A characterization of moral transitive acyclic directed graph Markov models as labeled trees

2003 ◽  
Vol 115 (1) ◽  
pp. 235-259 ◽  
Author(s):  
Robert Castelo ◽  
Arno Siebes
Keyword(s):  
Directed Graph ◽  
Markov Models ◽  
Labeled Trees ◽  
Acyclic Directed Graph

A Minimax Equality Related to the Longest Directed Path in an Acyclic Graph

1975 ◽  
Vol 27 (2) ◽  
pp. 348-351 ◽  
Author(s):  
K. Vidyasankar ◽  
D. H. Younger
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Directed Path ◽  
Acyclic Graph ◽  
Vertex Set ◽  
Acyclic Directed Graph

As an analog of a recently established minimax equality for directed graphs [1], I. Simon has suggested that the following be investigated.1.1. For a finite acyclic directed graph G, a minimum collection of directed coboundaries whose union is the edge set of G has cardinality equal to that of a maximum strong matching of G.This minimax equality is here proved, using a characterization of a maximum strong matching of an acyclic graph as the set of edges of a longest directed path in the graph.The terms employed in the above theorem are defined as follows. Let G be a finite directed graph with vertex set VG and edge set eG

scholarly journals Group gradations on Leavitt path algebras

2019 ◽  
Vol 19 (09) ◽  
pp. 2050165 ◽  
Author(s):  
Patrik Nystedt ◽  
Johan Öinert
Keyword(s):  
Directed Graph ◽  
Path Algebra ◽  
Graded Rings ◽  
Leavitt Path Algebra ◽  
Arbitrary Group ◽  
Graded Ring ◽  
Identity Component ◽  
Path Algebras ◽  
Leavitt Path Algebras

Given a directed graph [Formula: see text] and an associative unital ring [Formula: see text] one may define the Leavitt path algebra with coefficients in [Formula: see text], denoted by [Formula: see text]. For an arbitrary group [Formula: see text], [Formula: see text] can be viewed as a [Formula: see text]-graded ring. In this paper, we show that [Formula: see text] is always nearly epsilon-strongly [Formula: see text]-graded. We also show that if [Formula: see text] is finite, then [Formula: see text] is epsilon-strongly [Formula: see text]-graded. We present a new proof of Hazrat’s characterization of strongly [Formula: see text]-graded Leavitt path algebras, when [Formula: see text] is finite. Moreover, if [Formula: see text] is row-finite and has no source, then we show that [Formula: see text] is strongly [Formula: see text]-graded if and only if [Formula: see text] has no sink. We also use a result concerning Frobenius epsilon-strongly [Formula: see text]-graded rings, where [Formula: see text] is finite, to obtain criteria which ensure that [Formula: see text] is Frobenius over its identity component.

scholarly journals Digraphs with eulerian chains

1986 ◽  
Vol 41 (3) ◽  
pp. 298-303
Author(s):  
D. K. Skilton
Keyword(s):  
Directed Graph ◽  
Undirected Graphs ◽  
Survey Paper ◽  
Similar Work

AbstractAn eulerian chain in a directed graph is a continuous directed route which traces every arc of the digraph exactly once. Such a route may be finite or infinite, and may have 0, 1 or 2 end vertices. For each kind of eulerian chain, there is a characterization of those diagraphs possessing such a route. In this survey paper we strealine these characterizations, and then synthesize them into a single description of all digraphs having some eulerian chain. Similar work has been done for eulerian chains in undirected graphs, so we are able to compare corresponding results for graphs and digraphs.

scholarly journals The structure of intrinsic complexity of learning

1997 ◽  
Vol 62 (4) ◽  
pp. 1187-1201 ◽  
Author(s):  
Sanjay Jain ◽  
Arun Sharma
Keyword(s):  
Directed Graph ◽  
Learning Algorithm ◽  
Recursion Theory ◽  
Language Identification ◽  
Learning Problems ◽  
Pattern Languages ◽  
Language Classes ◽  
Resource Requirements ◽  
Intrinsic Complexity ◽  
Acyclic Directed Graph

AbstractLimiting identification of r.e. indexes for r.e. languages (from a presentation of elements of the language) and limiting identification of programs for computable functions (from a graph of the function) have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of “intrinsic” complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursion theory to compare and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, Kinber, and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification.The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages.Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open.

scholarly journals OBSTRUCTIONS TO A GENERAL CHARACTERIZATION OF GRAPH CORRESPONDENCES

2013 ◽  
Vol 95 (2) ◽  
pp. 169-188
Author(s):  
S. KALISZEWSKI ◽  
NURA PATANI ◽  
JOHN QUIGG
Keyword(s):  
Directed Graph ◽  
Discrete Space ◽  
Topological Graphs ◽  
Locally Compact ◽  
General Characterization ◽  
Product Systems ◽  
Vertex Set ◽  
Higher Rank

AbstractFor a countable discrete space $V$, every nondegenerate separable ${C}^{\ast } $-correspondence over ${c}_{0} (V)$ is isomorphic to one coming from a directed graph with vertex set $V$. In this paper we demonstrate why the analogous characterizations fail to hold for higher-rank graphs (where one considers product systems of ${C}^{\ast } $-correspondences) and for topological graphs (where $V$ is locally compact Hausdorff), and we discuss the obstructions that arise.

A characterization of HRV's nonlinear hidden dynamics by means of Markov models

1999 ◽  
Vol 46 (8) ◽  
pp. 978-986 ◽  
Author(s):  
R. Silipo ◽  
G. Deco ◽  
R. Vergassola ◽  
C. Gremigni
Keyword(s):  
Markov Models

scholarly journals GToTree: a user-friendly workflow for phylogenomics

2019 ◽  
Author(s):  
Michael D. Lee
Keyword(s):  
Markov Models ◽  
Link Type ◽  
File Formats ◽  
Evolutionary Inference ◽  
Computational Work ◽  
Command Line Tool ◽  
Genome Level ◽  
User Friendly ◽  
Reference Genomes

AbstractSummaryGenome-level evolutionary inference (i.e., phylogenomics) is becoming an increasingly essential step in many biologists’ work - such as in the characterization of newly recovered genomes, or in leveraging available reference genomes to guide evolutionary questions. Accordingly, there are several tools available for the major steps in a phylogenomics workflow. But for the biologist whose main focus is not bioinformatics, much of the computational work required - such as accessing genomic data on large scales, integrating genomes from different file formats, performing required filtering, stitching different tools together, etc. - can be prohibitive. Here I introduce GToTree, a command-line tool that can take any combination of fasta files, GenBank files, and/or NCBI assembly accessions as input and outputs an alignment file, estimates of genome completeness and redundancy, and a phylogenomic tree based on the specified singlecopy gene (SCG) set. While GToTree can work with any custom hidden Markov Models (HMMs), also included are 13 newly generated SCG-set HMMs for different lineages and levels of resolution, built based on searches of ~12,000 bacterial and archaeal high-quality genomes. GToTree aims to give more researchers the capability to make phylogenomic trees.AvailabilityGToTree is open-source and freely available for download from: github.com/AstrobioMike/GToTreeDocumentationgithub.com/AstrobioMike/GToTree/wikiImplementationGToTree is implemented primarily in bash, with helper scripts written in [email protected]

scholarly journals A Construction for the Hat Problem on a Directed Graph

10.37236/1994 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Rani Hod ◽  
Marcin Krzywkowski
Keyword(s):  
Directed Graph ◽  
Directed Graphs ◽  
Maximum Clique ◽  
Clique Number ◽  
Bipartite Graphs ◽  
The Other ◽  
Complete Graphs ◽  
Undirected Graphs ◽  
Asymptotically Optimal

A team of $n$ players plays the following game. After a strategy session, each player is randomly fitted with a blue or red hat. Then, without further communication, everybody can try to guess simultaneously his own hat color by looking at the hat colors of the other players. Visibility is defined by a directed graph; that is, vertices correspond to players, and a player can see each player to whom he is connected by an arc. The team wins if at least one player guesses his hat color correctly, and no one guesses his hat color wrong; otherwise the team loses. The team aims to maximize the probability of a win, and this maximum is called the hat number of the graph.Previous works focused on the hat problem on complete graphs and on undirected graphs. Some cases were solved, e.g., complete graphs of certain orders, trees, cycles, and bipartite graphs. These led Uriel Feige to conjecture that the hat number of any graph is equal to the hat number of its maximum clique.We show that the conjecture does not hold for directed graphs. Moreover, for every value of the maximum clique size, we provide a tight characterization of the range of possible values of the hat number. We construct families of directed graphs with a fixed clique number the hat number of which is asymptotically optimal. We also determine the hat number of tournaments to be one half.

Sign in / Sign up

Export Citation Format

Share Document