Mathematical Model Research Articles

Sensorless Position Control in High-Speed Domain of PMSM Based on Improved Adaptive Sliding Mode Observer

To improve the speed buffering and position tracking accuracy of medium–high-speed permanent magnet synchronous motor (PMSM), a sensorless control method based on an improved sliding mode observer is proposed. By the mathematical model of the built-in PMSM, an improved adaptive super-twisting sliding mode observer is constructed. Based on the LSTA-SMO with a linear term of observation error, a sliding mode coefficient can be adjusted in real time according to the change in rotational speed. In view of the high harmonic content of the output back electromotive force, the adaptive adjustment strategy for the back electromotive force is adopted. In addition, in order to improve the estimation accuracy and resistance ability of the observer, the rotor position error was taken as the disturbance term, and the third-order extended state observer (ESO) was constructed to estimate the rotational speed and rotor position through the motor mechanical motion equation. The proposed method is validated in Matlab and compared with the conventional linear super twisted observer. The simulation results show that the proposed method enables the observer to operate stably in a wide velocity domain and reduces the velocity estimation error to 6.7 rpm and the position estimation accuracy error to 0.0005 rad at high speeds, which improves the anti-interference capability.

How cultural innovations trigger the emergence of new pathogens

Cultural practices perceived to be adaptive—from clearing land for food production to medical innovations—can disseminate quickly through human populations. However, these same practices often have unintended maladaptive effects. A particularly consequential effect is the emergence of diseases. In numerous instances, a cultural change is followed by the appearance of a new pathogen. Here, we develop mathematical models to analyze the population processes through which cultural evolution precipitates the emergence of a new disease. We find that when a risk-bearing cultural practice spreads, emergence can be an unavoidable cost even if a safer alternative practice eventually evolves from the original. Social learning and a fitness advantage associated with the evolving practice drive early disease emergence but the two factors have distinct effects on the time to mutation of the pathogen and significant stochastic variation is observed. For example, a disease can take longer to emerge in a population that adopts the risk-bearing practice quickly than in a population that is slow to transition. Extending the model to explore the effects of an alternative practice evolving from the original, we find a nonmonotonic relationship between relative risk of the two practices and the median time to disease emergence. Our findings contribute to understanding how cultural evolution can shape pathogen evolution and highlight the unpredictability of disease emergence.

Mathematical modeling of deposition and erosion in porous media with branching channels

Mathematical modeling of deposition and erosion in porous media with branching channels

Rapid biphasic decay of intact and defective HIV DNA reservoir during acute treated HIV disease

AbstractDespite antiretroviral therapy (ART), HIV persists in latently-infected cells (the HIV reservoir) which decay slowly over time. Here, leveraging >500 longitudinal samples from 67 people living with HIV (PLWH) treated during acute infection, we developed a mathematical model to predict reservoir decay from peripheral CD4 + T cells. Nonlinear generalized additive models demonstrated rapid biphasic decay of intact DNA (week 0-5: t1/2 ~ 2.83 weeks; week 5-24: t1/2 ~ 15.4 weeks) that extended out to 1 year. These estimates were ~5-fold faster than prior decay estimates among chronic treated PLWH. Defective DNA had a similar biphasic pattern, but data were more variable. Predicted intact and defective decay rates were faster for PLWH with earlier timing of ART initiation, higher initial CD4 + T cell count, and lower pre-ART viral load. In this study, we advanced our limited understanding of HIV reservoir decay at the time of ART initiation, informing future curative strategies targeting this critical time.

Economic Justice in the Design of a Sugarcane-Derived Biofuel Supply Chain: A Fair Profit Distribution Approach

Background: In agricultural supply chains, unequal bargaining power often leads to economic inequality, particularly for farmers. The fair profit distribution (FPD) approach offers a solution by optimizing supply chain flows (materials, information, and money) to promote economic equity among members. However, our literature review highlights a gap in applying the FPD approach to the facility location-allocation problem in supply chain network design (SCND), particularly in sugarcane-derived biofuel supply chains. Methods: Consequently, we propose a multi-period optimization model based on FPD to design a sugarcane biofuel supply chain. The methodology involves four steps: constructing a conceptual model, developing a mathematical model, designing a solution strategy, and generating insights. This model considers both investment (crop development, biorefinery construction) and operational phases over a long-term planning horizon, focusing on farm location and crop allocation. Results: By comparing the FPD model to a traditional centralized planning supply chain (CSC) approach, we examine the impact of the planning horizon, number of farms, and sugarcane prices paid by biorefineries on financial performance. While the FPD model results in lower overall system profits, it fosters a fairer economic scenario for farmers. Conclusions: This study contributes to economic justice in supply chains and offers insights to promote fair trade among stakeholders.

Abstract B008: Therapy-protective peristromal niches mediate positive ecological interaction between therapy-sensitive and therapy-resistant cells, altering the evolutionary dynamics of acquired targeted therapy resistance in lung cancers

Abstract Pharmacological inhibitors of oncogenic signaling, such as drugs that target ALK kinase (ALKi) in ALK+ lung cancers, can induce strong and durable clinical responses. However, targeted therapies are not curative in advanced cancers and even strong responders eventually develop resistance. While therapy resistance is typically attributed to cell-intrinsic (epi)mutational characteristics of tumor cells, it can also result from interactions of tumor cells with the tumor microenvironment (TME). In contrast to the detailed elucidation of the molecular mediators of therapy resistance, our knowledge of the evolutionary dynamics underlying the resistance emergence, including the impact of TME, remains poorly defined. A key open question in understanding the evolutionary dynamics of therapy resistance is whether relapse results from an expansion of pre-existing therapy-resistant subpopulations or from a bona fide gradual evolutionary process. To elucidate this question, we integrated experimental mouse studies with mathematical modeling, interrogating therapeutic responses of therapy-naïve experimental xenograft ALK+ tumors, spiked-in with differentially labeled resistant cells. We found that ALKi treatment induced a rapid expansion of resistant cells, which drastically reduced the magnitude and duration of remissions. Surprisingly, our in silico analyses pointed to the existence of a strong positive ecological interaction between therapy-resistant and therapy-sensitive competitors. Using a combination of spatial analyses, experimental studies, and mathematical modeling, we found that this interaction was mediated by peristromal niches that protected therapy-sensitive tumor cells. Specifically, by limiting tumor regression, the therapy- induced expansion of resistant cells limited the loss of protective peristromal niches, while the subsequent resumption of tumor growth created new peristromal niches capable of supporting the survival and proliferation of therapy-sensitive cells. While this niche-mediated interaction had only a marginal impact on the transition from remission to relapse, enhanced survival of therapy-sensitive cells potentiated their ability to adapt to ALKi, leading to a higher diversity of resistance phenotypes. In summary, our study has revealed a new type of indirect, niche-mediated ecological interaction between therapy-resistant and therapy-sensitive cells. The rapid expansion of rare pre-existent resistant cells and fast transition to relapse challenge a common assumption of the pre-existence of therapy resistance. Finally, our results highlight the essentiality of TME considerations in understanding the evolutionary dynamic underlying the development of therapy resistance. Citation Format: Mark Robertson-Tessi, Bina Desai, Tatiana Miti, Pragya Kumar, Sagnik Yarlagadda, Rishi Shah, Robert Vander Velde, Daria Miroshnychenko, David Basanta, Alexander Anderson, Andriy Marusyk. Therapy-protective peristromal niches mediate positive ecological interaction between therapy-sensitive and therapy-resistant cells, altering the evolutionary dynamics of acquired targeted therapy resistance in lung cancers [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Tumor-body Interactions: The Roles of Micro- and Macroenvironment in Cancer; 2024 Nov 17-20; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2024;84(22_Suppl):Abstract nr B008.

Abstract A040: A novel stroma-mediated positive interaction between resistant and sensitive cells in non-small cell lung cancer facilitates drug resistance

Abstract Resistance to targeted therapies, particularly those inhibiting oncogenic tyrosine kinases (TKIs), presents a significant challenge in the treatment of advanced non-small cell lung cancer (NSCLC). Despite initial robust clinical responses, tumors often relapse due to the emergence of resistant cell populations. The origins of this resistance—whether it is pre-existing in a subset of tumor cells or arises de novo during treatment—remains a critical question in understanding and combating therapeutic failure. To investigate this, we developed in silico mathematical models that integrate both pre-existing and de novo resistance mechanisms within a framework that explicitly integrates the stromal niche. Our study focused on the evolutionary dynamics of NSCLC in response to therapy, using a hybrid agent-based spatial modeling framework (HAL) to simulate tumor behavior under treatment. These models were designed to simulate the complex interactions between resistant and sensitive tumor cells, mediated by the stroma, and to predict the timing of relapse based on these interactions. Our findings suggest that stroma-mediated interactions play a crucial role in the evolutionary dynamics of therapy responses, influencing the fitness and survival of both resistant and sensitive cells. Specifically, our models predict that pre-existing resistance is unlikely to be compatible with the long remission periods observed in a substantial subset of patients treated with advanced anaplastic lymphoma kinase (ALK) inhibitors. This conclusion was supported by the observed relapse times and volumetric tumor growth data from subsequent animal models. Moreover, our analyses highlight the importance of ecological factors within the tumor microenvironment in shaping the response to therapy. The spatial models we developed reveal that the stroma can foster positive interactions between resistant and sensitive cells, thereby accelerating the emergence of resistance. These insights underscore the need to consider the stromal niche when developing new therapeutic strategies and when interpreting the dynamics of drug resistance. In conclusion, our study provides new insights into the role of stroma in mediating resistance to TKIs in NSCLC. By combining mathematical modeling with experimental data, we have elucidated how stroma-mediated interactions between tumor cells can influence the evolution of resistance, challenging the assumption that pre-existing resistance alone drives relapses in TKI-treated patients. Our findings emphasize the need for adaptive therapeutic approaches that anticipate and disrupt these microenvironmental interactions to improve patient outcomes. Citation Format: Rishi M. Shah, Sagnik Yarlagadda, Mark Robertson-Tessi, Bina Desai, Tatiana Miti, Daria Miroshnychenko, David Basanta, Andriy Marusyk, Alexander Anderson. A novel stroma-mediated positive interaction between resistant and sensitive cells in non-small cell lung cancer facilitates drug resistance [abstract]. In: Proceedings of the AACR Special Conference in Cancer Research: Tumor-body Interactions: The Roles of Micro- and Macroenvironment in Cancer; 2024 Nov 17-20; Boston, MA. Philadelphia (PA): AACR; Cancer Res 2024;84(22_Suppl):Abstract nr A040.

Mathematical model and the solution of the capillary vibration in a nanoscale deformable

The capillary effect acts a key role in our daily life, and its vibration can significantly affect its mass transmission. Here, we aim to study the vibration of the capillary in a nanoscale deformable tube. First, we present the mathematical model, and then we give a detailed study on its vibration characteristics by means of the Hamiltonian‐based method, which is based on the variational principle and Hamiltonian. In the view of the energy conservation, the residual equations are introduced to determine the frequency‐amplitude formulation. We finally verify the effectiveness and reliability of the proposed method by comparing with existing method through the numerical results. The finding in this work is expected to be helpful for the study of the nonlinear vibration.

Mathematical Model of Counteract Bandits Terrorism in Nigeria

This paper explores a mathematical model for analyzing the dynamics of banditry and terrorism, focusing on equilibrium states and stability conditions. Key concepts include the reproduction number Rb, which serves as a threshold parameter indicating the potential for spread or decline of these activities. The study finds that a banditry-free equilibrium is locally asymptotically stable when Rb < 1, suggesting that the activities will decline over time. In contrast, Rb>0 indicates the possibility of globally stable coexistence equilibrium, where banditry and terrorism persist at endemic levels. The model also identifies invariant regions, ensuring that the system's trajectories remain within certain bounds, and guarantees unique and positive solutions, essential for real-world applicability. These findings provide critical insights for developing comprehensive strategies to mitigate banditry and terrorism, highlighting the importance of addressing both root causes and immediate symptoms

Geotechnical engineering surveys and soil testing in the construction of buildings and structures

The article suggests a way to increase the efficiency of geotechnical engineering surveys through the rational use of fast approximate methods of soil testing (“express methods”). Such tests are recommended to be carried out in large volume and considered as a means of assessing the geotechnical structure of the site as a whole. In this paper, these issues are considered by the example of determining the bearing capacity of piles according to static sounding data and static tests of full-scale piles. A mathematical model for assessing the information content of the test complex based on the concepts of information theory is proposed. Calculations based on this model show that the informativeness of a large number of approximate tests may (due to the heterogeneity of the soil) exceed the informativeness of a small number of accurate tests.

Application of an Improved State Feedback Control in the Selective Catalytic Reduction Denitrification Systems of Coal Power Units Under Variable Load Conditions

Selective catalytic reduction (SCR) flue gas denitrification systems are inherently complex, typically embodying characteristics of non-linearity, significant time delays, and susceptibility to multiple disturbances. In the context of coal power units engaging in deep load cycling and rapid frequency adjustment, conventional proportional-integral-derivative (PID) control struggles to meet the demands of effective control. This study introduces a control strategy that incorporates a “state observer + Linear Quadratic Regulator (LQR) state feedback + Improved Quantum Genetic Algorithm (IQGA) optimized PID”. Initially, local linear mathematical models of an SCR denitrification system at 340 MW, 450 MW, and 540 MW loads were used to design state observer and LQR state feedback control parameters for each operational condition. At a single load point, the IQGA was employed to optimize the outer loop PID parameters, followed by simulation experiments of load increases and decreases between 340 MW and 540 MW. The results demonstrated that, compared to two other strategies, the proposed approach reduced the overshoot by a minimum of 1.5% and shortened the adjustment time by 31.7% under conditions of step disturbances and internal perturbations. Throughout variable operational conditions, the strategy consistently exhibited minimal output fluctuations, rapid adjustment capabilities, strong disturbance rejection, and robust stability. This algorithm proves to be an effective method for controlling NOx concentrations, offering insights for precise ammonia injection control in future applications.

Analysis of a fractional order epidemiological model for tuberculosis transmission with vaccination and reinfection.

This study has been carried out using a novel mathematical model on the dynamics of tuberculosis (TB) transmission considering vaccination, endogenous re-activation of the dormant infection, and exogenous re-infection. We can comprehend the behavior of TB under the influence of vaccination from this article. We compute the basic reproduction number ( ) as well as the vaccination reproduction number ( ) using the next-generation matrix (NGM) approach. The theoretical analysis demonstrates that the disease-free equilibrium point is locally asymptotically stable, and the fractional order system is Ulam-Hyers type stable. We perform numerical simulation of our model using the Adams-Bashforth 3-step method to verify the theoretical results and to show the model outputs graphically. By performing data fitting, we observe that our formulated model produces results that closely match real-world data. Our findings indicate that vaccinating a limited segment of the population can effectively eradicate the disease. The numerical simulations also show that vaccination can reduce the number of susceptible and infectious individuals in the population. Moreover, the graphical representations illustrate that the number of infected individuals rises due to both exogenous reinfection and endogenous reactivation.

Computational model of a feeding copepod engaged in three modes of movement

Abstract Objectives: Copepods display distinct feeding modes to capture prey in the surrounding water. However, the mechanism and range of prey detection are not fully understood. Methods: Using the method of regularized Stokeslets, we constructed a mathematical model of the flow field around a copepod engaged in three modes of movement: sinking, swimming and hovering. The model assumes that the copepod is negatively buoyant with a simplified body and a pair of long antennae. We then introduced a rigid, neutrally buoyant sphere in the model to predict where potential prey items become detectable in theory. Key Findings: We find that the flow fields around the sinking and swimming models are generally unidirectional, while the flow around a hovering copepod has a significant cross-stream component. Our model shows that the volume of the surrounding fluid that is predicted to be inspected has distinctive shapes that resemble a thin sheet while sinking, a cylinder while swimming and a funnel while hovering. Conclusion: The results suggest that the most efficient mode of feeding depends on the distribution of prey items in the surrounding water.

Prediction of CO2 emissions to achieve net-zero objectives in the iron and steel sectors of North America

ABSTRACT Predictive models are widely used to create effective plans for reducing CO2 emissions in manufacturing. The Iron and Steel (I&S) industries play a crucial role in meeting international commitments to achieve Net-zero emissions by 2050. The objective of this study is to forecast carbon dioxide emissions from the I&S industries in North America through the utilization of a Multi-Objective Mathematical model. The proposed data-driven approach is integrated with various machine learning algorithms capable of accurately predicting future values with a small dataset. Additionally, sensitivity analyses under different scenarios are conducted to evaluate the impact of implementing proposed solutions by the research community. Results show a significant improvement in accuracy through the employment of the Whale Optimization Algorithm (WOA). Forecasts reveal a sustained increment of 0.7 MtCO2 every year spanning between 2022 and 2050. This study provides valuable information for stakeholders and policymakers as it allows a more precise evaluation to integrate new technologies to abate forthcoming CO2 emissions.

Methods for Checking the Reliability of Mathematical Models for Describing Deformation Processes of Polymer Textile Materials

Methods for Checking the Reliability of Mathematical Models for Describing Deformation Processes of Polymer Textile Materials

Assessment of the Ecological Safety of Honey with the Help of “Factor Area” Models

The man-made load on the environment and the decrease in biodiversity cause a direct negative environmental impact on the existence of honey bees and beekeeping products. The priority directions of the food industry are the use of high-quality environmentally friendly raw materials and the prevention of the ingress and formation of harmful substances in food products, including honey. This implies the need to develop methods for assessing the environmental safety of the studied raw materials and products. The purpose of this study was to implement a mathematical modeling method for studying the environmental safety of honey. Five types of honey were studied: Robinia, rapeseed, linden, buckwheat, and sunflower. Mathematical models were built according to the following parameters: total activity of β-emitting radionuclides; residues of levomycetin (chloramphenicol), nitrofuran (according to AOZ and AMOZ), metronidazole, and pesticides (according to hexachloran); and the content of water-insoluble substances (mechanical impurities) and heavy metals. On the basis of the obtained data and established quality criteria, calculation graphic models were built. Using algebraic methods, they derived new formulas for calculating quality coefficients. Multivariate analysis and programming methods were used to evaluate honey using mathematical modeling. The most and least ecologically dangerous contaminants and their share of influence for different types of honey were determined based on the complex of research on negative factors. The proposed mathematical models can be implemented for practical use in specialized laboratories as a tool for determining the environmental safety of honey of various botanical origins.

Application of mathematical models in predicting drug dosage and its efficacy

The purpose of the research is to form a comprehensive understanding of how mathematical models are used to interpret complex dynamics related to the distribution, metabolism and excretion of drugs in the human body. The use of mathematical models to predict the required dose of drug prescriptions and establish its effectiveness means a paradigm shift in the field of pharmacology.Methods. The methodology used in this study was aimed at identifying and analytically reviewing articles that correspond to the objectives of the study. The publications included in the analysis were analyzed and data extracted, focusing on key information such as the mathematical modeling methodology used, the exact predicted treatment effects, the populations studied, long-term prognostic effects, and the assessment of the use of various drug dosing regimens.Results. In total, 12 publications were analyzed, which used four different methodologies: models with the effects of several different conditions, models that take into account the occurrence of various discrete events, models based on the effects of informative signs taking into account the physiology of individuals, as well as survival models and generalized linear models.Conclusion. The conducted study of the current state of mathematical modeling in medical research for the purpose of comparative effectiveness is intended for practicing scientists and doctors in conducting further research and introducing innovations. Despite the challenges, the potential impact of these models aimed at bridging the gap between the controlled clinical environment and the real health context is undeniable. The use of mathematical modeling methods to predict the dosage of medicines will improve the quality and effectiveness of personalized medical appointments in the coming years.

Furniture Design of Smart Art Classroom Based on Interactive Analysis of Intelligent Sensing and ITIAS

This paper explores the design and optimization of smart art classroom furniture, addressing the evolving needs of modern art education environments. With the integration of intelligent technologies and sensor networks, the research aims to enhance the functionality, flexibility, and user experience of classroom furniture. It highlights the limitations of traditional classroom furniture and the need for adaptive, multifunctional designs that accommodate diverse learning behaviors and physical requirements. Through a combination of ITIAS interactive analysis and mathematical modeling, the study proposes a framework for developing furniture that supports privacy protection, dynamic updates, and better engagement in art education. The findings emphasize the importance of incorporating ergonomic, aesthetic, and technological considerations to improve teaching and learning outcomes in art classrooms.

Subcellular mRNA kinetic modeling reveals nuclear retention as rate-limiting.

Eukaryotic mRNAs are transcribed, processed, translated, and degraded in different subcellular compartments. Here, we measured mRNA flow rates between subcellular compartments in mouse embryonic stem cells. By combining metabolic RNA labeling, biochemical fractionation, mRNA sequencing, and mathematical modeling, we determined the half-lives of nuclear pre-, nuclear mature, cytosolic, and membrane-associated mRNAs from over 9000 genes. In addition, we estimated transcript elongation rates. Many matured mRNAs have long nuclear half-lives, indicating nuclear retention as the rate-limiting step in the flow of mRNAs. In contrast, mRNA transcripts coding for transcription factors show fast kinetic rates, and in particular short nuclear half-lives. Differentially localized mRNAs have distinct rate constant combinations, implying modular regulation. Membrane stability is high for membrane-localized mRNA and cytosolic stability is high for cytosol-localized mRNA. mRNAs encoding target signals for membranes have low cytosolic and high membrane half-lives with minor differences between signals. Transcripts of nuclear-encoded mitochondrial proteins have long nuclear retention and cytoplasmic kinetics that do not reflect co-translational targeting. Our data and analyses provide a useful resource to study spatiotemporal gene expression regulation.

Mathematical Model of Copper Nanofluid Flow Past a Spherical Enclosure

The study examined mathematical models for describing the behavior of copper nanoparticles in water base fluid. Coupled hydrodynamic governing equations of momentum, energy and concentration were non dimensionalized and solved using installed Laplace transform technique in Mathematica 12.3. The solution obtained were used to analyze the effect of the material parameters on the concentration, temperature and velocity profiles of the copper nanofluid. Results of the study using graphs reveal that an enhancement of the nanoparticle size results in a depreciation of the concentration of the copper nanofluid and escalate the temperature and velocity profiles of the copper nanofluid. Also, the twin effect of an increase in Thermophoresis and Brownian motion bring about a decrease in the concentration of the nanofluid and an increase in the temperature and velocity of the nanofluid. An increase in the radiation parameter, enhanced the temperature of the nanofluid and depreciate the concentration and velocity of the nanofluid while an increase in the magnetic Hartmann number inhibits the velocity of the nanofluid, while an enhancement of the Lewis and Prandtl numbers led to a depreciation of the concentration, an increase in the temperature is observed, for the velocity, it is enhanced by sharp increase in the lewis number and accordingly depreciates by an increase in the Prandtl number. The Reynolds number increase also escalates the velocity profile of the copper nanofluid. Generally, it was observed that the copper nanofluid in some cases react abnormally in the presence of some material parameters under investigation which is a reflection of its characteristics.