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Recently, many researchers have been interested in the application of chaos in cryptography. Specifically, numerous research works have been focusing on chaotic image encryption. A comprehensive survey can highlight existing trends and shed light on less-studied topics in the area of chaotic image encryption. In addition to such a survey, this paper studies the main challenges in this field, establishes an ecosystem for chaotic image encryption, and develops a future roadmap for further research in this area.

The papers within this issue explore cutting-edge CI techniques that promise to shape the future of problem-solving, data analysis, and intelligent systems. The paper titled \"MSGraph: Modeling multi-scale k-line sequences with graph attention network for profitable indices recommendation\" by C. Wang et al. Comparative results demonstrate that their method achieves state-of-the-art performance across all evaluation metrics.

We study two-player one-dimensional discrete Hotelling pure location games assuming that demand f ( d ) as a function of distance d is constant or strictly decreasing. We show that this game admits a best-response potential. This result holds in particular for f ( d ) = w d with 0 < w ≤ 1. For this case special attention will be given to the structure of the equilibrium set and a conjecture about the increasingness of best-response correspondences will be made. Nous étudions les jeux de localisation pure Hotelling discrets unidimensionnels à deux joueurs en supposant que la demande f ( d ) en fonction de la distance d est constante ou strictement décroissante. Nous montrons que ce jeu admet un potentiel de meilleure réponse. Ce ŕesultat vaut notamment pour f ( d ) = w d avec 0 < w ≤ 1. Dans ce cas, une attention particulière sera accordée à la structure de l’ensemble d’équilibre et une conjecture sur la croissance de la correspondance de meilleure réponse sera faite.

Dynamic mode decomposition (DMD) is a powerful tool for separating the background and foreground in videos. This algorithm decomposes a video into dynamic modes, called DMD modes, to facilitate the extraction of the near-zero mode, which represents the stationary background. Simultaneously, it captures the evolving motion in the remaining modes, which correspond to the moving foreground components. However, when applied to noisy video, this separation leads to degradation of the background and foreground components, primarily due to the noise-induced degradation of the DMD mode. This paper introduces a novel noise removal method for the DMD mode in noisy videos. Specifically, we formulate a minimization problem that reduces the noise in the DMD mode and the reconstructed video. The proposed problem is solved using an algorithm based on the plug-and-play alternating direction method of multipliers (PnP-ADMM). We applied the proposed method to several video datasets with different levels of artificially added Gaussian noise in the experiment. Our method consistently yielded superior results in quantitative evaluations using peak-signal-to-noise ratio (PSNR) and structural similarity (SSIM) compared to naive noise removal methods. In addition, qualitative comparisons confirmed that our method can restore higher-quality videos than the naive methods.

We consider a volume constraint problem for the nonlocal doubly nonlinear parabolic equation, called the nonlocal$ p $ -Sobolev flow, and introduce a nonlinear intrinsic scaling, converting a prototype nonlocal doubly nonlinear parabolic equation into the nonlocal$ p $ -Sobolev flow. This paper is dedicated to Giuseppe Mingione on the occasion of his 50th birthday, who is a maestro in the regularity theory of PDEs.

In this paper, we propose robust image-smoothing methods based on ℓ0 gradient minimization with novel gradient constraints to effectively suppress pseudo-edges. Simultaneously minimizing the ℓ0 gradient, i.e., the number of nonzero gradients in an image, and the ℓ2 data fidelity results in a smooth image. However, this optimization often leads to undesirable artifacts, such as pseudo-edges, known as the “staircasing effect”, and halos, which become more visible in image enhancement tasks, like detail enhancement and tone mapping. To address these issues, we introduce two types of gradient constraints: box and ball. These constraints are applied using a reference image (e.g., the input image is used as a reference for image smoothing) to suppress pseudo-edges in homogeneous regions and the blurring effect around strong edges. We also present an ℓ0 gradient minimization problem based on the box-/ball-type gradient constraints using an alternating direction method of multipliers (ADMM). Experimental results on important applications of ℓ0 gradient minimization demonstrate the advantages of our proposed methods compared to existing ℓ0 gradient-based approaches.

The Editors-in-Chief have retracted this article [1] because it showed evidence of peer review manipulation. In addition, the identity of the corresponding author could not be verified: Nagoya University have confirmed that Ikudol Miyamato has not been affiliated with their Graduate School of Mathematics.The authors have not responded to any correspondence regarding this retraction.

The objective of this study is to shed new light on the industrial flow structure embedded in microscopic supplier-buyer relations. We first construct directed networks from actual data from interfirm transaction relations in Japan; as one example, the dataset compiled by the Tokyo Shoko Research, Ltd. in 2016 contains five million links between one million firms. Then, we analyze the industrial flow structure of such a large-scale network with a special emphasis on its hierarchy and circularity. The Helmholtz-Hodge decomposition enables us to break down the flow on a directed network into two flow components: gradient flow and circular flow. The gradient flow between a pair of nodes is given by the difference of their potentials obtained by the Helmholtz-Hodge decomposition. The gradient flow runs from a node with higher potential to a node with lower potential; hence, the potential of a node shows its hierarchical position in a network. On the other hand, the circular flow component illuminates feedback loops built in a network. The potential values averaged over firms classified by the major industrial category describe hierarchical characteristics of sectors. The ordering of sectors according to the potential agrees well with the general idea of the supply chain. We also identify industrially integrated clusters of firms by applying a flow-based community detection method to the extracted circular flow network. We then find that each of the major communities is characterized by its main industry, forming a hierarchical supply chain with feedback loops by complementary industries such as transport and services.

In recent years, neural networks and cryptographic schemes have come together in war and peace; a cross-impact that forms a dichotomy deserving a comprehensive review study. Neural networks can be used against cryptosystems; they can play roles in cryptanalysis and attacks against encryption algorithms and encrypted data. This side of the dichotomy can be interpreted as a war declared by neural networks. On the other hand, neural networks and cryptographic algorithms can mutually support each other. Neural networks can help improve the performance and the security of cryptosystems, and encryption techniques can support the confidentiality of neural networks. The latter side of the dichotomy can be referred to as the peace. There are, to the best of our knowledge, no current surveys that take a comprehensive look at the many ways neural networks are currently interacting with cryptography. This survey aims to fill that niche by providing an overview on the state of the cross-impact between neural networks and cryptography systems. To this end, this paper will highlight the current areas where progress is being made as well as the aspects where there is room for future research to be conducted.