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There are two shortcomings existing in the current color image encryption. One is that high correlation between R , G , B components of the original image may be neglected, the other is that the encryption has little relationship with the plain image, and then it is vulnerable to be broken. In order to solve these two problems and present secure and effective image encryption scheme, we introduce a novel chaos-based image encryption algorithm for color images based on three-dimensional (3-D) bit-plane permutation. In the proposed algorithm, the color plain image is firstly converted to 24 bit planes by RGB splitting and bit plane decomposition, next three-dimensional bit-plane permutation is performed on bit planes, position sequences for permutation are obtained from the 3D Chen chaotic system, and then the three confused components are gotten. Secondly, three key matrices are generated by a 1D chaotic system and a multilevel discretization method, and finally, the color cipher image is obtained by diffusing the confused components using key matrices. The SHA 256 hash function value of the plain image is obtained and combined with the given parameters to calculate the parameters and initial values of the chaotic system, so that the proposed scheme highly depends on the plain image and it may effectively withstand known-plaintext and chosen-plaintext attacks. Simulation results and security analyses demonstrate that our algorithm not only has good encryption effect, but can also resist against common attacks, so it is reliable to be applied for image secure communications.

This paper details with a color image encryption algorithm based on bit-plane permutation and dynamic Deoxyribonucleic acid (DNA) technology (CIEA-BPD) is proposed by using Logistic map. The proposed scheme is using Logistic map for generating permutation sequence to shuffle the color bit planes of three components and masking matrices combined with DNA technology to diffuse the pixel value of the color image. Through classical security analysis, CIEA-BPD can withstand different attacks. Experimental results verify that CIEA-BPD can efficiently encrypt a random-like cipher-image with a high degree of security.

A quantum color image encryption algorithm based on geometric transformation and intensity channel diffusion was designed. Firstly, a plaintext image was transformed into a quantum state form using the quantum image representation based on HSI color space (QIRHSI) representation as a carrier. Next, a pseudo-random sequence was generated using the generalized logistic map, and the pixel positions permuted multiple two-point swap operations. Immediately afterward, the intensity values were changed by an intensity bit-plane cross-swap and XOR, XNOR operations. Finally, the intensity channel of the above image was diffused in combination with the pseudo-confusion sequence as produced by the quantum logistic map to perform a diffusion operation on the intensity bit-plane to obtain the ciphertext image. Numerical simulations and analyses show that the designed algorithm is implementable and robust, especially in terms of outstanding performance and less computational complexity than classical algorithms in terms of security perspective.

The multivariate multiscale complexity-entropy causality plane (MMCECP) is introduced for evaluating the dynamical complexity and long-range correlations of multivariate nonlinear systems. Numerical simulations from different classes of systems are applied to confirm the effectiveness of the proposed measure. We observe that the MMCECP not only can characterize the deterministic properties of the systems, but also can distinguish Gaussian and non-Gaussian processes. Moreover, it is immune to varying degrees of noises at large scales. Then we apply it to financial time series analysis, mainly investigating the classification of stock market dynamics. Empirical results illustrate that the MMCECP is robust and valid to detect the physical structures of stock markets.

How the brain processes information from external stimuli in order to perceive the world and act on it is one of the greatest questions in neuroscience. To address this question, different time series analyses techniques have been employed to characterize the statistical properties of brain signals during cognitive tasks. Typically, response-specific processes are addressed by comparing the time course of average event-related potentials in different trials type. Here, we analyze monkey local field potentials data during visual pattern discrimination called Go/No-Go task in the light of information theory quantifiers. We show that the Bandt–Pompe symbolization methodology to calculate entropy and complexity of data is a useful tool to distinguish response-related differences between Go and No-Go trials. We propose to use an asymmetry index to statistically validate trial-type differences. Moreover, by using the multi-scale approach and embedding time delays to downsample the data we can estimate the important time scales in which the relevant information has been processed.

Due to its capacity to unveil the dynamic characteristics of time series data, entropy has attracted growing interest. However, traditional entropy feature extraction methods, such as permutation entropy, fall short in concurrently considering both the absolute amplitude information of signals and the temporal correlation between sample points. Consequently, this limitation leads to inadequate differentiation among different time series and susceptibility to noise interference. In order to augment the discriminative power and noise robustness of entropy features in time series analysis, this paper introduces a novel method called Tsallis entropy-based complexity-improved permutation entropy casualty plane (TC-IPE-CP). TC-IPE-CP adopts a novel symbolization approach that preserves both absolute amplitude information and inter-point correlations within sequences, thereby enhancing feature separability and noise resilience. Additionally, by incorporating Tsallis entropy and weighting the probability distribution with parameter q, it integrates with statistical complexity to establish a feature plane of complexity and entropy, further enriching signal features. Through the integration of multiscale algorithms, a multiscale Tsallis-improved permutation entropy algorithm is also developed. The simulation results indicate that TC-IPE-CP requires a small amount of data, exhibits strong noise resistance, and possesses high separability for signals. When applied to the analysis of heart rate signals, fault diagnosis, and underwater acoustic signal recognition, experimental findings demonstrate that TC-IPE-CP can accurately differentiate between electrocardiographic signals of elderly and young subjects, achieve precise bearing fault diagnosis, and identify four types of underwater targets. Particularly in underwater acoustic signal recognition experiments, TC-IPE-CP achieves a recognition rate of 96.67%, surpassing the well-known multi-scale dispersion entropy and multi-scale permutation entropy by 7.34% and 19.17%, respectively. This suggests that TC-IPE-CP is highly suitable for the analysis of complex time series.

Complexity–entropy causality plane (CECP) is a diagnostic diagram plotting normalized Shannon entropy [Formula: see text] versus Jensen–Shannon complexity [Formula: see text] that has been introduced in nonlinear dynamics analysis to classify signals according to their degrees of randomness and complexity. In this study, we explore the applicability of CECP in hydrological studies by analyzing 80 daily stream flow time series recorded in the continental United States during a period of 75 years, surrogate sequences simulated by autoregressive models (with independent or long-range memory innovations), Theiler amplitude adjusted Fourier transform and Theiler phase randomization, and a set of signals drawn from nonlinear dynamic systems. The effect of seasonality, and the relationships between the CECP quantifiers and several physical and statistical properties of the observed time series are also studied. The results point out that: (1) the CECP can discriminate chaotic and stochastic signals in presence of moderate observational noise; (2) the signal classification depends on the sampling frequency and aggregation time scales; (3) both chaotic and stochastic systems can be compatible with the daily stream flow dynamics, when the focus is on the information content, thus setting these results in the context of the debate on observational equivalence; (4) the empirical relationships between [Formula: see text] and [Formula: see text] and Hurst parameter H, base flow index, basin drainage area and stream flow quantiles highlight that the CECP quantifiers can be considered as proxies of the long-term low-frequency groundwater processes rather than proxies of the short-term high-frequency surface processes; (6) the joint application of linear and nonlinear diagnostics allows for a more comprehensive characterization of the stream flow time series.

A primitive non-regular permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. This notation was first introduced in the work of Manning in the 1920s. In 1988, Delandtsheer and Doyen conjectured that line-primitivity can imply point-primitivity for the automorphism group of a finite linear space. Let G be an automorphism group of a nontrivial finite regular linear space S . We prove that, if G is extremely line-primitive, then S is a finite projective plane and G is extremely point-primitive. This result supports the Delandtsheer–Doyen conjecture. We then explore projective planes of order n admitting an extremely line-primitive automorphism group and bound the line rank of G with the polynomials related to n . In particular, if n is a prime power, then the two cases that the line rank of G attains the lower bound n + 1 or the upper bound n 2 + n + 3 3 are separately investigated.

To enhance privacy protection for specific regions within an image while preserving its overall visual integrity, this paper presents a visual encryption algorithm targeting partial privacy-sensitive areas. Initially, an improved time-varying delayed exponentially controlled chaotic system (1-TDEC) is proposed. It utilizes the current precision value to modify the system input in a time-varying manner, effectively alleviating the dynamic degradation, and making it more suitable for image encryption algorithm designs. Subsequently, the Mask-RCNN instance segmentation model is incorporated to capture the pixel coordinates of different contents in the image, allowing for access to specific area information as required. Furthermore, this encryption algorithm employs a comprehensive permutation process along with parallel bit-shift coupling, effectively transforming the image target areas into visually meaningless forms. It also separately encrypts each bit plane, enabling the encryptor to implement different decryption effects by assigning key streams with different lengths. Finally, the comprehensive performance analysis results highlight that the designed algorithm achieves a maximum information entropy value of 7.9998 in encrypted images. Moreover, its resistance to differential attacks (as measured by NPCR and UACI) and pixel correlation are infinitely close to the ideal state, significantly underscoring its security and effectiveness.

In this work, we propose the cumulative residual entropy (CRE) plane and CRE curve based on the weighted-multiscale cumulative residual Rényi/Tsallis permutation entropy and oscillation roughness exponent to analyze complex dynamic systems. The oscillation roughness exponent method and the cumulative residual distribution theorem adopted in our proposed methods are two core theories to depict more detailed information of complex dynamic systems in a more efficient way by reducing information loss and capture the statistics of the related time series’ roughness. Trials are operated on the logistic map model as numerical experiments, and we discover that our methods are capable of discriminating different types of complex data with high accuracy. Compared with the original methods, our methods are more superior in extracting more subtle details to distinguish different dynamic systems. In the experiments with the financial stocks, our methods are still found to be more reasonable in discriminating stock indices from different parts of the world by making comparisons with original methods.