An Error Compensation Method for Improving the Properties of a Digital Henon Map Based on the Generalized Mean Value Theorem of Differentiation

Continuous chaos may collapse in the digital world. This study proposes a method of error compensation for a two-dimensional digital system based on the generalized mean value theorem of differentiation that can restore the fundamental performance of chaotic systems. Different from other methods, the compensation sequence of our method comes from the chaotic system itself and can be applied to higher-dimensional digital chaotic systems. The experimental results show that the improved system is highly consistent with the real chaotic system, and it has excellent chaotic characteristics such as high complexity, randomness, and ergodicity.

Discretization of Fractional Operators: Analysis by Means of Advanced Computational Techniques

This paper studies the discretization of fractional operators by means of advanced clustering methods. The Grünwald–Letnikov fractional operator is approximated by series generated by the Euler, Tustin and generalized mean. The series for different fractional orders form the objects to be assessed. For this purpose, the several distances associated with the hierarchical clustering and multidimensional scaling computational techniques are tested. The Arc-cosine distance and the 3-dim multidimensional scaling produce good results. The visualization of the graphical representations allows a better understanding of the properties embedded in each type of approximation of the fractional operators.

Multitask Model for Person Re-identification by Attribute-aware

The image-based person re-identification problem can be transformed into a similar image retrieval problem. At present, most of the current identity-based methods do not consider pedestrian attributes. Moreover, many methods that consider pedestrian attributes and identities fail to fully simulate the relationship between pedestrian attributes and identities. In this article, we propose a new image-based person re-identification method by attribute-aware. Based on the introduction of instance batch normalization, the non-local module based on attention is used to transform the ResNet network structure to improve the feature extraction performance. After using generalized mean pooling for feature aggregation, the identity-based and attribute-based double stream network modules pay attention to the relationship between identities and pedetrian features, and the relationship between attributes and pedestrian features, so as to fully activate the relationship between pedestrian attributes and identities. Experiments are carried out on two classic person re-identification by attribute dataset Market-1501 and DukeMTMC-reID, and the results prove the effectiveness of the method. The method proposed in this paper has achieved the best performance on some evaluation metrics.

Generalized Mean-Field Fractional BSDEs With Non-Lipschitz Coefficients

In this paper we consider one dimensional generalized mean-field backward stochastic differential equations (BSDEs) driven by fractional Brownian motion, i.e., the generators of our mean-field FBSDEs depend not only on the solution but also on the law of the solution. We first give a totally new comparison theorem for such type of BSDEs under Lipschitz condition. Furthermore, we study the existence of the solution of such mean-field FBSDEs when the coefficients are only continuous and with a linear growth.

Second order rectifiability of varifolds of bounded mean curvature

We prove that the support of an m dimensional rectifiable varifold with a uniform lower bound on the density and bounded generalized mean curvature can be covered $$ {\mathscr {H}}^{m} $$ H m almost everywhere by a countable union of m dimensional submanifolds of class $$ {\mathcal {C}}^{2} $$ C 2 . The $$ {\mathcal {C}}^{2} $$ C 2 -regularity of the submanifolds is optimal.