Vision-Based Freezing of Gait Detection With Anatomic 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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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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A directed graph representation based on a statistical hypothesis testing and application to citation and association structures

IEEE Transactions on Systems Man and Cybernetics ◽

10.1109/tsmc.1984.6313203 ◽

1984 ◽

Vol SMC-14 (2) ◽

pp. 203-212 ◽

Cited By ~ 6

Author(s):

Sadaaki Miyamoto ◽

Kazuhiko Nakayama

Keyword(s):

Hypothesis Testing ◽

Directed Graph ◽

Graph Representation ◽

Statistical Hypothesis ◽

Statistical Hypothesis Testing

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Directed graph representation of half-rate additive codes over GF(4)

Designs Codes and Cryptography ◽

10.1007/s10623-010-9469-6 ◽

2010 ◽

Vol 59 (1-3) ◽

pp. 119-130 ◽

Cited By ~ 4

Author(s):

Lars Eirik Danielsen ◽

Matthew G. Parker

Keyword(s):

Directed Graph ◽

Graph Representation ◽

Additive Codes

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Upward topological analysis of large circuits using directed graph representation

IEEE Transactions on Circuits and Systems ◽

10.1109/tcs.1984.1085503 ◽

1984 ◽

Vol 31 (4) ◽

pp. 410-414 ◽

Cited By ~ 16

Author(s):

J. Starzyk ◽

E. Sliwa

Keyword(s):

Directed Graph ◽

Topological Analysis ◽

Graph Representation

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On reversal of graph orientation

Discrete Mathematics and Applications ◽

10.1515/dma-2002-0503 ◽

2002 ◽

Vol 12 (5) ◽

Cited By ~ 1

Author(s):

V.A. Kolmykov ◽

V.V. Menshikh

Keyword(s):

Linear Space ◽

Directed Graph ◽

Directed Graphs ◽

Graph Representation ◽

Simple Criterion ◽

Graph Orientation ◽

The Past ◽

Linear Representations ◽

Finite Dimensional

AbstractLet each vertex of a finite directed graph be associated with a finite-dimensional linear space and each arc, with a linear transformation of the corresponding space. Such objects are referred to as linear representations of graphs. They naturally arise in some fields of algebra and are deeply studied in the past three decades.Replacing all arcs entering into a sink by oppositely oriented ones, we arrive at a new directed graph. These two directed graphs are close to each other in the sense that the problem of classification of their representation are equivalent, as shown by Bernstein, Gelfand, and Ponomarev. Two orientations are equivalent if one is derived from another by means of a sequence of the above transformations.In the directed graph representation theory, of most interest are circuit-free orientations. In this paper, we give a simple criterion for equivalence of circuit-free orientations. We prove that two orientations are equivalent if and only if some integrals of these orientations are equal to each other.

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