scholarly journals Stability Analysis of Mathematical Model including Pathogen-Specific Immune System Response with Fractional-Order Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Bahatdin Daşbaşı
Keyword(s):  
Mathematical Model ◽  
T Cells ◽  
Immune System ◽  
Qualitative Analysis ◽  
Fractional Order ◽  
Memory T Cells ◽  
Equilibrium Points ◽  
System Response ◽  
Proposed Model ◽  
The Mathematical Model

In this study, the mathematical model examined the dynamics between pathogen and specific immune system cells (memory T cells) for diseases such as chronic infection and cancer in which nonspecific immune system cells are inadequate to destroy the pathogen and has been suggested by using a system of the fractional-order differential equation with multi-orders. Qualitative analysis of the proposed model reveals the equilibrium points giving important ideas about the proliferation of the pathogen and memory T cells. According to the results of this analysis, the possible scenarios are as follows: the absence of both pathogen and memory T cells, only the existence of pathogen, and the existence of both pathogen and memory T cells. The qualitative analysis of the proposed model has expressed the persistent situations of the disease where the memory T cells either do not be able to respond to the pathogen or continue to exist with the disease-causing pathogen in the host. Results of this analysis are supported by numerical simulations. In the simulations, the time-dependent size of the tumor population under the pressure of the memory T cells was tried to be estimated.

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.

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 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.

scholarly journals An Optimized Mathematical Model for Items Supplies Planning of a Logistic System

2016 ◽  
Vol 10 (10) ◽  
pp. 133
Author(s):  
Mohammad Ali Nasiri Khalili ◽  
Mostafa Kafaei Razavi ◽  
Morteza Kafaee Razavi
Keyword(s):  
Mathematical Model ◽  
Mixed Integer ◽  
Logistics System ◽  
Proposed Model ◽  
Multiple Objective Decision Making ◽  
System Requirements ◽  
Purchasing Logistics ◽  
The Cost ◽  
The Mathematical Model ◽  
First Time

Items supplies planning of a logistic system is one of the major issue in operations research. In this article the aim is to determine how much of each item per month from each supplier logistics system requirements must be provided. To do this, a novel multi objective mixed integer programming mathematical model is offered for the first time. Since in logistics system, delivery on time is very important, the first objective is minimization of time in delivery on time costs (including lack and maintenance costs) and the cost of purchasing logistics system. The second objective function is minimization of the transportation supplier costs. Solving the mathematical model shows how to use the Multiple Objective Decision Making (MODM) can provide the ensuring policy and transportation logistics needed items. This model is solved with CPLEX and computational results show the effectiveness of the proposed model.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

scholarly journals The impact of body mass index on adaptive immune cells in the human bone marrow

2020 ◽  
Author(s):  
Luca Pangrazzi ◽  
Erin Naismith ◽  
Carina Miggitsch ◽  
Jose’ Antonio Carmona Arana ◽  
Michael Keller ◽  
...  
Keyword(s):  
Body Mass Index ◽  
Bone Marrow ◽  
T Cells ◽  
Immune System ◽  
T Cell ◽  
Immune Cells ◽  
Memory T Cells ◽  
T Cell Subsets ◽  
Adaptive Immune ◽  
Adaptive Immune Cells

Abstract Background. Obesity has been associated with chronic inflammation and oxidative stress. Both conditions play a determinant role in the pathogenesis of age-related diseases, such as immunosenescence. Adipose tissue can modulate the function of the immune system with the secretion of molecules influencing the phenotype of immune cells. The importance of the bone marrow (BM) in the maintenance of antigen-experienced adaptive immune cells has been documented in mice. Recently, some groups have investigated the survival of effector/memory T cells in the human BM. Despite this, whether high body mass index (BMI) may affect immune cells in the BM and the production of molecules supporting the maintenance of these cells it is unknown.Methods. Using flow cytometry, the frequency and the phenotype of immune cell populations were measured in paired BM and PB samples obtained from persons with different BMI. Furthermore, the expression of BM cytokines was assessed. The influence of cytomegalovirus (CMV) on T cell subsets was additionally considered, dividing the donors into the CMV- and CMV+ groups.Results. Our study suggests that increased BMI may affect both the maintenance and the phenotype of adaptive immune cells in the BM. While the BM levels of IL-15 and IL-6, supporting the survival of highly differentiated T cells, and oxygen radicals increased in overweight persons, the production of IFNγ and TNF by CD8+ T cells was reduced. In addition, the frequency of B cells and CD4+ T cells positively correlated with BMI in the BM of CMV- persons. Finally, the frequency of several T cell subsets, and the expression of senescence/exhaustion markers within these subpopulations, were affected by BMI. In particular, the levels of bona fide memory T cells may be reduced in overweight persons.Conclusion. Our work suggests that, in addition to aging and CMV, obesity may represent an additional risk factor for immunosenescence in adaptive immune cells. Metabolic interventions may help in improving the fitness of the immune system in the elderly.

scholarly journals A Cognitive Computational Model Inspired by the Immune System Response

2014 ◽  
Vol 2014 ◽  
pp. 1-15
Author(s):  
Mohamed Abdo Abd Al-Hady ◽  
Amr Ahmed Badr ◽  
Mostafa Abd Al-Azim Mostafa
Keyword(s):  
Immune System ◽  
Computational Model ◽  
Cognitive Architecture ◽  
Intelligent Agent ◽  
System Response ◽  
Danger Theory ◽  
Proposed Model ◽  
Immune System Response ◽  
Fuzzy State

The immune system has a cognitive ability to differentiate between healthy and unhealthy cells. The immune system response (ISR) is stimulated by a disorder in the temporary fuzzy state that is oscillating between the healthy and unhealthy states. However, modeling the immune system is an enormous challenge; the paper introduces an extensive summary of how the immune system response functions, as an overview of a complex topic, to present the immune system as a cognitive intelligent agent. The homogeneity and perfection of the natural immune system have been always standing out as the sought-after model we attempted to imitate while building our proposed model of cognitive architecture. The paper divides the ISR into four logical phases: setting a computational architectural diagram for each phase, proceeding from functional perspectives (input, process, and output), and their consequences. The proposed architecture components are defined by matching biological operations with computational functions and hence with the framework of the paper. On the other hand, the architecture focuses on the interoperability of main theoretical immunological perspectives (classic, cognitive, and danger theory), as related to computer science terminologies. The paper presents a descriptive model of immune system, to figure out the nature of response, deemed to be intrinsic for building a hybrid computational model based on a cognitive intelligent agent perspective and inspired by the natural biology. To that end, this paper highlights the ISR phases as applied to a case study on hepatitis C virus, meanwhile illustrating our proposed architecture perspective.

A High Performance Model for Task Allocation in Distributed Computing System Using K-Means Clustering Technique

2018 ◽  
Vol 9 (3) ◽  
pp. 1-23 ◽  
Author(s):  
Harendra Kumar ◽  
Nutan Kumari Chauhan ◽  
Pradeep Kumar Yadav
Keyword(s):  
Mathematical Model ◽  
Distributed Computing ◽  
High Performance ◽  
Computing System ◽  
Performance Model ◽  
Communication Costs ◽  
Clustering Technique ◽  
Proposed Model ◽  
Two Stages ◽  
The Mathematical Model

Tasks allocation is an important step for obtaining high performance in distributed computing system (DCS). This article attempts to develop a mathematical model for allocating the tasks to the processors in order to achieve optimal cost and optimal reliability of the system. The proposed model has been divided into two stages. Stage-I, makes the ‘n' clusters of set of ‘m' tasks by using k-means clustering technique. To use the k-means clustering techniques, the inter-task communication costs have been modified in such a way that highly communicated tasks are clustered together to minimize the communication costs between tasks. Stage-II, allocates the ‘n' clusters of tasks onto ‘n' processors to minimize the system cost. To design the mathematical model, executions costs and inter tasks communication costs have been taken in the form of matrices. To test the performance of the proposed model, many examples are considered from different research papers and results of examples have compared with some existing models.

scholarly journals Research on Chaos Response of the Nonlinear Vibration System of Giant Magnetostrictive Actuator

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Hongbo Yan ◽  
Yu Niu ◽  
Hong Gao ◽  
Hongbo Hao
Keyword(s):  
Mathematical Model ◽  
Amplitude Spectrum ◽  
Experimental Simulation ◽  
System Response ◽  
Threshold Condition ◽  
Vibration System ◽  
Chaotic Response ◽  
Magnetostrictive Actuator ◽  
Excitation Force ◽  
The Mathematical Model

In the present study, the chaotic response of the nonlinear magnetostrictive actuator (GMA) vibration system is investigated. The mathematical model of the nonlinear GMA vibration system is established according to J-A hysteresis nonlinear model, quadratic domain rotation model, Newton’s third law, and principle of GMA structural dynamics by analyzing the working principle of GMA. Then, the Melnikov function method is applied to the threshold condition of the chaotic response of the system to obtain the sense of Smale horseshoe transformation. Furthermore, the mathematical model is solved to investigate the system response to the excitation force and frequency. Accordingly, the corresponding displacement waveform, phase plane trajectory, Poincaré map, and amplitude spectrum are obtained. The experimental simulation is verified using Adams software. The obtained results show that the vibration equation of the nonlinear GMA vibration system has nonlinear and complex motion characteristics with different motion patterns. It is found that the vibration characteristics of the system can be controlled through adjusting the excitation force and frequency.

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