Difference between revisions of "Team:Paris Bettencourt/Modeling"
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<h5>Mathematical resolution</h5> | <h5>Mathematical resolution</h5> | ||
− | Simple ordinary differential equations resolution methods are used to find the solutions of the previous equations \((5)\), \((6)\), and \((7)\). | + | Simple ordinary differential equations' resolution methods are used to find the solutions of the previous equations \((5)\), \((6)\), and \((7)\). |
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We expressed the time evolution of the mother cell, differentiated cell and vitamin number. | We expressed the time evolution of the mother cell, differentiated cell and vitamin number. | ||
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As you can see, the mother cell, the differentiated cell and the vitamin numbers follow an exponential law of time. | As you can see, the mother cell, the differentiated cell and the vitamin numbers follow an exponential law of time. | ||
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− | This result seems relevant. The model does not take into account the cells death and the nutrients present in the medium. | + | This result seems relevant. The model does not take into account the cells' death and the nutrients present in the medium. |
<h3>Stochastic model</h3> | <h3>Stochastic model</h3> | ||
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We used more parameters than the deterministic model. Indeed, because of the nature of the algorithm, we need a constant rate probability distribution. | We used more parameters than the deterministic model. Indeed, because of the nature of the algorithm, we need a constant rate probability distribution. | ||
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− | In order to do a simulation with laboratory data, we modelize the time probability distribution with a normalized | + | In order to do a simulation with laboratory data, we modelize the time probability distribution with a normalized Gaussian distribution using the <a href="http://fr.mathworks.com/help/stats/normrnd.html">normrnd</a> MATLAB function. |
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For each time distribution \(i\), we use the following time probability distribution. | For each time distribution \(i\), we use the following time probability distribution. | ||
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In the program, each cell is a structure containing three elements. | In the program, each cell is a structure containing three elements. | ||
<ul> | <ul> | ||
− | <li> | + | <li>The cell type. |
<ul> | <ul> | ||
<li>1 : mother cell.</li> | <li>1 : mother cell.</li> | ||
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</ul> | </ul> | ||
</li> | </li> | ||
− | <li> | + | <li>The next event type. |
<ul> | <ul> | ||
<li>1 : a mother cell becomes a differentiated cell.</li> | <li>1 : a mother cell becomes a differentiated cell.</li> | ||
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</ul> | </ul> | ||
</li> | </li> | ||
− | <li> | + | <li>The time before the next event.</li> |
</ul> | </ul> | ||
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If the cell is a mother cell, the cell can divide or differentiate. | If the cell is a mother cell, the cell can divide or differentiate. | ||
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− | If the cell is a | + | If the cell is a differentiated cell, the cell can only divide. |
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Revision as of 19:58, 17 September 2015