We introduce the fractional-order global optimal backpropagation machine, which is trained by an improved fractionalorder steepest descent method (FSDM). This is a fractional-order backpropagation neural network (FBPNN), a state-of-the-art fractional-order branch of the family of backpropagation neural networks (BPNNs), different from the majority of the previous classic first-order BPNNs which are trained by the traditional first-order steepest descent method. The reverse incremental search of the proposed FBPNN is in the negative directions of the approximate fractional-order partial derivatives of the square error. First, the theoretical concept of an FBPNN trained by an improved FSDM is described mathematically. Then, the mathematical proof of fractional-order global optimal convergence, an assumption of the structure, and fractional-order multi-scale global optimization of the FBPNN are analyzed in detail. Finally, we perform three (types of) experiments to compare the performances of an FBPNN and a classic first-order BPNN, i.e., example function approximation, fractional-order multi-scale global optimization, and comparison of global search and error fitting abilities with real data. The higher optimal search ability of an FBPNN to determine the global optimal solution is the major advantage that makes the FBPNN superior to a classic first-order BPNN.
Multi-focus image fusion is an increasingly important component in image fusion, and it plays a key role in imaging. In this paper, we put forward a novel multi-focus image fusion method which employs fractional-order derivative and intuitionistic fuzzy sets. The original image is decomposed into a base layer and a detail layer. Furthermore, a new fractional-order spatial frequency is built to reflect the clarity of the image. The fractional-order spatial frequency is used as a rule for detail layers fusion, and intuitionistic fuzzy sets are introduced to fuse base layers. Experimental results demonstrate that the proposed fusion method outperforms the state-of-the-art methods for multi-focus image fusion.
In this study, we focus on the controllability of fractional-order damped systems in linear and nonlinear cases with multiple time-varying delays in control. For the linear system based on the Mittag-Leffler matrix function, we define a controllability Gramian matrix, which is useful in judging whether the system is controllable or not. Furthermore, in two special cases, we present serval equivalent controllable conditions which are easy to verify. For the nonlinear system, under the controllability of its corresponding linear system, we obtain a sufficient condition on the nonlinear term to ensure that the system is controllable. Finally, two examples are given to illustrate the theory.
In this study, we discuss mainly the image denoising and texture retention issues. Usually, the time-fractional derivative has an adjustable fractional order to control the diffusion process, and its memory effect can nicely retain the image texture when it is applied to image denoising. Therefore, we design a new Rudin-Osher-Fatemi model with a time-fractional derivative based on a classical one, where the discretization in space is based on the integer-order difference scheme and the discretization in time is the approximation of the Caputo derivative (i.e., Caputo-like difference is applied to discretize the Caputo derivative). Stability and convergence of such an explicit scheme are analyzed in detail. We prove that the numerical solution to the new model converges to the exact solution with the order of
A novel color image encryption algorithm based on dynamic deoxyribonucleic acid (DNA) encoding and chaos is presented. A three-neuron fractional-order discrete Hopfield neural network (FODHNN) is employed as a pseudo-random chaotic sequence generator. Its initial value is obtained with the secret key generated by a fiveparameter external key and a hash code of the plain image. The external key includes both the FODHNN discrete step size and order. The hash is computed with the SHA-2 function. This ensures a large secret key space and improves the algorithm sensitivity to the plain image. Furthermore, a new three-dimensional projection confusion method is proposed to scramble the pixels among red, green, and blue color components. DNA encoding and diffusion are used to diffuse the image information. Pseudo-random sequences generated by FODHNN are employed to determine the encoding rules for each pixel and to ensure the diversity of the encoding methods. Finally, confusion II and XOR are used to ensure the security of the encryption. Experimental results and the security analysis show that the proposed algorithm has better performance than those reported in the literature and can resist typical attacks.
The fractional logistic map holds rich dynamics and is adopted to generate chaotic series. A watermark image is then encrypted and inserted into the original images. Since the encryption image takes the fractional order within (0, 1], it increases the key space and becomes difficult to attack. This study provides a robustwatermark method in the protection of the copyright of hardware, images, and other electronic files.
Membrane diffractive optical elements formed by fabricating microstructures on the substrates have two important characteristics, ultra-light mass (surface mass density<0.1 kg/m2) and loose surface shape tolerances (surface accuracy requirements are on the order of magnitude of centimeter). Large-aperture telescopes using a membrane diffractive optical element as the primary lens have super large aperture, light weight, and low cost at launch. In this paper, the research and development on space-based diffractive telescopes are classified and summarized. First, the imaging theory and the configuration of diffractive-optics telescopes are discussed. Then, the developments in diffractive telescopes are introduced. Finally, the development prospects for this technology used as a high-resolution space reconnaissance system in the future are summarized, and the critical and relevant work that China should carry out is put forward.
Deep learning models have achieved state-of-the-art performance in named entity recognition (NER); the good performance, however, relies heavily on substantial amounts of labeled data. In some specific areas such as medical, financial, and military domains, labeled data is very scarce, while unlabeled data is readily available. Previous studies have used unlabeled data to enrich word representations, but a large amount of entity information in unlabeled data is neglected, which may be beneficial to the NER task. In this study, we propose a semi-supervised method for NER tasks, which learns to create high-quality labeled data by applying a pre-trained module to filter out erroneous pseudo labels. Pseudo labels are automatically generated for unlabeled data and used as if they were true labels. Our semi-supervised framework includes three steps: constructing an optimal single neural model for a specific NER task, learning a module that evaluates pseudo labels, and creating new labeled data and improving the NER model iteratively. Experimental results on two English NER tasks and one Chinese clinical NER task demonstrate that our method further improves the performance of the best single neural model. Even when we use only pre-trained static word embeddings and do not rely on any external knowledge, our method achieves comparable performance to those state-of-the-art models on the CoNLL-2003 and OntoNotes 5.0 English NER tasks.
Rapidly increasing capacities, decreasing costs, and improvements in computational power, storage, and communication technologies have led to the development of many applications that carry increasingly large amounts of traffic on the global networking infrastructure. Smart devices lead to emerging technologies and play a vital role in rapid evolution. Smart devices have become a primary 24/7 need in today’s information technology world and include a wide range of supporting processing-intensive applications. Extensive use of many applications on smart devices results in increasing complexity of mobile software applications and consumption of resources at a massive level, including smart device battery power, processor, and RAM, and hinders their normal operation. Appropriate resource utilization and energy efficiency are fundamental considerations for smart devices because limited resources are sporadic and make it more difficult for users to complete their tasks. In this study we propose the model of mobile energy augmentation using cloud computing (MEACC), a new framework to address the challenges of massive power consumption and inefficient resource utilization in smart devices. MEACC efficiently filters the applications to be executed on a smart device or offloaded to the cloud. Moreover, MEACC efficiently calculates the total execution cost on both the mobile and cloud sides including communication costs for any application to be offloaded. In addition, resources are monitored before making the decision to offload the application. MEACC is a promising model for load balancing and power consumption reduction in emerging mobile computing environments.
We study the consensus of a family of recursive trees with novel features that include the initial states controlled by a parameter. The consensus problem in a linear system with additive noises is characterized as network coherence, which is defined by a Laplacian spectrum. Based on the structures of our recursive treelike model, we obtain the recursive relationships for Laplacian eigenvalues in two successive steps and further derive the exact solutions of first- and second-order coherences, which are calculated by the sum and square sum of the reciprocal of all nonzero Laplacian eigenvalues. For a large network size N, the scalings of the first- and second-order coherences are lnN and N, respectively. The smaller the number of initial nodes, the better the consensus bears. Finally, we numerically investigate the relationship between network coherence and Laplacian energy, showing that the firstand second-order coherences increase with the increase of Laplacian energy at approximately exponential and linear rates, respectively.
With the rapid increase of the size of applications and the complexity of the supercomputer architecture, topology-aware process mapping becomes increasingly important. High communication cost has become a dominant constraint of the performance of applications running on the supercomputer. To avoid a bad mapping strategy which can lead to terrible communication performance, we propose an optimized heuristic topology-aware mapping algorithm (OHTMA). The algorithm attempts to minimize the hop-byte metric that we use to measure the mapping results. OHTMA incorporates a new greedy heuristic method and pair-exchange-based optimization. It reduces the number of long-distance communications and effectively enhances the locality of the communication. Experimental results on the Tianhe-3 exascale supercomputer prototype indicate that OHTMA can significantly reduce the communication costs.
An autonomous five-dimensional (5D) system with offset boosting is constructed by modifying the well-known three-dimensional autonomous Liu and Chen system. Equilibrium points of the proposed autonomous 5D system are found and its stability is analyzed. The proposed system includes Hopf bifurcation, periodic attractors, quasi-periodic attractors, a one-scroll chaotic attractor, a double-scroll chaotic attractor, coexisting attractors, the bistability phenomenon, offset boosting with partial amplitude control, reverse period-doubling, and an intermittency route to chaos. Using a field programmable gate array (FPGA), the proposed autonomous 5D system is implemented and the phase portraits are presented to check the numerical simulation results. The chaotic attractors and coexistence of the attractors generated by the FPGA implementation of the proposed system have good qualitative agreement with those found during the numerical simulation. Finally, a sound data encryption and communication system based on the proposed autonomous 5D chaotic system is designed and illustrated through a numerical example.