Numerical Domains Research Articles

The impact of LMS-based mechanics course on the creativity of prospective physics teachers in the post-pandemic era: A quasi-experimental study

This quasi-experimental study examined the effect of a mechanics course delivered through a Learning Management System (LMS) on the creativity of prospective physics teachers at a teacher training college in Mataram, Indonesia. The study was conducted in the post-pandemic era. Using a pretest-posttest one-group design, the researchers evaluated changes in creativity across three domains: figural, numeric, and verbal. The results showed significant improvements in overall creativity, with the most critical gains observed in the figural domain. Further analysis revealed that fluency was the creative indicator with the most enhancement. In contrast, other indicators displayed varying degrees of improvement. These findings highlight the potential of LMS-based instruction in fostering creativity among future physics educators, particularly in the figural, numeric, and verbal domains. This study adds to the growing body of evidence supporting technology integration into teacher education, especially during times of crisis. Future research should explore more targeted instructional strategies within LMS environments and utilize comprehensive creativity assessment methods further to enhance creative learning experiences for prospective physics teachers.

Symbolic testing of floating-point bugs and exceptions

Numerical software are susceptible to floating-point bugs and exceptions, which may lead to severe threats like denial of service attacks. Static analysis techniques such as symbolic execution are effective in detecting general bugs which often cause memory error or program crash. Unfortunately, these methods do not deal well with numerical code as they do not support floating-point constraints and math functions symbolically. In this paper, we propose a new analysis framework YUSE, which can detect floating-point bugs by constructing constraints and exploring paths which contain floating-point expressions. Specifically, we introduce interval computation and interval constraint propagation in non-relational numerical abstract domains, and symbolically model math functions, to accurately detect floating-point bugs and exceptions. Moreover, we leverage two-phase constraint solving to enhance YUSE’s performance. Experimental results show that YUSE outperforms two state-of-the-art tools, Frama-c and Fpse-study, in terms of effectiveness and efficiency, with 1.4× and 7.1× faster than Frama-c and Fpse-study, respectively. Moreover, YUSE found 20 new bugs in real-world software, 12 of which were assigned CVE IDs and 8 of which were confirmed by developers.

Limits and Difficulties in the Design of Under-Approximation Abstract Domains

The main goal of most static analyses is to prove the absence of bugs : if the analysis reports no alarms then the program will not exhibit any unwanted behaviours. For this reason, they are designed to over-approximate program behaviours and, consequently, they can report some false alarms. O’Hearn’s recent work on incorrectness has renewed the interest in the use of under-approximations for bug finding , because they only report true alarms. In principle, Abstract Interpretation techniques can handle under-approximations as well as over-approximations, but, in practice, few attempts were developed for the former, notwithstanding the much wider literature on the latter. In this paper we investigate the possibility of exploiting under-approximation abstract domains for bug-finding analyses. First we restrict to consider concrete powerset domains and highlight some intuitive asymmetries between over- and under-approximations. Then, we prove that the effectiveness of abstract domains defined by Under-approximation Galois connection is limited, because the analysis is likely to return trivial results whenever common transfer functions are encoded in the program. To this aim, we introduce the original concepts of non-emptying functions and highly surjective function family and we prove the nonexistence of abstract domains able to under-approximate such functions in a non-trivial way. We show many examples of finite and infinite numerical domains, as well as other generic domains. In all such cases, we prove the impossibility of performing nontrivial analyses via under-approximating Galois connections.

Hybrid State Estimation: Integrating Physics-Informed Neural Networks with Adaptive UKF for Dynamic Systems

In this paper, we present a novel approach to state estimation in dynamic systems by combining Physics-Informed Neural Networks (PINNs) with an adaptive Unscented Kalman Filter (UKF). Recognizing the limitations of traditional state estimation methods, we refine the PINN architecture with hybrid loss functions and Monte Carlo Dropout for enhanced uncertainty estimation. The Unscented Kalman Filter is augmented with an adaptive noise covariance mechanism and incorporates model parameters into the state vector to improve adaptability. We further validate this hybrid framework by integrating the enhanced PINN with the UKF for a seamless state prediction pipeline, demonstrating significant improvements in accuracy and robustness. Our experimental results show a marked enhancement in state estimation fidelity for both position and velocity tracking, supported by uncertainty quantification via Bayesian inference and Monte Carlo Dropout. We further extend the simulation and present evaluations on a double pendulum system and state estimation on a quadcopter drone. This comprehensive solution is poised to advance the state-of-the-art in dynamic system estimation, providing unparalleled performance across control theory, machine learning, and numerical optimization domains.

Patellofemoral stabilization with and without cartilage restoration

Introduction/ObjectivesCartilage restoration as an adjunct to patellofemoral (PF) soft tissue and/or bony stabilization in patients with symptomatic PF instability remains controversial. Our purpose was to evaluate patients undergoing surgical stabilization for PF instability with or without concomitant cartilage restoration. MethodsRetrospective review of prospectively collected data identified patients undergoing surgical stabilization for recurrent patella instability, with or without concomitant cartilage restoration. Presurgical and postsurgical patient-reported outcomes were collected. Complications requiring reoperation were recorded. Statistically significant difference was set at P < .05. ResultsOne hundred thirty patients (144 knees) were included. One hundred thirteen knees in the isolated stabilization (STAB) and 31 knees in the Stabilization-Cartilage Restoration (STAB-CART) group. The average age was 20.64 and 25.03 in the STAB and STAB-CART groups (P = .034), respectively. STAB-CART group had significantly lower preoperative Knee injury and Osteoarthritis Outcomes Score (57.24 ± 17.45 vs 46.11 ± 14.74, P = .019) and Single Assessment Numeric Evaluation scores (43.15 ± 19.05 vs 26.85 ± 13.74, P = .002). Both groups statistically improved in all Knee injury and Osteoarthritis Outcomes Score, International Knee Documentation Committee, and Single Assessment Numeric Evaluation domains with no statistically significant differences at final follow-up between groups. Thirteen knees (11.5%) in the STAB and 6 knees (19.4%) in the STAB-CART group had complications requiring reoperation, including 6 and 3 revision stabilizations, respectively. There were no statistically significant differences in total major complications (P = .246) or medial PF ligament revision (P = .405). ConclusionsThe addition of cartilage restoration in patients undergoing soft tissue and/or bony PF stabilization appears to be safe and effective. Despite lower baseline scores, patients undergoing PF stabilization with cartilage restoration had similar final subjective outcome scores compared to the group without.

Adaptation of the Intelligence Structure Test, Latvian version: psychometric properties.

The Intelligence Structure Test (IST-2000R) is created to measure reasoning abilities and knowledge through verbal, numerical, and figural domains. The qualities of IST-2000R have shown its potential to be adapted and standardized in a Latvian sample to be used in psychological evaluation and research, thus satisfying the need for reliable measurement. The aim of this study was to investigate the psychometric properties of the Latvian version of IST-2000R. The adaptation sample consisted of 1,017 participants aged 15-65 (M = 31.8; SD = 10.94), of whom 36% were male. Participants were tested using the supervised offline administration mode (exploro.lv). The Ethics Committee of Riga Stradins University (RSU), Riga, Latvia, approved the study. The data show that the psychometric properties of the Latvian version of IST-2000R are in line with scientific norms. Thus, the test is considered to be reliable and may be used for psychological evaluation and research.

Generalized planning as heuristic search: A new planning search-space that leverages pointers over objects

Planning as heuristic search is one of the most successful approaches to classical planning but unfortunately, it does not trivially extend to Generalized Planning (GP); GP aims to compute algorithmic solutions that are valid for a set of classical planning instances from a given domain, even if these instances differ in their number of objects, the initial and goal configuration of these objects and hence, in the number (and possible values) of the state variables. State-space search, as it is implemented by heuristic planners, becomes then impractical for GP. In this paper we adapt the planning as heuristic search paradigm to the generalization requirements of GP, and present the first native heuristic search approach to GP. First, the paper introduces a new pointer-based solution space for GP that is independent of the number of classical planning instances in a GP problem and the size of those instances (i.e. the number of objects, state variables and their domain sizes). Second, the paper defines an upgraded version of our GP algorithm, called Best-First Generalized Planning (BFGP), that implements a best-first search in our pointer-based solution space for GP. Lastly, the paper defines a set of evaluation and heuristic functions for BFGP that assess the structural complexity of the candidate GP solutions, as well as their fitness to a given input set of classical planning instances. The computation of these evaluation and heuristic functions does not require grounding states or actions in advance. Therefore our GP as heuristic search approach can handle large sets of state variables with large numerical domains, e.g. integers.

Design space investigations of scramjet engines using reduced-order modeling

Conceptual design studies performed with reduced-order approaches allow feasibility and sizing considerations of air-breathing engines to be configured at an affordable computational cost. The present study is devoted to exploring the design space of a dual-mode ramjet engine operating in scramjet mode by means of reduced-order analysis to assess the effects of propulsive system design configurations on component level and overall performance characteristics. The approach proposed in this work combines axisymmetric flow configuration used for the design of supersonic/hypersonic intakes and solutions of one-dimensional flow governing equations coupled with finite-rate chemistry and thermophysical properties tables in the numerical domains of the combustor and nozzle components. The scramjet design space is generated by varying parameters which are flight Mach number and altitude, intake truncation angle, intake exit Mach number and equivalence ratio. Performance outputs of total pressure recovery factor, compression ratio, captured air mass flow rate, intake startability index, thrust, specific impulse, fuel consumption and overall efficiency are computed for each design scenario. The generated database is visualized via performance maps and analyzed in terms of propulsive characteristics. A feature importance study is also conducted to quantify the effects of design parameters on the propulsive performance.

Experimental and numerical analysis of the thermal performance of PCM-impregnated reticular structures obtained by additive manufacturing

This paper proposes a combined experimental and numerical analysis of the melting of three different paraffin waxes embedded in reticular structures fabricated by additive manufacturing. The parent material of the reticular structures is AlSi10Mg. Metal structures, having a 100 mm square base and a thickness of 20 mm, were printed between two 10 mm thick plates. Samples were positioned in an upright position and laterally heated applying different heat fluxes. Three different paraffins were tested, with different characteristic melting temperatures (42 °C, 55 °C, and 64 °C), which are suitable for electronics cooling applications. Four different structures were tested, having a cell length of 5 mm and 10 mm, and porosities of 0.87 and 0.93. Besides the experimental tests, numerical simulations of the melting phenomenon were carried out using a purely conductive model implemented in ANSYS Fluent. The discretized numerical domains represented just small repetitive portions of the test modules, thus allowing substantial computational time savings. This simplified method has been proven to yield results that are in good agreement with the experimental data. The main outcome of this work is the setup of the simplified numerical procedure, which was then validated and used to investigate the effectiveness of the considered structures in diffusing heat into the low thermal conductivity phase change materials. It was concluded that the best overall thermal performance can be obtained with low porosity and low cell size since this enables faster melting processes and better surface temperature control.

Metric error monitoring as a component of metacognitive processing.

Metacognitive processing constitutes one of the contemporary target domains in consciousness research. Error monitoring (the ability to correctly report one's own errors without feedback) is considered one of the functional outcomes of metacognitive processing. Error monitoring is traditionally investigated as part of categorical decisions where choice accuracy is a binary construct (choice is either correct or incorrect). However, recent studies revealed that this ability is characterized by metric features (i.e., direction and magnitude) in temporal, spatial, and numerical domains. Here, we discuss methodological approaches to investigating metric error monitoring in both humans and non-human animals and review their findings. The potential neural substrates of metric error monitoring measures are also discussed. This new scope of metacognitive processing can help improve our current understanding of conscious processing from a new perspective. Thus, by summarizing and discussing the perspectives, findings, and common applications in the metric error monitoring literature, this paper aims to provide a guideline for future research.

OMTPlan: A Tool for Optimal Planning Modulo Theories

OMTPlan is a Python platform for optimal planning in numeric domains via reductions to Satisfiability Modulo Theories (SMT) and Optimization Modulo Theories (OMT). Currently, OMTPlan supports the expressive power of PDDL2.1 level 2 and features procedures for both satisficing and optimal planning. OMTPlan provides an open, easy to extend, yet efficient implementation framework. These goals are achieved through a modular design and the extensive use of state-of-the-art systems for SMT/OMT solving.

Training artificial neural networks using substructuring techniques: Application to joint identification

The dynamic properties of assembled structures are governed by the substructure dynamics as well as the dynamics of the joints that are part of the assembly. It can be challenging to describe the physical interactions within the joints analytically, as slight modifications, such as static preload, temperature, etc. can lead to significant changes in the assembly’s dynamic properties. Therefore, characterizing the dynamic properties of joints typically involves experimental testing and subsequent model updating. In this paper, a machine-learning-based approach to joint identification is proposed that utilizes a physics-based computational model of the joint. The idea is to combine the computational model of the joint with dynamic substructuring techniques to train the machine-learning model. The flexibility of dynamic substructuring permits the enforcement of compatibility and equilibrium conditions between the component models from the experimental and numerical domains, facilitating the development of machine-learning models that can predict the dynamic properties of joints. The proposed approach provides an accurate data-driven method for joint identification in real structures, while reducing the number of measurements needed for the identification. The approach permits the identification of a full 12-DoF joint, enabling the coupling of 3D dynamic models of substructures. Compared to the standard decoupling approach, no spurious peaks are present in the reconstructed assembly response. The proposed approach is validated numerically and experimentally by reconstructing the assembly response and comparing the results with known assembly dynamics.

Hybrid SPH-FEM solver for metal cutting simulations on the GPU including thermal contact modeling

This paper presents a hybrid Smoothed Particle Hydrodynamics (SPH) – Finite Element Method (FEM) solver for metal cutting simulations on Graphics Processing Units (GPU). For the first time in chip formation simulation, the heat transfer between an SPH model of the workpiece, and a transient FEM temperature model for the cutting tool, is established. For validation, the performance of the modeled thermal contact between two numerical domains is compared with a commercial FEM software. The sensitivity of the implemented SPH-FEM contact parameters is investigated for the first time and further insights into the thermal modeling of cutting simulations are generated. Overall, the newly developed hybrid model saves the computational time on the cutting tool side in the pure SPH method and enables more efficient high-fidelity cutting simulations. By clearly defining the thermal contact at the tool-chip interface, the simulated tool surface temperature agrees well with the experimental measurements in the literature.

High-order gas-kinetic schemes with non-compact and compact reconstruction for implicit large eddy simulation

High-order gas-kinetic scheme (HGKS) with 5th-order non-compact reconstruction has been well implemented for implicit large eddy simulation (ILES) in nearly incompressible turbulent channel flows. In this study, the HGKS with higher-order non-compact reconstruction and compact reconstruction will be validated in turbulence simulation. For higher-order non-compact reconstruction, 7th-order reconstruction in both normal and tangential directions are implemented. On the other hand, the compact HGKS with 5th-order compact reconstruction in normal direction is developed. Current work aims to show the benefits of high-order non-compact reconstruction and compact reconstruction for ILES. The accuracy of HGKS is verified by numerical simulation of three-dimensional advection of density perturbation. For the non-compact 7th-order scheme, 16 Gaussian points are required on the cell-interface to preserve the order of accuracy. Then, HGKS with non-compact and compact reconstruction is used in the three-dimensional Taylor–Green vortex (TGV) problem and turbulent channel flows. Accurate ILES solutions have been obtained from HGKS. In terms of the physical modeling underlying the numerical algorithms, the compact reconstruction has the consistent physical and numerical domains of dependence without employing additional information from cells which have no any direct physical connection with the targeted cell. The compact GKS shows a favorable performance for turbulence simulation in resolving the multi-scale structures.

Flexibility across and flexibility within: The domain of integer addition and subtraction

To better understand the role that flexibility plays in students’ success on integer addition and subtraction problems, we examined students’ flexibility when solving open number sentences. We define flexibility as the degree to which a learner uses more than one strategy to solve a single task when prompted, as well as the degree to which a learner changes strategies when solving a range of tasks to accommodate task differences. We introduce the categorizations of flexibility within and flexibility across to distinguish these two ways of operationalizing flexibility. We examined flexibility and performance within and among three groups of students — 2nd and 4th graders who had negative numbers in their numerical domains, 7th graders, and college-track 11th graders. Profiles of five students are shared to provide insight in relation to the quantitative findings.

Early numerical skills and mathematical domains in students with autism spectrum disorders in primary school

Early numerical skills and mathematical domains in students with autism spectrum disorders in primary school

Energy assessment of potential locations for OWC instalation at the Portuguese coast

This work aims to determine the exploitable wave energy resource at five potential sites close to harbour protection facilities at the Portuguese coast, namely at the Azores archipelago, at Madeira Island and at Sines, on the coast of mainland Portugal. For that purpose, a third-generation wave model SWAN is used to transfer the offshore estimates of sea wave conditions to those points over the last 40 years. Sea states and wind fields are provided by the climate reanalysis datasets ERA5. Using sea states as boundary conditions and wind fields as forcings in the numerical domains of the SWAN model, the sea states were propagated shoreward, in order to estimate and analyse the wave conditions in the regions of interest. By combining the average energy flux per unit length of wave front and the probability of occurrence of each sea state, the average exploitable annual energy per unit length of wave crest can be computed. The variability of this energy flux is analysed since it is of paramount importance for the efficiency of Wave Energy Converters (WEC). This assessment showed that the best location for the installation of dual-chamber OWC devices is at the Azores archipelago.

Numerical fatigue damage analysis of a variable speed Francis pump-turbine during start-up in generating mode

Variable speed hydropower units offer a large spectrum of grid regulation services and may therefore contribute to the stability of future power supply systems. Full Size Frequency Converters (FSFC) already found real world application in Pumped Storage Hydropower Plants up to a rated power of 100 MW and are even considered scalable up to a few hundred MW. Apart from the extension of the power range and grid regulation capacities, the FSFC technology also provides new control possibilities during transient operations such as start-up in generating mode. Thus, harsh conditions with damaging impact on the hydromechanical components may be avoided by tuning the operating point trajectory in the start-up phase. In this paper, runner fatigue damage during start-up in generating mode of a 5 MW variable speed Francis pump-turbine prototype equipped with a FSFC is numerically analyzed. The fixed speed solution is compared to a variable speed solution following a BEP tracking control strategy. 1D hydraulic transient simulations provide boundary conditions for detailed 3-D CFD/FEA simulations. Full and reduced numerical domains are used and compared. The overall outcome of the present numerical study indicates an important reduction of partial damages using variable speed drives for turbine start-up manoeuvres.

Brief memory reactivations induce learning in the numeric domain

Learning of arithmetic facts such as the multiplication table requires time-consuming, repeated practice. In light of evidence indicating that reactivation of encoded memories can modulate learning and memory processes at the synaptic, system and behavioral levels, we asked whether brief memory reactivations can induce human learning in the numeric domain. Adult participants performed a number-fact retrieval task in which they learned arbitrary numeric facts. Following encoding and a baseline test, 3 passive, brief reactivation sessions of only 40 s each were conducted on separate days. Learning was evaluated in a retest session. Results showed reactivations induced learning, with improved performance at retest relative to baseline test. Furthermore, performance was superior compared to a control group performing test-retest sessions without reactivations, who showed significant memory deterioration. A standard practice group completed active-retrieval sessions on 3 separate days, and showed significant learning gains. Interestingly, while these gains were higher than those of the reactivations group, subjects showing reactivation-induced learning were characterized by superior efficiency relative to standard practice subjects, with higher rate of improvement per practice time. A follow-up long-term retention experiment showed that 30 days following initial practice, weekly brief reactivations reduced forgetting, with participants performing superior to controls undergoing the same initial practice without reactivations. Overall, the results demonstrate that brief passive reactivations induce efficient learning and reduce forgetting within a numerical context. Time-efficient practice in the numeric domain carries implications for enhancement of learning strategies in daily-life settings.

A Fair Performance Comparison between Complex-Valued and Real-Valued Neural Networks for Disease Detection.

Our aim is to contribute to the classification of anomalous patterns in biosignals using this novel approach. We specifically focus on melanoma and heart murmurs. We use a comparative study of two convolution networks in the Complex and Real numerical domains. The idea is to obtain a powerful approach for building portable systems for early disease detection. Two similar algorithmic structures were chosen so that there is no bias determined by the number of parameters to train. Three clinical data sets, ISIC2017, PH2, and Pascal, were used to carry out the experiments. Mean comparison hypothesis tests were performed to ensure statistical objectivity in the conclusions. In all cases, complex-valued networks presented a superior performance for the Precision, Recall, F1 Score, Accuracy, and Specificity metrics in the detection of associated anomalies. The best complex number-based classifier obtained in the Receiving Operating Characteristic (ROC) space presents a Euclidean distance of 0.26127 with respect to the ideal classifier, as opposed to the best real number-based classifier, whose Euclidean distance to the ideal is 0.36022 for the same task of melanoma detection. The 27.46% superiority in this metric, as in the others reported in this work, suggests that complex-valued networks have a greater ability to extract features for more efficient discrimination in the dataset.