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De Bruijn Graph
In graph theory, an -dimensional De Bruijn graph of symbols is a directed graph representing overlaps between sequences of symbols. It has vertices, consisting of all possible sequences of the given symbols; the same symbol may appear multiple times in a sequence. For a set of symbols the set of vertices is: :V=S^n=\. If one of the vertices can be expressed as another vertex by shifting all its symbols by one place to the left and adding a new symbol at the end of this vertex, then the latter has a directed edge to the former vertex. Thus the set of arcs (that is, directed edges) is :E=\. Although De Bruijn graphs are named after Nicolaas Govert de Bruijn, they were discovered independently by both De Bruijn and I. J. Good. Much earlier, Camille Flye Sainte-Marie implicitly used their properties. Properties * If , then the condition for any two vertices forming an edge holds vacuously, and hence all the vertices are connected, forming a total of edges. * Each vertex has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Radix
In a positional numeral system, the radix or base is the number of unique digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (base number) is ten, because it uses the ten digits from 0 through 9. In any standard positional numeral system, a number is conventionally written as with ''x'' as the string of digits and ''y'' as its base, although for base ten the subscript is usually assumed (and omitted, together with the pair of parentheses), as it is the most common way to express value. For example, (the decimal system is implied in the latter) and represents the number one hundred, while (100)2 (in the binary system with base 2) represents the number four. Etymology ''Radix'' is a Latin word for "root". ''Root'' can be considered a synonym for ''base,'' in the arithmetical sense. In numeral systems In the system with radix 13, for example, a string of digits such as 398 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kautz Graph
The Kautz graph K_M^ is a directed graph of degree M and dimension N+ 1, which has (M +1)M^ vertices labeled by all possible strings s_0 \cdots s_N of length N + 1 which are composed of characters s_i chosen from an alphabet A containing M + 1 distinct symbols, subject to the condition that adjacent characters in the string cannot be equal (s_i \neq s_). The Kautz graph K_M^ has (M + 1)M^ edges \ \, It is natural to label each such edge of K_M^ as s_0s_1 \cdots s_, giving a one-to-one correspondence between edges of the Kautz graph K_M^ and vertices of the Kautz graph K_M^. Kautz graphs are closely related to De Bruijn graphs. Properties * For a fixed degree M and number of vertices V = (M + 1) M^N, the Kautz graph has the smallest diameter of any possible directed graph with V vertices and degree M. * All Kautz graphs have Eulerian cycles. (An Eulerian cycle is one which visits each edge exactly once—This result follows because Kautz graphs have in-degree equal to ou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hamming Graph
Hamming graphs are a special class of graphs named after Richard Hamming and used in several branches of mathematics (graph theory) and computer science. Let be a set of elements and a positive integer. The Hamming graph has vertex set , the set of ordered -tuples of elements of , or sequences of length from . Two vertices are adjacent if they differ in precisely one coordinate; that is, if their Hamming distance is one. The Hamming graph is, equivalently, the Cartesian product of complete graphs .. In some cases, Hamming graphs may be considered more generally as the Cartesian products of complete graphs that may be of varying sizes.. Unlike the Hamming graphs , the graphs in this more general class are not necessarily distance-regular, but they continue to be regular and vertex-transitive. Special cases *, which is the generalized quadrangle *, which is the complete graph . *, which is the lattice graph and also the rook's graph *, which is the singleton gr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruijn Torus
In combinatorial mathematics, a De Bruijn torus, named after Dutch mathematician Nicolaas Govert de Bruijn, is an array of symbols from an alphabet (often just 0 and 1) that contains every possible matrix of given dimensions exactly once. It is a torus because the edges are considered wraparound for the purpose of finding matrices. Its name comes from the De Bruijn sequence, which can be considered a special case where (one dimension). One of the main open questions regarding De Bruijn tori is whether a De Bruijn torus for a particular alphabet size can be constructed for a given and . It is known that these always exist when , since then we simply get the De Bruijn sequences, which always exist. It is also known that "square" tori exist whenever and even (for the odd case the resulting tori cannot be square). The smallest possible binary "square" de Bruijn torus, depicted above right, denoted as de Bruijn torus (or simply as ), contains all binary matrices. ''B''2 Apar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Genome
In the fields of molecular biology and genetics, a genome is all the genetic information of an organism. It consists of nucleotide sequences of DNA (or RNA in RNA viruses). The nuclear genome includes protein-coding genes and non-coding genes, other functional regions of the genome such as regulatory sequences (see non-coding DNA), and often a substantial fraction of 'junk' DNA with no evident function. Almost all eukaryotes have mitochondria and a small mitochondrial genome. Algae and plants also contain chloroplasts with a chloroplast genome. The study of the genome is called genomics. The genomes of many organisms have been sequenced and various regions have been annotated. The International Human Genome Project reported the sequence of the genome for ''Homo sapiens'' in 200The Human Genome Project although the initial "finished" sequence was missing 8% of the genome consisting mostly of repetitive sequences. With advancements in technology that could handle sequenci ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Novo Sequence Assemblers
De novo sequence assemblers are a type of program that assembles short nucleotide sequences into longer ones without the use of a reference genome. These are most commonly used in bioinformatic studies to assemble genomes or transcriptomes. Two common types of de novo assemblers are greedy algorithm assemblers and De Bruijn graph assemblers. Types of de novo assemblers There are two types of algorithms that are commonly utilized by these assemblers: greedy, which aim for local optima, and graph method algorithms, which aim for global optima. Different assemblers are tailored for particular needs, such as the assembly of (small) bacterial genomes, (large) eukaryotic genomes, or transcriptomes. Greedy algorithm assemblers are assemblers that find local optima in alignments of smaller reads. Greedy algorithm assemblers typically feature several steps: 1) pairwise distance calculation of reads, 2) clustering of reads with greatest overlap, 3) assembly of overlapping reads into larg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bioinformatics
Bioinformatics () is an interdisciplinary field that develops methods and software tools for understanding biological data, in particular when the data sets are large and complex. As an interdisciplinary field of science, bioinformatics combines biology, chemistry, physics, computer science, information engineering, mathematics and statistics to analyze and interpret the biological data. Bioinformatics has been used for '' in silico'' analyses of biological queries using computational and statistical techniques. Bioinformatics includes biological studies that use computer programming as part of their methodology, as well as specific analysis "pipelines" that are repeatedly used, particularly in the field of genomics. Common uses of bioinformatics include the identification of candidates genes and single nucleotide polymorphisms (SNPs). Often, such identification is made with the aim to better understand the genetic basis of disease, unique adaptations, desirable properties (e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Koorde
In peer-to-peer networks, Koorde is a distributed hash table (DHT) system based on the Chord DHT and the De Bruijn graph (De Bruijn sequence). Inheriting the simplicity of Chord, Koorde meets hops per node (where is the number of nodes in the DHT), and hops per lookup request with neighbors per node. The Chord concept is based on a wide range of identifiers (e.g. 2) in a structure of a ring where an identifier can stand for both node and data. Node-successor is responsible for the whole range of IDs between itself and its predecessor. De Bruijn's graphs Koorde is based on Chord but also on the De Bruijn graph (De Bruijn sequence). In a -dimensional de Bruijn graph, there are nodes, each of which has a unique ID with bits. The node with ID is connected to nodes and . Thanks to this property, the routing algorithm can route to any destination in hops by successively "shifting in" the bits of the destination ID but only if the dimensions of the distance between and are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Distributed Hash Table
A distributed hash table (DHT) is a distributed system that provides a lookup service similar to a hash table: key–value pairs are stored in a DHT, and any participating node can efficiently retrieve the value associated with a given key. The main advantage of a DHT is that nodes can be added or removed with minimum work around re-distributing keys. ''Keys'' are unique identifiers which map to particular ''values'', which in turn can be anything from addresses, to documents, to arbitrary data. Responsibility for maintaining the mapping from keys to values is distributed among the nodes, in such a way that a change in the set of participants causes a minimal amount of disruption. This allows a DHT to scale to extremely large numbers of nodes and to handle continual node arrivals, departures, and failures. DHTs form an infrastructure that can be used to build more complex services, such as anycast, cooperative web caching, distributed file systems, domain name services, instant ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grid Network
Elex Media Komputindo is a publishing company in Indonesia which publishes books, comics, magazines, novels and other print media. Established on January 15, 1985, Elex Media Komputindo is a subsidiary of Kompas Gramedia Group. Elex is headquartered in Tanah Abang, Central Jakarta. Elex Media Komputindo is known as the pioneer of manga publishing in Indonesia, and is now one of the largest comic publishers in Indonesia. History Established in 1985, Elex Media initially published various electronic and computer-themed books. The founder of Kompas, Jakob Oetama, was interested in the potential of manga during his visit to Japan in the late 1980s. In 1991, Elex Media plunged into the manga publishing industry with the publication of Kyoko Mizuki's ''Candy Candy'' manga, originally published by Kodansha. Other manga like '' Kungfu Boy'', ''Doraemon'', and ''Dragon Ball'' began to follow. The decision of the New Order government to allow the establishment of private television sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Book Thickness
In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings into a ''book'', a collection of half-planes all having the same line as their boundary. Usually, the vertices of the graph are required to lie on this boundary line, called the ''spine'', and the edges are required to stay within a single half-plane. The book thickness of a graph is the smallest possible number of half-planes for any book embedding of the graph. Book thickness is also called pagenumber, stacknumber or fixed outerthickness. Book embeddings have also been used to define several other graph invariants including the pagewidth and book crossing number. Every graph with vertices has book thickness at most \lceil n/2\rceil, and this formula gives the exact book thickness for complete graphs. The graphs with book thickness one are the outerplanar graphs. The graphs with book thickness at most two are the subhamiltonian graphs, which are always planar; more generally, ev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
