On the Number of NK-Kauffman Networks Mapped into a Functional Graph

2016 ◽  
Vol 25 (4) ◽  
pp. 329-345
Author(s):  
Federico Zertuche ◽  
Keyword(s):  
Functional Graph

A model-based approach for systematic risk analysis

2008 ◽  
Vol 222 (1) ◽  
pp. 79-93 ◽  
Author(s):  
J-M Flaus
Keyword(s):  
Fault Diagnosis ◽  
Risk Analysis ◽  
Physical Damage ◽  
Functional Failure ◽  
Model Based ◽  
Functional Aspects ◽  
Functional Graph ◽  
Failure Propagation ◽  
Simultaneous Representation ◽  
Modelling Approach

A modelling approach based on a mixed structural/functional graph that allows the simultaneous representation of the structural and the functional aspects of a system is presented. This model provides a framework to formalize risk analysis while being as simple as possible. The focus of the proposed approach is to achieve in a common analysis a functional failure analysis and the identification of physical damage, these being the two complementary parts of a full risk analysis. The resulting failure propagation graph is useful for model-based reasoning for fault diagnosis, the detection of dangerous situations, and the prediction of critical events. In addition, the approach is modular and reusable. The approach is illustrated by its use on an example.

Grasping the connectivity of random functional graphs

2005 ◽  
Vol 42 (1) ◽  
pp. 1-19 ◽  
Author(s):  
David Romero ◽  
Federico Zertuche
Keyword(s):  
Directed Graph ◽  
Connected Components ◽  
Asymptotic Formulas ◽  
Expected Number ◽  
Functional Graph

A functional graph is a directed graph where every node has out-degree one (loops allowed). This paper deals with connectivity aspects of random functional graphs, like the expected number and size of connected components, cycles, and trajectories. Both exact and asymptotic formulas are provided.

scholarly journals On the heuristic of approximating polynomials over finite fields by random mappings

2016 ◽  
Vol 12 (07) ◽  
pp. 1987-2016 ◽  
Author(s):  
Rodrigo S. V. Martins ◽  
Daniel Panario
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Asymptotic Properties ◽  
Polynomials Over Finite Fields ◽  
Functional Graph ◽  
Random Mappings ◽  
Approximating Polynomials ◽  
Mapping Models ◽  
Quartic Polynomials ◽  
Class Of Functions

The behavior of iterations of functions is frequently approximated by the Brent–Pollard heuristic, where one treats functions as random mappings. We aim at understanding this heuristic and focus on the expected rho length of a node of the functional graph of a polynomial over a finite field. Since the distribution of preimage sizes of a class of functions appears to play a central role in its average rho length, we survey the known results for polynomials over finite fields giving new proofs and improving one of the cases for quartic polynomials. We discuss the effectiveness of the heuristic for many classes of polynomials by comparing our experimental results with the known estimates for different random mapping models. We prove that the distribution of preimage sizes of general polynomials and mappings have similar asymptotic properties, including the same asymptotic average coalescence. The combination of these results and our experiments suggests that these polynomials behave like random mappings, extending a heuristic that was known only for degree [Formula: see text]. We show numerically that the behavior of Chebyshev polynomials of degree [Formula: see text] over finite fields present a sharp contrast when compared to other polynomials in their respective classes.

Topological Analysis of Urban Street Networks

10.1068/b306 ◽  
2004 ◽  
Vol 31 (1) ◽  
pp. 151-162 ◽  
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.

scholarly journals The Effects of an Inductive Reasoning Learning Strategy Assisted by the GeoGebra Software on Students’ Motivation for the Functional Graph II Topic

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 143848-143861 ◽  
Author(s):  
Abdul Halim Abdullah ◽  
Noor Suhaily Misrom ◽  
Umar Haiyat Abdul Kohar ◽  
Mohd Hilmi Hamzah ◽  
Zakiah Mohamad Ashari ◽  
...  
Keyword(s):  
Learning Strategy ◽  
Inductive Reasoning ◽  
Functional Graph
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