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cosanlab · Jul 1, 2024 · e049b4e · e049b4e
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diff --git a/_images/ee62d7abf3ac1df4a62c09df57d94b8a674e19142df38edc9e2e2760cfdc57f3.png b/_images/ee62d7abf3ac1df4a62c09df57d94b8a674e19142df38edc9e2e2760cfdc57f3.png
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diff --git a/_images/f96aed2901e0031b17a1292b5f9576ef0dd276bb604e19bb5002d99f76223345.png b/_images/f96aed2901e0031b17a1292b5f9576ef0dd276bb604e19bb5002d99f76223345.png
diff --git a/notebooks/cryptography.html b/notebooks/cryptography.html
@@ -579,22 +579,22 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
         white-space: pre-wrap;
     }
   </style>
-  </div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Ijvtdxl 1
+  </div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Qdjmrao 1
 
 
-Mul Nvgdxl Xgguwd, wh Qxggzoij Jvgg, uo Mwaxlmxdmjulx, nvm v avo njw,
-hwl jum wno vafmxaxod, oxcxl dwwq ft voz rwwq rfd djx Rvlwoxdvyx;
-djxlx jx hwfob wiiftvduwo hwl vo ubgx jwfl, vob iwomwgvduwo uo v
-bumdlxmmxb wox; djxlx jum hvifgduxm nxlx lwfmxb uodw vbaulvduwo vob
-lxmtxid, rz iwodxatgvduoy djx guaudxb lxaovod wh djx xvlguxmd tvdxodm;
-djxlx voz fonxgiwax mxomvduwom, vlumuoy hlwa bwaxmdui vhhvulm
-ijvoyxb ovdflvggz uodw tudz vob iwodxatd vm jx dfloxb wcxl
-djx vgawmd xobgxmm ilxvduwom wh djx gvmd ixodflz; vob djxlx,
-uh xcxlz wdjxl gxvh nxlx twnxlgxmm, jx iwfgb lxvb jum wno jumdwlz
-nudj vo uodxlxmd njuij oxcxl hvugxb.  Djum nvm djx tvyx vd njuij
-djx hvcwfludx cwgfax vgnvzm wtxoxb:
+Txo Njzrao Azzxhr, hi Lazzybqd Djzz, xb Thfaotartdxoa, njt j fjb ndh,
+iho dxt hnb jfstafabr, bauao rhhl sm jby whhl wsr rda Wjohbarjea;
+rdaoa da ihsbc hqqsmjrxhb iho jb xcza dhso, jbc qhbthzjrxhb xb j
+cxtroattac hba; rdaoa dxt ijqszrxat naoa ohstac xbrh jcfxojrxhb jbc
+oatmaqr, wy qhbrafmzjrxbe rda zxfxrac oafbjbr hi rda ajozxatr mjrabrt;
+rdaoa jby sbnazqhfa tabtjrxhbt, joxtxbe iohf chfatrxq jiijxot
+qdjbeac bjrsojzzy xbrh mxry jbc qhbrafmr jt da rsobac huao
+rda jzfhtr abczatt qoajrxhbt hi rda zjtr qabrsoy; jbc rdaoa,
+xi auaoy hrdao zaji naoa mhnaozatt, da qhszc oajc dxt hnb dxtrhoy
+nxrd jb xbraoatr ndxqd bauao ijxzac.  Rdxt njt rda mjea jr ndxqd
+rda ijuhsoxra uhzsfa jznjyt hmabac:
 
-           &quot;XGGUWD WH QXGGZOIJ JVGG.
+           &quot;AZZXHR HI LAZZYBQD DJZZ.
 
 &quot;
 </pre></div>
@@ -661,8 +661,8 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
         white-space: pre-wrap;
     }
   </style>
-  </div><img alt="../_images/6ddc11abb6b52112ce08694a401fedda4d4a99a421db69ba6abb1b2e8fe7995b.png" src="../_images/6ddc11abb6b52112ce08694a401fedda4d4a99a421db69ba6abb1b2e8fe7995b.png" />
-<img alt="../_images/6997918ad9a348f35dc662e461af2e5c47b068841304ae60c10602e98200e9a4.png" src="../_images/6997918ad9a348f35dc662e461af2e5c47b068841304ae60c10602e98200e9a4.png" />
+  </div><img alt="../_images/3a978989f9c09c8afd4882fe741ce2de17419b75a696616bb60d2e812e6bbe53.png" src="../_images/3a978989f9c09c8afd4882fe741ce2de17419b75a696616bb60d2e812e6bbe53.png" />
+<img alt="../_images/dca76f0919c5b8a33feabd4c3989e531b9c329df8cb23b1fff92c3575abf5733.png" src="../_images/dca76f0919c5b8a33feabd4c3989e531b9c329df8cb23b1fff92c3575abf5733.png" />
 </div>
 </div>
 <p>As the above distribution shows us, even though each individual letter in the encrypted text no longer has the same occurance probability as it does in typical English text, the general shape of the re-ordered distribution is still the same. We can use this to build a first-pass remapping to attempt deciphering the encrypted text, substituting each encrypted letter with the English letter closest in usage frequency.</p>
@@ -823,7 +823,7 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
         white-space: pre-wrap;
     }
   </style>
-  </div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap J and O 	percent valid English words: 0.5160721105097512 
+  </div><div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap D and B 	percent valid English words: 0.5160721105097512 
 
 
 Fhabter 1
@@ -846,7 +846,7 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
 &quot;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap B and G 	percent valid English words: 0.6301505155453719 
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap C and Z 	percent valid English words: 0.6301505155453719 
 
 
 Fhabter 1
@@ -869,30 +869,30 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
 &quot;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap I and H 	percent valid English words: 0.7351821857016816 
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap W and M 	percent valid English words: 0.6855502442750102 
 
 
-Chabter 1
+Fhapter 1
 
 
-Sir Walter Elliot, of Kellynch Hall, in Somersetshire, was a man who,
-for his own amusement, never took ub any pook put the Paronetage;
-there he found occubation for an idle hour, and consolation in a
-distressed one; there his faculties were roused into admiration and
-resbect, py contemblating the limited remnant of the earliest batents;
-there any unwelcome sensations, arising from domestic affairs
-changed naturally into bity and contembt as he turned over
-the almost endless creations of the last century; and there,
-if every other leaf were bowerless, he could read his own history
-with an interest which never failed.  This was the bage at which
-the favourite volume always obened:
+Sir Walter Elliot, oc Kellynfh Hall, in Somersetshire, was a man who,
+cor his own amusement, never took up any book but the Baronetage;
+there he cound offupation cor an idle hour, and fonsolation in a
+distressed one; there his cafulties were roused into admiration and
+respeft, by fontemplating the limited remnant oc the earliest patents;
+there any unwelfome sensations, arising crom domestif accairs
+fhanged naturally into pity and fontempt as he turned over
+the almost endless freations oc the last fentury; and there,
+ic every other leac were powerless, he fould read his own history
+with an interest whifh never cailed.  This was the page at whifh
+the cavourite volume always opened:
 
-           &quot;ELLIOT OF KELLYNCH HALL.
+           &quot;ELLIOT OC KELLYNFH HALL.
 
 &quot;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap R and T 	percent valid English words: 0.8056729743610003 
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap Q and I 	percent valid English words: 0.8056729743610003 
 
 
 Chapter 1
@@ -915,7 +915,7 @@ <h2>Run the cell below to download data and prepare our environment!<a class="he
 &quot;
 </pre></div>
 </div>
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap S and K 	percent valid English words: 0.8100317359986304 
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>swap P and G 	percent valid English words: 0.8100317359986304 
 
 
 Chapter 1

diff --git a/notebooks/markov-properties.html b/notebooks/markov-properties.html
@@ -639,7 +639,7 @@ <h2>Markov Property:<a class="headerlink" href="#markov-property" title="Permali
 </div>
 </div>
 <div class="cell_output docutils container">
-<img alt="../_images/9b5520488d3b68e72c44cb206388e3aaf237c467718a44fdc68e2ffbe8f283f2.png" src="../_images/9b5520488d3b68e72c44cb206388e3aaf237c467718a44fdc68e2ffbe8f283f2.png" />
+<img alt="../_images/3746414c52c6308f330db166255b041a896ff4fe629c6e818476f97b62d72603.png" src="../_images/3746414c52c6308f330db166255b041a896ff4fe629c6e818476f97b62d72603.png" />
 </div>
 </div>
 <p><br/><big>This holds true for most real-life markov chain models, no matter the size of the model. For example:</big></p>
@@ -671,15 +671,15 @@ <h2>Markov Property:<a class="headerlink" href="#markov-property" title="Permali
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.2593 0.4643 0.2764]
- [0.2153 0.0049 0.7798]
- [0.7165 0.2668 0.0167]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.5123 0.3757 0.112 ]
+ [0.2856 0.1798 0.5345]
+ [0.5475 0.2395 0.213 ]]
 
-(S1, S1): 0.2593		(S1, S2): 0.4643		(S1, S3): 0.2764		(S2, S1): 0.2153		(S2, S2): 0.0049		(S2, S3): 0.7798		(S3, S1): 0.7165		(S3, S2): 0.2668		(S3, S3): 0.0167		
+(S1, S1): 0.5123		(S1, S2): 0.3757		(S1, S3): 0.112		(S2, S1): 0.2856		(S2, S2): 0.1798		(S2, S3): 0.5345		(S3, S1): 0.5475		(S3, S2): 0.2395		(S3, S3): 0.213		
 </pre></div>
 </div>
-<img alt="../_images/ee62d7abf3ac1df4a62c09df57d94b8a674e19142df38edc9e2e2760cfdc57f3.png" src="../_images/ee62d7abf3ac1df4a62c09df57d94b8a674e19142df38edc9e2e2760cfdc57f3.png" />
-<img alt="../_images/7012195e5f4789340e7f0e6aa42b8cb56bf901238a42a48ad0aedf9d64484bf6.png" src="../_images/7012195e5f4789340e7f0e6aa42b8cb56bf901238a42a48ad0aedf9d64484bf6.png" />
+<img alt="../_images/8a3c009f7f32a0e45e6b5ab7c9681b4a4fd120818deb5658e55b5775caa69de7.png" src="../_images/8a3c009f7f32a0e45e6b5ab7c9681b4a4fd120818deb5658e55b5775caa69de7.png" />
+<img alt="../_images/0f921ed20df485bda29b5be724a20489b0f3f6ead0bafe5fe885ab913837b0a5.png" src="../_images/0f921ed20df485bda29b5be724a20489b0f3f6ead0bafe5fe885ab913837b0a5.png" />
 </div>
 </div>
 <div class="cell docutils container">
@@ -711,17 +711,17 @@ <h2>Markov Property:<a class="headerlink" href="#markov-property" title="Permali
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.0912 0.1942 0.1537 0.1654 0.3955]
- [0.0173 0.1018 0.2343 0.2999 0.3468]
- [0.1786 0.1278 0.1457 0.2636 0.2844]
- [0.1592 0.254  0.1194 0.3328 0.1346]
- [0.1387 0.1288 0.3394 0.3869 0.0061]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.0959 0.2523 0.1152 0.1766 0.3599]
+ [0.2312 0.0024 0.3237 0.2029 0.2398]
+ [0.2459 0.2692 0.1883 0.1102 0.1864]
+ [0.0925 0.1985 0.2657 0.2921 0.1512]
+ [0.2147 0.2201 0.159  0.1955 0.2108]]
 
-(S1, S1): 0.0912		(S1, S2): 0.1942		(S1, S3): 0.1537		(S1, S4): 0.1654		(S1, S5): 0.3955		(S2, S1): 0.0173		(S2, S2): 0.1018		(S2, S3): 0.2343		(S2, S4): 0.2999		(S2, S5): 0.3468		(S3, S1): 0.1786		(S3, S2): 0.1278		(S3, S3): 0.1457		(S3, S4): 0.2636		(S3, S5): 0.2844		(S4, S1): 0.1592		(S4, S2): 0.254		(S4, S3): 0.1194		(S4, S4): 0.3328		(S4, S5): 0.1346		(S5, S1): 0.1387		(S5, S2): 0.1288		(S5, S3): 0.3394		(S5, S4): 0.3869		(S5, S5): 0.0061		
+(S1, S1): 0.0959		(S1, S2): 0.2523		(S1, S3): 0.1152		(S1, S4): 0.1766		(S1, S5): 0.3599		(S2, S1): 0.2312		(S2, S2): 0.0024		(S2, S3): 0.3237		(S2, S4): 0.2029		(S2, S5): 0.2398		(S3, S1): 0.2459		(S3, S2): 0.2692		(S3, S3): 0.1883		(S3, S4): 0.1102		(S3, S5): 0.1864		(S4, S1): 0.0925		(S4, S2): 0.1985		(S4, S3): 0.2657		(S4, S4): 0.2921		(S4, S5): 0.1512		(S5, S1): 0.2147		(S5, S2): 0.2201		(S5, S3): 0.159		(S5, S4): 0.1955		(S5, S5): 0.2108		
 </pre></div>
 </div>
-<img alt="../_images/0bcd42c8593ef1086abc72b89c645c91ade50c66d0d7dc2d2323b4a08779e920.png" src="../_images/0bcd42c8593ef1086abc72b89c645c91ade50c66d0d7dc2d2323b4a08779e920.png" />
-<img alt="../_images/83c4f63b225ea671fcb6a5302808996626b6d761aced25d8658261c59239583d.png" src="../_images/83c4f63b225ea671fcb6a5302808996626b6d761aced25d8658261c59239583d.png" />
+<img alt="../_images/3dfabcf56a576614294b73b382537289eebda32d8937db8cf178acba79f55e2c.png" src="../_images/3dfabcf56a576614294b73b382537289eebda32d8937db8cf178acba79f55e2c.png" />
+<img alt="../_images/71319b46d5e2b5077f49f970b5b24c97c914096e24025facfff81efa08840f3f.png" src="../_images/71319b46d5e2b5077f49f970b5b24c97c914096e24025facfff81efa08840f3f.png" />
 </div>
 </div>
 <p><br/>… even size-105 markov chains, but that will require a lot of computational power. So, let’s jump to a different type of markov chains/states…</p>
@@ -759,18 +759,18 @@ <h3>Absorbing Markov Chains and Absorbing States:<a class="headerlink" href="#ab
 </div>
 </div>
 <div class="cell_output docutils container">
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[1.     0.     0.    ]
- [0.1789 0.5566 0.2645]
- [0.5287 0.4513 0.02  ]]
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>P = [[0.3553 0.3861 0.2586]
+ [0.     1.     0.    ]
+ [0.66   0.0879 0.2521]]
 
-(S1, S1): 1.0		(S2, S1): 0.1789		(S2, S2): 0.5566		(S2, S3): 0.2645		(S3, S1): 0.5287		(S3, S2): 0.4513		(S3, S3): 0.02		
+(S1, S1): 0.3553		(S1, S2): 0.3861		(S1, S3): 0.2586		(S2, S2): 1.0		(S3, S1): 0.66		(S3, S2): 0.0879		(S3, S3): 0.2521		
 </pre></div>
 </div>
-<img alt="../_images/f96aed2901e0031b17a1292b5f9576ef0dd276bb604e19bb5002d99f76223345.png" src="../_images/f96aed2901e0031b17a1292b5f9576ef0dd276bb604e19bb5002d99f76223345.png" />
-<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>That is, S1 is the Absorbing State.
+<img alt="../_images/9444c5151d62ded6685f48aeb2814d30ad9613e3a0211c8d16f27342f2403645.png" src="../_images/9444c5151d62ded6685f48aeb2814d30ad9613e3a0211c8d16f27342f2403645.png" />
+<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>That is, S2 is the Absorbing State.
 </pre></div>
 </div>
-<img alt="../_images/c2d5459abfdafda37118f6a1d3416f591bfa4419f045bf85b4bda14e72661b1b.png" src="../_images/c2d5459abfdafda37118f6a1d3416f591bfa4419f045bf85b4bda14e72661b1b.png" />
+<img alt="../_images/ee7730c4afdacda8eeeb058689504b1a85c5251f489a853530523e71f222b163.png" src="../_images/ee7730c4afdacda8eeeb058689504b1a85c5251f489a853530523e71f222b163.png" />
 </div>
 </div>
 <p><br/>Such tranfer matrices have the form of: <span class="math notranslate nohighlight">\(P_{A\ ((m+n)\times(m+n))} = \begin{bmatrix}I_m&amp;O\\R&amp;Q_n\end{bmatrix}\)</span>.</p>

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+<img alt="../_images/9c799618a11f212604620a56f62710cffe4929f4b846eedf38559ac1c3264491.png" src="../_images/9c799618a11f212604620a56f62710cffe4929f4b846eedf38559ac1c3264491.png" />
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+<img alt="../_images/924d66a9f394326ff14e03938cd751c7cb2b47564b46f49d22ff6dec29332458.png" src="../_images/924d66a9f394326ff14e03938cd751c7cb2b47564b46f49d22ff6dec29332458.png" />
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