136 articles found
Mathematical Modelling from the Instrumentation of Improper Integrals
Enrique Mateus-Nieves, Hernández Montañez Wilfaver
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Improper integral; Mathematical modelling; Mathematical instrumentation.
Background: There is little clarity in the application of content related to improper integrals in university students, due to the absence of meaning, which prevents them from making a connection with everyday problem situations. Methods: we designed a mathematical modelling proposal where a specific situation involving the instrumentation, use and application of this type of integrals is experimented and solved with a population of engineering students, who learn to use them. Results: The importance of using mathematical modelling as a didactic-dynamic resource is highlighted because it helps students to reach an understanding of real situations involving improper integrals in different contexts. Conclusions: Despite the numerous errors detected in the students, this strategy made it possible to demonstrate the development of advanced mathematical thinking skills in young people.
Dual-Target Car-Ts With on- and off-Tumour Activity May Override Immune Suppression in Solid Cancers: A Mathematical Proof of Concept
Odelaisy León-Triana, Antonio Pérez-Martínez, Manuel Ramírez-Orellana, Víctor M. Pérez-García
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Mathematical oncology; CAR-T cells; mathematical immunology; mathematical modelling; immunotherapy of solid tumours; glioblastoma
Chimeric antigen receptor (CAR)-T cell-based therapies have achieved substantial successes against B-cell malignancies, what has led to a growing scientific and clinical interest on extending their use to solid cancers. However, results for solid tumours have been limited up to now, in part due to the immuno-suppressive tumour microenvironment, that is able to inactivate CAR-T cell clones. In this paper we put forward a mathematical model describing the competition of CAR-T and tumour cells, accounting for their immunosuppressive capabilities. Using the mathematical model, we show that the use of large numbers of CAR-T cells targeting the solid tumour antigens could overcome the cancer immunosuppressive potential. To achieve such high levels of CAR-T cells we propose and study computationaly, the manufacture and injection of CAR-T cells targeting two antigens: CD19 and a tumour-associated antigen. We study in-silico the resulting dynamics of the disease after the injection of this product and find that the expansion of the CAR-T cell population in the blood and lymphopoietic organs could lead to the massive generation of an army of CAR-T cells targetting the solid tumour, and potentially overcoming its inmune suppression capabilities. That strategy could benefit from the combination with PD-1 inhibitors and of low tumour loads. Our computational results provide a theoretical support for the treatment of different types of solid tumours using T-cells engineered with combination treatments of dual CARs with on- and off-tumour activity and anti-PD1 drugs after completion of classical cytoreductive treatments.
An Overview of Malaria Transmission Mechanisms, Control, and Modeling
Merveille Koissi Savi
Subject: Life Sciences, Other Keywords: Complexity; policy-recommendation; mathematical models
In sub-Saharan Africa, malaria is a leading cause of mortality and morbidity. As a result of the interplay between many factors, the control of this disease can be challenging. However, few studies have demonstrated malaria's complexity, control, and modeling although this perspective could lead to effective policy recommendations. This paper aims to be a didactic material providing the reader with an overview of malaria. More importantly, using a system approach lens, we intend to highlight the debated topics and the multifaceted thematic aspects of malaria transmission mechanisms, while showing the control approaches used as well as the model supporting the dynamics of malaria. As there is a large amount of information on each subject, we have attempted to provide a basic understanding of malaria that needs to be further developed. Nevertheless, this study illustrates the importance of using a multidisciplinary approach to designing next-generation malaria control policies.
Not Just Numbers: Mathematical Modelling and its Contribution to Anaerobic Digestion Processes
Subject: Engineering, Other Keywords: Mathematical modelling; Anaerobic digestion; Mechanistic models; Data-driven models; Mathematical analysis; Hybrid modelling; Thermodynamics
Mathematical modelling of bioprocesses has a long and notable history, with eminent contributions from fields including microbiology, ecology, biophysics, chemistry, statistics, control theory and mathematical theory. This richness of ideas and breadth of concepts provide great motivation for inquisitive engineers and intrepid scientists to try their hand at modelling, and this collaboration of disciplines has also delivered significant milestones in the quality and application of models for both theoretical and practical interrogation of engineered biological systems. The focus of this review is the anaerobic digestion process, which, as a technology that has come in and out of fashion, still remains a fundamental process for addressing the global climate emergency. Whether with conventional anaerobic digestion systems, biorefineries, or other anaerobic technologies, mathematical models are important tools that are used to design, monitor, control and optimise the process. Both highly structured, mechanistic models and data-driven approaches have been used extensively over half a decade, but recent advances in computational capacity, scientific understanding and diversity and quality of process data, presents an opportunity for the development of new modelling paradigms, augmentation of existing methods, or even incorporation of tools from other disciplines, to ensure that anaerobic digestion research can remain resilient and relevant in the face of emerging and future challenges.
How to Use Biomechanical Job Exposure Matrices (Jem) On Job History for Musculoskeletal Disorders? Mathematical Modeling on the Example of Severe Knee Pain in Constances
Guillaume Deltreil, Patrick Tardivel, Piotr Graczyk, Mikaël Escobar-Bach, Alexis Descatha
Subject: Medicine & Pharmacology, Other Keywords: Occupational; Musculskeletal; pain; lifecourse; mathematical modeling.
Introduction. Musculoskeletal disorders related to work might follow with a cumulative effect during working life. We aimed to develop a new model to allow to compare the accuracy of duration of work and intensity/frequency associations in application to severe knee pain. Methods. The CONSTANCES cohort is used with data from n=66553 subjects who were working at inclusion and coded. From a biomechanical job exposure matrix "JEM Constances", intensity/frequency of heavy lifting and kneeling/squatting were used and applied to the work history in comparison to severe knee pain. An innovative model was developed and evaluated, allowing to compare the accuracy of duration of work and intensity/frequency associations. Results. The mean age is 49 years at inception with 46 percent of women. The G model developed was slightly better than regular models. In men, odds ratios of the highest quartile for the duration and low intensity were not significant for both exposures, whereas intensity/duration were for every duration. Results in women were less interpretable. Conclusion. Though increased duration increased strength of association with severe knee pain, intensity/frequency were important predictors among men. Exposure estimation along working history should have emphasis on such parameters, though other outcomes should be studied such as women.
Two-Parameter CFAR Ship Detection Algorithm Based on Rayleigh Distribution in SAR Images
Ruochen Wu
Subject: Engineering, Other Keywords: SAR; Ship detecion; CFAR; Mathematical morphology
Synthetic Aperture Radar (SAR) is an active type of microwave remote sensing. Using the microwave imaging system, remote sensing monitoring of the land and global ocean can be done in any weather conditions around the clock. Detection of SAR image targets is one of the main needs of radar image interpretation applications. In this paper, an improved two-parameter CFAR algorithm based on Rayleigh distribution and morphological processing is proposed to perform ship detection and recognition in high resolution SAR images. Through simulation experiments, comprehensive study of the two algorithms for high resolution SAR image target detection is achieved. Finally, the results of ship detection experiments are compared and analyzed, and the effects of detection are evaluated according to the Rayleigh distribution model and algorithms.
Development Of Mathematics Teaching Materials Oriented Mathematic Literation And Life Enterpreneurship
Alpha Galih Adirakasiwi, Attin Warmi, Achmad Nawawi
Subject: Arts & Humanities, Other Keywords: Teaching materials, Mathematical literacy, Entrepreneurial Spirit
Mathematical literacy is a very hot issue in the development of mathematics learning, apart from mathematical literacy, another interesting thing is the entrepreneurial spirit that must be given from an early age, especially for vocational students. This research was conducted at SMK Rosma Karawang in the Department of Computer and Network Engineering, West Java Province with the XI grade students. The teaching materials developed by applying the principles of the development model developed with the ADDIE model consist of analysis, design, development, implementation and evaluation. This research and development model is considered suitable for developing teaching tools and materials which is used for the purposes of the learning process. Based on the results of data analysis and processing that have been carried out in this study, the development of teaching materials using the ADDIE model has met the appropriate and valid criteria by media, language and media expert valuators. Another result of developing this teaching material besides meeting the eligibility criteria is that the teaching materials developed are able to increase mathematical literacy and instill entrepreneurial spirit for students.
The Optimal Radiation Dose to Induce Robust Systemic Anti-Tumor Immunity
Jan Poleszczuk, Heiko Enderling
Subject: Medicine & Pharmacology, Oncology & Oncogenics Keywords: abscopal effect; radiotherapy; immunotherapy; mathematical model
Synergy of radiation and immune system is currently receiving significant attention in oncology as numerous studies have shown that cancer irradiation can induce strong antitumor immune responses. It remains unclear, however, what are the best radiation fractionation protocols to maximize the therapeutic benefits of this synergy. Here, we present a novel mathematical model that can be used to predict and dissect the complexity of the immune-mediated response at multiple tumor sites after applying focal irradiation and systemic immunotherapy. We successfully calibrate the proposed framework with published experimental data, in which two tumors were grown in mice at two spatially separated sites from which only one was irradiated using various radiation fractionation protocols with and without concurrent systemic immunotherapy. The proposed model is calibrated to fit the temporal dynamics of tumor volume at both sites and can predict changes in immune infiltration in the non-irradiated tumors. The model was then used to investigate additional radiation fractionation protocols. Model simulations suggest that the optimal radiation doses per fraction to maximize antitumor immunity are between 10-13 Gy, at least for the experimental setting used for model calibration. This work provides the framework for evaluating radiation fractionation protocols for radiation-induced immune-mediated systemic antitumor responses.
Linear Mathematical Model for Seam Tracking with an Arc Sensor in P-GMAW process
Wenji Liu, Liangyu Li, Ying Hong, Jianfeng Yue
Subject: Engineering, Industrial & Manufacturing Engineering Keywords: arc sensing; P-GMAW; mathematical model
Arc sensors have been used in seam tracking and widely studied since the 80s; commercial arc sensing products for T and V shaped grooves have been developed. However, it is difficult to use these arc sensors in narrow gap welding because arc stability and sensing accuracy are not satisfactory. Pulse gas melting arc welding (P-GMAW) has been successfully applied in narrow gap welding and all position welding processes, so it is worthwhile to research P-GMAW arc sensing technology. In this paper, we derived a linear mathematical P-GMAW model for arc sensing, and the assumptions for the model are verified through experiments and finite element methods. Finally, the linear characteristics of the mathematical model were investigated. In torch height changing experiments, uphill experiments, and groove angle changing experiments the P-GMAW arc signals all satisfied the linear rules. In addition, the faster the welding speed, the higher the arc signal sensitivities; the smaller the groove angle, the greater the arc sensitivities. The arc signal variation rate needs to be modified according to the welding power, groove angles, and swing or rotate speed.
On the Indian Tradition of Mathematical Names: A Scientific Analysis
Ashish Karn, Brett Rosiejka, Pankaj Badoni, Raman Kumar Singh
Subject: Mathematics & Computer Science, General Mathematics Keywords: Mathematical names; Hindu mathematical tradition; Indian social psyche; Mathematics and religion; Mathematics and society; Hindu mathematics
The current paper explores the potential interlink between names of individuals in a society and its collective social consciousness, particularly with reference to the pervasive occurrence of the 'mathematical names' in the current Hindu society in the Indian subcontinent and beyond. Initially, an attempt is made to put things into mathematical perspective by drawing a quick sketch of some of the stellar achievements of the Indian mathematicians. Under the six broad categories of geometry, trigonometry, numeration, arithmetic, algebra, and mathematics in the Vedic tradition, a concise simple description of these subdivisions is presented, underlining the names of the concepts and terms, sometimes by producing the textual references. Then, upon identification of such mathematical terms, an attempt is made to juxtapose these with the names current in the Indian Hindu society. By employing an extensive dataset of university student names in India and the directories of Facebook and LinkedIn, we produce both qualitative and quantitative evidence of the presence of such names in the Indian subcontinent. Evidently, these names reflect the impressions of the tremendously rich mathematical heritage left by the Hindu stalwart mathematicians. This hypothesis has also been examined by taking surveys of people bearing these mathematical names, as well as by documenting the 'conscious procedures' that go behind the naming of a Hindu Indian child. In trying to investigate if such a phenomenon is unique to the Indian tradition, a stark contrast with the 'names in mathematics' as prevalent in the European mathematical traditions is presented, as cultural roots of mathematics are explored. Further, we ascribe the presence of these names as the extant remains of the colossal impact of multifarious mathematical traditions existing in India. Interestingly, the present research also brings to the fore, certain unseen facets of the Indian Hindu society as regards the education of mathematics to women – through an indirect exploration of their names. We also show that the pervasive occurrence of these names is not merely the result of semantic chance events, but denotes the richness of the Indian mathematical legacy. Next, we also present cross-cultural comparisons to show the uniqueness of Indian mathematical and scientific traditions that led to the pervasiveness of 'mathematical names' in India. Finally, an attempt is made to clarify some subtle points on the associations between mathematics and religion in India and other cultures of the world. It is sincerely hoped that the present study may shed light on the cultural roots of mathematics and may furnish a new dimension in the study of mathematics, culture and civilizations across the world.
Identify the Mathematical Models Generated by the Table Curve 3 D Program
Emilian Mosnegutu, Mirela Panainte-Lehadus, Valentin Nedeff, Claudia Tomozei, Narcis Barsan, Dana Chitimus, Marcin Jasinski
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: mathematical models; Table Curve 3D; correlation coefficient
This article describes the methodology used to identify the mathematical model that describes the correlations between the input parameters of an experiment and the parameters being followed. As a technological process, the aerodynamic separation was chosen, respectively, the behavior of a solid particle within an ascending vertical airflow. The experimental data obtained were used to identify two parameters, the average linear velocity, and the angular velocity, and through the Table Curve 3D program was developed a mathematical model which describes the dependence between the input parameters (the shape and size of the solid particle and the velocity of the airflow) and the monitored parameters. In order to determine a single mathematical equation that describes as accurately as possible the correlation between the input variables and those obtained, a pyramid-type analysis was designed. The determination of the mathematical equation started from the number of equations generated by the Table Curve 3D program, then the equations with a correlation coefficient greater than 0.85 were chosen, and finally, the common equations were identified. Respecting the working methodology was identified one equation which has for the average linear velocity a correlation coefficient r2 between 0.88-0.99 and 0.86-0.99 for the angular velocity.
Modeling an Inverted Pendulum via Differential Equations and Reinforcement Learning Techniques
Siddharth Sharma
Subject: Mathematics & Computer Science, Numerical Analysis & Optimization Keywords: Reinforcement learning; Cartpole; Q Learning; Mathematical Modeling
The prevalence of differential equations as a mathematical technique has refined the fields of control theory and constrained optimization due to the newfound ability to accurately model chaotic, unbalanced systems. However, in recent research, systems are increasingly more nonlinear and difficult to model using Differential Equations only. Thus, a newer technique is to use policy iteration and Reinforcement Learning, techniques that center around an action and reward sequence for a controller. Reinforcement Learning (RL) can be applied to control theory problems since a system can robustly apply RL in a dynamic environment such as the cartpole system (an inverted pendulum). This solution successfully avoids use of PID or other dynamics optimization systems, in favor of a more robust, reward-based control mechanism. This paper applies RL and Q-Learning to the classic cartpole problem, while also discussing the mathematical background and differential equations which are used to model the aforementioned system.
Preprint BRIEF REPORT | doi:10.20944/preprints202004.0455.v1
Exploring Students' Understanding of Statistical Mean
Md Amiruzzaman
Subject: Mathematics & Computer Science, Probability And Statistics Keywords: statistics; mean; weighted mean; average; mathematical thinking
This study explores students' understanding of one measure of central tendency, the mean. A teaching experiment was conducted to understand how sixth-grade students made sense of this concept. Findings suggest that the students know how to solve mathematical problems related to mean using procedural understanding and lack of conceptual understanding.
A Hidden Markov Model for the Linguistic Analysis of the Voynich's Manuscript
Luis Acedo
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Hidden Markov Models; Mathematical Linguistics; Voynich Manuscript
Hidden markov models are a very useful tool in the modelling of time series and any sequence of data. In particular, they have been successfully applied to the field of mathematical linguistics. In this paper, we apply a hidden markov model to analyze the underlying structure of an ancient and complex manuscript, known as Voynich's manuscript, that remains still undeciphered. By assuming a certain number of internal states representations for the symbols of the manuscript we train the network by means of the $\alpha$ and $\beta$-pass algorithms to optimize the model. By this procedure, we are able to obtain the so-called transition and observation matrices in order to compare with known languages concerning the frequency of consonant and vowel sounds. From this analysis, we conclude that transitions occur between the two states with similar frequencies to other languages. Moreover, the identification of the vowel and consonant sounds matches some previous tentative bottom-up approaches to decode the manuscript.
A New Kind of Aesthetics – The Mathematical Structure of the Aesthetic
Akihiro Kubota, Hirokazu Hori, Makoto Naruse, Fuminori Akiba
Subject: Arts & Humanities, Theory Of Art Keywords: aesthetics; mathematical structure; category theory; natural intelligence
This paper proposes a new approach to investigation into the aesthetics. Specifically, it argues that it is possible to explain the aesthetic and its underlying dynamic relations with axiomatic structure (the octahedral axiom derived category) based on contemporary mathematics – namely, category theory – and through this argument suggests the possibility for discussion about the mathematical structure of the aesthetic. If there was a way to describe the structure of aesthetics with the language of mathematical structures and mathematical axioms – a language completely devoid of arbitrariness – then we would make possible a synthetical argument about the essential human activity of "the aesthetics", and we would also gain a new method and viewpoint on the philosophy and meaning of the act of creating a work of art and artistic activities. This paper presents one hypothesis as a first step in constructing the science of dynamic generative aesthetics based on axiomatic functionalism, which is in turn based on a new interdisciplinary investigation into the functional structure of aesthetics.
Mathematical and Artificial Intelligence Models for Zoonotic Foodborne Pathogens
Nisha Pillai, Mahalingam Ramkumar, Bindu Nanduri
Subject: Biology, Animal Sciences & Zoology Keywords: zoonotic pathogens; mathematical algorithms; machine learning; deep learning
Globally, zoonotic diseases have been on the rise in recent years. Predictive modelling approaches have been successfully used in the literature to identify the underlying causes of these zoonotic diseases. We examine the latest research in the field of predictive modeling that verifies the growth of zoonotic pathogens and assesses the factors associated with their spread. The results of our survey indicate that popular mathematical models can successfully be used in modeling the growth rate of these pathogens under varying storage temperatures. Additionally, some of them are used for the assessment of the inactivation of these pathogens based on various conditions. Based on the results of our study, machine learning models and deep learning are commonly used to detect pathogens within food items and to predict the factors associated with the presence of the pathogens.
A Wavelet Multiscale Mathematical Model for Quality of Life Index Measuring
Majed S. Balalaa, Anouar Ben Mabrouk
Subject: Social Sciences, Other Keywords: multi scale; quality of life; wavelets; mathematical models
Online: 1 March 2022 (13:32:59 CET)
The present paper is concerned with the study of the quality of life index. Such an index has become an important index for measuring the well-being of individuals. However, the quality of life index is always a subjective, intangible, and often hard to quantify with precision due to the lack of quantitative models dealing with. The main goal of the present paper is thus to propose a mathematical, quantitative model for the measurement of a quality of life index. The main novelty is firstly the construction of a wavelet dynamic multiscale model to quantify and investigate the effect of time scale on the quality of life index measuring. The proposed procedure is acted empirically on a sample corresponding to Saudi Arabia as a case of study during the period from 2003 to 2020 as part of the 2030-vision plan. Saudi Arabia has implemented the so-called 2030-vision plan where the quality of life improvement is one of the main goals to be attempted. The findings show that wavelets are capable to localize the time-wise behavior of the index contrarily to classical studies which estimate a global view of the index. Moreover, the study shows the link between the quality of life behavior and many other indices.
Preprint SHORT NOTE | doi:10.20944/preprints202201.0166.v1
Two Notes on the Theoretical Physics of ATP Synthase
Archit Chaturvedi
Subject: Physical Sciences, Applied Physics Keywords: Theoretical Biophysics; Mathematical Biophysics; Theoretical Biology; Molecular Biophysics
ATP Synthase is an essential molecule in cell and molecular biology. It is re sponsible for the production of ATP during cellular respiration, a molecule that provides the energy required to drive a number of cellular processes. In this paper, I explore the rotational physics of ATP Synthase's rotor, a part of the protein that spins during the production of ATP. Firstly, I discuss some elementary rotational kinematics of the rotor. I then derive two alternate formulations for the total lin ear acceleration of the rotor. Finally, I derive formulas for the moment of inertia, angular momentum, net torque, and kinetic energy of the rotor. Through this, I hope to provide a theoretical and mathematical insight into the mechanics of ATP Synthase during the production of ATP.
Determining COVID-19 Dynamics Using Physics Informed Neural Networks
Joseph Malinzi, Simanga Gwebu, Sandile Motsa
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Physics Informed Neural Networks; Mathematical modeling; COVID-19
The Physics Informed Neural Networks framework is applied to the understanding of the dynamics of Coronavirus of 2019. To provide the governing system of equations used by the framework, the Susceptible-Infected-Recovered-Death mathematical model is used. The study focused on finding the patterns of the dynamics of the disease which involves predicting the infection rate, recovery rate and death rate; thus predicting the active infections, total recovered, susceptible and deceased at any required time. The study used data that was collected on the dynamics of COVID-19 from the Kingdom of Eswatini between March 2020 and September 2021. The obtained results showed less errors thus making highly accurate predictions.
Graph Coverings for Investigating Non Local Structures in Proteins, Music and Poems
Michel Planat, Raymond Aschheim, Marcelo M Amaral, Fang Fang, Klee Irwin
Subject: Keywords: mathematical poetry; musical forms; protein foldings; graph coverings
It is shown how the secondary structure of proteins, musical forms and verses of poems are approximately ruled by universal laws relying on graph coverings. In this direction, one explores the group structure of a variant of the SARS-Cov-2 spike protein and the group structure of apolipoprotein-H, passing from the primary code with amino acids to the secondary structures organizing the foldings. Then one look at the musical forms employed in the classical and contemporary periods. Finally, one investigates in much detail the group structure of a small poem in prose by Charles Baudelaire and that of the Bateau Ivre by Arthur Rimbaud.
Targeting Malaria Hotspots to Reduce Transmission Incidence in Senegal
Kankoe Sallah, Roch Giorgi, El-Hadj Ba, Martine Piarroux, Renaud Piarroux, Badara Cisse, Jean Gaudart
Subject: Medicine & Pharmacology, Allergology Keywords: Malaria elimination; Mathematical model; Human mobility; Intervention chemotherapy
In central Senegal malaria incidences have declined from 2000 to 2010 in response to scaling-up of control measures and then remained stable, making elimination improbable. Additional control measures are needed to reduce transmission. We simulated chemoprophylaxis interventions targeting malaria hotspots, using a meta-population mathematical model based on differential equation framework and incorporating human mobility. The model was fitted to weekly malaria incidences from 45 villages. Three approaches for selecting intervention targets were compared: a) villages with malaria cases during the low transmission season of the previous year; b) villages with highest incidences during the high transmission season of the previous year; c) villages with highest connectivity with adjacent populations. Our modeling, considering human mobility, showed that the intervention strategies targeting hotspots would be effective in reducing malaria incidence in both targeted and untargeted areas. But whatever the intervention, pre-elimination stage (1-5 cases per 1,000 per year) would not be reached without simultaneously increasing vector control by more than 10%. Targeted interventions allow increasing overall malaria control and elimination potential.
Mathematical Modelling of the Dynamics of Tumor Growth and its Optimal Control
Jannatun Irana Ira, Md. Shahidul Islam, Jagadis Chandra Misra, Md. Kamrujjaman
Subject: Keywords: Mathematical models; tumor growth; chemotherapy; diffusion; optimal control
In the last few decades, the dynamics of tumor cells and their growths are presented via clinical, experimental, and theoretical approaches, which leads to the development of the new idea of multiple cancer therapies to control and reduce the death rate for earlier detection. In this paper, we discussed the dynamics of tumor cell growth and its treatment process. We analyzed some simple mathematical models and generalized the study to understand the growth of tumor cells. The main proposed model is a system of ordinary differential equations which combines interactions among natural killer cells, dendritic cells and cytotoxic CD8+ T cells. The model is solved numerically to explain how the tumor cells spread and become more dangerous as well as the treatment process of cancer. It is also studied that how the cell behaves in the presence of different therapy and drugs. The optimal control of chemotherapy has been discussed. It has also been explained how much the model is effective in reducing tumor cells over time. Finally, a couple of spatially distributed models are discussed for tumor cell growth.
Analysis and Prediction for the Spreading of Covid-19 Pandemic in India Using Mathematical Modeling
Nanda Poddar, Subham Dhar, Kajal Kumar Mondal, Gourab Saha
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Corona Virus; Covid-19; India; Pandemic; Mathematical modeling
In the present time, the biggest problem of the world is the outbreak of novel coronavirus. Novel coronavirus (COVID-19), this one name has become a part of our daily lives over the past few months. Beyond the boundaries of medical science, coronavirus is now the main subject of research in all fields like Applied Mathematics, Economy, Philosophy, Sociology, Politics upto living room. The epidemic has brought unimaginable changes in our traditional habits and daily routines. Thousands of people in our country are fighting with the rest of the world to survive in various new situations. There are different kinds of coronavirus appeared in different times. In this time, Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) is responsible for the coronavirus disease of 2019 (COVID-19). This virus was first identified towards the end of 2019 in the city of Wuhan in the province of Hubei in China. Within very short duration of time and very fast, it has spread throughout a large part of the world. In this study, the main aim is to investigate the spreading rate, death rate, recovery rate due to corona virus infection and to study the future of the coronavirus in India by using mathematical modeling based on the previous data. Mathematical models, in this situation, are the important tools in recruiting effective strategies to fight this epidemic. India is at high risk of spreading the disease and is facing many losses in socio-economic aspects. With current infection rates and existing levels of personal alertness, the number of infected people in India will increase at least in the next three months. Proper social awareness, maintain of social distance, large rate of testing and separation may break the chain of the Coronavirus-2.
COVID-19 Propagation Mathematical Modeling: The Case of Senegal
Mouhamadou Diaby, Oumar Diop, Almamy Konté, Abdou Sène
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: COVID-19; mathematical model; fitting strategy; reproduction number
The outburst of the CoVid-19 pandemic has raised several questions leading to a complex system in terms of modeling. Indeed, the modeling of the epidemic, at the level of a country, needs considering each of the different sources of contamination as well as the public health authorities' strategy, in a specific way. With this in mind, in the present paper, we develop a mathematical model of the CoVid-19 epidemic in Senegal. In the model, the population is subdivided into five compartments: susceptible, infected but asymptomatic, symptomatic, quarantined, and recovered immune people. In addition, due to its important impact on the propagation of the disease, we add one more variable: the number of infected objects. %\vspace{1mm} Therefore, the model corresponds to a system of six non-linear ordinary differential equations we submit to an analytical study to prove the relevancy of the model, simulate the evolution of the epidemic, and retrieve epidemiological parameters, namely the infection rate and the basic reproduction number, ${\cal R}_0$. Based on the senegalese territory CoVid-19 data, we simulate various scenarios as for the evolution of the epidemic in the country, in order to predict the peak and its magnitude with regard to the application of barrier measures. We also explore the option of collective immunity with special protection for vulnerable people. In doing so, non-available parameters are identified using some mathematical identification technics.
The Significance of the Detection Ratio for Predictions on the Outcome of an Epidemic - A Message from Mathematical Modelers
Jan Fuhrmann, Maria Vittoria Barbarossa
Subject: Medicine & Pharmacology, Other Keywords: COVID-19; mathematical model; detection ratio; testing; fatality
In attempting to predict the further course of the novel coronavirus (COVID-19) pandemic caused by SARS-CoV-2, mathematical models of different types are frequently employed and calibrated to reported case numbers. Among the major challenges in interpreting these data is the uncertainty about the amount of undetected infections, or conversely: the detection ratio. As a result, some models include assumptions about the percentage of detected cases among total infections while others completely neglect undetected cases. Here, we illustrate how model projections about case and fatality numbers vary significantly under varying assumptions on the detection ratio. Uncertainties in model predictions can be significantly reduced by representative testing, both for antibodies and active virus RNA, to uncover past and current infections that have gone undetected thus far.
Mathematical Model Describing HIV Infection with Time-Delayed CD4 T-Cell Activation
Hernán Darío Toro-Zapata, Carlos Andrés Trujillo-Salazar, Edwin Mauricio Carranza-Mayorga
Subject: Materials Science, Other Keywords: mathematical model; delay differential equations; HIV; immune system
A mathematical model, composed of two non-linear differential equations that describe the population dynamics of CD4 T cells in the human immune system, as well as viral HIV particles, is proposed. The invariance region is determined, classical equilibria stability analysis is performed using the basic reproduction number, and numerical simulations are carried out, in order to illustrate stability results. Later, the model is modified with a delay term, which describes the time that cells require for immunological activation. This generates a two-dimensional integro-differential system, which is transformed into a system with three ordinary differential equations, via auxiliary variable use. For the new model, equilibrium points are determined, their local stability is examined, and results are studied by way of numerical simulation.
Streamline's Shape Theory
Yuvaraj George
Subject: Physical Sciences, Applied Physics Keywords: General fluid mechanics; Mathematical Model; Streamline; Flow–structure interactions; Topological fluid dynamics
This article attempts to formulate a mathematical model for a potential explanation regarding the unavoidable impact of a rigid body's peculiar shape on the seamless flow over it. The solid body completely immersed in a Newtonian fluid and respectively has a relative open circuit flow on it will typically experience various observable phenomena like flow separation, flow transition, down-wash, stalling at the higher angle of attack, stalling velocity and how cambered airfoil can typically generate lift at a zero incidence angle. This article respectively represents an understanding of the laminar flow over a rigid body's external surface with due respect to its distinctive shape and size. This working paper formulates a more realistic and simplified mathematical model for open circuit laminar flow over a body, based on the historical data of aerodynamics and theoretical mechanics. This is intended to properly estimate forces on the continuous surface of the body in a laminar flow, to properly explain, understand and predict mentioned phenomena. Most of all the mechanism of streamline formation and its deformation with due regards to flow, shape and size of the body in an open-circuit laminar are formulated mathematically to enhance better design theory which can reduce experimentation while designing a streamlined body.
Ion Transport and Process of Water Dissociation in Electromembrane System with Bipolar Membrane: Modelling of Symmetrical Case
Stanislav Melnikov
Subject: Chemistry, Electrochemistry Keywords: bipolar membrane; mathematical modelling; water dissociation; water-splitting kinetics
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.
On the Dynamic Interaction of Social Processes and COVID-19 Infection Dynamics
Farai Nyabadza, Josiah Mushanyu, Rachel Waema Mbogo, Gift Muchatibaya
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: COVID-19; mathematical modelling; stability; dynamic social processes; simulations
Human behaviour was tipped as the mainstay in the control of further SARS-CoV-2 (COVID-19) spread especially after the lifting of restrictions by many countries. Countries in which restrictions were lifted soon after the first wave, had subsequent waves of the COVID-19 infections and it remains to be seen whether there will be more waves. In this paper, we formulate a deterministic model for COVID-19 incorporating dynamic non-pharmaceutical interventions, dubbed social dynamics. The model steady states are determined and their stability analysed. Numerical simulations are carried out to determine the pack of various parameters that influence the social dynamics. In South Africa, the first wave was the only wave in which the only interventions rested solely on human behavior. The model is thus fitted to COVID-19 data on the first wave in South Africa. The results presented in this paper have implications on the trajectory of the pandemic in the presence of changing social processes.
Wavelet Time Scale Modelling of Brand Sales and Prices
Tawfeeq Alanazi, Anouar Ben Mabrouk
Subject: Social Sciences, Marketing Keywords: Wavelets; Multi scale; Mathematical models; Brand sales.; Brand prices
Marketing is the manner of how to make our sales the best in the market, our prices the most accessible, our clients satisfactory, and thus our brand is the largest distributed. This needs sophisticated and advanced understanding of the total network related. Indeed, marketing data may be seen in different forms such as qualitative and quantitative. However, in the literature, it is easily noticed that large bibliography may be collected about qualitative studies, against few studies on the quantitative point of view. This is a major drawback that makes the marketing science still focusing on the design, although the market is strongly depending on quantities such as money and time. Indeed, marketing data may be a time series such as brand sales per specified periods, brand related-prices over specified periods, market shares, ..., etc. The purpose of the present work is to investigate some marketing models based on time series due to brands. We will precisely study the effect of the time scale on the persistence of brands sales in the market and on the forecasting of such a persistence according to the characteristics of the brand and the related market competition or competitors. Our study is acted on a sample of Saudi brands during the period November 22, 2017 to December 30, 2021.
COVID-19 Pandemic in Nigeria: Misconception Among Individuals, Impact on Animals and the Role of Mathematical Epidemiologists
Oluwasegun Micheal Ibrahim, Damilola Daniel Ekundayo
Subject: Behavioral Sciences, Applied Psychology Keywords: COVID-19; pandemic; misconception; mathematical modeling; infectious disease; Nigeria
In March 2020, the World Health Organization declared coronavirus disease 2019 (COVID-19), caused by the novel severe acute respiratory syndrome coronavirus 2, to be a pandemic. Since the declaration, Nigeria economy has been greatly impacted thus resulting in a recession. This paper considers a couple of misconceptions among Nigerian people in the COVID-19 pandemic era thereby causing the spread of the novel virus and hence making the situation difficult for the government to handle. In particular, we discuss the first and second waves of the pandemic as it affects the Nigerian people. The impact of the pandemic on animals and the role of mathematical epidemiologists in combatting the spread is discussed herein. We give some recommendations that could be adopted by the government and the good people of Nigeria to reduce the further spread of the virus.
A Multilayered Healthcare Architecture Using Relational Trust Network
Somyajit Chakraborty, Avijit Gayen
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: healthcare system; medical network; trust; mathematical modeling; complex network
Medical Trust-Network is one of the most promising fields of study in network science. Establishment of trust within medical entities ensures better treatment and increases better medical facilities. The word 'Trust' signifies a very important behavioral aspect between any human entities, especially among doctors and patients. To represent such relationships Trust Network Models are built to express the interactions between human entities within such networks. Though the idea of a Trust-Network has traditionally been one of the major areas of research, yet the concept of a medical trust network model is relatively a new domain. In this paper, we introduce an overall multilayered Trust Network to represent the entire healthcare architecture. More specifically our model is based on an evolutionary graph system with a discrete relationship between the three most important entities of any healthcare system, namely – Doctors, Departments, and Hospitals. Observations indicate that based on our model, the medical healthcare system is a multilayered model unlike a feed-forward model as indicated by previous studies.
Modelling of Fluid Flow and Residence Time Distribution in a Five-strand Tundish
Dong-Yuan Sheng, Qiang Yue
Subject: Materials Science, Metallurgy Keywords: mathematical model; water model; tundish; residence time distribution; mixing
The quantified residence time distribution (RTD) provides a numerical characterization of mixing in the continue casting tundish, thus allowing the engineer to better understand the metallurgical performance of the reactor. This paper describes a computational fluid dynamic (CFD) modelling study for analyzing the flow pattern and the residence time distribution in a five-strand tundish. Two passive scalar transport equations are applied to separately calculate the E-curve and F-curve in the tundish. The numerical modelling results are compared to the water modelling results for the validation of the mathematical model. The volume fraction of different flow regions (plug, mixed and dead) and the intermixing time during the ladle changeover are calculated to study the effects of the flow control device (FCD) on the tundish performance. The result shows that a combination of the U-baffle with deflector holes and the turbulence inhibitor has three major effects on the flow characteristics in the tundish: i) reduce the extent of the dead volume; ii) evenly distribute the liquid streams to each strand and iii) shorten the intermixing time during the ladle changeover operation.
Mathematical Modelling of Social Consciousness to Control the Outbreak of COVID-19
Md. Shahriar Mahmud, Md Kamrujjaman, J. Jubyrea, Md. Shahidul Islam
Subject: Keywords: coronavirus; COVID-19; consciousness; data analysis; mathematical model; control
Background: The world, now in an emergency of preventing the drastic spread of COVID-19. After the infection was first reported in December 2019, almost every country did not pay attention to this highly contaminated disease and failed to react swiftly. Now the whole universe is in an vulnerable state, loosing a great loss of lives and facing difficulties in all socio-economic aspects. That is why we have the urge to develop an efficient mathematical model (quarantine) based on social consciousness to control the epidemic. Methods: This is a quarantine mathematical model. The outcome of the system is dependent on social consciousness. We have calculated the awareness level by considering various socio-economic factor of each country. In our model, the parameters are Education Index, GDP per capita, population density, high literacy and stable economy. To maximize the efficiency of the model, it has to be implemented in initial stage. However, strict application of the method in vigorous stage of epidemic will also bring a satisfactory outcome. Results: Higher social consciousness will decrease the number of infected population dramatically while minimal or lower awareness will do a outburst. Conclusion: Outbreak will be in control of health care system, lower the death rate and will ensure social and economic stability.
Evaluation of Influence of Terrain Profile on the Physical Characteristics of Air Flow
Sharif E. Guseynov
Subject: Earth Sciences, Atmospheric Science Keywords: mathematical model; terrain profile; air flow fluctuations; asymptotic expansion
In the present paper, a measure of the influence of irregularities of the underlying surface (for instance, the real terrain profile) on the dynamics of air flow is estimated. It is shown that these irregularities significantly perturbing the pressure, density, velocity and temperature of air flow; for perturbed pressure, density, velocity and temperature of air flow the closed formulas in the Fourier integral form are obtained. In addition, in the present paper, it is proved that due to these perturbations, at a certain altitude of the atmosphere some surface of the "sturdy wall" form appears, on which the vertical and horizontal components of the air flow velocity become infinitesimal and infinitely large, respectively.
Mathematical Modelling to Study the Horizontal Transfer of Antimicrobial Resistance Genes in Bacteria: Current State of the Field and Recommendations
Quentin J. Leclerc, Jodi A. Lindsay, Gwenan M. Knight
Subject: Life Sciences, Other Keywords: antimicrobial resistance; horizontal gene transfer; mathematical modelling; epidemiology; microbiology
Antimicrobial resistance (AMR) is one of the greatest public health challenges we are currently facing. To develop effective interventions against this, it is essential to understand the processes behind the spread of AMR. These are partly dependent on the dynamics of horizontal transfer of resistance genes between bacteria, which can occur by conjugation (direct contact), transformation (uptake from the environment) or transduction (mediated by bacteriophages). Mathematical modelling is a powerful tool to investigate the dynamics of AMR, however its application to study the horizontal transfer of AMR genes is currently unclear. In this systematic review, we searched for mathematical modelling studies which focused on horizontal transfer of AMR genes. We compared their aims and methods using a list of predetermined criteria, and utilized our results to assess the current state of this research field. Of the 43 studies we identified, most focused on the transfer of single genes by conjugation in Escherichia coli in culture, and its impact on the bacterial evolutionary dynamics. Our findings highlight the existence of an important research gap on the dynamics of transformation and transduction, and the overall public health implications of horizontal transfer of AMR genes. To further develop this field and improve our ability to control AMR, it is essential that we clarify the structural complexity required to study the dynamics of horizontal gene transfer, which will require cooperation between microbiologists and modellers.
A Wavelet Quality of Life Multi-index and the Impact of Social Media during the Pandemic and the Crisis
Subject: Social Sciences, Sociology Keywords: Wavelets; Quality of life index; Pandemics, Social media; Mathematical models.
In the present paper, we investigate the impact of the timescale factor on the quality of life index behavior on specific time intervals characterized by the presence of socio-economic, political, and/or health severe movements such as pandemics and crises. We essentially aim to show that effectively the quality of life measuring based on a single index in the existing studies may be described more adequately by a variable index due to the social, political, economic, and also healthy environment. The variability discovered is expressed by the existence and the estimation of a multi-index instead of a single one relatively to many factors. Our focus is mainly on the effect of the COVID-19 pandemic on the quality of life. Our model is applied empirically to a sample corresponding to Saudi Arabia as a case of study during the period from January 1990 to December 2021 as the main period affected by the COVID-19 pandemic. The sample is based on social media conversations and texts discussing and describing the satisfaction with the quality of life. The study confirms effectively that the role of the timescale factor is more described when considering a multi-index rather than measurement on the whole time interval.
A Comparative Study of Three Mathematical Models for the Interaction between the Human Immune System and a Virus
Florian Munteanu
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: mathematical models; systems of ordinary differential equations; dynamical systems; stability
In this paper it will be considered three deterministic models for the study of the interaction between the human immune system and a virus: the logistic model, the Gompertz model, and the generalized logistic model (or Richards model). A qualitative analysis of this models based on dynamical systems theory will be performed, by studying the local behavior of the equilibria and obtaining local dynamics properties from the linear stability point of view. Also, we will compare this models in order to understanding which is more appropriate to models the interaction between the human immune system and a virus. It will be obtained some natural medical interpretations which are available for all three models and can be useful to the medical community.
Preprint ESSAY | doi:10.20944/preprints202201.0121.v2
Public Health Policy Pillars for the Sustainable Elimination of Zoonotic Schistosomiasis
Eva Janoušková, Jessica Clark, Olumayowa Kajero, Sergi Alonso, Poppy H. L. Lamberton, Martha Betson, Joaquín M. Prada
Subject: Life Sciences, Other Keywords: Schistosoma japonicum; Schistosoma mekongi; NTD; epidemiology; economics; sociology; mathematical modelling; zoonotic transmission
Schistosomiasis is a parasitic disease acquired through contact with contaminated freshwater. The definitive hosts are terrestrial mammals, including humans, with some Schistosoma species crossing the animal-human boundary through zoonotic transmission. An estimated 12 million people live at risk of zoonotic schistosomiasis caused by Schistosoma japonicum and Schistosoma mekongi, largely in the World Health Organization's Western Pacific Region and in Indonesia. Mathematical models have played a vital role in our understanding of the biology, transmission, and impact of intervention strategies, however, these have mostly focused on non-zoonotic Schistosoma species. Whilst these non-zoonotic-based models capture some aspects of zoonotic schistosomiasis transmission dynamics, the commonly-used frameworks are yet to adequately capture the complex epi-ecology of multi-host zoonotic transmission. However, overcoming these knowledge gaps goes beyond transmission dynamics modelling. To improve model utility and enhance zoonotic schistosomiasis control programmes, we highlight three pillars that we believe are vital to sustainable interventions at the implementation (community) and policy-level, and discuss the pillars in the context of a One-Health approach, recognising the interconnection between humans, animals and their shared environment. These pillars are: (1) human and animal epi-ecological understanding; (2) economic considerations (such as treatment costs and animal losses); and (3) sociological understanding, including inter- and intra-human and animal interactions. These pillars must be built on a strong foundation of trust, support and commitment of stakeholders and involved institutions.
Enriching Elementary School Mathematical Learning with the Steepest Descent Algorithm
Roberto Araya
Subject: Social Sciences, Accounting Keywords: Elementary Mathematics; STEM; Mathematical Modeling; Computational Thinking; Steepest Descent Algorithm
The Steepest Descent (or Ascent) algorithm is one of the most widely used algorithms in Science, Technology, Engineering, and Mathematics (STEM). However, this powerful mathematical tool is neither taught nor even mentioned in K12 education. We study whether it is feasible for elementary school students to learn this algorithm, while also aligning with the standard school curriculum. We also look at whether it can be used to create enriching activities connected to children's real-life experiences, thus enhancing the integration of STEM and fostering Computational Thinking. To address these questions, we conducted an empirical study in two phases. In the first phase, we tested the feasibility with teachers. In a face-to-face professional development work-shop with 457 mathematics teachers actively participating using an online platform, we found that after a 10-minute introduction they could successfully apply the algorithm and use it in a couple of models. They were also able to complete two complex and novel tasks: selecting models and adjusting the parameters of a model that uses the steepest descent algorithm. In a second phase, we tested the feasibility with 90 fourth graders from 3 low Socioeconomic Status (SES) schools. Using the same introduction and posing the same questions, we found that they were able to understand the algorithm and successfully complete the tasks on the online platform. Additionally, we found that close to 75% of the students completed the two complex modeling tasks and performed similarly to the teachers.
Subject: Social Sciences, Education Studies Keywords: Elementary Mathematics; STEM; Mathematical Modeling; Computational Thinking; Steepest Descent Algorithm
CFD Simulation and Optimization of Adiabatic Reaction Process of C-2 Hydrogenation
Wenjing Wei
Subject: Engineering, Biomedical & Chemical Engineering Keywords: C-2 hydrogenation adiabatic reactor; mathematical model; CFD simulation; optimization
In this paper, the computational fluid dynamics (CFD) method has been used to simulate the gas flow and the catalytic hydrogenation process of the C-2 hydrogenation adiabatic reactor in a practical ethylene production unit of a chemical plant. The laminar finite-rate model was used for the chemical reaction model. The standard two-equation model was used for the turbulence model. The exponent-function kinetic model was used for the reaction dynamics model. The simulation results were in good agreement with the actual industrial data obtained from the C-2 hydrogenation reactor, and the distributions of reaction parameters such as temperature and component concentrations in the reactor were further analyzed. Based on the validated CFD models, the structure and operating conditions of the reactor, as well as hydrogen load distribution ratios, are simulated for comparing the comprehensive performance metrics of ethylene selectivity and acetylene conversion rate; as a result, we can obtain the optimal temperature of 312 K, the optimal hydrogen/acetylene ratio of 0.10 as well as the optimal hydrogen load distribution ratio of 4:4:2, and the diameter/height ratio exerts a marginal effect on the selectivity, conversion rate and harmonic mean of the reactor.
The Mathematical Construction of the Battery Mechanism Function
Wen Li, Chen Zhang, Lei Mao, Xiaofang Cheng
Subject: Keywords: volt-ampere characteristics; battery mathematical model; mechanism function; fuel cell
The corrected mechanism model of battery voltammetric function is helpful to guide the development and application of battery. There are two scientific issues that need to be answered: First, how many mechanisms do batteries have; Second, how to establish the mechanism model separately under the overlapping of these mechanisms. Volt-ampere characteristics of both linear state and nonlinear state exist; the monotonic decreasing of volt-ampere characteristics indicates that the battery have only three kinds of mechanisms. Without changing the basic form of the function and under the principle of the mechanism function's working region considered, we propose a mechanism function which satisfies the monotonic decreasing characteristic of the voltammetric curve of battery, via the derivative law of each mechanism function in the voltammetric function of battery. By using the voltammetric data, the obtained cell mechanism function can accurately predict the potential (current or voltage) when the independent variable of the cell is zero, and provide the theoretical basis for the internal working mechanism of the cell, which can guide the practice.
Neural Differentiation Dynamics Controlled by Multiple Feedback Loop Motifs in a Comprehensive Molecular Interaction Network
Tsuyoshi Iwasaki, Ryo Takiguchi, Takumi Hiraiwa, Takahiro G. Yamada, Kazuto Yamazaki, Noriko Hiroi, Akira Funahashi
Subject: Life Sciences, Other Keywords: neural differentiation; regulatory motif; feedback regulation; signaling pathway; mathematical models
Computational simulation using mathematical models is a useful method for understanding the complex behavior of a living system. The majority of studies using mathematical models to reveal biological mechanisms uses one of the two main approaches: the bottom-up or the top-down approach. When we aim to analyze a large-scale network, such as a comprehensive knowledge-integrated model of a target phenomenon, for example a whole-cell model, the variation of analyses is limited to particular kind of analysis because of the size and complexity of the model. To analyze a large-scale regulatory network of neural differentiation, we developed a hybrid method that combines both approaches. To construct a mathematical model, we extracted network motifs, subgraph structures that recur more often in a metabolic network or gene regulatory network than in a random network, from a large-scale regulatory network, detected regulatory motifs among them, and combined these motifs. We confirmed that the model reproduced the known dynamics of HES1 and ASCL1 before and after differentiation, including oscillation and equilibrium of their concentrations. The model also reproduced the effects of overexpression and knockdown of the Id2 gene. Our model suggests that the characteristic change in HES1 and ASCL1 expression in the large-scale regulatory network is controlled by a combination of four feedback loops, including a large loop which has not been focused on. The model extracted by our hybrid method has the potential to reveal the critical mechanisms of neural differentiation. The hybrid method is applicable to other biological events.
An Inactivation Switch Enables Rhythms in a Neurospora Clock Model
Abhishek Upadhyay, Michael Brunner, Hanspeter Herzel
Subject: Life Sciences, Molecular Biology Keywords: circadian clock; mathematical modelling; molecular switch; Neurospora crassa; glucose compensation
An autonomous endogenous time-keeping is ubiquitous across many living organisms known as circadian clock when it has a period of about 24 hours. Interestingly, the fundamental design principle with a network of interconnected negative and positive feedback loops is conserved through evolution, although the molecular components differ. Filamentous fungus \textit{Neurospora crassa} is a well established chrono-genetics model organism to investigate the underlying mechanisms. The core negative feedback loop of the clock of \textit{Neurospora} is composed of the transcription activator White Collar Complex (WCC) (heterodimer of WC1 and WC2) and the inhibitory element called FFC complex which is made of FRQ (Frequency protein), FRH (Frequency interacting RNA Helicase) and CK1a (Casein kinase 1a). While exploring their temporal dynamics we investigate how limit cycle oscillations arise and how molecular switches support self-sustained rhythms. We develop a mathematical model of 10 variables with 26 parameters to understand the interactions and feedbacks among WC1 and FFC elements in nuclear and cytoplasmic compartments. We performed control and bifurcation analysis to show that our novel model produces robust oscillations with a wild-type period of 22.5 hrs. Our model reveals a switch between WC1 induced transcription and FFC assisted inactivation of WC1. Using the new model we also study possible mechanisms of glucose compensation. A fairly simple model with just 3 non-linearities helps to elucidate clock dynamics revealing a mechanism of rhythms production. The model can further be utilized to study entrainment and temperature compensation.
Mathematical Modelling of Human African Trypanosomiasis Using Control Measures
Hamenyimana Emanuel Gervas, Nicholas Kwasi-Do Ohene Opoku, Shamsuddeen Ibrahim
Subject: Mathematics & Computer Science, Computational Mathematics Keywords: Human African Trypanosomiasis (HAT), Mathematical modelling, optimal control, Control measures
Human African Trypanosomiasis (HAT) commonly known as sleeping sickness, is a neglected tropical vector borne disease caused by trypanosome protozoa. It is transmitted by bites of infected tsetse fly. In this paper we first present the vector-host model which describes the general transmission dynamics of HAT. In the tsetse fly population, the HAT is modelled by three compartments while in the human population, the HAT is modelled by four compartments. The next generation matrix approach is used to derive the basic reproduction number, R0, and also it is proved that if R0 ≤ 1 the disease free equilibrium is globally asymptotically stable, which means the disease dies out. The disease persist in the population if the value of R0 > 1. Furthermore, the optimal control model is determined by using the Pontryagin's maximum principle with control measures such as education, treatment and insecticides used to optimize the objective function. The model simulations confirm that the use of the three control measures are very efficient and effective to eliminate HAT in Africa.
Recent Advances of Malaria Parasites Detection Systems Based on Mathematical Morphology
Andrea Loddo, Cecilia Di Ruberto, Michel Kocher
Subject: Mathematics & Computer Science, Other Keywords: malaria; red blood cells segmentation; mathematical morphology; medical image analysis
This paper investigates existing mathematical morphology based techniques applied for performing malaria parasites detection and identification in both Giemsa and Leishman stained blood smears images. Malaria is an epidemic health disease and a rapid, accurate diagnosis is necessary for proper intervention. Generally, pathologists visually examine blood stained slides for malaria diagnosis; this kind of visual inspection is subjective, errorprone and time consuming. In order to cope with such issues, computer-aided methods have been increasingly evolved for abnormal erythrocyte and/or parasites detection, segmentation and semi/fully automated classification. The aim of this paper is to present a review of recent mathematical morphology based methods for malaria parasite detection.
Fighting Cancer with Mathematics and Viruses
Daniel N. Santiago, Johannes P. W. Heidbuechel, Wendy M. Kandell, Rachel Walker, Christine E. Engeland, Daniel Abate-Daga, Heiko Enderling
Subject: Life Sciences, Other Keywords: oncolytic virotherapy; combination therapy; mathematical model; immune system; cancer; immunotherapy
After decades of research, oncolytic virotherapy has recently advanced to clinical application, and currently a multitude of novel agents and combination treatments are being evaluated for cancer therapy. Oncolytic agents preferentially replicate in tumor cells, inducing tumor cell lysis and complex anti-tumor effects, such as innate and adaptive immune responses and the destruction of tumor vasculature. With the availability of different vector platforms and the potential of both genetic engineering and combination regimens to enhance particular aspects of safety and efficacy, the identification of optimal treatments for patient subpopulations or even individual patients becomes a top priority. Mathematical modeling can provide support in this arena by making use of experimental and clinical data to generate hypotheses about the mechanisms underlying complex biology and, ultimately, predict optimal treatment protocols. Increasingly complex models can be applied to account for therapeutically relevant parameters such as components of the immune system. In this review, we describe current developments in oncolytic virotherapy and mathematical modeling to discuss the benefit of integrating different modeling approaches into biological and clinical experimentation. Conclusively, we propose a mutual combination of these fields of research for more efficient development and effective treatments.
A Mathematical Spline-Based Model of Cardiac Left Ventricle Anatomy and Morphology
Sergei Pravdin
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: left ventricle; myofibre; myocardium structure; rule-based model; mathematical anatomy
Computer simulation of normal and diseased human heart activity requires a 3D anatomical model of the myocardium, including myofibres. For clinical applications, such a model has to be constructed based on routine methods of cardiac visualisation such as sonography. Symmetrical models are shown to be too rigid, so an analytical non-symmetrical model with enough flexibility is necessary. Based on previously made anatomical models of the left ventricle, we propose a new, much more flexible spline-based analytical model. The model is fully described and verified against DT-MRI data. We show a way to construct it on the basis of sonography data. To use this model in further physiological simulations, we propose a numerical method to utilise finite differences in solving the reaction-diffusion problem together with an example of scroll wave dynamics simulation.
Stability and Sensitivity Analysis of the COVID-19 Spread with Comorbid Diseases
Jonner Nainggolan, Moch. Fandi Ansori
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: mathematical model; COVID-19; comorbid disease; sensitivity analysis; basic reproduction number
This research investigates a model for the COVID-19 outbreak in Indonesia by analyzing comorbid diseases, self-quarantine, government-provided quarantine, and immunization regimens. Some model parameters are derived from academic journals, others are extrapolated from data collected by the Indonesian Ministry of Health in 2020, and others are assumed. Evaluation of the model reveals non-endemic equilibrium points, endemic equilibrium points, and the basic reproduction number (BRN). The contact rate and infected probability factors impact the increase in the number of COVID-19-infected individuals with comorbid disease within a group. According to the sensitivity analysis of the BRN, the key parameters impacting the spread of COVID-19 are the rate of susceptible recruitment, the rate of contact, the COVID-19 infection death rate, and the likelihood of infection. In addition, sensitivity analyses are provided to examine the effect of parameter changes on subpopulations. We discovered that the natural death rate is the most sensitive parameter based on the sensitivity index after reaching equilibrium. Symmetry aspects appear in some of the visualization of the model's solution and the BRN and parameters' sensitivity.
Mathematical Model of Pancreatic Cancer Cell Dynamics Considering the Set of Sequential Mutations and Interaction With the Immune System
Alexander Sergeevich Bratus, Nicholas R. Leslie, Michail Ruslanovich Chamo, Dmitry Sergeevich Grebennikov, Rostislav Sergeevich Savinkov, Gennady Alexeevich Bocharov, Daniil Vadimovich Yurchenko
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Pancreatic cancer; cancer evolution; tumour microenvironment; mathematical model; open quasispecies model
Pancreatic cancer represents one of the difficult problems of contemporary medicine. The development illness evolves very slowly, takes place in special sake (stroma) and manifests clinically close to a final stage. Another feature of this pathology is a coexistence (symbiotic) effect between cancer cells and normal cells inside stroma. All these aspects make it difficult to understand the pathogenesis of pancreatic cancer and develop a proper therapy. The emergence of pancreatic pre-cancer and cancer cells represents a branching stochastic process engaging populations of 64 cells differing in the number of acquired mutations. In this study we formulate and calibrate the mathematical model of pancreatic cancer using the quasispecies framework. The mathematical model incorporates the mutation matrix, fineness landscape matrix and the death rates. Each element of the mutation matrix presents the probability of appearing a specific mutation in the branching sequence of cells representing the accumulation of mutations. The model incorporates the cancer cell elimination by effect CD8 T cells (CTL). The down-regulation of the effector function of CTLs and exhaustion are parameterized. The symbiotic effect of coexistence of normal and cancer cells is considered. The computational predictions obtained with the model are consistent with empirical data. The modelling approach can be used to investigate other types of cancers and examine various treatment procedures.
Effect of Total Starch and Resistant Starch in Commercial Extruded Dog Foods on Gastric Emptying in Non-Racing Sled Dogs
Taylor L. Richards, Alexandra Rankovic, John P. Cant, Anna K. Shoveller, Jennifer L. Adolphe, Dan Ramdath, Adronie Verbrugghe
Subject: Biology, Anatomy & Morphology Keywords: canine, carbohydrates, grain-free, pet food, pharmacokinetic mathematical modelling, acetaminophen tracking.
Gastric emptying rate (GER) may impact diabetes and obesity in humans and could provide a method to reduce canine weight gain. Starch, the most common source of carbohydrates (CHOs) in pet food, is classified as rapidly or slowly digestible, or resistant to digestion. This study investigated starch source effects in commercial extruded dog foods on the GER of 11 healthy adult Siberian Huskies (5.63±0.72 years; mean±SEM). Test diets were classified as traditional, grain-free, whole-grain, and vegan. Dogs received each diet once, a glucose control twice, and acetaminophen (Ac) as a marker for GER in a randomized, partially-replicated, 6x6 Latin square design. Pre- and post-prandial blood samples were collected at 16 timepoints from -15 to 480 minutes. Serum Ac concentrations were assessed via standard spectrophotometric assays and fitted with a mathematical model to estimate parameters of GER. Data was analyzed using a repeated measures ANOVA, followed by a Tukey-Kramer post-hoc test when significant (p<0.05). More total emptying (p= 0.0430) occurred at faster rate (p=0.0668) in dogs fed the grain-free diet, which contained the lowest total starch (34.03 ± 0.23%) and highest resistant starch (0.52 ± 0.007%). This research may benefit future diet formulations to reduce the prevalence of canine weight gain.
A Mathematical Description of the Bone Marrow Dynamics of CAR T-Cell Therapy in B-cell Childhood Acute Lymphoblastic Leukemia
Álvaro Martínez-Rubio, Salvador Chulián, Cristina Blázquez Goñi, Antonio Pérez Martínez, Manuel Ramírez Orellana, Alfonso Navarro-Zapata, Cristina Ferreras, Victor Manuel Pérez-García, María Rosa
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: CAR T; Bone Marrow; Mathematical Model; Acute Lymphoblastic Leukemia; B cell
Chimeric Antigen Receptor (CAR) T-cell therapy has demonstrated high rates of response in recurrent B-cell Acute Lymphoblastic Leukemia in children and young adults. Despite this success, a fraction of patients experience relapse after treatment. Relapse is often preceded by recovery of healthy B cells, which suggests loss or dysfunction of CAR T cells in bone marrow. This site is harder to access, and thus is not monitored as frequently as peripheral blood. Understanding the interplay between B cells, leukemic cells and CAR T cells in bone marrow is paramount in ascertaining the causes of lack of response. In this paper, we put forward a mathematical model representing the interaction between constantly renewing B cells, CAR T cells and leukemic cells in the bone marrow. Our model accounts for the maturation dynamics of B cells and incorporates effector and memory CAR T cells. The model provides a plausible description of the dynamics of the various cellular compartments in bone marrow after CAR T infusion. After exploration of the parameter space, we found that the dynamics of CAR T product and disease were independent of the dose injected, initial B-cell load and tumor burden. We also show theoretically the importance of CAR T product attributes in determining therapy outcome, and have studied a variety of possible response scenarios, including second dosage schemes. We conclude by setting out ideas for the refinement of the model.
Problem Solving and Mathematical Modelling
Michael Gr. Voskoglou
Subject: Social Sciences, Education Studies Keywords: mathematics education; problem solving; mathematical modelling; application-oriented teaching of mathematics
Problem solving is one of the most important components of the human cognition that affects for ages the progress of the human society. Mathematical modelling is a special type of problem solving concerning problems related to science or everyday life situations. The present study is a review of the author's earlier works on problem solving and mathematical modelling from the scope of Education. Its real goal is that it presents in a systematic way and in a few pages only the results of many years research on the subject. This helps the reader to get a comprehensive idea about a very important topic belonging to the core of Mathematics Education, which is very useful to those wanting to study deeper the subject and get directions for further research in the area.
Mathematical Modeling of the Development of Confirmed Daily Infection Numbers in the COVID-19 Pandemic by a Special Exponential Function
Egbert Keller, Johannes Keller, Matthias Selg
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: COVID-19 pandemic; Sars-CoV-2; confirmed daily infections; mathematical model
The developments of confirmed daily Sars-CoV-2 infections can be modeled a posteriori in a comparatively simple and satisfactory way by means of a special exponential function: its exponential coefficient varies exponentially with time itself. This property enables the function to directly simulate the "daily case" curve fragments observed for the first waves of the current epidemics in a number of counties and countries. Linear combinations of two or more of the functions allow for the modeling of the complete curves observed in the vast majority of all regions for which case number developments have been tabulated.
The Silent Partners
Gal Almogy
Subject: Life Sciences, Virology Keywords: Mathematical model; SARS; COVID-19; Superspreaders; Viral outbreaks; H7N9; Influenza; zoonotic
Despite great advances in understanding the dynamics of viral epidemics, the emergence of rapidly spreading, highly pathogenic viruses remains a realistic and catastrophic possibility, which current health systems may not be able to fully contain. An intriguing feature in many recent zoonotic viral outbreaks is the presence of superspreaders, which are infected individuals that cause dramatically more new cases than the average. Here I study the effect of superspreaders on the early dynamics of emerging viruses that have not gained the capacity for efficient human-to-human transmission, i.e viruses with R0 < 1. I show that superspreaders have a higher chance of rapid extinction, but under crowded conditions can lead to outbreaks, causing far more cases than regular viruses. I suggest that outbreaks of highly pathogenic superspreaders are more likely when they coincide in time and space with an unrelated outbreak leading to increased hospital admission rates. These superspreader outbreaks may be difficult to detect, especially in the context of a different epidemic in progress, and can significantly affect mortality patterns observed in affected areas.
A Method Based on NLP for Twitter Spam Detection
Ratul Chowdhury, Kumar Gourav Das, Banani Saha, Samir Kumar Bandyopadhyay
Subject: Keywords: Twitter; Social Media; NLP; Tweet; User Categorizations and Mathematical Frame Work
Social networking applications such as Twitter have increasingly gained significance in terms of socio-economic, political, and religious as well as entertainment sectors. This in turn, has witnessed a wide gamut of information explosion in the social networking realm that can tend to be both useful as well as misleading at the same point of time. Spam detection is one such solution that caters to this problem through identification of irrelevant users and their data. However, existing research has so far laid primary focus on user profile information through activity detection and relevant techniques that may underperform when these profiles exhibit characteristics of temporal dependency, poor reflection of generated content from the user profile, etc. This is the primary motivation for this paper that addresses the aforementioned problem of user profiles by focusing on both profile information and content-based spam detection. To this end, this work delivers three significant contributions. Firstly, exhaustive use of Natural language processing (NLP) techniques has been rendered towards creation of a new comprehensive dataset with a wide range of content-based features. Secondly, this dataset has been fed into a customized state-of-art hybrid machine learning model that has been exclusively built using a combination of both machine learning and deep learning techniques. Extensive simulation based analysis not only records over 98% accuracy but also establishes the practical applicability of this proposal by proving that modeling based on the mixed profile and content-generated data is more capable of spam detection in contrast to each of these standalone approaches. Finally, a novel methodology based on logistic regression is proposed and supported by analytical formulations. This paves the way for the custom-built dataset to be analyzed and corresponding probabilities to be obtained that differentiate legitimate users from spammers. The obtained mathematical outcome can henceforth be used for future prediction of user categories through appropriate parameter tuning for any given dataset. This makes our method a truly generic one capable of identifying and classifying different user categories.
Effects of Mosquito Biology on Modeled Chikungunya Virus Invasion Potential in Florida
Cynthia C. Lord, L. Philip Lounibos, Joseph J. Pohedra, Barry W. Alto
Subject: Life Sciences, Virology Keywords: Chikungunya virus; invasion; transmission dynamics; Aedes aegypti; Aedes albopictus; mathematical model
: Arboviruses transmitted by Aedes aegypti and Ae. albopictus have been introduced to Florida on many occasions. Infrequently, these introductions lead to sporadic local transmission and, more rarely, sustained local transmission. Both mosquito species are present in Florida, with spatio-temporal variation in population composition. We developed a 2-vector compartmental, deterministic model to investigate factors influencing Chikungunya virus (CHIKV) establishment. The model includes a non-linear, temperature-dependent mosquito mortality function based on minimum mortality in a central temperature region. Latin Hypercube sampling was used to generate parameter sets used to simulate transmission dynamics, following the introduction of one infected human. The analysis was repeated for 3 values of the mortality function central temperature. Mean annual temperature was consistently important in the likelihood of epidemics, and epidemics increased as the central temperature increased. Ae. albopictus recruitment was influential at the lowest central temperature while Ae. aegypti recruitment was influential at higher central temperatures. Our results indicate that the likelihood of CHIKV establishment may vary, but overall Florida is permissive for introductions. Model outcomes were sensitive to the specifics of mosquito mortality. Mosquito biology parameters are variable, and improved understanding of this variation will improve our ability to predict the outcome of introductions.
Canonical Description of Group Theory: A Linear Order on All Finite Groups
Juan Pablo Ramirez
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Finite Group; Finite Permutation; Set Theory; Mathematical Structuralism; Type Theory; Tree; Data Type; Benacerraf's Identification Problem
We provide an axiomatic base for the set of natural numbers, that has been proposed as a canonical construction, and use this definition of $\mathbb N$ to find several results on finite group theory. Every finite group $G$, is well represented with a natural number $N_G$; if $N_G=N_H$ then $H,G$ are in the same isomorphism class. We have a linear order, on the quotient space of isomorphism classes of finite groups, that is well behaved with respect to cardinality. If $H,G$ are two finite groups such that $|H|=m<n=|G|$, then $H<\mathbb Z_n\leq G\leq\mathbb Z_{p_1}^{n_1}\oplus\mathbb Z_{p_2}^{n_2}\oplus\cdots\oplus\mathbb Z_{p_k}^{n_k}$ where $n=p_1^{n_1}p_2^{n_2}\cdots p_{k}^{n_k}$ is the prime factorization of $n$. We find a canonical order for the objects of $G$ and define equivalent objects of $G$, thus finding the automorphisms of $G$. The Cayley table of $G$ takes canonical block form, and we are provided with a minimal set of independent equations that define the group. We show how to find all groups of order $n$, and order them. We give examples using all groups with order smaller than $10$, and we find the canonical block form of the symmetry group $\Delta_4$. In the next section, we extend our results to the infinite case, which defines a real number as an infinite set of natural numbers. A real function is a set of real numbers, and a sequence of real functions $f_1,f_2,\ldots$ is well represented by a set of real numbers, as well. In general, we represent mathematical objects using the smallest possible data-type. In the last section, mathematical objects are well assigned to tree structures. We conclude with brief comments on type theory and future work on computational aspects of these representations.
A Mathematical Model for the COVID-19 Outbreak and Its Applications
Roman Cherniha, Vasyl' Davydovych
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: nonlinear mathematical model; modeling infectious diseases; logistic equation; integrability; exact solution
A mathematical model is proposed for quantitative description of the outbreak of novel coronavirus COVID-19 Although the model is relatively simple, the comparison with the public data shows that an exact solution solution of the model (with the correctly-specified parameters) leads to the results, which are in good agreement with the measured data in China and Austria. Prediction of the total number of the COVID-19 cases is discussed and examples are presented using the measured data in Austria, France and Poland.
Relative Contribution of PIN-containing Secretory Vesicles and Plasma Membrane PINs to the Directed Auxin Transport: Theoretical Estimation
Sander Hille, Maria Akhmanova, Matouš Glanc, Alexander Johnson, Jiří Friml
Subject: Biology, Plant Sciences Keywords: Polar Auxin Transport; PIN transporters; Secretion; 3D-SIM microscopy; Mathematical modeling
Intercellular transport of auxin is driven by PIN-formed (PIN) proteins. PINs are localized at the plasma membrane (PM) and on constitutively recycling endomembrane vesicles. Therefore, PINs can mediate auxin transport either by direct translocation across the PM or by pumping it into secretory vesicles (SVs), leading to its secretory release upon fusion with the PM. Which of these two mechanisms dominates is a matter of debate. Here we addressed the issue with a mathematical modeling approach. We demonstrate that the efficiency of secretory transport depends on SV size, half-life of PINs on the PM, pH, exocytosis frequency and PIN density. 3D-SIM microscopy was used to determine PIN density on the PM. Combing this data with published values of the other parameters, we show that the transport activity of PINs in SVs would have to be at least 1000x greater than on the PM in order to produce a comparable macroscopic auxin transport. If both transport mechanisms operated simultaneously and PINs were equally active on SVs and PM, the contribution of secretion to the total auxin flux would be negligible. In conclusion, while secretory vesicle-mediated transport of auxin is intriguing and theoretically possible model, it unlikely to be a major mechanism of auxin transport in planta.
Journal Ranking based on Publication Difficulty Factors (JRpDF): A Proposed Mathematical Algorithm
Saheer Al-Jaghoub, Hussein Al-Yaseen
Subject: Social Sciences, Library & Information Science Keywords: Journal ranking; Publication; Mathematical Algorithm; Academic Research; Promotion; Quantitative; Developing Countries.
Academic publishing appears to be the most important key of the academic functions (academic research, excellence in teaching and learning and community services). Selecting the right journal to publish research results is a challenge to academics. Yet, there is inadequate knowledge about a model specifically directed at the topic of the journal selection process with a mathematical certainty. The objectives of this research are: to identify the main factors that an author or researchers consider when selecting an academic journal for submitting a manuscript, and, to develop a mathematical algorithm of journal selection that provide the best journal choice with a mathematical certainty based on difficulty of each factor. Quantitative research through questionnaires has been applied as an appropriate instrument base to address the researcher's identification of the factors that should be considered when selecting a journal. Questionnaire developed and emailed to academics in 31 public and private universities in the developing countries. Academics reported that the most important publication difficulty factors were publishing in reputable journals, and publishing in a journal that has an impact factor. However, the most least publication difficulty factors were found to be: number of issues per year and if the journal is an open access. The proposed mathematical algorithm of journal's publication difficulty factors was developed and tested.
Potential Cost-Effectiveness of Pre-exposure Prophylaxis Combined with HIV Vaccines in the United States
Blythe J.S. Adamson, Josh J. Carlson, James G. Kublin, Louis P. Garrison, Jr.
Subject: Medicine & Pharmacology, Other Keywords: economic evaluation; mathematical modeling; HIV vaccines; pre-exposure prophylaxis; cost-effectiveness
This economic evaluation aims to support policy-making on the combined use of pre-exposure prophylaxis (PrEP) with HIV vaccines by evaluating the potential cost-effectiveness of implementation that would support the design of clinical trials for assessment of combined product safety and efficacy. The target study population is a cohort of men who have sex with men (MSM) in the United States. Policy strategies considered include standard HIV prevention, daily oral PrEP, HIV vaccine, and their combination. We constructed a Markov model based on clinical trial data and published literature. We used a payer perspective, monthly cycle length, a lifetime horizon, and a 3% discount rate. We assumed a price of $500 per HIV vaccine series in the base case. HIV vaccines dominated standard care and PrEP. At current prices,PrEP was not cost-effective alone or in combination. A combination strategy had the greatest health benefit but was not cost-effective (ICER=$463,448/QALY) as compared to vaccination alone. Sensitivity analyses suggest a combination may be valuable for higher-risk men with good adherence. Vaccine durability and PrEP drug prices were key drivers of cost-effectiveness. Results suggest that boosting potential may be key to HIV vaccine value.
Operations Research and Cost-Effective Spatial Conservation Planning: Data, Models, Tools and Future Directions
Diogo Alagador, Jorge O. Cerdeira
Subject: Biology, Ecology Keywords: Climate change; Ecological dynamics; Mathematical programming; Optimization; Spatial analysis; Systematic Conservation Planning
Biodiversity conservation questions human practices towards biodiversity and, therefore, largely conflicts with ordinary societal aspirations. Decisions on the location of protected areas, one of the most convincing conservation tools, reflect such a competitive endeavor. Operations Research (OR) brings a set of analytical models and tools capable of resolving the conflicting interests between ecology and economy. Recent technological advances have boosted the size and variety of data available to planners, thus challenging conventional approaches bounded on optimized solutions. New models and methods are requested to use such a massive amount of data in integrative schemes addressing a large variety of concerns. Here, we provide an overview on the past, present and future challenges that characterize spatial conservation models supported by OR. By enlarging the spatial, temporal, taxonomic and societal horizons of biodiversity conservation planners navigate around multiple bio-socioeconomic equilibria and are able to decide on cost-effective strategies to improve biodiversity persistence.
Formulation, Stability, Pharmacokinetic, and Modeling Studies for Tests of Synergistic Combinations of Orally Available Approved Drugs Against Ebola Virus In Vivo
Courtney L. Finch, Julie Dyall, Shuang Xu, Elizabeth A. Nelson, Elena Postnikova, Janie Y. Liang, Huanying Zhou, Lisa Evans DeWald, Craig J. Thomas, Amy Wang, Xin Xu, Emma Hughes, Patrick J. Morris, Jon C. Mirsalis, Linh H. Nguyen, Maria P. Arolfo, Bryan Koci, Michael R. Holbrook, Lisa E. Hensley, Peter B. Jahrling, Connie Schmaljohn, Lisa M. Johansen, Gene G. Olinger, Joshua T. Schiffer, Judith White
Subject: Medicine & Pharmacology, Allergology Keywords: filovirus; pandemic preparedness; synergy; viral pathogens; mathematical modeling; projected benefit in humans
Outbreaks of Ebola ebolavirus (EBOV) have been associated with high morbidity and mortality. Milestones have been reached recently in the management of EBOV disease (EVD) with licensure of an EBOV vaccine and two monoclonal antibody therapies. However, neither vaccines nor therapies are available for other disease-causing filoviruses. In preparation for such outbreaks, and for more facile and cost-effective management of EVD, we seek a cocktail containing orally available and room temperature stable drugs with strong activity against multiple filoviruses. We previously showed that (bepridil + sertraline) and (sertraline + toremifene) synergistically suppress EBOV in cell cultures. Here we describe steps towards testing these combinations in a mouse model of EVD. We identified a vehicle suitable for oral delivery of the component drugs and determined that, thus formulated the drugs are equally active against EBOV as preparations in DMSO, and they maintain activity upon storage in solution for up to seven days. Pharmacokinetic (PK) studies indicated that the drugs in the oral delivery vehicle are well tolerated in mice at the highest doses tested. Collectively the data support advancement of these combinations to tests for synergy in a mouse model of EVD. Moreover, mathematical modeling based on human oral PK projects that the combinations would be more active in humans than their component single drugs.
Collect and Treat Urban Wastewater to Fight the Pandemic Disease of COVID-19 Effectively
Abdol Aziz Shahraki
Subject: Engineering, Automotive Engineering Keywords: coronavirus; wastewater treatment techniques; mathematical model; statistical procedures; bacterial reactors, anaerobic ponds
This paper presents multidisciplinary and innovative research concerning fighting against coronavirus through wastewater collection and treatment. Studies suggest that coronavirus exists in the wastewaters. Untreated wastewater is proved to spread the virus. Coronavirus is attacking people globally and shrinking the economy. This paper highlights the idea that the coronavirus shall be defeated with the help of wastewater collection and treatment as well. The question addressed by this paper is will communities defeat the coronavirus without well-collected and treated wastewaters? This research aims to display the role of wastewaters in the spread of coronavirus in cities and to require their collection. The methods to achieve the goals are theoretical surveys, case study strategy, mathematical modeling, statistical procedures, forecasting of future, and dialectical discussions. The findings of this research demonstrate the need for carefully collected and treated wastewaters to overcome the coronavirus. This paper gives suitable techniques to collect and treat wastewater such as wastewater stabilization ponds, bacterial reactors, and anaerobic ponds. The innovative idea of this paper, its suggested indicators to select a certain wastewater treatment technique in every city, and its outcome will assist the global community to fight the coronavirus more effectively.
SARS-CoV-2 and Rohingya Refugee Camp, Bangladesh: Uncertainty and How the Government Took Over the Situation
Md. Kamrujjaman, MD. Shahriar Mahmud, Shakil Ahmed, Md. Omar Qayum, Mohammad Morshad Alam, Md Nazmul Hassan, Md Rafiul Islam, Kaniz Fatema Nipa, Ummugul Bulut
Subject: Life Sciences, Biochemistry Keywords: COVID-19; Rohingya Refugee camp; Mathematical model; Numerical results; Basic reproduction number.
{\bf Abstract.} \\ {\bf Background:} Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 burden among the Rohingya refugees of Bangladesh to keep up with the disease outbreak's pace, health needs, and disaster preparedness. \noindent{\bf Methodology and Findings:} To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a modified Susceptible-Exposed-Infectious Recovered (SEIR) transmission model. All the values of different parameters used in this model were from the Bangladesh Government's database and the relevant emerging literature. We addressed two different scenarios, i.e., the best-fitting model and good fitting model with unique consequences of COVID-19. Our best fitting model suggests that there will be good control over the transmission of the COVID-19 disease. At the end of December 2020, there will be only 169 confirmed COVID-19 cases in the Rohingya refugee camps. The average basic reproduction number ($ \mathcal{R}_{0} $) has been estimated to be 0.7563. \noindent{\bf Conclusion:} Our analysis suggests that, due to the extensive precautions from the Bangladesh government as well as other humanitarian organizations, the coronavirus disease will be under control if the maintenance continues like this. Although detailed and pragmatic preparedness should be adopted for the worst scenario.
Creative Mathematical Thinking in a Numbers Game
Joost Kruis, Claire Stevenson, Han L. J. van der Maas
Subject: Behavioral Sciences, Cognitive & Experimental Psychology Keywords: creative thinking; mathematical creativity; response processes; digital learning environment; online learning platform
Creative thinking is increasingly recognised as an essential ability that should be part of school curricula. Given the move towards online learning and assessment, we investigate whether mathematical creativity can be assessed at-scale in the Numbers game, an arithmetic game in Math Garden, a popular online math practice platform. In the Numbers game, a generalisation of the 24 Game, children are asked to figure out how to compute a target number using basic arithmetic operations and a given set of numbers. We argue that creative thinking is required when the search space is complex, and propose that the base-pattern, i.e., the sequence of the operations needed to solve a Numbers game item, indicates search space complexity. We then demonstrate that items with disordered base-patterns are more likely to require mathematical creativity to figure out. Specifically, our analysis shows that for items with only one solution sequence, those with disordered base-patterns are more difficult and take longer to solve compared to items with ordered base-patterns. For items where multiple solution sequences are possible, nine times out of ten children choose ordered over disordered base-patterns. We conclude that the Numbers game has potential for assessing mathematical creativity at-scale.
A Math Approach with Brief Cases towards Reducing Computational and Time Complexity in the Industrial Systems
Yaroslav Matviychuk, Tomáš Peráček, Natalya Shakhovska
Subject: Mathematics & Computer Science, Information Technology & Data Management Keywords: mathematical model; reduction; identification procedure; incorrectness; neural network; ordinary differential equation (ODE)
The paper proposes a new principle of finding and removing elements of mathematical model, redundant in terms of parametric identification of the model. It allows reducing computational and time complexity of the applications built on the model. Especially this is important for AI based systems, systems based on IoT solutions, distributed systems etc. Besides, the complexity reduction allows increasing an accuracy of mathematical models implemented. Despite the model order reduction methods are well known, they are extremely depended however on the problem area. Thus, proposed reduction principles can be used in different areas, what is demonstrated in this paper. The proposed method for the reduction of mathematical models of dynamic systems allows also the assessment of the requirements for the parameters of the simulator elements to ensure the specified accuracy of dynamic similarity. Efficiency of the principle is shown on the ordinary differential equations and on the neural network model. The given examples demonstrate efficient normalizing properties of the reduction principle for the mathematical models in the form of neural networks.
Mathematical Description of Elastic Phenomena which Uses Caputo or Riemann-Liouville Fractional Order Partial Derivatives is Nonobjective
Agneta M. Balint, Stefan Balint, Silviu Birauas
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: objectivity of a mathematical description; elastic phenomena description; fractional order partial derivative
In this paper it is shown that mathematical description of strain, constitutive law and dynamics obtained by direct replacement of integer order derivatives with Caputo or Riemann-Liouville fractional order partial derivatives, having integral representation on finite interval, in case of a guitar string, is nonobjective. The basic idea is that different observers, using this type of descriptions, obtain different results which cannot be reconciled, i.e. transformed into each other using only formulas that link the coordinates of the same point in two fixed orthogonal reference frames and formulas that link the numbers representing the same moment of time in two different choices of the origin of time measuring. This is not an academic curiosity! It is rather a problem: which one of the obtained results is correct?
Modelling SARS-COV2 Spread in London: Approaches to Lift the Lockdown
Lara Goscé, Andrew Phillips, Paula Spinola, Rishi K. Gupta, Ibrahim Abubakar
Subject: Keywords: COVID-19; coronavirus; SARS-CoV2; model; transmission model; mathematical model; lockdown; quarantine
Objective: To use mathematical models to predict the epidemiological impact of lifting the lockdown in London, UK, and alternative strategies to help inform policy in the UK. Methods: A mathematical model for the transmission of SARS-CoV2 in London. The model was parametrised using data on notified cases, deaths, contacts, and mobility to analyse the epidemic in the UK capital. We investigated the impact of multiple non pharmaceutical interventions (NPIs) and combinations of these measures on future incidence of COVID-19. Results: Immediate action at the early stages of an epidemic in the affected districts would have tackled spread. While an extended lockdown is highly effective, other measures such as shielding older populations, universal testing and facemasks can all potentially contribute to a reduction of infections and deaths. However, based on current evidence it seems unlikely they will be as effective as continued lockdown. In order to achieve elimination and lift lockdown within 5 months, the best strategy seems to be a combination of weekly universal testing, contact tracing and use of facemasks, with concurrent lockdown. This approach could potentially reduce deaths by 48% compared with continued lockdown alone. Conclusions: A combination of NPIs such as universal testing, contact tracing and mask use while under lockdown would be associated with least deaths and infections. This approach would require high uptake and sustained local effort but it is potentially feasible as may lead to elimination in a relatively short time scale.
Modification of the AFM Sensor by the Precisely Regulated Air Stream to Increase the Imaging Speed and Accuracy
Andrius Dzedzickis, Vytautas Bucinskas, Darius Viržonis, Nikolaj Sesok, Arturas Ulcinas, Igor Iljin, Ernestas Sutinys, Sigitas Petkevicius, Justinas Gargasas, Inga Morkvenaite-Vilkonciene
Subject: Engineering, Mechanical Engineering Keywords: atomic force microscopy; cantilever's mathematical model; dynamic characteristics; nonlinear stiffness; high speed
Increasing of the imaging rate of conventional atomic force microscopy (AFM) is almost impossible without impairing of the imaging quality, since the probe tip tends to lose contact with the sample. We propose to apply the additional nonlinear force on the upper surface of a cantilever, which will help to keep the tip and surface in contact. In practice this force can be produced by the precisely regulated airflow. Such an improvement affects the AFM system dynamics, which were evaluated using a mathematical model presented in this paper. The model defines the relationships between the additional nonlinear force, the pressure of the applied air stream and the initial air gap between the upper surface of the cantilever and the end of the air duct. It was found that the nonlinear force created by the stream of compressed air (aerodynamic force) prevents the contact loss caused by the high scanning speed or higher surface roughness, and at the same time has minimal influence on the interaction force, thus maintaining stable contact between the probe and the surface. This improvement allows to effectively increase the scanning speed by at least 10 times using a soft (spring constant of 0.2 N/m) cantilever by applying the air pressure of 40 Pa. If a stiff cantilever (spring constant of 40 N/m) is used, the potential of accuracy improvement reaches 92 times. This method is suitable for use with different types of AFM sensors and can be implemented practically without essential changes in AFM sensor design.
Dynamics of the Bacterial Community Associated with Phaeodactylum tricornutum Cultures
Fiona Wanjiku Moejes, Ovidiu Popa, Antonella Succurro, Julie Maguire, Oliver Ebenhöh
Subject: Biology, Other Keywords: microbial communities; host-microbe interactions; mathematical modelling; diatoms; synthetic ecology; algal biotechnology
The pennate diatom Phaeodactylum tricornutum is a model organism able to synthesize industrially-relevant molecules. Commercial-scale cultivation currently requires large monocultures, prone to bio-contamination. However, little is known about the identity of the invading organisms. To reduce the complexity of natural systems, we systematically investigated the microbiome of non-axenic P. tricornutum cultures from a culture collection in reproducible experiments. The results revealed a dynamic bacterial community that developed differently in "complete" and "minimal" media conditions. In complete media, we observed an accelerated "culture crash", indicating a more stable culture in minimal media. The identification of only four bacterial families as major players within the microbiome suggests specific roles depending on environmental conditions. From our results we propose a network of putative interactions between P. tricornutum and these main bacterial factions. We demonstrate that, even with rather sparse data, a mathematical model can be reconstructed that qualitatively reproduces the observed population dynamics, thus indicating that our hypotheses regarding the molecular interactions are in agreement with experimental data. Whereas the model in its current state is only qualitative, we argue that it serves as a starting point to develop quantitative and predictive mathematical models, which may guide experimental efforts to synthetically construct and monitor stable communities required for robust upscaling strategies.
Mathematical Modeling of the Growth Suppression of HER2+ Breast Cancer Colonies Under the Effect of Trastuzumab and PD-1/PD-L1 Inhibitor
Regina Padmanabhan, Hadeel Kheraldine, Ishita Gupta, Nader Meskin, Anas Hamad, Semir Vranic, Ala-Eddin Al Moustafa
Subject: Medicine & Pharmacology, Oncology & Oncogenics Keywords: HER2; PD-1/PD-L1; Mathematical model; HER2/PD-1 Interaction; Breast cancer
Immune checkpoint blockade (ICB)-based therapy is revolutionizing cancer treatment by fostering successful immune surveillance and effector cell responses against various types of cancers. However, patients with HER2+ cancers are yet to benefit from this therapeutic strategy. Precisely, several questions regarding the right combination of drugs, drug modality, and effective dose recommendations pertaining to the use of ICB-based therapy for HER2+ patients remain unanswered. In this study, we use a mathematical modeling-based approach to quantify the growth inhibition of HER2+ breast cancer (BC) cell colonies (ZR75) when treated with anti-HER2; trastuzumab (TZ) and anti-PD-1/PD-L1 (BMS-202) agents. Our data show that a combination therapy of TZ and BMS-202 can significantly reduce the viability of ZR75 cells and trigger several morphological changes. The combination decreased the cell's invasiveness along with altering several key pathways, such as Akt/mTor and ErbB2 compared to monotherapy. In addition, BMS-202 causes dose-dependent growth inhibition of HER2+ BC cell colonies alone, while this effect is significantly improved when used in combination with TZ. Based on the in-vitro monoculture experiments conducted, we argue that BMS-202 can cause tumor growth suppression not only by mediating immune response but also by interfering with the growth signaling pathways of HER2+ BC. Nevertheless, further studies are imperative to substantiate this argument and to uncover the potential crosstalk between PD-1/PD-L1 inhibitors and HER2 growth signaling pathways in breast cancer.
Evaluation Mathematical Models in SSCM and Gap Analysis
Zahra Ghorbani Ravand, Qi Xu
Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: SSCM; Mathematical Model; Systematic Literature Review; SSCM Modules; Sustainable Development Goals; Gap analysis
The main purpose of this paper is to present a comprehensive view of the application mathematical models in the designing and implementing SSCM beside to solving problems and making decision. The research questions are: what mathematical models are used for designing and implementing sustainable supply chain management, how to use them, which industries implemented in, what modules of SSCM depth in and finally finding the gaps of researches. The methodology of research is Systematic Literature review through peer review papers which are published in high ranking journals. In this paper, First, we search all papers through scientific data bases like Scopus, science direct, MDPI, Springer, Google Scholar, then, screening papers based on the criteria such as subject of paper, journals impact factor which is published in-should be peer review journal- and relative content of the papers. Finally, we selected 245 papers with three steps screening through 2806 papers that they have enough quality and relative to our research goals for context analysis. Through context analysis, first we categorized the information of the papers and drew the current situation of researches in the framework of our topic. Then, we evaluate and compare the goals of sustainability and current situation and found the gapes, then, offered new suggestions like implementing SSCMs models in pollutant industries like casting industry, Heavy industry, coal Industry and so on. On the other hand, there are gaps in researches in some modules of SSCM such as packaging, designing products, etc.
Magnetorheological Elastomer Stress Relaxation Behaviour During Compression: Experiment and Modelling
Mateusz Kukla, Łukasz Warguła, Krzysztof Talaśka, Dominik Wojtkowiak
Subject: Materials Science, Biomaterials Keywords: mechanical properties of advanced materials; magneto-rheological (MR); elastomer; stress relaxation; mathematical model
Materials characterised by magnetorheological properties are non-classic engineering materials. A significant increase in the interest of scientific community in materials from this group can be observed over the recent several years. The results of research presented in this article are oriented on the examination of said materials' mechanical properties. In order to do so, stress relaxation tests were conducted on cylindrical samples of magnetorheological elastomers loaded with compressive stress for various values of magnetic induction (B1 = 0 mT, B2 = 32 mT, B3 = 48 mT, and B4 = 64 mT) and temperature (T1 = 25° C, T2 = 30° C, and T3 = 40° C). The results of these tests indicate that the stiffness of examined samples increases along with the increase of magnetic field induction and decreases along with the increase of temperature. On this basis, it has been determined that: the biggest stress amplitude change caused by the influence of magnetic field was σ0ΔB = 12.7% and the biggest stress amplitude change caused by the influence of temperature was σ0ΔT = 11.3%. As a result of applying a mathematical model, it has been indicated that the stress relaxation in the examined magnetorheological elastomer for the adopted time range (t = 3600 s) has a hyperbolic decline nature. The collected test results point to examined materials being characterised by extensive rheological properties, which leads to a conclusion that it is necessary to conduct further tests in this scope.
Study of Transmission Dynamics of Novel COVID-19 by Using Mathematical Model
Thabet Abdeljawad
Subject: Keywords: Mathematical model; Novel coronavirus -19; Nonstandard finite difference scheme; Emigration rate. 1. Introduction
In this research work, we present a mathematical model for novel coronavirus -19 (NCOVID-19) which is consisted on three different compartments susceptible, infected and recovered classes abbreviated as under convex incident rate involving and emigration rate. We first derive the formulation of the model. Also, we give some qualitative aspects for the model including existence of equilibriums and its stability results by using various tools of nonlinear analysis. Then by mean of nonstandard finite difference scheme (NSFD), we simulate the results against the data of Wuhan city for the sixty days. By means of simulation, we show how protection, exposure, emigration, death and cure rates affect the susceptible, infected and recovered population with the passage of time involving emigration. On the basis of simulation, we observe the dynamical behavior due to emigration of susceptible and infected classes or one of these two.
The Impact of Isolation on the Transmission of COVID-19 and Estimation of Potential Second Epidemic in China
Haitao Song, Fang Liu, Feng Li, Xiaochun Cao, Hao Wang, Zhongwei Jia, Huaiping Zhu, Michael Li, Wei Lin, Hong Yang, Jianghong Hu, Zhen Jin
Subject: Keywords: COVID-19; mathematical model; basic reproduction number; potential second epidemic; isolation; close contacts
The first case of Corona Virus Disease 2019 (COVID-19) was reported in Wuhan, China in December 2019. Since then, COVID-19 has quickly spread out to all provinces in China and over 150 countries or territories in the world. With the first level response to public health emergencies (FLRPHE) launched over the country, the outbreak of COVID-19 in China is achieving under control in China. We develop a mathematical model based on epidemiology of COVID-19, incorporating the isolation of healthy people, confirmed cases and close contacts. We calculate the basic reproduction numbers 2.5 in China (excluding Hubei province) and 2.9 in Hubei province with the initial time on January 30 which show the severe infectivity of COVID-19, and verify that the current isolation method effectively contains the transmission of COVID-19. Under the isolation of healthy people, confirmed cases and close contacts, we find a noteworthy phenomenon that is the potential second epidemic of COVID-19, and estimate the peak time and value and the cumulative number of cases. Simulations show that the isolation of close contacts tracked measure can efficiently contain the transmission of the potential second epidemic of COVID-19. With isolation of all susceptible people or all infected people or both, there is no potential second epidemic of COVID-19. Furthermore, resumption of work and study can increase the transmission risk of the potential second epidemic of COVID-19.
Predicting the Cumulative Number of Cases for the COVID-19 Epidemic in China From Early Data
Zhihua Liu, Pierre Magal, Ousmane Seydi, Glenn Webb
Subject: Life Sciences, Other Keywords: corona virus; reported and unreported cases; isolation; quarantine; public closings; epidemic mathematical model
We model the COVID-19 coronavirus epidemic in China. We use early reported case data to predict the cumulative number of reported cases to a final size. The key features of our model are the timing of implementation of major public policies restricting social movement, the identification and isolation of unreported cases, and the impact of asymptomatic infectious cases.
Understanding Unreported Cases in the 2019-nCov Epidemic Outbreak in Wuhan, China, and the Importance of Major Public Health Interventions
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: corona virus; reported and unreported cases; isolation, quarantine; public closings; epidemic mathematical model
We develop a mathematical model to provide epidemic predictions for the 2019-nCov epidemic in Wuhan, China. We use reported case data up to January 31, 2020 from the Chinese Center for Disease Control and Prevention and the Wuhan Municipal Health Commission to parameterize the model. From the parameterized model we identify the number of unreported cases. We then use the model to project the epidemic forward with varying level of public health interventions. The model predictions emphasize the importance of major public health interventions in controlling 2019-nCov epidemics.
A Mathematical Model of the Transition from the Normal Hematopoiesis to the Chronic and Accelerated Acute Stages in Myeloid Leukemia
Lorand Gabriel Parajdi, Radu Precup, Eduard Alexandru Bonci, Ciprian Tomuleasa
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: mathematical modeling; dynamic system; steady state; stability; hematopoiesis; chronic myeloid leukemia; stem cells
A mathematical model given by a two - dimensional differential system is introduced in order to understand the transition process from the normal hematopoiesis to the chronic and accelerated acute stages in chronic myeloid leukemia. A previous model of Dingli and Michor is refined by introducing a new parameter in order to differentiate the bone marrow microenvironment sensitivities of normal and mutant stem cells. In the light of the new parameter, the system now has three distinct equilibria corresponding to the normal hematopoietic state, to the chronic state, and to the accelerated acute phase of the disease. A characterization of the three hematopoietic states is obtained based on the stability analysis. Numerical simulations are included to illustrate the theoretical results.
Quantification of the Energy Storage Contribution to Security of Supply through the F-Factor methodology
Spyros Giannelos, Predrag Djapic, Danny Pudjianto, Goran Strbac
Subject: Engineering, Electrical & Electronic Engineering Keywords: f-factors; energy storage; investments in electricity systems; mathematical optimization; security of supply
The ongoing electrification of the heat and transport sectors is expected to lead to a substantial increase in peak electricity demand over the coming decades, which may drive significant investment in network reinforcement in order to maintain a secure supply of electricity to consumers. The traditional way of security provision has been based on conventional investments such as the upgrade of the capacity of electricity transmission or distribution lines. However, the energy storage technology can also provide security of supply, thereby constituting a cost-efficient alternative to expensive conventional reinforcements. In this context, the current paper presents a methodology for the economic quantification of the security contribution of energy storage. This methodology makes use of mathematical optimization for the calculation of the F-factor metric, which reflects the optimal amount of peak demand reduction as compared to the power capability of the energy storage asset. In this context, a case study is presented in which the security contribution of energy storage is analyzed as a function of its power capability, energy capacity and efficiency as well as of characteristics of load patterns.
Equivalent Circulation Density Analysis of Geothermal Well by Coupling Temperature
Xiuhua Zheng, Chenyang Duan, Zheng Yan, Hongyu Ye, Zhiqing Wang, Bairu Xia
Subject: Engineering, Energy & Fuel Technology Keywords: wellbore pressure analysis; equivalent circulating density; geothermal well; wellbore temperature distribution; mathematical modeling
The accurate wellbore pressure control not only prevents from lost circulation/blowout and fracturing formation by managing density of drilling fluid, but also improves productivity by mitigating reservoir damage. The geothermal pressure calculated by constant parameters for geothermal well would bring big error easily, as the changes of physical, rheological and thermal properties of drilling fluids with temperature were neglected. This paper researches the wellbore pressure coupling by calculating the temperature distribution with existed model, fitting the rule of density of drilling fluid with temperature and establishing mathematical models to stimulate the wellbore pressures, which is expressed as the variation of Equivalent Circulating Density (ECD) under different conditions. With this method, temperature and ECDs in the wellbore of the first medium-deep geothermal well ZK212 Yangyi Geothermal Field in Tibet were determined, and the sensitivity analysis was simulated by assumed parameters, i.e. circulating time, flow rate, geothermal gradient, diameters of wellbore, rheological models and regimes, the results indicated the geothermal gradient and flow rate were the most influence parameters on the temperature and ECD distribution, and additives added in drilling fluid should be careful which would change the properties of drilling fluid and induce the temperature redistribution. To make sure the safe drilling, velocity of pipes tripping into the hole, depth and diameter of wellbore are considered to control the surge pressure.
HIV/AIDS Mathematical Model of Triangle Transmission
Cristian Camilo Espitia Morillo, João Frederico da Costa Azevedo Meyer
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: HIV/AIDS Mathematical Model; Basic Reproduction Number; Stationary Points; Local and Global Stability Analysis.
In this paper mathematical analysis of the HIV/AIDS deterministic model exposed in [Espitia, C. et. al. Mathematical Model of HIV/AIDS Considering Sexual Preferences Under Antiretroviral Therapy, a Case Study in San Juan de Pasto, Colombia, Journal of Computational Biology 29 (2022) 483–493] is made. The objective is to gain insight into the qualitative dynamics of the model determining the conditions for the persistence or effective control of the disease in the community through the study of basic properties such as positiveness and boundedness, calculus of basic reproduction number, stationary points such as disease free equilibrium (DFE), boundary equilibrium (BE) and endemic equilibrium (EE) are calculated, local stability (LAS) of disease free equilibrium. It research allow to conclude that the best way to reduce contagion and consequently to reach a DFE is thought to be the reduction of homosexual partners rate as they are the most affected population by the virus, and are therefore the most likely to become infected and to spread the infection. Increasing the departure rate of infected individuals, leads to a decrease in untreated infected heterosexual men and untreated infected women.
A Mathematical Interpretation and Validation of the Streamline's Shape Theory for Inviscid-Incompressible Flows & Viscid-Compressible Flows of the Newtonian Fluids
Subject: Physical Sciences, Acoustics Keywords: Fluid-Structure interactions; Topological fluid dynamics; General fluid mechanics; Mathematical fluid dynamics; Applied mathematics
This article objectively assesses, the hypothesis of the streamline's shape theory and its formulated equation. The deduction of proof uses algebra rather than first-order partial differential equations to address the specific hypothesis of "Streamline's shape theory" from the fundamental perspective of applied mathematics and scientifically derives mathematical relations of the axioms and corollaries in the field of fluid dynamics. The algebraic methods employed provide progressively more distinct and precise solutions compared to first-order partial differential equations. The foremost objective of this work is to evaluate if the formulations of the streamline's shape theory can have solutions for inviscid-incompressible and viscid-compressible flows of Newtonian fluids and to identify their nature. Secondly, to understand how the topology of the body and the free-stream conditions affect these solutions with due regards to the shape and size of the body interacting with the fluid flow. Finally, to explore the possibility of this theory to develop a CFD solver for streamline simulation to reduce the experimentation in the analysis of flow-structure interactions of Newtonian fluids and also to identify its scope of applications and limitations.
A Compartmental Epidemiological Model for the Dissemination of the COVID-19 Disease
Evangelos Matsinos
Subject: Mathematics & Computer Science, Analysis Keywords: Epidemiology; infectious disease; compartmental model; mathematical modelling and optimisation; COVID-19; SARS-CoV-2
A compartmental epidemiological model with seven groups is introduced herein, to account for the dissemination of diseases similar to the Coronavirus disease 2019 (COVID-19). In its simplified version, the model contains ten parameters, four of which relate to characteristics of the virus, whereas another four are transition probabilities between the groups; the last two parameters enable the empirical modelling of the effective transmissibility, associated in this study with the cumulative number of fatalities due to the disease within each country. The application of the model to the fatality data (the main input herein) of five countries (to be specific, of those which had suffered most fatalities by April 30, 2020) enabled the extraction of an estimate for the basic reproduction number $R_0$ for the COVID-19 disease: $R_0=4.91(33)$.
A Mathematical Model of COVID-19 Using Fractional Derivative: Outbreak in India with Dynamics of Transmission and Control
Amjad S. Shaikh, Iqbal N. Shaikh, Kottakkaran Sooppy Nisar
Subject: Mathematics & Computer Science, Analysis Keywords: mathematical models; coronavirus; caputo-fabrizio derivative; basic reproduction number; existence and stability; numerical simulations
Since the first case of 2019 novel coronavirus disease (COVID-19) detected on Jan 30, 2020, in India, the number of cases rapidly increased to 3819 cases including 106 deaths as of 5 April 2020. Taking this into account, in the present work, we are studying a Bats-Hosts-Reservoir-People transmission fractional-order COVID-19 model for simulating the potential transmission with the thought of individual social response and control measures by the government. The real data available about infectious cases from $14^{th}$ March to $26^{th}$ March 2020 is analysed and accordingly various parameters of the model are estimated or fitted. The Picard successive approximation technique and Banach's fixed point theory have been used for verification of the existence and stability criteria of the model. Numerical computations are done utilizing the iterative Laplace transform method. In the end, we illustrate the obtained results graphically. The purpose of this study is to estimate the effectiveness of preventive measures, predicting future outbreaks and potential control strategies using the mathematical model.
Predictive Modeling the Free Hydraulic Jumps Pressure through Advanced Statistical Methods
Seyed Nasrollah Mousavi, Renato Steinke Júnior, Eder Daniel Teixeira, Daniele Bocchiola, Narjes Nabipour, Amir Mosavi, Shahaboddin Shamshirband
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: mathematical modeling; characteristic points; extreme pressure; hydraulic jump; pressure fluctuations; standard deviation; stilling basin
Pressure fluctuations beneath hydraulic jumps downstream of Ogee spillways potentially damage stilling basin beds. This paper deals with the extreme pressures underneath free hydraulic jumps along a smooth stilling basin. The experiments were conducted in a laboratory flume. From the probability distribution of measured instantaneous pressures, the pressures with different non-exceedance probabilities (P*a%) could be determined. It was verified that the maximum pressure fluctuations, as well as the negative pressures, are located at the positions closest to the spillway toe. The minimum pressure fluctuations are located at the downstream of hydraulic jumps. It was possible to assess the cumulative curves of P*a% related to the characteristic points along the basin, and different Froude numbers. To benchmark, the results, the dimensionless forms of mean pressures, standard deviations, and pressures with different non-exceedance probabilities were assessed. It was found that an existing methodology can be used to interpret the present data, and pressure distribution in similar conditions, by using a new third-order polynomial relationship for the standard deviation (σ*X) with the determination coefficient (R2) equal to 0.717. It was verified that the new optimized adjustment gives more accurate results for the estimation of the maximum extreme pressures than the minimum extreme pressures.
Defining Kinetic Properties of HIV-Specific CD8+ T-cell Responses in Acute Infection
Yiding Yang, Vitaly V. Ganusov
Subject: Life Sciences, Immunology Keywords: acute HIV infection; vaccines; CD8$^+$ T cells; immune response; multiple epitopes; competition; mathematical model
Multiple lines of evidence indicate that CD8$^+$ T cells are important in the control of HIV-1 (HIV) replication. However, CD8$^+$ T cells induced by natural infection cannot eliminate the virus or reduce viral loads to acceptably low levels in most infected individuals. Understanding the basic quantitative features of CD8$^+$ T-cell responses induced during the course of HIV infection may therefore inform us about the limits that HIV vaccines, which aim to induce protective CD8$^+$ T-cell responses, must exceed. Using previously published experimental data from a cohort of HIV-infected individuals with sampling times from acute to chronic infection we defined the quantitative properties of CD8$^+$ T-cell responses to the whole HIV proteome. In contrast with a commonly held view, we found that the relative number of HIV-specific CD8$^+$ T-cell responses (response breadth) changed little over the course of infection (first 400 days post-infection), with moderate but statistically significant changes occurring only during the first 35 symptomatic days. This challenges the idea that a change in the T-cell response breadth over time is responsible for the slow speed of viral escape from CD8$^+$ T cells in the chronic infection. The breadth of HIV-specific CD8$^+$ T-cell responses was not correlated with the average viral load for our small cohort of patients. Metrics of relative immunodominance of HIV-specific CD8$^+$ T-cell responses such as Shannon entropy or the Evenness index were also not significantly correlated with the average viral load. Our mathematical-model-driven analysis suggested extremely slow expansion kinetics for the majority of HIV-specific CD8$^+$ T-cell responses and the presence of intra- and interclonal competition between multiple CD8$^+$ T-cell responses; such competition may limit the magnitude of CD8$^+$ T-cell responses, specific to different epitopes, and the overall number of T-cell responses induced by vaccination. Further understanding of mechanisms underlying interactions between the virus and virus-specific CD8$^+$ T-cell response will be instrumental in determining which T-cell-based vaccines will induce T-cell responses providing durable protection against HIV infection.
Elucidating Cellular Population Dynamics by Molecular Density Function Perturbations
Thanner Malai Perumal, Rudiyanto Gunawan
Subject: Mathematics & Computer Science, Analysis Keywords: mathematical modeling; biological networks; sensitivity analysis; programmed cell death; single cell dynamics; cell population
Studies performed at single-cell resolution have demonstrated the physiological significance of cell-to-cell variability. Various types of mathematical models and systems analyses of biological networks have further been used to gain a better understanding of the sources and regulatory mechanisms of such variability. In this work, we present a novel sensitivity analysis method, called molecular density function perturbation (MDFP), for the dynamical analysis of cellular heterogeneity. The proposed analysis is based on introducing perturbations to the density or distribution function of the cellular state variables at specific time points, and quantifying how such perturbations affect the state distribution at later time points. We applied the MDFP analysis to a model of signal transduction pathway involved in TRAIL (tumor necrosis factor-related apoptosis-inducing ligand)-induced apoptosis in HeLa cells. The MDFP analysis showed that caspase-8 activation regulates the timing of the switch-like increase of cPARP (cleaved poly(ADP-ribose) polymerase), an indicator of apoptosis. Meanwhile, the cell-to-cell variability in the commitment to apoptosis depended on mitochondrial outer membrane permeabilization (MOMP) and events following MOMP, including the release of Smac (second mitochondria-derived activator of caspases) and cytochrome-C from mitochondria, the inhibition of XIAP (X-linked inhibitor of apoptosis) by Smac and the formation of apoptosome.
Multi-Objective Optimization of Experiments Using Curvature and Fisher Information Matrix
Erica Manesso, Sridharan Srinath, Rudiyanto Gunawan
Subject: Engineering, Biomedical & Chemical Engineering Keywords: design of experiments; multi-objective optimization; Fisher information matrix; curvature; biological processes; mathematical modeling
The bottleneck in creating dynamic models of biological networks and processes often lies in estimating unknown kinetic model parameters from experimental data. In this regard, experimental conditions have a strong influence on parameter identifiability and should therefore be optimized to give the maximum information for parameter estimation. Existing model-based design of experiment (MBDOE) methods commonly rely on the Fisher Information Matrix (FIM) for defining a metric of data informativeness. When the model behavior is highly nonlinear, FIM-based criteria may lead to suboptimal designs since the FIM only accounts for the linear variation of the model outputs with respect to the parameters. In this work, we developed a multi-objective optimization (MOO) MBDOE, where model nonlinearity was taken into consideration through the use of curvature. The proposed MOO MBDOE involved maximizing data informativeness using a FIM-based metric and at the same time minimizing the model curvature. We demonstrated the advantages of the MOO MBDOE over existing FIM-based and other curvature-based MBDOEs in an application to the kinetic modeling of fed-batch fermentation of Baker's yeast.
Validation of the Cooling Model for TMCP Processing of Steel Sheets with Oxide Scale by Industrial Experiment Data
Emmanuil Beygelzimer, Yan Beygelzimer
Subject: Engineering, Industrial & Manufacturing Engineering Keywords: rolled flat products; accelerated cooling; temperature; mathematical model; oxide scale; Ther-mo-Mechanical Controlled Process
To verify the authors' mathematical model for water jet cooling of steel sheet, the previously performed experimental studies of temperature of the test plate in the roller quenching machine (RQM) were used. The calculated data of steel temperature evolution along the RQM length were compared with the readings of thermocouples inserted in the center of the test plate and at its surfaces. The core of the model is the dependence of the temperatures of film, transition and nucleate boiling regimes on the thickness of the oxide scale layer on the cooled surface. It was found that the model correctly takes into account the oxide scale on the sheet surface, flow rates and combinations of the RQM banks used, water temperature and other factors. For all experiments the calculated metal temperature corresponds well to the measured one. In the experiments with interrupted cooling, the calculated temperature plots repeat the characteristic changes in the experimental curves. The main uncertainty in the modeling of cooling in a wide temperature range can be contributed by the random nature of changes in the oxide scale thickness during water cooling. In this regard, the estimated thickness of the oxide scale layer should be considered as the main parameter for adapting the sheet temperature control process. The obtained data confirm the possibility of effective application of the model in the ACS of industrial TMCP (Thermo-Mechanical Controlled Process) systems.
A Mathematical Modeling Approach for Targeted Radionuclide and Chimeric Antigen Receptor-T Cell Combination Therapy
Vikram Adhikarla, Dennis Awuah, Alex Brummer, Enrico Caserta, Amrita Krishnan, Flavia Pichiorri, Megan Minnix, John E. Shively, Jeffrey Y.C. Wong, Xiuli Wang, Russell C. Rockne
Subject: Mathematics & Computer Science, Applied Mathematics Keywords: CAR T; Targeted Radionuclide Therapy; TRT; Mathematical Model; Multiple Myeloma; Immunotherapy; Daratumumab; CS1; Combination Therapy
Targeted radionuclide therapy (TRT) has recently seen a surge in popularity, with the use of radionuclides conjugated to small molecules and antibodies. Similarly, immunotherapy also has shown promising results – an example being chimeric antigen receptor (CAR) T-cells therapy in hematologic malignancies. Moreover, TRT and CAR T therapies possess unique features that require special consideration when determining how to dose, time, and sequence combination treatments, including the distribution of TRT dose in the body, the decay rate of the radionuclide, and the proliferation and persistence of the CAR-T cells. These characteristics complicate additive or synergistic effects of combination therapies and warrant a mathematical treatment which includes these dynamics in relation to the proliferation and clearance rates of the target tumor cells. Here we combine two previously published mathematical models in a multiple myeloma setting to explore the effects of dose, timing, and sequencing of TRT and CAR-T cell based therapies. We find that for a fixed TRT and CAR-T cell dose, the tumor proliferation rate is the most important parameter in determining the best timing of TRT and CAR T therapies.
Working Paper COMMUNICATION
Sensing and Delineating Mixed-VOC Composition in Air Using a Single Metal-Oxide Sensor
Govind S. Thakor, Ning Zhang, Rafael M. Santos
Subject: Engineering, Other Keywords: volatile organic compounds; air quality monitoring; metal oxide sensor; predictive mathematical model; gas composition estimation
Monitoring volatile organic compounds (VOCs) places a crucial role in environmental pollutants control and indoor air quality. In this study, a metal-oxide (MOx) sensor detector (used in a commercially available monitor) was employed to delineate the composition of air containing three common VOCs (ethanol, acetone and hexane) under various concentrations. Experiments with a single component and double components were conducted to investigate how the solvents interact with the metal oxide sensor. The experimental results revealed that the affinity between VOC and sensor was in the following order: acetone > ethanol > n-hexane. A mathematical model was developed, based on the experimental findings and data analysis, to convert the output resistance value of the sensor into concentration values, which in turn can be used to calculate a VOC-based air quality index. Empirical equations were established based on inferences of vapor composition versus resistance trends, and on an approach of using original and diluted air samples to generate two sets of resistance data per sample. The calibration of numerous model parameters allowed matching simulated curves to measured data. As such, the predictive mathematical model enabled quantifying not only the total concentration of sensed VOCs, but also estimating the VOC composition. This first attempt to obtain semi-quantitative data from a single MOx sensor, despite remaining selectivity challenges, is aimed at expanding the capability of mobile air pollutants monitoring devices.
High-dimensional Analysis of Single-cell Flow Cytometry Data Predicts Relapse in Childhood Acute Lymphoblastic Leukemia
Salvador Chulián, Álvaro Martínez-Rubio, Víctor Pérez-García, María Rosa, Cristina Blázquez-Goñi, Juan Francisco Rodríguez Gutiérrez, Lourdes Hermosín-Ramos, Águeda Molinos-Quintana, Teresa Caballero-Velázquez, Manuel Ramírez-Orellana, Ana Castillo Robleda, Juan Luis Fernández-Martínez
Subject: Medicine & Pharmacology, Allergology Keywords: Acute Lymphoblastic Leukaemia; Flow Cytometry Data; Fisher's Ratio; CD38; mathematical oncology; response biomarkers; personalized medicine
Artificial intelligence methods may help in unveliling information hidden in high-dimensional oncological data. Flow cytometry studies of haematological malignancies provide quantitative data with the potential to be used for the construction of response biomarkers. Many computational methods from the bioinformatics toolbox can be applied to these data but have not been exploited in their full potential in leukaemias, specifically for the case of childhood B-cell acute lymphoblastic leukemia. In this paper we analysed flow cytometry data obtained on diagnosis from 54 paediatric B-cell acute lymphoblastic leukemia patients from two local institutions. We constructed classifiers based on the Fisher's Ratio to quantify differences in expression levels of immunophenotypical markers between patients with relapsing and non-relapsing disease. The distribution of the marker CD38 was found and validated to have a strong discriminating power between both patient cohorts, thus providing a classifier.
A Cosmological Basis for E = mc2
Fulvio Melia
Subject: Physical Sciences, Astronomy & Astrophysics Keywords: general relativity: exact solutions; relativity and gravitation; observational cosmology; mathematical and relativistic aspects of cosmology
The Universe has a gravitational horizon with a radius Rh = c/H coincident with that of the Hubble sphere. This surface separates null geodesics approaching us from those receding, and as free-falling observers within the Friedmann-Lemaitre-Robertson-Walker spacetime, we see it retreating at proper speed c, giving rise to the eponymously named cosmological model Rh = ct. As of today, this cosmology has passed over 20 observational tests, often better than LCDM. The gravitational radius Rh therefore appears to be highly relevant to cosmological theory, and in this paper we begin to explore its impact on fundamental physics. We calculate the binding energy of a mass m within the horizon and demonstrate that it is equal to mc2. This energy is stored when the particle is at rest near the observer, transitioning to a purely kinetic form equal to the particle's escape energy when it approaches Rh. In other words, a particle's gravitational coupling to that portion of the Universe with which it is causally connected appears to be the origin of rest-mass energy.
PigLeg: Prediction of Swine Phenotype Using Machine Learning
Siroj Bakoev, Lyubov Getmantseva, Maria Kolosova, Olga Kostyunina, Duane Chartier, Tatiana V. Tatarinova
Subject: Biology, Animal Sciences & Zoology Keywords: artificial intelligence; bioinformatics; computational biology; data mining & machine learning; evolutionary studies; mathematical biology; animal behavior
Industrial pig farming is associated with negative technological pressure on the bodies of pigs. Leg weakness and lameness are the sources of significant economic loss in raising pigs. Therefore, it is important to identify predictors of limb condition. This work presents assessments of the state of limbs using indicators of growth and meat characteristics of pigs based on machine learning algorithms. We have evaluated and compared the accuracy of prediction for several ML classification algorithms (Random Forest, K-Nearest Neighbors, Artificial Neural Networks, C50Tree, Support Vector Machines, Naive Bayes, Generalized Linear Models, Boost, and Linear Discriminant Analysis) and have identified the Random Forest and K-Nearest Neighbors as the best performing algorithms for predicting pig leg weakness using a small set of simple measurements that can be taken at an early stage of animal development. Muscle Thickness, Back Fat amount, and Average Daily Gain serve as significant predictors of conformation of pig limbs. Our work demonstrates the utility and relative ease of using machine learning algorithms to assess the state of limbs in pigs based on growth rate and meat characteristics.
A Novel Patient-specific Protein Expression-based Algorithmic Model for Immune Checkpoint Inhibition Therapy Response Prediction in a Pan-cancer Cohort
Oluwaseun Adebayo Bamodu, Wei-Hong Cheng, Oluleke Bamodu, Wei-Hwa Lee, Kang-Yun Lee, Liang-Shun Wang, Tsu-Yi Chao, Chi-Tai Yeh
Subject: Biology, Physiology Keywords: pharmacogenomics; immune checkpoint blockade; immunotherapy; drug response prediction; algorithm; mathematical model; precision medicine; personalized medicine
Background: Accurate prediction of patients' response to therapy is clinically indispensable, howbeit challenging. With increased understanding of the human genome and malignancies, there is the renaissance of in silico pharmacogenomics with renewed interest in drug response predictability based on gene-drug interaction. Objective: Evidence-based transcript-proteome profiling is essential for synthesizing clinically applicable algorithms for predicting response to anticancer therapy, including immune checkpoint blockade (ICBT); thus, saving physicians' time, reducing polypharmacy, and curtailing unnecessary treatment expense. In this study, we tested and validated the hypothesis that a selected proteomic signature in ICBT-naïve patients is sufficient for the prediction of response to ICBT. Methods: Using a multimodal approach consisting of computational pharmacogenomics, transcript-proteome analytics, mathematical modeling, and machine learning systems; we delineated therapy-sensitivity and stratified patients into graduated response groups based on their proteomic profile. Protein expression levels in our cohort tissue specimens were evaluated based on T cell- and non-T cell- inflamed phenotypes by immunohistochemistry. Results: We established β-catenin, PDL1, CD3 and CD8 expression-based ICBT response model. Statistical regression models validated the predictive association between our predefined algorithms and therapeutic outcome. Interestingly, our 4-gene prediction classifier was constitutively independent of tumor tissue origin, correctly stratified patients into high-, low-, and non- responders pre-treatment, with high prediction accuracy, and exhibited good association with patients' performance status and prognosis (p < 0.01). Conclusion: Our findings demonstrate the possibility of accurate proteomics based ICBT response prediction and provide a putative basis for drug response prediction based on selective proteome profile in untreated cancer patients.
A New Set Theory for Analysis
Juan Ramirez
Subject: Mathematics & Computer Science, Analysis Keywords: General Topology, Axiomatic Set Theory, Real Analysis, Continuum, Graph Theory, Benacerraf's Identification Problem, Mathematical Structuralism
We present the real number system as a natural generalization of the natural numbers. First, we prove the co-finite topology, $Cof(\mathbb N)$, is isomorphic to the natural numbers. Then, we generalize these results to describe the continuum $[0,1]$. Then we prove the power set $2^{\mathbb Z}$ contains a subset isomorphic to the non-negative real numbers, with all its defining structure of operations and order. Finally, we provide two different constructions of the entire real number line. We see that the power set $2^{\mathbb N}$ can be given the defining structure of $\mathbb R$. The constructions here provided give simple rules for calculating addition, multiplication, subtraction, division, powers and rational powers of real numbers, and logarithms. The supremum and infimum are explicitly constructed by means of a well defined algorithm that ends in denumerable steps. In section 5 we give evidence our construction of $\mathbb N$ and $\mathbb R$ are canonical; these constructions are as natural as possible. In the same section, we propose a new axiomatic basis for analysis. In the last section we provide a series of graphic representations and physical models that can be used to represent the real number system. We conclude that the system of real numbers is completely defined by the order structure of $\mathbb N$.}
MIMO PID Controller Tuning Method for Quadrotor Based on LQR/LQG Theory
Rafael Guardeño, Manuel J. López, Víctor M. Sánchez
Subject: Engineering, Electrical & Electronic Engineering Keywords: PID tuning; LQR; LQG; sensors data fusion; quadrotor mathematical model; Kalman filter; MARG; robustness analysis
In this work a new pre-tuning multivariable PID controllers method for quadrotors is put forward. A procedure based on LQR/LQG theory is proposed for attitude and altitude control. With the aim of analyzing performance and robustness of the proposed method, a non-linear mathematical model of the DJI-F450 quadrotor is employed, where rotors dynamics, togheter with sensors drift/bias properties and noise characteristics of low-cost comercial sensors typically used in this type of applications (such as MARG with MEMS technology and LIDAR) are considered. In order to estimate the state vector and compensate bias/drift effects on rate gyros of the MARG, a combination of filtering and data fusion algorithms (Kalman filter and Madgwick algorithm for attitude estimation) are proposed and implemented. Performance and robutsness analysis of the control system is carried out by means of numerical simulations, which take into account the presence of uncertainty in the plant model and external disturbances. The obtained results show that the proposed pre-tuning method for multivariable PID controller is robust with respect to: a) parametric uncertainty in the plant model, b) disturbances acting at the plant input, c) sensors measurement and estimation errors.