 1 01 1 1 1 0 1 1 01 0 1 1 1 1 1 00 0 0 0 0 0 0 N N N NN N N N A-FG H I J K L M 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0000 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0000 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0000 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 00 01 1 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 001 0 0 0 0 0 0 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 001 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 3 3 6 4 8 8 a e c 5 4 6 3 3 2 3 2 3 3 23 1000 0 0 2 3 2 3 3 23 2 0 00 0 0 65 4420 4 4 3 3 3 2 0 0 0 6 6 73 6 4 7 4 85 89 9 0 0 1 3 4 0 5 0 0 0 1 213 2 2 0 0 1 4 5 5 02 2 3 3 1 3 3 02 2 3 3 1 3 3 The ApTreeMCLQ(A) unless there are A&XpTrees with Ct(A&X)=Ct(A). Ct(A)=Ct(AC)=Ct(AE)=Ct(AF)=Ct(AH)=3, so ACEFH-124MCLQ(A). Next check for MCLQs with Ct=Ct(A)-1=2. We have 2# CLQs: ACEFH-12, ACEFH-14 and ACEFH-24. Each Ct(A&XpTree)=2=CtA-1 expands one of these 3. (namely AB-12 AD-14 AG-24), Each expanded CLQ is maximal. We get new 2# MCLQ(A): ABCEFH-12 ACDEFH-14 ACEFGH-24 Next check MCLQs with Ct=Ct(A)-2=1. When we reach Ct=1 we simply check the #pTrees containing A (e.g., 1,2,4) for maximal with the 1 st step. The BpTreeMCLQ(B) unless Ct(B&X)=Ct(B). 3=Ct(B)=Ct(BC)=Ct(BE)=Ct(BF)=Ct(BH), so BCEFH-123MCLQ(B). Next check MCLQs w Ct=Ct(B)-1=2. We have 2# CLQs: BCEFH-12, BCEFH-13, BCEFH-23 . Each Ct(B&X)=2 expands one of these 3. (namely BA-12 BD-13 BG-23 ), Each expanded CLQ is max. We get 2# MCLQ(B): ABCEFH-12 BCDEFH-13 BCEFGH-23, but ABCEFH-12 not new. Next MCLQs w Ct=Ct(B)-2=1. Check #pTrees B (e.g., 1,2,3) w 1st step (only 3 is new). CMCLQ(C) unless Ct(C&X)=Ct(C). 6=Ct(C)=Ct(CE) so CE-123456MCLQ(C). Next check MCLQs w Ct=Ct(C)-1=5. We have 5# CLQs: CE-12345 CE-12346 CE-12356 CE-12456 CE-13456 CE-23456 Each Ct(C&X)=5 expands one of these, namely CF-12346 (expands to CEF-12346) The Ct(C&X)=4 are CG-2345 CH-1234 may expand MCLQ(C)s CEF-12346 CE-123456 (check in this order) CG-2345 expands CE-123456 to CEG-2345 and CH-1234 expands CEF-12346 to CEFH-1234) The Ct(C&X)=2 is CI-13 may expand MCLQ(C)s CEFH-1234 CEG-2345 CEF-12346 CE-123456 (check in this order). CI-13 expands CEFH-1234 to CEFHI-13 DMCLQ(D) unless Ct(D&X)=Ct(D). 4=Ct(D)=Ct(CD) =Ct(DE) so CDE-1345MCLQ(D). Next Ct=Ct(D)-1=3. 3# CLQ(D)s: DF-134 DG-345 DH-134, so we have DFH-134 and DG-345 Each expands a maximal: DFH-134 expands CDE-1345 to CDEFH-134. DG-345 expands CDE-1345 to CDEG-345 The Ct(D&X)=2 is DI-13 which expands CDEFH-134 to CDEFHI-13 C D E F H I 1 0 1 0 0 C D E G 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 2 C D E F H 1 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 C D E 1 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 4 C E F H I 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 C E F H 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C C E E C G F E 0 1 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 5 6 B C D E F G H I 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 B C D E F H B C E F G H 1 0 1 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 B C E F H 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 A B C D E F H I A B C E F G H A C D E F G H 1 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 1 A B C E F H A C D E F H A C E F G H 1 1 0 0 0 1 0 0 1 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 A C E F H 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3
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A file, R(A1..An), contains horizontal structures (horizontal records) processed vertically (vertical scans) R( A1 A2 A3 A4) Horizontal structures (records) Scanned vertically 010 011 010 010 101 010 111 111 111 111 110 111 010 010 000 000 110 110 101 101 001 001 001 001 001 000 001 111 100 101 100 100 horizontally process these basic Ptrees using one multi-operand logical AND. R[A1] R[A2] R[A3] R[A4] 010 011 010 010 101 010 111 111 R11 0 0 0 0 1 0 1 1 1-Dimensional Ptrees are built by recording the truth of the predicate “pure 1” recursively on halves, until there is purity, P11: 1. Whole file is not pure1 0 2. 1st half is not pure1  0 3. 2nd half is not pure1  0 4. 1st half of 2nd half not  0 5. 2nd half of 2nd half is  1 6. 1st half of 1st of 2nd is  1 But it is pure (pure0) so this 7. 2nd half of 1st of 2nd not 0 branch ends Ptrees: vertically partition; then compress each vertical bit slice into a basic Ptree; 0 0 0 01 1 10 111 111 110 111 010 010 000 000 110 110 101 101 001 001 001 001 001 000 001 111 100 101 100 100 R11 R12 R13 R21 R22 R23 R31 R32 R33 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 P11 P12 P13 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 P21 P22 P23 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 R41 R42 R43 0 0 1 1 1 1 1 1 P31 P32 P33 0 0 0 0 0 0 0 0 0 1 0 1 0 0 01 0 0 0 1 0 10 10 01 0001 01 01 01 10 01 10 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 P41 P42 P43 0 0 0 1 10 01 0 0 0 0 1 0 0 0 0 01 01 0100 01 01 10 01 Eg, to count, 111 000 001 100s, use “pure111000001100”: 0 23-level P11^P12^P13^P’21^P’22^P’23^P’31^P’32^P33^P41^P’42^P’43 = 0 0 22-level =2 01 21-level
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A data table, R(A1..An), containing horizontal structures (records) is processed vertically (vertical scans) Vertical Predicate-tree (P-tree) structuring: vertically partition table; compress each vertical bit slice into a basic Ptree; process P-trees using multi-operand logical ANDs. R( A1 A2 A3 A4) Horizontal structures (records) Scanned vertically 010 011 010 010 101 010 111 111 111 111 110 111 010 010 000 000 110 110 101 101 001 001 001 001 001 000 001 111 100 101 100 100 R[A1] R[A2] R[A3] R[A4] R11 0 0 0 0 1 0 1 1 The basic (1-D) Ptree for R11 is built by recording the truth of the predicate “pure 1” recursively on halves, until purity is reached. 1. Whole file is not pure1 0 2. 1st half is not pure1  0 3. 2nd half is not pure1  0 4. 1st half of 2nd half not  0 5. 2nd half of 2nd half is  1 6. 1st half of 1st of 2nd is  1 But it is pure (pure0) so this 7. 2nd half of 1st of 2nd not 0 branch ends 010 011 010 010 101 010 111 111 0 0 0 01 1 10 111 111 110 111 010 010 000 000 110 110 101 101 001 001 001 001 001 000 001 111 100 101 100 100 R11 R12 R13 R21 R22 R23 R31 R32 R33 0 0 0 0 1 0 1 1 1 1 1 1 0 1 1 1 0 1 0 0 1 0 1 1 P11 P12 P13 1 1 1 1 0 0 0 0 1 1 1 1 1 1 0 0 1 1 0 1 0 0 0 0 P21 P22 P23 1 1 1 1 0 0 0 0 1 1 0 0 0 0 0 0 R41 R42 R43 0 0 1 1 1 1 1 1 P31 P32 P33 0 0 0 0 0 0 0 0 0 1 0 1 0 0 01 0 0 0 1 0 10 10 01 0001 01 01 01 10 01 10 0 0 0 0 1 1 1 1 1 0 0 0 0 1 0 0 0 0 1 0 1 1 0 1 0 0 P41 P42 P43 0 0 0 1 10 01 0 0 0 0 1 0 0 0 0 01 01 0100 01 01 10 01 Eg, to count, 111 000 001 100s, use “pure111000001100”: 0 23-level P11^P12^P13^P’21^P’22^P’23^P’31^P’32^P33^P41^P’42^P’43 = 0 0 22-level =2 01 21-level
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Using Hex for 8 bits Dec. Hex. Binary Dec. Hex. Binary 0 0 0000 8 8 1000 1 1 0001 9 9 1001 2 2 0010 10 A 1010 3 3 0011 11 B 1011 4 4 0100 12 C 1100 5 5 0101 13 D 1101 6 6 0110 14 E 1110 7 7 0111 15 F 1111 ----------------------------------------------------- Hex 12 AB 02 77 02 Binary 0001 0010 1010 1011 0000 0010 0111 0111 0000 0010 Rick Graziani [email protected] Hex 3C 1A B4 8F C9 Binary 0011 1100 0001 1010 1011 0100 1000 1111 1100 1001 Hex 99 00 7D FF 5C Binary 1001 1001 0000 0000 0111 1101 1111 1111 0101 1100 30
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Depth First Bipartite Max Clique Mine on G9 Find all MCLQs containing A: The ApTree is a MCLQ unless there are pairwise ANDs with same count. A B C D E F G H I J K L M N A A A A A AA AAAA A A B B B B B BB B B BB B B CC CCCC B C D E F GH IJKL M N A C D E F GH I J KL M N EF GHIL D D D D D D D D D E E EE F F F F C E F G H I J K L F G HI E G H I GG HH I J J J J J J J K K K K KKK K K L L L L L L M M M MMMMM H I G I H C E F G H I L C D E F G H I J L C E F G H I A-F G H I J K L N 1 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 01 1000 0 0 1 1 0 1 1 11 0000 0 0 0 0 0 0 0 00 0000 0 0 0 1 1 1 1 11 0000 0 0 0 0 0 0 0 00 0000 0 0 1 1 1 1 1 01 1 0 00 0 0 1 1 0 1 1 11 0 0 00 0 0 0 1 1 1 1 11 1 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 11 0110 11 1100 11 1110 11 1100 10 1000 11 1 0 1 1 0 0 0 00 0 0 0 0 0 0 0 11 1 1 1 1 0 0 0 11 1 1 1 0 0 0 0 11 0 1 0 0 0 0 0 1 0 11 1 1 10 1 1 11 1 1 10 0 1 00 10 11 11 10 11 11 11 10 00 00 00 10 11 10 00 01 10 11 10 00 1 0 1 0 0 00 000 0 0 00 000 0 0 00 000 0 0 00 000 0 0 00 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 000000 000000 000000 000000 000000 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 1 0 1 0 1 1 1 0 0 0 1 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 11 0000 00 0000 00 0000 00 0000 00 0000 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 1 0 10 1 1 10 0 0 00 0 1 11 0 0 00 10 10 11 10 00 00 00 11 00 00 00 10 00 11 11 00 10 01 11 11 0 0 1 1 1 00 000 0 0 00 000 0 0 00 000 0 0 00 000 0 0 00 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 000000 000000 000000 000000 000111 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0000 00 0000 00 0000 00 0000 00 0000 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0 0 00 0 0 00 00 00 00 00 00 00 00 01 00 00 00 00 11 01 10 01 01 11 00 10 1 1 1 0 0 00 001 1 1 00 001 1 1 00 011 1 1 00 110 1 1 00 011 0 1 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 0 000 0 0 0 0 0 1 101 1 1 0 0 0 0 110 1 1 000011 000011 000111 001101 000110 00 0 0 0 0 0 0 00 1 1 1 0 1 1 01 1 1 1 0 1 1 01 0 1 1 1 1 1 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 1 1 1 0 1 1 01 1 1 1 0 1 1 01 0 1 1 1 1 1 00 0 0 0 0 0 0 N N N NN N N N A-FG H I J K L M 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0000 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0000 0 0 0 0 0 00 0000 0 0 0 0 0 0 0 00 0 0 00 0 0 00 0000 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 00 01 1 0 0 0 0 0 0 0 0 0 0 0 000 0 0 0 0 0 0 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 001 0 0 0 0 0 0 0 0 00 00 0 0 0 0 0 0 0 0 0 0 0 0 001 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 00 0 0 0 0 0 0 3 3 6 4 8 8 a e c 5 4 6 3 3 2 3 2 3 3 23 1000 0 0 2 3 2 3 3 23 2 0 00 0 0 65 4420 4 4 3 3 3 2 0 0 0 6 6 73 6 4 7 4 85 89 9 0 0 1 3 4 0 5 0 0 0 1 213 2 2 0 0 1 4 5 5 02 2 3 3 1 3 3 02 2 3 3 1 3 3 The EpTree is a MCLQ(E) unless there are pairwise ANDs with that EpTree having Ct=Ct(E)=8. None, so E-12345679MCLQ(E). Next check for MCLQs with Ct=Ct(E)-1=7. E1234567 E1234569 E1234579 E1234679 E1235679 E1245679 E1345679 E2345679 are 7 non-Maximal-CLQs. Each Ct(EXpTree)=7=CtE-1, expands one of the 7 into a MCLQ(E). We first check if any pairs give have the same #set by pairwise ANDing them: None give the same #set (There is just one E-AND, EH1234679) 12 3 4 5 6 7 9 Each Ct(EXpTree)=6=Ct(E)-2 (EF, EG) expands one. 1 ANDs, EF&EG= EFG-2347 st …Each Ct(EXpTree)=3=Ct(E)-5 (i.e., EI) expands one into a MCLQ(E). When Ct=1 check the #pTrees containing E (12345679) for maximal using 1st step above. The MpTree is a MCLQ(M) unless there are pairwise M-ANDs with it having Ct=Ct(M)=3. Then Ct(MI)=Ct(MJ)=Ct)ML)=Ct(MN)=3. 11 11 11 10 11 01 10 11 11 11 00 00 11 10 11 00 00 00 00 11 11 01 11 10 00 11 11 11 10 00 01 10 01 00 00 10 11 11 01 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 87 8 7 4 4 4 4 Next check for MCLQs with Ct=Ct(M)-1=2. Combine the LetSets of those with the same NumSet. Then combine their LetSets with the LetSet of the , Ct(MG)=Ct(MH)=2 are non-Maximal-CLQs, because they expand IJLMN(12,13,14) to GIJLMN(13,14) and HIJLMN(12,13). When Ct=1 check #pTrees containing M(12,13,14). I J L M H I J L M N G H I J L M N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 A B C D E F G H I J K L M N b c d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 1 1 1 0 1 1 1 1 0 1 0 0 0 1 1 1 0 1 1 1 4 6 7 0 1 0 0 0 0 0 0 0 0 0 1 1 0 0 1 0 0 G I J L M N H I J L M N 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 0 1 2 0 0 0 2 I J L M N 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0 0 0 3 A B C D E F H I A B C E F G H B C D E F G H I A C D E F G H 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 1 C D E G C E F H C E F H 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 E G E H E F E E E I I G G F H 0 1 0 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1 0 0 1 1 1 1 0 0 0 1 0 0 0 0 0 0 1 1 0 0 1 1 1 1 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 3 4 6 6 7 E 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 8
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