A note on exact solutions of the logistic map

Maritz, Milton F.

doi:10.1063/1.5125097

Cited by 12 publications

(7 citation statements)

References 16 publications

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“…When 3.6 < a < 4, the system is chaotic at (0,1). In this paper, a = 3.8 is adopted, and this choice has proved to be valuable to make the system in a chaotic state [10].…”

Section: Chaotic Mappingmentioning

confidence: 99%

Skin texture recognition of leg images based on chaotic mapping reorganization feature

Tang¹,

Huang²

2023

Third International Conference on Intelligent Computing and Human-Computer Interaction (ICHCI 2022)

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In criminal and victim identification, when information such as fingerprint and facial images cannot be obtained, the development of other new bio-metric recognition has become an important task. It is found from investigations that the lower leg is often exposed in an evidence image. If we can use the information to identify the identity of the suspect, it will be a great break-through for criminal investigation. Unlike faces or fingerprints, the image of a lower leg does not have many discriminative features. Therefore, capturing more information from an image has become the key to the success of recognition. Despite the rapid development of deep learning in recent years and the wide application of convolutional neural networks in biometric recognition, they are very dependent on a large amount of training data. In this paper, we propose a recognition method based on the combination of chaotic mapping and local binary pattern (LBP), which captures the nonlinear features of the image. Experimental results show that the method proposed in this paper has a better recognition rate and an encouraging performance.

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“…When 3.6 < a < 4, the system is chaotic at (0,1). In this paper, a = 3.8 is adopted, and this choice has proved to be valuable to make the system in a chaotic state [10].…”

Section: Chaotic Mappingmentioning

confidence: 99%

Skin texture recognition of leg images based on chaotic mapping reorganization feature

Tang¹,

Huang²

2023

Third International Conference on Intelligent Computing and Human-Computer Interaction (ICHCI 2022)

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“…The logistic map [May 1976] is a quadratic first-order recurrence defined by 𝑥 𝑛+1 = 𝑟 • 𝑥 𝑛 (1 − 𝑥 𝑛 ) and well-known for its chaotic behavior. A famous fact about the logistic map is that it does not have an analytical solution for most values of 𝑟 [Maritz 2020]. By neglecting condition 1, we can easily devise a loop modeling the logistic map:…”

Section: On the Necessity Of The Conditions Ensuring Moment-computabi...mentioning

confidence: 99%

This is the Moment for Probabilistic Loops

Marcel¹,

Stankovič²,

Bartocci³

et al. 2022

Preprint

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We present a novel static analysis technique to derive higher moments for program variables for a large class of probabilistic loops with potentially uncountable state spaces. Our approach is fully automatic, meaning it does not rely on externally provided invariants or templates. We employ algebraic techniques based on linear recurrences and introduce program transformations to simplify probabilistic programs while preserving their statistical properties. We develop power reduction techniques to further simplify the polynomial arithmetic of probabilistic programs and define the theory of moment-computable probabilistic loops for which higher moments can precisely be computed. Our work has applications towards recovering probability distributions of random variables and computing tail probabilities. The empirical evaluation of our results demonstrates the applicability of our work on many challenging examples.CCS Concepts: • Mathematics of computing → Markov processes; • Computing methodologies → Symbolic and algebraic algorithms.

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“…It has also been conjectured that such general expression could be valid for other (possibly all) values of µ. This has been explored in [30], where the authors take advantage of ( 18) to find a representative power series…”

Section: Cos Xmentioning

confidence: 99%

“…subject to the constraint F µ (0) = 0. As described in [30], a 0 should be 0 to satisfy the constraint, all the odd coefficients in (19) are zero, a 2 is arbitrary and can be set to 1 for simplicity, and the remaining coefficients are obtained by the recursion…”

Section: Cos Xmentioning

confidence: 99%

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Reorganizing local image features with chaotic maps: an application to texture recognition

Florindo¹

2020

Preprint

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Despite the recent success of convolutional neural networks in texture recognition, model-based descriptors are still competitive, especially when we do not have access to large amounts of annotated data for training and the interpretation of the model is an important issue. Among the model-based approaches, fractal geometry has been one of the most popular, especially in biological applications. Nevertheless, fractals are part of a much broader family of models, which are the non-linear operators, studied in chaos theory. In this context, we propose here a chaos-based local descriptor for texture recognition. More specifically, we map the image into the three-dimensional Euclidean space, iterate a chaotic map over this three-dimensional structure and convert it back to the original image. From such chaos-transformed image at each iteration we collect local descriptors (here we use local binary patters) and those descriptors compose the feature representation of the texture. The performance of our method was verified on the classification of benchmark databases and in the identification of Brazilian plant species based on the texture of the leaf surface. The achieved results confirmed our expectation of a competitive performance, even when compared with some learning-based modern approaches in the literature.

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A note on exact solutions of the logistic map

Cited by 12 publications

References 16 publications

Skin texture recognition of leg images based on chaotic mapping reorganization feature

Skin texture recognition of leg images based on chaotic mapping reorganization feature

This is the Moment for Probabilistic Loops

Reorganizing local image features with chaotic maps: an application to texture recognition

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