Hierarchies of chaotic maps on continua

2013 ◽  
Vol 34 (6) ◽  
pp. 1897-1913 ◽  
Author(s):  
LOGAN HOEHN ◽  
CHRISTOPHER MOURON
Keyword(s):  
Chaotic Maps ◽  
Weakly Mixing ◽  
Will Force

AbstractLet $f: X\longrightarrow X$ be a map of a continuum. In this paper we examine the following dynamical conditions on $f$: (1) $f$ is continuum-wise fully expansive; (2) $f$ is weakly continuum-wise fully expansive; (3) $f$ is mixing; (4) $f$ is weakly mixing. We first show that (1) implies (2), (2) implies (3) and (3) implies (4). Then we investigate what topological conditions will force the reverse implications to hold and give examples of when the reverse conditions do not hold. In particular, a map of the universal dendrite is given that is weakly mixing but not mixing.

scholarly journals Transitive dendrite map with zero entropy

2016 ◽  
Vol 37 (7) ◽  
pp. 2077-2083 ◽  
Author(s):  
JAKUB BYSZEWSKI ◽  
FRYDERYK FALNIOWSKI ◽  
DOMINIK KWIETNIAK
Keyword(s):  
Topological Entropy ◽  
Chaotic Maps ◽  
Dendrite Map ◽  
Zero Entropy ◽  
Weakly Mixing ◽  
Entropy Estimates

Hoehn and Mouron [Hierarchies of chaotic maps on continua. Ergod. Th. & Dynam. Sys.34 (2014), 1897–1913] constructed a map on the universal dendrite that is topologically weakly mixing but not mixing. We modify the Hoehn–Mouron example to show that there exists a transitive (even weakly mixing) dendrite map with zero topological entropy. This answers the question of Baldwin [Entropy estimates for transitive maps on trees. Topology40(3) (2001), 551–569].

Artificial intelligence as a moving force of improvement and innovative development in education and pedagogic

2019 ◽  
pp. 21-30
Author(s):  
M. G. Koliada ◽  
T. I. Bugayova
Keyword(s):  
Artificial Intelligence ◽  
Intelligent Systems ◽  
Intelligent System ◽  
Interaction Analysis ◽  
Educational Data Mining ◽  
Main Task ◽  
Intellectual System ◽  
Will Force ◽  
To Come ◽  
Artificial Intelligence Systems

The article discusses the history of the development of the problem of using artificial intelligence systems in education and pedagogic. Two directions of its development are shown: “Computational Pedagogic” and “Educational Data Mining”, in which poorly studied aspects of the internal mechanisms of functioning of artificial intelligence systems in this field of activity are revealed. The main task is a problem of interface of a kernel of the system with blocks of pedagogical and thematic databases, as well as with the blocks of pedagogical diagnostics of a student and a teacher. The role of the pedagogical diagnosis as evident reflection of the complex influence of factors and reasons is shown. It provides the intelligent system with operative and reliable information on how various reasons intertwine in the interaction, which of them are dangerous at present, where recession of characteristics of efficiency is planned. All components of the teaching and educational system are subject to diagnosis; without it, it is impossible to own any pedagogical situation optimum. The means in obtaining information about students, as well as the “mechanisms” of work of intelligent systems based on innovative ideas of advanced pedagogical experience in diagnostics of the professionalism of a teacher, are considered. Ways of realization of skill of the teacher on the basis of the ideas developed by the American scientists are shown. Among them, the approaches of researchers D. Rajonz and U. Bronfenbrenner who put at the forefront the teacher’s attitude towards students, their views, intellectual and emotional characteristics are allocated. An assessment of the teacher’s work according to N. Flanders’s system, in the form of the so-called “The Interaction Analysis”, through the mechanism of fixing such elements as: the verbal behavior of the teacher, events at the lesson and their sequence is also proposed. A system for assessing the professionalism of a teacher according to B. O. Smith and M. O. Meux is examined — through the study of the logic of teaching, using logical operations at the lesson. Samples of forms of external communication of the intellectual system with the learning environment are given. It is indicated that the conclusion of the found productive solutions can have the most acceptable and comfortable form both for students and for the teacher in the form of three approaches. The first shows that artificial intelligence in this area can be represented in the form of robotized being in the shape of a person; the second indicates that it is enough to confine oneself only to specially organized input-output systems for targeted transmission of effective methodological recommendations and instructions to both students and teachers; the third demonstrates that life will force one to come up with completely new hybrid forms of interaction between both sides in the form of interactive educational environments, to some extent resembling the educational spaces of virtual reality.

Detection of Malicious Spatial-Domain Steganography over Noisy Channels Using Convolutional Neural Networks

2020 ◽  
Vol 2020 (4) ◽  
pp. 76-1-76-7
Author(s):  
Swaroop Shankar Prasad ◽  
Ofer Hadar ◽  
Ilia Polian
Keyword(s):  
State Of The Art ◽  
Visual Quality ◽  
Channel Noise ◽  
Detection Accuracy ◽  
Noisy Channel ◽  
Noisy Channels ◽  
Reliable Transmission ◽  
Reliable Detection ◽  
Natural Noise ◽  
Will Force

Image steganography can have legitimate uses, for example, augmenting an image with a watermark for copyright reasons, but can also be utilized for malicious purposes. We investigate the detection of malicious steganography using neural networkbased classification when images are transmitted through a noisy channel. Noise makes detection harder because the classifier must not only detect perturbations in the image but also decide whether they are due to the malicious steganographic modifications or due to natural noise. Our results show that reliable detection is possible even for state-of-the-art steganographic algorithms that insert stego bits not affecting an image’s visual quality. The detection accuracy is high (above 85%) if the payload, or the amount of the steganographic content in an image, exceeds a certain threshold. At the same time, noise critically affects the steganographic information being transmitted, both through desynchronization (destruction of information which bits of the image contain steganographic information) and by flipping these bits themselves. This will force the adversary to use a redundant encoding with a substantial number of error-correction bits for reliable transmission, making detection feasible even for small payloads.

Multi-level Security Based On Dynamic Magic Cube And Chaotic Maps

2017 ◽  
pp. 106
Author(s):  
Dhaher Abass Redha ◽  
Marwa Mohamed ali Mohsen
Keyword(s):  
Chaotic Maps ◽  
Multi Level ◽  
Magic Cube

scholarly journals A Novel S-Box Dynamic Design Based on Nonlinear-Transform of 1D Chaotic Maps

Electronics ◽  
2021 ◽  
Vol 10 (11) ◽  
pp. 1313
Author(s):  
Wenhao Yan ◽  
Qun Ding
Keyword(s):  
Chaotic Systems ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Logistic Map ◽  
Sample Entropy ◽  
One Dimension ◽  
Linear Combinations ◽  
Dynamic Design ◽  
Construction Methods ◽  
Low Dimensional

In this paper, a method to enhance the dynamic characteristics of one-dimension (1D) chaotic maps is first presented. Linear combinations and nonlinear transform based on existing chaotic systems (LNECS) are introduced. Then, a numerical chaotic map (LCLS), based on Logistic map and Sine map, is given. Through the analysis of a bifurcation diagram, Lyapunov exponent (LE), and Sample entropy (SE), we can see that CLS has overcome the shortcomings of a low-dimensional chaotic system and can be used in the field of cryptology. In addition, the construction of eight functions is designed to obtain an S-box. Finally, five security criteria of the S-box are shown, which indicate the S-box based on the proposed in this paper has strong encryption characteristics. The research of this paper is helpful for the development of cryptography study such as dynamic construction methods based on chaotic systems.

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