Finding a chain graph in a bipartite permutation graph

2016 ◽  
Vol 116 (9) ◽  
pp. 569-573 ◽  
Author(s):  
Masashi Kiyomi ◽  
Yota Otachi
Keyword(s):  
Chain Graph ◽  
Permutation Graph ◽  
A Chain

ACYCLIC MATCHINGS IN SUBCLASSES OF BIPARTITE GRAPHS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250050 ◽  
Author(s):  
B. S. PANDA ◽  
D. PRADHAN
Keyword(s):  
Time Algorithm ◽  
Bipartite Graphs ◽  
Maximum Cardinality ◽  
Chain Graph ◽  
Matching Problem ◽  
Permutation Graph ◽  
Complexity Result ◽  
Np Complete ◽  
A Chain ◽  
Acyclic Matching

A set M ⊆ E is called an acyclic matching of a graph G = (V, E) if no two edges in M are adjacent and the subgraph induced by the set of end vertices of the edges of M is acyclic. Given a positive integer k and a graph G = (V, E), the acyclic matching problem is to decide whether G has an acyclic matching of cardinality at least k. Goddard et al. (Discrete Math.293(1–3) (2005) 129–138) introduced the concept of the acyclic matching problem and proved that the acyclic matching problem is NP-complete for general graphs. In this paper, we propose an O(n + m) time algorithm to find a maximum cardinality acyclic matching in a chain graph having n vertices and m edges and obtain an expression for the number of maximum cardinality acyclic matchings in a chain graph. We also propose a dynamic programming-based O(n + m) time algorithm to find a maximum cardinality acyclic matching in a bipartite permutation graph having n vertices and m edges. Finally, we strengthen the complexity result of the acyclic matching problem by showing that this problem remains NP-complete for perfect elimination bipartite graphs.

scholarly journals On Strongly Sum Difference Quotient Labeling of One-Point Union of Graphs, Chain and Corona Graphs

2015 ◽  
Vol 61 (1) ◽  
pp. 101-108
Author(s):  
A.D. Akwu
Keyword(s):  
Difference Quotient ◽  
Chain Graph ◽  
Quotient Graph ◽  
The Third ◽  
A Chain ◽  
Corona Product ◽  
Corona Graphs

Abstract In this paper we study strongly sum difference quotient labeling of some graphs that result from three different constructions. The first construction produces one- point union of graphs. The second construction produces chain graph, i.e., a concatenation of graphs. A chain graph will be strongly sum difference quotient graph if any graph in the chain, accepts strongly sum difference quotient labeling. The third construction is the corona product; strongly sum difference quotient labeling of corona graph is obtained.

CHARACTERIZATION OF ESSENTIAL GRAPHS BY MEANS OF THE OPERATION OF LEGAL MERGING OF COMPONENTS

2004 ◽  
Vol 12 (supp01) ◽  
pp. 43-62 ◽  
Author(s):  
MILAN STUDENÝ
Keyword(s):  
Bayesian Networks ◽  
Bayesian Network ◽  
Equivalence Class ◽  
Chain Graph ◽  
Induced Subgraphs ◽  
Alternative Characterization ◽  
Main Observation ◽  
A Chain ◽  
Chain Graphs

One of the most common ways of representing classes of equivalent Bayesian networks is the use of essential graphs which are also known in the literature as completed patterns or completed pdags. The name essential graph was proposed by Andersson, Madigan and Perlman who also gave a graphical characterization of essential graphs. In this paper an alternative characterization of essential graphs is presented. The main observation is that every essential graph is the largest chain graph within a special class of chain graphs. More precisely, every equivalence class of Bayesian networks is contained in an equivalence class of chain graphs without flags (= certain induced subgraphs). A special operation of legal merging of (connectivity) components for a chain graph without flags is introduced. This operation leads to an algorithm for finding the essential graph on the basis of any graph in that equivalence class of chain graphs without flags which contains the equivalence class of a Bayesian network. In particular, the algorithm may start with any Bayesian network.

scholarly journals Chain Graph Models to Elicit the Structure of a Bayesian Network

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Federico M. Stefanini
Keyword(s):  
Graphical Models ◽  
Bayesian Methods ◽  
Prior Distribution ◽  
Graph Model ◽  
Structural Features ◽  
Chain Graph ◽  
Graph Models ◽  
Degree Of Belief ◽  
Statistical Background ◽  
A Chain

Bayesian networks are possibly the most successful graphical models to build decision support systems. Building the structure of large networks is still a challenging task, but Bayesian methods are particularly suited to exploit experts’ degree of belief in a quantitative way while learning the network structure from data. In this paper details are provided about how to build a prior distribution on the space of network structures by eliciting a chain graph model on structural reference features. Several structural features expected to be often useful during the elicitation are described. The statistical background needed to effectively use this approach is summarized, and some potential pitfalls are illustrated. Finally, a few seminal contributions from the literature are reformulated in terms of structural features.

Unbalanced, capacitatedp-median problems on a chain graph with a continuum of link demands

Networks ◽  
1991 ◽  
Vol 21 (2) ◽  
pp. 133-163 ◽  
Author(s):  
Hanif D. Sherali ◽  
Thomas P. Rizzo
Keyword(s):  
Chain Graph ◽  
A Chain ◽  
Median Problems

Observation of Atom Rows in Thorium Pyromellitate Using a Field Emission STEM

1977 ◽  
Vol 35 ◽  
pp. 80-81
Author(s):  
H. Todokoro ◽  
S. Nomura ◽  
T. Komoda
Keyword(s):  
Field Emission ◽  
Amorphous Carbon ◽  
Carbon Film ◽  
Dark Field Image ◽  
Dark Field ◽  
Amorphous Carbon Film ◽  
Atomic Size ◽  
Wide Range ◽  
A Chain

It is interesting to observe polymers at atomic size resolution. Some works have been reported for thorium pyromellitate by using a STEM (1), or a CTEM (2,3). The results showed that this polymer forms a chain in which thorium atoms are arranged. However, the distance between adjacent thorium atoms varies over a wide range (0.4-1.3nm) according to the different authors.The present authors have also observed thorium pyromellitate specimens by means of a field emission STEM, described in reference 4. The specimen was prepared by placing a drop of thorium pyromellitate in 10-3 CH3OH solution onto an amorphous carbon film about 2nm thick. The dark field image is shown in Fig. 1A. Thorium atoms are clearly observed as regular atom rows having a spacing of 0.85nm. This lattice gradually deteriorated by successive observations. The image changed to granular structures, as shown in Fig. 1B, which was taken after four scanning frames.

Time-Resolved Cryo-Electron Microscopy of Oscillating Microtubules

1990 ◽  
Vol 48 (1) ◽  
pp. 502-503
Author(s):  
Eva-Maria Mandelkow ◽  
Ron Milligan
Keyword(s):  
Electron Microscopy ◽  
Dynamic Instability ◽  
Entire Solution ◽  
Reaction Scheme ◽  
Time Resolved ◽  
X Ray ◽  
X Ray Scattering ◽  
A Chain ◽  
Ray Scattering

Microtubules form part of the cytoskeleton of eukaryotic cells. They are hollow libers of about 25 nm diameter made up of 13 protofilaments, each of which consists of a chain of heterodimers of α-and β-tubulin. Microtubules can be assembled in vitro at 37°C in the presence of GTP which is hydrolyzed during the reaction, and they are disassembled at 4°C. In contrast to most other polymers microtubules show the behavior of “dynamic instability”, i.e. they can switch between phases of growth and phases of shrinkage, even at an overall steady state [1]. In certain conditions an entire solution can be synchronized, leading to autonomous oscillations in the degree of assembly which can be observed by X-ray scattering (Fig. 1), light scattering, or electron microscopy [2-5]. In addition such solutions are capable of generating spontaneous spatial patterns [6].In an earlier study we have analyzed the structure of microtubules and their cold-induced disassembly by cryo-EM [7]. One result was that disassembly takes place by loss of protofilament fragments (tubulin oligomers) which fray apart at the microtubule ends. We also looked at microtubule oscillations by time-resolved X-ray scattering and proposed a reaction scheme [4] which involves a cyclic interconversion of tubulin, microtubules, and oligomers (Fig. 2). The present study was undertaken to answer two questions: (a) What is the nature of the oscillations as seen by time-resolved cryo-EM? (b) Do microtubules disassemble by fraying protofilament fragments during oscillations at 37°C?

Do Event-Related Brain Potentials Reflect Mental (Cognitive) Operations?

2002 ◽  
Vol 16 (3) ◽  
pp. 129-149 ◽  
Author(s):  
Boris Kotchoubey
Keyword(s):  
Cognitive Processes ◽  
Point Of View ◽  
Internal Variables ◽  
Brain Potentials ◽  
Cognitive Operations ◽  
External Variables ◽  
Series Of Experiments ◽  
Mental Operations ◽  
A Chain ◽  
Processing Mechanisms

Abstract Most cognitive psychophysiological studies assume (1) that there is a chain of (partially overlapping) cognitive processes (processing stages, mechanisms, operators) leading from stimulus to response, and (2) that components of event-related brain potentials (ERPs) may be regarded as manifestations of these processing stages. What is usually discussed is which particular processing mechanisms are related to some particular component, but not whether such a relationship exists at all. Alternatively, from the point of view of noncognitive (e. g., “naturalistic”) theories of perception ERP components might be conceived of as correlates of extraction of the information from the experimental environment. In a series of experiments, the author attempted to separate these two accounts, i. e., internal variables like mental operations or cognitive parameters versus external variables like information content of stimulation. Whenever this separation could be performed, the latter factor proved to significantly affect ERP amplitudes, whereas the former did not. These data indicate that ERPs cannot be unequivocally linked to processing mechanisms postulated by cognitive models of perception. Therefore, they cannot be regarded as support for these models.

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