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new file mode 100644 index 0000000..abf0c0a Binary files /dev/null and b/_images/f03e528aea54bb8821bce6ba17b7089cf92a5f96a4df1a0688069d78484c664e.png differ diff --git a/notebooks/cryptography.html b/notebooks/cryptography.html index 35afd04..73125f6 100644 --- a/notebooks/cryptography.html +++ b/notebooks/cryptography.html @@ -579,22 +579,22 @@

Run the cell below to download data and prepare our environment!
Buwtsfh 1
+  
Xucvmfi 1
 
 
-Gmh Lwvsfh Fvvmcs, cx Dfvvojbu Uwvv, mj Gckfhgfsgumhf, lwg w kwj luc,
-xch umg clj wkygfkfjs, jfrfh sccd yt wjo qccd qys suf Qwhcjfswif;
-sufhf uf xcyjz cbbytwsmcj xch wj mzvf ucyh, wjz bcjgcvwsmcj mj w
-zmgshfggfz cjf; sufhf umg xwbyvsmfg lfhf hcygfz mjsc wzkmhwsmcj wjz
-hfgtfbs, qo bcjsfktvwsmji suf vmkmsfz hfkjwjs cx suf fwhvmfgs twsfjsg;
-sufhf wjo yjlfvbckf gfjgwsmcjg, whmgmji xhck zckfgsmb wxxwmhg
-buwjifz jwsyhwvvo mjsc tmso wjz bcjsfkts wg uf syhjfz crfh
-suf wvkcgs fjzvfgg bhfwsmcjg cx suf vwgs bfjsyho; wjz sufhf,
-mx frfho csufh vfwx lfhf tclfhvfgg, uf bcyvz hfwz umg clj umgscho
-lmsu wj mjsfhfgs lumbu jfrfh xwmvfz.  Sumg lwg suf twif ws lumbu
-suf xwrcyhmsf rcvykf wvlwog ctfjfz:
+Gpi Hcjmfi Fjjpnm, nr Yfjjlzxu Ucjj, pz Gnbfigfmgupif, hcg c bcz hun,
+rni upg nhz cbegfbfzm, zfsfi mnny ev czl onny oem muf Ocinzfmctf;
+mufif uf rneza nxxevcmpnz rni cz pajf unei, cza xnzgnjcmpnz pz c
+apgmifggfa nzf; mufif upg rcxejmpfg hfif inegfa pzmn cabpicmpnz cza
+ifgvfxm, ol xnzmfbvjcmpzt muf jpbpmfa ifbzczm nr muf fcijpfgm vcmfzmg;
+mufif czl ezhfjxnbf gfzgcmpnzg, cipgpzt rinb anbfgmpx crrcpig
+xucztfa zcmeicjjl pzmn vpml cza xnzmfbvm cg uf meizfa nsfi
+muf cjbngm fzajfgg xifcmpnzg nr muf jcgm xfzmeil; cza mufif,
+pr fsfil nmufi jfcr hfif vnhfijfgg, uf xneja ifca upg nhz upgmnil
+hpmu cz pzmfifgm hupxu zfsfi rcpjfa.  Mupg hcg muf vctf cm hupxu
+muf rcsneipmf snjebf cjhclg nvfzfa:
 
-           "FVVMCS CX DFVVOJBU UWVV.
+           "FJJPNM NR YFJJLZXU UCJJ.
 
 "
@@ -619,9 +619,9 @@

Run the cell below to download data and prepare our environment! -../_images/124783abe30f1a45c8f6b6b43a0a1c658e7d14d3cf2a114a6e4f88c2eb3c6b1e.png -../_images/64494d1c0e8f25e7e06c356f7611e26701ad598bc95087ceffac11cb288a3025.png +

../_images/d863bd207e933224ae76ec4c5283607a6cd48dd89fb8623c027ce9fca4db386e.png +../_images/4c702f95cee8b47820a0be3ba987bfd4416a4affb7f2f3ff53a8f1df05df6e96.png +../_images/c40ac6da54e32be865424b76e8261b8d45c1faabbd8f981e53ce8df044973fb2.png

From the above distributions, you can see that some letters are used consistently more frequently than others across these texts. Let’s take a look at the distribution defined be the average of all of these texts:

@@ -642,8 +642,8 @@

Run the cell below to download data and prepare our environment! -../_images/8f0de5ed877c593cb53833a58cf6186c57ba2d3b28729a24d833553e67e00f02.png + ../_images/28afffafaf72639b51f069c40daa7420ae99c910dd3fd0d7865c1cb551ce9e6c.png +../_images/603686bb2aae188643989561ac1df192d9229dee6415df0834202b7e25e9d7eb.png

With this knowledge about expected patterns of letter occurances, let’s see how they compare to the statistics of our encrypted text.

@@ -661,8 +661,8 @@

Run the cell below to download data and prepare our environment! -../_images/06b0e64495e11b35d0607e10672e296106bb2410318b18ca83ed9fdb459b1f47.png + ../_images/b0ffc5e40e375eef6071fe8e29a4a9dafd0f3aecf26c0c72c47c577d00f5f315.png +../_images/2a22ca9380cae98737d6145d1fbc7e0141c3ab0dae0c6b58eb0e166348bb3077.png

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.

@@ -823,7 +823,7 @@

Run the cell below to download data and prepare our environment!
swap U and J 	percent valid English words: 0.5160721105097512 
+  
swap U and Z 	percent valid English words: 0.5160721105097512 
 
 
 Fhabter 1
@@ -846,7 +846,7 @@ 
Run the cell below to download data and prepare our environment!
swap Z and V 	percent valid English words: 0.6301505155453719 
+
swap A and J 	percent valid English words: 0.6301505155453719 
 
 
 Fhabter 1
@@ -869,7 +869,7 @@ 
Run the cell below to download data and prepare our environment!
swap B and X 	percent valid English words: 0.7351821857016816 
+
swap X and R 	percent valid English words: 0.7351821857016816 
 
 
 Chabter 1
@@ -892,7 +892,7 @@ 
Run the cell below to download data and prepare our environment!
swap Q and T 	percent valid English words: 0.8056729743610003 
+
swap O and V 	percent valid English words: 0.8056729743610003 
 
 
 Chapter 1
@@ -915,7 +915,30 @@ 
Run the cell below to download data and prepare our environment!
swap E and N 	percent valid English words: 0.8100317359986304 
+
swap D and W 	percent valid English words: 0.8099658936778203 
+
+
+Chapter 1
+
+
+Sir Walter Elliot, of Kellynch Hall, in Somersetshire, was a man who,
+for his own amusement, never took up any book but the Baronetage;
+there he found occupation for an idle hour, and consolation in a
+distressed one; there his faculties were roused into admiration and
+respect, by contemplating the limited remnant of the earliest patents;
+there any unwelcome sensations, arising from domestic affairs
+changed naturally into pity and contempt as he turned over
+the almost endless creations of the last century; and there,
+if every other leaf were powerless, he could read his own history
+with an interest which never failed.  This was the page at which
+the favourite volume always opened:
+
+           "ELLIOT OF KELLYNCH HALL.
+
+"
+

+

+
swap D and Q 	percent valid English words: 0.8171690435744479 
 
 
 Chapter 1
diff --git a/notebooks/markov-properties.html b/notebooks/markov-properties.html
index 9ade916..239231a 100644
--- a/notebooks/markov-properties.html
+++ b/notebooks/markov-properties.html
@@ -557,7 +557,7 @@ 
Markov Property:
+../_images/71f0b4ea8867f39d6e2ea3ae0a673b2b49a10c420352cc1bebad333c79a4036e.png
 

 

 

@@ -614,7 +614,7 @@ 
Markov Property:
+../_images/d05bcfd839b849d4867e5e7b29f0daef2ab304b1818ae90a24f0c098e111a08e.png
 

 

 
In fact, we find that if \(S_n = S_S\), then \(S_{n+1} = S_S\).

@@ -639,7 +639,7 @@ 
Markov Property:
-../_images/001a784c446eedac4310e565bb5afee36ef24f3515b8045f2bdd4f3c093420f7.png
+../_images/f03e528aea54bb8821bce6ba17b7089cf92a5f96a4df1a0688069d78484c664e.png
 

 

 

This holds true for most real-life markov chain models, no matter the size of the model. For example:

@@ -671,15 +671,15 @@ 
Markov Property:
-
P = [[0.0686 0.2234 0.7079]
- [0.1632 0.4229 0.414 ]
- [0.2265 0.7077 0.0658]]
+
P = [[0.2289 0.1474 0.6237]
+ [0.6085 0.3802 0.0113]
+ [0.279  0.3466 0.3744]]
 
-(S1, S1): 0.0686		(S1, S2): 0.2234		(S1, S3): 0.7079		(S2, S1): 0.1632		(S2, S2): 0.4229		(S2, S3): 0.414		(S3, S1): 0.2265		(S3, S2): 0.7077		(S3, S3): 0.0658		
+(S1, S1): 0.2289		(S1, S2): 0.1474		(S1, S3): 0.6237		(S2, S1): 0.6085		(S2, S2): 0.3802		(S2, S3): 0.0113		(S3, S1): 0.279		(S3, S2): 0.3466		(S3, S3): 0.3744		
 

 

-../_images/e01f3489391b5b9ef61ac272f1bc7e0925b2a6ce8693a1a36bfdabd63e55fefb.png
-../_images/dd60e879c62cdd2d80da7b98a6a793a3eac6ec3f3144b2dc8cafe632d635c489.png
+../_images/59af4626c4f2160d9b807d50511bf1634a5d9c1e9249b4c3a51c2a2b111405c7.png
+../_images/5fcffda2b99d9a41f43cd0da9bf15d3a7872f3ad68267619988404cc8cd475e3.png
 

 

 

@@ -711,17 +711,17 @@ 
Markov Property:
-
P = [[0.248  0.1642 0.2624 0.2632 0.0622]
- [0.0404 0.1524 0.0644 0.3747 0.3681]
- [0.2573 0.3681 0.0636 0.1906 0.1205]
- [0.4714 0.0347 0.3545 0.0625 0.0769]
- [0.1694 0.0486 0.0535 0.3424 0.3862]]
+
P = [[0.3719 0.2724 0.169  0.0804 0.1062]
+ [0.4993 0.0137 0.1791 0.0699 0.2381]
+ [0.1485 0.1948 0.2291 0.2232 0.2044]
+ [0.4368 0.1322 0.0428 0.1249 0.2633]
+ [0.2379 0.3152 0.0768 0.1954 0.1748]]
 
-(S1, S1): 0.248		(S1, S2): 0.1642		(S1, S3): 0.2624		(S1, S4): 0.2632		(S1, S5): 0.0622		(S2, S1): 0.0404		(S2, S2): 0.1524		(S2, S3): 0.0644		(S2, S4): 0.3747		(S2, S5): 0.3681		(S3, S1): 0.2573		(S3, S2): 0.3681		(S3, S3): 0.0636		(S3, S4): 0.1906		(S3, S5): 0.1205		(S4, S1): 0.4714		(S4, S2): 0.0347		(S4, S3): 0.3545		(S4, S4): 0.0625		(S4, S5): 0.0769		(S5, S1): 0.1694		(S5, S2): 0.0486		(S5, S3): 0.0535		(S5, S4): 0.3424		(S5, S5): 0.3862		
+(S1, S1): 0.3719		(S1, S2): 0.2724		(S1, S3): 0.169		(S1, S4): 0.0804		(S1, S5): 0.1062		(S2, S1): 0.4993		(S2, S2): 0.0137		(S2, S3): 0.1791		(S2, S4): 0.0699		(S2, S5): 0.2381		(S3, S1): 0.1485		(S3, S2): 0.1948		(S3, S3): 0.2291		(S3, S4): 0.2232		(S3, S5): 0.2044		(S4, S1): 0.4368		(S4, S2): 0.1322		(S4, S3): 0.0428		(S4, S4): 0.1249		(S4, S5): 0.2633		(S5, S1): 0.2379		(S5, S2): 0.3152		(S5, S3): 0.0768		(S5, S4): 0.1954		(S5, S5): 0.1748		
 

 

-../_images/d5c7a9caf2153c0f30b4a0e2c0bd8dd97dd8b56900788d13e9c244c9cf49919d.png
-../_images/30191a731b9e2fb391963ee711567c9bb3730b30ea4c881072c041241adb5a2a.png
+../_images/d34a7177499f21a94c5de66ec50d88d1c9e72ebb201aa1e15c3ca16df1651346.png
+../_images/a99f8f15317b66ba3c37db5d80462d28db0bc444a32b685d8f88651033f8e145.png
 

 

 

… 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…

@@ -759,18 +759,18 @@ 
Absorbing Markov Chains and Absorbing States:
-
P = [[0.343  0.3319 0.3251]
- [0.     1.     0.    ]
- [0.592  0.1755 0.2325]]
+
P = [[1.     0.     0.    ]
+ [0.0346 0.475  0.4904]
+ [0.2121 0.3603 0.4276]]
 
-(S1, S1): 0.343		(S1, S2): 0.3319		(S1, S3): 0.3251		(S2, S2): 1.0		(S3, S1): 0.592		(S3, S2): 0.1755		(S3, S3): 0.2325		
+(S1, S1): 1.0		(S2, S1): 0.0346		(S2, S2): 0.475		(S2, S3): 0.4904		(S3, S1): 0.2121		(S3, S2): 0.3603		(S3, S3): 0.4276		
 

 

-../_images/96c622fed9dbdb97b069b1db43410f11b96da9e5328bd19a5f1ca462c5b221ab.png
-
That is, S2 is the Absorbing State.
+../_images/9d0ba67d90265d45e113cf76c6b66e6da779509a756ce133dbff804520cd156e.png
+
That is, S1 is the Absorbing State.
 

 

-../_images/721eade9aee70e21d3e29e82660c47d1779f55a1f859616a7ad2e439273ff00c.png
+../_images/bcf3c175deb0f608bd61a5de43b7fa853b33eb9b0b0834ad41beb912f1e4ddd1.png
 

 

 

Such tranfer matrices have the form of: \(P_{A\ ((m+n)\times(m+n))} = \begin{bmatrix}I_m&O\\R&Q_n\end{bmatrix}\).

diff --git a/notebooks/network-theory.html b/notebooks/network-theory.html
index 90043c1..759ae2e 100644
--- a/notebooks/network-theory.html
+++ b/notebooks/network-theory.html
@@ -495,7 +495,7 @@ 
Network Structures and Small-worldness:
-../_images/4720e75188dcb9ce8a9a439d8590c57974d4eb9671462c120f6c4d1f50a5b745.png
+../_images/b09cc08f5923763f0a4fc2abd501a6083b0b8275ad8b7948470e0c3b2597ad8c.png
 

 

 
@@ -569,7 +569,7 @@ 
Network Metrics:
-../_images/ae145a57ce16fbc3e7a869804e9214f5a23cbfe33e1f0d7db6118f72fa5c0883.png
+../_images/b840a33b98cc5bcb076fc3c06d2190f1fa06715d7409949a832e2bc289588640.png
 

 

 

@@ -647,7 +647,7 @@ 
Community Structures – Modularity and Clustering:
 

 

-../_images/36a254fad87f49a0aba69089920d0e6530956e3784c1bde6d9a50fdd519efe7d.png
+../_images/3cab07ab4c7cc7585c2aae9ef602bcdfd78cffb77f804fc643c04f311c7dc2a6.png
 

 

 
diff --git a/searchindex.js b/searchindex.js
index f1944dd..3fd9751 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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