Critical curves of rotations Roberts, John A.G.; Saito, Asaki; Vivaldi, Franco
Indagationes mathematicae,
2/2024
Journal Article
Recenzirano
Odprti dostop
In rotations with a binary symbolic dynamics, a critical curve is the locus of parameters for which the boundaries of the partition that defines the symbolic dynamics are connected via a prescribed ...number of iterations and symbolic itinerary. We study the arithmetical and geometrical properties of these curves in parameter space.
We define the class of rapidly left expansive cellular automata, which contains Wolfram's Rule 30, fractional multiplication automata, and many others. Previous results on aperiodicity of columns in ...space-time diagrams of certain cellular automata generalize to this new class. We also present conditions that imply periodic behavior in cellular automata and use these to prove new results on rapidly left expansive cellular automata that originate from the theory of distribution modulo 1.
We present a detailed study on the dynamic behavior of pressure fluctuations in degenerated combustion instability Gotoda et al. Phys. Rev. E 92 (2015) 052906 in a lean premixed gas-turbine model ...combustor in terms of symbolic dynamics, statistical complexity, complex networks, and nonlinear forecasting. The permutation spectrum test enables us to extract nonlinear determinism in degenerated combustion instability. The possible presence of chaotic dynamics in degenerated combustion instability is reasonably shown by considering the multiscale complexity–entropy causality plane incorporating a scale-dependent approach.
•We studied the dynamic behavior of degenerated combustion instability.•Nonlinear forecasting has potential use for extracting nonlinear determinism.•The multiscale CECP is valid for exploring the presence of chaotic dynamics.•Complex networks are useful for dealing with combustion dynamics.
Decidable problems in substitution shifts Béal, Marie-Pierre; Perrin, Dominique; Restivo, Antonio
Journal of computer and system sciences,
August 2024, 2024-08-00, Letnik:
143
Journal Article
Recenzirano
Odprti dostop
In this paper, we investigate the structure of the most general kind of substitution shifts, including non-minimal ones, and allowing erasing morphisms. We prove the decidability of many properties ...of these morphisms with respect to the shift space generated by iteration, such as aperiodicity, recognizability and (under an additional assumption) irreducibility, or minimality.
The prediction of personality traits offers valuable insights into human behaviour, more specifically in psychology, healthcare, and social science. In this paper, we present a novel methodology for ...personality trait prediction using a dual-pipeline architecture. The model architecture leverages Long Short-Term Memory (LSTM) networks with batch normalization for capturing sequential dependencies in data and incorporates temporal attention heads for feature extraction. By combining these parallel pipelines, our network effectively utilizes both LSTM and attention mechanisms to create a comprehensive representation of input data. The network’s goal is to predict the OCEAN (openness, conscientiousness, extraversion, agreeableness and neuroticism) traits using physiological signals including: EEG, ECG and GSR. Including attention mechanisms enables the model to focus on critical moments in these signals, resulting in significantly improved prediction accuracy. Experimental evaluations demonstrate the superior performance of our method compared to traditional machine learning methods on two publicly available datasets: ASCERTAIN and AMIGOS. Our source code is accessible at https://github.com/deepakkumar-iitr/AT3NET.
In this paper, order pattern recurrence plot (OPRP) and order pattern recurrence quantification analysis (OPRQA) are proposed to quantify recurrence characteristics of complex systems. The method ...uses the recurrence of order patterns in symbolic sequence to explore the order structure of the original data, in which the color of the symbol is employed to distinguish different order patterns. The main advantage of the approach is its robustness with respect to non-stationary data and low requirements for the length of the required time series. The method is demonstrated to be effective in synthetic data and real data. As demonstrated in simulation models, the conclusion is that the method can not only make a distinction between chaotic system and random noise but also quantify various bifurcation transition scenarios like period doubling or other phenomena associated with chaos-to-chaos transitions in logistic map. In empirical analysis, this approach helps observe the different performance of the time series before, during and after the financial crisis. In addition, differences of stocks between developing countries and developed countries are reflected in OPRP and quantified by the corresponding OPRQA. The proposed method brings together recurrence plots and symbolic dynamics to empower researchers with effective means to visualize and quantify complex behavior in dynamic system.
•Construct recurrence network using order patterns to analyse complex system.•The advantage is robust to noise and low requirements for data length.•Distinguish between chaotic system and random noise.•Quantify the differences in stock markets of developing and developed countries.
We propose a general framework for proving that a compact, infinite-dimensional map has an invariant set on which the dynamics is semiconjugated to a subshift of finite type. The method is then ...applied to certain Poincaré map of the Kuramoto-Sivashinsky PDE on the line with odd and periodic boundary conditions and with parameter ν=0.1212. We give a computer-assisted proof of the existence of symbolic dynamics and countable infinity of periodic orbits with arbitrary large periods.
The paper concerns the mean hyperbolicity of the skew-product flows induced by the perturbation equations driven by varieties of non-periodic forcings. The weakly averaged horseshoe can be ...constructed as a mean hyperbolic invariant set in the Poincare section for high dimensional phase space. Due to the non-periodic property, the Poincare return map restricted to the weakly averaged horseshoe region can semi-conjugate to the full Bernoulli shift on infinite symbols, which implies the infinitely many independent choices on the length of return time. As a direct application of mean hyperbolicity, we extend the shadowing lemma due to Liao to the general nonautonomous dynamical systems.
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