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public:de_bruijn [2016/07/06 18:15]
malhotra [Background] 		public:de_bruijn [2022/01/28 17:57] (current)
haggerty
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 In this wiki page, we provide a basic introduction to de Bruijn sequences. The link below leads to a page containing software and instructions for creating your own sequences. In this wiki page, we provide a basic introduction to de Bruijn sequences. The link below leads to a page containing software and instructions for creating your own sequences.
  
-<WRAP info round box 25% LEFT>**More information**\\ \\ \\ [[:public:carry-over_designs|Introduction to carry-over designs]]</WRAP> +**More information**\\ \\ [[:public:carry-over_designs|Introduction to carry-over designs]] \\ \\ 
-<WRAP info round box 25%>**Link to Software**\\ \\ [[:public:de_bruijn_software|Path-guided de Bruijn software and instructions]]</WRAP>+**Link to Software**\\ \\ [[:public:de_bruijn_software|Path-guided de Bruijn software and instructions]]
 =====Motivation===== =====Motivation=====
 A hash function is a central computational and cryptographic technique in which variable length data are mapped to a fixed length variable. One application of this in cryptography is a "checksum" operation, which boils down an arbitrary message into a small, fixed-length variable called a hash code. A given message can only result in one valid hash code, so tampering with the message can be discovered by detecting a change in the hash. A hash function is a central computational and cryptographic technique in which variable length data are mapped to a fixed length variable. One application of this in cryptography is a "checksum" operation, which boils down an arbitrary message into a small, fixed-length variable called a hash code. A given message can only result in one valid hash code, so tampering with the message can be discovered by detecting a change in the hash.
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 which is clearly vast for even modest values of //k// and //n//. Note that any one of these unique sequences may further be used to create //k!// derivative sequences by permuting the assignment of labels in the alphabet. which is clearly vast for even modest values of //k// and //n//. Note that any one of these unique sequences may further be used to create //k!// derivative sequences by permuting the assignment of labels in the alphabet.
  
-Cyclic sequences of this kind are a subject of study in discrete mathematics and have been discovered independently many times. Nicolaas Govert de Bruijn (pronounced roughly [[https://cfn.upenn.edu/aguirre/public/debruijn/forvo_nl_860689_deBruijn.mp3|“duh-BROUN”]]{{:public:logos:mp3_icon.png?20}}), working with Tanja van Ardenne-Ehrenfest, formalized the sequences for //k//>2. After a long life and a productive career, NG de Bruijn [[ http://www.science.uva.nl/math/#item1329781416|died on February 17, 2012.]]+Cyclic sequences of this kind are a subject of study in discrete mathematics and have been discovered independently many times. Nicolaas Govert de Bruijn (pronounced roughly “duh-BROUN”), working with Tanja van Ardenne-Ehrenfest, formalized the sequences for //k//>2. After a long life and a productive career, NG de Bruijn died on February 17, 2012.
 =====Generation of de Bruijn sequences===== =====Generation of de Bruijn sequences=====
 {{  :public:seqs:k3n2_graph.png?350}} {{  :public:seqs:k3n2_graph.png?350}}
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 We have produced a command line (c code) executable which may be used to produce path guided de Bruijn sequences. We have produced a command line (c code) executable which may be used to produce path guided de Bruijn sequences.
  
-<WRAP info round box 200px center>**Link to Software**\\ \\ [[:public:de_bruijn_software|Path-guided de Bruijn software and instructions]]</WRAP>+**Link to Software**\\ \\ [[:public:de_bruijn_software|Path-guided de Bruijn software and instructions]]
  
  
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 ====Type 1, Index 1 sequence==== ====Type 1, Index 1 sequence====
  
-[[t1i1_sequences|Type 1 Index 1 sequences]], initially described by [[http://adsabs.harvard.edu/abs/1955Natur.176..748F|Finnery and Outhwaite in 1956]] are //n//=2 counterbalanced sequences of //k// labels, for //k// > 5. T1I1 sequences have the property of presenting permuted blocks of the labels over the course of the sequence, with repetition of the labels at the boundaries of each block. They were introduced for use in fMRI by [[http://www.ncbi.nlm.nih.gov/sites/entrez?Db=pubmed&Cmd=ShowDetailView&TermToSearch=17376705|GK Aguirre (2007)]].+[[t1i1_sequences|Type 1 Index 1 sequences]], initially described by [[http://adsabs.harvard.edu/abs/1955Natur.176..748F|Finnery and Outhwaite in 1956]] are //n//=2 counterbalanced sequences of //k// labels, for //k// > 5. T1I1 sequences have the property of presenting permuted blocks of the labels over the course of the sequence, with repetition of the labels at the boundaries of each block. They were introduced for use in fMRI by [[https://pubmed.ncbi.nlm.nih.gov/17376705/|GK Aguirre (2007)]].
public/de_bruijn.1467828958.txt.gz · Last modified: 2016/07/06 18:15 by malhotra

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