Advanced Mathematical Models Research Articles

Data-driven recurrent neural networks modeling of cyanobacteria growth in bubble columns reactors under sparging with CO2-enriched Air

Cultivating carbohydrate-enriched microalgae in photobioreactors is a recognized method for converting atmospheric carbon dioxide (CO2) into valuable resources, offering a solution to combat industrial CO2 emissions. Achieving global carbon neutrality by 2050 necessitates an annual reduction of approximately 1.4 gigatons of CO2. To address this challenge, we developed a machine learning-based black box model using data from the Institute of Advanced Materials for Sustainable Manufacturing at ITESM. This dataset encompasses hourly operational parameters collected over eleven months, including temperature, pressure, and flow rate. These parameters were essential for a microalgal cultivation experiment using the cyanobacterium Desertifilum tharense and CO2-enriched air. Two 100-L photobioreactor systems were employed. Leveraging the sequential dataset, we deployed a long short-term memory network (LSTM) to predict CO2 percentages at reactor outlets, indirectly indicating algae biomass production. Seven input variables were selected on the basis of their impact on system behavior. Using advanced machine learning time series mathematical models can boost process intensification tasks through advanced process optimization, simulation, and control goals.

Recent Advances in Mathematical Modeling of Reaction Kinetics: A Critical Review

Recent Advances in Mathematical Modeling of Reaction Kinetics: A Critical Review

Use of Mathematical Modeling Tools to Support Decision-Making in Medicine

This research paper focuses on the development of advanced mathematical models for disease diagnosis and prediction, and the subsequent creation of automated systems based on these models. These systems leverage a range of mathematical models and incorporate cutting-edge information technology achievements to provide medical professionals with valuable decision-making support. By amalgamating mathematical rigor and technological innovation, this research endeavors to enhance the accuracy and efficiency of medical diagnoses, thereby improving patient care and healthcare outcomes. This study delves into the persistent need for contemporary information systems, where information plays a crucial role in decision-making. It aims to provide an objective approach to addressing pressing medical challenges, particularly in disease diagnosis and prediction, enhancing the effectiveness of these critical tasks. Automated medical information systems, built on advanced mathematical models, significantly empower physicians. Machine diagnostics, relying on deterministic logic, the phase interval method, and information-probabilistic logic, bolster diagnostic capabilities. Functional entropy enables individuals to handle vague information, aiding decision-making. Assessing imprecision and uncertainty computationally diminishes subjectivity, while employing fuzzy set theory enhances diagnostic modeling. Mathematical models assess diagnostic indicators, and linguistic variables quantify resemblance. The diagnostic model for primary biliary cirrhosis and active hepatitis utilizes a diagnostic table and gradient projection. This comprehensive study advances medical diagnostics through mathematical models and automated systems, addressing critical healthcare challenges.

Research on the Application and Optimization of Mathematical Models in Financial Market Risk Management

This paper applied mathematical models to conduct an in-depth discussion and empirical analysis of financial market risk management. The daily rate of return data on the S&P 500 index, selected through data processing, included data cleaning, return calculation, data standardization, construction of the GARCH (1, 1) model, and a Copula model for predicting and analyzing risks. Empirical results indicate that the GARCH model has good simulation in capturing the market volatility change, while the Copula model holds clear advantages in modeling multivariate risk dependencies. In the modern economy, managing risks in the financial market plays a vital role. Optimization algorithms such as genetic algorithms and Bayesian optimization significantly improve the prediction accuracy and computational efficiency of the model. Compared with traditional historical simulation methods, these models perform better in risk prediction indicators (VaR and ES), proving their practicality and effectiveness in actual risk management. The research results verify that advanced mathematical models and optimization methods have important application value in financial market risk management, providing a scientific decision-making basis for investors and risk managers.

The Evaluation and Development of University English Teaching Quality Based on Wireless Network Artificial Intelligence

This study introduces a novel approach to address deficiencies in prior teaching quality assessment systems by establishing a mathematical model for evaluation. Utilizing a neural network trained via a particle swarm optimization algorithm (PSO), the method develops a BP (Backpropagation) model fine-tuned by PSO to capture the intricate relationships among diverse indicators influencing teachers’ teaching quality assessment and resulting evaluations. Empirical findings highlight the effectiveness of artificial neural networks in constructing a comprehensive evaluation framework accommodating a wide spectrum of systematic assessments. This approach not only optimizes teaching methodologies but also augments overall teaching efficacy and the quality of educational delivery in a holistic manner. Moreover, it fosters the cultivation of multifaceted individuals proficient in English application skills, contributing to the development of high-quality talent in practical and complex domains. The convergence of advanced mathematical modeling techniques and computational methods, alongside the utilization of numerous indicators, aligns with combinatorial principles, exploring the permutations and relationships of diverse factors impacting teaching quality assessment.

Matlab Class for Rapid Visualization of Missile-Target Engagement Scenarios

In this paper, the authorial Matlab Battlespace Visualization Class (MBVC) is proposed to plan, design, and compose the preliminary version of the desired computer animation, which can then be used both as a background for the discussion of the final composition and as an individual project for public presentation, providing a visual reference for missile-target engagement simulations. As a design tool, the MBVC allows us the combination of the advanced mathematical models of missile guidance loop elements (implemented in the discrete form as program scripts) with the capabilities offered by open, powerful, and flexible 3D graphical engine. As a visualization tool, the MBVC allows the designers to present their research findings in both an illustrative and informative way, providing a visual reference for the computer simulation. The class is freely available for scientific, engineering or educational use.

Computational Engineering Advancements: General Review of Mathematical Modeling in Computer Engineering Applications

The comprehensive review explored the advancements in computational engineering with a focus on the role of mathematical modeling in computer engineering applications. The research investigated various mathematical models that used in different computer engineering fields, including software engineering, hardware design, and networking. It also examined the importance of mathematical modeling and its impact on solving complex engineering problems. The study highlighted emerging trends in mathematical modeling, such as reduced-order modeling, multiscale modeling, and uncertainty quantification. It also explored cutting-edge computational tools and techniques, such as high-performance computing, GPU acceleration, and meshless methods, which enabled engineers to conduct more efficient and accurate simulations. Furthermore, the integration of artificial intelligence and machine learning in mathematical modeling was discussed, emphasized the growing significance of data-driven models and surrogate modeling in computer engineering applications. The research identified industries that was benefit from enhanced computational engineering approaches, including aerospace, energy, healthcare, finance, and manufacturing. Through case studies, successful implementations of mathematical models in real-world engineering projects were presented, showcasing the practical implications of these advancements. The review also addressed challenges in adopting advanced mathematical models, such as computational complexity, data limitations, and model interpretability, and proposes potential solutions to address these issues.

Splitting for strength: Manipulating polymerization reactor split ratios to control mechanical and rheological properties in bimodal polyethylene resins

AbstractThis study integrates advanced mathematical modeling and experimental methodologies to investigate the simultaneous impact of modifications in the split ratio and molecular weight (MW) of chains on the rheological and mechanical properties of bimodal polyethylene (BiPE) resins. The outcomes underscored the viability of fine‐tuning the molecular weight distribution (MWD) of a BiPE resin by augmenting the MW of high molecular weight (HMW) chains while simultaneously diminishing their proportion in the final alloy formulation. In addition, the experimental results illuminated the prospect of attaining a targeted melt flow index for the final polymers by elevating the MW of HMW chains alongside an increase in the proportion of low molecular weight chains. Significantly, these adjustments resulted in remarkable enhancements in the shear thinning index and strain hardening modulus of the fabricated resins.

ANALYSIS OF RESEARCH ON PLANETARY GEARBOXES OF ARMORED VEHICLES (REVIEW ARTICLE)

The work is devoted to the review of modern trends in the research and use of planetary gearboxes of armored vehicles. An analysis of the areas of application of mechanical transmissions was carried out. The advantages and disadvantages of using gear gearboxes as part of mechanical transmissions are described. The design features of the use of gears in transmissions are considered. The requirements for gear gearboxes as part of transmissions are defined. The advantages and disadvantages of using planetary gearboxes and their areas of use are analyzed. The classification of mechanical adjustable gears according to general features, as well as individual ones, is considered. An overview of the fulfillment of the conditions for increasing reliability was carried out, taking into account the design features of stepped gearboxes, which are divided into three groups: simple gearboxes (with fixed shaft axes); planetary gearboxes (with movable shaft axes); combined (combination of a simple and planetary gearbox in one unit). A brief review of modern approaches to planetary gear box modeling, taking into account inertial, elastic, dissipative, transformer and frictional properties, taking into account other characteristic features of the planetary series, is carried out. An analysis of known ways of solving problems of such modeling was carried out. Modern methods of calculating the strength of planetary gearboxes, including those with partial destruction, and corresponding software complexes are analyzed. The need for the development of more advanced mathematical models that adequately describe the stress-strain state in gear engagements has been identified. Keywords: design, planetary gearboxes, mechanical transmission, influence of operating factors, diagnostic parameters, synthesis of kinematic schemes

MODELING A RED BLOOD CELL CYTOSKELETON: INSIGHTS AND TIPS

The aim of this work is to provide a clear and ready-to-implement mathematical model to describe the red blood cell (RBC) cytoskeleton. The motivation for this methodo- logy work lies in the lack of available sources facilitating the implementation of computational (in silico) modelling of RBC mechanical properties. Our approach adopts a worm-like chain force model to mimic an individual spectrin deformation and the virtual work principle to extrapolate the spectrin network dynamics. We report modelling tips using coarse-grained scaling techniques and optical tweezers experiments. We validate the model in virtual expe- riments gaining insights on single spectrin equilibrium, the impact of cytoskeletal symmetry defects on system behaviour, and stress transmission and distribution within the network. By performing these virtual experiments, we elucidate the role that the cytoskeleton plays in de- termining the remarkable RBC mechanical behaviour. These findings emphasise the need to consider the cytoskeleton component in the latest and most advanced single-cell mathematical models.

Facilitating “Omics” for Phenotype Classification Using a User-Friendly AI-Driven Platform: Application in Cancer Prognostics

Precision medicine approaches often rely on complex and integrative analyses of multiple biomarkers from “omics” data to generate insights that can help with either diagnostic, prognostic, or therapeutical decisions. Such insights are often made using machine learning (ML) models that perform sample classification for a particular phenotype (yes/no). Building such models is a challenge and time-consuming, requiring advanced coding skills and mathematical modelling expertise. Artificial intelligence (AI) is a methodological solution that has the potential to facilitate, optimize, and scale model development. In this work, we developed an AI-based, user-friendly, and code-free platform that fully automated the development of predictive models from quantitative “omics” data. Here, we show the application of this tool with the development of cancer survival prognostics models using real-life data from breast, lung, and renal cancer transcriptomes. In comparison to other models, our generated models rendered performances with competitive sensitivities (72–85%), specificities (76–85%), accuracies (75–85%), and Receiver Operating Characteristic curves with superior Areas Under the Curve (ROC-AUC of 77–86%). Further, we reported the associated sets of genes (biomarkers) and their expression patterns that were predictive of cancer survival. Moreover, we made our models available as online tools to generate prognostic predictions based on the gene expressions of the biomarkers. In conclusion, we demonstrated that our tool is a robust, user-friendly solution for developing bespoke predictive tools from “omics” data, which facilitate precision medicine applications to the point-of-care.

APPLICATIONS OF MATHEMATICAL MODELLING IN PHARMACEUTICAL FORMULATION AND PROCESS DEVELOPMENT

Pharmaceutical development and authorization stages have high requirements that increase labour and costs. Risks for product quality and process robustness also increase in parallel with complex practices existing in the pharmaceutical industry and emerging as a result of developments. Although it is challenging to eliminate parameters leading to increased risks, there is need to appropriately manage the risks likewise arrange decision making processes. Designing and optimizing formulation and production processes to deliver the predetermined product quality is known as Quality by Design (QbD) in pharmaceutical development. In terms of data and knowledge, QbD can be carried out using a variety of technologies in this process. Mathematical modelling is one of these tools allows for the quick formation of subject knowledge, which may subsequently be used in an independent or integrated manner and to produce Design of Experiments (DOE). Response surface method (RSM), Artificial Neural Network (ANN), Genetic Algorithm (GA) are some of the assistive technologies used in mathematical modelling that enables to enlighten the effect of formulation and process variables on product quality attributes. The use of advanced mathematical modelling techniques in formulation and process development has become widespread and it appears to be beneficial in different areas of pharmaceutical development.

Thermodynamic Evaluation of the Surface Tension and Viscosity of Liquid Quaternary Alloys: The Ti-Al-Cr-Nb System

Surface tension and viscosity of complex Ti-based industrial alloys are important for simulation of liquid assisted industrial processes such as casting, joining, crystal growth and infiltration. Modelling of the interface and mass transport during liquid-solid phase transition requires reliable surface tension and viscosity data. Therefore, to obtain accurate predictions of microstructural evolution during solidification related processes, only reliable input data are necessary. In the case of liquid Ti-Al alloys, the experimental difficulties related to high temperature measurements and reactivity of these alloys with supporting materials or containers as well as inevitable presence of oxygen may lead to data gaps including a complete lack of property data. An alternative for container-based methods are containerless processing techniques that offer a significant accuracy improvement and / or make possible to measure temperature and composition dependent thermophysical properties of metallic melts, as in the case of the Ti-Al-Cr-Nb system. Advanced mathematical models and computer simulations, developed in several theoretical frameworks, can be used to compensate the missing data; on the other side, for the validation of theoretical models, the experimental data are used. In the present work, an evaluation of the surface tension and viscosity of liquid Ti-Al-Cr-Nb alloys by means of the predictive models and a comparison to the available experimental data were done. The proposed methodology is a tool to assess the reliability of thermophysical properties data of multicomponent alloy systems.

A Forward Solution Algorithm of 6RUS Parallel Mechanism Based on Dual Quaternion Method

The 6RUS parallel manipulator is a highly versatile and widely used robotic mechanism with six degrees of freedom. Its intricate kinematic structure and its capability to perform complex motion tasks have garnered significant research interest in recent years. The kinematic analysis of the 6RUS mechanism plays a crucial role in understanding its operational characteristics and optimizing its performance for various applications. In this paper, we present a state-of-the-art kinematic algorithm for the 6RUS parallel manipulator. Our algorithm is aimed at addressing the challenges associated with accurately determining the pose and motion of the end-effector relative to the base, considering the complexity of the mechanism’s architecture. By leveraging advanced mathematical modeling techniques and utilizing efficient computational algorithms, our proposed algorithm offers improved accuracy, efficiency, and robustness in determining the kinematic parameters of the 6RUS mechanism. The key contributions of this work include the development of a comprehensive forward and inverse kinematic model for the 6RUS parallel manipulator, incorporating the effects of joint constraints, singularities, and workspace limitations. We also present a detailed analysis of the algorithm’s performance in comparison to existing approaches, demonstrating its superiority in terms of computational efficiency and accuracy. The proposed kinematic algorithm holds significant potential for enhancing the design, control, and trajectory planning of 6RUS parallel manipulators. It provides a solid foundation for advanced applications such as robotic surgery, industrial automation, and virtual reality systems. The results presented in this paper contribute to the growing body of knowledge in parallel manipulator research and pave the way for future developments in the field.

Pitfalls of Using Multinomial Regression Analysis to Identify Class-Structure-Relevant Variables in Biomedical Data Sets: Why a Mixture of Experts (MOE) Approach Is Better

Recent advances in mathematical modeling and artificial intelligence have challenged the use of traditional regression analysis in biomedical research. This study examined artificial data sets and biomedical data sets from cancer research using binomial and multinomial logistic regression. The results were compared with those obtained with machine learning models such as random forest, support vector machine, Bayesian classifiers, k-nearest neighbors, and repeated incremental clipping (RIPPER). The alternative models often outperformed regression in accurately classifying new cases. Logistic regression had a structural problem similar to early single-layer neural networks, which limited its ability to identify variables with high statistical significance for reliable class assignments. Therefore, regression is not per se the best model for class prediction in biomedical data sets. The study emphasizes the importance of validating selected models and suggests that a “mixture of experts” approach may be a more advanced and effective strategy for analyzing biomedical data sets.

Two-Leak Case Diagnosis Based on Static Flow Model for Liquid Transmission Pipelines.

The article deals with a diagnosis of multiple leaks from liquid transmission pipelines using analytical methods. Such solutions, based on advanced mathematical models of pipeline flow dynamics, usually turn out to be very complex and time-consuming. However, under certain operating conditions, a simpler approach may also be useful. Such an idea is presented in this paper, proposing two simplified methods for diagnosing double leakages. In principle, these methods apply to both simultaneous and non-simultaneous leaks. The first one uses a static model of a pipeline involving two leaks and takes advantage of the minimization of the objective function defined as the squared deviation of the modeled pressures from the pressures measured on the pipeline. The second method uses a pipeline flow model of a static type in combination with a gradient indicator aimed at detecting leaks and employing algorithms assigned to determining the location and size of leaks. The results of methods' validation, based on tests carried out with the use of measurement data obtained from an experimental water pipeline, were also presented. The outcomes of the performed tests proved the methods' effectiveness in terms of detection, isolation, localization, and intensity estimation of both simultaneous and non-simultaneous double leakages.

Development, validation, and testing of advanced mathematical models for the optimization of BESS operation

Current decarbonization strategies are driven by the fast-paced diffusion of non-programmable renewable energy sources (NP-RESs), mainly through solar and wind power generation. Energy storage technologies are emerging as key solutions for coping with the variability and low-inertia characteristics of NP-RESs. Particularly, battery energy storage systems (BESS) are diffusing more widely for both behind-the-meter (BTM) and utility-scale applications. In this context, we still lack a shared solution on how to proceed from the on-field data collected about the performance of BESS to reliable and fast mathematical formulations for operational optimization. This study provides a validated modeling framework that can be exploited during or after BESS commissioning to (i) identify and derive the useful parameters to characterize BESS performances, (ii) formalize them in a mathematical formulation while being aware of its specific trade-off between accuracy and computational effort, and (iii) exploit the selected BESS model within a multi-energy system optimization problem. We discuss three different modeling approaches that we developed for optimizing BESS operation, with each providing a different balance between modeling accuracy and computational effort. These three mathematical models were validated against a numerical simulation model based on on-field performance data, and they were eventually tested on a reference case study. The results indicate that it is possible to restrict the average error in estimating BESS efficiency while simultaneously limiting the computational effort of the model. Regarding the operation of BESS, the conducted simulations demonstrate that an approximate BESS model may result in an overestimation of the expected revenues.

The Whole Is Greater Than The Sum of Its Parts: Large-scale Phenomena Arising from Small-Scale Biophysical Processes.

The symposium "Large-scale biological phenomena arising from small-scale biophysical processes" at the SICB 2023 Annual General Meeting focused on the cross-disciplinary exploration of emergent phenomena in biology. Interactions between cells or organisms at small scales within a system can govern patterns occurring at larger scales in space, time, or biological complexity. This theme recurs in many sub-disciplines of biology, including cell and developmental biology, evolution, and ecology. This symposium, and the associated special issue introduced here, showcases a wide range of cross-disciplinary collaborations among biologists, physicists, and engineers. Technological advancements in microscopy and microfluidics, as well as complementary advances in mathematical modelling and associated theory demonstrate the timeliness of this issue. This introduction seeks to provide useful background information to place the studies within this issue in a broader biophysical context and highlight similarities in ideas and approaches across systems and sub-disciplines. We hope to demonstrate that cross-disciplinary research linking small-scale biophysics to larger-scale emergent phenomena can help us understand problems ranging from single-cell behaviors to tissue formation and function, evolution of form, and the dynamics of communities.

Mathematical modeling, analysis and control in soft robotics: a survey

This paper reviews some recent advances in mathematical modeling, analysis and control, both from the theoretical and numerical viewpoints, in the emergent field of soft robotics. The presentation is not focused on specific prototypes of soft robots, but in a more general description of soft smart materials. The goal is to provide a unified and rigorous mathematical approach to open-loop control strategies for soft materials that hopefully might lay the seeds for future research in this field.

Glymphatic transport is reduced in rats with spontaneous pituitary tumor.

Pituitary tumor in patients induces adverse alterations in the brain, accompanied by cognitive deficits. Dysfunction of glymphatic waste clearance results in accumulation of neurotoxic products within the brain, leading to cognitive impairment. However, the status of glymphatic function in the brain with pituitary tumor is unknown. Using magnetic resonance imaging (MRI) and an advanced mathematical modeling, we investigated the changes of glymphatic transport in the rats carrying spontaneous pituitary tumor. Rats (22-24 months, female, Wistar) with and without pituitary tumor (n = 7/per group) underwent the identical experimental protocol. MRI measurements, including T2-weighted imaging and dynamic 3D T1-weighted imaging with intracisternal administration of contrast agent, were performed on each animal. The contrast-induced enhancement in the circle of Willis and in the glymphatic influx nodes were observed on the dynamic images and verified with time-signal-curves (TSCs). Model-derived parameters of infusion rate and clearance rate that characterize the kinetics of glymphatic tracer transport were evaluated in multiple representative brain regions. Our imaging data demonstrated a higher incidence of partially enhanced circle of Willis (86 vs. 14%; p < 0.033) and a lower incidence of enhancement in glymphatic influx nodes of pituitary (71 vs. 100%) and pineal (57 vs. 86%) recesses in the rats with pituitary tumor than in the rats with normal appearance of pituitary gland, indicating an intensification of impaired peri-vascular pathway and impeded glymphatic transport due to the presence of pituitary tumor. Consistently, our kinetic modeling and regional cerebral tissue quantification revealed significantly lower infusion and clearance rates in all examined regions in rats with spontaneous pituitary tumor than in non-tumor rats, representing a suppressed glymphatic transport in the brain with pituitary tumor. Our study demonstrates the compromised glymphatic transport in the rat brain with spontaneous pituitary tumor. The reduced efficiency in cerebral waste clearance increases the risk for neurodegeneration in the brain that may underlie the cognitive impairment commonly seen in patients with pituitary tumors.