Modeling Equations Research Articles

HiDeS: a higher-order-derivative-supervised neural ordinary differential equation for multi-robot systems and opinion dynamics.

This paper addresses the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics by introducing a novel framework called higher-order-derivative-supervised (HiDeS) NODE. This method extends traditional NODE frameworks by incorporating higher-order derivatives and their interactions into the modeling process, thereby enabling the capture of intricate system behaviors. In addition, the HiDeS NODE employs both the state vector and its higher-order derivatives as supervised signals, which is different from conventional NODEs that utilize only the state vector as a supervised signal. This approach is designed to enhance the predicting capability of NODEs. Through extensive experiments in the complex fields of multi-robot systems and opinion dynamics, the HiDeS NODE demonstrates improved modeling and predicting capabilities over existing models. This research not only proposes an expressive and predictive framework for dynamic systems but also marks the first application of NODEs to the fields of multi-robot systems and opinion dynamics, suggesting broad potential for future interdisciplinary work. The code is available at https://github.com/MengLi-Thea/HiDeS-A-Higher-Order-Derivative-Supervised-Neural-Ordinary-Differential-Equation.

Bidirectional Power Control Strategy for On-Board Charger Based on Single-Stage Three-Phase Converter

To solve the problems of large switching losses and the need for large-capacity electrolytic capacitances in three-phase DC/AC on-board chargers for vehicle-to-grid (V2G) applications, this paper proposes a single-stage bidirectional high-frequency isolated converter that eliminates the need for large-capacity capacitances. Combined with the proposed modulation scheme, it can theoretically reduce the switching loss by about two-thirds with the three-phase converter compared with the conventional modulation scheme, improving the converter’s operating efficiency and power density. Firstly, based on the characteristics of the proposed topology, a hybrid modulation scheme is proposed, which combines a phase-shift modulation scheme based on double modulation waves and a sawtooth carrier with a 1/3 modulation scheme, and the theoretical feasibility of the hybrid modulation scheme is verified using a mathematical modeling equation. Secondly, this paper provides a detailed analysis of the four operating modes of the two full-bridge circuits and the commutation process of the three-phase converter within 1/6 of the fundamental frequency cycle (P1 modulation interval). Then, the control strategy is given for the constant-current and constant-voltage charging and constant-current discharging for electric vehicle batteries. Finally, simulation results verify the correctness of the proposed topology and modulation scheme in vehicle–grid interaction.

Analysis of active and passive control of fluid with fractional derivative

Numerous researchers have been drawn to the rheology of non-Newtonian fluids because of their diverse uses in the engineering and manufacturing fields, such as lubrication, plastic processing, and mining. Additionally, the characteristics of magnetohydrodynamics non-Newtonian fluids permit its widespread application in computer hard drives, loudspeakers, magnetic resonance imaging, the administration of magnetic medicines, and magnetic hyperthermia. The current work is focused on the analysis of heat and mass transfer in a magnetohydrodynamics Brinkman nanofluid flows across a vertical plate because of these possible uses. The modeling also takes into account the passive and active control of the Brinkman nanofluid. Using suitable nondimensional variables, ordinary differential equations are created from the modeling equations, and the Laplace transform method is used to solve these equations. Semi-analytical solutions for temperature, concentration, and velocity are found after employing the Laplace transform approach to address the issue.

Modeling of heat and mass transfer in the discontinuum approximation

The article presents a theoretical analysis of the governing equations expressing the fundamental conservation laws in the continuum and discontinuum approximations, and methods for solving problems of hydrodynamics as one of the most important subfields of continuum mechanics. This article is an attempt to more accurately describe physicochemical macro-processes. It is shown that the most suitable equations for computer modeling are the conservation laws under natural constraints on the minimum spatial and time scales, i.e., equations without partial derivatives and constraints on the solution smoothness. Using the continuity and thermal conductivity equations, a phenomenological method for constructing and numerically solving the governing equations is presented, and comparison with the traditional approach is given.

A comparative analysis of multivariate approaches for data analysis in management sciences

The researchers use the SEM-based multivariate approach to analyze the data in different fields, including management sciences and economics. Partial least square structural equation modeling (PLS-SEM) and covariance-based structural equation modeling (CB-SEM) are powerful data analysis techniques. This paper aims to compare both models, their efficiencies and deficiencies, methodologies, procedures, and how to employ the models. The outcomes of this paper exhibited that the PLS-SEM is a technique that combines the strengths of structural equation modeling and partial least squares. It is imperative to know that the PLS-SEM is a powerful technique that can handle measurement error at the highest levels, trim and unbalanced datasets, and latent variables. It is beneficial for analyzing relationships among latent constructs that may not be candidly witnessed and might not be applied in situations where traditional SEM would be infeasible. However, the CB-SEM approach is a procedure that pools the strengths of both structural equation modeling and confirmatory factor analysis. The CB-SEM is a dominant multivariate technique that can grip multiple groups and indicators; it is beneficial for analyzing relationships among latent variables and multiple manifest variables, which can be directly observed. The paper concluded that the PLS-SEM is a more suitable technique for analyzing relations among latent constructs, generally for a small dataset, and the measurement error is high. However, the CB-SEM is suitable for analyzing compound latent and manifest constructs, mainly when the goal is to generalize results to specific population subgroups. The PLS-SEM and CB-SEM have specific efficiencies and deficiencies that determine which technique to use depending on resource availability, the research question, the dataset, and the available time.

Modeling of reaction–desorption process by core–shell particles dispersed in continuously stirred tank reactor (CSTR)

Abstract Transient responses of reaction–desorption process were predicted from mathematical solutions of modeling equations for CSTR (continuously stirred tank reactor) containing core–shell adsorbent particles. Analytical solutions on the core–shell particles were derived for core–shell spherical, cylindrical, and slab-type morphologies, assuming inert-cores. Unlike continuous adsorber, CSTRs for reaction–desorption process containing spherical particles exhibited the slowest reduction rate of concentration of adsorbate, because the amount of adsorbed component on the particles is the largest among three kinds of particle shapes. Factors affecting the transient concentration in bulk medium of reaction–desorption process were investigated by adjusting inert-core thickness, inlet flow rate, initial concentration of reactant in inflow stream, amount of adsorbent, and Thiele modulus. Concentration profile inside the particles as well as average intra-particle concentration could be also predicted for comparison with bulk concentration of CSTR. For non-linear isotherm and non-linear reaction kinetics, concentration of active component could be predicted by solving non-linear coupled differential equation using finite element method. For connected CSTRs in series, systems of reaction-diffusion equations were solved by finite element method to study the effect of number of connected reactors. When the number of reactors was sufficiently large, the reactor system could be approximated to fixed bed reactor for reaction–desorption process.

Pengaruh Kualitas Produk Dan Costumer Review Terhadap Keputusan Pembelian Di Lazada

This study aims to analyze the effect of product quality variables, customer reviews, and service quality on purchasing decisions at Lazada. With a case study studied on consumers who shop at the Lazada application in Srondol Kulon Village, Banyumanik District, Semarang City. The research method in this research is a quantitative approach. The population in this study were all buyers on the Lazada Application in Srondol Kulon Village, Banyumanik District, Semarang City, while the sample taken in this study was 100 Lazada Application users. Determination of the sample size using the method of non-proprability sampling technique and selection of respondents with purposive sampling technique. Data analysis in this study using the SmartPLS version 3 program. The data analysis technique used is the Structural Equation Modeling (SEM) equation model. From the results of the analysis and discussion of this study, it shows that the product quality variable has a significant influence on purchasing decisions, the customer review variable does not have a significant influence on purchasing decisions, and the service quality variable has a significant influence on purchasing decisions.

ASSESSMENT OF THE ENERGY FACILITY IMPACT ON ENVIRONMENTAL POLLUTION

Problem statement. The task of assessing the influence of the boiler house on atmospheric air pollution is under consideration. Carrying out such an assessment is very important when locating boiler houses near residential areas. Since the weather conditions for each region are characterized by a change in the direction of the wind, the intensity of atmospheric diffusion, the appearance of a calm, it is important to have information about the formation of pollution zones in sedimentary zones. To solve this important problem, it is very important to use mathematical modeling, since it is currently impossible to create a sufficient number of observation posts near the objects of the fuel and energy complex. The purpose of the article. Numerical analysis of the influence of the boiler house on the intensity of atmospheric air pollution under different weather conditions. Methodology. The 3D equation of convective-diffusion transport is used to estimate the pollution zones formed in the atmospheric air when it is emitted from the boiler house pipe. The model takes into account atmospheric stratification, impurity emission intensity, wind profile, wind speed. Numerical integration of the equation of convective-diffusion transport of impurities is carried out using finite-difference schemes. The modeling equation is split into an equation for the convective transport of the pollutant and an equation for the dispersion of the pollutant due to atmospheric diffusion. The equation describing the change in the concentration of the impurity in the atmospheric air as a result of the emission of the pollutant from the pipe is solved separately. At the next stage, finite-difference schemes are built that allow solving the splitting equation. Scientific novelty. On the basis of the constructed numerical model, the zones of atmospheric air pollution during the emission of CO from the pipe of the boiler house are determined. A numerical model is proposed that allows forecasting atmospheric air pollution for different weather conditions within the framework of one program package. Practical significance. On the basis of the proposed numerical model, the forecasting of the zones of chemical pollution of the atmospheric air in the settlement zone in which the boiler house is located was carried out. The results of the computational experiment are presented.

EXPRESS CALCULATION OF OXYGEN REGIME IN WASTEWATER FACILITIES

Problem statement. The efficiency of biological water purification depends significantly on the concentration of dissolved oxygen in the volume of the bioreactor. But during the operation of bioreactors, the oxygen regime changes, so it is important to predict the oxygen concentration for different modes of operation of treatment plants. Simplified mathematical models are used to calculate the oxygen regime, but these models are designed for typical bioreactors. An important task is the development of effective multivariate numerical models for evaluating the oxygen regime in reactors of different geometric shapes, which differ from “classical” reactors. The purpose of the article. Development of a CFD model for operational evaluation of the oxygen regime in bioreactors. Methodology. For mathematical modeling of the oxygen regime in the bioreactor, a two-dimensional mass transfer equation is used, which takes into account the place of oxygen supply from the aerator located in the building, the hydrodynamics of the flow in the bioreactor, and the diffusion process. The potential motion model was used to solve the hydrodynamic problem. Numerical integration of modeling equations is carried out by using finite-difference splitting schemes. At each splitting step, the difference equations are solved using explicit schemes. This allows a simple computer implementation of the numerical model. Scientific novelty. A multifactor two-dimensional CFD model was developed, which allows for a quick assessment of the oxygen regime in a bioreactor used for wastewater treatment. Practical significance. The developed CFD model and computer code can be used at the stage of designing or re-engineering bioreactors in order to find the optimal location of aerators in the structure. Conclusions. The software implementation of the developed numerical model was carried out. The results of a computational experiment on the study of the wastewater treatment process in a sedimentation tank are presented.

COMPLEX ASSESSMENT OF POLLUTION ZONES IN EXTREME SITUATIONS AT ENERGY FACILITIES

Problem statement. The task of forecasting damage zones under various types of man-made load in the event of an extreme situation at a gas station is considered. Comprehensive forecasting includes the determination of areas of chemical, thermal and mechanical contamination in the event of an extreme situation at a gas station. The purpose of the article. Development of a theoretical toolkit and a package of programs for complex forecasting of chemical, thermal and chemical environmental pollution zones in the event of an extreme situation at a gas station. Methodology. Forecasting of zones of chemical, thermal and mechanical pollution of the environment in the event of an extreme situation at a gas station uses the fundamental equations of the mechanics of a solid environment: the mass transfer equation is used to calculate zones of chemical pollution; the energy equation is used to determine the zones of thermal pollution of the atmospheric air; Newton's second law is used to calculate mechanical contamination zones. Integration of modeling equations is carried out numerically. A specialized package of programs for comprehensive forecasting of environmental pollution has been created. Scientific novelty. A specialized package of programs based on developed numerical models is proposed for the assessment of chemical, thermal and mechanical pollution zones that arise in the event of an extreme situation at a gas station. On the basis of the developed numerical models, an assessment of complex environmental pollution during an extreme situation at a gas station in the city of Dnipro was carried out. Practical significance. The developed numerical models are implemented in the form of a package of application programs with a wide working range. The program package is focused on solving problems in the field of environmental safety and occupational health and safety. Determining the zones of chemical, thermal and mechanical pollution of the environment with the help of the developed program package will be important in the development of the plan for localization and liquidation of emergency situations and accidents. Conclusions. An effective tool for theoretical analysis of pollution zones formed during an extreme situation at gas stations has been created. The results of computational experiments are presented.

Solubility of digitoxin in supercritical CO2: Experimental study and modeling

In this communication, the solubility of digitoxin drug in supercritical CO2 was studied at different operating conditions (311 < T (K) < 343, 120 < P (bar) < 300). The results revealed digitoxin drug solubility (in mole fraction) was between 0.095 × 10−5 to 1.12 × 10−5. In the case of thermodynamic solubility modeling, cubic and non-cubic equation of states i.e. SAFT (statistical associating fluid theory), SRK (Soave-Redlich-Kwong) and sPC-SAFT (simplified perturbed chain SAFT) EoSs and six density-based correlations (Chrastil, Kumar-Johnston (KJ), Mendez-Santiago-Teja (MST), Garlapati and Madras (GM), Bartle et al. and Sung-Shim models) were considered. All used equations indicated reasonable behavior with appropriate accuracy for the solubility of the digitoxin drug. Meanwhile, sPC-SAFT EoS and Kumar-Johnston correlation with AARD% set to 8.96 % and 6.25 %, respectively exhibited greater accuracy in fitting the solubility data. Moreover, total, solvation and vaporization enthalpies of the digitoxin/supercritical carbon dioxide binary mixture were calculated based on KJ, Chrastil and Bartle et al. models.

Hybrid machine learning model and predictive equations for compressive stress-strain constitutive modelling of confined ultra-high-performance concrete (UHPC) with normal-strength steel and high-strength steel spirals

Stress-strain constitutive model for confined ultra-high-performance concrete (UHPC) plays a pivotal role in the design and modelling of UHPC structures. However, while extensive research exists on the stress-strain responses of unconfined UHPC, a notable dearth of studies focuses on the stress-strain constitutive model for confined UHPC. Accordingly, this study introduces a novel hybrid machine learning (ML)-based stress-strain constitutive model for UHPC confined with normal-strength steel (NSS) or high-strength steel (HSS) spirals. Given the limited experimental data available, a numerical model was developed and validated against experimental results of confined UHPC. Subsequently, it was employed to generate a comprehensive dataset of confined UHPC stress-strain responses, which were then used to train the hybrid ML model. Hyperparameters of the model are subsequently optimized using Optuna along with a cross-validation technique. The optimized hybrid ML model exhibited exceptional accuracy in predicting the stress-strain response of confined UHPC with NSS or HSS spirals, as demonstrated by high coefficients of determination (R2) values ranging from 0.905 to 0.999 and low error metrics across varying stress levels and datasets. Moreover, the capability of the model to simultaneously predict both stress and strain responses was further validated through canonical correlation analysis (CCA). The results of the analysis demonstrated robust predictive performance of the model, with high CCA scores that ranged between 93.3% and 99.4%. To facilitate the practical implementation of the model, an end-to-end interactive software tool is developed. In addition, this study proposes predictive equations for the peak and ultimate stress-strain responses of confined UHPC. The evaluation of the developed predictive equations demonstrates their efficacy in accurately predicting the stress-strain responses of confined UHPC, as evidenced by the high R2 values, which ranged from 83–91%.

Cognitive deficits and enhancements in youth from adverse conditions: An integrative assessment using Drift Diffusion Modeling in the ABCD study.

Childhood adversity can lead to cognitive deficits or enhancements, depending on many factors. Though progress has been made, two challenges prevent us from integrating and better understanding these patterns. First, studies commonly use and interpret raw performance differences, such as response times, which conflate different stages of cognitive processing. Second, most studies either isolate or aggregate abilities, obscuring the degree to which individual differences reflect task-general (shared) or task-specific (unique) processes. We addressed these challenges using Drift Diffusion Modeling (DDM) and structural equation modeling (SEM). Leveraging a large, representative sample of 9-10 year-olds from the Adolescent Brain Cognitive Development (ABCD) study, we examined how two forms of adversity-material deprivation and household threat-were associated with performance on tasks measuring processing speed, inhibition, attention shifting, and mental rotation. Using DDM, we decomposed performance on each task into three distinct stages of processing: speed of information uptake, response caution, and stimulus encoding/response execution. Using SEM, we isolated task-general and task-specific variances in each processing stage and estimated their associations with the two forms of adversity. Youth with more exposure to household threat (but not material deprivation) showed slower task-general processing speed, but showed intact task-specific abilities. In addition, youth with more exposure to household threat tended to respond more cautiously in general. These findings suggest that traditional assessments might overestimate the extent to which childhood adversity reduces specific abilities. By combining DDM and SEM approaches, we can develop a more nuanced understanding of how adversity affects different aspects of youth's cognitive performance. RESEARCH HIGHLIGHT: To understand how childhood adversity shapes cognitive abilities, the field needs analytical approaches that can jointly document and explain patterns of lowered and enhanced performance. Using Drift Diffusion Modeling and Structural Equation Modeling, we analyzed associations between adversity and processing speed, inhibition, attention shifting, and mental rotation. Household threat, but not material deprivation, was mostly associated with slower task-general processing speed and more response caution. In contrast, task-specific abilities were largely intact. Researchers might overestimate the impact of childhood adversity on specific abilities and underestimate the impact on general processing speed and response caution using traditional measures.

Wide-field illumination diffuse optical tomography within a framework of single-pixel time-domain spatial frequency domain imaging.

We present a wide-field illumination time-domain (TD) diffusion optical tomography (DOT) for three-dimensional (3-D) reconstruction within a shallow region under the illuminated surface of the turbid medium. The methodological foundation is laid on the single-pixel spatial frequency domain (SFD) imaging that facilitates the adoption of the well-established time-correlated single-photon counting (TCSPC)-based TD detection and generalized pulse spectrum techniques (GPST)-based reconstruction. To ameliorate the defects of the conventional diffusion equation (DE) in the forward modeling of TD-SFD-DOT, mainly the low accuracy in the near-field region and in profiling early-photon migration, we propose a modified model employing the time-dependent δ-P1 approximation and verify its improved accuracy in comparison with both the Monte Carlo and DE-based ones. For a simplified inversion process, a modified GPST approach is extended to TD-SFD-DOT that enables the effective separation of the absorption and scattering coefficients using a steady-state equivalent strategy. Furthermore, we set up a single-pixel TD-SFD-DOT system that employs the TCSPC-based TD detection in the SFD imaging framework. For assessments of the reconstruction approach and the system performance, phantom experiments are performed for a series of scenarios. The results show the effectiveness of the proposed methodology for rapid 3-D reconstruction of the absorption and scattering coefficients within a depth range of about 5 mean free pathlengths.

Experimental analysis and modeling of micro-texture and vickers hardness impact on polished stone value in high-friction aggregates

This article intends to study the influence of micro-texture and Vickers hardness on the Polished Stone Value (PSV) of four types of high friction aggregates (90# Bauxite, 75# Bauxite, Basalt, and Granite) during the long-term polishing process. For this purpose, profile roughness, Vickers hardness, and PSV were tested. The relationship between profile roughness, Vickers hardness, and PSV was analyzed with gray correlation analysis and mathematical fitting. The results show that arithmetic mean roughness (Ra) and maximum height (Rz) influenced PSV significantly while root mean square height (Rq), skewness (Rsk), kurtosis (Rku), and load length ratio (Rmr (c)) had a relatively weak effect. Because of the high correlation with PSV, Ra and Rz were chosen as indicators, and the relationship between variables (Ra, Rz) and PSV was established. There is a good linear relationship between the attenuation rate of Ra and Rz per polishing cycle (K1 and K2) and Vickers hardness. Finally, a model of estimation of the polished stone value of high friction aggregate based on micro-texture and Vickers hardness during the long-term polishing process is developed. Measuring the profile roughness and Vickers hardness to obtain Ra, Rz, and H correlation values and substituting them into the modeling equations in this paper can be used for optimal selection and life estimation of high friction aggregates, which belong to the raw materials, and the optimal selection of high friction aggregates will be helpful for the design of wear-resistant coatings, especially for high friction surface treatments.

The key role of market orientation in innovation ambidexterity in agribusiness firms

AbstractThe objective of this study is to examine the relationships between market orientation, organizational culture, proactive management, organizational climate, and organizational structure on the innovative orientation (exploitative and exploratory innovation). Little research has been conducted to examine the relationship between these organizational dimensions and innovation orientation. This study offers this and provides a particular type of companies (agribusiness) and context (Extremadura, Spain). Quantitative approach, by using structural modelling equations, to analyze data from 151 innovative agri-food firms was used in this study. Then, using a fuzzy set qualitative comparative analysis (fsQCA), was carried out to obtain additional insights. The main result find that market orientation plays a key role both in exploitative and exploratory innovation in agribusiness firms. Innovation exploitation is influenced by the firm’s organic structure. Results from fsQCA provide valuable findings showing that innovation exploitation and exploration result from distinct organizational configurations, thus providing valuable insights for decision and policy-making.

MEDIASI MOTIVASI KERJA PADA HUBUNGAN KOMPENSASI DAN GAYA KEPEMIMPINAN TERHADAP SEMANGAT KERJA

Abstract is written concisely and factually, includes the background of research, the purpose of research, the method of research, the result of research, conclusion, and recommendation. Abstract is written in one paragraph, font Times New Roman 11, italic and 1 spacing. This study aims to determine the effect of compensation and leadership style on employee morale with motivation as an intervening variable at CV. Jati Sarana Mulia. The data for this study were obtained from distributing questionnaires to 65 employees of CV. Jati Sarana Mulia. The sampling technique in this study is total sampling, where the total sample and population used in this study are the same in number. The data analysis method used in this study is the Structural Equation Modeling equation model using variance or component based structural equation modeling. After analyzing the data, the results of this study indicate that compensation has a positive and significant effect on employee morale. Motivation has a positive and significant effect on employee morale. Leadership style has no effect on employee morale. Compensation has a positive and significant effect on work motivation. Leadership style has a positive and significant effect on work motivation. Compensation has a positive and significant effect on morale through motivation. Leadership style has no effect on morale through motivation.

Experimental and numerical analysis of the forced draft wet cooling tower

Cooling towers are essentially large boxes designed to maximize the evaporation of water. The inlet water temperature and water to air mass flow rate ratio (L/G) significantly affect the performance of the cooling tower. The number of a transfer unit (NTU), Merkel number (Me), Lewis number (Le), and efficiency of the cooling tower define the performance of the forced cooling tower. In this research paper, different inlet water temperatures ranging from 28 °C to 42 °C and (L/G) ranging from 0.5, 1, and 1.5 were used to investigate the performance of the forced cooling tower. Mathematical modeling equations were used to calculate NTU, Me, Le, and efficiency at different inlet water temperatures and (L/G). Engineering equation solver (EES) software was used to solve these mathematical modeling equations. Further, an experimental investigation was carried to find forced cooling tower performance at different inlet water temperatures and (L/G), and results were compared with the theoretical results. The results revealed that increasing the inlet water temperature, NTU, Me, Le, and efficiency increased and were directly related to each other. Further, NTU and efficiency were increased by increasing (L/G). At the same time, the Me and Le reduced with (L/G). Finally, an acceptable and better agreement has been obtained between experimental and theoretical results. Based on obtained results, it has been concluded that higher values of inlet water temperature and (L/G) provided the higher performance of the forced cooling tower.

Consistent travelling wave characteristic of space–time fractional modified Benjamin–Bona–Mahony and the space–time fractional Duffing models

Study on solitary wave phenomenon are closely related on the dynamics of the plasma and optical fiber system, which carry on broad range of wave propagation. The space–time fractional modified Benjamin–Bona–Mahony equation and Duffing model are important modeling equations in acoustic gravity waves, cold plasma waves, quantum plasma in mechanics, elastic media in nonlinear optics, and the damping of material waves. This study has effectively developed analytical wave solutions to the aforementioned models, which may have significant consequences for characterizing the nonlinear dynamical behavior related to the phenomenon. Conformable derivatives are used to narrate the fractional derivatives. The expanded tanh-function method is used to look into such kinds of resolutions. An ansatz for analytical traveling wave solutions of certain nonlinear evolution equations was originally a power sequence in tanh. The discovered explanations are useful, reliable, and applicable to chaotic vibrations, problems of optimal control, bifurcations to global and local, also resonances, as well as fusion and fission phenomena in solitons, scalar electrodynamics, the relation of relativistic energy–momentum, electromagnetic interactions, theory of one-particle quantum relativistic, and cold plasm. The solutions are drafted in 3D, contour, listpoint, and 2D patterns, and include multiple solitons, bell shape, kink type, single soliton, compaction solitary wave, and additional sorts of solutions. With the aid of Maple and MATHEMATICA, these solutions were verified and discovered that they were correct. The mentioned method applied for solving NLFPDEs has been designed to be practical, straightforward, rapid, and easy to use.

P148 Longitudinal single-cell data informs deterministic modelling of inflammatory bowel disease

Abstract Background Crucial contributions to our understanding of the inflammatory process in inflammatory bowel disease (IBD) have been made using single cell level approaches. Extracting mechanistic details of cell and gene dynamics would be critical to understanding the mechanisms mediating mucosal healing and predicting response to specific therapies. However, this remains challenging. Therefore, our aim was to use ordinary differential equations (ODEs) for mathematical modelling of cell abundance and prediction of biological processes in IBD. Methods We used mathematical modelling of published longitudinal single-cell mRNA sequencing (scRNA-seq) data from DSS colitis in mice to simulate cellular dynamics during IBD. We validated our predictions using pseudo-bulk gene expression analysis and flow cytometry. We also analysed a published microarray dataset from colonic biopsies of 51 IBD patients prior to infliximab treatment. Results Based on the scRNA-seq data, we used our mathematical model to predict the immune dynamics of a different mouse colitis protocol. We validated these predictions experimentally using flow cytometry and found good agreement between model simulation and experimental data (predicted vs. observed, Pearson's rho=0.92). We found that the estimated turnover rates predicted the protein level of the proliferation marker KI-67 (rho=0.88) in DSS colitis. Finally, we wanted to investigate whether our mathematical model reflected processes in human IBD. We reasoned that genes correlated with epithelial cell dynamics might be indicative of mucosal healing after DSS retrieval. We found more highly correlated genes when using simulated epithelial abundance compared to experimentally measured epithelial abundance. Many genes associated with tight junctions (Cldn8, Cftr, Crb3, Jam2) were among the highly positively correlated genes and genes associated with inflammation (Il1b, Jak2, Il10ra) were among the negatively correlated genes with epithelial cell abundance. We then looked for differentially expressed (DE) genes in pre-treatment colon biopsies between responders and non-responders to infliximab. We found a significant overlap of 25 positively correlated genes with upregulated DE genes in responders, i.e. associated with tight junctions, and 73 negatively correlated genes with upregulated genes in non-responders, i.e. associated with inflammatory pathways. Conclusion We demonstrate that mathematical modelling of colonic cell dynamics provides insight into IBD progression and treatment response. Furthermore, our results suggest that pre-treatment barrier integrity may predict and influence response to infliximab treatment.