Showing papers on "Mathematical model published in 2022"

Application of Mathematical Modeling in Prediction of COVID-19 Transmission Dynamics

Abstract: Abstract The entire world has been affected by the outbreak of COVID-19 since early 2020. Human carriers are largely the spreaders of this new disease, and it spreads much faster compared to previously identified coronaviruses and other flu viruses. Although vaccines have been invented and released, it will still be a challenge to overcome this disease. To save lives, it is important to better understand how the virus is transmitted from one host to another and how future areas of infection can be predicted. Recently, the second wave of infection has hit multiple countries, and governments have implemented necessary measures to tackle the spread of the virus. We investigated the three phases of COVID-19 research through a selected list of mathematical modeling articles. To take the necessary measures, it is important to understand the transmission dynamics of the disease, and mathematical modeling has been considered a proven technique in predicting such dynamics. To this end, this paper summarizes all the available mathematical models that have been used in predicting the transmission of COVID-19. A total of nine mathematical models have been thoroughly reviewed and characterized in this work, so as to understand the intrinsic properties of each model in predicting disease transmission dynamics. The application of these nine models in predicting COVID-19 transmission dynamics is presented with a case study, along with detailed comparisons of these models. Toward the end of the paper, key behavioral properties of each model, relevant challenges and future directions are discussed.

Application of Mathematical Modeling in Prediction of COVID-19 Transmission Dynamics

Abstract: Abstract The entire world has been affected by the outbreak of COVID-19 since early 2020. Human carriers are largely the spreaders of this new disease, and it spreads much faster compared to previously identified coronaviruses and other flu viruses. Although vaccines have been invented and released, it will still be a challenge to overcome this disease. To save lives, it is important to better understand how the virus is transmitted from one host to another and how future areas of infection can be predicted. Recently, the second wave of infection has hit multiple countries, and governments have implemented necessary measures to tackle the spread of the virus. We investigated the three phases of COVID-19 research through a selected list of mathematical modeling articles. To take the necessary measures, it is important to understand the transmission dynamics of the disease, and mathematical modeling has been considered a proven technique in predicting such dynamics. To this end, this paper summarizes all the available mathematical models that have been used in predicting the transmission of COVID-19. A total of nine mathematical models have been thoroughly reviewed and characterized in this work, so as to understand the intrinsic properties of each model in predicting disease transmission dynamics. The application of these nine models in predicting COVID-19 transmission dynamics is presented with a case study, along with detailed comparisons of these models. Toward the end of the paper, key behavioral properties of each model, relevant challenges and future directions are discussed.

Mathematical modelling of electric vehicle adoption: A systematic literature review

Abstract: As decarbonisation is becoming increasingly important, many countries have placed an emphasis on decarbonising their transportation sector through electrification to support the transition to net zero. As such, research regarding the adoption of electric vehicles has drastically increased in recent years. Mathematical modelling plays an important role in optimising a transition to electric vehicles. This article describes a systematic literature review of existing works which perform mathematical modelling of the adoption of electric motor vehicles. In this study, 53 articles containing mathematical models of electric vehicle adoption are reviewed systematically to answer 6 research questions regarding the process of modelling transitions to electric vehicles. The mathematical modelling techniques observed in existing literature are discussed, along with the main barriers to electric vehicle adoption, and future research directions are suggested. • Mathematical modelling is important in optimising transitions to electric vehicles. • The most common modelling techniques are discrete choice modelling and agent based modelling. • Lack of successful business models is a significant barrier to EV adoption.

Reassessment of Thin-Layer Drying Models for Foods: A Critical Short Communication

Abstract: Modeling the thin-layer drying of foods is based on describing the moisture ratio versus time data by using a suitable mathematical model or models. Several models were proposed for this purpose and almost all studies were related to the application of these models to the data, a comparison and selecting the best-fitted model. A careful inspection of the existing drying data in literature revealed that there are only a limited number of curves and, therefore, the use of some models, especially the complex ones and the ones that require a transformation of the data, should be avoided. These were listed based on evidence with the use of both synthetic and published drying data. Moreover, the use of some models were encouraged, again based on evidence. Eventually, some suggestions were given to the researchers who plan to use mathematical models for their drying studies. These will help to reduce the time of the analyses and will also avoid the arbitrary usage of the models.

Mathematical models of neuronal growth

Abstract: The establishment of a functioning neuronal network is a crucial step in neural development. During this process, neurons extend neurites-axons and dendrites-to meet other neurons and interconnect. Therefore, these neurites need to migrate, grow, branch and find the correct path to their target by processing sensory cues from their environment. These processes rely on many coupled biophysical effects including elasticity, viscosity, growth, active forces, chemical signaling, adhesion and cellular transport. Mathematical models offer a direct way to test hypotheses and understand the underlying mechanisms responsible for neuron development. Here, we critically review the main models of neurite growth and morphogenesis from a mathematical viewpoint. We present different models for growth, guidance and morphogenesis, with a particular emphasis on mechanics and mechanisms, and on simple mathematical models that can be partially treated analytically.

A Short Review on Computational Hydraulics in the Context of Water Resources Engineering

Abstract: The term “hydraulics” is concerned with the conveyance of water that can consist of very simple processes to complex physical processes, such as flow in open rivers, flow in pipes, the flow of nutrients/sediments, the flow of groundwater to sea waves. The study of hydraulics is primarily a mixture of theory and experiments. Computational hydraulics is very helpful to quantify and predict flow nature and behavior. The mathematical model is the backbone of the computational hydraulics that consists of simple to complex mathematical equations with linear and/or non-linear terms and ordinary or partial differential equations. Analytical solution to these mathematical equations is not feasible in the majority of cases. In these consequences, mathematical models are solved using different numerical techniques and associated schemes. In this manuscript, we aim to review hydraulic principles along with their mathematical equations. Then we aim to learn some commonly used numerical techniques to solve different types of differential equations related to hydraulics. Among them, the Finite Difference Method (FDM), Finite Element Method (FEM) and Finite Volume Method (FVM) have been discussed along with their use in real-life applications in the context of water resources engineering.

Drug Carriers: A Review on the Most Used Mathematical Models for Drug Release

Abstract: Carriers are protective transporters of drugs to target cells, facilitating therapy under each points of view, such as fast healing, reducing infective phenomena, and curing illnesses while avoiding side effects. Over the last 60 years, several scientists have studied drug carrier properties, trying to adapt them to the release environment. Drug/Carrier interaction phenomena have been deeply studied, and the release kinetics have been modeled according to the occurring phenomena involved in the system. It is not easy to define models’ advantages and disadvantages, since each of them may fit in a specific situation, considering material interactions, diffusion and erosion phenomena, and, no less important, the behavior of receiving medium. This work represents a critical review on main mathematical models concerning their dependency on physical, chemical, empirical, or semi-empirical variables. A quantitative representation of release profiles has been shown for the most representative models. A final critical comment on the applicability of these models has been presented at the end. A mathematical approach to this topic may help students and researchers approach the wide panorama of models that exist in literature and have been optimized over time. This models list could be of practical inspiration for the development of researchers’ own new models or for the application of proper modifications, with the introduction of new variable dependency.

Review of Mathematical Modelling Techniques with Applications in Biosciences

Abstract: Modelling can provide intellectual frameworks that are necessary to translate data into knowledge. Mathematical modelling has played an important role in many applications, such as ecology, genetics, engineering, psychology, sociology, physics and computer science, in recent years. This study focused on reviewing mathematical modelling and its applications to biological systems by tracing many metabolic activities of cellular interactions on the one hand and between the spread of epidemics and population growth on the other hand. Various mathematical equations have played fundamental roles in the formation of these systems for model development procedures by describing them mathematically and establishing relationships that characterise the dynamics of a biological phenomenon. Consequently, the creation of new mathematical representations and simulation algorithms is important to the success of biological modelling initiatives. Finally, the optimisation approach performs its primary role in directing and controlling interactions by adjusting the parameters that provide the best possible result for the system

Electrical and Mathematical Modeling of Supercapacitors: Comparison

Abstract: Supercapacitors are energy storage devices with high electrical power densities and long spanlife. Therefore, supercapacitor-based energy storage systems have been employed for a variety of applications. The modelling and simulation of SCs have been of great interest to this objective. This paper presents an electrical schema and mathematical modelling of three models of supercapacitors. The first is the RC model, the second is the two-branch model and the third is the multi-branch model. The objective of this modelling is to choose the best model that can respect the same behaviour of the experimental model. These models are compared with an experimental model. This comparison prove that the response voltage of the multi-branch model correctly describes the behaviour of the experimental model of Belhachemi. The disadvantage of this model is the slow simulation duration in MATLAB/Simulink. The RC model represented the faster model in terms of simulation. The choice of 15 branches in parallel in multi-branch models gives good results and correctly describes the reel model. The automatic charge and discharge voltage of SCs reduce by reducing the charge current.

Modeling of the Drying Process of Apple Pomace

Abstract: Understanding biological materials is quite complicated. The material apple pomace is biologically unstable has been dried under certain conditions. Modeling the pomace drying is necessary to understand the heat and mass transport mechanism and is a prerequisite for the mathematical description of the entire process. Such a model plays an important role in the optimization or control of working conditions. Modeling of the pomace drying process is difficult as apple pomace is highly heterogeneous, as it consists of flesh, seeds, seed covers, and petioles of various sizes, shapes and proportions. A simple mathematical model (Page) was used, which describes well the entire course of the drying process. This is used to control the process. In turn, complex mathematical models describe the phenomena and scientifically explain the essence of drying. Mathematical modeling of the dewatering process is an indispensable part of the design, development and optimization of drying equipment.

Dynamic Modeling of Bucket-Soil Interactions Using Koopman-DFL Lifting Linearization for Model Predictive Contouring Control of Autonomous Excavators

Abstract: A lifting-linearization method based on the Koopman operator and Dual Faceted Linearization is applied to the control of a robotic excavator. In excavation, a bucket interacts with the surrounding soil in a highly nonlinear and complex manner. Here, we propose to represent the nonlinear bucket-soil dynamics with a set of linear state equations in a higher-dimensional space. The space of independent state variables is augmented by adding variables associated with nonlinear elements involved in the bucket-soil dynamics. These include nonlinear resistive forces and moment acting on the bucket from the soil, and the effective inertia of the bucket that varies as the soil is captured into the bucket. Variables associated with these nonlinear resistive and inertia elements are treated as additional state variables, and their time evolution is represented as another set of linear differential equations. The lifted linear dynamic model is then applied to Model Predictive Contouring Control, where a cost functional is minimized as a convex optimization problem thanks to the linear dynamics in the lifted space. The lifted linear model is tuned based on a data-driven method by using a soil dynamics simulator. Simulation experiments on homogeneous soil verify the effectiveness of the proposed lifting linearization compared to its counterpart.

Modeling the Clustering of Dispersed Systems Using Dynamic Models

Abstract: A mathematical method for modeling the processes of structure information of dispersed systems and composite materials is proposed using dynamic models that take account of energy, structural and rheological features of interparticle interaction. The conditions of the processes of spontaneous formation of floccules and clusters are considered. Mathematical models of clusters structure formation in dispersed systems are constructed, the parameters of clusters and the prescription-technological conditions of their formation are determined. Control possibility of the processes of disperse systems structure formation in order to obtain the optimal parameters of the structure and properties of composite materials on the basis of the proposed models and mathematical methods is shown.

Ontology of Mathematical Modeling Based on Interval Data

Abstract: An ontological approach as a tool for managing the processes of constructing mathematical models based on interval data and further use of these models for solving applied problems is proposed in this article. Mathematical models built using interval data analysis are quite effective in many applications, as they have “guaranteed” predictive properties, which are determined by the accuracy of experimental data. However, the application of mathematical modeling methods is complicated by the lack of software tools for the implementation of procedures for constructing this type of mathematical models, creating an ontological model that operates by the categories of the subject area of mathematical modeling, regardless of the modeling object proposed in this article. This approach has made it possible to generate tools for mathematical modeling of various objects based on the interval data analysis for any software development environment selected by the user. The technology of creating the software on the basis of the developed ontological superstructure for mathematical modeling using the interval data for different objects, as well as various forms of user interface implementation, is presented in this article. A number of schemes, which illustrate the technology of using the ontological approach of mathematical modeling based on interval data, are presented, and the features of its interpretation when solving environmental monitoring problems are described.

Optimizing the future: how mathematical models inform treatment schedules for cancer.

Abstract: For decades, mathematical models have influenced how we schedule chemotherapeutics. More recently, mathematical models have leveraged lessons from ecology, evolution, and game theory to advance predictions of optimal treatment schedules, often in a personalized medicine manner. We discuss both established and emerging therapeutic strategies that deviate from canonical standard-of-care regimens, and how mathematical models have contributed to the design of such schedules. We first examine scheduling options for single therapies and review the advantages and disadvantages of various treatment plans. We then consider the challenge of scheduling multiple therapies, and review the mathematical and clinical support for various conflicting treatment schedules. Finally, we propose how a consilience of mathematical and clinical knowledge can best determine the optimal treatment schedules for patients.

Detailed mathematical and simulation model of a synchronous generator

Abstract: Synchronous generator theory has been known since the beginning of its use, but the modelling and analysis of synchronous generators is still very existent in the present-day. Modern digital computers enable development of detailed simulation models, thus individual power system elements, including synchronous generators, are represented by the highest degree order models in power system simulation software packages. In this paper, first, a detailed mathematical model of a synchronous generator is described. Then, a simulation model of a synchronous generator developed based on the presented mathematical model. Finally, a transient stability after a short-circuit is simulated using real generator parameters.

Mathematical relationships between spinal motoneuron properties

Abstract: Our understanding of the behaviour of spinal alpha-motoneurons (MNs) in mammals partly relies on our knowledge of the relationships between MN membrane properties, such as MN size, resistance, rheobase, capacitance, time constant, axonal conduction velocity, and afterhyperpolarization duration. We reprocessed the data from 40 experimental studies in adult cat, rat, and mouse MN preparations to empirically derive a set of quantitative mathematical relationships between these MN electrophysiological and anatomical properties. This validated mathematical framework, which supports past findings that the MN membrane properties are all related to each other and clarifies the nature of their associations, is besides consistent with the Henneman's size principle and Rall's cable theory. The derived mathematical relationships provide a convenient tool for neuroscientists and experimenters to complete experimental datasets, explore the relationships between pairs of MN properties never concurrently observed in previous experiments, or investigate inter-mammalian-species variations in MN membrane properties. Using this mathematical framework, modellers can build profiles of inter-consistent MN-specific properties to scale pools of MN models, with consequences on the accuracy and the interpretability of the simulations.Muscles receive their instructions through electrical signals carried by tens or hundreds of cells connected to the command centers of the body. These ‘alpha-motoneurons’ have various sizes and electrical characteristics which affect how they transmit signals. Previous experiments have shown that these properties are linked; for instance, larger motoneurons transfer electrical signals more quickly. The exact nature of the mathematical relationships between these characteristics, however, remains unclear. This limits our understanding of the behaviour of motoneurons from experimental data. To identify the equations linking eight motoneuron properties, Caillet et al. analysed published datasets from experimental studies on cat motoneurons. This approach uncovered simple mathematical associations: in fact, only one characteristic needs to be measured experimentally to calculate all the other properties. The relationships identified were also consistent with previously accepted approaches for modelling motoneuron activity. Caillet et al. then validated this mathematical framework with data from studies on rodents, showing that some of the equations hold true for different mammals. This work offers a quick and easy way for researchers to calculate the characteristics of a motoneuron based on a single observation. This will allow non-measured properties to be added to experimental datasets, and it could help to uncover the diversity of motoneurons at work within a population.

Aircraft Deconfliction via Mathematical Programming: Review and Insights

Abstract: Computer-aided air traffic management has increasingly attracted the interest of the operations research community. This includes, among other tasks, the design of decision support tools for the detection and resolution of conflict situations during flight. Even if numerous optimization approaches have been proposed, there has been little debate toward homogenization. We synthesize the efforts made by the operations research community in the past few decades to provide mathematical models to aid conflict detection and resolution at a tactical level. Different mathematical representations of aircraft separation conditions are presented in a unifying analysis. The models, which hinge on these conditions, are then revisited, providing insight into their computational performance.

Corrected Inertial Torques of Gyroscopic Effects

Abstract: The published manuscripts in the area of gyroscope theory were presented mainly by the simplified approaches in which mathematical models contain many uncertainties. New research in machine dynamics opened breakthrough directions in gyroscopic effects of rotating objects that give the correct solutions. The pioneering work meets many problems when solving the scientific innovations that are accompanied by successes and omissions. New mathematical models for the gyroscopic inertial torques were derived with incorrect processing of the integral equations that give distorted results. The gyroscopic devices in engineering manifest gyroscopic effects as the action of the inertial torques which computing is crucial for mathematical describing of their motions. The corrected mathematical processing of the equations for the inertial torques acting in a gyroscope is presented in this manuscript.

Mathematical Modeling: A Conceptual Approach of Linear Algebra as a Tool for Technological Applications

Abstract: Mathematical modeling is the field of applied mathematics in charge of mathematically model problems, situations, and phenomena of the world where we live. The models are sets of equations that describe the behavior of these phenomena, which can be of physical nature, such as the equations that describe the movement of planets and the behavior of atoms and charged particles, social nature, such as economic models of the relationship between industry sectors or how to handle a eucalyptus forest most sustainably and profitably, and others. There are also optimization models to index webpages or encrypt information within images, for example. Each of those models uses different and sophisticated mathematical tools, like calculus and especially linear algebra, which is the scope of this article. Some models work better in the form of matrices and vectors, which facilitate the visualization of the calculations to be performed. Many of them can be converted into algorithms to make possible the aid of computational resources and achieve the solutions in a faster and more practical way. Mathematically modeling a situation or phenomenon is the first step to figure out possible solutions and, with adjustments whenever they are necessary, make predictions concerning the studied subject.

System parameter exploration of ship maneuvering model for automatic docking/berthing using CMA-ES

Abstract: Accurate maneuvering estimation is essential to establish autonomous berthing control. The system-based mathematical model is widely used to estimate the ship’s maneuver. Commonly, the system parameters of the mathematical model are obtained by the captive model test (CMT), which is time-consuming to construct an accurate model suitable for complex berthing maneuvers. System identification (SI) is an alternative to constructing the mathematical model. However, SI on the mathematical model of ship’s maneuver has been only conducted on much simpler maneuver: turning and zig-zag. Therefore, this study investigates the SI on a mathematical model capable of berthing maneuver. The main contributions of this study are as follows: (i) construct the system-based mathematical model on berthing by optimizing system parameters with a reduced amount of model tests than the CMT-based scheme; (ii) Find the favorable choice of objective function and type of training data for optimization. Global optimization scheme CMA-ES explored the system parameters of the MMG model from the free-running model’s trajectories. The berthing simulation with the parameters obtained by the proposed method showed better agreement with the free-running model test than parameters obtained by the CMT. Furthermore, the proposed method required fewer data amounts than a CMT-based scheme.

A novel mathematical model to describe the transmission dynamics of tooth cavity in the human population

Abstract: In the history of mathematical modeling, a number of deadly diseases in humans, animals, birds, and plants have been studied by using various types of mathematical models. In this group, the cavity is a dental infection, which is found in thousands of humans. Nowadays, a cavity is the most common disease in human teeth. As per our knowledge, to date, there is no mathematical model in the literature to understand the dynamics of the cavity. In this article, we fulfill this requirement by defining a non-linear delay-type mathematical model to describe the dynamics of cavities in human teeth. First, we propose an integer-order model and check the boundedness and positivity of the solution, and equilibrium points with their local and global asymptotically stability. After that, we generalize the integer-order delay-type model into a fractional sense to capture the memory effects. We prove the existence of a unique global solution of the fractional-order model in the Caputo derivative sense. The numerical solution of the proposed fractional-order model is given with the help of the predictor-corrector method. We do the all necessary graphical simulations to understand the model dynamics appropriately. The main motivation of this paper is to introduce a first mathematical delay-type model to describe the cavity problem in human teeth.

Mathematical modelling, numerical and experimental analysis of one-degree-of-freedom oscillator with Duffing-type stiffness

Abstract: The aim of the work is to develop and test simple mathematical models suitable for fast and realistic simulations of bifurcation dynamics of systems with a double potential well generated by a pair of repulsive magnets positioned transversely to the direction of motion, where there are motion resistances typical for rolling guides found in industry. Mathematical modelling of a harmonically forced one-degree-of-freedom oscillator with magnetically modified elasticity generating a double symmetrical minimum of potential was carried out. The system is composed of a cart moving along a linear rolling bearing with inertial excitation by means of a stepper motor with an unbalanced disk. The stiffness is realized by a pair of neodymium magnets of axes perpendicular to the direction of motion, in a position corresponding to the static equilibrium position of the oscillator, with additional mechanical linear springs, which generate a system similar to the Duffing system. Different models of the interaction force between cylindrical neodymium magnets were developed. The model parameters are estimated based on experimental data. Then the model is validated through additional experimental and numerical bifurcation analysis of the system. A very good agreement between numerical simulations and experimental data is obtained.

Open problems in mathematical biology

Abstract: Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.

Mathematical Modeling of COVID-19 and Prediction of Upcoming Wave

Abstract: We investigate the problem of mathematical modeling of new corona virus (COVID-19) spread in practical scenarios in various countries, specifically in India, the United States of America (USA), France, Brazil, and Turkey. We propose a mathematical model to characterize COVID-19 disease and predict the new/upcoming wave of COVID-19. This prediction is very much required to prepare medical set-ups and proceed with future plans of action. A mixture Gaussian model is proposed to characterize the COVID-19 disease. Specifically, the data corresponding to new active cases of COVID-19 per day is considered, and then we try to fit the data to a mathematical function. It is observed that the Gaussian mixture model is suitable to characterize the new active cases of COVID-19. Further, it is assumed that there are N waves of COVID-19 and the information of each upcoming wave is present in the current and previous waves as well. By using this concept, prediction of the upcoming wave can be performed. A close match between analytical results and the available results shows the correctness of the considered model.

Mathematical Modeling to Estimate Photosynthesis: A State of the Art

Abstract: Photosynthesis is a process that indicates the productivity of crops. The estimation of this variable can be achieved through methods based on mathematical models. Mathematical models are usually classified as empirical, mechanistic, and hybrid. To mathematically model photosynthesis, it is essential to know: the input/output variables and their units; the modeling to be used based on its classification (empirical, mechanistic, or hybrid); existing measurement methods and their invasiveness; the validation shapes and the plant species required for experimentation. Until now, a collection of such information in a single reference has not been found in the literature, so the objective of this manuscript is to analyze the most relevant mathematical models for the photosynthesis estimation and discuss their formulation, complexity, validation, number of samples, units of the input/output variables, and invasiveness in the estimation method. According to the state of the art reviewed here, 67% of the photosynthesis measurement models are mechanistic, 13% are empirical and 20% hybrid. These models estimate gross photosynthesis, net photosynthesis, photosynthesis rate, biomass, or carbon assimilation. Therefore, this review provides an update on the state of research and mathematical modeling of photosynthesis.

Justifying the actuator type selection for the flow-line conveyor system with vibration-assisted transportation of bulk material

Abstract: Vibratory feeders are widespread in the production processes of mining companies. For this reason, optimized design and fine-tuned operation of a flow-line conveyor system feeding material to separators with X-ray fluorescent spectrometer sensors can increase the diamond production capacity and improve the energy conversion efficiency by reducing the power consumption. This study considers vibration-assisted transportation of bulk material layer in vibratory feeders and develops a mathematical model of an electromagnetic drive using mathematical modeling. The analysis methods include theoretical studies of technical documentation of flow and transport systems in general and vibration feeders in particular, mathematical modeling of technical systems using the MatLab software package and Simulink application. The research included theoretical studies of transportation of a layer of bulk material at different vibration frequencies and amplitudes. A mathematical model has been developed describing the vibration-assisted transportation of bulk material in the feeder tray. The resulting calculated data has been compared with experimental data. A mathematical model of an electromagnetic drive with a control system that stabilizes feeder performance has been developed, which allows adjusting the optimal basic feeder vibration frequency at a known resonant frequency. The obtained results can be applied to the processing factories for mineral separation of diamond-containing rocks to calculate the power of the feeder drive and the selection of the type of power system in terms of optimality for the technological process and the energy efficiency of electrical equipment.

Geometric analysis enables biological insight from complex non-identifiable models using simple surrogates

Abstract: An enduring challenge in computational biology is to balance data quality and quantity with model complexity. Tools such as identifiability analysis and information criterion have been developed to harmonise this juxtaposition, yet cannot always resolve the mismatch between available data and the granularity required in mathematical models to answer important biological questions. Often, it is only simple phenomenological models, such as the logistic and Gompertz growth models, that are identifiable from standard experimental measurements. To draw insights from complex, non-identifiable models that incorporate key biological mechanisms of interest, we study the geometry of a map in parameter space from the complex model to a simple, identifiable, surrogate model. By studying how non-identifiable parameters in the complex model quantitatively relate to identifiable parameters in surrogate, we introduce and exploit a layer of interpretation between the set of non-identifiable parameters and the goodness-of-fit metric or likelihood studied in typical identifiability analysis. We demonstrate our approach by analysing a hierarchy of mathematical models for multicellular tumour spheroid growth experiments. Typical data from tumour spheroid experiments are limited and noisy, and corresponding mathematical models are very often made arbitrarily complex. Our geometric approach is able to predict non-identifiabilities, classify non-identifiable parameter spaces into identifiable parameter combinations that relate to features in the data characterised by parameters in a surrogate model, and overall provide additional biological insight from complex non-identifiable models.