scholarly journals Statistical Complexity Analysis of Turing Machine tapes with Fixed Algorithmic Complexity Using the Best-Order Markov Model

Entropy ◽  
2020 ◽  
Vol 22 (1) ◽  
pp. 105
Author(s):  
Jorge M. Silva ◽  
Eduardo Pinho ◽  
Sérgio Matos ◽  
Diogo Pratas
Keyword(s):  
Markov Model ◽  
Turing Machine ◽  
Complexity Analysis ◽  
Simple Algorithm ◽  
Algorithmic Complexity ◽  
Dynamic Complexity ◽  
Statistical Complexity ◽  
Symbolic Sequences ◽  
Probabilistic Function ◽  
Global And Local

Sources that generate symbolic sequences with algorithmic nature may differ in statistical complexity because they create structures that follow algorithmic schemes, rather than generating symbols from a probabilistic function assuming independence. In the case of Turing machines, this means that machines with the same algorithmic complexity can create tapes with different statistical complexity. In this paper, we use a compression-based approach to measure global and local statistical complexity of specific Turing machine tapes with the same number of states and alphabet. Both measures are estimated using the best-order Markov model. For the global measure, we use the Normalized Compression (NC), while, for the local measures, we define and use normal and dynamic complexity profiles to quantify and localize lower and higher regions of statistical complexity. We assessed the validity of our methodology on synthetic and real genomic data showing that it is tolerant to increasing rates of editions and block permutations. Regarding the analysis of the tapes, we localize patterns of higher statistical complexity in two regions, for a different number of machine states. We show that these patterns are generated by a decrease of the tape’s amplitude, given the setting of small rule cycles. Additionally, we performed a comparison with a measure that uses both algorithmic and statistical approaches (BDM) for analysis of the tapes. Naturally, BDM is efficient given the algorithmic nature of the tapes. However, for a higher number of states, BDM is progressively approximated by our methodology. Finally, we provide a simple algorithm to increase the statistical complexity of a Turing machine tape while retaining the same algorithmic complexity. We supply a publicly available implementation of the algorithm in C++ language under the GPLv3 license. All results can be reproduced in full with scripts provided at the repository.

scholarly journals Concurrent Phenomena at the Reaction Path of the SN2 Reaction CH3Cl + F−. Information Planes and Statistical Complexity Analysis

Entropy ◽  
2013 ◽  
Vol 15 (12) ◽  
pp. 4084-4104 ◽  
Author(s):  
Moyocoyani Molina-Espíritu ◽  
Rodolfo Esquivel ◽  
Juan Angulo ◽  
Jesús Dehesa
Keyword(s):  
Complexity Analysis ◽  
Reaction Path ◽  
Statistical Complexity ◽  
Sn2 Reaction

Permutation Min-Entropy and Statistical Complexity Analysis of Electricity Spot Price

2015 ◽  
Vol 14 (04) ◽  
pp. 1550040 ◽  
Author(s):  
Qingju Fan ◽  
Dan Li
Keyword(s):  
Temporal Dynamics ◽  
Complexity Analysis ◽  
Spot Price ◽  
Temporal Correlations ◽  
Price Series ◽  
Statistical Complexity ◽  
Electricity Spot Price ◽  
Insight Into ◽  
Refined Classification

In this study, we investigate the subtle temporal dynamics of California 1999–2000 spot price series based on permutation min-entropy (PME) and complexity-entropy causality plane. The dynamical transitions of price series are captured and the temporal correlations of price series are also discriminated by the recently introduced PME. Moreover, utilizing the CECP, we provide a refined classification of the monthly price dynamics and obtain an insight into the stochastic nature of price series. The results uncover that the spot price signal presents diverse temporal correlations and exhibits a higher stochastic behavior during the periods of crisis.

Research on Attention EEG Based on the Multiscale Jensen-Shannon Divergence

2014 ◽  
Vol 529 ◽  
pp. 675-678
Author(s):  
Zheng Xia Zhang ◽  
Si Qiu Xu ◽  
Er Ning Zhou ◽  
Xiao Lin Huang ◽  
Jun Wang
Keyword(s):  
Time Series ◽  
Brain Function ◽  
Complexity Analysis ◽  
Function Parameter ◽  
Function Evaluation ◽  
Analysis Method ◽  
Eeg Signals ◽  
Eyes Closed ◽  
Statistical Complexity ◽  
Jensen Shannon Divergence

The article adopted the multiscale Jensen-Shannon Divergence analysis method for EEG complexity analysis. Then the study found that this method can distinguish between three different status (Eyes closed, count, in a daze) acquisition of EEG time series. It showed that three different states of EEG time series have significant differences. In each state of the three different states (Eyes closed, count, in a daze), we aimed at comparing and analyzing the statistical complexity of EEG time series itself and the statistical complexity of EEG time series shuffled data. It was found that there are large amounts of nonlinear time series in the EEG signals. This method is also fully proved that the multiscale JSD algorithm can be used to analyze attention EEG signals. The multiscale Jensen-Shannon Divergence statistical complexity can be used as a measure of brain function parameter, which can be applied to the auxiliary clinical brain function evaluation in the future.

scholarly journals Fact-Alternating Mutex Groups for Classical Planning

2018 ◽  
Vol 61 ◽  
pp. 475-521
Author(s):  
Daniel Fišer ◽  
Antonín Komenda
Keyword(s):  
Linear Programming ◽  
Theoretical Analysis ◽  
Complexity Analysis ◽  
Simple Algorithm ◽  
Finite Domain ◽  
Initial State ◽  
Pruning Algorithm ◽  
Dead End ◽  
New Type ◽  
Np Complete

Mutex groups are defined in the context of STRIPS planning as sets of facts out of which, maximally, one can be true in any state reachable from the initial state. The importance of computing and exploiting mutex groups was repeatedly pointed out in many studies. However, the theoretical analysis of mutex groups is sparse in current literature. This work provides a complexity analysis showing that inference of mutex groups is as hard as planning itself (PSPACE-Complete) and it also shows a tight relationship between mutex groups and graph cliques. This result motivates us to propose a new type of mutex group called a fact-alternating mutex group (fam-group) of which inference is NP-Complete. Moreover, we introduce an algorithm for the inference of fam-groups based on integer linear programming that is complete with respect to the maximal fam-groups and we demonstrate how beneficial fam-groups can be in the translation of planning tasks into finite domain representation. Finally, we show that fam-groups can be used for the detection of dead-end states and we propose a simple algorithm for the pruning of operators and facts as a preprocessing step that takes advantage of the properties of fam-groups. The experimental evaluation of the pruning algorithm shows a substantial increase in a number of solved tasks in domains from the optimal deterministic track of the last two planning competitions (IPC 2011 and 2014).

Research on Attention EEG Based on Jensen-Shannon Divergence

2014 ◽  
Vol 884-885 ◽  
pp. 512-515
Author(s):  
Zheng Xia Zhang ◽  
Si Qiu Xu ◽  
Er Ning Zhou ◽  
Xiao Lin Huang ◽  
Jun Wang
Keyword(s):  
Time Series ◽  
Brain Function ◽  
Complexity Analysis ◽  
The State ◽  
Function Evaluation ◽  
Eeg Signals ◽  
Alpha Wave ◽  
Eyes Closed ◽  
Statistical Complexity ◽  
Jensen Shannon Divergence

The article adopted the Jensen - Shannon Divergence analysis method for alpha wave EEG complexity analysis, used to quantify the three different status (Eyes closed, count, idle) degree of coupling between acquisition of EEG time series. The algorithm are used to calculate the statistical complexity of alpha wave EEG signals then T test, the results show that the state of eyes closed and idle under the coupling degree between EEG time series, and the state of eyes closed and counting, counting and daze cases EEG time series have significant differences. Thus JSD algorithm can be used to analyze EEG signals attention, statistical complexity can be used as a measure of brain function parameters and would be applied to the auxiliary clinical brain function evaluation in the future.

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