Modeling Tasks Research Articles

German and Taiwanese secondary students’ mathematical modelling task value profiles and their relation to mathematical knowledge and modelling performance

German and Taiwanese secondary students’ mathematical modelling task value profiles and their relation to mathematical knowledge and modelling performance

3D Modeling of rural environments from multiscale aerial imagery

Given the increasing attention to environmental preservation and sustainable development, the digitization of rural landscapes stands out as a pivotal strategy for effective environmental management and sustainability, land use planning, and preservation of cultural heritage. This work proposes a novel methodology for generating 3D models of rural landscapes by integrating multiscale data sources. Although Unmanned Aerial Vehicles (UAV) simplify the acquisition of multi-source data, their coverage is typically restricted to small landscapes due to their limited range and flight time. On the other hand, although the use of aerial images provides a broader view of the terrain, it is important to note that the low resolution of these images interferes with the task of accurate 3D modeling. Given these challenges, we propose a methodology that combines UAV data and high-resolution aerial imagery provided by the Spanish National Orthophoto Program (PNOA). This multi-source data integration is crucial to generating detailed and accurate 3D models of rural environments. The proposed methodology involves three steps: (1) semantic segmentation of aerial images identifying features such as vegetation, ground, and human-made structures, (2) estimation of the Digital Elevation Model (DEM), and (3) 3D modeling of rural environments using the point clouds generated from UAV images. The conducted experiments demonstrate the effectiveness of our approach identifying and representing previously mentioned features. Thus, this work presents advances in 3D representation techniques for real scenarios, contributing to the coordination of land utilization and environmental sustainability in rural landscapes.

Exploring Alternative Approaches to Language Modeling for Learning from Data and Knowledge

Despite their extensive application in language understanding tasks, large language models (LLMs) still encounter challenges including hallucinations - occasional fabrication of information - and alignment issues - lack of associations with human-curated world models (e.g., intuitive physics or common-sense knowledge). Moreover, the black-box nature of LLMs presents significant obstacles in training them effectively to achieve desired behaviors. In particular, modifying the concept embedding spaces of LLMs can be highly intractable. This process involves analyzing the implicit impact of such adjustments on the myriad parameters within LLMs and the resulting inductive biases. We propose a novel architecture that wraps powerful function approximation architectures within an outer, interpretable read-out layer. This read-out layer can be scrutinized to explicitly observe the effects of concept modeling during the training of the LLM. Our method stands in contrast with gradient-based implicit mechanisms, which depend solely on adjustments to the LLM parameters and thus evade scrutiny. By conducting extensive experiments across both generative and discriminative language modeling tasks, we evaluate the capabilities of our proposed architecture relative to state-of-the-art LLMs of similar sizes. Additionally, we offer a qualitative examination of the interpretable read-out layer and visualize the concepts it captures. The results demonstrate the potential of our approach for effectively controlling LLM hallucinations and enhancing the alignment with human expectations.

Metacognitive Awareness as a Predictor of Mathematical Modeling Competency Among Preservice Elementary Teachers

<p style="margin-left:28px; text-align:justify">Mathematical modeling offers a promising approach to improving mathematics education. This study aims to determine if the concept of metacognitive awareness in the learning process is associated with mathematical modeling. This study also considers the interaction effect of sex and academic year level on both variables. Focusing the study on preservice elementary teachers might address potential issues and targeted intervention in their preparation program concerning their ability to teach and guide young learners in modeling activities. The research sample includes 140 preservice elementary teachers at Central Luzon State University, Philippines. Data collection used an adapted metacognitive awareness inventory and a validated researcher-made mathematical modeling competency test aligned with the K-12 mathematics curriculum in the Philippines. Results revealed that the preservice elementary teachers had a high metacognitive awareness and mathematical modeling competency, ranging from 22 to 31 out of 36 points. Besides, Factorial ANOVA indicates that academic year level positively affects both variables regardless of sex, and stepwise regression analysis unveiled that information management, declarative knowledge, and planning significantly predict 41.4% of the mathematical modeling competency variance. This suggests that developing metacognitive awareness supports preservice elementary teachers in performing modeling tasks that improve their competency level in mathematics.</p>

TypeQL: A Type-Theoretic & Polymorphic Query Language

Relational data modeling can often be restrictive as it provides no direct facility for modeling polymorphic types, reified relations, multi-valued attributes, and other common high-level structures in data. This creates many challenges in data modeling and engineering tasks, and has led to the rise of more flexible NoSQL databases, such as graph and document databases. In the absence of structured schemas, however, we can neither express nor validate the intention of data models, making long-term maintenance of databases substantially more difficult. To resolve this dilemma, we argue that, parallel to the role of classical predicate logic for relational algebra, contemporary foundations of mathematics rooted in type theory can guide us in the development of powerful new high-level data models and query languages. To this end, we introduce a new polymorphic entity-relation-attribute (PERA) data model, grounded in type-theoretic principles and accessible through classical conceptual modeling, with a near-natural query language: TypeQL. We illustrate the syntax of TypeQL as well as its denotation in the PERA model, formalize our model as an algebraic theory with dependent types, and describe its stratified semantics.

“Image-Spectral” fusion monitoring of small cotton samples nitrogen content based on improved deep forest

Accurate monitoring of nitrogen nutrition is crucial for improving cotton yield and quality, as well as the ecological environment. The mainstream method for monitoring nutrition is to establish traditional machine learning (ML) models using a single data source. However, this approach has limitations such as limited access to feature information, model-fitting problems, and limited generalization. Deep learning (DL), on the other hand, has shown promise in complex nonlinear modeling tasks due to its flexible structure. However, it has its limitations, such as the fact that agronomic sample collection and testing are usually labor- and material-intensive, resulting in sample sizes that are too small to meet its training conditions. Therefore, there is an urgent need for DL models that can effectively integrate features from multiple data sources and accurately monitor crop nitrogen content, especially in scenarios with small samples. In this study, we conducted indoor pot experiments using the cotton variety Xinluzao 53 and subjected it to six nitrogen treatments. The data sources for our analysis included hyperspectral and digital images of the cotton leaves. To enhance representation learning capabilities, we enriched the multi-class base learners within each layer of the deep forest (DF) model and introduced skip connections. These enhancements improved the quality of inversion for both hyperspectral and digital image datasets. We then developed image-spectral fusion models, which combined the DF structure with stacking ensemble learning. Our focus was on three levels of fusion: feature-level fusion, decision-level fusion, and secondary decision-level fusion. This approach aimed to further enhance the accuracy and stability of nitrogen content inversion. The DF model satisfied the training condition for small samples. Compared to traditional ML algorithms and the original DF algorithm, the improved DF model achieved an increase in validation set R2 of 13.4–28.5% and 10.9–14.9%, respectively. These findings highlight the enhanced accuracy and stability of the improved DF model. Additionally, compared to the optimal inversion model using two single data sources, the “Image-Spectral” three-level fusion models exhibited improvements in validation set R2 of 8.6–9.3%, 10.5–11.2%, and 11.8–12.5% for feature-level, decision-level, and secondary decision-level fusion, respectively. The improved DF and three-level fusion model collectively contributed to the increased accuracy of cotton nitrogen content inversion. Among these models, the secondary decision-level fusion model demonstrated the most marked improvement. This methodology provides valuable insights into monitoring crop phenotypic parameters in situations with limited sample sizes.

Predictors of social risk for post-ischemic stroke reintegration

After stroke rehabilitation, patients need to reintegrate back into their daily life, workplace and society. Reintegration involves complex processes depending on age, sex, stroke severity, cognitive, physical, as well as socioeconomic factors that impact long-term outcomes post-stroke. Moreover, post-stroke quality of life can be impacted by social risks of inadequate family, social, economic, housing and other supports needed by the patients. Social risks and barriers to successful reintegration are poorly understood yet critical for informing clinical or social interventions. Therefore, the aim of this work is to predict social risk at rehabilitation discharge using sociodemographic and clinical variables at rehabilitation admission and identify factors that contribute to this risk. A Gradient Boosting modelling methodology based on decision trees was applied to a Catalan 217-patient cohort of mostly young (mean age 52.7), male (66.4%), ischemic stroke survivors. The modelling task was to predict an individual’s social risk upon discharge from rehabilitation based on 16 different demographic, diagnostic and social risk variables (family support, social support, economic status, cohabitation and home accessibility at admission). To correct for imbalance in patient sample numbers with high and low-risk levels (prediction target), five different datasets were prepared by varying the data subsampling methodology. For each of the five datasets a prediction model was trained and the analysis involves a comparison across these models. The training and validation results indicated that the models corrected for prediction target imbalance have similarly good performance (AUC 0.831–0.843) and validation (AUC 0.881 - 0.909). Furthermore, predictor variable importance ranked social support and economic status as the most important variables with the greatest contribution to social risk prediction, however, sex and age had a lesser, but still important, contribution. Due to the complex and multifactorial nature of social risk, factors in combination, including social support and economic status, drive social risk for individuals.

Modified failproof physics-informed neural network framework for fast and accurate optical fiber transmission link modeling

Physics-informed neural networks (PINNs) have recently emerged as an important and ground-breaking technique in scientific machine learning for numerous applications including in optical fiber communications. However, the vanilla/baseline version of PINNs is prone to fail under certain conditions because of the nature of the physics-based regularization term in its loss function. The use of this unique regularization technique results in a highly complex non-convex loss landscape when visualized. This leads to failure modes in PINN-based modeling. The baseline PINN works very well as an optical fiber model with relatively simple fiber parameters and for uncomplicated transmission tasks. Yet, it struggles when the modeling task becomes relatively complex, reaching very high error, for example, numerous modeling tasks/scenarios in soliton communication and soliton pulse development in special fibers such as erbium-doped dispersion compensating fibers. We implement two methods to circumvent the limitations caused by the physics-based regularization term to solve this problem, namely, the so-called scaffolding technique for PINN modeling and the progressive block learning PINN modeling strategy to solve the nonlinear Schrödinger equation (NLSE), which models pulse propagation in an optical fiber. This helps PINN learn more accurately the dynamics of pulse evolution and increases accuracy by two to three orders of magnitude. We show in addition that this error is not due to the depth or architecture of the neural network but a fundamental issue inherent to PINN by design. The results achieved indicate a considerable reduction in PINN error for complex modeling problems, with accuracy increasing by up to two orders of magnitude.

Towards a formal ontology of engineering functions, behaviours, and capabilities

In both applied ontology and engineering, functionality is a well-researched topic, since it is through teleological causal reasoning that domain experts build mental models of engineering systems, giving birth to functions. These mental models are important throughout the whole lifecycle of any product, being used from the design phase up to diagnosis activities. Though a vast amount of work to model functions has already been carried out, the literature has not settled on a shared and well-defined approach due to the variety of concepts involved and the modeling tasks that functional descriptions should satisfy. The work in this paper posits the basis and makes some crucial steps towards a rich ontological description of functions and related concepts, such as behaviour, capability, and capacity. A conceptual analysis of such notions is carried out using the top-level ontology DOLCE as a framework, and the ensuing logical theory is formally described in first-order logic and OWL, showing how ontological concepts can model major aspects of engineering products in applications. In particular, it is shown how functions can be distinguished from the implementation methods to realize them, how one can differentiate between capabilities and capacities of a product, and how these are related to engineering functions.

Use of dynamic simulation and Forrester diagrams to describe the growth of lettuce (Lactuca sativa L.) under field conditions

The use of computational tools to describe some processes of crop growth has evolved in recent decades and remains an area of active research, where more and more applications are incorporated with the integration of a greater number of mathematical tools, statistics, and computational calculation efficiency, simplifying the tasks of modeling and visualizing the components of the system used. Current research proposes a dynamic growth model for lettuce cultivation using Forrester diagrams to evaluate different scenarios involving five growth functions and five lettuce cultivars in field conditions of the Bailadores region (Venezuelan Andes, 2550 m a.s.l.). The lettuce variety Coastal Star achieved the greatest accumulation of dry matter used as a response in each model. The logistics of growth function was properly adjusted to the experimental data compared to the other models. The proposed diagram model can be used as a basis for the construction of more complex models that incorporate other physiological variables of the crop and the growth environment.

Machine Learning and Deep Learning Strategies for Chinese Hamster Ovary Cell Bioprocess Optimization

The use of machine learning and deep learning has become prominent within various fields of bioprocessing for countless modeling and prediction tasks. Previous reviews have emphasized machine learning applications in various fields of bioprocessing, including biomanufacturing. This comprehensive review highlights many of the different machine learning and multivariate analysis techniques that have been utilized within Chinese hamster ovary cell biomanufacturing, specifically due to their rising significance in the industry. Applications of machine and deep learning within other bioprocessing industries are also briefly discussed.

One-shot neuroanatomy segmentation through online data augmentation and confidence aware pseudo label

Recently, deep learning-based brain segmentation methods have achieved great success. However, most approaches focus on supervised segmentation, which requires many high-quality labeled images. In this paper, we pay attention to one-shot segmentation, aiming to learn from one labeled image and a few unlabeled images. We propose an end-to-end unified network that joints deformation modeling and segmentation tasks. Our network consists of a shared encoder, a deformation modeling head, and a segmentation head. In the training phase, the atlas and unlabeled images are input to the encoder to get multi-scale features. The features are then fed to the multi-scale deformation modeling module to estimate the atlas-to-image deformation field. The deformation modeling module implements the estimation at the feature level in a coarse-to-fine manner. Then, we employ the field to generate the augmented image pair through online data augmentation. We do not apply any appearance transformations cause the shared encoder could capture appearance variations. Finally, we adopt supervised segmentation loss for the augmented image. Considering that the unlabeled images still contain rich information, we introduce confidence aware pseudo label for them to further boost the segmentation performance. We validate our network on three benchmark datasets. Experimental results demonstrate that our network significantly outperforms other deep single-atlas-based and traditional multi-atlas-based segmentation methods. Notably, the second dataset is collected from multi-center, and our network still achieves promising segmentation performance on both the seen and unseen test sets, revealing its robustness. The source code will be available at https://github.com/zhangliutong/brainseg.

Fault-sketch: A framework for modeling geological faults and displacements

Geological faults, which result from rock fracturing and displacement in the subsurface, play an important role in shaping the Earth’s crust. Modeling fault surfaces and their impact on rock formations is, thus, useful for various geological applications. However, due to the complex configurations of faults, the modeling process can become difficult, requiring a framework with a specialized modeling toolkit.The primary challenge in fault modeling lies in properly correlating the geometry of faults with their effects on rock layers and other fault surfaces during displacement. To address this, we have developed a series of operators designed for fault modeling. In this manner, we present Fault-Sketch, a Sketch-Based Interface and Modeling (SBIM) framework that tackles the task of fault modeling and captures their influence on various geological structures. This framework enables the creation of surfaces as a result of rock configurations that have previously been largely overlooked in the existing literature.The collection of operators presented in Fault-Sketch are built upon a data structure fit for the purpose of consistently representing fault surfaces and their boundaries together with the influence they cause both on other surfaces and on the volumes they bound. Moreover, the operators are designed to mimic the geologic processes relevant to fault creation and displacement to facilitate their use by domain experts.

AI-driven non-intrusive uncertainty quantification of advanced nuclear fuels for digital twin-enabling technology

In response to the urgent need to establish AI/ML-integrated Digital Twin (DT) technology within next-generation nuclear systems, advancements in modeling methods and simulation codes are necessary. The increased complexity of models demands significant computational resources to quantify their uncertainties. To address this challenge, a data-driven non-intrusive uncertainty quantification method via polynomial chaos expansion is introduced as an efficient strategy within the finite element analysis-based fuel performance code BISON. Models of UO2 and U3Si2 fuels, alongside SiC/SiC cladding material, were prepared to demonstrate the proposed method. The impact of four independent uncertain input variables on the system output was quantified, requiring fewer than 100 BISON simulations for each model. This approach not only accelerates the modeling and simulation task but also enhances the reliability in the development of DT-enabling technologies.

DataXflow: Synergizing data-driven modeling with best parameter fit and optimal control – An efficient data analysis for cancer research

Building data-driven models is an effective strategy for information extraction from empirical data. Adapting model parameters specifically to data with a best fitting approach encodes the relevant information into a mathematical model. Subsequently, an optimal control framework extracts the most efficient targets to steer the model into desired changes via external stimuli. The DataXflow software framework integrates three software pipelines, D2D for model fitting, a framework solving optimal control problems including external stimuli and JimenaE providing graphical user interfaces to employ the other frameworks lowering the barriers for the need of programming skills, and simultaneously automating reoccurring modeling tasks. Such tasks include equation generation from a graph and script generation allowing also to approach systems with many agents, like complex gene regulatory networks. A desired state of the model is defined, and therapeutic interventions are modeled as external stimuli. The optimal control framework purposefully exploits the model-encoded information by providing those external stimuli that effect the desired changes most efficiently. The implementation of DataXflow is available under https://github.com/MarvelousHopefull/DataXflow.We showcase its application by detecting specific drug targets for a therapy of lung cancer from measurement data to lower proliferation and increase apoptosis. By an iterative modeling process refining the topology of the model, the regulatory network of the tumor is generated from the data. An application of the optimal control framework in our example reveals the inhibition of AURKA and the activation of CDH1 as the most efficient drug target combination. DataXflow paves the way to an agile interplay between data generation and its analysis potentially accelerating cancer research by an efficient drug target identification, even in complex networks.

Near-earth asteroids classification using NGBoost classifier

Near-Earth asteroids (NEAs) are celestial bodies that orbit within close to Earth, offering valuable insights into the early solar system's formation and posing potential hazards due to impact events. This work presents a comprehensive overview of NEAs, encompassing their historical significance, characteristics, impact hazards, and prospects. The study outlines the NASA Asteroids Classification Dataset and discusses its importance for research on asteroid classification and risk assessment. Furthermore, the methodology section delineates the utilization of the NGBoost classifier for predictive modeling tasks, detailing data collection, preprocessing, model training, evaluation, and result interpretation. Results from the NGBoost classifier demonstrate high accuracy and performance metrics in classifying asteroids, underscoring its efficacy in advancing asteroid classification efforts and informing planetary defense strategies. NEAs pose a potential threat to our planet, and their classification is essential for understanding their properties and predicting their trajectories accurately. In this research, we explore the application of NGBoost, a powerful gradient-boosting framework, for classifying NEAs based on their orbital and physical characteristics. We present a dataset comprising features extracted from known NEAs and non-NEAs and demonstrate the efficacy of NGBoost in accurately distinguishing between these classes. Our results indicate promising performance metrics with 99.22% accuracy, suggesting that NGBoost holds potential as a valuable tool in asteroid classification.

From the Lab to the Wild: Affect Modeling Via Privileged Information

How can we reliably transfer affect models trained in controlled laboratory conditions ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-vitro</i> ) to uncontrolled real-world settings ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in-vivo</i> )? The information gap between in-vitro and in-vivo applications defines a core challenge of affective computing. This gap is caused by limitations related to affect sensing including intrusiveness, hardware malfunctions and availability of sensors. As a response to these limitations, we introduce the concept of privileged information for operating affect models in real-world scenarios (in the wild). Privileged information enables affect models to be trained across multiple modalities available in a lab, and ignore, without significant performance drops, those modalities that are not available when they operate in the wild. Our approach is tested in two multimodal affect databases one of which is designed for testing models of affect in the wild. By training our affect models using all modalities and then using solely raw footage frames for testing the models, we reach the performance of models that fuse all available modalities for both training and testing. The results are robust across both classification and regression affect modeling tasks which are dominant paradigms in affective computing. Our findings make a decisive step towards realizing affect interaction in the wild.

PyDTS: A Python Toolkit for Deep Learning Time Series Modelling.

In this article, the topic of time series modelling is discussed. It highlights the criticality of analysing and forecasting time series data across various sectors, identifying five primary application areas: denoising, forecasting, nonlinear transient modelling, anomaly detection, and degradation modelling. It further outlines the mathematical frameworks employed in a time series modelling task, categorizing them into statistical, linear algebra, and machine- or deep-learning-based approaches, with each category serving distinct dimensions and complexities of time series problems. Additionally, the article reviews the extensive literature on time series modelling, covering statistical processes, state space representations, and machine and deep learning applications in various fields. The unique contribution of this work lies in its presentation of a Python-based toolkit for time series modelling (PyDTS) that integrates popular methodologies and offers practical examples and benchmarking across diverse datasets.

Құрамында бор бар силикохромды қолдану арқылы төмен көміртекті феррохромды балқыту процесін термодинамикалық модельдеу

The TERRA program for calculating multicomponent heterogeneous systems, based on the principle of maximum entropy, was used to study systems with a complex chemical composition, in which the task of numerical modeling is chemical and phase transformations play an important role. The effect of charge composition and temperature on the chemical and phase composition of melting products was studied, the degree of transition of charge elements into metal was determined, and optimal conditions for obtaining the alloy were found. The thermodynamic analysis of the ferrochromium production process showed that in order to approach the real process of low-carbon ferrochromium smelting, it is necessary to take into account the degree of silicon use by introducing oxygen into the working fluid to oxidize excess silicon according to the calculation. On the basis of the performed thermodynamic analysis, it is also shown that the choice of the process temperature (1750-1800°C and more) is associated with the kinetic conditions of melting, the melting temperature of the formed metal and slag. Therefore, it is expected that the presence of boron oxide, in addition to stabilizing slag from decomposition, will reduce its melting point, and the early appearance of the liquid phase due to low-temperature boron phases will ensure a shift in the reduction reactions of chromium with silicon to the low-temperature region. All these provisions will be implemented during high-temperature experimental work on the development of technological parameters.

MRG-T: Mask-Relation-Guided Transformer for Remote Vision-Based Pedestrian Attribute Recognition in Aerial Imagery

Nowadays, with the rapid development of consumer Unmanned Aerial Vehicles (UAVs), utilizing UAV platforms for visual surveillance has become very attractive, and a key part of this is remote vision-based pedestrian attribute recognition. Pedestrian Attribute Recognition (PAR) is dedicated to predicting multiple attribute labels of a single pedestrian image extracted from surveillance videos and aerial imagery, which presents significant challenges in the computer vision community due to factors such as poor imaging quality and substantial pose variations. Despite recent studies demonstrating impressive advancements in utilizing complicated architectures and exploring relations, most of them may fail to fully and systematically consider the inter-region, inter-attribute, and region-attribute mapping relations simultaneously and be stuck in the dilemma of information redundancy, leading to the degradation of recognition accuracy. To address the issues, we construct a novel Mask-Relation-Guided Transformer (MRG-T) framework that consists of three relation modeling modules to fully exploit spatial and semantic relations in the model learning process. Specifically, we first propose a Masked Region Relation Module (MRRM) to focus on precise spatial attention regions to extract more robust features with masked random patch training. To explore the semantic association of attributes, we further present a Masked Attribute Relation Module (MARM) to extract intrinsic and semantic inter-attribute relations with an attribute label masking strategy. Based on the cross-attention mechanism, we finally design a Region and Attribute Mapping Module (RAMM) to learn the cross-modal alignment between spatial regions and semantic attributes. We conduct comprehensive experiments on three public benchmarks such as PETA, PA-100K, and RAPv1, and conduct inference on a large-scale airborne person dataset named PRAI-1581. The extensive experimental results demonstrate the superior performance of our method compared to state-of-the-art approaches and validate the effectiveness of mask-relation-guided modeling in the remote vision-based PAR task.