Decomposition Problem Research Articles

Timely Device Status Updates in Industrial Wireless Monitoring Systems Under Resource Constraints

In Industrial Internet of Things (IIoT), it is essential to acquire timely device status information to ensure efficient operation. In this article, we consider a wireless monitoring system in IIoT and employ the concept of Age of Information (AoI) to characterize the timeliness of device status information in the system. Considering the impact of resource constraints on information acquisition, we apply a pull-based model to control the entire process of sampling, transmission, and processing associated with device status updates, which constitutes a system-wide AoI minimization problem. The formulated problem is a mixed-integer nonconvex problem, due to the temporal correlation of AoI and the intractability of the implicit AoI-associated objective function. We introduce the concept of average AoI earnings to equivalently substitute the optimization objective. The original problem in consecutive time slots is decomposed into the per-time slot average AoI earnings maximization problem to deal with the temporal correlation of AoI. Then, an online slot-by-slot optimization algorithm (SBSA) is proposed to control device status updates without long-term system state information. Simulation results show that SBSA can significantly improve the AoI performance of the system. However, the problem decomposition in SBSA inevitably brings approximation error. Hence, based on the actual transmission and processing in the system, we get the lower bound of the system total AoI by designing a multislot optimization algorithm (MSA) and analyze the approximate error caused by SBSA. Through simulation results, SBSA has a substantially lower computational complexity, while maintaining acceptable approximation error in comparison to MSA.

A Review of Population-Based Metaheuristics for Large-Scale Black-Box Global Optimization—Part I

Scalability of optimization algorithms is a major challenge in coping with the ever-growing size of optimization problems in a wide range of application areas from high-dimensional machine learning to complex large-scale engineering problems. The field of large-scale global optimization is concerned with improving the scalability of global optimization algorithms, particularly, population-based metaheuristics. Such metaheuristics have been successfully applied to continuous, discrete, or combinatorial problems ranging from several thousand dimensions to billions of decision variables. In this two-part survey, we review recent studies in the field of large-scale black-box global optimization to help researchers and practitioners gain a bird’s-eye view of the field, learn about its major trends, and the state-of-the-art algorithms. Part I of the series covers two major algorithmic approaches to large-scale global optimization: 1) problem decomposition and 2) memetic algorithms. Part II of the series covers a range of other algorithmic approaches to large-scale global optimization, describes a wide range of problem areas, and finally, touches upon the pitfalls and challenges of current research and identifies several potential areas for future research.

Recursive Decomposition Network for Deformable Image Registration.

Deformation decomposition serves as a good solution for deformable image registration when the deformation is large. Current deformation decomposition methods can be categorized into cascade-based methods and pyramid-based methods. However, cascade-based methods suffer from heavy computational burdens and long inference time due to their structures of repeated subnetworks, while the effectiveness of pyramid-based methods is constrained by their limited numbers of resolution levels. In this paper, to address both the insufficient and inefficient decomposition problems in current deformation decomposition methods, we propose a recursive decomposition network (RDN) to offer a novel solution for deformable image registration. Stage-wise recursion can efficiently decompose a large deformation into different pyramid estimation stages without using repeated subnetworks like in cascade-based methods. Level-wise recursion can sufficiently decompose the deformation inside each resolution level instead of only one-time estimation like in pyramid-based methods. Extensive experiments and ablation studies on two representative datasets validate the effectiveness and efficiency of our proposed RDN.

Sparse Aitken–Schwarz domain decomposition with application to Darcy flow

This paper focuses on the acceleration of the Schwarz method by the Aitken’s acceleration of the convergence technique by considering the special structure of the Schwarz’s error operator between two consecutive iterates on the domain decomposition’s interfaces. The new proposed method, called Sparse Aitken–Schwarz method, builds a low-rank space for each subdomain to approximate the true solution on its interfaces instead of building a low-rank space associated to the gathered subdomains’ interfaces solution as the Aitken–Schwarz technique does. We show that the resulting method is better than the full GMRES method applied to the global interface problem as the low-rank space generated is a space whose dimension is larger than the size of Krylov space for the same number of local solving. The Sparse Aitken–Schwarz has better robustness to noise than the Aitken–Schwarz. Weak and strong scaling results on a two-level parallel implementation show the improvements of the Sparse Aitken–Schwarz over the Aitken–Schwarz on a 3D Darcy flow application with randomly distributed permeability fields with high contrast values (Berenguer & Al, Aitken’s acceleration of the Schwarz process using singular value decomposition for heterogeneous 3D groundwater flow problems, Computers & Fluids 80:320-326, 2013).

Lightweight noncommutative key exchange protocol for IoT environments

Network communications are expanding rapidly in many fields, including telecommunications, the Internet of Things, space, consumer electronics, and the military, with different privacy and security issues at stake in each of these areas. The Internet of Things (IoT) has drawn increased attention from academic and industrial researchers over the last few decades. In this environment, keys are routinely exchanged through a public protocol to support the highly secure IoT domain and thwart security threats from unauthorized parties. The environment for IoT devices is subject to numerous limitations, including those related to processing, memory, and energy. These devices need to pass through a gateway or sink to connect to the network. Additionally, the environment must enable secure communication between gateways and IoT devices, even when the devices are disconnected from the rest of the network. In this paper, a lightweight key exchange protocol for IoT environments is presented, allowing the gateway and the IoT device to communicate over an open channel. Our proposed protocol improves security by utilizing noncommutative structures and polynomials over noncommutative rings. The underlying idea is to use the generalized decomposition problem associated with noncommutative rings. Furthermore, how the suggested protocol can achieve key certification and perfect onward secrecy is addressed. Results show this protocol is a strong candidate for key sharing and secure communication between IoT devices. We put our methodology into practice and the results of our experiments demonstrate enhancement of security levels. Finally, the performance analysis of the suggested protocol is compared with some other protocols, in terms of security, communication, and computing overhead.

Secured distributed algorithms without hardness assumptions

We study algorithms in the LOCAL model that produce secured output. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the output of other vertices, with a certain probability. As the extensive research in the distributed algorithms field yielded efficient decentralized algorithms, the discussion about the security of distributed algorithms was somewhat neglected. Nevertheless, many protocols and algorithms were devised in the research area of secure multi-party computation problem. However, the focus in those protocols was to work for every function f at the expense of increasing the round complexity, or the necessity of several computational assumptions. We present a novel approach, which identifies and develops those algorithms that are inherently secure (which means they do not require any further constructions). This approach yields efficient secure algorithms for various labeling and decomposition problems without requiring any hardness assumption, but only a private randomness generator in each vertex.

Application of interactive Genetic Algorithm in landscape planning and design

In order to improve the design effect of garden landscape space environment and optimize the structure of garden landscape space environment, an optimization design method of garden landscape space environment based on interactive genetic algorithm was proposed. Landscape space environment design is built with image visual feature space distributed monitoring model and fuzzy pixel area feature fusion reconstruction model, and the landscape space environment design of the image by multistage decomposition and pixel gray characteristics, established landscape space environment design image visual feature reconstruction model. The method also combines block area template matching method is landscape space environment design of the image features visual reconstruction and visual space distributed detection, information fusion using similarity model reconstructs the landscape space environment design of image visual perception process of information fusion, in order to extract fuzzy characteristic landscape space environment design of the image, Finally, interactive genetic algorithm is used to realize the quality assessment of landscape art information fusion perception and visual reconstruction. The simulation results show that compared with the traditional method, the visual reconstruction quality of landscape spatial environment design image processed by this method is better, the image recognition accuracy is higher, and the output signal-to-noise ratio is improved by 14.6%. The experimental results prove that the introduction of interactive genetic algorithm in landscape planning and design can effectively solve the problems of multi-level feature decomposition and pixel feature separation in the process of landscape design, optimize the landscape spatial environment structure, and achieve good landscape spatial environment design effect.

Dimensionality Reduction and Classification of Hyperspectral Remote Sensing Image Feature Extraction

Terrain classification is an important research direction in the field of remote sensing. Hyperspectral remote sensing image data contain a large amount of rich ground object information. However, such data have the characteristics of high spatial dimensions of features, strong data correlation, high data redundancy, and long operation time, which lead to difficulty in image data classification. A data dimensionality reduction algorithm can transform the data into low-dimensional data with strong features and then classify the dimensionally reduced data. However, most classification methods cannot effectively extract dimensionality-reduced data features. In this paper, different dimensionality reduction and machine learning supervised classification algorithms are explored to determine a suitable combination method of dimensionality reduction and classification for hyperspectral images. Soft and hard classification methods are adopted to achieve the classification of pixels according to diversity. The results show that the data after dimensionality reduction retain the data features with high overall feature correlation, and the data dimension is drastically reduced. The dimensionality reduction method of unified manifold approximation and projection and the classification method of support vector machine achieve the best terrain classification with 99.57% classification accuracy. High-precision fitting of neural networks for soft classification of hyperspectral images with a model fitting correlation coefficient (R2) of up to 0.979 solves the problem of mixed pixel decomposition.

A hybrid optimization framework for UAV reconnaissance mission planning

Applying unmanned aerial vehicles (UAVs) in military reconnaissance missions arises in recent years. It refers to using finite UAVs to reconnoiter some enemy targets with limited battery power, aiming at collecting valuable information as much as possible. While existing methods like heuristics and intelligent optimization methods have been widely applied, their performance on large-scale reconnaissance mission planning problems (RMPPs) is still unsatisfactory. This study proposes a hybrid optimization framework, namely, EA-DRL, to improve the optimization effect based on a problem decomposition strategy. In detail, the RMPP is decomposed into a target selection subproblem and a path planning subproblem. An evolutionary algorithm and a deep reinforcement learning method are proposed to solve them, respectively. Updating solutions to these two subproblems iteratively eventually completes the optimization of the given RMPP. Experimental results on different types of RMPP instances show great effectiveness and strong generalization ability of the proposed framework EA-DRL.

Boosting semi-supervised face recognition with raw faces

Deep facial recognition benefits significantly from large-scale training data; however, the bottleneck of high labeling costs persists. Therefore, to reduce the labeling costs, it is desirable to train a model using limited labeled data and abundant unlabeled data ( i.e. , semi-supervised learning). However, existing semi-supervised learning methods present two primary challenges: (1) The possibility of identity overlaps between the unlabeled and labeled data. These overlaps can affect the correctness of pseudo-labels of the unlabeled set. (2) Different pseudo-labels generated by the clustering algorithm may belong to the same individual ( i.e. , over-decomposition problem). Thus, in this study, instead of experimenting with non-overlapping conditions, we apply smooth labels to exploit the potential of those samples that are similar to the identities in the labeled set. For samples that are not similar to the labeled set, we introduce a dual clustering strategy to remedy the over-decomposition problem caused by single clustering. With the upgraded semi-supervised framework, we recycle the discarded samples during purification of MS-Celeb-1 M (MS1M) to further scale up the training set, which offers a considerable performance boost of 94.39% on the IJB-C dataset. • Pioneering use of raw unlabeled data. • Utilizing of overlaps by relaxing the intra-class constraint with label smoothing. • Dual clustering strategy to address the over decomposition problem caused by a single clustering.

Синтез управління стабілізацією геостаціонарного супутника у точці стояння

Розроблено методи та алгоритми балістичного забезпечення управління стабілізацією довготи точки стояння геостаціонарного супутника (ГСС). Еволюція поточних координат ГСС моделювалася диференціальними рівняннями руху матеріальної точки у центральному гравітаційному полі з урахуванням обмежених структурно-параметричних збурень відомої інтенсивності, викликаних загальним впливом Сонця, Місяця, відмінністю гравітаційного поля Землі від центрального тощо. Конкретне математичне моделювання цих збурень не розглядалося, використовувалися лише властивості їх загальної обмеженості за нормою. Для синтезу управління застосовувався відомий в теорії керування орієнтацією (кутовим положенням космічного апарата) аналог — метод декомпозиції загальної задачі синтезу на кінематичну і динамічну. Для їх вирішення використовувалися відомі узагальнення прямого методу Ляпунова дослідження стійкості розвʼязків диференціальних рівнянь на дослідження стійкості замкнених обмежених множин (конкретно багатовимірних еліпсоїдів) у їх фазових просторах. Поряд із методом синтезу управління стабілізацією довготи точки стояння ГСС запропоновано методи еліпсоїдального оцінювання, викликані впливом згаданих збурень помилок стабілізації, що встановилися. Методи засновані на побудові зовнішніх еліпсоїдальних оцінок множин досяжнос­ті та граничних множин у фазових просторах динамічних систем з обмеженими структурно-параметричними збуреннями. Запропоновано також метод отримання гарантованих інтервальних оцінок помилок стабілізації, що встановилися, по кожній з координат. Ефективність запропонованих методів керування ілюструється результатами компʼютер­ного моделювання.

Intrinsic image decomposition using physics-based cues and CNNs

Intrinsic image decomposition is the decomposition of an image into its reflectance and shading components. The intrinsic image decomposition problem is inherently ill-posed, since there can be multiple solutions to compute the intrinsic components forming the same image. In this paper, we explore the use of physics-based priors. We also propose a new architecture that separates the learning components in a stacked manner. We explore various ways of integrating such priors into a deep learning system. Our method is trained and tested on a large synthetic garden dataset to assess its performance. It is evaluated and compared to state-of-the-art methods using two standard intrinsic datasets. Finally, the pre-trained network is tested on real world images to show the generalisation capabilities of the network.

Decompositions of quasirandom hypergraphs into hypergraphs of bounded degree

We prove that any quasirandom uniform hypergraph H H can be approximately decomposed into any collection of bounded degree hypergraphs with almost as many edges. In fact, our results also apply to multipartite hypergraphs and even to the sparse setting when the density of H H quickly tends to 0 0 in terms of the number of vertices of H H . Our results answer and address questions of Kim, Kühn, Osthus and Tyomkyn; and Glock, Kühn and Osthus as well as Keevash. The provided approximate decompositions exhibit strong quasirandom properties which are very useful for forthcoming applications. Our results also imply approximate solutions to natural hypergraph versions of long-standing graph decomposition problems, as well as several decomposition results for (quasi)random simplicial complexes into various more elementary simplicial complexes such as triangulations of spheres and other manifolds.

Multilevel field-split preconditioners with domain decomposition for steady and unsteady flow problems

With the incremental applications of Newton–Krylov methods for solving large sparse nonlinear systems of equations, the design of robust and scalable linear preconditioners plays an essential role for the whole solver. In this paper, we investigate the family of field-split (FS) preconditioners with different combinations of physics-based and domain decomposition methods, applied to the two typical fluid problems, i.e., the unsteady flow through fractured porous media and the steady buoyancy driven flow. In the implementation, several new versions of FS preconditioners are considered under the framework of the domain decomposition technique: additive FS, multiplicative FS, Schur-complement FS, and the constrained pressure residual (CPR) method, where the inverse of corresponding matrices is approximated by using the restricted additive Schwarz (RAS) algorithm. Rigorous eigenvalue analysis for various FS preconditioners is also provided for facilitating the design of algorithms. In particular, our approach further enhances the numerical performance by presenting a family of multilevel field-split methods for efficiently preconditioning. Numerical experiments are presented to demonstrate the robustness and parallel scalability of the proposed preconditioning strategies for both standard benchmarks as well as realistic flow problems on a supercomputer.

The symmetric rank and decomposition of m-order n-dimensional (n = 2,3,4) symmetric tensors over the binary field

Firstly, we propose an algebraic method to compute the symmetric rank and symmetric rank decomposition for symmetric tensors over the binary field, when the order is at least the dimension minus one. Then we discuss Comon's conjecture and rank decomposition for low dimension symmetric tensors. For 2×2×⋯×2 symmetric tensors over the binary field, we show Comon's conjecture is true except for one special tensor (actually matrix), and the rank decomposition problem is solved when the order is greater than or equal to 4. For 3×3×⋯×3 symmetric tensors over the binary field, we prove Comon's conjecture is true when the order is greater than or equal to 4, and obtain the unique rank decomposition when the order is greater than or equal to 6. Finally, for 4×4×⋯×4 symmetric tensors over the binary field, we show Comon's conjecture is true and obtain the unique rank decomposition when the order is greater than or equal to 8.

All-Solid-State Photo-Assisted Li-CO2 Battery Working at an Ultra-Wide Operation Temperature.

At present, photoassisted Li-air batteries are considered to be an effective approach to overcome the sluggish reaction kinetics of the Li-air batteries. And, the organic liquid electrolyte is generally adopted by the current conventional photoassisted Li-air batteries. However, the superior catalytic activity of photoassisted cathode would in turn fasten the degradation of the organic liquid electrolyte, leading to limited battery cycling life. Herein, we tame the above limitation of the traditional liquid electrolyte system for Li-CO2 batteries by constructing a photoassisted all-solid-state Li-CO2 battery with an integrated bilayer Au@TiO2/Li1.5Al0.5Ge1.5(PO4)3 (LAGP)/LAGP (ATLL) framework, which can essentially improve battery stability. Taking advantage of photoelectric and photothermal effects, the Au@TiO2/LAGP layer enables the acceleration of the slow kinetics of the carbon dioxide reduction reaction and evolution reaction processes. The LAGP layer could resolve the problem of liquid electrolyte decomposition under illumination. The integrated double-layer LAGP framework endows the direct transportation of heat and Li+ in the entire system. The photoassisted all-solid-state Li-CO2 battery achieves an ultralow polarization of 0.25 V with illumination, as well as a high round-trip efficiency of 92.4%. Even at an extremely low temperature of -73 °C, the battery can still deliver a small polarization of 0.6 V by converting solar energy into heat to achieve self-heating. This study is not limited to the Li-air batteries but can also be applied to other battery systems, constituting a significant step toward the practical application of all-solid-state photoassisted Li-air batteries.

Best sparse rank-1 approximation to higher-order tensors via a truncated exponential induced regularizer

Best sparse tensor rank-1 approximation consists of finding a projection of a given data tensor onto the set of sparse rank-1 tensors, which is important in sparse tensor decomposition and related problems. Existing models used ℓ0 or ℓ1 norms to pursue sparsity. In this work, we first construct a truncated exponential induced regularizer to encourage sparsity, and prove that this regularizer admits a reweighted property. Lower bounds for nonzero entries and upper bounds for the number of nonzero entries of the stationary points of the associated optimization problem are studied. By using the reweighted property of the regularizer, we develop an iteratively reweighted algorithm for solving the problem, and establish its convergence to a stationary point without any assumption. In particular, we show that if the parameter of the regularizer is small enough, then the support of the iterative points will be fixed after finitely many steps. Numerical experiments illustrate the effectiveness of the proposed model and algorithm.

Enhancement and Noise Suppression of Single Low-Light Grayscale Images

Low-light images have low contrast and high noise, making them not easily readable. Most existing image-enhancement methods focus on color images. In the present study, an enhancement and denoising algorithm for single low-light grayscale images is proposed. The algorithm is based on the multi-exposure fusion framework. First, on the basis of the low-light tone-mapping operators, the optimal virtual exposure image is constructed according to the information entropy criterion. Then, the latent low-rank representation is applied to two images to generate low-ranking parts and saliency parts to reduce noise after fusion. Next, the initial weight map is constructed based on the information contained in the decomposed images, and an adaptive weight refined algorithm is proposed to restore as much structural information as possible and keep the details while avoiding halo artifacts. When solving the weight maps, the decomposition and optimization of the nonlinear problem is converted into a total variation model, and an iterative method is used to reduce the computational complexity. Last, the normalized weight map is used for image fusion to obtain the enhanced image. The experimental results showed that the proposed method performed well both in the subjective and objective evaluation of state-of-the-art enhancement methods for low-light grayscale images.

Single-shot retinal image enhancement using untrained and pretrained neural networks priors integrated with analytical image priors

Retinal images acquired using fundus cameras are often visually blurred due to imperfect imaging conditions, refractive medium turbidity, and motion blur. In addition, ocular diseases such as the presence of cataracts also result in blurred retinal images. The presence of blur in retinal fundus images reduces the effectiveness of the diagnosis process of an expert ophthalmologist or a computer-aided detection/diagnosis system. In this paper, we put forward a single-shot deep image prior (DIP)-based approach for retinal image enhancement. Unlike typical deep learning-based approaches, our method does not require any training data. Instead, our DIP-based method can learn the underlying image prior while using a single degraded image. To perform retinal image enhancement, we frame it as a layer decomposition problem and investigate the use of two well-known analytical priors, i.e., dark channel prior (DCP) and bright channel prior (BCP) for atmospheric light estimation. We show that both the untrained neural networks and the pretrained neural networks can be used to generate an enhanced image while using only a single degraded image. The proposed approach is time and memory-efficient, which makes the solution feasible for real-world resource-constrained environments. We evaluate our proposed framework quantitatively on five datasets using three widely used metrics and complement that with a subjective qualitative assessment of the enhancement by two expert ophthalmologists. For instance, our method has achieved significant performance for untrained CDIPs coupled with DCP in terms of average PSNR, SSIM, and BRISQUE values of 40.41, 0.97, and 34.2, respectively, and for untrained CDIPs coupled with BCP, it achieved average PSNR, SSIM, and BRISQUE values of 40.22, 0.98, and 36.38, respectively. Our extensive experimental comparison with several competitive baselines on public and non-public proprietary datasets validates the proposed ideas and framework.

The Impact of Intelligent Accounting Information Management on Corporate Governance Information Transparency

In order to improve the transparency of corporate governance information, this paper combines intelligent accounting information technology to analyze the information transparency in the process of corporate governance, analyzes the fast adaptive neighbor clustering algorithm, and realizes the joint spectral embedding of data by creating block diagonal anchor graphs. Moreover, this paper re-selects anchor points from the spectral embedding data and constructs a new block diagonal anchor graph. In addition, using the principle of adaptive nearest neighbor clustering, this paper performs structured graph learning on the block diagonal anchor graph matrix. After derivation, the Laplace eigenvalue decomposition problem of the whole graph in adaptive nearest neighbor clustering can be transformed into a block matrix singular value decomposition problem. The regression analysis shows that there is a linear correlation between the advanced degree of intelligent accounting information management technology and the transparency of corporate governance information.