scholarly journals Universal Structures and the logic of Forbidden Patterns

2009 ◽  
Vol 5 (2) ◽  
Author(s):  
Florent Madelaine
Keyword(s):  
Forbidden Patterns

Constraints for generating graphs with imposed and forbidden patterns: an application to molecular graphs

Constraints ◽  
2019 ◽  
Vol 25 (1-2) ◽  
pp. 1-22
Author(s):  
Mohamed Amine Omrani ◽  
Wady Naanaa
Keyword(s):  
Molecular Graphs ◽  
Forbidden Patterns

scholarly journals Constraint Satisfaction, Logic and Forbidden Patterns

2007 ◽  
Vol 37 (1) ◽  
pp. 132-163 ◽  
Author(s):  
Florent Madelaine ◽  
Iain A. Stewart
Keyword(s):  
Constraint Satisfaction ◽  
Forbidden Patterns

scholarly journals Embedded Dimension and Time Series Length. Practical Influence on Permutation Entropy and Its Applications

Entropy ◽  
2019 ◽  
Vol 21 (4) ◽  
pp. 385 ◽  
Author(s):  
David Cuesta-Frau ◽  
Juan Pablo Murillo-Escobar ◽  
Diana Alexandra Orrego ◽  
Edilson Delgado-Trejos
Keyword(s):  
Time Series ◽  
Classification Performance ◽  
Permutation Entropy ◽  
Series Length ◽  
Stability Point ◽  
Long Time ◽  
Model Time Series ◽  
The Stability ◽  
Forbidden Patterns ◽  
Short Time

Permutation Entropy (PE) is a time series complexity measure commonly used in a variety of contexts, with medicine being the prime example. In its general form, it requires three input parameters for its calculation: time series length N, embedded dimension m, and embedded delay τ . Inappropriate choices of these parameters may potentially lead to incorrect interpretations. However, there are no specific guidelines for an optimal selection of N, m, or τ , only general recommendations such as N > > m ! , τ = 1 , or m = 3 , … , 7 . This paper deals specifically with the study of the practical implications of N > > m ! , since long time series are often not available, or non-stationary, and other preliminary results suggest that low N values do not necessarily invalidate PE usefulness. Our study analyses the PE variation as a function of the series length N and embedded dimension m in the context of a diverse experimental set, both synthetic (random, spikes, or logistic model time series) and real–world (climatology, seismic, financial, or biomedical time series), and the classification performance achieved with varying N and m. The results seem to indicate that shorter lengths than those suggested by N > > m ! are sufficient for a stable PE calculation, and even very short time series can be robustly classified based on PE measurements before the stability point is reached. This may be due to the fact that there are forbidden patterns in chaotic time series, not all the patterns are equally informative, and differences among classes are already apparent at very short lengths.

Forbidden Patterns

2012 ◽  
pp. 327-337 ◽  
Author(s):  
Johannes Fischer ◽  
Travis Gagie ◽  
Tsvi Kopelowitz ◽  
Moshe Lewenstein ◽  
Veli Mäkinen ◽  
...  
Keyword(s):  
Forbidden Patterns

scholarly journals Forbidden patterns and shift systems

2008 ◽  
Vol 115 (3) ◽  
pp. 485-504 ◽  
Author(s):  
José María Amigó ◽  
Sergi Elizalde ◽  
Matthew B. Kennel
Keyword(s):  
Forbidden Patterns

Quantifying stochasticity in the dynamics of delay-coupled semiconductor lasers via forbidden patterns

2010 ◽  
Vol 368 (1911) ◽  
pp. 367-377 ◽  
Author(s):  
Jordi Tiana-Alsina ◽  
Javier M. Buldú ◽  
M. C. Torrent ◽  
Jordi García-Ojalvo
Keyword(s):  
Time Series ◽  
Semiconductor Lasers ◽  
Optical Feedback ◽  
Low Frequency ◽  
Lag Time ◽  
Lasing Threshold ◽  
Switching Dynamics ◽  
Forbidden Patterns ◽  
Coherence Collapse ◽  
Coupled Semiconductor

We quantify the level of stochasticity in the dynamics of two mutually coupled semiconductor lasers. Specifically, we concentrate on a regime in which the lasers synchronize their dynamics with a non-zero lag time, and the leader and laggard roles alternate irregularly between the lasers. We analyse this switching dynamics in terms of the number of forbidden patterns of the alternate time series. The results reveal that the system operates in a stochastic regime, with the level of stochasticity decreasing as the lasers are pumped further away from their lasing threshold. This behaviour is similar to that exhibited by a single semiconductor laser subject to external optical feedback, as its dynamics shifts from the regime of low-frequency fluctuations to coherence collapse.

scholarly journals Sorting with two stacks in parallel

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Michael Albert ◽  
Mireille Bousquet-Mélou
Keyword(s):  
Generating Function ◽  
Square Lattice ◽  
North West ◽  
International Audience ◽  
Asymptotic Number ◽  
Upper Half Plane ◽  
Recent Activity ◽  
The 1960S ◽  
The Moment ◽  
Forbidden Patterns

International audience At the end of the 1960s, Knuth characterised in terms of forbidden patterns the permutations that can be sorted using a stack. He also showed that they are in bijection with Dyck paths and thus counted by the Catalan numbers. Subsequently, Pratt and Tarjan asked about permutations that can be sorted using two stacks in parallel. This question is significantly harder, and the associated counting question has remained open for 40 years. We solve it by giving a pair of equations that characterise the generating function of such permutations. The first component of this system describes the generating function $Q(a,u)$ of square lattice loops confined to the positive quadrant, counted by the length and the number of North-West and East-South factors. Our analysis of the asymptotic number of sortable permutations relies at the moment on two intriguing conjectures dealing with this series. Given the recent activity on walks confined to cones, we believe them to be attractive $\textit{per se}$. We prove these conjectures for closed walks confined to the upper half plane, or not confined at all. Nous énumérons les permutations triables par deux piles en parallèle. Cette question était restée ouverte depuis les travaux de Knuth, Pratt et Tarjan dans les années 70. Notre solution consiste en une paire d’équations qui caractérisent la série génératrice. La première composante de ce système décrit la série $Q(a,u)$ des chemins fermés confinés dans le quart de plan positif, comptés selon leur longueur et le nombre de facteurs Nord-Ouest ou Est-Sud. Notre analyse du comportement asymptotique du nombre de permutations triables repose à ce stade sur deux conjectures remarquables portant sur $Q(a; u)$. Nous les prouvons pour les chemins fermés non confinés, ou confinés au demi-plan supérieur.

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