Repetitive Calculations Research Articles

Shortest-path tree-based method for calculating visible area with time- and memory-saving preprocessing

Visibility has extensive application in areas such as architecture, urban planning, and security. This study proposes a novel approximation method, called the shortest-path tree-based method (SPT-based method), for calculating the visible area using a random Delaunay network on a 2D plane. Various methods are available for calculating the visible area, including exact and approximation methods. However, it is difficult to calculate the visible area repeatedly in a space that has a vast number of obstacles while achieving efficient time and memory usage. The SPT-based method focuses on time- and memory-saving preprocessing. To achieve an efficient calculation of the visible area, we discretised a plane using a random Delaunay network and approximated the visible area using Dijkstra’s method. To evaluate the efficiency of the proposed method, we compared the calculation time, accuracy, and memory usage of the plane-sweep, ray-trace, brute-force, and SPT-based methods while considering the influence of the number of obstacles. This study provides valuable insights for researchers and practitioners for choosing the most suitable approach for their specific needs. Overall, the proposed method offers a time- and memory-efficient solution for calculating the visible area, making it suitable for a detailed analysis of the visual environment and providing a heuristic solution to the art gallery problem requiring repetitive calculations.

Reinforcement Learning for Submodel Assignment in Adaptive Modeling of Turbulent Flames

Reinforcement learning (RL), an unsupervised machine learning approach, is innovatively introduced to turbulent combustion modeling and demonstrated through the automated construction of submodel assignment criteria within the framework of zone-adaptive combustion modeling (AdaCM). In AdaCM, the appropriate combustion submodel—whether the cost-effective species transport model or the advanced transported probability density function (TPDF) method—is adaptively assigned to different regions based on a criterion crucial for performance. The use of RL avoids the extensive manual optimization that involves repetitive calculations and struggles to account for multiple factors. Specifically, RL agents observe local variables as the state and determine the appropriate submodel through a policy. The policy is refined to maximize a reward measuring both accuracy and efficiency through the interaction between RL agents and the AdaCM solver. The methodology is demonstrated for a turbulent non-premixed jet flame, and a sophisticated RL criterion exhibiting a nonlinear and nonmonotonic dependency on the two-dimensional state of mixture fraction and Damköhler number is learned. The AdaCM with the trained criterion provides predictions that are nearly indistinguishable from those obtained using the TPDF method for the whole computational domain, while substantially reducing the computational cost with the speedup of 3.4 and only 22% of cells for TPDF.

Automatization of theoretical kinetic data generation for tabulated TS models building - Part 1: Application to 1,3-H-shift reactions

Estimation of kinetic parameters is a key aspect of chemical combustion modeling and several approaches were developed to approximate unknown data. In this work, a code in Python was developed to build tables of transition state (TS) models automatically for intramolecular H-shift reactions in alkyl radicals. The code generates the kinetic rules for all the possible combinations of methyl-substituted reactions based on the structures of the minimal, non-substituted, reactant, TS, and product. The code is able to create and differentiate multiple transition state configurations, considering the axial and equatorial positions for the cyclic substituents and including all the possible pathways for the reactions, which is shown to be an important feature in performing accurate automatic kinetic calculations. Each structure is automatically submitted to geometry optimization and electronic energy calculations, as well as the relaxed scans of the torsional modes identified by the code. From the results of electronic calculations, the rate constants for each pathway are obtained automatically by the application of the transition state theory with tunneling corrections, in a defined temperature range. The kinetic coefficients, as well as the modified Arrhenius parameters, are then assembled and organized to create a final table that connects the kinetic data with TS structure characteristics. These tables can be directly applied as a kinetic data source for reaction mechanism development. The ability of the code to generate reliable rate constants was tested for 1,3-H-shift reactions and the results were compared with theoretical data manually produced, and showed a good agreement. In particular, the code was able to create all the transition state configurations, with an exhaustive description of all possible reaction pathways, using a rigorous and systematic counting based on symmetry, stereocenters, and diastereomers. The proposed method leads to more accurate results on these aspects, compared to repetitive hand calculations of dozens of rate constants.

An investigation on anisotropic soil slope stability by LS-SVM and LEM approaches

Purpose This study aims to use regression Least-Square Support Vector Machine (LS-SVM) as a probabilistic model to determine the factor of safety (FS) and probability of failure (PF) of anisotropic soil slopes. Design/methodology/approach This research uses machine learning (ML) techniques to predict soil slope failure. Due to the lack of analytical solutions for measuring FS and PF, it is more convenient to use surrogate models like probabilistic modeling, which is suitable for performing repetitive calculations to compute the effect of uncertainty on the anisotropic soil slope stability. The study first uses the Limit Equilibrium Method (LEM) based on a probabilistic evaluation over the Latin Hypercube Sampling (LHS) technique for two anisotropic soil slope profiles to assess FS and PF. Then, using one of the supervised methods of ML named LS-SVM, the outcomes (FS and PF) were compared to evaluate the efficiency of the LS-SVM method in predicting the stability of such complex soil slope profiles. Findings This method increases the computational performance of low-probability analysis significantly. The compared results by FS-PF plots show that the proposed method is valuable for analyzing complex slopes under different probabilistic distributions. Accordingly, to obtain a precise estimate of slope stability, all layers must be included in the probabilistic modeling in the LS-SVM method. Originality/value Combining LS-SVM and LEM offers a unique and innovative approach to address the anisotropic behavior of soil slope stability analysis. The initiative part of this paper is to evaluate the stability of an anisotropic soil slope based on one ML method, the Least-Square Support Vector Machine (LS-SVM). The soil slope is defined as complex because there are uncertainties in the slope profile characteristics transformed to LS-SVM. Consequently, several input parameters are effective in finding FS and PF as output parameters.

Artificial intelligence algorithm for neoplastic cell percentage estimation and its application to copy number variation in urinary tract cancer.

Bladder cancer is characterized by frequent mutations, which provide potential therapeutic targets for most patients. The effectiveness of emerging personalized therapies depends on an accurate molecular diagnosis, for which the accurate estimation of the neoplastic cell percentage (NCP) is a crucial initial step. However, the established method for determining the NCP, manual counting by a pathologist, is time-consuming and not easily executable. To address this, artificial intelligence (AI) models were developed to estimate the NCP using nine convolutional neural networks and the scanned images of 39 cases of urinary tract cancer. The performance of the AI models was compared to that of six pathologists for 119 cases in the validation cohort. The ground truth value was obtained through multiplexed immunofluorescence. The AI model was then applied to 41 cases in the application cohort that underwent next-generation sequencing testing, and its impact on the copy number variation (CNV) was analyzed. Each AI model demonstrated high reliability, with intraclass correlation coefficients (ICCs) ranging from 0.82 to 0.88. These values were comparable or better to those of pathologists, whose ICCs ranged from 0.78 to 0.91 in urothelial carcinoma cases, both with and without divergent differentiation/ subtypes. After applying AI-driven NCP, 190 CNV (24.2%) were reclassified with 66 (8.4%) and 78 (9.9%) moved to amplification and loss, respectively, from neutral/minor CNV. The neutral/minor CNV proportion decreased by 6%. These results suggest that AI models could assist human pathologists in repetitive and cumbersome NCP calculations.

Nanosecond laser cleaning method for high-capacity fast storage and data multiplexing in ARM architecture

As the application of laser cleaning technology continues to expand, various fields have put forward higher requirements for the performance and quality of the operation, and at present, laser cleaning has problems such as low efficiency in handling repetitive tasks, and the system deployment and maintenance costs are high. This paper proposes a nanosecond laser cleaning method based on ARM architecture with high-capacity fast storage and data reuse, integrating high-capacity fast storage technique and data reuse strategy to optimize the laser cleaning process. In this paper, SDRAM is used to store and record the laser scanning path, Cache is integrated to weaken the data calling delay and improve the system response speed, and the scanning cycle is finely adjusted by combining positional modulation laser frequency technology to avoid the edge erosion caused by the motor deceleration and to ensure the homogeneity and accuracy of laser cleaning. The results indicate that, under the same output point conditions, the dynamic phase difference spiral algorithm in this paper outperforms the linear filling algorithm in terms of speed and data filling efficiency, reducing the burden of repetitive task calculations. While maintaining surface erosion uniformity during cleaning, excessive erosion is prevented, leading to a comprehensive enhancement in the overall efficiency and performance of laser cleaning operations.

Real-time hierarchical parallel rendering and display of light field images

Light field display technology has attracted considerable interest due to its remarkable 3D display capabilities and compatibility. However, the real-time capture of massive light field image data remains a significant challenge in this field. To improve rendering efficiency and achieve high-quality 3D display, a real-time hierarchical parallel rendering method is proposed. The method parallelizes the rendering pipeline of light field images from multi-levels. Firstly, instancing technology is exploited for parallel rendering of high-dimensional orthogonal parallax information. Secondly, perspective coherence of parallax, lighting, and texture information are used for the parallel rendering of one dimensional parallax effects. Thirdly, the data processing process has been simplified and accelerated by using parallel scanning slicing algorithms and parallel pixel recombination. This multi-level parallel processing architecture significantly reduces the loops and repetitive calculations. An efficient rendering pipeline was developed to achieve real-time rendering of 200 viewpoint light field images with anisotropic lighting effects at a 4 K resolution. The frame rate is 40 frames per second (fps). Compared to traditional methods, this algorithm reduces the time required to render one frame of light image by 17 times. A light field display system was made to validate the effectiveness of the method. High performance 3D images were outputted using the rendered light field images.

Slow sound mode prediction and band structure calculation in 1D phononic crystal nanobeams using an artificial neural network.

Phononic crystals, which are artificial crystals formed by the periodic arrangement of materials with different elastic coefficients in space, can display modulated sound waves propagating within them. Similar to the natural crystals used in semiconductor research with electronic bandgaps, phononic crystals exhibit the characteristics of phononic bandgaps. A gap design can be utilized to create various resonant cavities, confining specific resonance modes within the defects of the structure. In studies on phononic crystals, phononic band structure diagrams are often used to investigate the variations in phononic bandgaps and elastic resonance modes. As the phononic band frequencies vary nonlinearly with the structural parameters, numerous calculations are required to analyze the gap or mode frequency shifts in phononic band structure diagrams. However, traditional calculation methods are time-consuming. Therefore, this study proposes the use of neural networks to replace the time-consuming calculation processes of traditional methods. Numerous band structure diagrams are initially obtained through the finite-element method and serve as the raw dataset, and a certain proportion of the data is randomly extracted from the dataset for neural network training. By treating each mode point in the band structure diagram as an independent data point, the training dataset for neural networks can be expanded from a small number to a large number of band structure diagrams. This study also introduces another network that effectively improves mode prediction accuracy by training neural networks to focus on specific modes. The proposed method effectively reduces the cost of repetitive calculations.

Memory Shapelet Learning for Early Classification of Streaming Time Series.

Early classification predicts the class of the incoming sequences before it is completely observed. How to quickly classify streaming time series without losing interpretability through early classification method is a challenging problem. A novel memory shapelet learning framework for early classification is proposed in this article. First, a memory distance matrix is introduced to store the historical characteristics of streaming time series, which can alleviate repetitive calculations caused by the growing length of time series. Second, early interpretable shapelets are extracted in the proposed method by optimizing both accuracy objective and earliness objective simultaneously. The proposed method employs end-to-end learning, which allows the model to directly learn early shapelets without the necessity of searching for numerous candidate shapelets. Third, an objective function of memory shapelet learning is proposed by overall considering accuracy and earliness, which can be optimized by gradient descent algorithm. Finally, experiments are conducted on benchmark dataset UCR, Tennessee Eastman process, and real-world aluminum electrolysis process in China. Comparable results with other state-of-the-art methods demonstrate the superior performance of the proposed method in interpretability, accuracy, earliness, and time complexity.

Fast Multilabel Feature Selection via Global Relevance and Redundancy Optimization.

Information theoretical-based methods have attracted a great attention in recent years and gained promising results for multilabel feature selection (MLFS). Nevertheless, most of the existing methods consider a heuristic way to the grid search of important features, and they may also suffer from the issue of fully utilizing labeling information. Thus, they are probable to deliver a suboptimal result with heavy computational burden. In this article, we propose a general optimization framework global relevance and redundancy optimization (GRRO) to solve the learning problem. The main technical contribution in GRRO is a formulation for MLFS while feature relevance, label relevance (i.e., label correlation), and feature redundancy are taken into account, which can avoid repetitive entropy calculations to obtain a global optimal solution efficiently. To further improve the efficiency, we extend GRRO to filter out inessential labels and features, thus facilitating fast MLFS. We call the extension as GRROfast, in which the key insights are twofold: 1) promising labels and related relevant features are investigated to reduce ineffective calculations in terms of features, even labels and 2) the framework of GRRO is reconstructed to generate the optimal result with an ensemble. Moreover, our proposed algorithms have an excellent mechanism for exploiting the inherent properties of multilabel data; specifically, we provide a formulation to enhance the proposal with label-specific features. Extensive experiments clearly reveal the effectiveness and efficiency of our proposed algorithms.

Computationally efficient robust adaptive filtering algorithm based on improved minimum error entropy criterion with fiducial points

Recently, there has been a strong interest in the minimum error entropy (MEE) criterion derived from information theoretic learning, which is effective in dealing with the multimodal non-Gaussian noise case. However, the kernel function is shift invariant resulting in the MEE criterion being insensitive to the error location. An existing solution is to combine the maximum correntropy (MC) with MEE criteria, leading to the MEE criterion with fiducial points (MEEF). Nevertheless, the algorithms based on the MEEF criterion usually require higher computational complexity. To remedy this problem, an improved MEEF (IMEEF) criterion is devised, aiming to avoid repetitive calculations of the aposteriori error, and an adaptive filtering algorithm based on gradient descent (GD) method is proposed, namely, GD-based IMEEF (IMEEF-GD) algorithm. In addition, we provide the convergence condition in terms of mean sense, along with an analysis of the steady-state and transient behaviors of IMEEF-GD in the mean-square sense. Its computational complexity is also analyzed. Simulation results demonstrate that the computational requirement of our algorithm does not vary significantly with the error sample number and the derived theoretical model is highly consistent with the learning curve. Ultimately, we employ the IMEEF-GD algorithm in tasks such as system identification, wind signal magnitude prediction, temperature prediction, and acoustic echo cancellation (AEC) to validate the effectiveness of the IMEEF-GD algorithm.

ТЕОРЕТИЧЕСКИЕ АСПЕКТЫ ВЗАИМОДЕЙСТВИЯ ОЗОНА С ЗЕРНОМ

Despite the popularization of ozone technologies in agriculture, the theoretical aspects of the interaction of an ozone-air mixture with grain material remain under study. The simplified assumption that the change in the amount of ozone absorbed by the grain is proportional to the initial gas concentration does not accurately describe this process. Attempts to analytically determine a certain constant of the rate of ozone absorption by a unit of grain volume were also unsuccessful. The resulting expression was transcendental at that time. Its solution was possible only when performing repetitive calculations, that is, using the iteration method on a personal computer. The use of the modern Matlab application software package made it possible to establish a constant rate of ozone absorption per unit grain volume. However, the experiments have shown that during the experiment this constant changes significantly, including depending on the conditions, therefore this theoretical approach requires clarification. The laws known in physics describing the diffusion process have been adapted to the ozone treatment process. The application of the Langmuir-Schaefer equation for the number of ozone molecules adsorbed on the grain surface and Fick's second law made it possible to determine the rate of ozone diffusion and the change in ozone concentration over time, taking into account the characteristics of the grain pile. A dependence was obtained for the ozone diffusion coefficient, which characterizes the ability of grains to absorb ozone through cell membranes, and the ozone decomposition constants. Under normal storage conditions, these temperature-dependent values can be considered constant. The analytically obtained dependences will allow us to determine the ozone diffusion coefficient and the ozone decomposition constant experimentally.

Solution of the Schrödinger equation using quadratic B-Spline collocation on non-uniform grids

This paper applies orthogonal collocation based on quadratic B-spline basis functions to solve the Schrödinger equation on uniform and non-uniform grids. The method is well suited for solving different cases of soliton solutions for which the solution behaviour is very complicated. The solutions are found to be consistent with the exact solutions for various non-uniform cases. The overall numerical scheme is proven to be unconditionally stable and utilizes minimal memory storage due to the sparse matrix systems associated with B-spline basis functions. This could prove particularly useful in machine learning applications where repetitive calculations are needed and large amounts of data need to be processed. We found that using non-uniform grids as compared to uniform grids had a profound effect in capturing the correct solution dynamics especially in the 3-soliton case.

Profile of Student Metacognition in Solving Elementary Linear Algebra Problems Viewed from Tempo Conceptual Cognitive Style

Metacognition is one of the factors that influences students' success in solving mathematical problems. On the other hand, the reality in the field is that students experience difficulties in solving mathematical problems related to Elementary Linear Algebra because they contain a lot of repetitive calculations, so they require high levels of perseverance and accuracy. This research aims to describe students' metacognitive profiles in solving Elementary Linear Algebra problems in terms of cognitive style. The cognitive style chosen is the conceptual cognitive style of pacing through Matching Familiar Figures Tests with research subjects being mathematics students at Nahdlatul Ulama University, Purwokerto. The resulting metacognition profile was obtained from Elementary Linear Algebra problem-solving test data and interviews, which were analyzed and concluded through a series of method triangulation processes. The research results show that students are reflective and impulsive in carrying out all activities that are indicators of metacognitive awareness and regulation, as well as several indicators from metacognitive evaluation. Fast, accurate students carry out all activities that become indicators of metacognitive awareness, regulation, and evaluation. Meanwhile, slowly, inaccurate students carry out all activities that are indicators of metacognitive awareness and several indicators of metacognitive regulation but still need to be able to carry out activities of metacognitive evaluation.

Optimal Operating Mode for Modular Enumeration Technology

The technology of modular enumeration is based on the minimizing of repetitive calculations - their results are stored in RAM and used as needed. While this technology can be used for different types of problems to be solved, optimal parameters of modular enumeration operating mode are known only in the case of solving discrete optimization problems with Boolean variables. The paper contains proofs of two theorems, permitting modular enumeration optimal operating mode determination in general case. The paper also contains examples of solution by modular enumeration optimal organization related to the two problems i. e. the search for the numerical value of multiple integral and that for a globally optimal solution to an extreme problem with Boolean variables, the last being based on knapsack problem solution.

An anonymous authentication scheme with conditional privacy-preserving for Vehicular Ad hoc Networks based on zero-knowledge proof and Blockchain

Recently, Vehicular Ad hoc Networks (VANETs) have gained extensive attention in both academia and industry. VANETs play a seminal role in smart transportation by enhancing driving convenience and traffic efficiency through real-time information interaction. Despite this, ensuring secure authentication and privacy preservation remains two challenging issues in VANETs. The existence of security schemes that are vulnerable to privacy and security issues or have substantial computation and communication overheads shows the necessity for further research in this area. Therefore, in this article, we present an anonymous authentication scheme based on Zero-Knowledge Proof. To be more specific, we adopted Simulation Extractable Zero-Knowledge SNARKs (SE zk-SNARKs) to achieve anonymity and conditional privacy. Although zk-SNARK proofs are succinct and fast to verify, the time required for proof generation poses a major obstacle in using zk-SNARKs in a time-sensitive VANET environment. To overcome this drawback, we focus on key components of the proof statement, separating the repetitive calculations, and archiving in the Blockchain, which serves as an immutable data storage. By omitting repetitive calculations, our proposed scheme becomes lightweight enough to run efficiently on VANETs. Security analysis showed that the proposed protocol satisfied security and privacy requirements. Additionally, a computation cost analysis is provided to demonstrate the significant advantage of our proposed scheme. ProVerif is used to verify the strong secrecy of the protocol, and the results show that privacy can be guaranteed in the proposed scheme.

A BEM broadband topology optimization strategy based on Taylor expansion and SOAR method—Application to 2D acoustic scattering problems

AbstractIn this article, an innovative method is proposed for broadband topology optimization of sound‐absorbing materials adhering to the surface of a sound barrier structure. Helmholtz equation for the acoustic problems is solved using the boundary element method, while sensitivities of the objective function with respect to a large number of design variables are calculated via a sensitivity analysis method originated from the adjoint variable method (AVM), and the optimal solution is obtained by the method of moving asymptotes (MMA). Since the traditional single‐frequency topology optimization is frequency dependent, that is, the optimal solution at a certain frequency may not be optimal at other frequencies, broadband topology optimization of sound‐absorbing materials is conducted in this work. To address the problem of tremendous computational cost due to repetitive calculations at each discrete frequency point during broadband optimization, Taylor expansion of the Hankel function is performed to decouple the frequency dependent and independent terms in the BEM equations. For large‐scale problems, a reduced‐order model that retains the essential structures and key properties of the original model is built using the second‐order Arnoldi (SOAR) method. The accuracy and feasibility of the proposed algorithms are finally validated via some two‐dimensional numerical examples.

Application of machine learning algorithms and Sentinel-2 satellite for improved bathymetry retrieval in Lake Victoria, Tanzania

Estimating bathymetric information is vital for aquaculture and navigation applications. Free, high-resolution satellite imagery provides a cost-effective solution for routine bathymetric measurements. We tested six algorithms to retrieve water depth in the Mwanza Gulf of Lake Victoria using Sentinel-2 satellite imagery: the conventional Stumpf method, Random Forest (RF), Gradient Boosting Machine (GBM), Extreme Gradient Boosting (XGB), Neural Network (NNET), and Support Vector Machine (SVM). In-situ depth points collected via echo sounders were used to train and validate the algorithms. Performance evaluation metrics included coefficient of determination (R2), mean absolute error (MAE), root-mean-square error (RMSE), and spatial autocorrelation of residuals. Among the algorithms tested, the Stumpf model exhibited moderate performance with an R2 of 0.441, higher MAE (2.078 m), and RMSE (2.964 m) values. The RF algorithm improved performance with an R2 of 0.957, lower MAE (0.476 m), and RMSE (0.823 m). The GBM and XGB algorithms achieved R2 values of 0.960 and 0.956, respectively, with low MAE (0.484 m for GBM, 0.482 m for XGB) and RMSE (0.795 m for GBM, 0.830 m for XGB) values. The NNET algorithm outperformed the GBM and XGB models, obtaining an R2 of 0.963, the lowest MAE (0.438 m), and RMSE (0.761 m). The SVM algorithm demonstrated the best performance with an R2 of 0.965, the lowest MAE (0.403 m), and RMSE (0.745 m), implying the highest accuracy in depth estimation. SVM also showed stable generalization across different locations with insignificant spatial autocorrelation of residuals. Therefore, SVM is recommended for repetitive bathymetry calculations.

Adaptive phase-field modelling of fracture propagation in poroelastic media using the scaled boundary finite element method

A scaled boundary finite element-based phase field formulation is proposed to model two-dimensional fracture in saturated poroelastic media. The mechanical response of the poroelastic media is simulated following Biot’s theory, and the fracture surface evolution is modelled according to the phase field formulation. To avoid the application of fine uniform meshes that are constrained by the element size requirement when adopting phase field models, an adaptive refinement strategy based on quadtree meshes is adopted. The unique advantage of the scaled boundary finite element method is conducive to the application of quadtree adaptivity, as it can be directly formulated on quadtree meshes without the need for any special treatment of hanging nodes. Efficient computation is achieved by exploiting the unique patterns of the quadtree cells. An appropriate scaling is applied to the relevant matrices and vectors according the physical size of the cells in the mesh during the simulations. This avoids repetitive calculations of cells with the same configurations. The proposed model is validated using a benchmark with a known analytical solution. Numerical examples of hydraulic fractures driven by the injected fluid in cracks are modelled to illustrate the capabilities of the proposed model in handling crack propagation problems involving complex geometries.

CFD-modeling of fluid flow in Ansys Fluent using Python-based code for automation of repeating calculations

CFD-modeling for numerical investigation is used in a wide range of applied tasks, e.g. in fluid mechanics. To better understand the effect of operational parameters on the final results, some tasks are associated with carrying out monotonous, repetitive calculations for a wide range of operational parameters such as velocity, flow direction and temperature. In this paper, a Python-based code for automation of the repeating calculations in CFD-modeling was developed and described. The automation code was tested for CFD-modeling in Ansys Fluent for two flow dynamic tasks: a simple 2D-geometry — NACA0018 airfoil, and a complex 3D-geometry — packed bed with heat transfer. Three different computers with various computational power were used for the comparison. The results of CFD-modeling were compared with the experimental data. The efficiency of using Python-based code was evaluated through comparison with the results of manual (without automation) calculation. It was established that the application of the Python-based code does not affect the accuracy of numerical results. At the same time, utilization of the Python-based code can save up to 25% of computation time for the simple 2D-geometries with a moderately low number of elements in the mesh, and up to 15% for the complex 3D-geometries with a number of elements in several millions. The compiled Python-based code is attached as supplementary material to this paper.