Data-driven discrete fractional chaotic systems, new numerical schemes and deep learning.

Parameter estimation is important in data-driven fractional chaotic systems. Less work has been reported due to challenges in discretization of fractional calculus operators. In this paper, several numerical schemes are newly derived for delay fractional difference equations of Caputo and Riemann-Liouville types.

Caputo-Hadamard fractional differential equations on time scales: Numerical scheme, asymptotic stability, and chaos.

This study investigates Caputo-Hadamard fractional differential equations on time scales. The Hadamard fractional sum and difference are defined for the first time. A general logarithm function on time scales is used as a kernel function.

Adaptive Learning Neural Network Method for Solving Time-Fractional Diffusion Equations.

A neural network method for solving fractional diffusion equations is presented in this letter. An adaptive gradient descent method is proposed to minimize energy functions. Due to the memory effects of the fractional calculus, the gradient of energy function becomes much more complicated, and we suggest a simplified method.

Primal-Dual Fixed Point Algorithms Based on Adapted Metric for Distributed Optimization.

This article considers distributed optimization by a group of agents over an undirected network. The objective is to minimize the sum of a twice differentiable convex function and two possibly nonsmooth convex functions, one of which is composed of a bounded linear operator. A novel distributed primal-dual fixed point algorithm is proposed based on an adapted metric method, which exploits the second-order information of the differentiable convex function.

Fractional calculus with exponential memory.

The standard definition of the Riemann-Liouville integral is revisited. A new fractional integral is proposed with an exponential kernel. Furthermore, some useful properties such as composition relationship of the new fractional integral and Leibniz integral law are provided.

Fractional q-deformed chaotic maps: A weight function approach.

The fractional derivative holds long-time memory effects or non-locality. It successfully depicts the dynamical systems with long-range interactions. However, it becomes challenging to investigate chaos in the deformed fractional discrete-time systems.

Distributed Nesterov Gradient and Heavy-Ball Double Accelerated Asynchronous Optimization.

In this article, we come up with a novel Nesterov gradient and heavy-ball double accelerated distributed synchronous optimization algorithm, called NHDA, and adopt a general asynchronous model to further propose an effective asynchronous algorithm, called ASY-NHDA, for distributed optimization problem over directed graphs, where each agent has access to a local objective function and computes the optimal solution via communicating only with its immediate neighbors. Our goal is to minimize a sum of all local objective functions satisfying strong convexity and Lipschitz continuity. Consider a general asynchronous model, where agents communicate with their immediate neighbors and start a new computation independently, that is, agents can communicate with their neighbors at any time without any coordination and use delayed information from their in-neighbors to compute a new update.

New variable-order fractional chaotic systems for fast image encryption.

New variable-order fractional chaotic systems are proposed in this paper. A concept of short memory is introduced where the initial point in the Caputo derivative is varied. The fractional order is defined by the use of a piecewise constant function which leads to rich chaotic dynamics.

Wrist-ankle Acupuncture Increases Pain Thresholds in Healthy Adults.

Context • Wrist-ankle acupuncture (WAA) has been used to relieve both chronic and acute pain in China. Some research has shown that WAA can increase the pain thresholds in pain patients, but the ability of WAA to affect the pain thresholds in healthy adults is unknown. Objective • The study intended to assess the influence of WAA on the pain thresholds of healthy adults.

Riesz Riemann-Liouville difference on discrete domains.

A Riesz difference is defined by the use of the Riemann-Liouville differences on time scales. Then the definition is considered for discrete fractional modelling. A lattice fractional equation method is proposed among which the space variable is defined on discrete domains.

[Expression and clinical significance of a disintegrin and metalloprotease 8 (ADAM8) and epidermal growth factor receptor (EGFR) in non-small cell lung cancer].

Background & Objective: Up-regulation of a disintegrin and metalloprotease 8 (ADAM8) is correlated with genesis, progression, invasion, and metastasis of tumors. However, the expression of ADAM8, especially its correlation to epidermal growth factor receptor (EGFR), has seldom been reported in non-small cell lung cancer (NSCLC). This study was to investigate expressions of ADAM8 and EGFR in NSCLC, and to analyze their correlations.