Upward topological analysis of large circuits using directed graph representation

Studying coevolutionary systems in the context of simplified models (i.e., games with pairwise interactions between coevolving solutions modeled as self plays) remains an open challenge since the rich underlying structures associated with pairwise-comparison-based fitness measures are often not taken fully into account. Although cyclic dynamics have been demonstrated in several contexts (such as intransitivity in coevolutionary problems), there is no complete characterization of cycle structures and their effects on coevolutionary search. We develop a new framework to address this issue. At the core of our approach is the directed graph (digraph) representation of coevolutionary problems that fully captures structures in the relations between candidate solutions. Coevolutionary processes are modeled as a specific type of Markov chains—random walks on digraphs. Using this framework, we show that coevolutionary problems admit a qualitative characterization: a coevolutionary problem is either solvable (there is a subset of solutions that dominates the remaining candidate solutions) or not. This has an implication on coevolutionary search. We further develop our framework that provides the means to construct quantitative tools for analysis of coevolutionary processes and demonstrate their applications through case studies. We show that coevolution of solvable problems corresponds to an absorbing Markov chain for which we can compute the expected hitting time of the absorbing class. Otherwise, coevolution will cycle indefinitely and the quantity of interest will be the limiting invariant distribution of the Markov chain. We also provide an index for characterizing complexity in coevolutionary problems and show how they can be generated in a controlled manner.

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Solving Geometry Friends using Monte-Carlo Tree Search with directed graph representation

2014 IEEE Conference on Computational Intelligence and Games ◽

10.1109/cig.2014.6932923 ◽

2014 ◽

Cited By ~ 1

Author(s):

Hyun-Tae Kim ◽

Du-Mim Yoon ◽

Kyung-Joong Kim

Keyword(s):

Monte Carlo ◽

Directed Graph ◽

Graph Representation ◽

Tree Search ◽

Monte Carlo Tree Search

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Topological Analysis of Urban Street Networks

Environment and Planning B Planning and Design ◽

10.1068/b306 ◽

2004 ◽

Vol 31 (1) ◽

pp. 151-162 ◽

Cited By ~ 313

Author(s):

Bin Jiang ◽

Christophe Claramunt

Keyword(s):

Topological Analysis ◽

Small World ◽

Clustering Coefficient ◽

Graph Representation ◽

Small World Networks ◽

Street Network ◽

Scale Free ◽

Urban Street ◽

Street Networks ◽

Functional Graph

The authors propose a topological analysis of large urban street networks based on a computational and functional graph representation. This representation gives a functional view in which vertices represent named streets and edges represent street intersections. A range of graph measures, including street connectivity, average path length, and clustering coefficient, are computed for structural analysis. In order to characterise different clustering degrees of streets in a street network they generalise the clustering coefficient to a k-clustering coefficient that takes into account k neighbours. Based on validations applied to three cities, the authors show that large urban street networks form small-world networks but exhibit no scale-free property.

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Inference Procedures for Ordering Theory

Journal of Educational Statistics ◽

10.3102/10769986002003217 ◽

1977 ◽

Vol 2 (3) ◽

pp. 217-232 ◽

Cited By ~ 6

Author(s):

Frank B. Baker ◽

Lawrence J. Hubert

Keyword(s):

Directed Graph ◽

Permutation Test ◽

Test Procedure ◽

Point Of View ◽

Hierarchical Organization ◽

Graph Representation ◽

Data Set ◽

Test Items ◽

Basic Framework

Given observations on a set of n dichotomously scored test items representing certain skills or tasks, ordering theory attempts to identify a hierarchical organization among the n items. Using this basic framework, a directed graph representation for the empirically obtained hierarchy is discussed along with several assumptions that are necessary from a substantive point of view to justify the analysis that ordering theory provides. Furthermore, a permutation test procedure is introduced that allows a formal comparison of a postulated hierarchy among the n items to the hierarchy elicited from the available data set.

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Estimating Transactions Given Balance Sheets and an Income Statement

Issues in Accounting Education ◽

10.2308/iace.2000.15.3.393 ◽

2000 ◽

Vol 15 (3) ◽

pp. 393-411 ◽

Cited By ~ 2

Author(s):

Anil Arya ◽

John C. Fellingham ◽

Douglas A. Schroeder

Keyword(s):

Linear Algebra ◽

Directed Graph ◽

Traditional Approach ◽

Financial Statements ◽

Graph Representation ◽

Accounting System ◽

Balance Sheets ◽

Systematic Fashion ◽

Income Statement ◽

Double Entry

One way to develop an appreciation for the power and beauty of doubleentry is to derive consistent transaction vectors, i.e., start with financial statements and derive the transaction amounts that could have generated the statements. Working backward to uncover transactions (the inverting exercise) complements the more traditional approach of working forward from transactions to financial statements. In addition, the approach highlights a fundamental accounting activity: aggregation. Financial statements summarize a firm's transactions using only a relatively small number of account balances. A consequence of aggregation is that there are infinite consistent transaction vectors. However, because these infinite solutions are all prepared in accordance with double-entry, they are linked to each other in a systematic fashion. We show how a directed graph representation of the accounting system can be used as a parsimonious means of characterizing all consistent transaction vectors. As the number of accounts and transactions are increased, the inverting exercise becomes tedious if one does not make use of the directed graph. To emphasize this point, the inverting exercise is conducted using a set of published financial statements. We also discuss the issue of picking the most likely transaction vector from the set of consistent transaction vectors. The authors have used this note in undergraduate, M.B.A., and Ph.D. classes. For the Ph.D. class, the note has been supplemented by the more rigorous analyses in the linear algebra literature and the accounting literature.

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