A numerical algorithm to compute the topological entropy of multimodal maps is proposed. This algorithm results from a closed formula containing the so-called min-max symbols, which are closely related to the kneading symbols. Furthermore, it simplif...
The classification of time series using machine learning (ML) analysis and entropy-based features is an urgent task for the study of nonlinear signals in the fields of finance, biology and medicine, including EEG analysis and Brain–Computer Int...
The effective integration of geochemical data with multisource geoscience data is a necessary condition for mapping mineral prospects. In the present study, based on the maximum entropy principle, a maximum entropy model (MaxEnt model) was establishe...
We derive an algorithm to recursively determine the lap number (minimal number of monotonicity segments) of the iterates of twice differentiable l-modal map, enabling to numerically calculate the topological entropy of these maps. The algorithm is ob...
A rapid development and growing popularity of additive manufacturing technology leads to new challenging tasks allowing not only a reliable monitoring of the progress of the 3D printing process but also the quality of the printed objects. The automat...
Thematic maps of spatial data are constructed by using standard thematic classification methods that do not allow management of the uncertainty of classification and, consequently, evaluation of the reliability of the resulting thematic map. We propo...
In this review paper, the hot compressive deformation mechanisms and processing maps of high-entropy alloys (HEAs) with different chemical compositions and crystal structures are analyzed. The stress exponent (n1) values measured from the series of c...
Data classification is an automatic or semi-automatic process that, utilizing artificial intelligence algorithms, learns the variable and class relationships of a dataset for use a posteriori in situations where the class result is unknown. For many...
The aim of this short note is to compute the topological entropy for a family of skew-product maps, whose base is a subshift of finite type, and the fiber maps are homeomorphisms defined in one dimensional spaces. We show that the skew-product map do...
The effectiveness of feature extraction is a critical aspect of fault diagnosis for petrochemical machinery and equipment. Traditional entropy analysis methods are prone to disruption by noise, parameter sensitivity, and sudden entropy variations. Th...
Catheter ablation of critical electrical propagation sites is a promising tool for reducing the recurrence of atrial fibrillation (AF). The spatial identification of the arrhythmogenic mechanisms sustaining AF requires the evaluation of electrograms...
A map without equilibrium has been proposed and studied in this paper. The proposed map has no fixed point and exhibits chaos. We have investigated its dynamics and shown its chaotic behavior using tools such as return map, bifurcation diagram and Ly...
A continuous map f of the interval is chaotic iff there is an increasing of nonnegative integers T such that the topological sequence entropy of f relative to T, hT(f), is positive [4]. On the other hand, for any increasing sequence of nonnegative in...
Knowledge structures are often represented in the form of networks or maps of concepts. The coherence and connectivity of such knowledge representations is known to be closely related to knowledge production, acquisition and processing. In this study...
A hypsometric map is a type of map used to represent topographic characteristics by filling different map areas with diverging colors. The setting of appropriate diverging colors is essential for the map to reveal topographic details. When lunar real...
A novel fault diagnosis scheme was developed to address the difficulty of feature extraction for planetary gearboxes using refined composite multiscale fluctuation dispersion entropy (RCMFDE) and supervised manifold mapping. The RCMFDE was first util...
The transition from a chaotic to a periodic state in the Duffing chaotic oscillator detection system is crucial in detecting weak signals. However, accurately determining the critical threshold for this transition remains a challenging problem. Tradi...
The characterization of spatiotemporal complexity remains a challenging task. This holds in particular for the analysis of data from fluorescence imaging (optical mapping), which allows for the measurement of membrane potential and intracellular calc...
The dynamics of the Caputo-fractional variable-order difference form of the Tinkerbell map are studied. The phase portraits, bifurcation, and largest Lyapunov exponent (LLE) were employed to demonstrate the presence of chaos over a different fraction...
This paper introduces a novel fractional Ikeda-based memristor map and investigates its non-linear dynamics under commensurate and incommensurate orders using various numerical techniques, including Lyapunov exponent analysis, phase portraits, and bi...
In this paper, we present an innovative 3D fractional Hénon-based memristor map and conduct an extensive exploration and analysis of its dynamic behaviors under commensurate and incommensurate orders. The study employs diverse numerical techni...
Vibration monitoring and analysis are important methods in wind turbine gearbox fault diagnosis, and determining how to extract fault characteristics from the vibration signal is of primary importance. This paper presents a fault diagnosis approach b...
Assessing Landslide Susceptibility Mapping (LSM) contributes to reducing the risk of living with landslides. Handling the vagueness associated with LSM is a challenging task. Here we show the application of hybrid GIS-based LSM. The hybrid approach e...
With the emergence of visual sensors and their widespread application in intelligent systems, precise and interpretable visual explanations have become essential for ensuring the reliability and effectiveness of these systems. Sensor data, such as th...
Rainfall-induced floods often cause significant loss of life as well as damage to infrastructure and crops. Synthetic Aperture Radar (SAR) Earth Observation Satellites (EOS) can be used to determine the extent of flooding over large geographical area...
High-resolution permafrost mapping is an important direction in permafrost research. Arxan is a typical area with permafrost degradation and is situated on the southern boundary of the permafrost region in Northeast China. With the help of Google Ear...
High-entropy/multicomponent alloy (HEA/MCA) has received significant research attention in the last decade. There is a dearth of data-driven works dedicated to assessing and visualizing the HEA/MCA literature from a global perspective. To this end, w...
AlCoCrFeNiTi0.5 high-entropy alloy (HEA) shows excellent properties in hardness and corrosion resistance. AlCoCrFeNiTi0.5 HEA was prepared using a non-consumable vacuum arc furnace. Hot-deformation behavior of AlCoCrFeNiTi0.5 HEA was explored under 1...
Remote sensing images are important data sources for land cover mapping. As one of the most important artificial features in remote sensing images, buildings play a critical role in many applications, such as population estimation and urban planning....
Complex networks of coupled maps of matrices (NCMM) are investigated in this paper. It is shown that a NCMM can evolve into two different steady states—the quiet state or the state of divergence. It appears that chimera states of spatiotemporal diver...
Flooding poses a significant threat as a prevalent natural disaster. To mitigate its impact, identifying flood-prone areas through susceptibility mapping is essential for effective flood risk management. This study conducted flood susceptibility mapp...
In the clinical electrophysiological practice, reading and comparing electroencephalographic (EEG) recordings are sometimes insufficient and take too much time. Tools coming from the information theory or nonlinear systems theory such as entropy and...
Fisheries surveys over broad spatial areas are crucial in defining and delineating appropriate fisheries management areas. Yet accurate mapping and tracking of fishing activities remain largely restricted to developed countries with sufficient resour...
The increasingly serious imbalance between the supply and demand of water resources necessitates the establishment of a scientific and reasonable comprehensive evaluation method for industrial water use efficiency (WUE). In this study, a general meth...
Approximation of entropies of various types using machine learning (ML) regression methods are shown for the first time. The ML models presented in this study define the complexity of the short time series by approximating dissimilar entropy techniqu...
In this paper, the entropy generation minimization (EGM) method is applied to an industrial heat transfer problem: the forced convective cooling of a LED-based spotlight. The design specification calls for eighteen diodes arranged on a circular coppe...
Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required). This is achieved through the consideration of co-compact cov...
The aim of this paper is to show that the Tsallis-type (q-additive) entropic chain rule allows for a wider class of entropic functionals than previously thought. In particular, we point out that the ensuing entropy solutions (e.g., Tsallis entropy) c...
Weak invariants are time-dependent observables with conserved expectation values. Their fluctuations, however, do not remain constant in time. On the assumption that time evolution of the state of an open quantum system is given in terms of a complet...
In this paper, we focus on evolution from an equilibrium state in a power law form by means of q-exponentials to an arbitrary one. Introducing new q-Gibbsian equalities as the necessary condition of self-organization in nonextensive open systems, we...
The aim of this paper is to show that
The main result of this paper is a proof using real analysis of the monotonicity of the topological entropy for the family of quadratic maps, sometimes called Milnor’s Monotonicity Conjecture. In contrast, the existing proofs rely in one way or...
We review some analytic, measure-theoretic and topological techniques for studying ergodicity and entropy of discrete dynamical systems, with a focus on Boole-type transformations and their generalizations. In particular, we present a new proof of th...
In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space...
We consider open non-twist Hamiltonian systems represented by an area-preserving two-dimensional map describing incompressible planar flows in the reference frame of a propagating wave, and possessing exits through which map orbits can escape. The co...
Landslide susceptibility maps are very important tools in the planning and management of landslide prone areas. Qualitative and quantitative methods each have their own advantages and dis-advantages in landslide susceptibility mapping. The aim of thi...
The twisted reflection operators are defined on the hyperbolic plane. They are then specialized in hyperbolic reflections, according to which the desymmetrized
The methods for nonlinear time series analysis were used in the presented research to reveal eye movement signal characteristics. Three measures were used: approximate entropy, fuzzy entropy, and the Largest Lyapunov Exponent, for which the multileve...
We study continuous countably-piecewise monotone interval maps and formulate conditions under which these are conjugate to maps of constant slope, particularly when this slope is given by the topological entropy of the map. We confine our investigati...
The limit of validity of ordinary statistical mechanics and the pertinence of Tsallis statistics beyond it is explained considering the most probable evolution of complex systems processes. To this purpose we employ a dissipative Landau–Ginzbur...
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