scholarly journals A General Mechano-Pharmaco-Biological Model for Bone Remodeling Including Cortisol Variation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1401
Author(s):  
Rabeb Ben Kahla ◽  
Abdelwahed Barkaoui ◽  
Moez Chafra ◽  
João Manuel R. S. Tavares
Keyword(s):  
Mathematical Model ◽  
Bone Remodeling ◽  
Cell Populations ◽  
Biological Models ◽  
Mass Variation ◽  
Proposed Model ◽  
The Future ◽  
Mechanical Models ◽  
General Mathematical Model ◽  
Current Article

The process of bone remodeling requires a strict coordination of bone resorption and formation in time and space in order to maintain consistent bone quality and quantity. Bone-resorbing osteoclasts and bone-forming osteoblasts are the two major players in the remodeling process. Their coordination is achieved by generating the appropriate number of osteoblasts since osteoblastic-lineage cells govern the bone mass variation and regulate a corresponding number of osteoclasts. Furthermore, diverse hormones, cytokines and growth factors that strongly link osteoblasts to osteoclasts coordinated these two cell populations. The understanding of this complex remodeling process and predicting its evolution is crucial to manage bone strength under physiologic and pathologic conditions. Several mathematical models have been suggested to clarify this remodeling process, from the earliest purely phenomenological to the latest biomechanical and mechanobiological models. In this current article, a general mathematical model is proposed to fill the gaps identified in former bone remodeling models. The proposed model is the result of combining existing bone remodeling models to present an updated model, which also incorporates several important parameters affecting bone remodeling under various physiologic and pathologic conditions. Furthermore, the proposed model can be extended to include additional parameters in the future. These parameters are divided into four groups according to their origin, whether endogenous or exogenous, and the cell population they affect, whether osteoclasts or osteoblasts. The model also enables easy coupling of biological models to pharmacological and/or mechanical models in the future.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

scholarly journals Will SARS-CoV-2 Become Just Another Seasonal Coronavirus?

Viruses ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 854
Author(s):  
Alexander B. Beams ◽  
Rebecca Bateman ◽  
Frederick R. Adler
Keyword(s):  
Mathematical Model ◽  
Herd Immunity ◽  
Population Heterogeneity ◽  
Emerging Pathogens ◽  
Wide Range ◽  
The Future ◽  
General Mathematical Model ◽  
The Right ◽  
Over Time ◽  
Partial Immunity

The future prevalence and virulence of SARS-CoV-2 is uncertain. Some emerging pathogens become avirulent as populations approach herd immunity. Although not all viruses follow this path, the fact that the seasonal coronaviruses are benign gives some hope. We develop a general mathematical model to predict when the interplay among three factors, correlation of severity in consecutive infections, population heterogeneity in susceptibility due to age, and reduced severity due to partial immunity, will promote avirulence as SARS-CoV-2 becomes endemic. Each of these components has the potential to limit severe, high-shedding cases over time under the right circumstances, but in combination they can rapidly reduce the frequency of more severe and infectious manifestation of disease over a wide range of conditions. As more reinfections are captured in data over the next several years, these models will help to test if COVID-19 severity is beginning to attenuate in the ways our model predicts, and to predict the disease.

scholarly journals General mathematical model of the roadmap fight against cartels

2019 ◽  
pp. 36-41
Author(s):  
Yu. G. Vasin ◽  
T. Yu. Rudaya
Keyword(s):  
Mathematical Model ◽  
Probabilistic Models ◽  
Proposed Model ◽  
The Social ◽  
General Mathematical Model ◽  
Road Maps ◽  
The Subject ◽  
State Programs ◽  
Constituent Elements ◽  
Forecast Function

The article offers a description of the general algorithm for the formation of a mathematical (stochastic) model of countering cartels as a massive negative social and legal phenomenon. The specified model allows to realize (calculate) the forecast function is a necessary element of state programs (“road maps”) to counter illegal manifestations. The formation of a mathematical model should be preceded by a stage of theoretical modeling, which establishes the constituent elements and relationships of the subject of study. It is proved that the prognostic model of the social-legal phenomenon should be based on the provisions of probability theory. A specific technique is proposed for calculating a system of stochastic indicators (mathematical expectation and standard deviation) of the corresponding model on a single methodological basis. Proposals were made for forecasting methods in relation to quantitative probabilistic models of fighting cartels. The importance of the constant (periodic) verification of the initial statistical data and the correct interpretation of the results of prediction calculations is substantiated. The directions of the practical use of the proposed model for the creation of a comparative monitoring system for the cartelization of the EAEU product markets are proposed.

scholarly journals A mathematical model of bone remodeling dynamics for normal bone cell populations and myeloma bone disease

2010 ◽  
Vol 5 (1) ◽  
pp. 28 ◽  
Author(s):  
Bruce P Ayati ◽  
Claire M Edwards ◽  
Glenn F Webb ◽  
John P Wikswo
Keyword(s):  
Mathematical Model ◽  
Bone Remodeling ◽  
Bone Disease ◽  
Bone Cell ◽  
Cell Populations ◽  
Myeloma Bone Disease ◽  
Normal Bone

scholarly journals Analysis of the mitigation strategies for COVID-19: from mathematical modelling perspective

2020 ◽  
Author(s):  
S. M. Kassa ◽  
H.J.B. Njagarah ◽  
Y. A. Terefe
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Backward Bifurcation ◽  
Mitigation Strategies ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Proposed Model ◽  
The Future ◽  
Parameter Values ◽  
Disease Free

AbstractIn this article, a mathematical model for the transmission of COVID-19 disease is formulated and analysed. It is shown that the model exhibits a backward bifurcation at ℛ0 = 1 when recovered individuals do not develop a permanent immunity for the disease. In the absence of reinfection, it is proved that the model is without backward bifurcation and the disease free equilibrium is globally asymptotically stable for ℛ0 < 1. By using available data, the model is validated and parameter values are estimated. The sensitivity of the value of ℛ0 to changes in any of the parameter values involved in its formula is analysed. Moreover, various mitigation strategies are investigated using the proposed model and it is observed that the asymptomatic infectious group of individuals may play the major role in the re-emergence of the disease in the future. Therefore, it is recommended that in the absence of vaccination, countries need to develop capacities to detect and isolate at least 30% of the asymptomatic infectious group of individuals while treating in isolation at least 50% of symptomatic patients to control the disease.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

A Mathematical Model for the Anaerobic Digestion Process Applied to a Mixture of Night Soil and Septic Tank Sludge

1986 ◽  
Vol 18 (7-8) ◽  
pp. 239-248 ◽  
Author(s):  
Sung Ryong Ha ◽  
Dwang Ho Lee ◽  
Sang Eun Lee
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Biomass Concentration ◽  
Gas Production ◽  
Septic Tank ◽  
Volatile Acid ◽  
Hydraulic Residence Time ◽  
Anaerobic Digestion Process ◽  
Digestion Process ◽  
Proposed Model

Laboratory scale experiments were conducted to develop a mathematical model for the anaerobic digestion of a mixture of night soil and septic tank sludge. The optimum mixing ratio by volume between night soil and septic tank sludge was found to be 7:3. Due to the high solids content in the influent waste, mixed-liquor volatile suspended solids (MLVSS) was not considered to be a proper parameter for biomass concentration, therefore, the active biomass concentration was estimated based on deoxyribonucleic acid (DNA) concentration in the reactor. The weight ratio between acidogenic bacteria and methanogenic bacteria in the mixed culture of a well-operated anaerobic digester was approximately 3:2. The proposed model indicates that the amount of volatile acid produced and the gas production rate can be expressed as a function of hydraulic residence time (HRT). The kinetic constants of the two phases of the anaerobic digestion process were determined, and a computer was used to simulate results using the proposed model for the various operating parameters, such as BOD5 and volatile acid concentrations in effluent, biomass concentrations and gas production rates. These were consistent with the experimental data.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

scholarly journals Stability Analysis and Existence of Solutions for a Modified SIRD Model of COVID-19 with Fractional Derivatives

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1431
Author(s):  
Bilal Basti ◽  
Nacereddine Hammami ◽  
Imadeddine Berrabah ◽  
Farid Nouioua ◽  
Rabah Djemiat ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Existence And Uniqueness ◽  
Fractional Derivatives ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Biological Models ◽  
Uniqueness Of Solutions ◽  
Caputo Fractional Derivatives ◽  
Single Form ◽  
Stability Results

This paper discusses and provides some analytical studies for a modified fractional-order SIRD mathematical model of the COVID-19 epidemic in the sense of the Caputo–Katugampola fractional derivative that allows treating of the biological models of infectious diseases and unifies the Hadamard and Caputo fractional derivatives into a single form. By considering the vaccine parameter of the suspected population, we compute and derive several stability results based on some symmetrical parameters that satisfy some conditions that prevent the pandemic. The paper also investigates the problem of the existence and uniqueness of solutions for the modified SIRD model. It does so by applying the properties of Schauder’s and Banach’s fixed point theorems.

scholarly journals Content Dependent Representation Selection Model for Systems Based on MPEG DASH

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1843
Author(s):  
Jelena Vlaović ◽  
Snježana Rimac-Drlje ◽  
Drago Žagar
Keyword(s):  
Mathematical Model ◽  
Spatial Information ◽  
Relevant Literature ◽  
Video Quality ◽  
Similarity Index ◽  
Video Encoding ◽  
Adaptation Algorithm ◽  
Subjective Testing ◽  
Proposed Model ◽  
The Mathematical Model

A standard called MPEG Dynamic Adaptive Streaming over HTTP (MPEG DASH) ensures the interoperability between different streaming services and the highest possible video quality in changing network conditions. The solutions described in the available literature that focus on video segmentation are mostly proprietary, use a high amount of computational power, lack the methodology, model notation, information needed for reproduction, or do not consider the spatial and temporal activity of video sequences. This paper presents a new model for selecting optimal parameters and number of representations for video encoding and segmentation, based on a measure of the spatial and temporal activity of the video content. The model was developed for the H.264 encoder, using Structural Similarity Index Measure (SSIM) objective metrics as well as Spatial Information (SI) and Temporal Information (TI) as measures of video spatial and temporal activity. The methodology that we used to develop the mathematical model is also presented in detail so that it can be applied to adapt the mathematical model to another type of an encoder or a set of encoding parameters. The efficiency of the segmentation made by the proposed model was tested using the Basic Adaptation algorithm (BAA) and Segment Aware Rate Adaptation (SARA) algorithm as well as two different network scenarios. In comparison to the segmentation available in the relevant literature, the segmentation based on the proposed model obtains better SSIM values in 92% of cases and subjective testing showed that it achieves better results in 83.3% of cases.

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