Decomposition Problem Research Articles

Practical sketching‐based randomized tensor ring decomposition

AbstractBased on sketching techniques, we propose two practical randomized algorithms for tensor ring (TR) decomposition. Specifically, on the basis of defining new tensor products and investigating their properties, the two algorithms are devised by applying the Kronecker sub‐sampled randomized Fourier transform and TensorSketch to the alternating least squares subproblems derived from the minimization problem of TR decomposition. From the former, we find an algorithmic framework based on random projection for randomized TR decomposition. We compare our proposals with the existing methods using both synthetic and real data. Numerical results show that they have quite decent performance in accuracy and computing time.

Reflections and Decomposition in Problem Based Learning

Problem Based Learning and Computational Thinking together have been applied in several studies, proven to be effective to bring out the best of problem solving. While both of them share several common features, computational thinking is a way of solving problems in problem based learning. One of the major components that direct a student towards critical thinking and self-directed learning are reflections. The components of computational thinking can be used to intervene reflections. This paper proposes to use decomposition for reflections. A multi method study was conducted on 37 students who were asked to write reflections for software architectural problems. The data was qualitatively analyzed using structural, in vivo and focused coding. Further, we used ttest to quantitatively analyze the data after receiving evaluation parameters from the qualitative analysis. The results are presented in this paper along with the themes generated and how reflections are effective when decomposition is explicitly stated. The work positively contributes towards design of effective PBL reflections. Keywords—Computational Thinking; Decomposition; Problem Based learning; Reflections.

Fenton Reaction in vivo and in vitro. Possibilities and Limitations.

The review considers the problem of hydrogen peroxide decomposition and hydroxyl radical formation in the presence of iron in vivo and in vitro. Analysis of the literature data allows us to conclude that, under physiological conditions, transport of iron, carried out with the help of carrier proteins, minimizes the possibility of appearance of free iron ions in cytoplasm of the cell. Under pathological conditions, when the process of transferring an iron ion from a donor protein to an acceptor protein can be disrupted due to modifications of the carrier proteins, iron ions can enter cytosol. However, at pH values close to neutral, which is typical for cytosol, iron ions are converted into water-insoluble hydroxides. This makes it impossible to decompose hydrogen peroxide according to the mechanism of the classical Fenton reaction. A similar situation is observed in vitro, since buffers with pH close to neutral are used to simulate free radical oxidation. At the same time, iron hydroxides are able to catalyze decomposition of hydrogen peroxide with formation of a hydroxyl radical. Decomposition of hydrogen peroxide with iron hydroxides is called Fenton-like reaction. Studying the features of Fenton-like reaction in biological systems is the subject of future research.

A neuro-fuzzy modular system for modeling nonlinear systems

The real world is nonlinear and in the control application field, this aspect needs to be resolved to build models so we need to refer to nonlinear system modeling techniques. Neuro-fuzzy systems and modular neural networks (NNs) are among the best modeling approaches for nonlinear systems. The combined features of both approaches provide better models. Thus, we propose in this paper a neuro-fuzzy modular architecture for modeling nonlinear systems. The modular architecture consists of dividing a nonlinear problem into several simpler subproblems. We assigned to each subproblem an NN. Each NN provides individual solutions that will be combined to provide a general solution to the original problem. In this respect, the decomposition of the original problem is based on a fuzzy decision mechanism. This mechanism consists of a set of fuzzy rules for processing nonlinear problems using two different strategies. The first involves training only the network weights, and the second adds the fuzzy set parameters to the training step. A comparative study of both strategies reveals the competence of the second strategy in providing better accuracy and simplicity. Using the neuro-fuzzy combination among the modular NNs reduces the complexity of the original problem and achieves much better performance. The proposed architecture is evaluated by two second-order nonlinear systems, a numerical system and a real system called “the chemical reactor,” which is used to carry out a chemical reaction not only in chemical and biochemical engineering, but also in the petrochemical industry. For both systems, the proposed approach provides better performance in terms of the learning time, learning error, and number of neurons.

Dynamic mode decomposition for blindly separating mixed signals and decrypting encrypted images

In this paper, we introduce the dynamic mode decomposition considering a lag $ \tau $ ($ \tau $-DMD) for solving the blind source separation (BSS) problem of chaotic signals and images. $ \tau $-DMD can be used in BSS-based image decryption with good separation performance. The unmixing problem was formulated as a modal decomposition problem. $ \tau $-DMD was applied on separating linear mixed chaotic signals showing a better separation performance than the existing blind source separation algorithms (Amuse, SOBI, FastICA and JADE). In addition, the case of adding noise in the mixing process was considered, and wavelet de-nosing before $ \tau $-DMD improved the separation performance. For the application, $ \tau $-DMD can be used to remove the noise in electrocardiograms (ECG) and the ocular artifacts in electroencephalograms (EEG). $ \tau $-DMD can also be applied in image processing, showing good separation performance of $ \tau $-DMD for both synthetic mixtures and real-life mixed texts. Structural similarity index measurement (SSIM) and peak signal-to-noise ratio (PSNR) were selected as the evaluation criteria. We tested the separation performance of $ \tau $-DMD on natural images, fingerprint images, and real-life text images and compared the results with other methods. Furthermore, $ \tau $-DMD was applied to decrypt the BSS-based encrypted images. In the process of encryption, we set up the underdetermined problem of BSS by mixing the original and key images, and then $ \tau $-DMD was used to extract the original images in the process of decryption with the secret seeds provided. Two simulations were performed to illustrate the performance of $ \tau $-DMD for image decryption, showing a better decryption results than FastICA.

Конструкция уравновешенных функций с высокой нелинейностью и другими криптографическими свойствами

We present an iterative construction that can be used to construct balanced functions with high nonlinearity. Using this construction, we obtained Boolean functions in an even number n ⩾ 18 of variables which have no linear structures with nonlinearity 2n-1 - (2n/2-1 + 2n/2-3 + 2n/2-5 + 2n/2-7). Additional conditions are given under which the functions obtained using the construction will be correlation immune. We also present results concerning “bent sum decomposition problem”.

A Study of Marketing Capabilities and Their Performance Impact Based on SWOT Matrix Modeling

Abstract Marketing capability is a vital resource capability, this paper first utilizes the gradient descent algorithm to calculate the matrix decomposition problem and mine the relevant data of marketing capability. Then combined with the ANP algorithm, it solves the problem of the SWOT algorithm being unquantifiable. It constructs a SWOT-ANP strategy analysis model, and empirically examines the influence of enterprise strategy and performance. The model is applied to the enterprise’s marketing capability, with performance relationship as the target layer, SWOT as the criterion layer, and the weight values of 15 influencing factors are calculated through the network hierarchy. The weight of the opportunity layer in the local weight is higher than that of the disadvantage layer, which leads to the influence of sub-influence factors, and the highest weight of the disadvantage influence factor is 0.04388 lower than the lowest influence factor of opportunity. Combining with the factor intensity score value, the integrated performance influence of O, T, S, and W is calculated to be 8.438, 6.00747, 7.42637, and 7.69062, respectively, and the sample is obtained through the strategy positioning The development strategy of the enterprise is S-T strategy.

Adaptive sparse estimation of nonlinear chirp signals using Laplace priors.

The identification of nonlinear chirp signals has attracted notable attention in the recent literature, including estimators such as the variational mode decomposition and the nonlinear chirp mode estimator. However, most presented methods fail to process signals with close frequency intervals or depend on user-determined parameters that are often non-trivial to select optimally. In this work, we propose a fully adaptive method, termed the adaptive nonlinear chirp mode estimation. The method decomposes a combined nonlinear chirp signal into its principal modes, accurately representing each mode's time-frequency representation simultaneously. Exploiting the sparsity of the instantaneous amplitudes, the proposed method can produce estimates that are smooth in the sense of being piecewise linear. Furthermore, we analyze the decomposition problem from a Bayesian perspective, using hierarchical Laplace priors to form an efficient implementation, allowing for a fully automatic parameter selection. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm is found to yield reliable estimates even when encountering signals with crossed modes. The method's practical potential is illustrated on a whale whistle signal.

Effect and its mechanism of potassium persulfate on aerobic composting process of vegetable wastes.

Vegetable waste (VW) is a potential organic fertilizer resource. As an important way to utilize vegetable wastes, aerobic composting of VW generally has the problems of long fermentation cycle and incomplete decomposition of materials. In this study, 0.3-1.2% of potassium persulfate (KPS) was added to promote the maturity of compost. The results showed that the addition of KPS promoted the degradation of materials, accelerated the temperature rise of compost. KPS also promoted the formation of humic substances (HS). Compared with the control, HS contents of treatments with KPS addition increased by 7.81 ~ 17.52%. Fourier transform infrared (FTIR) spectroscopy and scanning electron microscope (SEM) analysis reveal the mechanism of KPS affecting the composting process: KPS stimulated the degradation of various organic substances such as lignin at high temperature stage, and the degradation of lignin could accelerate the release and decomposition of other components; KPS made the structure of the material looser, with more voids and pores, and more specific surface area of the material, which was more suitable for microbial degradation activities. Therefore, the addition of KPS can promote the decomposition of organic matter in the early stage of composting, accelerate the process of thermophilic phase, and shorten the composting process and improve product maturity.

Experimenting with computational thinking for knowledge transfer in engineering robotics

AbstractBackgroundDespite its obvious relevance to computer science, computational thinking (CT) is transdisciplinary with the potential of impacting one's analytical ability. Although countless efforts have been invested across K‐12 education, there is a paucity of research at the postsecondary level about the extent to which CT can contribute to sustainable learning outcomes.ObjectivesThe current study examines how a series of Arduino‐based robotics learning activities capture the fuller essence of concepts related to CT.MethodsCollege students (n = 50) completed a series of six robotics learning activities. Think‐alouds, student reflections and performance scores were used to assess students' CT through a robotics challenge in virtual and physical learning environments.Results and ConclusionsStudents verbalized CT concepts related to algorithmic thinking much more than abstraction, problem decomposition and testing and debugging. Students exposed to active learning performed better in a virtual robotics challenge compared to their peers in a traditional‐oriented classroom. Students' scores on the physical robotics challenge increased as a function of the number of references they made to CT concepts during the think‐alouds. It is possible to design pedagogical experiences that tap into various dimensions of CT at incremental levels of complexity through a series of Arduino‐based robotics activities. With the integration of an online simulation, students can visualize and transfer their CT skills between a virtual and physical learning environment, thus leading to more sustainable learning outcomes.

Aturan Cramer Berbantuan Excel pada Materi Rangkaian Listrik Searah Dua Loop untuk Mengukur Kemampuan Berpikir Komputasi Peserta Didik

Computational thinking is one of the abilities needed in the 21st century. One of the subjects that requires this ability is physics. One material that is considered difficult is dynamic electrical circuits. The aim of this research is to measure students' computational thinking abilities in solving two-loop electrical circuit problems using Cramer's rules with the help of Microsoft Excel. This research method is included in qualitative descriptive research with a research sample of 10 class XII students at a high school in Banyuwangi. The data collection technique is in the form of student test results in the form of essay questions or descriptions where each question refers to an indicator of computational thinking. The research results showed that 6 people were in the good category for problem decomposition indicators, 8 people were pattern recognition indicators, 7 people were indicators of algorithmic thinking, and 6 people were indicators of abstraction and generalization

A Decomposition Method for Both Additively and Nonadditively Separable Problems

Problem decomposition is crucial for coping with large-scale global optimization problems, which relies heavily on highly precise variable grouping methods. The state-of-the-art decomposition methods identify separability based on the finite differences principle, which is valid only for additively separable functions but not applicable to non-additively separable functions. Therefore, we need to investigate separability in more depth in order to propose a more general principle and design more universal decomposition methods. In this paper, we conduct a comprehensive theoretical investigation on separability, the core of which is proposing an innovative separability identification principle: the minimum points shift principle. By utilizing the new principle, we develop a general separability grouping (GSG) method that can handle both additively and non-additively separable functions with high accuracy. In addition, we design a new set of benchmark functions based on non-additive separability, which compensates for the lack of non-additively separable functions in the previous test suites. Extensive experiments demonstrate that the proposed GSG achieves high grouping accuracy on both new and CEC series benchmark problems, especially on non-additively separable problems Finally, we verify that the proposed GSG can effectively improve the optimization performance of non-additively separable problems through optimization experiments.

Infrared Small-Target Detection Based on Background-Suppression Proximal Gradient and GPU Acceleration

Patch-based methods improve the performance of infrared small target detection, transforming the detection problem into a Low-Rank Sparse Decomposition (LRSD) problem. However, two challenges hinder the success of these methods: (1) The interference from strong edges of the background, and (2) the time-consuming nature of solving the model. To tackle these two challenges, we propose a novel infrared small-target detection method using a Background-Suppression Proximal Gradient (BSPG) and GPU parallelism. We first propose a new continuation strategy to suppress the strong edges. This strategy enables the model to simultaneously consider heterogeneous components while dealing with low-rank backgrounds. Then, the Approximate Partial Singular Value Decomposition (APSVD) is presented to accelerate solution of the LRSD problem and further improve the solution accuracy. Finally, we implement our method on GPU using multi-threaded parallelism, in order to further enhance the computational efficiency of the model. The experimental results demonstrate that our method out-performs existing advanced methods, in terms of detection accuracy and execution time.

Microporomechanics of quasi-brittle rocks: Theoretical formulations and analytical simulations

Hydromechanical coupling is one of the essential theoretical and practical issues in rock mechanics and rock engineering. In geological context, it is critically important to incorporate the effect of pore pressure into the constitutive equations with full account of cracking-induced material anisotropies and friction-related plastic deformation. Focus here is put on poromechanical formulations for quasi-brittle rocks weakened by microcracks and saturated with pore fluid pressure. The linear homogenization method applied to derive the effective properties and system free energy is combined with the irreversible thermodynamics and the problem decomposition. Constitutive derivations include the determination of the system free energy, state equations associated with and evolution laws of the internal variables, closed-form failure criterion, etc. Inherent coupling between anisotropic unilateral damage, friction-induced plastic deformation and the fluid pressure constitutes one of significant novelties of the work. Continuities required for the total free energy, macroscopic stress and the global porosity are guaranteed at any opening-closure transition of cracks. Through strength and deformation coupling analyses, the effects of fluid pressure on material strength and deformation are elucidated and also validated by experiments we performed upon a sandstone.

Hierarchical Multiagent Formation Control Scheme via Actor-Critic Learning.

This article presents a nearly optimal solution to the cooperative formation control problem for large-scale multiagent system (MAS). First, multigroup technique is widely used for the decomposition of the large-scale problem, but there is no consensus between different subgroups. Inspired by the hierarchical structure applied in the MAS, a hierarchical leader-following formation control structure with multigroup technique is constructed, where two layers and three types of agents are designed. Second, adaptive dynamic programming technique is conformed to the optimal formation control problem by the establishment of performance index function. Based on the traditional generalized policy iteration (PI) algorithm, the multistep generalized policy iteration (MsGPI) is developed with the modification of policy evaluation. The novel algorithm not only inherits the advantages of high convergence speed and low computational complexity in the generalized PI algorithm but also further accelerates the convergence speed and reduces run time. Besides, the stability analysis, convergence analysis, and optimality analysis are given for the proposed multistep PI algorithm. Afterward, a neural network-based actor-critic structure is built for approximating the iterative control policies and value functions. Finally, a large-scale formation control problem is provided to demonstrate the performance of our developed hierarchical leader-following formation control structure and MsGPI algorithm.

Approximated decompositions for computational continuum mechanics

Solid and fluid mechanics problems often involve the computation of eigenvalues and eigenvectors. One has short algebraic expressions for the Euler equations and the perfect gas equation of state. However, algebraic expressions for solid mechanics models can become substantial. Computing the eigenvalues and eigenvectors algebraically for different models can become cumbersome. Also, larger formulae may result in increased overall computational time. Internal energy plays a significant role in modeling the medium, and thermodynamic consistency is indispensable. The models should correctly capture heat transfer, mechanical response, and fluid flow, e.g., in mechanocaloric and bone remodeling (BR) problems. In mechanocaloric problems, temperature variation occurs because of load and unload stresses. In BR problems, several mathematical models were developed for modeling its behavior. Flexibility for testing different models is an essential requirement. Hence, our goal is to propose and test approximated eigensystem and singular value (SVD) decompositions for continuum mechanics problems. We tested the resolution and accuracy of our propositions in benchmarking CFD problems. For the solid mechanics, we solved a few classical problems, verified the accuracy, and solved mechanocaloric tests and bar under tension. Although more expensive, the approximated eigensystem decomposition is more flexible. It is high-order and high-resolution, can capture heat transfer, fluid flow, discontinuities, and mechanical response, and can model real-world applications. The SVD is a viable possibility and can be used to adjust the computational time of severe situations, but it needs to be improved.

A safety framework for flow decomposition problems via integer linear programming.

Many important problems in Bioinformatics (e.g. assembly or multiassembly) admit multiple solutions, while the final objective is to report only one. A common approach to deal with this uncertainty is finding "safe" partial solutions (e.g. contigs) which are common to all solutions. Previous research on safety has focused on polynomially time solvable problems, whereas many successful and natural models are NP-hard to solve, leaving a lack of "safety tools" for such problems. We propose the first method for computing all safe solutions for an NP-hard problem, "minimum flow decomposition" (MFD). We obtain our results by developing a "safety test" for paths based on a general integer linear programming (ILP) formulation. Moreover, we provide implementations with practical optimizations aimed to reduce the total ILP time, the most efficient of these being based on a recursive group-testing procedure. Experimental results on transcriptome datasets show that all safe paths for MFDs correctly recover up to 90% of the full RNA transcripts, which is at least 25% more than previously known safe paths. Moreover, despite the NP-hardness of the problem, we can report all safe paths for 99.8% of the over 27 000 non-trivial graphs of this dataset in only 1.5 h. Our results suggest that, on perfect data, there is less ambiguity than thought in the notoriously hard RNA assembly problem. https://github.com/algbio/mfd-safety.

A Markov constraint to uniquely identify elementary flux mode weights in unimolecular metabolic networks

Elementary flux modes (EFMs) are minimal, steady state pathways characterizing a flux network. Fundamentally, all steady state fluxes in a network are decomposable into a linear combination of EFMs. While there is typically no unique set of EFM weights that reconstructs these fluxes, several optimization-based methods have been proposed to constrain the solution space by enforcing some notion of parsimony. However, it has long been recognized that optimization-based approaches may fail to uniquely identify EFM weights and return different feasible solutions across objective functions and solvers. Here we show that, for flux networks only involving single molecule transformations, these problems can be avoided by imposing a Markovian constraint on EFM weights. Our Markovian constraint guarantees a unique solution to the flux decomposition problem, and that solution is arguably more biophysically plausible than other solutions. We describe an algorithm for computing Markovian EFM weights via steady state analysis of a certain discrete-time Markov chain, based on the flux network, which we call the cycle-history Markov chain. We demonstrate our method with a differential analysis of EFM activity in a lipid metabolic network comparing healthy and Alzheimer’s disease patients. Our method is the first to uniquely decompose steady state fluxes into EFM weights for any unimolecular metabolic network.

GSDerainNet: A Deep Network Architecture Based on a Gaussian Shannon Filter for Single Image Deraining

With the continuous advancement of target detection technology in remote sensing, target detection technology in images captured by drones has performed well. However, object detection in drone imagery is still a challenge under rainy conditions. Rain is a common severe weather condition, and rain streaks often degrade the image quality of sensors. The main issue of rain streaks removal from a single image is to prevent over smoothing (or underclearing) phenomena. Aiming at the above problems, this paper proposes a deep learning (DL)-based rain streaks removal framework called GSDerainNet, which properly formulates the single image rain streaks removal problem; rain streaks removal is aptly described as a Gaussian Shannon (GS) filter-based image decomposition problem. The GS filter is a novel filter proposed by us, which consists of a parameterized Gaussian function and a scaled Shannon function. Two-dimensional GS filters exhibit high stability and effectiveness in dividing an image into low- and high-frequency parts. In our framework, an input image is first decomposed into a low-frequency part and a high-frequency part by using the GS filter. Rain streaks are located in the high-frequency part. We extract and separate the rain features of the high-frequency part through a deep convolutional neural network (CNN). The experimental results obtained on synthetic data and real data show that the proposed method can better suppress the morphological artifacts caused by filtering. Compared with state-of-the-art single image rain streaks removal methods, the proposed method retains finer image object structures while removing rain streaks.

On solving elliptic obstacle problems by constant abs-linearization

We consider optimal control problems governed by an elliptic variational inequality of the first kind, namely the obstacle problem. The variational inequality is treated by penalization, which leads to optimization problems governed by a nonsmooth semi-linear elliptic PDE. The CALi algorithm is then applied for the efficient solution of these nonsmooth optimization problems. The special feature of the optimization algorithm CALi is the treatment of the nonsmooth Lipschitz-continuous operators abs, max and min, which allows to explicitly exploit the nonsmooth structure. Stationary points are located by appropriate decomposition of the optimization problem into so-called smooth constant abs-linearized problems. Each of these constant abs-linearized problems can be solved by classical means. The comprehensive algorithmic concept is presented, and its performance is discussed through examples.