Modeling Equations Research Articles

Description and Modeling of Relevant Demographic and Laboratory Variables in a Large Oncology Cohort to Generate Virtual Populations

Background/Objectives: Pathophysiological variability in patients with cancer is associated with differences in responses to pharmacotherapy. In this work, we aimed to describe the demographic characteristics and hematological, biochemical, and coagulation variables in a large oncology cohort and to develop, optimize, and provide open access to modeling equations for the estimation of variables potentially relevant in pharmacokinetic modeling. Methods: Using data from 1793 patients with cancer, divided into training (n = 1259) and validation (n = 534) datasets, a modeling network was developed and used to simulate virtual oncology populations. All analyses were conducted in RStudio 4.3.2 Build 494. Results: The simulation network based on sex, age, biogeographic origin/ethnicity, and tumor type (fixed or primary factors) was successfully validated, able to predict age, height, weight, alpha-1-acid glycoprotein, albumin, hemoglobin, C-reactive protein and lactate dehydrogenase serum levels, platelet–lymphocyte and neutrophil–lymphocyte ratios, and hematocrit. This network was then successfully extrapolated to simulate the laboratory variables of eight oncology populations (n = 1200); only East Asians, Sub-Saharan Africans, Europeans, only males, females, patients with an ECOG performance status equal to 2, and only patients with pancreas cancer or ovarian cancer. Conclusions: this network constitutes a valuable tool to predict relevant characteristics/variables of patients with cancer, which may be useful in the evaluation and prediction of pharmacokinetics in virtual oncology populations, as well as for model-based optimization of oncology treatments.

New equivalent resistance formula of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m\ imes n$$\\end{document} rectangular resistor network represented by Chebyshev polynomials

In the process of exploring the field of circuits, obtaining the exact solution of the equivalent resistance between two nodes in a resistor network has become an important problem. This paper aims to introduce Chebyshev polynomial of the second kind to improve the equivalent resistance formula of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m\ imes n$$\\end{document} rectangular resistor network, thereby improving the calculation efficiency. Additionally, the discrete sine transform of the first kind (DST-I) is utilized to solve the modeling equation. Under the condition of applying the new equivalent resistance formula, several equivalent resistance formulas with different parameters are given, and three-dimensional views are used to illustrate them. Six comparison tables are provided to showcase the advantages of the improved explicit formula in terms of computational efficiency, as well as the relationship between resistivity and the maximum size of the resistor network that the formula can effectively handle. This may provide more convenient and effective technical support for research and practice in electronic engineering and other related fields.

TorchSISSO: A PyTorch-based implementation of the sure independence screening and sparsifying operator for efficient and interpretable model discovery

Symbolic regression (SR) is a powerful machine learning approach that searches for both the structure and parameters of algebraic models, offering interpretable and compact representations of complex data. Unlike traditional regression methods, SR explores progressively complex feature spaces, which can uncover simple models that generalize well, even from small datasets. Among SR algorithms, the Sure Independence Screening and Sparsifying Operator (SISSO) has proven particularly effective in the natural sciences, helping to rediscover fundamental physical laws as well as discover new interpretable equations for materials property modeling. However, its widespread adoption has been limited by performance inefficiencies and the challenges posed by its FORTRAN-based implementation, especially in modern computing environments. In this work, we introduce TorchSISSO, a native Python implementation built in the PyTorch framework. TorchSISSO leverages GPU acceleration, easy integration, and extensibility, offering a significant speed-up and improved accuracy over the original. We demonstrate that TorchSISSO matches or exceeds the performance of the original SISSO across a range of tasks, while dramatically reducing computational time and improving accessibility for broader scientific applications.

The housing quality impacts on women’s self-efficacy during the outbreak of the COVID-19 pandemic: A case study of Kerman, Iran

ABSTRACT This study investigates the impact of housing quality on women's self-efficacy during the COVID-19 pandemic lockdowns using a mixed-method approach. By employing Interpretive Structural Modelling (ISM) and Structural Equation Modelling (SEM), the research initially identified key housing quality indicators through ISM, which was guided by an extensive literature review and expert interviews. These indicators were subsequently incorporated into a Likert scale questionnaire administered to 466 women in Kerman Province, Iran, who were directly affected by the pandemic. The SEM analysis revealed a positive and significant correlation between secure housing environments and well-constructed residential structures with women's self-efficacy during the pandemic. In contrast, access to urban services did not exhibit a significant impact. This study highlights the critical role of housing quality in supporting women's health and well-being during crises and provides valuable insights for urban planning and policy development aimed at alleviating psychosocial stress among women in confined settings, thereby enhancing overall family life satisfaction.

A Review on the Mathematical Modelling of the Grain Storage Ecosystemin Storage Structures and Bags

The grain storage ecosystem comprises of biotic and abiotic factors that interact during grain storage, and their interaction affects the quality of the stored grains over time. The understanding and management of the complex interaction of the biotic and abiotic factors in the stored grain ecosystem is crucial to decision-making and in the development of management strategies for grain farmers and elevators. Mathematical modelling has emerged as an essential approach in tackling complex systems such as the stored grain ecosystem. This review explores the application of mathematical modelling in the grain storage ecosystem and synthesizes the existing literature, highlighting the various mathematical models and approaches to solving issues relating to the grain storage ecosystem. The review will be helpful to researchers and stored grain experts in the grain industry on the various mathematical modelling approaches and equations that can be employed to solve problems associated with grain storage in order to better manage the quality of stored grain.

Estimate Mass Density Value as A Priori Information for Gravity by using Bayesian Markov Chain Monte Carlo (MCMC)

<p class="Abstract">In the gravity method, information about mass density value is very important because it will influence the characteristic of the 1-D gravity acceleration graph. However, it is quite difficult to guess the mass density value so that is suitable to the 1-D acceleration graph. This is called “a priori” information. Trial and error way is one way to solve this problem. It is a very random value guess also. To make sure that the initial guess of mass density is a good parameter, Bayesian Markov Chain Monte Carlo (MCMC) can be used. It generates many possibilities from the guess value and then these possibilities will be selected to the best one by likelihood way. The validation is expressed by the random graph as a consequence of the iteration number step of the possibilities. This research is started by using certain values of mass density to create a synthetic model for the field data in Banggai Sula because the area has a complex geology. The synthetic model is used because the gravity forward modelling equation has the sinusoidal form. After Bayesian MCMC is applied to the initial mass density value, it will produce a new mass density value or the estimation value with its response to the 1-D gravity acceleration synthetic graph. Finally, this information will be very useful to create the 2D or 3D inverse modelling in Gravity.</p>

Process Intensification in Distillation using HiGee Rotating Packed Bed

For decades, improving the gas-side mass transfer coefficient in rotating packed beds has been a formidable challenge. Distillation, often limited by gas-phase resistance, requires substantial innovation to enhance these coefficients. Rotating packed beds offer a distinct advantage over conventional columns, primarily due to the intense micro-mixing within fluid channels. This micro-mixing significantly boosts mass transfer between phases and facilitates rapid attainment of steady-state conditions, making them a superior choice for processes where gas-side resistance is the bottleneck. The current study emphasis on the mass transfer performance of rotating packed for acetone water system with two different packing materials viz., wire mesh and ceramic beads. Working principle of HiGee, typical flow pattern, modeling equations have been discussed in this paper. The effects of rotational speed, gas flow rates and radial thickness of the packing on mass transfer performance were also investigated. The mass transfer coefficients of the rotating packed bed HiGee were increased with increasing the rotational speed. The Height Equivalent to Theoretical Plates (HETP) of the rotating packed bed used in this study was 5-6 times less than the conventional packed columns. This study contributes to significantly advancing the industrial applications of rotating packed beds.

Performance of wind turbine system based on a brushless doubly fed reluctance generator and a six pulse bridge cycloconverter

In this paper, a variable speed wind energy conversion system (WECS) made with a six pulse bridge cycloconverter and a brushless doubly fed reluctance generator (BDFRG) is investigated. The novelty of the proposed work is to use a brushless doubly fed reluctance generator and a six pulses cycloconverter for working in high power and for reducing the cost, also the proposed work use a maximum power point tracking algorithm to capture the optimal power available in the wind in order to increase the efficiency of the system. The power control of this system is applied, to capture the maximum power from the wind by using a maximum power point tracking (MPPT) control technique, to achieve the independent control of the active and reactive powers exchanged between the wind generator and the grid, also to test the possibility to operate in two quadrant modes (subsynchronous and supersynchronous modes). The dynamic modeling equations that describe the suggested system are presented here. The results of the simulation are shown in order to illustrate the performance and efficiency of this system.

The Fulfillment of Psychological Contract and Job Satisfaction in Reducing Procrastination of Employees Working in the Public SectorPublic Sector

This research aims to examine the factors that influence procrastination among education staff at a university. The research used mono methods: quantitative method, survey strategy, and cross-sectional research design. The data were collected by questionnaires distributed offline and online via Google Forms to 145 education staff at a state university in Yogyakarta. The data were analyzed using the Structural Equation Modeling equation based on Partial Least Square (SEM PLS). The research found that achievement motivation and organizational commitment influence procrastination directly and through the mediation of fulfilling the psychological contract. Meanwhile, job satisfaction does not significantly affect procrastination, nor does it mediate the influence of achievement motivation and organizational commitment on procrastination. The research results were then discussed according to the characteristics of organizations in the public sector in higher education.

Research on Sevengill Eel Population and Ecosystem Stability Based on Sex Ratio Changes

This study utilizes mathematical modeling, including difference and differential equations, to analyze the impact of gender ratio changes in seven-gill eels on ecosystem dynamics. The model incorporates population growth, gender ratio variations, and interactions with other ecosystem components. The findings reveal that a balanced sex ratio supports optimal population growth and ecosystem stability, while a male-dominated population reduces biodiversity and increases resource competition. Food availability and predator presence significantly affect the sex ratio, influencing the ecosystem's overall health. Using the TOPSIS method, the study determines that a higher proportion of females is most beneficial for ecosystem stability. Maintaining an optimal sex ratio is essential for ecosystem health, providing valuable insights for conservation and management efforts.

A Review of Comprehensive Guidelines for Computational Fluid Dynamics (CFD) Validation in Solar Chimney Power Plants: Methodology and Manzanares Prototype Case Study

This review provides a comprehensive examination of CFD modeling procedures for SCPP, with an emphasis on the detailed methodologies and a case study of the Manzanares prototype in Spain. The introduction delineates the historical context and physical modeling principles of solar chimneys, while highlighting their potential in industrial applications. The governing equations are meticulously discussed, covering assumptions in both 2D and 3D CFD modeling, the continuity and momentum equations, and the selection and accuracy of turbulence models, particularly the k-ε equations. The review also delves into heat transfer modeling, encompassing the energy equation and radiation modeling. Analytical evaluations of turbine pressure drop ratios and performance metrics for power generation efficiency are critically analyzed. The establishment of boundary conditions in solar chimney applications, including sky temperature assessments and distinctions between 2D and 3D boundary conditions, is extensively explored. Mesh generation techniques for both 2D and 3D CFD models are presented, supported by case studies. Parametric studies and experimental investigations are scrutinized to elucidate their impact on the performance of solar chimneys. The temperature–entropy diagram for an idealized Brayton cycle is introduced as a conceptual framework for efficiency analysis. Validation of the CFD codes, both 2D and 3D, against experimental data is performed to ensure model accuracy. The review further examines energy balance approaches in modeling solar chimneys, presenting state-of-the-art CFD results and discussing their implications in both 2D and 3D contexts. The synthesis of these findings culminates in a comprehensive conclusion, offering insights into the future directions and potential advancements in the CFD modeling of solar chimneys. This work aims to serve as a definitive reference for researchers and practitioners in the field, providing a robust foundation for the development and optimization of SCPP technology.

Review of physics-informed machine-learning inversion of geophysical data

We review five types of physics-informed machine-learning (PIML) algorithms for inversion and modeling of geophysical data. Such algorithms use the combination of a data-driven machine-learning (ML) method and the equations of physics to model or invert geophysical data (or both). By incorporating the constraints of physics, PIML algorithms can effectively reduce the size of the solution space for ML models, enabling them to be trained on smaller data sets. This is especially advantageous in scenarios in which data availability may be limited or expensive to obtain. In this review, we restrict the physics to be that from the governing wave equation, either as a constraint that must be satisfied or by using numerical solutions of the wave equation for modeling and inversion. This approach ensures that the resulting models adhere to physical principles while leveraging the power of ML to analyze and interpret complex geophysical data. There are several potential benefits of PIML compared to standard numerical modeling or inversion of seismic data computed by, for example, finite-difference solutions to the wave equation. 1) Empirical tests suggest that PIML algorithms constrained by the physics of wave propagation can sometimes resist getting stuck in a local minima compared with standard full-waveform inversion (FWI). 2) After the weights of the neural network are found by training, then the forward and inverse operations by PIML can be more than several orders of magnitude more efficient than FWI. However, the computational cost for general training can be enormous. 3) If the ML inversion operator [Formula: see text] is locally trained on a small portion of the recorded data [Formula: see text], then there is sometimes no need for millions of training examples that aim for global generalization of [Formula: see text]. The benefit is that the locally trained [Formula: see text] can be used to economically invert the remaining test data [Formula: see text] for the true velocity [Formula: see text], where [Formula: see text] can comprise more than 90% of the recorded data.

Exploring Selectivity of Supercritical-CO2 for Vitamin E Extraction from Canola Seeds

AbstractThe objective of the current study was to investigate the selectivity of supercritical-CO2 for extraction and concentration of Vitamin E components from canola seeds. The selectively extracted Vitamin E in supercritical-CO2 solvent was related to pressure, temperature, and density through the developed thermodynamic modeling approach. The results suggested that increased pressure and density would enhance the selectivity of supercritical-CO2 solvent, consequently obtaining highly concentrated Vitamin E. The thermodynamic modeling equations have correlated the selectivity of supercritical-CO2 solvent for extracting Vitamin E in terms of processing conditions including pressure, temperature, and density of the supercritical-CO2 solvent fluid. The activity coefficient in thermodynamic modeling was involved with those key parameters that are important in determining selectivity, concentration, and extraction results. The supercritical-CO2 solvent can be made highly selective by precisely controlling the operating pressure and temperature. This allowed the supercritical-CO2 solvent to achieve the desired density in the supercritical phase, thereby enhancing the selectivity for targeted components. The thermodynamic mathematical modeling offered valuable insights for enhancing extraction processes in industrial settings. A high regression coefficient via linear structural modeling analysis indicated that the response equation fitted with the experimental data (R2 = 0.8737). The experimental results for the separation parameters provide optimal selectivity of supercritical-CO2 solvent for extracting and concentrating Vitamin E compounds for establishing commercial production.

Identification Of Accountability With Competence, Community Participation And Information Technology In The Village Of Langkat District

This study aims to examine the effect of village government competence, community participation and utilization of information technology on accountability in villages in the Langkat Regency area. This research design is associative quantitative research. Data collection using a questionnaire with 244 respondents consisting of Planning, Budgeting, Administration, Reporting and Data Compilation in 47 villages in the Langkat Regency area. This research uses the SEM-Partial Least Square (PLS) approach. PLS is a component or variant-based Structural Equation Modeling (SEM) equation model. The results of this study indicate that the competence of village government, community participation and utilization of information technology have a positive effect on the accountability of village financial management. The implications of the results of this study prove that village financial accountability can be identified by factors of village government competence, community participation and the use of information technology that is adopted effectively and on target.

How Wanghong Live Streamers Affect Online Users’ Purchasing Behavior on Live Streaming Platforms: A PLS-SEM Approach

ABSTRACT Considering the distinct effects of the Wanghong group in retaining online consumers, more and more live streamers tend to accept the Wanghong economy and aim to become Wanghong live streamers. Although existing scholars have investigated the relationship between live streamers and online consumers, limited studies have discussed how Wanghong live streamers affect online consumers’ watching interest and lead to their final purchasing behaviors. To explore their purchasing decision-making process, this paper draws on the Attention-Interest-Desire-Action (AIDA) model and divides the process into Attention, Interest, Desire, and Action units. Through the data analysis based on the partial least squares path modeling and variance-based structural equation modeling (PLS-SEM), both attractive appearance and social interaction designed by Wanghongs positively affect online consumers’ watching interest, generate their purchasing desires, and cause their final purchasing behaviors. The research results are helpful for related scholars and network industries to understand the interactive mechanism between online consumers and Wanghongs. Exploring the distinct effect of this group will be beneficial in driving the development of the Wanghong economy and improving the environment of live streaming economy.

Fishermen Empowerment: The Key Role of Human Capital and Joint Business Group Performance in Improving Welfare in Kendari City, Indonesia

This study examines the influence of human capital and the performance of joint business groups on the empowerment of fishing communities in Kendari City. The research was conducted in Kendari City, Southeast Sulawesi Province, from October to December 2023. The study population comprises all fishermen who are members of the Joint Business Group, abbreviated as KUB, in Nambo Subdistrict, Kendari City, amounting to 142 individuals. The sample for this study was determined using the census method, which entailed the inclusion of the entire population, or 142 fishermen, as a sample. The exogenous variables in the study, namely human capital and the performance of the fishermen Joint Business Group (KUB), while the endogenous variable, namely the empowerment of the fishing community itself. The research data were analyzed using descriptive statistics to describe or describe the status of human capital variables, the performance of the Joint Business Group (KUB), and the empowerment of fishing communities. Inferential statistics were used to describe and explain the fishing community empowerment model with Partial Least Square (PLS), a Structural Equation Modeling (SEM) equation model. The results show that human capital has a positive and significant effect on the performance of joint business groups and the empowerment of fishing communities. In addition, the performance of joint business groups has a positive and significant contribution in improving the empowerment of fishing communities. The indirect effect of human capital is positive and significant through the performance of joint business groups on the empowerment of fishing communities in Kendari City. So that the empowerment of fishing communities will be able to be achieved by increasing the human capital of fishermen through the effective implementation of the Joint Business Group (KUB) program as a forum for learning and community self-development.

Risk conscious investment

The risk conscious investor is defined as the maximizer of a conservative valuation or a dynamic nonlinear expectation. Both the static and dynamic problems are addressed using distortions of tail probabilities or distortions of tail measures. The multivariate static problem is solved in the context of the multivariate bilateral gamma model. For the dynamic model states and their transitions are modeled in two ways. The first defines states by a parametric model for the return distribution with transitions described by a continuous-time finite state Markov chain between the distributional possibilities. In the second model states are represented by the first four power variations with transitions given by (OU) equations for modeling stochastically the first four power variations as Tempered Fractional Lévy Processes (TFLP). Numerical solutions for policy functions are implemented in trading 768 equity assets over seven years ending December 2021.

Modeling of Filtration and Heat and Mass Transfer Processes in Groundwater

Purpose. The method of mathematical modeling is an important tool for solving complex problems involving the analysis of groundwater dynamics and heat and mass transfer processes in them when studying their contamination from various anthropogenic sources in the event of accidental spills of chemically hazardous substances, etc. The main purpose of the article is to develop a set of mathematical models for calculating the process of filtration of non-pressure groundwater, mass transfer of impurities and the process of heat transfer in groundwater. Methodology. The two-dimensional Boussinesq equation of filtration was used to predict the dynamics of groundwater. The two-dimensional equation of convective-diffusive transport of impurities was used to model the processes of mass transfer in groundwater. The process of freezing of individual sections of the groundwater flow is modeled using the Laplace equation for the velocity potential (calculation of the flow velocity field in a time-varying geometry) and the two-dimensional equation of heat transfer in groundwater. Finite difference schemes were used to solve the modeling equations of groundwater dynamics and heat and mass transfer. Findings. A set of mathematical models has been developed to calculate the process of filtration of non-pressure groundwater and its chemical contamination. The experiment has confirmed the adequacy of the constructed numerical model of filtration of a non-pressure groundwater flow. An effective mathematical model was developed that allows determining the temperature fields in groundwater during the operation of a well used to freeze certain sections of the flow. The results of computer modeling indicate the effectiveness of the developed mathematical models. Originality. Effective mathematical models for predicting the level of chemical contamination of groundwater, its dynamics and thermal regime are proposed. The constructed mathematical models make it possible to determine the dynamics of changes in the temperature regime of groundwater during the operation of wells through which refrigerant is supplied to freeze individual areas. A computer program has been developed that allows for a comprehensive assessment of groundwater conditions. Practical value. A set of computer programs has been developed to conduct a computational experiment to study the processes of filtration, chemical contamination of groundwater and heat transfer processes in them. This set of programs can be used for the scientific substantiation of engineering solutions aimed at protecting groundwater.

Development and validation of the Upstream Social Interaction Risk Scale (U-SIRS-13): a scale to assess threats to social connectedness among older adults.

Social interactions are essential to social connectedness among older adults. While many scales have been developed to measure various aspects of social connectedness, most are narrow in scope, which may not be optimally encompassing, practical, or relevant for use with older adults across clinical and community settings. Efforts are needed to create more sensitive scales that can identify "upstream risk," which may facilitate timey referral and/or intervention. The purposes of this study were to: (1) develop and validate a brief scale to measure threats to social connectedness among older adults in the context of their social interactions; and (2) offer practical scoring and implementation recommendations for utilization in research and practice contexts. A sequential process was used to develop the initial instrument used in this study, which was then methodologically reduced to create a brief 13-item scale. Relevant, existing scales and measures were identified and compiled, which were then critically assessed by a combination of research and practice experts to optimize the pool of relevant items that assess threats to social connectedness while reducing potential redundancies. Then, a national sample of 4,082 older adults ages 60 years and older completed a web-based questionnaire containing the initial 36 items about social connection. Several data analysis methods were applied to assess the underlying dimensionality of the data and construct measures of different factors related to risk, including item response theory (IRT) modeling, clustering techniques, and structural equation modeling (SEM). IRT modeling reduced the initial 36 items to create the 13-item Upstream Social Interaction Risk Scale (U-SIRS-13) with strong model fit. The dimensionality assessment using different clustering algorithms supported a 2-factor solution to classify risk. The SEM predicting highest risk items fit exceptionally well (RMSEA = 0.048; CFI = 0.954). For the 13-item scale, theta scores generated from IRT were strongly correlated with the summed count of items binarily identifying risk (r = 0.896, p < 0.001), thus supporting the use of practical scoring techniques for research and practice (Cronbach's alpha = 0.80). The U-SIRS-13 is a multidimensional scale with strong face, content, and construct validity. Findings support its practical utility to identify threats to social connectedness among older adults posed by limited physical opportunities for social interactions and lacking emotional fulfillment from social interactions.

Inflation and dark matter from the low entropy hypothesis and modeling mechanism of modified gravity

Abstract The hypothesis of low entropy in the initial state of the Universe usually explains the observed entropy increase is in only one time direction: the thermodynamic arrow of time. The Hamiltonian formalism is commonly used in the context of general relativity. The set of Lagrange multipliers are introduced in the formalism, and they are corresponding to the Hamiltonian constraints which are written in terms of ‘weak equality’—the equality is satisfied if the constraints hold. Follow the low-entropy hypothesis, we postulate a modeling mechanism—a weak equality (of modeling) that holds only on the subspace of the theory space of physical models defined by some modeling constraints. By applying the modeling mechanism, we obtain a specific model of modified gravity under specific modeling conditions. We derive a novel equation of modeling from the mechanism, that describes how different gravitational models emerge. The solution of the modeling equation naturally turns out to be the model of R 2-gravity (with additional terms) if ordinary matter is negligible. We also found that this mechanism leads to two models: large-field inflation and wave-like dark matter (DM). Interestingly, the wave-like DM model is supported by the most recent observations of Einstein rings.