Exercise and also fatfree mass in the course of progress plus later life

In distributed learning and optimization, a network of multiple computing units coordinates to solve a large-scale problem. This article focuses on dynamic optimization over a decentralized network. We develop a communication-efficient algorithm based on the alternating direction method of multipliers (ADMM) with quantized and censored communications, termed DQC-ADMM. At each time of the algorithm, the nodes collaborate to minimize the summation of their time-varying, local objective functions. Through local iterative computation and communication, DQC-ADMM is able to track the time-varying optimal solution. Different from traditional approaches requiring transmissions of the exact local iterates among the neighbors at every time, we propose to quantize the transmitted information, as well as adopt a communication-censoring strategy for the sake of reducing the communication cost in the optimization process. To be specific, a node transmits the quantized version of the local information to its neighbors, if and only if the value sufficiently deviates from the one previously transmitted. We theoretically justify that the proposed DQC-ADMM is capable of tracking the time-varying optimal solution, subject to a bounded error caused by the quantized and censored communications, as well as the system dynamics. Through numerical experiments, we evaluate the tracking performance and communication savings of the proposed DQC-ADMM.Modeling, prediction, and recognition tasks depend on the proper representation of the objective curves and surfaces. Polynomial functions have been proved to be a powerful tool for representing curves and surfaces. Until now, various methods have been used for polynomial fitting. With a recent boom in neural networks, researchers have attempted to solve polynomial fitting by using this end-to-end model, which has a powerful fitting ability. However, the current neural network-based methods are poor in stability and slow in convergence speed. In this article, we develop a novel neural network-based method, called Encoder-X, for polynomial fitting, which can solve not only the explicit polynomial fitting but also the implicit polynomial fitting. The method regards polynomial coefficients as the feature value of raw data in a polynomial space expression and therefore polynomial fitting can be achieved by a special autoencoder. The entire model consists of an encoder defined by a neural network and a decoder defined by a polynomial mathematical expression. We input sampling points into an encoder to obtain polynomial coefficients and then input them into a decoder to output the predicted function value. The error between the predicted function value and the true function value can update parameters in the encoder. The results prove that this method is better than the compared methods in terms of stability, convergence, and accuracy. In addition, Encoder-X can be used for solving other mathematical modeling tasks.This article proposes an adaptive neural network (NN) output feedback optimized control design for a class of strict-feedback nonlinear systems that contain unknown internal dynamics and the states that are immeasurable and constrained within some predefined compact sets. NNs are used to approximate the unknown internal dynamics, and an adaptive NN state observer is developed to estimate the immeasurable states. By constructing a barrier type of optimal cost functions for subsystems and employing an observer and the actor-critic architecture, the virtual and actual optimal controllers are developed under the framework of backstepping technique. In addition to ensuring the boundedness of all closed-loop signals, the proposed strategy can also guarantee that system states are confined within some preselected compact sets all the time. This is achieved by means of barrier Lyapunov functions which have been successfully applied to various kinds of nonlinear systems such as strict-feedback and pure-feedback dynamics. Besides, our developed optimal controller requires less conditions on system dynamics than some existing approaches concerning optimal control. The effectiveness of the proposed optimal control approach is eventually validated by numerical as well as practical examples.Recurrent neural networks (RNNs) can be used to operate over sequences of vectors and have been successfully applied to a variety of problems. However, it is hard to use RNNs to model the variable dwell time of the hidden state underlying an input sequence. In this article, we interpret the typical RNNs, including original RNN, standard long short-term memory (LSTM), peephole LSTM, projected LSTM, and gated recurrent unit (GRU), using a slightly extended hidden Markov model (HMM). Based on this interpretation, we are motivated to propose a novel RNN, called explicit duration recurrent network (EDRN), analog to a hidden semi-Markov model (HSMM). It has a better performance than conventional LSTMs and can explicitly model any duration distribution function of the hidden state. The model parameters become interpretable and can be used to infer many other quantities that the conventional RNNs cannot obtain. Therefore, EDRN is expected to extend and enrich the applications of RNNs. The interpretation also suggests that the conventional RNNs, including LSTM and GRU, can be made small modifications to improve their performance without increasing the parameters of the networks.This article investigates the problem of the decentralized adaptive output feedback saturated control problem for interconnected nonlinear systems with strong interconnections. A decentralized linear observer is first established to estimate the unknown states. Then, an auxiliary system is constructed to offset the effect of input saturation. With the aid of graph theory and neural network technique, a decentralized adaptive neuro-output feedback saturated controller is designed in a nonrecursive manner. POMHEX nmr A sufficient criterion is established to achieve the uniform ultimate boundedness (UUB) of the closed-loop system. An application example of autonomous underwater vehicle (AUV) is provided to verify the effectiveness of the developed algorithm.