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Leveraging public AI tools to explore systems biology resources in mathematical modeling
Predictive mathematical modeling is an essential part of systems biology and is interconnected with information management. Systems biology information is often stored in specialized formats to facilitate data storage and analysis. These formats are not designed for easy human readability and thus require specialized software to visualize and interpret results. Therefore, comprehending modeling and underlying networks and pathways is contingent on mastering systems biology tools, which is particularly challenging for users with no or little background in data science or system biology. To address this challenge, we investigated the usage of public Artificial Intelligence (AI) tools in exploring systems biology resources in mathematical modeling. We tested public AI’s understanding of mathematics in models, related systems biology data, and the complexity of model structures. Our approach can enhance the accessibility of systems biology for non-system biologists and help them understand systems biology without a deep learning curve.
Mathematical Modeling of Microbial Community Dynamics: A Methodological Review
Microorganisms in nature form diverse communities that dynamically change in structure and function in response to environmental variations. As a complex adaptive system, microbial communities show higher-order properties that are not present in individual microbes, but arise from their interactions. Predictive mathematical models not only help to understand the underlying principles of the dynamics and emergent properties of natural and synthetic microbial communities, but also provide key knowledge required for engineering them. In this article, we provide an overview of mathematical tools that include not only current mainstream approaches, but also less traditional approaches that, in our opinion, can be potentially useful. We discuss a broad range of methods ranging from low-resolution supra-organismal to high-resolution individual-based modeling. Particularly, we highlight the integrative approaches that synergistically combine disparate methods. In conclusion, we provide our outlook for the key aspects that should be further developed to move microbial community modeling towards greater predictive power.
Mathematical model of marine diesel engine simulator for a new methodology of self propulsion tests
As a vessel operates in the open seas, a marine diesel engine simulator whose engine rotation is controlled to transmit through propeller shaft is a new methodology for the self propulsion tests to track the fuel saving in a real time. Considering the circumstance, this paper presents the real time of marine diesel engine simulator system to track the real performance of a ship through a computer-simulated model. A mathematical model of marine diesel engine and the propeller are used in the simulation to estimate fuel rate, engine rotating speed, thrust and torque of the propeller thus achieve the target vessel’s speed. The input and output are a real time control system of fuel saving rate and propeller rotating speed representing the marine diesel engine characteristics. The self-propulsion tests in calm waters were conducted using a vessel model to validate the marine diesel engine simulator. The simulator then was used to evaluate the fuel saving by employing a new mathematical model of turbochargers for the marine diesel engine simulator. The control system developed will be beneficial for users as to analyze different condition of vessel’s speed to obtain better characteristics and hence optimize the fuel saving rate.
Investigating key cell types and molecules dynamics in PyMT mice model of breast cancer through a mathematical model
The most common kind of cancer among women is breast cancer. Understanding the tumor microenvironment and the interactions between individual cells and cytokines assists us in arriving at more effective treatments. Here, we develop a data-driven mathematical model to investigate the dynamics of key cell types and cytokines involved in breast cancer development. We use time-course gene expression profiles of a mouse model to estimate the relative abundance of cells and cytokines. We then employ a least-squares optimization method to evaluate the model’s parameters based on the mice data. The resulting dynamics of the cells and cytokines obtained from the optimal set of parameters exhibit a decent agreement between the data and predictions. We perform a sensitivity analysis to identify the crucial parameters of the model and then perform a local bifurcation on them. The results reveal a strong connection between adipocytes, IL6, and the cancer population, suggesting them as potential targets for therapies.
Within-host mathematical models of hepatitis B virus infection: Past, present, and future
Mathematical modeling has been instrumental in enhancing our understanding of the viral dynamics of hepatitis B virus (HBV) infection. We give a primer on HBV infection in humans and a brief overview of the development of within-host mathematical models of HBV infection. In the last decade, models have advanced from considering chronic HBV infections under therapy to the pathogenesis of infection. We also summarize estimates of key viral dynamic parameters that have varied greatly among studies, and show that they impact model predictions. Here, future directions for mathematical modeling of HBV infection are proposed to better understand emerging therapies, the HBV life cycle, predicting cure, and the mechanisms involved in the immune response to HBV.
Optimization of Cooling Water Flow Rate in Nuclear and Thermal Power Plants Based on a Mathematical Model of Cooling Systems{sup 1}
A mathematical model and algorithms are proposed for automatic calculation of the optimum flow rate of cooling water in nuclear and thermal power plants with cooling systems of arbitrary complexity. An unlimited number of configuration and design variants are assumed with the possibility of obtaining a result for any computational time interval, from monthly to hourly. The structural solutions corresponding to an optimum cooling water flow rate can be used for subsequent engineering-economic evaluation of the best cooling system variant. The computerized mathematical model and algorithms make it possible to determine the availability and degree of structural changes for the cooling system in all stages of the life cycle of a plant.
Effect of hydrophobic ionic liquids aqueous solubility on metal extraction from hydrochloric acid media: Mathematical modelling and trivalent thallium behavior
A mathematical model to explain cations’ solubility of both protic and aprotic ionic liquids in a wide range of hydrochloric acid solutions has been developed. The concept of this model is based on an assumption of the mineral acid extraction into the organic phase, formation of a salt there between an ionic liquid cation and chloride-anion due to ions recombination and partial salt back-extraction. The proposed approach allows estimating corresponding extraction constants. Comparison of calculated and experimentally measured solubility product constants shows that they are in good agreement. It has been determined also that the more the hydrophilicity of the ionic liquids’ cation the more hydrochloric acid is extracted. Furthermore, this model has been utilized to facilitate analysis of thallium transfer into hydrophobic ionic liquids providing insights into the mechanism of metal extraction.
A Mathematical Model of the Dynamics of Cytokine Expression and Human Immune Cell Activation in Response to the Pathogen Staphylococcus aureus
Cell-based mathematical models have previously been developed to simulate the immune system in response to pathogens. Mathematical modeling papers which study the human immune response to pathogens have predicted concentrations of a variety of cells, including activated and resting macrophages, plasma cells, and antibodies. This study aims to create a comprehensive mathematical model that can predict cytokine levels in response to a gram-positive bacterium, S. aureus by coupling previous models. To accomplish this, the cytokines Tumor Necrosis Factor Alpha (TNF-α), Interleukin 6 (IL-6), Interleukin 8 (IL-8), and Interleukin 10 (IL-10) are included to quantify the relationship between cytokine release from macrophages and the concentration of the pathogen, S. aureus, ex vivo. Partial differential equations (PDEs) are used to model cellular response and ordinary differential equations (ODEs) are used to model cytokine response, and interactions between both components produce a more robust and more complete systems-level understanding of immune activation. In the coupled cellular and cytokine model outlined in this paper, a low concentration of S. aureus is used to stimulate the measured cellular response and cytokine expression. Results show that our cellular activation and cytokine expression model characterizing septic conditions can predict ex vivo mechanisms in response to gram-negative and gram-positive bacteria. Our simulations provide new insights into how the human immune system responds to infections from different pathogens. Novel applications of these insights help in the development of more powerful tools and protocols in infection biology.
Mathematical Modeling and Analysis of a Wide Bandwidth Bipolar Power Supply for the Fast Correctors in the APS Upgrade
This paper presents the mathematical modeling and analysis of a wide bandwidth bipolar power supply for the fast correctors in the APS Upgrade. A wide bandwidth current regulator with a combined PI and phase-lead compensator has been newly proposed, analyzed, and simulated through both a mathematical model and a physical electronic circuit model using MATLAB and PLECS. The proposed regulator achieves a bandwidth with a -1.23dB attenuation and a 32.40° phase-delay at 10 kHz for a small signal less than 1% of the DC scale. The mathematical modeling and design, simulation results of a fast corrector power supply control system are presented in this paper.
Mathematical models for base calibration in industrial robots
Mathematical models for the control systems of industrial robots permit calibration of the base, which is a single coordinate space for the industrial robot and the components being manipulated. Calibration of the base precedes operation of the robot. Control systems for industrial robots permit the storage and use of several calibrated bases in programming robot motion.
Bioelectrochemical reactor to manage anthropogenic sulfate pollution for freshwater ecosystems: Mathematical modeling and experimental validation
Anthropogenic sulfate loading into otherwise low-sulfate freshwater systems can cause significant ecological consequences as a biogeochemical stressor. To address this challenge, in situ bioremediation technologies have been developed to leverage naturally occurring microorganisms that transform sulfate into sulfide rather than implementing resource-intensive physio-chemical processes. However, bioremediation technologies often require the supply of electron donors to facilitate biological sulfate reduction. Bioelectrochemical systems (BES) can be an alternative approach for supplying molecular hydrogen as an electron donor for sulfate-reducing bacteria through water electrolysis. Although the fundamental mechanisms behind BESs have been studied, limited research has evaluated the design and operational parameters of treatment systems when developing BESs on a scale relevant to environmental systems. Further, this study aimed to develop an application-based mathematical model to evaluate the performance of BESs across a range of reactor configurations and operational modes. The model was based on sulfate transformation by hydrogenotrophic sulfate-reducing bacteria coupled with the recovery of solid iron sulfide species formed by the oxidative dissolution of dissolved ferrous iron from a stainless steel anode. Sulfate removal closely corresponded to the rate of electrolytic hydrogen production and hydraulic residence time but was less sensitive to specific microbial rate constants. The mathematical model results were compared to experimental data from a pilot-scale BES tested with nonacidic mine drainage as a case study. The close agreement between the mathematical model and the pilot-scale BES experiment highlights the efficacy of using a mathematical model as a tool to develop a conceptual design of a scaled-up treatment system.
Optimal control of mathematical models for the radiotherapy of gliomas: the scalar case
This paper deals with the optimal control of a mathematical model of glioma progression incorporating the basic facts of the evolution of primary brain tumors. We will consider a model of the simplest possible kind, based on the Fischer-Kolmogorov equations, using ideas from Pérez-García (Mathematical models for the radiotherapy of gliomas (preprint), 2016). The control is the 2n-tuple (t{sub 1},..., t{sub n}; d{sub 1},..., d{sub n}), where d{sub i} is the i-th applied radiotherapy dose an t{sub i} is the i-th administration for 1 ≤ i ≤ n. We search for controls that maximize the survival time, that is, the time at which the tumor mass reaches a critical value M{sub ∗}, over the class of admissible radiation times and doses. We present theoretical and numerical results that justify the relevance of the model and the existence of potential medical applications.
Considerations for improving the biosphere assessment methodology and the associated conceptual and mathematical models for application to LLW/ILW radioactive wastes in Spain - 15194
We give consideration to future needs in assessment studies relating to the disposal of very low level radioactive waste (VLLW), low level radioactive waste (LLW) and intermediate level radioactive waste (ILW) in Spain. As these wastes are primarily disposed at El Cabril, particular attention is given to the characteristics of that site. The focus is on post-closure performance assessment studies and specifically on the biosphere aspect of those studies. In particular, it gives consideration to the assessment methodology that should be used, taking into account the recommendations made in the international BIOMASS and BIOCLIM programs, as well as more recent developments. It then goes on to consider the conceptual models of the biosphere that should be developed and comments on how these should be transformed into mathematical models. The issues arising in conceptual and mathematical model development are illustrated by reference to El Cabril, but several of these issues would also be applicable to other engineered facilities excavated from the surface in a variety of geographical and geological contexts. (authors)
Cold-Cap Temperature Profile Comparison between the Laboratory and Mathematical Model
The rate of waste vitrification in an electric melter is connected to the feed-to-glass conversion process, which occurs in the cold cap, a layer of reacting feed on top of molten glass. The cold cap consists of two layers: a low temperature (~100°C – ~800°C) region of unconnected feed and a high temperature (~800°C – ~1100°C) region of foam with gas bubbles and cavities mixed in the connected glass melt. A recently developed mathematical model describes the effect of the cold cap on glass production. For verification of the mathematical model, a laboratory-scale melter was used to produce a cold cap that could be cross-sectioned and polished in order to determine the temperature profile related to position in the cold cap. The cold cap from the laboratory-scale melter exhibited an accumulation of feed ~400°C due to radiant heat from the molten glass creating dry feed conditions in the melter, which was not the case in the mathematical model where wet feed conditions were calculated. Through the temperature range from ~500°C – ~1100°C, there was good agreement between the model and the laboratory cold cap. Differences were observed between the two temperature profiles due to the temperature of the glass melts and the lack of secondary foam, large cavities, and shrinkage of the primary foam bubbles upon the cooling of the laboratory-scale cold cap.
A mathematical model of the passage of an asteroid-comet body through the Earth’s atmosphere
In the paper, a mathematical model and a numerical algorithm are proposed for modeling the complex of phenomena which accompany the passage of a friable asteroid-comet body through the Earth’s atmosphere: the material ablation, the dissociation of molecules, and the radiation. The proposed model is constructed on the basis of the Navier-Stokes equations for viscous heat-conducting gas with an additional equation for the motion and propagation of a friable lumpy-dust material in air. The energy equation is modified for the relation between two its kinds: the usual energy of the translation of molecules (which defines the temperature and pressure) and the combined energy of their rotation, oscillation, electronic excitation, dissociation, and radiation. For the mathematical model of atmosphere, the distribution of density, pressure, and temperature in height is taken as for the standard atmosphere. An asteroid-comet body is taken initially as a round body consisting of a friable lumpy-dust material with corresponding density and significant viscosity which far exceed those for the atmosphere gas. A numerical algorithm is proposed for solving the initial-boundary problem for the extended system of Navier-Stokes equations. The algorithm is the combination of the semi-Lagrangian approximation for Lagrange transport derivatives and the conforming finite element method for other terms. The implementation of these approaches is illustrated by a numerical example.