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Keywords = cobweb graph

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18 pages, 8423 KB  
Article
Symmetric Image Encryption Algorithm Based on a New Product Trigonometric Chaotic Map
by Qing Lu, Linlan Yu and Congxu Zhu
Symmetry 2022, 14(2), 373; https://doi.org/10.3390/sym14020373 - 13 Feb 2022
Cited by 35 | Viewed by 3003
Abstract
In the present work, a neotype chaotic product trigonometric map (PTM) system is proposed. We demonstrate the chaotic characteristics of a PTM system by using a series of complexity criteria, such as bifurcation diagrams, Lyapunov exponents, approximate entropy, permutation entropy, time-series diagrams, cobweb [...] Read more.
In the present work, a neotype chaotic product trigonometric map (PTM) system is proposed. We demonstrate the chaotic characteristics of a PTM system by using a series of complexity criteria, such as bifurcation diagrams, Lyapunov exponents, approximate entropy, permutation entropy, time-series diagrams, cobweb graphs, and NIST tests. It is proved that the PTM system has a wider chaotic parameter interval and more complex chaotic performance than the existing sine map system. In addition, a novel PTM based symmetric image encryption scheme is proposed, in which the key is related to the hash value of the image. The algorithm realizes the encryption strategy of one-graph-one-key, which can resist plaintext attack. A two-dimensional coordinate traversal matrix for image scrambling and a one-dimensional integer traversal sequence for image pixel value transformation encryption are generated by the pseudo-random integer generator (PRING). Security analysis and various simulation test results show that the proposed image encryption scheme has good cryptographic performance and high time efficiency. Full article
(This article belongs to the Special Issue Discrete and Continuous Memristive Nonlinear Systems and Symmetry)
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21 pages, 1940 KB  
Article
A Comparison of Forecasting Mortality Models Using Resampling Methods
by David Atance, Ana Debón and Eliseo Navarro
Mathematics 2020, 8(9), 1550; https://doi.org/10.3390/math8091550 - 10 Sep 2020
Cited by 22 | Viewed by 4223
Abstract
The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death [...] Read more.
The accuracy of the predictions of age-specific probabilities of death is an essential objective for the insurance industry since it dramatically affects the proper valuation of their products. Currently, it is crucial to be able to accurately calculate the age-specific probabilities of death over time since insurance companies’ profits and the social security of citizens depend on human survival; therefore, forecasting dynamic life tables could have significant economic and social implications. Quantitative tools such as resampling methods are required to assess the current and future states of mortality behavior. The insurance companies that manage these life tables are attempting to establish models for evaluating the risk of insurance products to develop a proactive approach instead of using traditional reactive schemes. The main objective of this paper is to compare three mortality models to predict dynamic life tables. By using the real data of European countries from the Human Mortality Database, this study has identified the best model in terms of the prediction ability for each sex and each European country. A comparison that uses cobweb graphs leads us to the conclusion that the best model is, in general, the Lee–Carter model. Additionally, we propose a procedure that can be applied to a life table database that allows us to choose the most appropriate model for any geographical area. Full article
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