Decomposition Problem Research Articles

Architecture and enhanced-algorithms to manage servers-processes into network: a management system.

This work investigates minimizing the makespan of multiple servers in the case of identical parallel processors. In the case of executing multiple tasks through several servers and each server has a fixed number of processors. The processors are generally composed of two processors (core duo) or four processors (quad). The meaningful format of the number of processors is 2k, and k≥0. The problem is to find a schedule that minimizes the makespan on 2k processors. This problem is identified as NP-hard one. A new network architecture is proposed based on the addition of server management. In addition, two novel algorithms are proposed to solve the addressed scheduling problems. The proposed algorithms are based on the decomposition of the main problem in several sub-problems that are applied to develop new heuristics. In each level of the generated tree, some results are saved and used to decompose the set of processes into subsets for the next level. The proposed methods are experimentally examined showing that the running time of the proposed heuristics is remarkably better than its best rival from the literature. The application of this method is devoted to the network case when there are several servers to be exploited. The experimental results show that in 87.9% of total instances, the most loaded and least loaded subset-sum heuristic (MLS) reaches the best solution. The best-proposed heuristic reaches in 87.4% of cases the optimal solution in an average time of 0.002 s compared with the best of the literature which reaches a solution in an average time of 1.307 s.

Hybrid Projection Methods for Solution Decomposition in Large-Scale Bayesian Inverse Problems

Hybrid Projection Methods for Solution Decomposition in Large-Scale Bayesian Inverse Problems

Decompositions of endomorphisms into a sum of roots of the unity and nilpotent endomorphisms of fixed nilpotence

For n≥2 and fixed k≥1, we study when an endomorphism f of Fn, where F is an arbitrary field, can be decomposed as t+m where t is a root of the unity endomorphism and m is a nilpotent endomorphism with mk=0. For fields of prime characteristic, we show that this decomposition holds as soon as the characteristic polynomial of f is algebraic over its base field and the rank of f is at least nk, and we present several examples that show that the decomposition does not hold in general. Furthermore, we completely solve this decomposition problem for k=2 and nilpotent endomorphisms over arbitrary fields (even over division rings). This somewhat continues our recent publications in Linear Multilinear Algebra (2022) and Int. J. Algebra Comput. (2022) as well as it strengthens results due to Cǎlugǎreanu-Lam in J. Algebra Appl. (2016).

On singular value decomposition for split quaternion matrices and applications in split quaternionic mechanics

In the theoretical studies and numerical computations of split quaternionic quantum mechanics, the singular value decomposition theorem of split quaternion matrices plays an essential role. In general the problem of singular value decomposition over split quaternion algebra has hitherto remained tangential for split quaternion matrices. In this paper, by means of a real representation matrix of a split quaternion matrix, the singular value decomposition of split quaternion matrices is studied, the singular value decomposition theorem and the corresponding algorithm for split quaternion matrices are given. Finally, three applications for solving the split quaternion least squares problem and the wave separation problem are given based on the singular value decomposition over split quaternion algebra.

Unsupervised neural decoding of signals recorded by thin-film electrode arrays implanted in muscles using autoencoding with a physiologically derived optimisation criterion

We present an autoencoder that learns the discharge times of individual motor units (MU) by processing multichannel electromyogram (EMG) recordings obtained by electrode arrays implanted in muscles, thereby providing a neural interface with the spinal cord. To this end, after preprocessing of the EMG via convolutive sphering, the encoder is constrained to apply an orthogonal transformation to the spatial data and the optimisation criterion enforces a temporal sparsity constraint. These constraints are based on the theoretical modelling of EMG generation. This decomposition method was evaluated on both simulated and experimental signals. For simulated signals, with a ratio of 1.5 between observations and sources, the average detection accuracy was 94% for up to 60 sources for SNR 20 dB. Moreover, the detection accuracy did not significantly decrease when decreasing the SNR to values as low as 0 dB. Experimental signals were collected in humans with thin-film invasive electrodes implanted in the tibialis anterior muscle. The results showed an accuracy on experimental data >90%. Moreover, the proposed method outperformed a state-of-the-art blind source separation approach in terms of the number of reliably detected motor units. In conclusion, we have proposed the first fully unsupervised neural network approach to the problem of neural decoding of intramuscular EMG time series by translating the available theoretical knowledge on the signal properties into an autoencoding architecture tailored to the decomposition problem.

Approximation-Aware Task Deployment on Heterogeneous Multicore Platforms With DVFS

Heterogeneous multi-core platforms, such as ARM big.LITTLE are widely used to execute embedded applications under multiple and contradictory constraints, such as energy consumption and real-time execution. To fulfill these constraints and optimize system performance, application tasks should be efficiently mapped on multi-core platforms. Embedded applications are usually tolerant to approximated results but acceptable Quality-of-Service (QoS). Modeling embedded applications by using the elastic task model, namely, Imprecise Computation (IC) task model, can balance system QoS, energy consumption, and real-time performance during task deployment. However, state-of-the-art approaches seldom consider the problem of IC task deployment on heterogeneous multi-core platforms. They typically neglect task migration, which can improve the solutions due to its flexibility during the task deployment process. This paper proposes a novel QoS-aware task deployment method to maximize system QoS under energy and real-time constraints, where frequency assignment, task allocation, scheduling, and migration are optimized simultaneously. The task deployment problem is formulated as mixed-integer non-linear programming. Then, it is linearized to mixed-integer linear programming to find the optimal solution. Furthermore, based on problem structure and problem decomposition, we propose a novel heuristic with low computational complexity. The sub-problems regarding frequency assignment, task allocation, scheduling, and adjustment are considered and solved in sequence. Finally, the simulation results show that the proposed task deployment method improves the system QoS by 31.2% on average (up to 112.8%) compared to the state-of-the-art methods and the designed heuristic achieves about 53.9% (on average) performance of the optimal solution with a negligible computing time.

Image Desnowing via Deep Invertible Separation

Images taken on snowy days often suffer from severe negative visual effects caused by snowflakes. The task of removing snowflakes from a snowy image is known as image desnowing, which is challenging as image details are easily mistakenly treated and thus may be significantly lost during snowflake removal. Leveraging invertible neural networks (INNs), this paper presents a deep learning-based method for single image desnowing, which can remove snowflakes accurately while preserving image details well. Interpreting desnowing as an image decomposition problem, we propose an INN composed of two asymmetric interactive paths for predicting a latent image and a snowflake layer respectively. Such an INN is able to progressively refine the features of both latent images and snowflake layers for disentanglement, while retaining all information possibly relevant to latent image reconstruction. In addition, an attentive coupling layer supervised by snowflake masks is introduced to enhance feature dismantlement and a coupling-in-coupling structure is developed for further improvement. Extensive experiments show that, the proposed method outperforms existing ones on three benchmark datasets of synthetic and real-world images, and meanwhile it also shows advantages in terms of model size and computational efficiency.

Examining STEM Students' Computational Thinking Skills through Interactive Practicum Utilizing Technology

This research study explores and compares the computational thinking skills demonstrated by STEM students during interactive practicums involving both virtual laboratories and physical laboratories. The objectives of the study are to assess the performance of computational thinking skills in each practicum setting and to determine any differences between the two environments. An experimental approach was adopted, and 106 first-year STEM students from a distinguished private university in Indonesia participated in the study. The students were divided into two groups, one using virtual labs and the other using physical labs. The study employed a portfolio instrument to assess various aspects of computational thinking, including problem reformulation, recursion, problem decomposition, abstraction, and systematic testing. The findings show that both groups of students achieved "good" scores for computational thinking skills. However, students in the virtual labs group demonstrated superior skills compared to the physical labs group. The aspects of problem reformulation and abstraction received the highest scores in both groups, while problem decomposition received the lowest scores. A MANOVA test confirmed statistically significant differences in computational thinking skills between the two practicum environments. The study suggests that the use of virtual labs can positively impact students' computational thinking abilities. The results have implications for educators and institutions seeking to enhance students' computational thinking skills and design effective STEM practicums.

Sensitivity Analysis and System Attribute Importance for Conceptual Aircraft Design with the Advanced Morphological Approach

The search for a rational design subspace of aircraft configurations can be addressed by using the advanced morphological approach (AMA). It allows the decomposition of design problems into functional and/or characteristic attributes and their technological implementation options. These are systemized in a morphological matrix (MM). Based on expert evaluations of each option, an exhaustive space is generated containing option combinations as possible solutions. Therefore, extensive MMs lead to immense solution spaces that are hard to analyze. However, removing attributes without justification might leave potential rational solutions out of scope. In this context, a sensitivity analysis technique is suggested based on analysis of variance (ANOVA) tests for use with the AMA. It can be applied to assess the sensitivity of solution scores against the attribute options and their importance. As a result, optimization of the MM and solution space can be achieved and improvement proposals can be drawn for future problem statements with the AMA. This is demonstrated on the data from a previously conducted AMA workshop on the conceptual design of a search and rescue aircraft.

Performance evaluation of LU matrix decomposition using the SYCL standard

The object of this study is the performance of the SYCL standard tools when solving the LU matrix decomposition problem. SYCL is a fairly new technology for parallel computing in heterogeneous systems, so the topic of evaluating the performance of the standard on specific tasks in the field of parallel computing is relevant. In the study, the algorithm of parallelized LU decomposition of a square matrix was implemented by means of the SYCL standard and standard C++, and an experiment was conducted to test the implementation in a heterogeneous system with several types of processors. During testing, the program received square matrices of various dimensions as input, and the output was the execution time of the LU schedule on the selected processor. The obtained results, presented in the form of tabular and graphic data, show the advantage of the implementation of the SYCL standard over ordinary C++ by more than 2 times when using a graphics processor. It was experimentally shown that the implementation on SYCL is almost not inferior in speed to the implementation on ordinary C++ when executed on a central processor. Such results are caused both by the high possibility of parallelizing the LU schedule algorithm itself, and by the great work of the developers of the standard on its optimization. The obtained results indicate the possibility of speeding up the solution of the LU decomposition of the matrix and similar algorithms by means of SYCL when using heterogeneous systems with processors optimized for data parallelism. The results of the study can be used in justifying the choice of technology for solving LU matrix decomposition problems or problems with a similar parallelization scheme.

Rolling Horizon Based Temporal Decomposition for the Offline Pickup and Delivery Problem with Time Windows

The offline pickup and delivery problem with time windows (PDPTW) is a classical combinatorial optimization problem in the transportation community, which has proven to be very challenging computationally. Due to the complexity of the problem, practical problem instances can be solved only via heuristics, which trade-off solution quality for computational tractability. Among the various heuristics, a common strategy is problem decomposition, that is, the reduction of a large-scale problem into a collection of smaller sub-problems, with spatial and temporal decompositions being two natural approaches. While spatial decomposition has been successful in certain settings, effective temporal decomposition has been challenging due to the difficulty of stitching together the sub-problem solutions across the decomposition boundaries. In this work, we introduce a novel temporal decomposition scheme for solving a class of PDPTWs that have narrow time windows, for which it is able to provide both fast and high-quality solutions. We utilize techniques that have been popularized recently in the context of online dial-a-ride problems along with the general idea of rolling horizon optimization. To the best of our knowledge, this is the first attempt to solve offline PDPTWs using such an approach. To show the performance and scalability of our framework, we use the optimization of paratransit services as a motivating example. Due to the lack of benchmark solvers similar to ours (i.e., temporal decomposition with an online solver), we compare our results with an offline heuristic algorithm using Google OR-Tools. In smaller problem instances (with an average of 129 requests per instance), the baseline approach is as competitive as our framework. However, in larger problem instances (approximately 2,500 requests per instance), our framework is more scalable and can provide good solutions to problem instances of varying degrees of difficulty, while the baseline algorithm often fails to find a feasible solution within comparable compute times.

Learning the Finer Things: Bayesian Structure Learning at the Instantiation Level

Successful machine learning methods require a trade-off between memorization and generalization. Too much memorization and the model cannot generalize to unobserved examples. Too much over-generalization and we risk under-fitting the data. While we commonly measure their performance through cross validation and accuracy metrics, how should these algorithms cope in domains that are extremely under-determined where accuracy is always unsatisfactory? We present a novel probabilistic graphical model structure learning approach that can learn, generalize and explain in these elusive domains by operating at the random variable instantiation level. Using Minimum Description Length (MDL) analysis, we propose a new decomposition of the learning problem over all training exemplars, fusing together minimal entropy inferences to construct a final knowledge base. By leveraging Bayesian Knowledge Bases (BKBs), a framework that operates at the instantiation level and inherently subsumes Bayesian Networks (BNs), we develop both a theoretical MDL score and associated structure learning algorithm that demonstrates significant improvements over learned BNs on 40 benchmark datasets. Further, our algorithm incorporates recent off-the-shelf DAG learning techniques enabling tractable results even on large problems. We then demonstrate the utility of our approach in a significantly under-determined domain by learning gene regulatory networks on breast cancer gene mutational data available from The Cancer Genome Atlas (TCGA).

The process of modeling the decomposition of petroleum products in water

Sunken marine power plants are one of the most dangerous types of marine pollution. The reason for this is that various types of petroleum products settle at the bottom of the sea and can remain there for a long time, which causes irreparable harm to the marine and environment. Recently, the problem of decomposition of petroleum products in water has become particularly relevant. Oil and its toxic components can quickly destroy the ecosystem, which will entail dramatic consequences for living organisms. To solve this problem, it is necessary to conduct modeling of decomposition processes, both in laboratory conditions and on real objects. In this article, we will consider the main approaches and stages of modeling the decomposition of petroleum products from sunken ships in water.

Islamic Scholar Thought on Intrapreneurial Leadership Characteristic Framework for Islamic Education Institutions

There is a growing expectation for universities to contribute to the country's innovation system, especially bringing students to become entrepreneurs and job creators. This research is aimed at developing a model of Islamic scholar thought on intrapreneurial leadership characteristic framework for Islamic Education Institutions. This study employs the Analytic Network Process (ANP) method in three steps, first problem decomposition via in-depth interviews with expert respondents, second, quantifying the model via a pair-wise comparison questionnaire, and third, synthesis and analysis to derive the most priority criteria and strategies. The model was developed with valuable input from three Indonesian religious leaders with experience in Islamic education. The findings indicate that the most important criterion for having the character of an intrapreneurial leader in an Islamic Education Institution along with its sub-criteria is leadership (trustworthy and responsible), followed by behavior (self-confidence and self-motivation), religiosity (worship and tawakkal), good governance (entrepreneurial culture and learning and teaching), and the last priority is skills (leadership skills and networking). This paper also discovered that, within Islamic educational institutions, a focus on constant innovation and a clear human resource vision and mission is a top priority for shaping the personalities of future leaders. This strategy emphasizes the significance of fostering an innovative culture within the institution and providing a clear vision and mission to guide the development of human resources. At the end of the paper's structure, this study offers policy implications and recommendations for how Islamic schools can incorporate intrapreneurial leadership practices into their educational system.

Panpsychism and Physical Idealism

There is a significant convergence between some contemporary panpsychist theories and idealism. Traditional phenomenal, macro idealism has been widely criticised for its implausible account of physical facts. This paper examines three idealism friendly contemporary panpsychist philosophies and suggests that with some revisions a plausible realist and physical idealism can be articulated. Taking from information-theoretic models of consciousness and metaphysical arguments for the ontological primacy of mind, it is suggested via a Schelling inspired perspective that aspects of consciousness??? intrinsic nature provide a promising approach to the decomposition problem which is currently a significant challenge to pan/cosmopsychist theories.

Cooperative Coevolutionary CMA-ES With Landscape-Aware Grouping in Noisy Environments

Many real-world optimization tasks suffer from noise. So far, the research on noise-tolerant optimization algorithms is still restricted to low-dimensional problems with less than 100 decision variables. In reality, many problems are high-dimensional. Cooperative coevolutionary (CC) algorithms based on a divide-and-conquer strategy are promising in solving complex high-dimensional problems. However, noisy fitness evaluations pose a challenge in problem decomposition for CC. The state-of-the-art grouping methods, such as differential grouping and recursive differential grouping, are unable to work properly in noisy environments. Because it is impossible to distinguish whether the change of one variable’s difference value is caused by noise or the perturbation of its interacting variables. As a result, every pair of variables will be identified as nonseparable in these methods. In this paper, we study how to group decision variables with covariance matrix adaptation evolution strategy (CMA-ES) in noisy environments and subsequently propose a landscape-aware grouping (LAG) method. Instead of detecting pairwise interacting variables, we directly identify a nonseparable subcomponent. To this end, we propose to use two convergence features, variable convergence time and accumulative path, to describe variables’ fitness landscapes; then, variables are clustered according to these two features. Numerical experiments show that LAG can more effectively identify interactive decision variables in the presence of multiplicative noise than the differential grouping and some of its variants. Up to 500 dimensions, the performance of cooperative coevolutionary CMA-ES with landscape-aware grouping (CC-CMAES-LAG) is competitive compared with existing CC algorithms and uncertainty-handling CMA-ES (UH-CMA-ES).

A Deep Reinforcement Learning Based Real-Time Solution Policy for the Traveling Salesman Problem

The rapid development of logistics and navigation has led to increasing demand for solving route optimization problems in real-time. The traveling salesman problem (TSP) tends to require fast and reliable online solutions, which may not be met by traditional iterative optimization algorithms. In this work, a real-time solution policy is proposed for TSP. The idea is to build a mapping between city information and optimal solutions using deep neural networks. Therefore, when given a new set of city coordinates, the optimal route can be directly and quickly calculated without iteration. Considering the recent advancement in computer vision with deep convolutional neural networks (DCNNs), an image representation is proposed to convert TSP to a computer vision problem. A problem decomposition method is introduced to reduce the mapping complexity. Taking advantage of the powerful fitting capabilities of DCNN, a deep reinforcement learning method is designed without any labeling requirement. The proposed method is superior for real-time applications compared with other algorithms.

Analysis of Biology Teacher’s Computational Thinking Skills in Environmental Learning

Computational Thinking Skills are needed in learning. These skills must be owned by teachers and students with the aim that the demands contained in the curriculum can be achieved. One way that can be done is with a training program. The research objective was to determine the effect of training on the computational thinking skills of teachers and students in learning. The method used in this research is quasi-experimental research. The sampling technique used purposive sampling. The research sample consisted of 6 teachers and 167 students. The instrument used was a questionnaire in the form of a test given to the teacher and a student response questionnaire to learning. The results of data analysis regarding the questionnaire show that the teacher's computational thinking skills based on 4 indicators obtained an average percentage score of 75% (decomposition), 78% (pattern recognition), 83% (abstraction), and 77% (algorithm). To train students' computational skills, teachers usually train the following abilities: problem decomposition, usually teachers get used to giving complex problems, think algorithms, teachers apply problem-based learning, collaborative, cooperative, and project-based, pattern recognition, teachers use innovative learning media and abstract thinking, the teacher gives high-order thinking questions, and literacy and numeracy questions. And for the results of data analysis through questionnaires, students' responses to learning obtained an average value of 79%, with these results the learning process based on computational thinking skills that have been implemented is included in the interesting category

Decomposition of musculoskeletal structures from radiographs using an improved CycleGAN framework

This paper presents methods of decomposition of musculoskeletal structures from radiographs into multiple individual muscle and bone structures. While existing solutions require dual-energy scan for the training dataset and are mainly applied to structures with high-intensity contrast, such as bones, we focused on multiple superimposed muscles with subtle contrast in addition to bones. The decomposition problem is formulated as an image translation problem between (1) a real X-ray image and (2) multiple digitally reconstructed radiographs, each of which contains a single muscle or bone structure, and solved using unpaired training based on the CycleGAN framework. The training dataset was created via automatic computed tomography (CT) segmentation of muscle/bone regions and virtually projecting them with geometric parameters similar to the real X-ray images. Two additional features were incorporated into the CycleGAN framework to achieve a high-resolution and accurate decomposition: hierarchical learning and reconstruction loss with the gradient correlation similarity metric. Furthermore, we introduced a new diagnostic metric for muscle asymmetry directly measured from a plain X-ray image to validate the proposed method. Our simulation and real-image experiments using real X-ray and CT images of 475 patients with hip diseases suggested that each additional feature significantly enhanced the decomposition accuracy. The experiments also evaluated the accuracy of muscle volume ratio measurement, which suggested a potential application to muscle asymmetry assessment from an X-ray image for diagnostic and therapeutic assistance. The improved CycleGAN framework can be applied for investigating the decomposition of musculoskeletal structures from single radiographs.

Traveling Wave Method

A survey of the development of the traveling wave method for one-dimensional media is presented. The main results and changes in the statement of the problem of representing solutions of linear systems of partial differential equations in terms of “traveling waves” (more precisely, in terms of a system of wave transport equations) are presented. It is shown that as the study of systems becomes more complicated, the problem of representing the solution by the traveling wave method turns out to be applicable not only for hyperbolic systems but also for systems containing (even implicitly) both parabolic and elliptic components and thereby approaches the general problem of decomposition of an arbitrary system of linear equations into a system of first-order equations with a main part of the canonical type and with a subordinate linear part.