-
Notifications
You must be signed in to change notification settings - Fork 36
/
Copy pathlearn-lang-diary-part-four.lyx
17705 lines (13666 loc) · 352 KB
/
learn-lang-diary-part-four.lyx
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
#LyX 2.3 created this file. For more info see http://www.lyx.org/
\lyxformat 544
\begin_document
\begin_header
\save_transient_properties true
\origin unavailable
\textclass article
\begin_preamble
\usepackage{url}
\usepackage{slashed}
\end_preamble
\use_default_options false
\maintain_unincluded_children false
\language english
\language_package default
\inputencoding utf8
\fontencoding global
\font_roman "times" "default"
\font_sans "helvet" "default"
\font_typewriter "cmtt" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\use_microtype false
\use_dash_ligatures false
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref true
\pdf_bookmarks true
\pdf_bookmarksnumbered false
\pdf_bookmarksopen false
\pdf_bookmarksopenlevel 1
\pdf_breaklinks true
\pdf_pdfborder true
\pdf_colorlinks true
\pdf_backref false
\pdf_pdfusetitle true
\papersize default
\use_geometry false
\use_package amsmath 2
\use_package amssymb 2
\use_package cancel 1
\use_package esint 0
\use_package mathdots 1
\use_package mathtools 1
\use_package mhchem 0
\use_package stackrel 1
\use_package stmaryrd 1
\use_package undertilde 1
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 0
\use_minted 0
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\is_math_indent 0
\math_numbering_side default
\quotes_style english
\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
\listings_params "basicstyle={\ttfamily},basewidth={0.45em}"
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header
\begin_body
\begin_layout Title
Language Learning Diary - Part Four
\end_layout
\begin_layout Date
Sept 2021 - Dec 2021
\end_layout
\begin_layout Author
Linas Vepstas
\end_layout
\begin_layout Abstract
The language-learning effort involves research and software development
to implement the ideas concerning unsupervised learning of grammar, syntax
and semantics from corpora.
This document contains supplementary notes and a loosely-organized semi-chronol
ogical diary of results.
The notes here might not always makes sense; they are a short-hand for
my own benefit, rather than aimed at you, dear reader!
\end_layout
\begin_layout Section*
Introduction
\end_layout
\begin_layout Standard
Part Four of the diary on the language-learning effort continues work on
the English dataset.
\end_layout
\begin_layout Section*
Summary Conclusions
\end_layout
\begin_layout Standard
A summary of what is found in this part of the diary:
\end_layout
\begin_layout Itemize
Connector sequences or
\begin_inset Quotes eld
\end_inset
disjuncts
\begin_inset Quotes erd
\end_inset
are the
\begin_inset Quotes eld
\end_inset
jigsaw pieces
\begin_inset Quotes erd
\end_inset
extracted from maximum planar spanning-graph (MPG) parses of English sentences.
How many connectors are there on a typical jigsaw piece? Answer: 2.25 on
average.
These are closely modeled by a log-normal distribution.
This is good news for English, where we expect nouns to typically have
1, 2 or 3 connectors, and verbs and prepositions to have 2,3,4.
Adjectives, adverbs and determiners typically have only 1 connector.
Thus the observed distribution matches what one would expect to find.
\end_layout
\begin_layout Itemize
The number of words having any given number of connector sequences also
follows a log-normal distribution.
\end_layout
\begin_layout Itemize
The merger of some top-ranked similar words is explored in detail.
For example, the merger of
\begin_inset Quotes eld
\end_inset
is
\begin_inset Quotes erd
\end_inset
-
\begin_inset Quotes erd
\end_inset
was
\begin_inset Quotes erd
\end_inset
into one word-class.
It seems to go well.
\end_layout
\begin_layout Itemize
It appears that there are cliques or almost-cliques of similar words.
That is, not just word pairs, but groups of 3 or 4 or more words that are
all similar to one-another.
This suggests that such
\begin_inset Quotes eld
\end_inset
in-groups
\begin_inset Quotes erd
\end_inset
of similar words should be merged.
A half-dozen different such in-groups are explored in detail.
They look pretty good.
\end_layout
\begin_layout Itemize
The above leads to a break-through, an important advance in the theory.
One must merge together not only groups of similar words, but only those
disjuncts that are shared by a majority of the words in the in-group.
This is a two-step process: first, an in-group of similar words is selected.
Then, one looks to see what traits (disjuncts) the members of that in-group
have in common.
Only those traits that most group members share are voted into the group.
This solves an important clustering problem: it generalizes, without generalizi
ng over-broadly.
I think this is a major advance in the theory, here.
\end_layout
\begin_layout Itemize
I believe that the result of merging as described above corresponds (strongly)
to word-senses.
(Or it should correspond.) This remains unexplored.
\end_layout
\begin_layout Itemize
How big should an in-group be? The sizes of a dozen different groups are
explored, as a function of the similarity between group members.
It appears that, as one loosens the restrictions on group membership, the
size of the group grows at first very slowly (not at all) and then grows
explosively.
The ideal group size is then the largest group below the explosive-growth
threshold.
\end_layout
\begin_layout Itemize
A good judgment of similarity is needed.
This was explored in great depth in the Diary Part Three.
The mutual information (MI) survives as a good way of judging similarity.
Below, it is discovered that an even better judgment is given by the average
of the MI and the log-frequency.
That is, extremely rare words can have a huge MI, but this is boring, because
the words are rare.
We want to know what words are common (frequent) and also have a large
MI.
This is provided by the average.
Pulling it all together, this results in a square-root in the expression:
\begin_inset Formula
\[
\mbox{ranked}MI\left(w,u\right)=\log_{2}\frac{f\left(w,u\right)}{\sqrt{f\left(w\right)f\left(u\right)}}
\]
\end_inset
where
\begin_inset Formula $f$
\end_inset
is effectively a dot-product.
See below for details.
This is...
surprising, unheard-of in the literature (I've never seen it before).
Its got some nice properties, including being scale free (thus suggesting
it lives on a projective space.
Perhaps some information-theoretic analog of the Fubini-Study metric? Mathemati
cally, its quite intriguing.) Again, this is a pretty big break-through,
as compared to earlier efforts.
\end_layout
\begin_layout Itemize
The above ranked-MI is explored in considerable detail for the English dataset.
It looks pretty good.
\end_layout
\begin_layout Itemize
This part of the diary ends with the first mega-merge, where the top two-thousan
d most similar and most highly ranked words (similarity measured by ranked-MI)
are merged together according to the in-group algo above.
It
\begin_inset Quotes eld
\end_inset
works
\begin_inset Quotes erd
\end_inset
, in that it doesn't crash, and the results still look reasonable after
a few thousand merges (and many days of CPU time.) Thus, the time is ripe
for exploring in detail the results of this merge.
This is done in the next part, Diary Part Five.
But first, an assortment of
\begin_inset Quotes eld
\end_inset
minor
\begin_inset Quotes erd
\end_inset
(but difficult) bugs have to be fixed (and mostly have been!? Tune in next
week for the continuing adventures...)
\end_layout
\begin_layout Standard
To recap: two important things are found.
First, there appears to be a major break-through: the in-group shared-trait
merge algorithm is discovered, and it seems very promising.
Next, averaging together the MI with the word-frequency gives the rankd-MI
similarity, which seems to provide an ideal way of ranking frequent similar
words.
\end_layout
\begin_layout Subsection*
TODO List
\end_layout
\begin_layout Standard
Some items previously explored, but worth looking at again, with the latest
datasets.
\end_layout
\begin_layout Itemize
Words with the lowest self-MI - what are they? What do they mean?
\end_layout
\begin_layout Section*
Expt-4/5/6 – Miscellany – Sept 2021
\end_layout
\begin_layout Standard
Diary Part Three carried out the bulk of experiment-4 with trimming until
it was discovered that trimming to a minimum support of two is even better.
Assorted data analysis was done.
There are still a few more interesting questions about those datasets.
\end_layout
\begin_layout Subsection*
Length of disjuncts
\end_layout
\begin_layout Standard
For a given length of disjunct, how many sections have a disjunct of that
length? (Counted with multiplicity) Previously, in Diary Part Two page
14 this was a Gaussian, centered at 8.
But this was for a fake language, not for English.
Based on what we expect for English, 8 is an alarmingly large number.
So, some graphs:
\begin_inset Foot
status collapsed
\begin_layout Plain Layout
Data for graphs prepared with `utils/similarity-graphs.scm`
\end_layout
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Graphics
filename en-sims-p3/djlen-dist.eps
width 80text%
\end_inset
\end_layout
\begin_layout Standard
The above shows the number of disjuncts of a given length.
That is, fixing the length, just count how many disjuncts there are.
Also shown is an eyeballed fit using the log-normal distribution.
As before, this is defined as
\end_layout
\begin_layout Standard
\begin_inset Formula
\[
N\left(x;\mu,\sigma\right)=\frac{1}{x\sigma\sqrt{2\pi}}\exp\left(-\frac{\left(\ln x-\mu\right)^{2}}{2\sigma^{2}}\right)
\]
\end_inset
In this graph, shown is
\begin_inset Formula $\mu=0.81$
\end_inset
and
\begin_inset Formula $\sigma=0.27$
\end_inset
.
Note that
\begin_inset Formula $\exp0.81\approx2.25$
\end_inset
and so we can take the average length of a disjunct as 2.25.
This is really pretty nice for English, I guess – we expect common-sense
lengths: transitive verbs with a length of 2 (subject, object); common
nouns with a length of 2 (determiner, verb-connector) or 3 (determiner,
adjective, verb connector); both determiners and modifiers (adjectives,
adverbs) should have a length of 1.
Punctuation, ditransitive verbs, quotations, etc.
have more complex structure.
So above looks healthy.
\end_layout
\begin_layout Standard
How about the observation count of the number of words that have some disjunct
length? Below:
\end_layout
\begin_layout Standard
\align center
\begin_inset Graphics
filename en-sims-p3/djlen-sect-dist.eps
width 80text%
\end_inset
\end_layout
\begin_layout Standard
So this shows three very similar curves.
These are:
\end_layout
\begin_layout Description
number: How many disjuncts there are of a given length.
\end_layout
\begin_layout Description
support: How many sections there are, with that section having a disjunct
of the given length.
\end_layout
\begin_layout Description
count: The number of observations of sections having a disjunct of the given
length.
\end_layout
\begin_layout Standard
Recall that a
\begin_inset Quotes eld
\end_inset
section
\begin_inset Quotes erd
\end_inset
is just a word-disjunct pair.
Thus,
\begin_inset Quotes eld
\end_inset
support
\begin_inset Quotes erd
\end_inset
is when we tally 1 if a section exists, else 0, and
\begin_inset Quotes eld
\end_inset
count
\begin_inset Quotes erd
\end_inset
is how many times that particular pair was observed.
\end_layout
\begin_layout Standard
Looking at that graph, all three have almost the same log-normal distribution,
with the mean inching ever so slightly lower.
The nice behavior persists.
\end_layout
\begin_layout Standard
One last graph: for any given disjunct length, how many unique words are
there that have a disjunct with that length? Shown below.
\end_layout
\begin_layout Standard
\align center
\begin_inset Graphics
filename en-sims-p3/djlen-word-dist.eps
width 80text%
\end_inset
\end_layout
\begin_layout Standard
So its similar to the above, but wider.
Note that any given word might be counted repeatedly, since it might have
disjuncts of various different lengths.
So, to read this graph correctly: there are very few words having disjuncts
of length 8 (two of them, to be precise).
Most words don't have that many disjuncts.
Here's the table:
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="12" columns="2">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
length
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
num words
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
5446
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
14146
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
7762
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
4
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
3776
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
5
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1080
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
6
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
338
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
7
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
66
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
8
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
9
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
0
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
10
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
11
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
That is, there are 5446 words that have disjuncts of length 1, and 14146
words with disjuncts of length 2, and so on.
Recall this dataset has a total of 15083 words, and so apparently, there
are some words that do NOT have any disjuncts of length 2! This is somewhat
surprising.
I wonder what those are.
Lets take a quick look.
\end_layout
\begin_layout Standard
There are
\begin_inset Formula $937=15083-14146$
\end_inset
words that do NOT have disjuncts of length two.
Looking over the list, they are junk.
Here's the top-10, their observation count and their rank in the list of
all words.
\begin_inset VSpace defskip
\end_inset
\end_layout
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="11" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
word
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
count
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
rank
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
DR
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
128
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
1996
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
**********
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
100
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2344
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
Trelawney
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
97
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2390
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
).=
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
96
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2404
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
*********
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
79
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2704
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
U. S
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
76
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
2786
\end_layout