Numerical Operations Research Articles

Number line estimation patterns and their relationship with mathematical performance

There is ongoing debate regarding what performance on the number line estimation task represents and its role in mathematics learning. The patterns followed by children’s estimates on the number line task could provide insight into this. This study investigates children’s estimation patterns on the number line task and assesses whether mathematics achievement is associated with these estimation patterns. Singaporean children (n = 324, Age M = 6.2 years, Age SD = 0.3 years) in their second year of kindergarten were assessed on the number line task (0-100) and their mathematical performance (Numerical Operations and Mathematical Reasoning subtests from WIAT II). The results show that most children’s number line estimation patterns can be explained by at least one mathematical model (i.e., linear, logarithmic, unbounded power model, one-cycle power model, two-cycle power model). But the findings also highlight the high percentage of participants for which more than one model shows similar support. Children’s mathematical achievement differed based on the models that best explained children’s estimation patterns. Children whose estimation patterns corresponded to a more advanced model tended to show higher mathematical achievement. Limitations of drawing conclusions regarding what performance on the number line task represents based on models that best explain the estimation patterns are discussed.

Tuning and interpretation of electronic transport properties with

Electronic transport coefficients such as the electrical conductivity, the termo-power, and the charge carrier concentration are routinely measured in a variety of application areas such as electronics or thermoelectric power-generation and cooling. Using fitting procedures, those measurements are used to infer microscopic features of the samples. The code ▪ facilitates the estimation of electronic structure parameters such as the effective masses and band energies improving the current approach by increasing the complexity of the band structure representation. The software is designed with a server-client architecture to enhance performance and scalability. The server is implemented in the Julia programming language. We illustrate the design and the efficiency of the code with selected applications, which are relevant to the optimization of thermoelectric materials. Program summaryProgram Title:▪CPC Library link to program files:https://doi.org/10.17632/494nj6ftbv.1Developer's repository link:https://github.com/marcofornari/etransport.gitLicensing provisions: GPLv3Programming language: Julia, Python.Nature of problem: Electronic transport measurements are routinely used to link the functional properties exploited in electronics and energy sciences applications with the underlying electronic structure of the material under investigation. Experimentalists collect data of derived and integrated physical quantities, from which they estimate properties and parameters, e.g., nature of the conduction mechanisms and effective mass. The interpretation is based on simplistic models that rarely represent the complexity of the band structure. The code ▪ improves the current state of the art and facilitates the estimation of effective masses and energies from experimental measurements of electrical conductivity, Seebeck coefficients, and carrier concentration using a multi-valley anisotropic parabolic band structure as a model for the unknown real band structure. Experimental data can be imported and visualized to facilitate the comparison with theoretical analysis.Solution method: The Boltzmann equation within the relaxation-time approximation is used to compute the electronic transport tensors from the electronic density of states characterized in terms of a set of effective masses tensors mi⁎ and critical energies ϵi. Numerical and analytical techniques are adopted to integrate the Boltzmann equation efficiently. By tuning the features of the density of states, temperature, Fermi level, and the functional expression for the relaxation time, the software streamlines the reconstruction of the underlying electronic properties from experimental data.Additional comments including restrictions and unusual features: The software is designed with a server-client architecture to enhance performance and scalability. The server is implemented in the Julia programming language as a stand-alone library. It performs all the numerical operations to compute the transport tensors from a set of multi-valley parabolic band structures. The client is implemented either as a command-line user interface (CLI) or a graphical user interface (GUI) written in the Python programming language. The communications between the server and clients are handled by a REST API, where the data are exchanged using JSON payloads.

A new approach for the Modified Local Green’s Function Method applied to solid mechanics problems

The Modified Local Green’s Function Method (MLGFM) is an integral method that does not need a previous explicit fundamental solution or a Green’s function, since projections of Green’s functions, determined by Finite Element Method, are used as fundamental solution to solve problems. As demonstrated in previous works, the MLGFM presents good convergence for potential, displacements, boundary flux and tractions, although the obtaining of the Green’s function projections can require a high computational effort. This paper proposes an alternative formulation to the MLGFM that avoids the need to obtain these projections and consequently reduces the number of numerical operations. The new formulation presents the same accuracy as the previous one but with less computational effort, and it is applied to some problems in solid mechanics and compared with the standard Finite Element Method and the Boundary Element Method.

Left multiplication operators on the Riordan group

In this paper, we introduce the left multiplication operators on the Riordan group, and carry out a systematic study on them. By using these operators, we obtain a family H of infinite Riordan subgroups. This family includes not only some well-known subgroups, but also the subgroup families introduced recently in literature. Fundamental properties of the left multiplication operators and the subgroup family H are presented. The Riordan involutions and pseudo-involutions, the stabilizer subgroups in family H, and the n-th commutator subgroup of any subgroup in family H are studied. Some further applications of the left multiplication operators are also provided. In particular, we study a class of left multiplication operators which are closely related to the diagonal translation operator and the [m]-complementary operator, and enrich the theory of complementary Riordan arrays. Moreover, we introduce and study the higher-level lifts of Riordan arrays as well as the vertical and horizontal 1/m Riordan arrays. As a result, it can be found that the left multiplication operators provide a unified approach to numerous subgroups, operators and transformations of the Riordan group.

A finite volume flux coordinate independent approach

We present a novel family of schemes as the merging between a one-dimensional advection scheme with the flux coordinate independent approach. The scheme can be used to discretize the field-aligned Navier-Stokes equations in three dimensions. Our approach consists of three major steps: (i) the formulation of the one-dimensional scheme in a locally field-aligned coordinate system, (ii) a numerical evaluation of the surface integrals over the field-aligned finite volumes and (iii) the introduction of smoothing into the numerical transformation operators to ensure stability of the resulting scheme.We study this approach at the example of a staggered finite volume scheme with a field-aligned cylinder as initial condition. We show superior stability and conservative properties over previous direct discretizations. In particular, the relative mass conservation is improved by several orders of magnitude. Without smoothing in the transformation operators the scheme is prone to oscillations in both parallel and perpendicular directions. In the presence of strong perpendicular gradients, additional parallel diffusion is needed to control spurious oscillations in the perpendicular planes.We provide parallel implementations for various platforms including GPUs freely in the C++ library Feltor

Achieving Revocable Attribute Group-Based Encryption for Mobile Cloud Data: A Multi-Proxy Assisted Approach

Although proxy-assisted revocable attribute-based encryption provides fine-grained privacy protection and reduces the decryption cost of data users, it inherits several disadvantages in outsourcing decryption. The decryption capability in outsourcing decryption is divided into two parts: the outsourcing transformation key and the user decryption key. The proxy server utilizes transformation keys to transform the ciphertext which can only be decrypted by the users who generated the transformation key. When multiple users with the same attributes request outsourcing transformation, the proxy server must do numerous transformation operations, increasing the computing overhead of the proxy server and the user request response time. To address the aforementioned issues, we propose a multi-proxy assisted revocable attribute group-based encryption (MP-RAGBE) scheme. We form a user group out of users who have the same attributes and send the transformation keys directly to the proxy server. Users in the same group can decrypt the transformed ciphertext, and only a small number of transformation keys need to be updated when revocation occurs. The security and experimental analyses show that the proposed scheme meets the defined security requirements while significantly reducing user request response time, the overhead of transformation key generation, transmission, and ciphertext transformation.

Investigation of numerical and experimental assessment of melting behavior of phase change material in U tube heat exchanger

This study analyzes the melting process and temperature changes of a phase change material (PCM) in a U-tube heat exchanger, both experimentally and numerically. In the study, PCM was placed in a U-tube heat exchanger body and hot water was sent to the heat exchanger with a flow rate of 1.75 l/min and a temperature of 60 °C. In the study, the equations valid for continuity, momentum and energy were solved numerically by considering the phase change effects. The melting process was simulated and the melting percentages of the PCM at different time intervals were calculated to show the transition zones from the solid phase to the liquid phase. The PCM was initially subjected to hot water at 333 K at 300 K. In the experimental study, the PCM temperature reaches 306 K between the first 700–1200 min and melting is observed. This temperature is 303 K for numerical operation. After 3800 min, the PCM was observed to have completely melted for experimental and numerical study. The hardest and slowest melting part of the PCM is the area farthest from the center of the heat exchanger. In the comparison, approximately 4% error rate was determined between the measured and calculated values.

Exploring Gaussian elimination based solution methods of electric systems using circuit principles

AbstractIn power system simulation, the mathematical solution methods are typically regarded as pure numerical operations, which are independent of the circuit principles. In this letter, it is demonstrated that the computational procedures in the commonly used numerical solution methods for circuit equations are essentially equivalent to the basic principles of electricity. The computational procedures of the representative Gaussian elimination based solution methods (including GE and pivoting method for sparsity of GE/LU) are comprehensively analyzed and their deep relationships with the circuit principles are revealed: the computation process of these mathematics based numerical solution methods can be completely explained using circuit principles. The interesting findings could help understand the computational process of solution methods from the circuit perspective, which may also guide the design of new circuit solution methods.

Channel model for the dual-polarization b-modulated nonlinear frequency-division multiplexing optical transmission systems.

We consider optical transmission systems based on the nonlinear frequency division multiplexing (NFDM) concept, i.e., the systems employing the nonlinear Fourier transform (NFT) for signal processing and data modulation. Our work specifically addresses the double-polarization (DP) NFDM setup that utilizes the so-called b-modulation, the most efficient NFDM method proposed up-to-date. We extend the previously-developed analytical approach based on the adiabatic perturbation theory for the continuous nonlinear Fourier spectrum (b-coefficient) onto the DP case to obtain the leading order of continuous input-output signal relation, i.e., the asymptotic channel model, for an arbitrary b-modulated DP-NFDM optical communication system. Our main result is in deriving the relatively simple analytical expressions for the power spectral density of the components of effective conditionally Gaussian input-dependent noise emerging inside the nonlinear Fourier domain. We also demonstrate that our analytical expressions are in remarkable agreement with direct numerical results if one extracts the "processing noise" arising due to the imprecision of numerical NFT operations.

Generalized Distribution Feeder Switching with Fuzzy Indexing for Energy Saving

The objective of this study is to analyze feeder loss minimization and load balance under given constrains. Effective methods are required for feeder switching/reconfiguration. Feeder switching is a mixed-integer large-scale combinatorial problem for optimization, not easily solvable with classical optimization techniques, especially involving a great number of switches. This paper proposes a fuzzy indexing algorithm for feeder switching, with membership functions defined for switches such as thermometers or indices. The optimal switches can be determined through fuzzy index operations. With membership functions defined, the developed method used numerical operations for indices instead of the “set” operation or the min-max operations of traditional fuzzy algorithms. The optimization problem becomes a simple numeric calculation instead of a large-scale sorting problem and is much faster than most algorithms. It greatly reduces the computation time and enhances efficiency, which is suitable for either planning or operation purposes. Many algorithms were tested with three typical examples chosen for illustration, including the “optimal” results with an exhausted search. It shows that the proposed algorithm is very effective and can balance the load to reduce the loss and costs in obtaining the solution.

Comparative study of ternary hybrid nanofluids with role of thermal radiation and Cattaneo-Christov heat flux between double rotating disks

Heat and mass transfer are crucial to numerous technical and commercial operations, including air conditioning, machinery power collectors, crop damage, processing food, heat transfer mechanisms, and cooling, among numerous others. The fundamental purpose of this research is to use the Cattaneo-Christov heat flux model to disclose an MHD flow of ternary hybrid nanofluid through double discs. The results of a heat source and a magnetic field are therefore included in a system of PDEs that model the occurrences. These are transformed into an ODE system using similarity replacements. The first-order differential equations that emerge are then handled using the computational technique Bvp4c shooting scheme. The Bvp4c function in MATLAB is used to numerically solve the governing equations. The influence of the key important factors on velocity, temperature, nanoparticles concentration, and is illustrated visually. Furthermore, increasing the volume fraction of nanoparticles improves thermal conduction, increasing the heat transfer rate at the top disc. The graph indicates that a slight increase in melting parameter rapidly declines the velocity distribution profile of nanofluid. The temperature profile was boosted due to the growing outcomes of the Prandtl number. The increasing variations of the thermal relaxation parameter decline the thermal distribution profile. Furthermore, for some exceptional instances, the obtained numerical answers were compared to previously disclosed data, yielding a satisfactory compromise. We believe that this discovery will have far-reaching ramifications in engineering, medicine, and the field of biomedical technology. Additionally, this model can be used to examine biological mechanisms, surgical techniques, nano-pharmacological drug delivery systems, and the therapy of diseases like cholesterol using nanotechnology.

ALGORITHM FOR PROCESSING GAS SENSOR’S RESPONSE KINETICS DATA USING EXTENDED EXPONENTIAL FUNCTION WITHOUT NUMERICAL DIFFERENTIATION

The features of the use of computer technologies for processing experimental data for solv-ing the problems of automation of research of materials for gas sensitive sensors are con-sidered. An algorithm for processing the kinetic dependence of the response of gas sensors based on the model of an extended exponential function are proposed, which does not use numerical differentiation operations when finding the parameters of this model. This allows to signifi-cantly reduce the influence of the presence of data spread in the coordinates of the approxi-mating diagrams that are used in calculating the model parameters, increase the accuracy of their determination and contribute to the implementation of an automated information measuring system for the process of computer processing and analysis of experimental data.

The Impact of Industry 4.0 on Innovative Organisations, A Thematic Review using the PRISMA Statement 2020

The fast growth of technologies during the Industry 4.0 era resulted in new or evolved organisations forming. Throughout the Fourth Industrial Revolution, the interaction between technology and humans evolved. Furthermore, the skills and capacities of individuals and organisations are changing due to the abundance of technology. This study investigated the impact of industry 4.0 on innovative organisations and used thematic analysis to identify the major themes. VOS viewer content analysis and critical terms of occurrences analysis were used to identify the major themes. In addition, the PRISMA statement 2020 is applied for the methodological part. The results indicate three significant themes business models, innovative organisations, and digital transformation. The findings show that changes in the global economy and market needs are forcing businesses to adopt technical breakthroughs made possible by digital transformation. it is considered that adequate resources, experienced and capable workers, and well-organized, adequately adaptable, and creative procedures are required for innovative organisations. In addition, HRM practises in the digital era must incorporate teleworking, promote employee engagement in achieving the aim of digital transformation, and incentivise a proper leadership style. Also, technological advancement drives businesses to innovate in their everyday production, supply, value chains, and numerous operations, allowing them to adapt quickly to client requests.
 

Digital technology implementation and impact of artificial intelligence based on bipolar complex fuzzy Schweizer–Sklar power aggregation operators

Digital technology refers to any technology that uses digital signals or electronic data to process, store, and transmit information. Some examples of digital technologies include social media platforms, cloud computing, artificial intelligence, virtual and augmented reality, and blockchain technology. Digital technology has the potential to play a significant role in achieving sustainable development goals by providing solutions for a wide range of environmental, social, and economic challenges. In this manuscript, we investigate digital technology implementation under sustainable development and would find which area of sustainable development is most in need of digital technology. Further, we investigate the operational laws based on Schweizer–Sklar t-norm and t-conorm and originate aggregation operators based on these deduced operational laws under the environment of bipolar complex fuzzy set that is bipolar complex fuzzy Schweizer–Sklar power averaging, bipolar complex fuzzy Schweizer–Sklar power weighted averaging, bipolar complex fuzzy Schweizer–Sklar power geometric and bipolar complex fuzzy Schweizer–Sklar power weighted geometric operators and then we deduce techniques of decision-making utilizing these originated operators. Afterward, we tackle a numerical example related to the digital technology implementation under sustainable development by considering artificial data and finding the area of sustainable development which is most in need of digital technology. Moreover, we reveal the impact of one of the digital technologies that are artificial intelligence in the field of healthcare and study a numerical example by considering hypothetical data by employing the originated technique of decision-making. At the last, we do a comparison of the deduced operators with numerous current operators to reveal the superiority and benefits of the deduced operators.

A Q-Learning Proposal for Tuning Genetic Algorithms in Flexible Job Shop Scheduling Problems

Genetic algorithms (GAs) belong to the category of evolutionary algorithms and are frequently utilized for resolving challenging combinatorial problems. However, they typically require customization to suit a particular problem type, and their performance is heavily influenced by numerous hyperparameters and reproduction operators. In this work, we propose a Reinforcement Learning approach for fine-tuning Genetic Algorithms in Flexible Job Shop Scheduling problems (FJSP), where the main parameters involved in the genetic algorithm operators are trained to allocate the most promising values. The approach returns an optimized schedule taking into account given constraints specific to the scenario, such as the relationship among release date, due date, and processing time, which machines must be selected out of a set of alternative machines, or which sequence-dependent setup time can be filtered.
 The approach takes input data in the form of FJSP instances by varying the numbers of jobs and machines and then uses the NSGA-II algorithm to generate solutions. These solutions are stored in a Solutions module and they are analyzed using a Principal components analysis (PCA) to identify clusters of similar instances and solutions. The Q-Learning module then generates hyperparameters for each iteration of the NSGA-II algorithm based on information from the previous modules. A toy example is presented to better understand the behavior of the proposal and the results obtained for optimizing further instances of the problem in a more efficient way.

The relationship between math anxiety and math performance: The moderating role of visuospatial working memory

According to the processing efficiency theory (PET), math anxiety would interfere with working memory resources, negatively affecting mathematical abilities. To date, few studies have explored how the interaction between math anxiety and working memory would affect different types of math tasks, especially in primary school children. Therefore, the purpose of this study was to explore whether the interplay between math anxiety and working memory would influence performance in numerical operations (i.e., math fluency task) and mathematical reasoning (i.e., math reasoning task) in a group of primary school children (N = 202). Results showed that visuospatial working memory appeared to moderate the relationship between math anxiety and math performance when the math fluency task was considered, indicating that participants with higher levels of working memory were more negatively affected by math anxiety. No interaction effect was found for the math reasoning task in which students’ scores were explained only by visuospatial working memory. The findings suggest that math anxiety and visuospatial working memory interact to influence performance in the math fluency task and that this effect may vary depending on the strategies used to complete the task. On the other hand, results on the math reasoning task showed that visuospatial working memory continues to have a positive effect on the math performance independently of math anxiety. The implications in the educational setting are discussed, pointing to the importance of monitoring and intervention studies on affective factors.

Predicting flow in porous media: a comparison of physics-driven neural network approaches

This paper presents the development of physics-informed machine learning models for subsurface flows, specifically for determining pressure variation in the subsurface without the use of numerical modeling schemes. The numerical elliptic operator is replaced with a neural network operator and includes comparisons of several different machine learning models, along with linear regression, support vector regression, lasso, random forest regression, decision tree regression, light weight gradient boosting, eXtreme gradient boosting, convolution neural network, artificial neural network, and perceptron. The mean of absolute error of all models is compared, and error residual plots are used as a measure of error to determine the best-performing method.

土壤有机质含量的高光谱成像预测研究

Soil nutrient content is an important index to evaluate the growing environment of crops. Rapid access to soil nutrient information is an important requirement for the development of modern precision agriculture, while the detection of soil organic matter content is a necessary condition for understanding the basic soil fertility and implementing crop precision cultivation. In this paper, the soil of rural fields in the southeast of Shanxi Province before sowing was taken as the research object. 111 soil samples to be tested were collected. After the process of drying, impurity removal and grinding, the hyperspectral data of the Region of interest (ROI) of the samples were collected, and then the chemical determination of soil organic matter content was conducted. The original spectral data matrix was pretreated by numerical transformation operations, such as arithmetic mean, average deviation, 1st derivation, natural logarithm and mixed multiplication, and a Partial least square regression (PLSR) quantitative analysis model was established. In these models, the obtained prediction set RP value under the pretreatment of F(A)*ln(AD) was the highest, reaching 0.8859. For spectral data preprocessed by F(A)* Ln (AD), the Competitive adaptive reweighted sampling (CARS) algorithm and Random frog (RF) algorithm were used to select key variables. The PLSR model was established by using F(A)* Ln (AD)&CARS data processing method, and the RP value was increased to 0.9545. The prediction results can accurately reflect the real content of soil organic matter. The results of this study can provide theoretical support for the application of hyperspectral imaging technology in the determination of soil organic matter content, and provide a reference for the rapid detection of other soil components.

Cognition and learning difficulties in a representative sample of school-aged children with cerebral palsy

BackgroundNearly half of all children with CP experience intellectual impairment, with impacts on academic achievement. AimsTo assess cognitive and academic functioning for primary-school aged children with CP Methods and proceduresThis population-based cohort study assessed 93 participants (male n = 62; mean = 9 years 9 months, SD 1 y 1.8 months) on measures of fluid and crystallised intelligence (Raven’s Coloured Progressive Matrices, Peabody Picture Vocabulary Test) and academic achievement (Wechsler Individual Achievement Test). Analyses included t-tests, Pearson’s chi-square and regression. Outcomes and results41 (44.1%) children met criteria consistent with intellectual developmental disorder. Academic skills were significantly below population means on word reading (M= 85.4, SD = 19.3), t(66) = −6.2, p < .001; spelling (M=83.3, SD=19.7) t(65) = −6.87, p < .001; and numerical operations (M=72.9, SD=21.7) Z = 66.0, p < .001. Cognitive ability was associated with GMFCS level (χ² (1, N = 93) = 16.15, p < .001) and diagnosis of epilepsy (χ² (2, N = 93) = 11.51 p = .003). Crystallised and fluid intelligence together accounted for 65% of the variance in word reading, 56% in spelling and 52% in numerical operations. ImplicationsMany children with CP experience academic challenges. Screening is recommended for all children with CP and full psychoeducational assessment undertaken when children with CP experience academic difficulties.

A universally applicable 0D combustion model with a novel analysis of the critical factors affecting combustion in spark-ignition engines

Notwithstanding the continuous technological development of spark-ignition engines, the physics of in-cylinder phenomena has not been explicitly clarified to date. Furthermore, the advent of diverse engine technologies and in-cylinder compositions has increased the difficulty of understanding these phenomena using existing analysis methods. Under those circumstances, the modeling based on the fundamental combustion behaviors is becoming critical for analyzing combustion. Built upon the zero-dimensional flame surface density model, therefore, the models proposed herein attempt to reproduce a vast majority of combustion behaviors revealed to date, such as differential diffusion, thermo-diffusive instability, cutoff scales, distributed reaction, and flame quenching. As a result, we successfully predicted the combustion of numerous operating points of four different SI engines, including the extremely lean operating points of gasoline/air mixture up to [Formula: see text]. Furthermore, the extensive thermodynamic ranges are explored for the validation of the models with the aid of continuously variable valve timing modules; the pressure and the calculated temperature of the unburned mixture at ignition timing are varied from 4.5 to 28.6 bar and 559–794 K, respectively. In this study, we suggest an expression for a fully-developed turbulent flame speed well-fitted with the explored ranges of chemical and thermodynamic states by inspecting the influencing factors for flame wrinkling. Additionally, we analyze combustion using the developed models and identify several distinctive features of both stoichiometric and lean-burn points. Lastly, this study reveals the importance of flame thickness (or inner cutoff), which has a comparable or more severe effect on early flame propagation compared to planar laminar flame speed.