Locally-Constrained de Bruijn Codes: Properties, Enumeration, Code Constructions, and Applications

Author(s):  
Yeow Meng Chee ◽  
Tuvi Etzion ◽  
Han Mao Kiah ◽  
Sagi Marcovich ◽  
Alexander Vardy ◽  
...  
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Author(s):  
Martina Rahija ◽  
Annegret Weng
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ZusammenfassungDe-Bruijn-Folgen in der Zauberkunst wurden bereits von mehreren Autoren vorgeschlagen und auch mit Erfolg auf der Bühne eingesetzt (siehe z. B. [2, 4, 11]). Insbesondere gibt es dazu einen bekannten effektvollen Trick mit einem Skatspiel bestehend aus $$32$$ 32  Karten. Dieser setzt nicht voraus, dass sich der Zauberer die De-Bruijn-Folge und die Kodierung in Kartenwerte merken muss, da er alle notwendigen Informationen berechnen kann.In diesem Artikel gehen wir auf die mathematischen Grundlagen spezieller, durch lineare Abbildungen generierte De-Bruijn-Folgen ein. Mit der Theorie gelingt es uns, den Trick von $$32$$ 32  Karten auf das Pokerspiel mit $$52$$ 52  Karten bzw. auf das Kartenspiel „Set“  mit $$81$$ 81  Karten zu übertragen. In beiden Fällen kann sich der Zauberer mit etwas Übung die nötigen Informationen errechnen und muss dadurch wenig memorieren.


2021 ◽  
Vol 16 (1) ◽  
Author(s):  
Kingshuk Mukherjee ◽  
Massimiliano Rossi ◽  
Leena Salmela ◽  
Christina Boucher

AbstractGenome wide optical maps are high resolution restriction maps that give a unique numeric representation to a genome. They are produced by assembling hundreds of thousands of single molecule optical maps, which are called Rmaps. Unfortunately, there are very few choices for assembling Rmap data. There exists only one publicly-available non-proprietary method for assembly and one proprietary software that is available via an executable. Furthermore, the publicly-available method, by Valouev et al. (Proc Natl Acad Sci USA 103(43):15770–15775, 2006), follows the overlap-layout-consensus (OLC) paradigm, and therefore, is unable to scale for relatively large genomes. The algorithm behind the proprietary method, Bionano Genomics’ Solve, is largely unknown. In this paper, we extend the definition of bi-labels in the paired de Bruijn graph to the context of optical mapping data, and present the first de Bruijn graph based method for Rmap assembly. We implement our approach, which we refer to as rmapper, and compare its performance against the assembler of Valouev et al. (Proc Natl Acad Sci USA 103(43):15770–15775, 2006) and Solve by Bionano Genomics on data from three genomes: E. coli, human, and climbing perch fish (Anabas Testudineus). Our method was able to successfully run on all three genomes. The method of Valouev et al. (Proc Natl Acad Sci USA 103(43):15770–15775, 2006) only successfully ran on E. coli. Moreover, on the human genome rmapper was at least 130 times faster than Bionano Solve, used five times less memory and produced the highest genome fraction with zero mis-assemblies. Our software, rmapper is written in C++ and is publicly available under GNU General Public License at https://github.com/kingufl/Rmapper.


2006 ◽  
Vol 41 (9) ◽  
pp. 172-183 ◽  
Author(s):  
Jason Hickey ◽  
Aleksey Nogin ◽  
Xin Yu ◽  
Alexei Kopylov
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Author(s):  
Jarno Alanko ◽  
Bahar Alipanahi ◽  
Jonathen Settle ◽  
Christina Boucher ◽  
Travis Gagie
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Author(s):  
Yaw-Ling Lin ◽  
Charles Ward ◽  
Bharat Jain ◽  
Steven Skiena

Author(s):  
Istvan Szentandrasi ◽  
Michal Zacharias ◽  
Jiri Havel ◽  
Adam Herout ◽  
Marketa Dubska ◽  
...  

2005 ◽  
Vol 298 (1-3) ◽  
pp. 321-333 ◽  
Author(s):  
Boris Shapiro ◽  
Michael Shapiro ◽  
Alek Vainshtein
Keyword(s):  

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