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The contamination of soil due to activities involved in crude oil exploration and production, and oil spillage emanating from pipeline vandalization, sabotage, theft, corrosion of pipeline and the enterprises of artisanal refineries pose health and ecological problems. This is especially as crude oil contains chemical compounds which are grouped into the Total Petroleum Hydrocarbons (TPH), and known to be toxic, mutagenic, and carcinogenic. Bioremediation is currently being explored as a cost effective and environmentally friendly methods of remediating the soil from this contaminant. Thus, the current work is aimed at developing a mathematical model for the bioremediation process. This was carried out while assuming that the process of degradation is a first order reaction, and the principle of the law of conservation of mass was applied. A linear model ( ) was developed relating the instantaneous concentration of TPH, initial concentration of TPH and time duration of the bioremediation. The model fitted well to the experimental data as shown by the result of the statistical analysis where the Analysis of Variance (ANOVA) showed a p-value of 0.004 suggesting that the model is statistically significant. The p-values of the model variables such as time duration of the bioremediation was 0.004, this suggested that the variable is significant. The model can be used as a supporting tool in the management of the biodegradation of TPH to predict the degradation concentration of TPH during the bioremediation process at ambient condition of temperature and pressure using cow dung, wire croton and their combination as a carbon source. KEYWORDS: Bioremediation; cow dung; wire croton; degradation; Mathematical modelling

For polymeric materials, the relaxation spectrum contains complete information about the time-dependent part of the material response. The contribution of different numerical schemes, i.e., different methods of reconstructing the dynamic relaxation modulus, to the accuracy of the approximation by calculating the corresponding relaxation spectra is investigated by analysing experimental data for four types of polysaccharides. It was found that there is no unique mathematical approach for the calculation of relaxation spectra that ensures a satisfactory approximation of the experimentally determined dynamic moduli for the selected types of polymeric materials. It is recommended to combine different numerical methods in parallel to achieve a reasonable approximation of the material functions. Pri polimernih materialih relaksacijski spekter vsebuje popolne informacije o časovno odvisnem delu odziva materiala. Z analizo eksperimentalnih podatkov za štiri vrste polisaharidov raziskujemo prispevek različnih numeričnih shem, tj. različnih metod rekonstrukcije dinamičnega relaksacijskega modula, k natančnosti aproksimacije z izračunom pripadajočih relaksacijskih spektrov. Ugotovljeno je bilo, da ne obstaja edinstven matematični pristop za izračun relaksacijskih spektrov, ki bi zagotavljal zadovoljivo aproksimacijo eksperimentalno določenih dinamičnih modulov za izbrane vrste polimernih materialov. Priporočljivo je vzporedno kombinirati različne numerične metode, da dosežemo razumno aproksimacijo funkcij materiala.

Concentrating solar power (CSP) is a high-potential renewable energy source that can leverage various thermal applications. CSP plant development has therefore become a global trend. However, the designing of a CSP plant for a given solar resource condition and financial situation is still a work in progress. This study aims to develop a mathematical model to analyze the levelized cost of electricity (LCOE) of Thermal Energy Storage (TES)-integrated CSP plants in such circumstances. The developed model presents an LCOE variation for 18 different CSP configurations with TES incorporated for Rankine, Brayton, and combined power generation cycles, under regular TES materials and nano-enhanced TES materials. The model then recommends the most economical CSP plant arrangement. Within the scope of this study, it was found that the best configuration for electricity generation is a solar power tower with nano-enhanced phase change materials as the latent heat thermal energy storage medium that runs on the combined cycle. This returns an LCOE of 7.63 ct/kWh with a 22.70% CSP plant efficiency. The most favorable option in 50 MW plants is the combined cycle with a regular TES medium, which has an LCOE of 7.72 ct/kWh with a 22.14% CSP plant efficiency.

To achieve a fully automatic artificial pancreas (AP), i.e., an AP without the need for meal announcements, the intraperitoneal (IP) route is explored. This route has faster dynamics than the typical subcutaneous (SC) route. Model predictive control (MPC) is the most promising control algorithm, but it requires a predictive and identifiable model. This paper presents the design of such a model for MPC-based dual hormone IP APs. This model is trained and tested on recorded data from anesthetized pigs. Animal experiments show that the saturation of the hepatic first-pass effect is essential in how IP insulin and IP glucagon affect glucose levels. These physiological phenomena must be modeled to estimate the system behavior for various conditions. This, in turn, increases the number of parameters and complicates system identification. The availability of rich experimental data from 26 animal trials motivated the design of a technique to exploit this prior information to ensure the identifiability of our model. Through this technique, most parameters were either modeled as body weight functions or common among animals. The correlation between parameter values and body weight is discovered utilizing prior data from various animal experiments, such as blood glucose, plasma insulin, and glucagon levels, in which hormones were administered intraperitoneally or intravenously. This method simplifies the system identification for every new subject while keeping the model’s essential details that improve the prediction capability relative to comparable models. The model can be exploited in MPC or any other model-based controller of a bi-hormonal IP AP. It can also be used as a simulator to develop control approaches for single and bi-hormonal IP APs.

Design and optimization of microalgae processes have traditionally relied on the application of unsegregated mathematical models, thus neglecting the impact of cell-to-cell heterogeneity. However, there is experimental evidence that the latter one, including but not limited to variation in mass/size, internal composition and cell cycle phase, can play a crucial role in both cultivation and downstream processes. Population balance equations (PBEs) represent a powerful approach to develop mathematical models describing the effect of cell-to-cell heterogeneity. In this work, the potential of PBEs for the analysis and design of microalgae processes are discussed. A detailed review of PBE applications to microalgae cultivation, harvesting and disruption is reported. The review is largely focused on the application of the univariate size/mass structured PBE, where the size/mass is the only internal variable used to identify the cell state. Nonetheless, the need, addressed by few studies, for additional or alternative internal variables to identify the cell cycle phase and/or provide information about the internal composition is discussed. Through the review, the limitations of previous studies are described, and areas are identified where the development of more reliable PBE models, driven by the increasing availability of single-cell experimental data, could support the understanding and purposeful exploitation of the mechanisms determining cell-to-cell heterogeneity.

Optically pure fluorinated organic azides represent synthetically valuable building blocks in a range of industrial applications. Since direct fluorination of molecules is challenging from both economic and environmental perspective, the development of novel methods for modifying existing fluorinated synthons is highly desirable. In this work, enantioselective azidolysis of fluorinated aromatic epoxides catalysed by halohydrin dehalogenase (HHDH) was explored. A series of 11 fluorinated epoxides were evaluated as substrates from the viewpoint of hydrolytic stability and enzyme kinetics. Synthesis of enantiopure (R)-2-azido-1-[4-(trifluoromethyl)phenyl]ethanol with HheC-W249P variant was selected for detailed kinetic investigation. Reaction bottlenecks were identified and discussed from the reaction engineering perspective. Epoxide hydrolysis, enzyme inhibitions and operational stability decay were found to undesirably affect the reaction outcome. Understanding the kinetic limitations and applying model-based process simulations enabled the selection of reactor type and initial conditions favouring biotransformation. High substrate loadings are not suitable since they support hydrolysis, enzyme deactivation, and substrate inhibition. By selecting a repetitive batch reactor set-up, the reaction yield of 95% could be obtained, together with the increase in the reaction selectivity of 100% compared to the batch reactor. To the best of our knowledge, the developed mathematical model represents so far the first of its kind with HHDH enzymes, thus bringing valuable insights into kinetic and catalytic performance of this enzyme group, as well as the reaction type. It is expected that, with minor adaptations, it could be generalized and applied to give qualitative insight into behaviour of similar systems.

Among all hydrocarbons, the methane molecule contains the highest amount of hydrogen with respect to carbon. Therefore, the catalytic decomposition of methane is considered as an efficient approach to produce hydrogen along with nanostructured carbon product. On the other hand, the presence of hydrogen in the composition of the initial gas mixture is required for the stable operation of the catalyst. In present work, the experiments on the catalytic decomposition of methane–hydrogen mixture were performed in a flow-through quartz reactor equipped with McBain balances under atmospheric pressure. The catalyst NiO-CuO/Al2O3 was prepared by the mechanochemical activation technique. The maximum carbon yield of 34.9 g/gcat was obtained after 2 h of experiment at 610 °C. An excess of hydrogen in the reaction mixture provided the long-term activity of the nickel–copper catalyst. The durability tests ongoing for 6 h within a temperature range of 525–600 °C showed no noticeable deactivation of the catalyst. Two kinetic models, D1a and M1a, were proposed for the studied decomposition of the methane–hydrogen mixture over the nickel–copper catalyst. The kinetic constants for these models were determined by means of mathematical modelling.

International audience; Context Crop rotations, within-field mixtures, and landscape mosaics including susceptible and resistant crops are three commonly adopted crop diversification strategies that can limit crop epidemics. Typically, the effects of crop diversification at these three scales have been studied separately, on single pathogen species, and with low environmental variability. Objectives We aim to compare the disease-limitation effect of these three types of crop diversification on two highly damaging fungal pathogens of wheat Puccinia recondita (WLR) and Zymoseptoria tritici (STB) and under varying weather conditions (warmer or cooler climate for WLR, wetter or drier conditions for STB). Methods We built a dynamic mathematical model of epidemics at the field scale (based on classical Susceptible-Exposed-Infectious-Removed epidemiological models) embedded in a spatially explicit landscape grid framework. We use it to simulate an agricultural landscape in which diversification translates into different proportions of wheat and resistant crops in the landscape. Results In our simulations, for both pathogens and in all weather conditions, within-field crop mixtures had the greatest impact in limiting epidemics, crop rotations were second-best, while landscape mosaics were the least effective. We also found that the threshold above which further addition of resistant plants to crop mixtures would not cause further disease limitation to be dependent on weather conditions. The more favorable the weather is for pathogens the more resistant plants are required. Conclusions Our findings imply that interactions between spatial scale of crop diversification, pathogen characteristics and weather conditions should be considered in order to maximize benefits from disease-regulation properties of diversified cropping systems under climate change.

The theoretical model for a packed porous catalytic particle of the slab, cylindrical, and spherical geometries shape in fixed-bed electrochemical reactors is discussed. These particles have internal mass concentration and temperature gradients in endothermic or exothermic reactions. The model is based on a nonlinear reaction–diffusion equation containing a nonlinear term with an exponential relationship between intrinsic reaction rate and temperature. The porous catalyst particle’s concentration is obtained by solving the nonlinear equation using Akbari-Ganji’s method. A simple and closed-form analytical expression of the effectiveness factor for slab, cylindrical, and spherical geometries was also reported for all values of Thiele modulus, activation energy, and heat reaction. The accordance with results of a reliable numerical method shows the good accuracy that their approximate solution yields.

BackgroundCrimean-Congo haemorrhagic fever (CCHF) is a priority emerging pathogen for which a licensed vaccine is not yet available. We aim to assess the feasibility of conducting phase III vaccine efficacy trials and the role of varying transmission dynamics.MethodsWe calibrate models of CCHF virus (CCHFV) transmission among livestock and spillover to humans in endemic areas in Afghanistan, Turkey and South Africa. We propose an individual randomised controlled trial targeted to high-risk population, and use the calibrated models to simulate trial cohorts to estimate the minimum trial endpoints necessary to analyse vaccine efficacy, sample size and follow-up time in the three settings.ResultsUnder assumptions of a minimum vaccine efficacy of 60%, the minimum sample size needed to accrue the required 150 clinical endpoints in a minimum follow-up time of 6 months is estimated to be 34,000 (CrI 95%, 16,750 – 88,725) and 37,000 (CrI 95%, 13,000 – 77,250) in Afghanistan and Turkey, respectively. The results suggest that for South Africa the low endemic transmission levels will not permit achieving the necessary conditions for conducting this trial within a realistic follow-up time. In a scenario of CCHFV infection (rather than clinical case) as trial endpoint, the required sample size is reduced by 70% to 80% in Afghanistan and Turkey, and in South Africa, a trial becomes feasible for large sample sizes (>75,000) and vaccine efficacy of >70%. Increased expected vaccine efficacy >60% will reduce the required number of trial endpoints and thus the sample size and follow-time in phase III trials.ConclusionsUnderlying endemic transmission levels will play a central role in defining the feasibility of phase III vaccine efficacy trials. Endemic settings in Afghanistan and Turkey offer conditions under which such studies could feasibly be conducted.

The code necessary to replicate the results presented in Chapters 3&4 of the thesis. Note that due to licensing agreements all climate reanalysis data has been excluded from this repository, but these freely available from the ERA5 hourly land reanalysis dataset on Copernicus In this repository are the following files: AMgam.csv - The output of a GAMM that defines a relationship between temperature, adult wing length and mortality AO2.jl - The implementation of the phenotypically plastic model to predict the population dynamics of Aedes albopictus Dat_read_Clim_Make.R - Example of how to produce the climate data necessary to replicate the results of the thesis. This file reproduces all climate data from Europe. Dens_Temp_WL.xlsx - A collection of all the life-history traits used to parametrise the reaction norms used in the mosquito models Fin_LSurv.csv -The output of a GAMM that defines a relationship between temperature, larval density and larval through-stage survival LDgam.csv -The output of a GAMM that defines a relationship between temperature, larval density and larval stage duration Parametrisation.Rmd - The reaction norm fitting process R_0_comp.jl- Produces outputs from the SIR model RMSE_fit.jl- Used to find the scaling factor and time shift that maximises R^2 between prediction and field observation RO2.jl- Produces outputs for the model for the population dynamics of Aedes albopictus SO2.jl- The SIR model for dengue vectored by Aedes albopictus WL_re.csv-The output of a GAMM that defines a relationship between temperature, larval density and adult wing length

Surface irrigation methods enable a lower cost of investment and energy requirements than pressurized systems if they are designed and managed properly. The aim of this investigation was to devise a new simulation model that would enable the determination of the optimum water application time and furrow length in a blocked end furrow system. The infiltration properties of the soil, net irrigation water requirement of the crop and inflow to the furrow constitute the main variables of this process. Deep percolation and the cross-sectional area of the wetting pattern where the net irrigation water requirement of the crop is met along the furrow are the main components that were simulated interactively in the model. They were described as a function of time. The proposed model devised in this investigation was run for two different sample applications. While values of 93 and 94% water application efficiencies were obtained by running the USDA SCS method for the first and second sample applications, respectively, values of 92 and 94% were obtained, respectively, from the proposed model. These results indicate that the proposed model can be used in the design of a blocked end furrow system.

Background In countries with mature generalized HIV epidemics such as Uganda, there are still groups of individuals that are disproportionately affected. Among the key populations in Uganda are fishing communities, which make up about 10% of the population. Compared to the general population, HIV prevalence and incidence among individuals living in these communities is high. This high HIV burden has been attributed to several factors including limited access to prevention and treatment services as well as ongoing high-risk sexual behaviour. Methods We investigated the impact of combined HIV prevention interventions on HIV transmission dynamics in high-risk fishing communities in Uganda using a deterministic compartmental model. The model was calibrated to seroprevalence data from a census performed in 2014. To account for remaining uncertainty in the calibrated model parameters, 50 000 simulated scenarios were modelled to investigate the impact of combined prevention interventions. Results The projected HIV incidence decreased from 1.87 per 100 PY without intervention scale-up to 0.25 per 100 PY after 15 years (2014–2029) of intervention scale-up. A potential combination achieving this 87% reduction in incidence over 15 years in Ugandan FCs included condom use in about 60% of sexual acts, 23% of susceptible men circumcised, 87% of people living with HIV aware of their status, 75% of those on ART, and about 3% of susceptible individuals on oral PrEP. Uncertainty analysis revealed relative reductions in incidence ranging from 30.9 to 86.8%. Sensitivity analyses suggested that condom use and early ART were the most important interventions. Conclusion Reducing HIV incidence, as well as prevalence and AIDS-related mortality, in these high-risk fishing communities in Uganda is attainable over 15 years with a combination prevention package. Our projected intervention coverage levels are well within the national targets set by the Uganda government and enable coming close to reaching the UNAIDS 95-95-95 targets to end AIDS as a public health threat by 2030.

System identification (SI) is a method of determining a mathematical model for a system given a set of input-output data. A representation is made using a mathematical model based on certain specified assumptions. In SI, model structure selection is a step where a model structure perceived as an adequate system representation is selected. A typical rule is that the final model must have a good balance between parsimony and accuracy. As a popular search method, genetic algorithm (GA) is used for selecting a model structure. However, the optimality of the final model depends much on the effectiveness of GA operators. This paper presents a mating technique named single parent mating (SPM) in GA for use in a real robotic SI. This technique is based on the chromosome structure of the parents such that a single parent is sufficient in achieving mating that eases the search for the optimal model. The results show that using three different objective functions (Akaike information criterion, Bayesian information criterion and parameter magnitude–based information criterion 2) respectively, GA with the mating technique is able to find more optimal models than without the mating technique. Validations show that the selected models using the mating technique are acceptable.

Plant diseases pose a significant threat to food security, and fungal plant pathogens can be particularly damaging due to enormous evolutionary potential. Two major control strategies for fungal pathogens include chemical control with fungicides and use of disease-resistant cultivars. Both strategies are threatened by pathogen evolution leading to fungicide resistance and loss of cultivar efficacy (‘cultivar breakdown’). Both fungicide resistance and cultivar breakdown can be characterised as qualitative or quantitative, depending on the genetic basis for resistance/breakdown. Mathematical models have an important role in understanding fungicide resistance and cultivar breakdown, and modelling studies offer numerous advantageous over experimental studies. We present a model of qualitative fungicide resistance and one of quantitative fungicide resistance and cultivar breakdown. The model of qualitative resistance extends a model from the literature, while the quantitative resistance model is entirely novel. Both models are parameterised to address Septoria, the most prevalent disease of wheat. Although qualitative resistance has been widely studied, many single-site fungicides (i.e. those challenged by qualitative resistance) face widespread resistance, meaning that quantitative resistance is increasingly important. However, the mechanisms underlying quantitative resistance/breakdown are more complex and suitable data for model fitting is harder to source. We present the first model of quantitative resistance to be fitted to field data for both fungicide resistance and cultivar breakdown. Fungicide mixtures can help delay resistance. Although many studies focus on mixtures of fungicides to which resistance is qualitative, the optimal strategy is not characterised if the initial resistance frequencies (RFs) to two fungicides in a mixture differ. Past work showed that equal selection for single resistant strains in the first year was the optimal strategy when initial RFs were equal but did not consider when the initial RFs differ. We show that this strategy is often sub-optimal if the initial RFs differ and present an alternative strategy based on equalising RFs in the breakdown year. We test the robustness of this strategy to changes in parameters controlling fungicide efficacy and pathogen epidemiology, including between-season pathogen sexual reproduction. Previous modelling studies of Septoria neglected pathogen sexual reproduction, for simplicity, despite evidence that sexual reproduction is an important part of Septoria’s life cycle. We use the quantitative resistance model to determine how the number of fungicide applications per year affects resistance development, disease severity and yield. We consider how the optimal strategy varies depending on the time-frame of interest, before exploring how cultivar and fungicide control can be optimally combined to control the pathogen whilst minimising degradation of host and fungicide. We explore the effect of fungicide dose and compare the recommendations from the quantitative resistance model to those from the qualitative resistance model. Most fungicide resistance studies consider strategies which are fixed in time – i.e. rely on the same tactic used every year until failure. We present a flexible approach to optimise time-variable strategies, based on dynamic programming. This allows us to address an otherwise computationally infeasible problem to find the optimal strategy when time-variable strategies are permitted. We compare the improvement offered by the optimal time-variable strategy to the optimal fixed-time strategy., BBSRC DTP funding

Bacteria are constantly sensing their environment, and must respond as it changes. Some of their most common systems for sensing and responding to change are alternative sigma factors. These are a type of transcription factor, and unique in that they integrate into the RNA polymerase molecule itself, often with dramatic effect on the bacterium’s transcriptional program. They exist in great diversity, both within and across bacterial species. Recent advances in single-cell experimental techniques have enabled studies of alternative sigma factor responses in individual cells, revealing a range of possible behaviours. These are often heterogeneous across isogenic populations, suggesting that sigma factor systems are highly noisy. In this thesis, we use stochastic modelling techniques to study what responses alterna- tive sigma factors can generate, and how these are generated. First, we present the Catalyst.jl tool for modelling chemical reaction networks. It is a useful systems biology tool that we will use to implement models of one general, and two specific (σV and σB , both in Bacillus subtilis), sigma factor circuits. Our σV model demonstrates how this circuit’s bistability properties can generate the heterogeneous activation dynamics observed experimentally. It makes additional predictions (including a memory of previous environmental conditions) that are then validated experimentally. Next, our σB model shows how this circuit’s properties enable it to generate two distinct responses, single pulse and stochastic pulsing dynamics, both previously observed in experiments. We show that, by tuning system parameters, the network can be biased towards either response behaviour, and that it can generate previously unobserved ones. Finally, we note that both the σV and the σB circuit generate their response through a mixed positive/negative feedback loop (a common alternative sigma factor circuit motif). We use this fact to build a general sigma factor model. In it, we predict a range of behaviours that these circuits should be capable of producing, including both previously observed and novel ones. We also predict how the circuit can be modulated to generate each behaviour. Our work provides detailed insight into two alternative sigma factor systems. In addition, it explains a general response mechanism these systems use, and how it can be tuned. This will be useful for synthetic biology applications, where alternative sigma factors can be used as controllers of synthetic circuits. It also reveals how bacteria can use alternative sigma factors to enable a range of strategies to respond to environmental change., This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No.721456

[EN] Due to developments in the financial marketplace, digitalization of finance and easy access to financial products, financial literacy is becoming increasingly important. The paper at hand introduces parts of a learning environment for mathematics classes that focuses on mathematical modelling and financial literacy. After theoretical considerations, two worksheets are presented, which deal with influences of the interest rate on the repayment of loans. Based on the description of a test run, the usability of the worksheets in class is concluded., [ES] Debido a la evolución del mercado financiero, la digitalización de las finanzas y el fácil acceso a los productos financieros, la alfabetización financiera es cada vez más importante. El artículo que nos ocupa presenta partes de un entorno de aprendizaje para clases de matemáticas que se centra en la modelización matemática y la alfabetización financiera. Tras las consideraciones teóricas, se presentan dos propuestas de trabajo que tratan sobre la influencia del tipo de interés en la devolución de los préstamos. A partir de la descripción de una prueba, se concluye la utilidad de las hojas de trabajo en clase.

Formulation of the problem. Formulation of the problem. Mathematical modelling is a very important component of mathematics education, because by applying the mathematical theories to practical needs of our everyday life increases the student interest for mathematics. The main steps of the mathematical modelling process include analysis of the given real world problem, formulation of the problem and construction of the mathematical model (mathematization), solution and control of the model and implementation of the final mathematical results to the real situation. Mathematization possesses the greatest difficulty among the steps of the MM process, because it involves a deep abstracting process, which is not always easy to be achieved by a non-expert. It is sometimes, however, the transition from the solution of the model to the real world (control and/or implementation of the model) that presents difficulties for students too. An example is given to illustrate this remark. Materials and methods. In this paper soft sets are used as tools for developing a model for assessing human activities in a parametric manner and an example is presented (assessment of football players performance) to illustrate its applicability under real situations. A soft set, being a parametrized family of subsets of the universal set of the discourse, is a generalization of the concept of fuzzy set designed on the purpose of dealing with the existing uncertainty in a parametric manner. The theory of soft sets has found many and important applications to several sectors of the human activity like decision making, parameter reduction, data clustering and data dealing with incompleteness, etc. Results. The soft set assessment model is applied for evaluating student mathematical modelling skills with respect to the parameters excellent, very good, good, mediocre, and failed. It serves both for assessing the general performance of a student class and the individual performance of each student with respect to the steps of the mathematical modelling process. Conclusions. The constructed in this paper model is very useful in cases where the assessment has qualitative rather than quantitative characteristics and could also be applied to a variety of other cases for assessing human and/or machine (e.g. computer programs) activities.

Introduction/purpose: A static absorber is capable of neutralizing any signal either in the physical or virtual domain and its analysis will be presented in this paper. Methods: The approach used here includes purely scientific thoughts as well as a model with its explanations evaluated step by step applying highly sophisticated computer tools for design and simulation. No empirical results will be attached, only claims with their evidence. Results: The crucial outcome of this research is a completely new approach to binary systems that are now observed as a set of real numbers. Conclusion: The purpose of this research is to introduce something brand-new that can be used in cyber industry while a dynamic variation of the absorber is still under development.

This work aims to apply the SIR-type compartmental model (Susceptible - Infected - Removed) in the evolution of Covid-19 in Paraíba's State and Campina Grande City. For that, the parameters of the model were considered to be variable during time evolution, within an appropriate range. The system of differential equations was solved numerically using the Euler method. The parameters were obtained by adjusting the model to the infected data provided by the Paraíba Health Department. According to the results obtained, the model describes the infected population well. There was a reduction in the effective reproduction number in Paraíba and the town of Campina Grande. It is noteworthy that understanding the dynamics of infection transmission and evaluating the effectiveness of control measures is crucial to assess the potential for sustained transmission to occur in new areas. The model can also be applied to describe epidemic dynamics in other regions and countries.

The objective of this study was to develop mathematical functions to predict deflection for radial and bias tires. In order to develop the models, the data were obtained from the tire manufacturing companies and organized in Excel first and then transferred to Minitab® for stepwise regression analysis. The variables considered in the study were inflation pressure, load and tire width and overall diameter. Tire width (w) and overall diameter (d) was considered in a multiplication form. The tire deflection models in two different form (linear and non-linear) were developed for both, radial and bias tires. The model selection was achieved by three different criteria and % differences between the measured and predicted data. Based on the results of applying model selection criteria, the models for radial and bias tire in non-linear form were found to be adequate for predicting the tire deflection. The results from the stepwise analysis indicated that the load on tire was the predominant variable in the models and made the highest contribution to the prediction functions. The developed models were verified against to published literature data and found a good agreement.

Effective planning and optimization of rail transport operations depends on effective and reliable forecasting of demand. The results of transport performance forecasts usually differ from measured values because the mathematical models used are inadequate. In response to this applicative need, we report the results of a study whose goal was to develop, on the basis of historical data, an effective mathematical model of rail passenger transport performance that would allow to make reliable forecasts of future demand for this service. Several models dedicated to this type of empirical data were proposed and selection criteria were established. The models used in the study are: the seasonal naive model, the Exponential Smoothing (ETS) model, the exponential smoothing state space model with Box–Cox transformation, ARMA errors, trigonometric trend and seasonal components (TBATS) model, and the AutoRegressive Integrated Moving Average (ARIMA) model. The proposed time series identification and forecasting methods are dedicated to the processing of time series data with trend and seasonality. Then, the best model was identified and its accuracy and effectiveness were assessed. It was noticed that investigated time series is characterized by strong seasonality and an upward trend. This information is important for planning a development strategy for rail passenger transport, because it shows that additional investments and engagement in the development of both transport infrastructure and superstructure are required to meet the existing demand. Finally, a forecast of transport performance in sequential periods of time was presented. Such forecast may significantly improve the system of scheduling train journeys and determining the level of demand for rolling stock depending on the season and the annual rise in passenger numbers, increasing the effectiveness of management of rail transport.

We investigate the problem of mathematical modeling of new corona virus (Covid19) in Poland and tries to predict the upcoming wave. A Gaussian mixture model is proposed to characterize the COVID-19 disease and to predict a new / future wave of COVID-19. This prediction is very much needed to prepare for medical setup and continue with the upcoming program. Specifically, data related to the new confirmed cases of COVID-19 per day are considered, and then we attempt to predict the data and statistical activity. A close match between actual data and analytical data by using the Gaussian mixture model shows that it is a suitable model to present new cases of COVID-19. In addition, it is thought that there are N waves of COVID-19 and that information for each future wave is also present in current and previous waves as well. Using this concept, predictions of a future wave can be made.

Актуальность исследования связана с обостряющимися вопросами регулирования углеродных выбросов при сжигании твердого топлива и повышением экологических требований к теплоэнергетическим станциям. Цель: с помощью математического моделирования исследовать перспективы рециркуляции СО2 на угольных электростанциях с внутрицикловой газификацией, провести анализ эффективности процесса газификации топлива в условиях oxyfuel, определить оптимальные режимы переработки каменного угля и оценить возможность реализации этих режимов с точки зрения технологических ограничений. Объект: процесс газификации угольной пыли в дутье с разным составом и начальной температурой. Метод: математическое моделирование процесса термохимической конверсии угольной пыли в одномерной стационарной постановке. Результаты. Построены расчетные зависимости характеристик процесса газификации (химический КПД, температура выходящего газа) от удельного расхода дутья ([alpha]=0,1-0,7), концентрации кислорода в нем (20-30 %) и начальной температуры (373-1373 К) для смесей O2/N2 и O2/CO2. Определены оптимальные значения удельных расходов и максимальные значения химического КПД во всем диапазоне параметров. Оценен вклад теплофизических и реакционных свойств газа в изменение химического КПД процесса при смене состава дутья. Для исследования эффективности нагрева дутья используется критерий, учитывающий внешний подвод теплоты. Анализ показывает что, перегрев воздушного дутья не дает положительного эффекта на состав продуктов газификации из-за существования жестких стехиометрических ограничений; перегрев углекислотного дутья позволяет не только повысить химический КПД, но и улучшить стабильность процесса при низких значениях удельного расхода дутья. The relevance of the study is associated with growing issues of regulating carbon emissions of solid fuel combustion and increasing environmental requirements for heat power plants. The aims of the study are investigation of CO2 recycling prospects at coal-fired power plants with internal gasification using mathematical modeling based on an analysis of the fuel conversion processes efficiency, determination of the coal processing optimal modes and evaluation of possibility of implementing these modes from the point of view of technological limitations. Object of the study is pulverized coal gasification in the atmospheres with different composition and initial temperature. Research method: mathematical modeling of the process of pulverized coal thermochemical conversion in one-dimensional stationary statement. Results. The author has plotted the calculated dependences of gasification characteristics (cold gas efficiency, temperature of the produced gas) on the specific flow rate of the gasification agent ([alpha]=0,1-0,7), oxygen concentration (20-30 %) and the initial temperature (373-1373 K) for O2/N2 and O2/CO2 mixtures. The optimal values of specific flow rates and the maximum values of cold gas efficiency in the entire range of parameters are determined. The author estimated the contribution of the thermophysical properties and gas reactivity to the change in the cold gas efficiency of the process when changing the composition of the gasification agent. To study the efficiency of heating oxidizer, the author used the criterion that takes into account heat external supply. The analysis shows that air overheating does not give a positive effect on composition of gasification products due to the strict stoichiometric restrictions; overheating of carbon dioxide allows not only increasing cold gas efficiency, but also improving process stability at low values of specific oxidizer consumption.

This is a commentary on the ESM 2021 Special Issue on Innovations in Measuring and Fostering Mathematical Modelling Competencies. We have grouped the ten studies into three themes: competencies, fostering, and measuring. The first theme and the papers therein provide a platform to discuss the cognitivist backgrounds to the different conceptualizations of mathematical modelling competencies, based on the modelling cycle. We suggest theoretical widening through a competence continuum and enriching of the modelling cycle with overarching, analytic dimensions for creativity, tool use, metacognition, and so forth. The second theme and the papers therein showcase innovative ideas on fostering and on the definition and analysis thereof. These reveal the need for a social turn in modelling research in order to capture aspects of student collaboration and agency, as well as tensions in fostering when tasks are derived from real-world scenarios, but socio-mathematical norms come from the (pure) mathematics classroom. The third theme, measuring, and the papers therein offer insights into the challenges of positivist research that aims to develop innovative measurement instruments that are both reliable and valid, particularly in light of student group work, cultural background, and other socio-cultural aspects. Drawing on the three discussions, we go on to make recommendations for further research.

Prey-predator system is enormously complex and nonlinear interaction between species. Such complexity regularly requires development of new approaches which involves more factors in analysis of its population dynamics. In this paper, we formulate a modified Lotka-Volterra model that incorporates factors such as refuge prey and immigrants. We investigate the effects of refuge prey and immigrants by varying the refuge factor, with and without immigrants. The results show that with Holling’s type I functional response, the proposed model is asymptotically convergent when a refuge prey factor is introduced. Moreover, with Holling’s type II functional response, the proposed mathematical model is unstable and does not converge. However, with Holling’s type III functional response in a system, the proposed mathematical model is asymptotically stable. These results point out the following remarks: The effects of refuge prey on stability of the dynamical system vary depending on the type of functional response, and when the predator population increases, the likelihood of prey extinction declines when the proportion of preys in refuge population increases. Hence, the factor of refuge prey is crucial for controlling the population of the predator and obtaining balances between prey and predator in the ecosystem. Keywords: Refuge prey, stability, prey-predator, immigrants, Mathematical modelling

In this paper some innovative aspects of the mathematical modelling of classic epidemiology problems for the study of models related to the COVID-19 pandemic dynamics are presented. In addition, they are compared to real-world data using numerical methods in order to approximate the solutions. One of these models includes a non-transmitting compartment and another one, a delay-differential equation in the SIR-type method. Finally, a comparative discussion of the results is also presented.

The approach to the formalization of the generation of problem situations applicable to the development of tutoring programs consisting of many tasks is considered. The main errors arising during the software-based generation of parameters are specified. Mathematical modeling of parametrical generation algorithms examined by examples of tasks that make up complex tests on mathematics for secondary schools. The parametric generation method proposed in the article allows getting the large quantitative variations in task problem situations. Thereby, every learner will get a personal unique set of tasks. The structure and functionality of web-tests complex consisting of tasks generated via the proposed method are described. The subject of research in the article is the process of computer training in mathematics. The goal is to develop a method for task generation for mathematical disciplines. Tasks. Research and analysis of the set of mathematical problems. Parameterization of each task and development method and algorithms for automated generation parameters with the determination of incorrect combinations of parameters or problem situations that have no solution. Estimation of borders of admissible for approximate answers. Evaluation of the user solution of a single task and a sequence of tasks. The general objective of the work is to make the software product consisting of a sequence of mathematics tasks. The software should have an extended user interface for the graphical presentation of various problem situations in various mathematical topics. The program must be accessible via the Internet. The following results were obtained: developed methods and algorithms of task generation, which provide correct problem situations and unique parameter sets for each user; described the program complex structure and developed the software system of mathematical web-tests provides two levels of difficulty. Conclusion. The scientific novelty lies in the development of the method of task generation for interactive web tests on the mathematics and its computer implementation with the possibility of graphical representation of tasks and checking of tasks correctness.

Notch signalling is a well-conserved signalling pathway that regulates cell fate through cell-cell communication. A typical feature of Notch signalling is ‘lateral inhibition’, whereby two neighbouring cells of equivalent state of differentiation acquire different cell fates. Recently, mathematical and computational approaches have addressed the Notch dynamics in Drosophila neural development. Typical examples of lateral inhibition are observed in the specification of neural stem cells in the embryo and sensory organ precursors in the thorax. In eye disc development, Notch signalling cooperates with other signalling pathways to define the evenly spaced positioning of the photoreceptor cells. The interplay between Notch and epidermal growth factor receptor signalling regulates the timing of neural stem cell differentiation in the optic lobe. In this review, we summarize the theoretical studies that have been conducted to elucidate the Notch dynamics in these systems and discuss the advantages of combining mathematical models with biological experiments.

A model is proposed that describes the transfer of ions and the process of water dissociation in a system with a bipolar membrane and adjacent diffusion layers. The model considers the transfer of four types of ions: the cation and anion of salt and the products of water dissociation – hydrogen and hydroxyl ions. To describe the process of water dissociation, a model for accelerating the dissociation reaction with the participation of ionogenic groups of the membrane is adopted. The boundary value problem is solved numerically using COMSOL® Multiphysics 5.5 software. An analysis of the results of a numerical experiment shows that, at least in a symmetric electromembrane system, there is a kinetic limitation of the water dissociation process, apparently associated with the occurrence of water recombination reaction at the of the bipolar region. An interpretation of the entropy factor (β) is given as a characteristic length which shows the possibility of an ion that appeared as a result of the water dissociation reaction to be removed from the reaction zone without participating in recombination reactions.

Radiosensitizers have proven to be an effective method of improving radiotherapy outcomes, with the distribution of particles being a crucial element to delivering optimal treatment outcomes due to the short range of effect of these particles. Here we present a computational model for the transport of nanoparticles within the tumour, whereby the fluid velocity and particle deposition are obtained and used as input into the convection-diffusion equation to calculate the spatio-temporal concentration of the nanoparticles. The effect of particle surface charge and injection locations on the distribution of nanoparticle concentration within the interstitial fluid and deposited onto cell surfaces is assessed. The computational results demonstrate that negatively charged particles can achieve a more uniform distribution throughout the tumour as compared to uncharged or positively charged particles, with particle volume within the fluid being 100% of tumour volume and deposited particle volume 44.5%. In addition, varying the injection location from the end to the middle of the tumour caused a reduction in particle volume of almost 20% for negatively charged particles. In conclusion, radiosensitizing particles should be negatively charged to maximise their spread and penetration within the tumour. Choosing an appropriate injection location can further improve the distribution of these particles.

This paper presents the results of an experimental study of adhesive joint strength with consideration of the inaccuracy of the hardener dosage, in the context of evaluating the degradation of joints when used either at ambient or elevated temperatures. The butt joint strength characteristics were assessed for two types of adhesives—rigid and flexible—and two curing scenarios—with and without heat curing. An excess hardener was shown to be significantly more unfavourable than its deficiency, which can ultimately be considered as a recommendation for forming epoxy adhesive joint assemblies. In order to fully understand the relationship between the analysed mechanical properties of the material and the influence of component ratio excesses and heating, a process of fitting basic mathematical models to the obtained experimental data was also performed.

The choice of an objective function in constructing a mathematical model of an experimental wide-angle X-ray diffraction curve of semi-crystalline polymers is discussed., To decompose a wide-angle X-ray diffraction (WAXD) curve of a semi-crystalline polymer into crystalline peaks and amorphous halos, a theoretical best-fitted curve, i.e. a mathematical model, is constructed. In fitting the theoretical curve to the experimental one, various functions can be used to quantify and minimize the deviations between the curves. The analyses and calculations performed in this work have proved that the quality of the model, its parameters and consequently the information on the structure of the investigated polymer are considerably dependent on the shape of an objective function. It is shown that the best models are obtained employing the least-squares method in which the sum of squared absolute errors is minimized. On the other hand, the methods in which the objective functions are based on the relative errors do not give a good fit and should not be used. The comparison and evaluation were performed using WAXD curves of seven polymers: isotactic polypropyl­ene, polyvinylidene fluoride, cellulose I, cellulose II, polyethyl­ene, polyethyl­ene terephthalate and polyamide 6. The methods were compared and evaluated using statistical tests and measures of the quality of fitting.

A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.

The combat capabilities of modern means of warfare in the air largely depend on the reliable operation of on-board electronic means (OEM) and weapon control systems of fighter aircraft. Therefore, in the course of military operations, each of the warring parties seeks to disorganise the operation of the enemy's radio-electronic systems and weapon controls as much as possible and ensure the stable operation of their own OEM by all means. This task is assigned to the means of electronic warfare (EW). During air combat, this task is assigned to the aircraft jamming station, whose place and role in modern air combat is constantly growing. The efficiency of the operation of this system is directly related to the aircraft survivability during a combat mission. This study considers the developed approach to the output of initial data on modelling the operation of airborne radars in conditions of interference and simultaneous active counteraction to enemy interference stations. The authors in this study have suggested a mathematical description of the air combat situation, which occurs when using methods of active countermeasures to enemy airborne interference systems by changing the parameters of the operation of the airborne gun-laying radar (AGLR). Indicators and criteria that characterise the effectiveness of the operation of airborne radars, depending on the method of counteraction used, were proposed, including a sequence of possible applications of the known four methods of counteraction, taking into account the features of their application.

Given the escalating healthcare costs around the world (more than 10% of the world's GDP) and increasing demand hospitals are under constant scrutiny in terms of managing services with limited resources and tighter budgets. Hospitals endeavour to find sustainable solutions for a variety of challenges ranging from productivity enhancements to resource allocation. For instance, in the UK, evidence suggests that hospitals are struggling due to increased delayed transfers of care, bed-occupancy rates well above the recommended levels of 85% and unmet A&E performance targets. In this paper, we present a hybrid forecasting-simulation-optimisation model for an NHS Foundation Trust in the UK. Using the Hospital Episode Statistics dataset for A&E, outpatient and inpatient services, we estimate the future patient demands for each speciality and model how it behaves with the forecasted activity in the future. Discrete event simulation is used to capture the entire hospital within a simulation environment, where the outputs is used as inputs into a multi-period integer linear programming (MILP) model to predict three vital resource requirements (on a monthly basis over a 1-year period), namely beds, physicians and nurses. We further carry out a sensitivity analysis to establish the robustness of solutions to changes in parameters, such as nurse-to-bed ratio. This type of modelling framework is developed for the first time to better plan the needs of hospitals now and into the future.

Wastewater heat recovery upstream of wastewater treatment plants (WWTPs) poses a risk to treatment performance, i.e. the biological processes. In order to perform a sustainability analysis, a detailed prediction of the temperature dynamics over the WWTP is needed. A comprehensive set of heat balance equations was included in a plant-wide process model and validated for the WWTP in Linköping, Sweden, to predict temperature variations over the whole year in a temperate climate. A detailed model for the excess heat generation of biological processes was developed. The annual average temperature change from influent to effluent was 0.78 °C with clear seasonal variations; 45% of the temperature change arises from processes other than the activated sludge unit. Hence, plant-wide energy modelling was necessary to predict in-tank temperature in the biological treatment steps. The energy processes with the largest energy gains were solar radiation and biological processes, while the largest losses were from conduction, convection and atmospheric radiation. Tanks with large surface areas have a significant impact on the heat balance regardless of biological processes. Simulating a 3 °C lower influent temperature, the temperature in the activated sludge unit dropped by 2.8 °C, which had a negative impact on nitrogen removal. HIGHLIGHTS The annual average temperature change (ΔT) was +0.78 °C from influent to effluent.; Biological processes had the largest energy contribution.; 45% of ΔT arises from other processes than activated sludge. Hence, plant-wide energy modelling is necessary.; ΔT shows strong seasonal variation in colder climates. Dynamic parameters are necessary.; Tanks with large open surface areas have significant impact on the heat balance.

Tijuana, Mexico, has a concentrated HIV epidemic among overlapping key populations (KPs) including people who inject drugs (PWID), female sex workers (FSW), their male clients, and men who have sex with men (MSM). We developed a dynamic HIV transmission model among these KPs to determine the extent to which their unmet prevention and treatment needs is driving HIV transmission. Over 2020-2029 we estimated the proportion of new infections acquired in each KP, and the proportion due to their unprotected risk behaviours. We estimate that 43.7% and 55.3% of new infections are among MSM and PWID, respectively, with FSW and their clients making-up 10% of new infections. Projections suggest 93.8% of new infections over 2020-2029 will be due to unprotected sex between MSM or unsafe injecting drug use. Prioritizing interventions addressing sexual and injecting risks among MSM and PWID are critical to controlling HIV in Tijuana.Tijuana, México, tiene una epidemia de VIH concentrada en poblaciones claves (PC) superpuestas que incluyen personas que se inyectan drogas (PID), trabajadoras sexuales (MTS), sus clientes hombres, y hombres que tienen sexo con hombres (HSH). Desarrollamos un modelo dinámico de transmisión de VIH en estas PC para determinar hasta dónde sus necesidades no atendidas de prevención y tratamiento dirigen la transmisión del VIH. Para 2020–2029 estimamos la proporción de nuevas infecciones adquiridas en cada PC, y la proporción atribuida a sus comportamientos de riesgo sin protección. Estimamos que 43.7% y 55.3% de nuevas infecciones se dan en HSH y PID, respectivamente, con MTS y clientes conformando 10% de nuevas infecciones. Las proyecciones sugieren que 93.8% de nuevas infecciones en 2020–2029 se deberán a sexo sin protección en HSH o uso inseguro de drogas inyectables. Dar prioridad a intervenciones que atienden los riesgos sexual y de inyección en HSH y PID es crítico para controlar el VIH en Tijuana.

Mathematics constitutes a key component in engineering education. Engineering students are traditionally offered a number of mathematics courses which provide the knowledge needed at the workplace. Unfortunately, many students perceive mathematics as a discipline that teaches mostly procedures not relevant to their future careers and often view it as one of the main obstacles on their way to an engineering degree. In this paper, we discuss how introducing university students in a standard Differential Equations course to mathematical modelling (MM), a powerful strategy for solving real-life problems, contributes to the development of their mathematical competencies, motivates their interest to mathematics, promotes the use of advanced mathematical thinking, methods of applied mathematics, and digital computational tools.

Individual differences in semantic categorization are commonplace. Individuals apply a word like SPORTS to different instances because they employ different conditions for category membership (vagueness in criteria) or because they differ regarding the extent to which they feel the term can be applied given fixed conditions (vagueness in degree). Three individuals may, for instance, disagree as to whether chess and hiking are SPORTS, because one believes SPORTS are competitive in nature, while the other two require SPORTS to be effortful (vagueness in criteria). On the basis of whether they consider hiking sufficiently effortful or not, the latter two individuals might still disagree as to whether to call it a SPORT (vagueness in degree). We investigated whether there are systematic age-related differences in semantic categorization by analyzing the categorization decisions of 1,868 adults for eight semantic categories with a formal model that allows the two sources of categorization differences to be disentangled. We found that young and older adults assess instances differently with respect to the categorization conditions and that older adults employ a lower threshold for category membership than young adults do. We recommend that these criteria and degree differences are taken into account in studies of age-related semantic processing. ispartof: Journal of Cognition vol:2 issue:1 pages:1-20 ispartof: location:England status: published

Advances in functional magnetic resonance spectroscopy (fMRS) have enabled the quantification of activity-dependent changes in neurotransmitter concentrations in vivo. However, the physiological basis of the large changes in GABA and glutamate observed by fMRS (>10%) over short time scales of less than a minute remain unclear as such changes cannot be accounted for by known synthesis or degradation metabolic pathways. Instead, it has been hypothesized that fMRS detects shifts in neurotransmitter concentrations as they cycle from presynaptic vesicles, where they are largely invisible, to extracellular and cytosolic pools, where they are detectable. The present paper uses a computational modelling approach to demonstrate the viability of this hypothesis. A new mean-field model of the neural mechanisms generating the fMRS signal in a cortical voxel is derived. The proposed macroscopic mean-field model is based on a microscopic description of the neurotransmitter dynamics at the level of the synapse. Specifically, GABA and glutamate are assumed to cycle between three metabolic pools: packaged in the vesicles; active in the synaptic cleft; and undergoing recycling and repackaging in the astrocytic or neuronal cytosol. Computational simulations from the model are used to generate predicted changes in GABA and glutamate concentrations in response to different types of stimuli including pain, vision, and electric current stimulation. The predicted changes in the extracellular and cytosolic pools corresponded to those reported in empirical fMRS data. Furthermore, the model predicts a selective control mechanism of the GABA/glutamate relationship, whereby inhibitory stimulation reduces both neurotransmitters, whereas excitatory stimulation increases glutamate and decreases GABA. The proposed model bridges between neural dynamics and fMRS and provides a mechanistic account for the activity-dependent changes in the glutamate and GABA fMRS signals. Lastly, these results indicate that echo-time may be an important timing parameter that can be leveraged to maximise fMRS experimental outcomes.

In this study, which will provide a visionary perspective on the design and manufacture of armed unmanned aerial vehicles and their different generations in the future; A concept design of a mini unmanned aerial vehicle suitable for Special Forces and military tactical use was made. The vehicle which is a tactical armed unmanned aerial vehicle (AUAV) with a weapon system capable of shooting at horizontal, vertical and intermediate angles, tracking the target in motion, aiming and firing. The mathematical modeling of the design for the weapon system was created using complex numbers. The mathematical modeling was transferred to the computer calculations programs. The parametric data calculated were verified by simulations made on the computer., Silahlı insansız hava araçlarının ve bu araçların gelecekteki farklı nesillerinin tasarım ve imalatına vizyonlu bir bakış açısı sunacak bu çalışmada; özel kuvvetler ve askeri taktik kullanım alanına uygun, mini insansız hava aracı konsept tasarımı yapılmıştır. Söz konusu araç; yatay, dikey ve ara açılarda atış yapabilen, hedefi hareket halinde takip eden, nişan alıp ateşleme yapabilen bir silah sistemine sahip taktik silahlı insansız hava aracıdır (SİHA). Tasarımın, silah sistemine ait matematiksel modellemesi karmaşık sayılar kullanılarak oluşturulmuştur. Yapılan matematiksel modelleme bilgisayar ortamına aktarılmıştır. Elde edilen parametrik veriler, bilgisayar ortamında yapılan simülasyonlar ile doğrulanmıştır.

Flagellar motility is critical to natural and many forms of assisted reproduction. Rhythmic beating and wave propagation by the flagellum propels sperm through fluid and enables modulation between penetrative progressive motion, activated side-to-side yaw and hyperactivated motility associated with detachment from epithelial binding. These motility changes occur in response to the properties of the surrounding fluid environment, biochemical activation state, and physiological ligands, however a parsimonious mechanistic explanation of flagellar beat generation that can explain motility modulation is lacking. In this paper we present the Axonemal Regulation of Curvature, Hysteretic model (ARCH), a curvature control-type theory based on switching of active moment by local curvature, embedded within a geometrically nonlinear elastic model of the flagellum exhibiting planar flagellar beats, together with nonlocal viscous fluid dynamics. The biophysical system is parameterised completely by four dimensionless parameter groupings. The effect of parameter variation is explored through computational simulation, revealing beat patterns that are qualitatively representative of penetrative (straight progressive), activated (highly yawing) and hyperactivated (non-progressive) modes. Anaylsis of the flagellar limit cycles and associated swimming velocity reveals a cusp catastrophe between progressive and non-progressive modes, and hysteresis in the response to changes in critical curvature parameter. Quantitative comparison to experimental data on human sperm exhibiting typical penetrative, activated and hyperactivated beats shows a good fit to the time-average absolute curvature profile along the flagellum, providing evidence that the model is capable of providing a framework for quantitative interpretation of imaging data., 14 pages, 4 figures main manuscript

Copyright © 2022 The Authors. Objectives: Over time, papers or reports may come to be taken for granted as evidence for some phenomenon. Researchers cite them without critically re-examining findings in the light of subsequent work. This can give rise to misleading or erroneous results and conclusions. We explore whether this has occurred in the widely reported outbreak of SARS-CoV-2 at a rehearsal of the Skagit Valley Chorale in March 2020, where it was assumed, and subsequently asserted uncritically, that the outbreak was due to a single infected person. Study design: Review of original report and subsequent modelling and interpretations. Methods: We reviewed and analysed original outbreak data in relation to published data on incubation period, subsequent modelling drawing on the data, and interpretations of transmission characteristics of this incident. Results: We show it is vanishingly unlikely that this was a single point source outbreak as has been widely claimed and on which modelling has been based. Conclusion: An unexamined assumption has led to erroneous policy conclusions about the risks of singing, and indoor spaces more generally, and the benefits of increased levels of ventilation. Although never publicly identified, one individual bears the moral burden of knowing what health outcomes have been attributed to their actions. We call for these claims to be re-examined and for greater ethical responsibility in the assumption of a point source in outbreak investigations. Funding: None declared.

This research investigated an alternate method for establishing the complex coefficients used in an electric vehicle’s mathematical energy consumption model. While other methods for creating electric vehicle energy models exist, it would be beneficial to have a rapid and inexpensive technique that remains accurate. Producing a mathematical energy model for such a vehicle has the challenge of determining its aerodynamic drag and rolling resistance coefficients. Currently and most often, expensive and tedious (time-consuming) methods are used to find these coefficients. Computational fluid dynamics (CFD), wind tunnel testing, and extensive mathematics make this objective challenging. For this work, a solar-powered electric vehicle provided the source data to derive its coefficients cost-effectively and efficiently. Data were collected during a road test of the solar electric vehicle from South Africa to Namibia stretching over 2000 km, in which all required energy variables were recorded. The collected data were used in an optimisation routine to establish the two coefficients by minimising the actual and modelled energy consumption error and controlling the driving speed. The outcome of the optimisation routine produced accurate coefficients with a final error value of less than 5% when applied to a validation data set not used during optimisation. With minor modifications, this method may be integrated into any electric vehicle computer system to autonomously identify its two hard-to-find coefficients while driving, which can be used to provide an accurate and realistic driving range estimation to the driver.

One of the main inducers of autophagy-dependent self-cannibalism, called ULK1, is tightly regulated by the two sensor molecules of nutrient conditions and energy status, known as mTOR and AMPK kinases, respectively. Recently, we developed a freely available mathematical model to explore the oscillatory characteristic of the AMPK-mTOR-ULK1 regulatory triangle. Here, we introduce a systems biology analysis to explain in detail the dynamical features of the essential negative and double-negative feedback loops and also the periodic repeat of autophagy induction upon cellular stress. We propose an additional regulatory molecule in the autophagy control network that delays some of AMPK’s effect on the system, making the model output more consistent with experimental results. Furthermore, a network analysis on AutophagyNet was carried out to identify which proteins could be the proposed regulatory components in the system. These regulatory proteins should satisfy the following rules: (1) they are induced by AMPK; (2) they promote ULK1; (3) they down-regulate mTOR upon cellular stress. We have found 16 such regulatory components that have been experimentally proven to satisfy at least two of the given rules. Identifying such critical regulators of autophagy induction could support anti-cancer- and ageing-related therapeutic efforts.

For a theoretical analysis of mass transfer processes in electromembrane systems, the Nernst–Planck and Poisson equations (NPP) are generally used. In the case of 1D direct-current-mode modelling, a fixed potential (for example, zero) is set on one of the boundaries of the considered region, and on the other—a condition connecting the spatial derivative of the potential and the given current density. Therefore, in the approach based on the system of NPP equations, the accuracy of the solution is significantly affected by the accuracy of calculating the concentration and potential fields at this boundary. This article proposes a new approach to the description of the direct current mode in electromembrane systems, which does not require boundary conditions on the derivative of the potential. The essence of the approach is to replace the Poisson equation in the NPP system with the equation for the displacement current (NPD). Based on the system of NPD equations, the concentration profiles and the electric field were calculated in the depleted diffusion layer near the ion-exchange membrane, as well as in the cross section of the desalination channel under the direct current passage. The NPD system, as well as NPP, allows one to describe the formation of an extended space charge region near the surface of the ion-exchange membrane, which is important for describing overlimiting current modes. Comparison of the direct-current-mode modelling approaches based on NPP and NPD showed that the calculation time is less for the NPP approach, but the calculation accuracy is higher for the NPD approach.

Worldwide, mosquito monitoring and control programs consume large amounts of resources in the effort to minimise mosquito-borne disease incidence. On-site larval monitoring is highly effective but time consuming. A number of mechanistic models of mosquito development have been developed to reduce the reliance on larval monitoring, but none for Ross River virus, the most commonly occurring mosquito-borne disease in Australia. This research modifies existing mechanistic models for malaria vectors and applies it to a wetland field site in Southwest, Western Australia. Environmental monitoring data were applied to an enzyme kinetic model of larval mosquito development to simulate timing of adult emergence and relative population abundance of three mosquito vectors of the Ross River virus for the period of 2018–2020. The model results were compared with field measured adult mosquitoes trapped using carbon dioxide light traps. The model showed different patterns of emergence for the three mosquito species, capturing inter-seasonal and inter-year variation, and correlated well with field adult trapping data. The model provides a useful tool to investigate the effects of different weather and environmental variables on larval and adult mosquito development and can be used to investigate the possible effects of changes to short-term and long-term sea level and climate changes.

COVID19 is the most impactful pandemic of recent times worldwide. It is a highly infectious disease that is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2 virus), To date there is specific drug nor vaccination against COVID19. Therefor the need for novel and pioneering anti-COVID19 is of paramount importance. In this direction, computer-aided drug design constitutes a very promising antiviral approach for the discovery and analysis of drugs and molecules with biological activity against SARS-CoV2. In silico modelling takes advantage of the massive amounts of biological and chemical data available on the nature of the interactions between the targeted systems and molecules, as well as the rapid progress of computational tools and software. Herein, we describe the potential of the merging of mathematical modelling, artificial intelligence and learning techniques into seamless computational pipelines for the rapid and efficient discovery and design of potent anti- SARS-CoV-2 modulators.

Production of concrete and reinforced concrete products in the conditions of the Republic of Belarus and in the countries with similar climatic conditions requires heat treatment in heat-technological installations in order to achieve the desired strength of the products at the appointed time, which consumes a great amount of thermal energy. In this case, the purpose of equipment operating modes is associated with a number of difficulties when it comes to new products of complex spatial configuration and structure. The optimality criteria of such modes are, as a rule, the duration and temperature limits of processing, providing the required strength with minimal energy consumption. In the conditions of serial production in the case of structurally simple objects, the assignment of heat treatment modes is carried out empirically. As the analysis shows, the modes obtained in this way do not meet the above criteria, especially from the standpoint of energy saving. The paper, using a mathematical model previously developed by the authors, proposes dependencies for calculating the optimal modes of heat treatment of concrete products that are distinguished by a complex spatial shape and multi-component structure. The method is based on three-dimensional transfer equations, taking into account internal sources of heat release due to the ongoing hydration reaction of the active components of the cement clinker, and the boundary conditions corresponding to the structure of the processed product, as well as the type of heat technology device for accelerated hydration. Equations are proposed for calculating the amount of heat energy supplied to the processed product providing a given strength at a specified time. On the example of a manufactured industrial concrete product and for the conditions of an actually used device for accelerated hydration, a comparison has been made between two limiting modes of heat treatment: with isothermal exposure and in its absence. As a result of the performed calculations, the dependences of energy consumption, temperature fields and the degree of hydration in the product for both modes have been obtained and an energy-saving mode of heat treatment corresponding to the case under consideration has been developed. It is shown that the used numerical method allows to solve problems of this type and to achieve thermal energy savings.