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. Furthermore, by incorporating a randomized coordinate activation mechanism, we propose a randomized asynchronous iterative distributed algorithm that allows each agent to randomly and independently decide whether to perform an update or remain unchanged at each iteration, and thus alleviates the communication cost. Moreover, the proposed algorithms adopt nonidentical stepsizes to endow each agent with more independence. Numerical simulation results substantiate the feasibility of the proposed algorithms and the correctness of the theoretical results.

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. New fractional difference equations and their equivalent fractional sum equations are presented by the use of fundamental theorems. Gronwall inequality, asymptotical stability conditions, and two discrete-time Mittag-Leffler functions of Hadamard type are obtained. Numerical schemes are provided and chaos in fractional discrete-time logistic equation and neural network equations are reported.

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. Numerical examples with one-layer and two-layer neurons show the effectiveness of the method.

Time-sequential graph adversarial learning for brain modularity community detection.

Brain community detection is an efficient method to represent the communities of brain networks. However, time-variable functions of the brain and the intricate brain community structure impose a great challenge on it. In this paper, a time-sequential graph adversarial learning (TGAL) framework is proposed to detect brain communities and characterize the structure of communities from brain networks. In the framework, a novel time-sequential graph neural network is designed as an encoder to extract efficient graph representations by spatio-temporal attention mechanism. Since it is difficult to capture the community structure, the measurable modularity loss is used to optimize by maximizing the modularity of the community. In addition, the framework employs an adversarial scheme to guide the learning of representation. The effectiveness of our model is shown through experiments on the real-world brain network datasets, and the great performance of brain community detection demonstrates the advantage of the proposed framework.

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. Exact solutions of the fractional homogeneous equation and the non-homogeneous equations are given, respectively. Finally, a finite difference scheme is proposed for solving fractional nonlinear differential equations with exponential memory. The results show the efficiency and convenience of the new fractional derivative.

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. Delays are arbitrary, unpredictable, and time-varying but bounded. The theoretical analysis of NHDA is based on analyzing the interaction among the consensus, the gradient tracking, and the optimization processes. As for the analysis of ASY-NHDA, we equivalently transform the asynchronous system into an augmented synchronous system without delays and prove its convergence through using the generalized small gain theorem. The results show that NHDA and ASY-NHDA converge to the optimal solution at a linear convergence as long as the largest step size is positive and less than an explicitly estimated upper bound, and the largest momentum parameter is nonnegative and less than an upper bound. Finally, we demonstrate the advantages of ASY-NHDA through simulations.

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. This study turns to fractional quantum calculus on the time scale and reports chaos in fractional q-deformed maps. The discrete memory kernels are used, and a weight function approach is proposed for fractional modeling. Rich q-deformed dynamics are demonstrated, which shows the methodology's efficiency.

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. The predictor-corrector method is adopted, and numerical solutions of fractional delay equations are obtained. Then, this concept is extended to fractional difference equations, and generalized chaotic behaviors are discussed numerically. Finally, the new fractional chaotic models are applied to block image encryption and each block has a different fractional order. The new chaotic system improves security of the image encryption and saves the encryption time greatly.

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. Design • This is an observational study. Setting • This study was conducted in the School of Traditional Chinese Medicine at the Second Military Medical University (Shanghai, China). Participants • Participants were 50 healthy university students aged 19-23 y. Intervention • In the theory of WAA, each side of the body and each limb are longitudinally divided into 6 regions, with 1 needling point defined for each region at the wrist or ankle. The theory indicates that needling a point should relieve pain in a point's corresponding region. For the study, a needle was inserted and retained for 30 min in the Upper 2 point of the left wrist of each participant. Outcome Measures • The pressure pain threshold was measured by a handheld algometer at a position in the left Upper 2 region corresponding to the site of the needling and at positions in the right Upper 2 region as well as the left and right Upper 3 regions not corresponding to the site of the needling. The measurements were taken at 40 min before needling, 5 min after needling, 30 min after needling when the needles were removed, and 70 min after needling. Results • The immediate influence of the WAA on the pain threshold was not significant at 5 min after needling (P > .05). However, at 30 min after needling when the needles were removed, the increases in the pain thresholds were statistically significant when compared to those at 40 min before needling, which were the measurements at baseline (P ≤ .01). At 70 min after needling, the pain thresholds remained higher than those at 40 min before needling (P < .05). From 40 min before needling to 70 min after needling, the pain thresholds in the different positions showed a continuous increase. Conclusions • The WAA had an analgesic effect on pressure-induced pain not only in the corresponding but also in the noncorresponding regions of the needling point in healthy adults. The immediate analgesic effect of the WAA at 5 min after needling was not obvious, but the effects at 30 min and 70 min after needling were statistically significant.

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. Finite memory effects are introduced into the lattice system and the numerical formulae are given. Adomian decomposition method is adopted to solve the fractional partial difference equations numerically.

[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. METHODS: Expressions of ADAM8 and EGFR in 49 specimens of NSCLC, 28 specimens of adjacent lung tissues and 13 specimens of benign lung tissues were detected using tissue microarray (TMA) and immunohistochemistry (IHC). The interrelationship between the two factors and their correlations to clinicopathologic features of NSCLC were analyzed. RESULTS: ADAM8 and EGFR were mainly expressed in the cytoplasm and on the cell membrane. The positive rates of ADAM8 and EGFR were significantly higher in NSCLC than in adjacent lung tissues and benign lung tissues (73.5% vs. 10.7% and 15.4%, 69.4% vs. 14.2% and 23.1%, P<0.01). The positive rates of ADAM8 and EGFR were slightly lower in squamous cell carcinoma than in adenocarcinoma (73.1% vs. 80.0%, 65.4% vs. 75.0%, P>0.05), while were significantly higher in stage N1-N3 NSCLC than in stage N0 (85.7% vs. 42.8%, 82.8 vs. 35.7%, P<0.01) and significantly higher in stage III-IV NSCLC than in stage I-II (90.0% vs. 62.1%, 90.0% vs. 65.5%, P<0.05). The expression of ADAM8 was positively correlated to EGFR (r=0.589, P<0.01), with a kappa value of 0.522. CONCLUSION: ADAM8 and EGFR are overexpressed in NSCLC, and their expressions are consistent.