Predicting protein folds with structural repeats using a chain graph model

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.

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A Discrete Chain Graph Model for 3d+t Cell Tracking with High Misdetection Robustness

Computer Vision – ECCV 2012 - Lecture Notes in Computer Science ◽

10.1007/978-3-642-33712-3_11 ◽

2012 ◽

pp. 144-157 ◽

Cited By ~ 12

Author(s):

Bernhard X. Kausler ◽

Martin Schiegg ◽

Bjoern Andres ◽

Martin Lindner ◽

Ullrich Koethe ◽

...

Keyword(s):

T Cell ◽

Cell Tracking ◽

Graph Model ◽

Chain Graph

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Finding a chain graph in a bipartite permutation graph

Information Processing Letters ◽

10.1016/j.ipl.2016.04.006 ◽

2016 ◽

Vol 116 (9) ◽

pp. 569-573 ◽

Cited By ~ 1

Author(s):

Masashi Kiyomi ◽

Yota Otachi

Keyword(s):

Chain Graph ◽

Permutation Graph ◽

A Chain

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

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/aicu-2014-0026 ◽

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.

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NP-Hard, Capacitated, Balancedp-Median Problems on a Chain Graph with a Continuum of Link Demands

Mathematics of Operations Research ◽

10.1287/moor.13.1.32 ◽

1988 ◽

Vol 13 (1) ◽

pp. 32-49 ◽

Cited By ~ 46

Author(s):

Hanif D. Sherali ◽

Frederick L. Nordai

Keyword(s):

Np Hard ◽

Chain Graph ◽

A Chain ◽

Median Problems

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

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488504002576 ◽

2004 ◽

Vol 12 (supp01) ◽

pp. 43-62 ◽

Cited By ~ 8

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.

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ACYCLIC MATCHINGS IN SUBCLASSES OF BIPARTITE GRAPHS

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830912500504 ◽

2012 ◽

Vol 04 (04) ◽

pp. 1250050 ◽

Cited By ~ 4

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.

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