scholarly journals A mathematical investigation of different growth rates in simultaneous tumors at two distant sites

2021 ◽  
Author(s):  
Farjana Aktar
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Simulated Annealing Algorithm ◽  
The Other ◽  
Sensitivity Analyses ◽  
Small Tumour ◽  
System A ◽  
Set Up ◽  
Parameter Values ◽  
The Mathematical Model

Experimental data demonstrates that simultaneous injection of cancer cells at two distinct sites often results in one large and one small tumour. Unbalanced tumour-stimulating inflammation is hypothesized to be the cause of this growth rate separation, causing one tumour to grow faster than the other. Here, a mathematical model for immune recruitment and competition between two cancer sites is developed to explore the role of tumour-promoting inflammation in the observed growth rate separation. Due to the experimental set-up, immune predation may be neglected, focusing the model on tumour-promoting immune actions. A new mathematical model with localized immune recruitment and competition between the two cancer sites is developed using a multi-compartment ODE system. A simulated annealing algorithm is used to fit the model to control data (one tumour burden). Stability and parameter sensitivity analyses are used to explore the mathematical model and parameter space. Next, the two-tumour scenario is predicted by testing parameter values tied to possible biological mechanisms of action. The model predicts that indeed inflammation may be a contributor to growth rate separation observed in simultaneous tumour growth, if one site is pre-inflamed compared to the other.

scholarly journals A mathematical investigation of different growth rates in simultaneous tumors at two distant sites

2021 ◽  
Author(s):  
Farjana Aktar
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Simulated Annealing Algorithm ◽  
The Other ◽  
Sensitivity Analyses ◽  
Small Tumour ◽  
System A ◽  
Set Up ◽  
Parameter Values ◽  
The Mathematical Model

Experimental data demonstrates that simultaneous injection of cancer cells at two distinct sites often results in one large and one small tumour. Unbalanced tumour-stimulating inflammation is hypothesized to be the cause of this growth rate separation, causing one tumour to grow faster than the other. Here, a mathematical model for immune recruitment and competition between two cancer sites is developed to explore the role of tumour-promoting inflammation in the observed growth rate separation. Due to the experimental set-up, immune predation may be neglected, focusing the model on tumour-promoting immune actions. A new mathematical model with localized immune recruitment and competition between the two cancer sites is developed using a multi-compartment ODE system. A simulated annealing algorithm is used to fit the model to control data (one tumour burden). Stability and parameter sensitivity analyses are used to explore the mathematical model and parameter space. Next, the two-tumour scenario is predicted by testing parameter values tied to possible biological mechanisms of action. The model predicts that indeed inflammation may be a contributor to growth rate separation observed in simultaneous tumour growth, if one site is pre-inflamed compared to the other.

Experimental test of vision-based navigation and system identification of an unmanned underwater survey vehicle (SAGA) for the yaw motion

2019 ◽  
Vol 41 (8) ◽  
pp. 2160-2170 ◽  
Author(s):  
Seda Karadeniz Kartal ◽  
M. Kemal Leblebicioglu ◽  
Emre Ege
Keyword(s):  
Mathematical Model ◽  
System Identification ◽  
Navigation System ◽  
Unknown Parameters ◽  
Navigation Data ◽  
State Measurement ◽  
Suitable Combination ◽  
Set Up ◽  
Parameter Values ◽  
The Mathematical Model

In this study, a nonlinear mathematical model for an unmanned underwater survey vehicle (SAGA) is obtained. The structure of the mathematical model of the vehicle comes from a Newton–Euler formulation. The yaw motion is realized by a suitable combination of right and left thrusters. The navigation problem is solved by using the inertial navigation system and vision-based measurements together. These are integrated to more accurately obtain navigation data for the vehicle. In addition, the magnetic compass is used to support the attitude information of the vehicle. A pool experimental set-up is designed to test the navigation system. Performance of the resultant navigation system can be analysed by creating suitable system state, measurement and noise models. The navigational data for the vehicle has been improved using a Kalman filter. The mathematical model of the vehicle includes some unknown parameters such as added mass and damping coefficients. It is not possible to determine all the parameter values as their effects on the state of the system are usually negligible. On the other hand, most of the ‘important’ parameters are obtained based on a system identification study of the vehicle using this estimated navigational data for coupled motion. This study is performed in a MATLAB/Simulink environment.

Research on Dynamic Balance Method of Precision Centrifuge

2014 ◽  
Vol 945-949 ◽  
pp. 777-780
Author(s):  
Tao Liu ◽  
Yong Xu ◽  
Bo Yuan Mao
Keyword(s):  
Mathematical Model ◽  
Balance Control ◽  
Dynamic Balance ◽  
Dynamic Balancing ◽  
Structure Characteristics ◽  
Balance System ◽  
Simulation Results ◽  
Set Up ◽  
System Controller ◽  
The Mathematical Model

Firstly, according to the structure characteristics of precision centrifuge, the mathematical model of its dynamic balancing system was set up, and the dynamic balancing scheme of double test surfaces, double emendation surfaces were established. Then the dynamic balance system controller of precision centrifuge was designed. Simulation results show that the controller designed can completely meet the requirements of precision centrifuge dynamic balance control system.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

Condition Monitoring Technology for Connecting Part and Sliding Part of Reciprocating Compressor

2017 ◽  
Author(s):  
Yoshifumi Mori ◽  
Takashi Saito ◽  
Yu Mizobe
Keyword(s):  
Mathematical Model ◽  
Natural Frequencies ◽  
Error Function ◽  
Connecting Rod ◽  
Value Analysis ◽  
Before And After ◽  
The Difference ◽  
Bending Modes ◽  
Parameter Values ◽  
The Mathematical Model

We focused on vibration characteristics of reciprocating compressors and constructed the mathematical model to calculate the natural frequencies and modes for crank angles and proposed a method to estimate the degree and the suspicious portion of failure by difference of temporal parameter values obtained using measuring data in operation and the mathematical model. In this paper, according to the proposed method, a case study is carried out using the field data, where the data were acquired before and after the failures occurred in the connecting parts of connecting rod, to prospect the difference between each parameter value for two operating states. Inspecting resonant characteristics each in the frequency response data relating to the natural frequencies for bending modes of the piston rod, we determined two resonant frequencies, which could correspond to the 1st and 2nd mode about bending of the piston rod. To equate the calculated each natural frequency from eigen value analysis based on the proposed model with each resonant frequency, we define the error function for the identified problem, namely optimum problem. In the identified results, it is found that some parameter values have much difference and the corresponding failure could occur around the connecting rod. We could show the possibility to detect both the change of the parameter values and the deterioration parts for two different kinds of the operating states by our proposed method.

A guaranteed deterministic approach to margining on exchange-traded derivatives market: Numerical experiment

2021 ◽  
Vol 57 (4) ◽  
pp. 76
Author(s):  
Sergey Smirnov
Keyword(s):  
Mathematical Model ◽  
Risk Management ◽  
Critical Role ◽  
Deterministic Approach ◽  
Computational Framework ◽  
Modern Approach ◽  
System A ◽  
Lipschitz Constants ◽  
Isaacs Equations ◽  
The Mathematical Model

The article discusses a modern approach to risk management of the central counterparty,primarily the issue of the sufficiency of its financial resources, including the provision of clearingmembers, the capital of the central counterparty and the mutual liability fund. The main subject is the margining system, responsible for an adequate level of collateral for clearing members, that plays critical role in risk management, being the vanguard in protecting against losses associated with default by clearing members and the most sensitive to market risk part of the central counterparty’s skin of the game. A system of margining a portfolio of options and futures in the derivatives market is described, with default management based on the methodology proposed by a number of inventors, registered in 2004. For this system, a mathematical model of margining (i.e. determining the required level of the collateral) is built, based on the ideology of a guaranteed deterministic approach to superhedging: Bellman–Isaacs equations are derived from the economic meaning of the problem. A form of these equations, convenient for calculations, is obtained. Lipschitz constants for the solutions of Bellman–Isaacs equations are estimated. A computational framework for efficient numerical solution of these equations is created. Numerical experiments are carried out on some model examples to demonstrate the efficiency of the system. These experiments also show practical implications of marginsubadditivity — a crucial property of the mathematical model.

Effect of superfused insulin on cerebral cortical glucose utilization in awake goats

1987 ◽  
Vol 253 (4) ◽  
pp. E418-E427
Author(s):  
D. A. Pelligrino ◽  
D. J. Miletich ◽  
R. F. Albrecht
Keyword(s):  
Mathematical Model ◽  
Cerebrospinal Fluid ◽  
Metabolic Regulation ◽  
Glucose Utilization ◽  
The Other ◽  
Insulin Administration ◽  
Cortical Tissue ◽  
Control Tissue ◽  
The Mathematical Model ◽  
Test Control

The effect on cortical cerebral glucose utilization (CMRglu) of intracerebral insulin administration in awake goats was studied. The insulin was superfused in a mock cerebrospinal fluid (CSF) solution employing chronically implanted cranial windows. Two windows were implanted bilaterally: one window over an equivalent portion of each parietal cortex. With one window used to deliver insulin/CSF and the other used to simultaneously deliver CSF alone (control), changes in CMRglu were assessed using a modification of a sequential 2-[3H]- then 2-[14C]deoxy-D-glucose (2DG) technique originally described by Altenau and Agranoff (Brain Res. 153: 375-381, 1978). Initial experiments employing 125I-insulin demonstrated that the superfusion procedure increased insulin levels only in the outer 1 mm of cortical tissue exposed to insulin containing perfusate. Additional preliminary evaluations, using conditions known to alter CMRglu, generally established that present methods were adequate to induce and detect CMRglu changes. However, it was also shown experimentally and using a mathematical model that 2-[3H]DG test/control tissue ratios could be influenced by subsequent changes in CMRglu and the dephosphorylation rate. Thus 3H ratios could not be used to establish preexperimental test/control CMRglu relationships as the originally devised model assumed but could be employed to indicate changes in dephosphorylation. The mathematical model allowed for improved estimates of CMRglu changes from 2-[14C]DG/2-[3H]DG test over control tissue ratios. Even with these corrections, insulin was estimated to cause no more than an 8-15% increase in cortical CMRglu. A very limited role for insulin, at least in cerebral cortical metabolic regulation, is thus indicated.

Theoretical and Experimental Study of the Dynamics of the Tripod-Ball Sliding Joint With Clearance

2001 ◽  
Author(s):  
Jia Xiaohong ◽  
Ji Linhong ◽  
Jin Dewen ◽  
Zhang Jichuan
Keyword(s):  
Mathematical Model ◽  
Equations Of Motion ◽  
Experimental Studies ◽  
Active System ◽  
New Concepts ◽  
Sliding Joint ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model ◽  
Kane Method

Abstract Clearance is inevitable in the kinematic joints of mechanisms. In this paper the dynamic behavior of a crank-slider mechanism with clearance in its tripod-ball sliding joint is investigated theoretically and experimentally. The mathematical model of this new-type joint is established, and the new concepts of basal system and active system are put forward. Based on the mode-change criterion established in this paper, the consistent equations of motion in full-scale are derived by using Kane method. The experimental rig was set up to measure the effects of the clearance on the dynamic response. Corresponding experimental studies verify the theoretical results satisfactorily. In addition, due to the nonlinear elements in the improved mathematical model of the joint with clearance, the chaotic responses are found in numerical simulation.

scholarly journals Multiple states for flow through a collapsible tube with discontinuities

2014 ◽  
Vol 761 ◽  
pp. 105-122 ◽  
Author(s):  
A. Siviglia ◽  
M. Toffolon
Keyword(s):  
Past History ◽  
Steady State Solution ◽  
External Pressure ◽  
The Other ◽  
Critical Conditions ◽  
Actual State ◽  
Collapsible Tube ◽  
Set Up ◽  
Parameter Values ◽  
Flow States

AbstractWe study the occurrence of the multiple steady states that flows in a collapsible tube can develop under the effect of: (i) geometrical alterations (e.g. stenosis), (ii) variations of the mechanical properties of the tube wall, or (iii) variations of the external pressure acting on the conduit. Specifically, if the approaching flow is supercritical, two steady flow states are possible in a restricted region of the parameter space: one of these flow states is wholly supercritical while the other produces an elastic jump that is located upstream of the variation. In the latter case the flow undergoes a transition through critical conditions in the modified segment of the conduit. Both states being possible, the actual state is determined by the past history of the system, and the parameter values show a hysteretic behaviour when shifting from one state to the other. First we set up the problem in a theoretical framework assuming stationary conditions, and then we analyse the dynamics numerically in a one-dimensional framework. Theoretical considerations suggest that the existence of multiple states is associated with non-uniqueness of the steady-state solution, which is confirmed by numerical simulations of the fully unsteady problem.

Discussion of Seepage Calculation for Geomembrane Earthrock Dams

2013 ◽  
Vol 740 ◽  
pp. 530-534
Author(s):  
Yun Feng Peng ◽  
Kun Jiang
Keyword(s):  
Mathematical Model ◽  
Permeability Coefficient ◽  
The Other ◽  
Observation Data ◽  
Control Material ◽  
Feedback Analysis ◽  
Leakage Flux ◽  
Seepage Control ◽  
Sources Of Error ◽  
The Mathematical Model

As a new kind of seepage control material, the geomembrane has been widely used in earthrock dam, yet the seepage calculation of the geomembrane earthrock dam has not been studied on theory. Based on seepage mechanism in geomembrane, this thesis classifies the seepage into two types: one is permeability of geomembrane itself; the other is defect leakage flux in geomembrane. Based on feedback analysis of geomembrane earthrock dam with observation data, the permeability coefficient of geomembrane can be obtain on average, so the problem that the defects in geomembranes are difficult to ascertain is solved. At last, the sources of error in seepage calculation for geomembrane earthrock dams by method of clay equivalency were discussed. Analyzed the count error, and corrected the mathematical model.

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