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This paper presents an extensive study of linear and logistic regression algorithms implemented with 1T1R memristor crossbars arrays. Using a sophisticated simulation platform that wraps circuit-level simulations of 1T1R crossbars and physics-based models of RRAM (memristors), we elucidate the impact of device variability on algorithm accuracy, convergence rate and precision. Moreover, a smart pulsing strategy is proposed for practical implementation of synaptic weight updates that can accelerate training in real crossbar architectures. Stochastic multi-variable linear regression shows robustness to memristor variability in terms of prediction accuracy but reveals impact on convergence rate and precision. Similarly, the stochastic logistic regression crossbar implementation reveals immunity to memristor variability as determined by negligible effects on image classification accuracy but indicates an impact on training performance manifested as reduced convergence rate and degraded precision. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to derive cubature formulas using bivariate degree-graded alternative shifted Jacobi polynomials and present some of their applications through a method for fast and explicit construction of operational integration matrices in this polynomial basis. First, we take the non-degree-graded alternative shifted Jacobi polynomial basis over the interval [ 0 , 1 ] and introduce a corresponding degree-graded polynomial basis. We then construct sparse and well-structured operational integration matrices in that basis. The main advantage of the proposed idea is the low computational complexity which is derived through vector–matrix multiplications without change of bases. As an application, a fast and accurate numerical algorithm based on the obtained cubature formula is developed for the approximate solution of nonlinear multi-dimensional integral equations which arise in the theory of nonlinear parabolic boundary value problems as well as the mathematical modeling of the spatio-temporal development of an epidemic. It is shown that such a matrix representation of cubature formula in terms of the bivariate degree-graded basis gives an approximate solution with a higher order accuracy. The experimental results also illustrate that smaller size and lower orders of the operational matrix and basis functions can obtain a favorable approximate solution. [ABSTRACT FROM AUTHOR]

• The overall contour clarity of the image mainly depends on the edge distribution of the image. In our approach, the Laplace operator is used to sharpen the image, which can improve the quality of the image. • In the process of image style transfer, in order to reduce the iterative time. The image is first down-sampled to reduce the resolution, and then the generated image is super-resolution reconstructed. • Large number of evaluation experiments are conducted to show the effect of our proposed method. In deep learning, multi-robot systems intelligently cooperate to perform a complex task, and improve the performance of a single robot through communication, collaboration and sharing of information. Intelligent collaborative work makes the research and application of multi-robot systems develop rapidly. The traditional image style transfer algorithm mainly uses mathematical modeling to characterize the texture of the picture, and combines the content image with the style image to achieve the effect of style transfer. This style transfer algorithm ignores the edge distribution of the image, which makes the contour of the generated image blurred, and it takes a long time in the iterative process of style transfer, and the effect is poor. Therefore, this paper proposes a ceramic decoration pattern style migration algorithm based on the ESPCN model. The algorithm uses the Laplace operator to sharpen the image to highlight the edge distribution, and then uses downsampling to generate low-resolution images to reduce the iteration time of image style transfer. The final generated image uses ESPCN super-resolution reconstruction to reconstruct the low-resolution image. Converted to high-resolution images. The experimental results show that multiple image evaluation indicators show that the edge distribution of the generated image is clear, the iteration time is shortened, and the image quality and definition are improved. [ABSTRACT FROM AUTHOR]

The performance of the existing frequency control strategies for MT-HVDC systems relies on the accuracy of the mathematical models. However, it is hard to obtain the exact mathematical models of MT-HVDC systems. To deal with this challenge, this paper presents a distributed cooperative frequency control strategy for MT-HVDC systems by using a reinforcement learning method, i.e., value iteration algorithm. Specifically, the proposed control strategy is data driven and hence model free. Besides, the proposed control strategy is distributed in the sense that each AC area only requires the local and neighboring information, rather than the information of all the AC areas. Moreover, the proposed control strategy makes the connected AC areas compensate load disturbances together by sharing their power reserves via HVDC grids, which greatly decreases the operation costs of MT-HVDC systems. The performance of the proposed control strategy is validated by cases study. [ABSTRACT FROM AUTHOR]

A multi-purpose mechanical platform to track moving objects in three-dimensional space has been developed. It is composed of one main microcontroller board that processes all system data, two cameras, three motors, and one secondary microcontroller board to position a platform with three degrees of freedom. The system computes the optical flow and moves the cameras accordingly, tracking motion within the visual scene. The platform operates autonomously. To the best of our knowledge, there are no similar systems reported with low-resolution image sensors and low-cost microcontrollers. Existing solutions rely on personal computers and advanced FPGAs to process image data. This article concludes that the optical flow operation is efficient even using an image sensor with very low resolution. Thus, the system complexity and image data processing are alleviated significantly. The platform can be easily adapted to different application scenarios by adding new peripherals, sensors, or image processing algorithms. A detailed description of the system design and experimental results are provided. [ABSTRACT FROM AUTHOR]

The convergence of the waveform relaxation (WR) method is demonstrated for a class of circuits: Chains of identical and symmetrical passive subcircuits. The WR algorithm uses resistive coupling to implement the iteration. Every part is modeled as a symmetric and reciprocal linear two-port network. The iteration matrices of the WR operator are constructed for the Gauss-Jacobi and Gauss-Seidel relaxations in the Fourier domain. An upperbound estimate of the spectral radius of the WR operator is presented. It demonstrates the convergence of the method independently of the number of cascaded parts in the chain and the coupling resistance. [ABSTRACT FROM AUTHOR]

This paper proposes a marginal multi-object Bayesian filter with multiple hypotheses to track multiple objects in the presence of object appearing and object disappearing, missed detection and clutter. This filter delivers the probability of existence and probability density function of each object. A mathematical model for searching K-best hypotheses is set up by the maximization of the generalized joint likelihood ratios of hypotheses, which results in a 2-dimensional assignment problem. The K-best hypotheses can be acquired by using the Murty algorithm to solve the 2-dimensional assignment problem. According to the K-best hypotheses, the existence probabilities and probability density functions of objects are formed. Furthermore, an implementation of this filter for a linear Gaussian system is developed and is extended to nonlinear observations. Experimental result demonstrates that the proposed filter outperforms other available filters at various numbers of clutter and different detecting probabilities. [ABSTRACT FROM AUTHOR]

In this article, we provide numerical simulations to show the importance and the effects of fractional order derivatives in psychological studies. As it is well-known, complex variables are more realistic for defining structures in different cases. In this paper, we evidence that such dynamics become more realistic when we use fractional derivatives. We study a non-integer order, non-linear mathematical model for defining a love story of Layla and Majnun (a couple in a romantic relationship). We exemplify all necessary practical calculations to study this serious psychological phenomena. The existence of the unique solution for the given model is exhibited. We use a very recent and strong modified Predictor-Corrector algorithm to evaluate the model structure. Stability of the proposed method is also given. We exemplify that the given complex fractional model is more realistic and represents reality more closely. The proposed model is very basic, significant, and efficient at introducing distinct natures by only replacing one control parameter. In this study, we found that in some of the cases there are stable limit cycles, in some cases periodic behaviours and sometimes transiently chaotic solutions exist which cannot be observed for integer order models at same parameter values. The principal contribution of this article is to exhibit the importance of non-integer order derivatives for analysing complex dynamics. The use of complex variables makes this study more effective because they have both magnitude and phase to better explore the love and can describe different emotions such as coexisting love and hate. [ABSTRACT FROM AUTHOR]