Mathematical Validation Research Articles

DEVELOPMENT OF AUGMENTED REALITY-BASED MATHEMATICS LEARNING MEDIA TO FACILITATE STUDENTS' MATHEMATICAL COMPUTATIONAL THINKING SKILLS

The development of digital technology has positively impacted the world of education, especially in creating more interactive and innovative learning media. The integration of Augmented Reality (AR) in learning is one of the innovations that can provide new learning experiences for students by presenting visualizations of abstract concepts in real life. This research aims to develop AR-based mathematics learning media to facilitate students' mathematical computational thinking skills. The research method used is Research and Development (R&D) with the ADDIE development model (Analysis, Design, Development, Implementation, Evaluation). The research subjects involved 16 Insan Cendekia Sheikh Yusuf Gowa High School students. The research instruments used included product validation sheets, learner and teacher response questionnaires, and mathematical computational thinking ability tests. Analysis of research data focused on analyzing the validity, practicality, and effectiveness of Augmented Reality-based mathematics learning media. The results showed that the Augmented Reality-based mathematics learning media developed had met the criteria of validity, practicality, and effectiveness.

Hybrid Brown-Bear and Hippopotamus Algorithms with Fractional Order Chaos Maps for Precise Solar PV Model Parameter Estimation

The rise in photovoltaic (PV) energy utilization has led to increased research on its functioning, as its accurate modeling is crucial for system simulations. However, capturing nonlinear current–voltage traits is challenging due to limited data from cells’ datasheets. This paper presents a novel enhanced version of the Brown-Bear Optimization Algorithm (EBOA) for determining the ideal parameters for the circuit model. The presented EBOA incorporates several modifications aimed at improving its searching capabilities. It combines Fractional-order Chaos maps (FC maps), which support the BOA settings to be adjusted in an adaptive manner. Additionally, it integrates key mechanisms from the Hippopotamus Optimization (HO) to strengthen the algorithm’s exploitation potential by leveraging surrounding knowledge for more effective position updates while also improving the balance between global and local search processes. The EBOA was subjected to extensive mathematical validation through the application of benchmark functions to rigorously assess its performance. Also, PV parameter estimation was achieved by combining the EBOA with a Newton–Raphson approach. Numerous module and cell varieties, including RTC France, STP6-120/36, and Photowatt-PWP201, were assessed using double-diode and single-diode PV models. The higher performance of the EBOA was shown by a statistical comparison with many well-known metaheuristic techniques. To illustrate this, the root mean-squared error values achieved by our scheme using (SDM, DDM) for RTC France, STP6-120/36, and PWP201 are as follows: (8.183847 × 10−4, 7.478488 × 10−4), (1.430320 × 10−2, 1.427010 × 10−2), and (2.220075 × 10−3, 2.061273 × 10−3), respectively. The experimental results show that the EBOA works better than alternative techniques in terms of accuracy, consistency, and convergence.

Reliability and Sustainability Integrated Design Optimization for Engineering Structures with Active Machine Learning Technique

Recent strategic plans from many governments share the same emphasis on sustainable development goals. The construction industry is recognized as one of the primary contributors to greenhouse gas emissions. Stimulated by such political and practical requirements, this research aims to develop a reliability and sustainability integrated design optimization (RSIDO) framework for engineering structures. Statistical modelling is conducted which provides probabilistic models for embodied carbon coefficients (ECCs). The proposed RSIDO framework contains three main stages. The first stage solves the classical reliability-based design optimization (RBDO) problem. The second stage conducts the reliability-based embodied carbon quantification to define the sustainable reliability constraint. Lastly, the new sustainable probabilistic design constraint is embedded in the design question. Furthermore, to overcome the computational difficulty, an active-learning extended-support vector regression (AL-X-SVR) technique is proposed to improve the computational efficiency of the proposed framework. The embedded regression algorithm is presented with consolidated theoretical backgrounds. Further, an active learning strategy is implemented to select the learning samples efficiently. The applicability and effectiveness of the proposed AL-X-SVR method are demonstrated using a highly nonlinear-constrained mathematical validation. Additionally, the RSIDO framework is demonstrated through three engineering applications. This research contributes a comprehensive framework that not only addresses reliability and sustainability but also enhances computational efficiency, thereby introducing an innovative approach to design optimization in building engineering.

Nonlinear dynamics of the complex periodic coupled system via a proportional generalized fractional derivative

Abstract The objective of this work is to study the intricate dynamics of nonlinear periodic coupled systems, introducing a novel approach based on the proportional fractional generalized derivative. We establish and rigorously derive sufficient conditions for the existence, uniqueness, and stability of solutions for these systems. This ensures the mathematical validity of the systems, making them reliable for simulations, predictions, and control design. This represents a significant advancement in the field of fractional-order systems. Our analysis utilizes the Banach contraction mapping principle and the Leray-Schauder alternative to ensure the well-posedness of the system. We present a detailed mathematical analysis to discuss the stability outcomes, making the results accessible and readily applicable to a wide range of problems. Furthermore, to showcase the versatility and practical implications of our approach, we present a concrete example. This demonstration highlights the novelty and impact of our research, underscoring the power of the Caputo generalized proportional fractional derivative-based periodic coupled system.

UNRAVELING THE IMPACT OF THE MEMORY, THE COMPETITION, AND THE LINEAR HARVESTING ON A LOTKA-VOLTERRA MODEL

The harvesting of population has a dominant influence in balancing the ecosystem. In this manuscript, the impact of harvesting in addition to competition, and memory effect on a prey-predator interaction following the Lotka-Volterra model is studied. The mathematical validation is provided by proofing that all solutions of the model are always exist, non-negative, and bounded. Obeying Matignon condition, Lyapunov function, and generalized LaSalle invariance principle, the local and global stability are investigated. To complete the analytical results, some numerical simulations are given to show the occurrence of forward bifurcation and the impact of the memory index. All results state that three possible circumstances may occur namely the extinction of both populations, the prey-only population, and the co-existence of both populations.

Applications of distance measure between dual hesitant fuzzy sets in medical diagnosis and weighted dual hesitant fuzzy sets in making decision

This paper introduces a novel distance measure for dual hesitant fuzzy sets (DHFS) and weighted dual hesitant fuzzy sets (WDHFS), with a rigorous proof of the triangular inequality to ensure its mathematical validity. The proposed measure extends the normalized Hamming, generalized, and Euclidean distance measures to dual hesitant fuzzy elements (DHFE), offering a broader framework for handling uncertainty in fuzzy environments. Additionally, the utilization of a score function is shown to simplify the computation of these distance measures. The practical relevance of the proposed measure is demonstrated through its application in medical diagnosis and decision-making processes. A comparative analysis between the newly introduced distance measure denoted as χ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi$$\\end{document}, and an existing measure, χ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\chi _1$$\\end{document} is performed to underscore the superiority and potential advantages of the new approach in real-world scenarios.

Mathematical modelling and validation of the mechanical properties of HVOF-sprayed WC-12Co coatings considering the phase composition and defects generated at different process parameters

The thermal spraying process involves many machine-based parameters or independent variables (fuel flow rate, oxygen flow rate, powder feed rate, stand-off distance and many others in the HVOF process). Any combination of these parameters produces only two measurable responses, namely, particle temperature and particle velocity. In this current work, first, the machine-based spray parameters are varied in specific ways to produce different particle temperatures at near-constant velocities and vice-versa. This approach has reduced the number of independent variables to only two. These two factors further influence the in-flight particle reactions, thereby affecting the phase composition and the microstructural defects in the as-sprayed coatings. The X-ray diffraction patterns of the as-sprayed coatings revealed the presence of W2C, W, Co3W9C4, and amorphous Co-W-C phases apart from the WC phase. The W2C and W originated owing to the decarburization of the WC phase. On the other hand, the dissolution of the carbide in molten binder led to the formation of Co3W9C4 and the amorphous Co-W-C phase. The nano-hardness of both the carbide and binder phases increased with an increase in particle temperature owing to a higher degree of decarburization and carbide dissolution respectively. The porosity was the most significant micro-structural defect present in the as-sprayed coatings. An increase in either particle temperature or velocity reduced the porosity present in the as-sprayed coatings. The mechanical properties (microhardness, elastic modulus and indentation fracture toughness) tend to improve as porosity decreases. A comprehensive mathematical model is proposed to predict the mechanical properties of as-sprayed coatings as a function of composition and defects. Finally, the process maps of mechanical properties were plotted in temperature-velocity space.

GEPAF: A non-monotonic generalized activation function in neural network for improving prediction with diverse data distributions characteristics

The world today has made prescriptive analytics that uses data-driven insights to guide future actions. The distribution of data, however, differs depending on the scenario, making it difficult to interpret and comprehend the data efficiently. Different neural network models are used to solve this, taking inspiration from the complex network architecture in the human brain. The activation function is crucial in introducing non-linearity to process data gradients effectively. Although popular activation functions such as ReLU, Sigmoid, Swish, and Tanh have advantages and disadvantages, they may struggle to adapt to diverse data characteristics. A generalized activation function named the Generalized Exponential Parametric Activation Function (GEPAF) is proposed to address this issue. This function consists of three parameters expressed: α, which stands for a differencing factor similar to the mean; σ, which stands for a variance to control distribution spread; and p, which is a power factor that improves flexibility; all these parameters are present in the exponent. When p=2, the activation function resembles a Gaussian function. Initially, this paper describes the mathematical derivation and validation of the properties of this function mathematically and graphically. After this, the GEPAF function is practically implemented in real-world supply chain datasets. One dataset features a small sample size but exhibits high variance, while the other shows significant variance with a moderate amount of data. An LSTM network processes the dataset for sales and profit prediction. The suggested function performs better than popular activation functions when a comparative analysis of the activation function is performed, showing at least 30% improvement in regression evaluation metrics and better loss decay characteristics.

Nonlinear mathematical modeling of frequency-temperature dependent viscoelastic materials for tire applications

Understanding and accurately reproducing the realistic response of rubber materials to external stimuli is a crucial research topic that involves all the engineering fields and beyond where these materials are used. This study introduces an innovative nonlinear fractional derivative generalized Maxwell model designed to effectively capture and replicate the experimental behavior of viscoelastic materials. The proposed model addresses the limitations observed in conventional fractional models, providing greater versatility which makes it more suitable for describing the intricate behavior of polymeric materials. Through rigorous mathematical validation, the proposed model demonstrates coherence with the underlying physics of the viscoelastic behavior. To address the identification procedure, the pole-zero formulation is adopted, employing a multi-objective optimization to obtain the optimum, able to replicate the dynamic moduli trends. Satisfying results have been validated over a wide dataset of 10 different materials, demonstrating an extended capability of adapting to different variations than classical widely-used fractional models. Furthermore, the model has proven to be valid even employing a reduced amount of experimental data limited only to low, high-frequency plateaus and around the glass transition temperature, which could be fundamental for optimizing resources in experimental investigations.

Enhancing stochastic optimization: investigating fixed points of chaotic maps for global optimization

<p>Chaotic maps, despite their deterministic nature, can introduce controlled randomness into optimization algorithms. This chaotic map behaviour helps overcome the lack of mathematical validation in traditional stochastic methods. The chaotic optimization algorithm (COA) uses chaotic maps that help it achieve faster convergence and escape local optima. The effective use of these maps to find the global optimum would be possible only with a complete understanding of them, especially their fixed points. In chaotic maps, fixed points repeat indefinitely, disrupting the map's characteristic unpredictability. While using chaotic maps for global optimization, it is crucial to avoid starting the search at fixed points and implement corrective measures if they arise in between the sequence. This paper outlines strategies for addressing fixed points and provides a numerical evaluation (using Newton's method) of the fixed points for 20 widely used chaotic maps. By appropriately handling fixed points, researchers and practitioners across diverse fields can avoid costly failures, improve accuracy, and enhance the reliability of their systems.</p>

Application of the Biological Toxicity Effect Ratio (BER) Method for Advancing Water Quality Criteria Derivation.

Water quality criteria (WQC) serve as a scientific foundation for pollutant risk assessment and control in aquatic ecosystems. The development of regionally differentiated WQC tailored to specific regional characteristics has become an emerging trend. However, the current WQC is constrained by a lack of regional species toxicity data. To address these limitations, this study proposes the biological toxicity effect ratio (BER) method, which indirectly reflects the toxicity sensitivity of the overall aquatic ecosystem through the toxicity information on a limited number of species, enabling rapid WQC prediction. Using the established WQC in China and the USA as a case study, we combined mathematical derivation and data validation to evaluate the BER method. Among various species-taxon groups of freshwater organisms, planktonic crustaceans demonstrated the highest predictive accuracy. Our analysis further revealed that species toxicity sensitivity and regional variability jointly influence the prediction accuracy. Regardless of the evaluation indexes, planktonic crustaceans emerged as the most suitable species-taxon group for the BER method. Additionally, the BER method is particularly applicable to pollutants with conserved mechanisms across species. This study systematically explores the feasibility of using the BER method and offers new insights for deriving regionally differentiated WQC.

Improved solution thermodynamics modeling in pervaporation

The current work features a system-level design of pervaporation processes (typically utilized to break azeotropes) that is solution thermodynamics-based (inclusive of validated excess thermodynamic properties). Unlike the standard pervaporation modeling methodology in the literature, the current method (referred to here as PervapS3) deconstructs the membrane module into its constituent units, and the material and energy flows were mathematically validated. These amendments to the previous methodology (i.e., leaf-wise modeling, mathematical validation, and inclusion of excess thermodynamic properties) revealed significant deviations in key parameter values. For a given large-scale pervaporation process dehydrating aqueous isopropanol, the total membrane area and energy requirement calculated were up to 22% and 19% less than the values calculated using the previous methodology. Moreover, due to the inclusion of excess thermodynamic properties in the PervapS3 method, the minimum separation work and the second law (thermodynamic) efficiency were up to 94% and 78% less. In other words, the previous pervaporation modeling methodology overestimated membrane area, energy requirement, minimum separation work, and second law efficiency. Considering a conventional azeotropic distillation process for comparison with pervaporation, it was observed that the simulation-based distillation models from the literature were inclusive of the system non-idealities. Per the previous method, the non-ideal second law efficiency of azeotropic distillation would be compared against the ideal second law efficiency of pervaporation, overestimating the latter. The non-ideal second law efficiency must be employed to facilitate a fairer and more accurate comparison of disparate separation technologies.

Digital Twins in Type 1 Diabetes: A Systematic Review.

Digital twin is a new concept that is rapidly gaining recognition especially in the medical field. Indeed, being a virtual representation of real-world entities and processes, a digital twin can be used to accurately represent the patients' disease, clarify the treatment target, and realize personalized and precise therapies. However, despite being a revolutionary concept, the diffusion of digital twins in type 1 diabetes (T1D) is still limited. In this systematic review, we analyzed structure, operating conditions, and characteristics of digital twins being developed for T1D. Our search covered published documents until March 2024: 220 publications were identified, 37 of which were duplicated entries; in addition, 173 publications were removed after inspection of titles, abstracts, and keywords; and finally, 11 publications were fully reviewed, of which 8 were deemed eligible for inclusion. We found that all eight methodologies are not comprehensive multi-scale virtual replicas of the individual with T1D, but they all focus on describing glucose-insulin metabolism, aiming to simulate glucose concentration resultant from therapeutic interventions. In this review, we will compare and analyze different factors characterizing these digital twins, such as operating principles (mathematical model, twinning procedure, validation and assessment) and the key aspects for practical adoption (inclusion of physical activity, data required for twinning, open-source availability). We will conclude the paper listing which, in our opinion, are the current limitations and future directives of digital twins in T1D, hoping that this article can be helpful to researchers working on diabetes technologies to further develop the use of such an important instrument.

Introducing bimodal sea-states in a hybrid model for nearshore wave processes

HySwash has been recently developed as a fast and effective hybrid method to predict nearshore wave processes under unimodal wave conditions. However, global wave climates, and especially those in the tropical regions where coral reefs are hosted, are usually exposed to multiple incoming wave systems, resulting in several energy peaks corresponding to coexisting swells and wind seas. Moreover, although the full distribution of wave runup can have a significant impact on the assessment of vulnerable low-lying tropical regions, predictive models of flooding usually synthesize wave runups to an extreme percentile value, overlooking its full distribution. To enhance the capabilities of HySwash, in the present work, the inclusion of bimodality, as well as the prediction of the complete wave runup distribution is presented. This involves adapting the sampling, selection, and interpolation algorithms together with the hydrodynamic modeling that constitutes the original HySwash methodology. The positive mathematical validation reinforces the applicability of HySwash for a variety of coastal applications. Furthermore, a comparison is conducted between extreme wave runups induced by bimodal sea states and unimodal sea states, providing insights into the impact of multimodality on wave runup extremes.

A model for saturated–unsaturated flow with fractures acting as capillary barriers

AbstractHigh‐resolution modeling of the flow dynamics in fractured soils is highly complex and computationally demanding as it requires precise geometrical description of the fractures in addition to resolving a multiphase free‐flow problem inside the fractures. In this paper, we present an idealized model for saturated–unsaturated flow in fractured soils that preserves the core aspects of fractured flow dynamics using an explicit representation of the fractures. The model is based on Richards’ equation in the matrix and hydrostatic equilibrium in the fractures. While the first modeling choice is standard, the latter is motivated by the difference in flow regimes between matrix and fractures, that is, the water velocity inside the fractures is considerably larger than in the soil even under saturated conditions. On matrix/fracture interfaces, the model permits water exchange between matrix and fractures only when the capillary barrier offered by the presence of air inside the fractures is overcome. Thus, depending on the wetting conditions, fractures can either act as impervious barriers or as paths for rapid water flow. Since in numerical simulations each fracture face in the computational grid is a potential seepage face, solving the resulting system of nonlinear equations is a nontrivial task. Here, we propose a general framework based on a discrete‐fracture matrix approach, a finite volume discretization of the equations, and a practical iterative technique to solve the conditional flow at the interfaces. Numerical examples support the mathematical validity and the physical applicability of the model.

DEVELOPMENT OF INTERACTIVE MULTIMEDIA LEARNING MATHEMATICS LEARNING MEDIA USING ADOBE FLASH CS6

Ongoing advancements have profoundly reshaped the development of educational media, with validity being a pivotal factor in creating high-quality products, representing a critical phase in their development. In essence, validity holds a key position in the production of superior educational materials. The primary objective of this study is to design and assess the validity of interactive multimedia-based mathematics learning tools using Adobe Flash CS6. This research belongs to the category of Research and Development (R&D) or developmental research. The methodology adopted for this developmental research follows a modified Plomp procedure, involving three of its five stages: the initial investigation phase, the development phase or prototyping, and the assessment phase. To gauge the validity of the media, the research employs a validation sheet as the data collection instrument. The analysis process entails scoring based on assessments made by the validator. The outcomes of the validation testing indicate that the media is deemed highly valid, achieving an impressive validation rate of 90.59%. The media is now deemed ready for use with only minor revisions required. One notable advantage of this learning media is its compact size, ensuring compatibility with all computer types, including those with low specifications.

Enhancing milk quality assessment with watermelon (Citrullus lanatus) urease immobilized on VS2-chitosan nanocomposite beads using response surface methodology

An eco-friendly hydrothermal method synthesized VS2 nanosheets. Several spectroscopic and microscopic approaches (TEM) were used to characterize the produced VS2 nanosheet microstructure. VS2, Chitosan, and nanocomposite were used to immobilize watermelon (Citrullus lanatus) urease. Optimization using the Response Surface Methodology and the Box-Behnken design yielded immobilization efficiencies of 65.23 %, 72.52 %, and 87.68 % for chitosan, VS2, and nanocomposite, respectively. The analysis of variance confirmed the mathematical model's validity, enabling additional research. AFM, SEM, FTIR, Fluorescence microscopy, and Cary Eclipse Fluorescence Spectrometer showed urease conjugation to the matrix. During and after immobilization, FTIR spectra showed a dynamic connectivity of chemical processes and bonding. The nanocomposite outperformed VS2 and chitosan in pH and temperature. Chitosan and VS2-immobilized urease were more thermally stable than soluble urease, but the nanocomposite-urease system was even more resilient. The nanocomposite retained 60 % of its residual activity after three months of storage. It retains 91.8 % of its initial activity after 12 reuse cycles. Nanocomposite-immobilized urease measured milk urea at 23.62 mg/dl. This result was compared favorably to the gold standard p-dimethylaminobenzaldehyde spectrophotometric result of 20 mg/dl. The linear range is 5 to 70 mg/dl, with a LOD of 1.07 (±0.05) mg/dl and SD of less than 5 %. The nanocomposite's ksel coefficient for interferents was exceptionally low (ksel < 0.07), indicating urea detection sensitivity. Watermelon urease is suitable for dairy sector applications due to its availability, immobilization on nanocomposite, and reuse.

Student profiles based on in‐game performance and help‐seeking behaviours in an online mathematics game

AbstractWell‐designed online educational games can improve students' math knowledge, skills and engagement; however, more research is needed to understand how to formatively assess components of students' mathematical understanding and learning as students solve problems in online educational games. In this study, we examined how 7th‐grade students' (N = 760) in‐game performance (ie, strategy efficiency, mathematical validity of the first action, mathematical errors) and help‐seeking behaviours (ie, hint requests) correlated with their algebraic knowledge in an online mathematics game. The k‐means cluster analysis identified four groups of students based on their in‐game metrics, and some variabilities in their in‐game performance were found. Although hint requests were available, only a few students showed a high percentage of hint requests during their gameplay. The regression analysis revealed that students' in‐game performance and help‐seeking behavioural patterns explained a significant amount of variance in students' algebraic knowledge above and beyond their prior knowledge. Our results suggest that how students interact with the online learning game is related to their later math performance, and qualitative aspects of student behaviours captured using log data provide meaningful information to students' algebraic understanding. Practitioner notesWhat is already known about this topic Well‐designed online educational games can improve students' math knowledge, skills, and engagement. Several studies found that some in‐game metrics, such as in‐game progress or correctness of tasks, are positively associated with learning outcomes. However, many studies used simple metrics like the correctness of each task or the number of problems completed to measure students' performance in the game. Few studies measured more in the moment or qualitative aspects of student in‐game performance, for example, how efficiently students solved problems in the game. What this paper adds In‐game metrics measuring more in the moment and qualitative aspects of students' problem‐solving explained a significant amount of variance in students' algebraic knowledge above and beyond students' prior knowledge. Students' strategy efficiency and strategic planning were positively associated with students' math problem‐solving performance. Although hints were available for almost all problems, only a few students exhibited a high level of help‐seeking behaviours, and the students with the lowest in‐game performance who needed help the most showed low help‐seeking behaviours. Implications for practice and/or policy Classifying students into profiles could provide ways to identify students with different levels of problem‐solving skills and help teachers provide more personalized instruction. Teachers could use this information as a formative assessment to identify the core areas of intervention needed, particularly for students struggling with math concepts taught in the game. Instructional strategies that make hints more appealing or engaging to students might be needed.

Abstract 7381: Mathematical modeling and validation of mechanistic target of rapamycin and N-myristoyltransferase signaling pathways in breast cancer

Abstract Hormone receptor-positive (HR+) breast cancer (BC) makes up approximately 65% of all breast cancers diagnosed. The prognosis for early-stage disease is excellent with mainstay endocrine therapy (ET). Despite the effectiveness of standard ET, as many as 41% of HR+ early-stage BC diagnosed women will experience distant recurrence. The resistance to endocrine therapy and recurrence is partly attributed to the activation of the insulin pathway and the independence of HR+ BC cells on the ER pathway for their growth. Earlier, we demonstrated the crosstalk between insulin/mTOR and ER pathways. N-myristoyltransferase (NMT) exists in humans in two paralogues (NMT1 and NMT2) that catalyze myristoylation reaction. Recent studies from our laboratory demonstrated that NMTs are downstream targets of insulin and ER pathways. In this study, we have designed mathematical models using differential equations to study the activation of the insulin pathway and its effect on NMT. The mathematical modeling incorporated the partition of cellular organelles and the sequential flow of information with cascades of equations representing signaling reactions. The activated mathematical model was designed by activating the insulin receptor (IR) or insulin-like growth factor receptor (IGF1R) and compared with the control model. The mathematical models were validated by wet lab experiments. The HR+ BC cells (MCF7) were treated with insulin or IGF1 for short term and long term. The expression patterns of NMT1, NMT2, and mTOR were determined by cell fractionation and western blot analysis. The results revealed the correlation between the differential expression patterns of NMTs and the proliferation of MCF7 cells when the insulin pathway was activated by insulin or IGF. The mathematical modeling was validated by simulations and data fittings. The results demonstrated that differential equation-based mathematical modeling could predict the NMT-related oncogenic changes in HR+ BC cells. Citation Format: Abinash Meher, Shailly Varma Shrivastav, Anouska Agarwal, Sheen Dube, Stephanie Portet, Anuraag Shrivastav. Mathematical modeling and validation of mechanistic target of rapamycin and N-myristoyltransferase signaling pathways in breast cancer [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 7381.

Design and Analysis of a Low Voltage Simulink Model (LVSM) of IEEE 57 Bus

The present power system is gaining momentum towards designing equivalent circuit models. The Ward and REI methods involve the admittance reduction method as well as being merged with the EMS model to derive boundary parameters, but these methods are limited and valid for a predefined condition. Therefore, it is required to design an equivalent circuit that adopts the real power system for analysis. In this paper, a new method is proposed to design a scaled-down power system model without changing the impedance of components. In this regard, a Low Voltage Simulink Model (LVSM) of the IEEE 57 bus network was designed in MATLAB/ Simulink so that it could be useful for laboratory model design purposes. The main objectives of this paper are to propose a mathematical procedure to scale down the network parameters and design a 3-phase LVSM of an IEEE 57 bus power system network within the Simulink platform. The performance of LVSM was analyzed with no-load, balanced load, and unbalanced load models. These simulation studies were validated and compared with the theoretical results to prove that the proposed LVSM modeling has good mathematical accuracy, robustness, and validity for practical model implementation.