Mathematical Modeling Techniques Research Articles

Regional Deposition: Deposition Models.

Modeling particle deposition in the human lung requires information about the morphology of the lung in terms of simple geometric units, e.g., characterizing bronchial airways by straight cylindrical tubes. Five different regional deposition models are discussed in this section with respect to morphometric lung models and related mathematical modeling techniques: 1) one-dimensional cross-section or "trumpet" model, 2) deterministic symmetric generation or "single-path" model, 3) deterministic asymmetric generation or "multiple-path" model, 4) stochastic asymmetric generation or "multiple-path" model, and 5) single-path computational fluid and particle dynamics (CFPD) model. Current deposition models can predict the following regional deposition quantities relevant for the administration of medical aerosols: 1) regional bronchial and alveolar deposition, 2) generational lung deposition, 3) lobar deposition, 4) generational lobar deposition, and 5) generational surface deposition. Although deposition fractions predicted by the different models depend on the selection of a specific morphometric lung model and a specific set of analytical deposition equations, all models predict the same trends as functions of particle diameter and breathing parameters. In general, the overall agreement between the modeling predictions obtained by the various deposition models and the available experimental evidence indicates that current deposition models correctly predict regional and generational deposition.

Selective suppression of amplitudes of frictional oscillations

Maintenance of sanitary codes and standards during operation of railway sorting sta-tions, in particular, standards which concern noise levels, is now the most pressing task. The analysis of noise has been carried out during operation of brake beams of car hump retarders with car wheelsets; the most problem frequency ranges have been revealed. On the basis of mod-elling bench tests with application of techniques of physical and mathematical modelling and tribospectral identification of friction processes we carried out selection of noise-suppressing cladding material which would reduce the level of acoustic noise at interaction of metal surfaces. Results of operational trials have confirmed efficiency of the chosen material in noise reduction.

Methods of mathematical modeling for predicting university entry into TOP-100 world university rankings

Subject. The article focuses on mathematical methods for predicting university entry into TOP-100 World University Rankings. Objectives. The purpose of the study is to develop mathematical modeling techniques for predicting university entry into TOP-100 World University Rankings. Methods. We consider two approaches in mathematical simulation for the said purpose. The first approach employs population dynamics equations, including the Verhulst and the Lotka-Volterra equations. The second approach uses linear algebraic equation in three variables together with the variables constraints. Results. Population dynamics equations enable to model improvement in university performance expressed by Total Score or Overall Score indicator, to define intra-university competition and competition between universities of the World University Rankings. Linear algebraic equations provide projections of a university's specified position in the world rankings. We made clear mathematical statement of the problems; solved the problem that relates to entering TOP-100 of three global rankings (ARWU, THE, QS) by the Moscow State University and St. Petersburg University. Conclusions. We assume that the offered approaches will be useful for university managers who monitor and guide their university positioning.

Opportunities for Quantitative Translational Modeling in Oncology.

A 2-day meeting was held by members of the UK Quantitative Systems Pharmacology Network (<http://www.qsp-uk.net/>) in November 2018 on the topic of Translational Challenges in Oncology. Participants from a wide range of backgrounds were invited to discuss current and emerging modeling applications in nonclinical and clinical drug development, and to identify areas for improvement. This resulting perspective explores opportunities for impactful quantitative pharmacology approaches. Four key themes arose from the presentations and discussions that were held, leading to the following recommendations: Evaluate the predictivity and reproducibility of animal cancer models through precompetitive collaboration. Apply mechanism of action (MoA) based mechanistic models derived from nonclinical data to clinical trial data. Apply MoA reflective models across trial data sets to more robustly quantify the natural history of disease and response to differing interventions. Quantify more robustly the dose and concentration dependence of adverse events through mathematical modelling techniques and modified trial design.

Mathematical Modelling, Simulation and Optimisation of Microneedles for Transdermal Drug Delivery: Trends and Progress.

In the last two decades, microneedles (MNs) have received significant interest due to their potential for painless transdermal drug delivery (TDD) and minimal skin damage. MNs have found applications in a range of research and development areas in drug delivery. They have been prepared using a variety of materials and fabrication techniques resulting in MN arrays with different dimensions, shapes, and geometries for delivery of a variety of drug molecules. These parameters play crucial roles in determining the drug release profiles from the MNs. Developing mathematical modelling, simulation, and optimisation techniques is vital to achieving the desired MN performances. These will then be helpful for pharmaceutical and biotechnological industries as well as professionals working in the field of regulatory affairs focusing on MN based TDD systems. This is because modelling has a great potential to reduce the financial and time cost of both the MNs’ studies and manufacturing. For example, a number of robust mathematical models for predicting the performance of the MNs in vivo have emerged recently which incorporate the roles of the structural and mechanical properties of the skin. In addressing these points, this review paper aims to highlight the current status of the MN modelling research, in particular, the modelling, simulation and optimisation of the systems for drug delivery. The theoretical basis for the simulation of MN enhanced diffusion is discussed within this paper. Thus, this review paper provides a better understanding of the modelling of the MN mediated drug delivery process.

Car integral performance index simulation

Introduction . The paper is devoted to the comparison and evaluation of the quality of a car using the method of mathematical simulation of the integral performance index. The work objectives were to develop a mathematical modeling technique for the integral performance index, to draw up a step sequence of quality assessment, to analyze most common brands of passenger cars on the domestic market, to sum up and validate the result obtained. Materials and Methods . The sequence of simulating the integral performance index is proposed. Numerical modeling of the integral performance index is carried out on the example of six most common brands of passenger cars on the domestic market. Results . A method of modeling the integral performance index is developed. A step sequence of the analysis is described. An additive form of determining the integral performance index which provides combining single, unrelated quality indices into a complex indicator in the process of comparison is proposed. Discussion and Conclusions . The proposals presented can be used in the process of assessing and diagnosing the competitiveness of not only cars, but also of other products with a large set of independent quality indicators.

Verbal modeling of microprocesses of continuous oil and grease adsorption

The use of oils and greases in various fields of activity leads to their contamination by hazardous substances. Regeneration of properties is performed by various technologies, in particular, by continuous adsorption purification. For the automatic control of multicomponent purification it is necessary to know the mechanisms of substances interaction in the adsorber. A mathematical model that is adequate to the actual adsorption course, will ensure high control efficiency by meeting the quality requirements for the materials and reducing production emissions into the environment.It is important to create a mathematical model of the processes in adsorber, which would give an adequate reflection of substances behavior in it when changing properties of raw materials and adsorbent, that are continuously flow into this apparatus. Main modern modeling methods use generalized properties of input material flows and are based on the approximation of empirical adsorption data. We have chosen a method for describing behavior of substances in adsorber, which is supposed to determine the driving forces that occur between molecules of contaminated oils or greases (OG) on the one hand and adsorbent on the other. Existing studies on the properties of contaminated materials as nanosystems provide grounds for this.It is suggested to consider adsorbent and contaminated OG that enter the adsorber as separate objects with features of nanosystems. The environment in adsorber has been investigated as a collection of these systems and the new one – "adsorbent – contaminated OG" – whose properties are formed not additively but dynamically by the action of intermolecular forces.The properties of each of the nanosystems and the forces that are proposed to consider as driving forces in these systems are determined. Purification of contaminated OG is performed on polar adsorbents. In the adsorbent there are important the size of entrance windows, the structure of granules (elementary cells) and the elemental composition, which affects its polarity, and in the adsorbent – the size of molecules and their component composition. The most influential forces that act during the process are electrostatic ones – orientation and induction forces.It is shown under what scenarios the adsorbent granules can be filled in the presence of several contaminants. It was determined that the adsorption of resin molecules, followed by sulfur and aromatic hydrocarbons, takes place first. The paraffins that underlie the greases are not adsorbed by the adsorbent granules due to the adsorption selectivity, which is characterized by the attraction forces between molecule and adsorbent surface. The adsorption rate of such components will be low compared to pollutants due to the adsorption heat effect, which is the lowest in case of paraffins.Authors suggest to consider multicomponent adsorption as a phenomenon that implies the presence of innumerable random microprocesses. Such a verbal model made it possible to identify mathematical modeling techniques that would be appropriate to use when creating model for a control system.The developed model gives an idea of the relationship between the adsorbent particles and contaminated OG at the molecular level and allows us to consider multi-component adsorption purification of oils and greases as random processes. It is shown that the creation of control systems for this process will require such mathematical support, which should use methods of probability theory, adaptation and artificial intelligence.

Prediction of European Stock Indexes Using Neuro-fuzzy Technique

Purpose of the article: The paper is focused on the forecast of stock markets of the Central European countries, known as V4, by means of soft computing. The tested model is constructed by a combination of fuzzy logic and artificial neural networks. A total of four SAX, PX, BUX, WIG stock indices differing in their liquidity and efficiency are selected for the forecast. Methodology/methods: The methods of analysis, synthesis and techniques of mathematical neuro-fuzzy modelling were used to achieve this goal. The proposed neuro-fuzzy decisionmaking model consists of 3 input variables, one block of rules (with 21 fuzzy rules) and one output variable predicting the normalized price of stock indexes of the selected countries. The input variables have three attributes (L – large, M – medium, and S – small). Scientific aim: The aim of the paper is to create a suitable model that will be used to forecast stock indices of the Central European countries with a relatively low error. Findings: The developed ANFIS model is a suitable tool for predicting stock indexes. The importance of the neuro-fuzzy model can be seen especially in the fact that it shows a strong predictive capacity of both efficient and less efficient stock markets. Conclusions: The paper discussed the design of the neuro-fuzzy model as a supporting tool for predicting the selected stock indexes listed on the European stock markets. For further research, it would be appropriate to extend the proposed model with other significant fundamental indicators, or to incorporate technical and psychological indicators and to monitor the strength of the revised model also in several stock markets, for example according to the geographical distribution.

EMPLOYEE SHUTTLE BUS ROUTING PROBLEM

Recently, companies have started to use engineering techniques more than ever due to competitive market conditions, high costs, and limited budgets. To be able to reduce incurred costs and increase profitability, companies deeply analyze all the existing processes carefully. In this work, the Employee Shuttle Bus management process of an international company, which is located in Gebze, is considered, analyzed, and improved through mathematical modeling technique. Unified and Area-Based solution alternatives are developed by extending the mathematical formulation of the widely studied School Bus Routing Problem. Both proposed methods and the current situation of the company have been implemented on GAMS and solved by the CPLEX solver. It has been observed that proposed methods have provided significant cost reduction with respect to the current situation of the company. Among the newly developed methods, the Area-Based method has provided the best cost reduction amounts with less resource usage and shorter tour lengths.

Influence of near dry wirecut electrical discharge machining parameters on kerf width in Monel 400

Abstract This work explains the more refined and subtle analysis on one of the significant response parameters in kerf width upon machining Monel 400. Machining was done under near-dry ambiance with the support of the mathematical modeling technique of Response Surface Methodology (RSM) and the more sophisticated predictive computational modeling in an artificial neural network (ANN). Driving control elements considered for this WEDM process were pulse-on and off time (TON and TOFF), Voltage (V), Wire Feed (WF), Air inlet pressure and Water flow rate. The impact on the intermittent zone that prevails between the surface of the material in the spark zone and the wire during the process has not only being influenced by the control parameters but also by the dielectric medium. The implications of di-electric medium maintained at near dry conditions were given utmost importance and considerations in this investigation. The execution of the RSM and created ANN models are contrasted and trial consequences of Kerf Width for their adequacy. The examination demonstrates that ANN shows more exact expectation contrasted with the RSM models.

Review of Mathematical Methodology for Electric Power Optimization Problems

Electric power system is a physical energy system consisting of power generation, substations, transmission, distribution, and consumption. The objective of power system optimization is to improve power system security, economy, and reliability. This paper summarizes the classical mathematical optimization methods and modeling techniques of power system optimization associated with system planning, operation, and control. Along with the development of electric power industry, the concept of Energy Internet is addressed, which consists of power network, gas network, and transportation network. Under such new environments, electric power optimization faces some challenging with respect to the cooperation of multi-energy networks. According to the design structure and operational characteristics of the Energy Internet, some research areas of electric power optimization are presented from the view of mathematical optimization modeling and calculation. The aim is to provide some optimization methodology to solve the optimal issues of power system under the background of Energy Internet.

Reliability-Centered Maintenance Task Planning for Overhead Electric Power Distribution Networks

In this paper, it is presented an approach to match technically and economically the reliability of electricity distribution networks through an optimization methodology consisting of the mathematical model and metaheuristic solution technique to obtain an optimized plan for efficient management of maintenance tasks. The problem of maintenance tasks is formulated as a mixed dynamic nonlinear multi-objective optimization model, in which costs to perform maintenance tasks on equipment and/or components that make up the electric distribution network are minimized, while they have their reliability maximized. The constraints of this model are the individual and group electricity supply interruption duration and frequency indices, and availability of financial and human resources. The solution of this problem is obtained through a specialized non-dominated sorting genetic algorithm multi-objective metaheuristic, which provides a set of non-dominated solutions very close to the optimal Pareto frontier. Each solution at this frontier represents a maintenance plan able to assist the making decision of the operators in distribution companies for managing the maintenance crews.

Effect of Porous Medium and Copper Heat Sink on Cooling of Heat-Generating Element

Cooling of heat-generating elements is a challenging problem in engineering. In this article, the transient free convection of a temperature-dependent viscosity liquid inside the porous cavity with copper radiator and the heat-generating element is studied using mathematical modeling techniques. The vertical and top walls of the chamber are kept at low constant temperature, while the bottom wall is kept adiabatic. The working fluid is a heat-conducting liquid with temperature-dependent viscosity. A mathematical model is developed based on dimensionless stream function, vorticity, and temperature variables. The governing properties are the variable viscosity, geometric parameters of the radiator, and size of thermally insulated strip on vertical surfaces of the cavity. The effect of these parameters on the energy transport and circulation patterns are analyzed numerically. Based on the numerical results obtained, recommendations are given on the optimal values of the governing parameters for the effective operation of the cooling system. It is shown that the optimal number of radiator fins for the cooling system configuration under consideration is 3. In addition, the thermal insulation of the vertical walls and the increased thickness of the radiator fins have a negative effect on the operation of the cooling system.

Mathematical Approaches to Network Science: Modeling and Analysis

Network science, a multidisciplinary field, employs mathematical approaches to model and analyze complex systems as networks or graphs. This paper provides an overview of the fundamental concepts, mathematical modeling techniques, analysis methods, and applications of network science. It emphasizes the importance of mathematical approaches in understanding the structure and dynamics of networks in various domains, including social, biological, and technological networks. The paper also discusses challenges such as scalability and incorporating dynamics, along with future research directions. Overall, mathematical approaches are essential for advancing network science and unlocking new insights into complex systems.

Physiologically Based Pharmacokinetic Modeling of Propranolol in Relation to CYP2D6 Genotypes

Propranolol, used to treat high blood pressure and irregular heart rate, is mainly metabolized by cytochrome P450 2D6 (CYP2D6) to 4‐hydroxypropranolol (4‐OHP) and CYP1A2 to N‐desisoprophylpropranolol (N‐DIP). Physiologically based pharmacokinetic (PBPK) modeling is a mathematical modeling technique for predicting the absorption, distribution, metabolism and excretion (ADME) of synthetic or natural chemical substances in humans and other animal species. We investigated whether the pharmacokinetics of propranolol was altered by the different CYP2D6 genotypes in Korean subjects. Then, through in vitro study of propranolol, the metabolic capacity of propranolol was measured according to the CYP2D6 genotypes. And we developed the PBPK model of propranolol related to CYP2D6 genetic polymorphism. Twenty‐five volunteers were grouped as CYP2D6 *wt ⁄ *wt (*wt=1 or 2, n=7), CYP2D6 *1/ *10 (n=3), CYP2D6 *1 ⁄ *5 (n=4) and CYP2D6 *10 ⁄ *10 (n=11) according to their genotypes. Propranolol hydrochloride 40 mg (Pranol®) was administered orally once to each subject in these four groups. The CYP2D6 *1, CYP2D6 *10 and CYP1A2 *1 were incubated with 0.5–100 μM propranolol for 60 min at 37 □. Then the metabolites were extracted, and the concentration was analyzed by liquid chromatography‐mass spectrometry. PBPK modeling of propranolol was developed and optimized using PK‐sim® software. And, validation of PBPK model was conducted by comparing the predicted values with observed values from comparison the pharmacokinetic studies. In clinical data, AUCend, AUCinf, Cmax and oral clearance of propranolol were significantly different in CYP2D6 genetic polymorphism (P&lt;0.005, respectively). Depending on the physico‐chemical parameters and ADME of each genotype, PBPK model of propranolol was developed. For metabolism, input values of in vitro Vmax of 4‐OHP in the presence of recombinant enzyme for CYP2D6 *1, CYP2D6 *10, and CYP1A2 *1 were 2.41, 0.344 and 0.383 pmol/min/pmol, respectively. And, input values of Km of 4‐OHP for CYP2D6 *1, CYP2D6 *10, and CYP1A2 *1 were 2.852, 8.914 and 6.95 μM, respectively. Input values of in vitro Vmax of N‐DIP in the presence of recombinant enzyme for CYP2D6 *1, CYP2D6 *10, and CYP1A2 *1 were 9.782, 7.891 and 11.18 pmol/min/pmol, respectively. And, input values of Km of N‐DIP for CYP2D6 *1, CYP2D6 *10, and CYP1A2 *1 were 162.8, 339.1 and 158.4 μM, respectively. The AUCinf mean of simulated PBPK model were 111.77, 184.74, 296.13, 370.85 ng·h/ml in CYP2D6 *wt ⁄ *wt, CYP2D6 *1 / *10, CYP2D6 *1 ⁄ *5 and CYP2D6 *10 ⁄ *10, respectively. The developed PBPK model of propranolol successfully described the pharmacokinetics of each CYP2D6 genotype group and its simulated values were within acceptance criterion (99.998% confidence interval). These results will be beneficial in prescribing the appropriate dosage of propranolol considering inter‐individual differences through this mechanical approach. In addition, the PBPK modeling of propranolol in relation to CYP2D6 genotypes will be applicable to the treatment of various ethnic groups, ages, and patients. The observed and predicted pharmacokinetics for propranolol with acceptance criterion range in CYP2D6 genotype groups. Genotype Cmax (ng/mL) AUCend (ng*h/mL) AUCinf (ng*h/mL) Tmax (h) T1/2 (h) CYP2D6*wt/*wt (n=7) Observed 21.93±5.74 132.2±41.39 150.07±40.34 1.79±0.27 4.04±0.94 Predicted 30.70 111.53 111.77 1.90 2.83 Aceeptance range 14.49–33.19 80.79–216.30 98.09–229.60 1.41–2.27 2.80–5.84 CYP2D6*1/*10 (n=3) Observed 32.30±5.92 149.28±62.51 165.18±71.82 1.50±0.50 3.27±0.61 Predicted 34.74 181.01 184.74 1.95 4.37 Aceeptance range 20.66–50.51 55.55–401.16 59.36–459.66 0.68–3.33 2.08–5.14 CYP2D6*1/*5 (n=4) Observed 43.75±16.07 245.37±100.75 255.58±99.22 1.75±0.29 3.72±1.14 Predicted 51.88 286.96 296.13 1.95 5.02 Aceeptance range 20.51–93.32 105.85–568.78 115.06–567.70 1.23–2.48 1.96–7.06 CYP2D6*10/*10 (n=11) Observed 48.77±17.07 339.82±106.89 360.32±110.67 2.27±0.82 4.68±1.38 Predicted 62.70 357.72 370.85 2.00 5.14 Aceeptance range 31.51–75.48 229.04–504.19 245.02–529.88 1.45–3.56 3.23–6.78

Notch ligand Dll4 impairs cell recruitment to aortic clusters and limits blood stem cell generation.

Hematopoietic stem cells (HSCs) develop from the hemogenic endothelium in cluster structures that protrude into the embryonic aortic lumen. Although much is known about the molecular characteristics of the developing hematopoietic cells, we lack a complete understanding of their origin and the three-dimensional organization of the niche. Here, we use advanced live imaging techniques of organotypic slice cultures, clonal analysis, and mathematical modeling to show the two-step process of intra-aortic hematopoietic cluster (IACH) formation. First, a hemogenic progenitor buds up from the endothelium and undergoes division forming the monoclonal core of the IAHC. Next, surrounding hemogenic cells are recruited into the IAHC, increasing their size and heterogeneity. We identified the Notch ligand Dll4 as a negative regulator of the recruitment phase of IAHC. Blocking of Dll4 promotes the entrance of new hemogenic Gfi1+ cells into the IAHC and increases the number of cells that acquire HSC activity. Mathematical modeling based on our data provides estimation of the cluster lifetime and the average recruitment time of hemogenic cells to the cluster under physiologic and Dll4-inhibited conditions.

Review of effect of meso scale combustor wall material, Catalytic material, & Porous media on flame Stabilization

In recent trends demand of energy for portable devices like notebook, microsatellite, laptops, UAV are increasing at high rate, a high energy density hydrocarbon fuel creates opportunity to alternate chemical Li-ion batteries with micro combustion based power generation system. Mainly, this review focus on experimental, mathematical modelling techniques, and numerical simulation performed on heat recirculating combustor to find the effect of combustor wall material, catalytic material and porous media. It also summarizes the electricity generation possibilities with micro combustor turbine, thermo electric material & thermo-photovolatic combustion system. The effect of combustor wall material, catalytic material, and porous media on flame stabilization are enlisted with its summary.

Real-Time Modeling and Correction of Sensor Inputs and Outputs for Increased Accuracy and Reliability

Mathematical modeling was employed for automatic, real-time interrogation and correction of amperometric electrochemical gas sensors (AES) deployed in instruments for industrial hygiene applications. The interrogation involved two steps which were analyzed using various mathematical modeling techniques to determine the “goodness” of the sensor and to correct its output for small changes due to aging and environmental conditions. The first interrogation was a physical interrogation of the flow path into the sensor by supplying a driving force at the face of the sensor, either by exhaled human breath, or by acoustic sound pressure applied to diffusion barriers protecting the sensor, ensuring that the flow path was sufficiently open for detection of hazardous gases. The second interrogation was an electronic interrogation of the sensor itself, achieved by applying a small potential or current pulse to the working electrode of the sensor and deconvoluting its response to make small corrections to the sensor signal. These two steps provide periodic, real-time, and automatic surveillance and correction of AES, increasing robustness, reliability and accuracy, and user confidence, while decreasing calibration frequency, maintenance, and cost-of-ownership. Validation testing over sensors of various designs indicated a greater than 98% reliability of the sensor/instrument interrogation technique.

Methodological Development of Mathematical Modeling Techniques in Health Care

The advancement of mathematical model has utilized for simulating the output of medical is a development area over medicine whereas the modeling can be mentioned with several activities namely simulation or decision analysis and predictive modeling. However, the traditional modeling technique utilized in planning of health service, assessment reports and its efficiency, financing about health care and assessment in budget impact, assessment in health economics, surveillance of infectious disease and other health care application. Therefore, the mathematical modelling is performed as a frequent and timely benefit in order to make rapid decision making while facing investigation with several issues like time elapsing, unusual and unethical particularly projected for future. This paper focused in applying the mathematical modeling to accomplish an optimal decision making in healthcare whereas this study discuss about the specific modeling concepts namely decision tree and fuzzified rule tables on evaluation of health economics and better service planning that my replicate the individual experience or patients cohorts.

Mathematical modelling supports the existence of a threshold hydrogen concentration and media-dependent yields in the growth of a reductive acetogen

The bacterial production of acetate via reductive acetogenesis along the Wood–Ljungdahl metabolic pathway is an important source of this molecule in several environments, ranging from industrial bioreactors to the human gastrointestinal tract. Here, we contributed to the study of reductive acetogens by considering mathematical modelling techniques for the prediction of bacterial growth and acetate production. We found that the incorporation of a hydrogen uptake concentration threshold into the models improves their predictions and we calculated this threshold as 86.2 mM (95% confidence interval 6.1–132.6 mM). Monod kinetics and first-order kinetics models, with the inclusion of two candidate threshold terms or reversible Michaelis–Menten kinetics, were compared to experimental data and the optimal formulation for predicting both growth and metabolism was found. The models were then used to compare the efficacy of two growth media for acetogens. We found that the recently described general acetogen medium was superior to the DSMZ medium in terms of unbiased estimation of acetogen growth and investigated the contribution of yeast extract concentration to acetate production and bacterial growth in culture. The models and their predictions will be useful to those studying both industrially and environmentally relevant reductive acetogenesis and allow for straightforward adaptation to similar cases with different organisms.