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| dm:abstract.caravagna [11/01/2011 alle 07:45 (14 anni fa)] – creata Fosca Giannotti | dm:abstract.caravagna [11/01/2011 alle 07:45 (14 anni fa)] (versione attuale) – Fosca Giannotti |
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| Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. Deterministic modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), an extension of ordinary ones where the derivative of the unknown function depends on past-states of the system. Stochastic modeling is done by using non- Markovian stochastic processes, namely processes whose sojourn time in a state and the probability of a transition are not necessarily exponentially distributed. Moreover, in the literature Delay Stochastic Simulation Algorithms (DSSAs) have been proposed as extension of a well-known Stochastic Simulation Algorithm (SSA) for non-delayed models. | Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting in more compact models. Deterministic modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), an extension of ordinary ones where the derivative of the unknown function depends on past-states of the system. Stochastic modeling is done by using non- Markovian stochastic processes, namely processes whose sojourn time in a state and the probability of a transition are not necessarily exponentially distributed. Moreover, in the literature Delay Stochastic Simulation Algorithms (DSSAs) have been proposed as extension of a well-known Stochastic Simulation Algorithm (SSA) for non-delayed models. |
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| In the first part of the thesis we study different DSSAs. The first two algorithms we present treat delays by means of some scheduling policy. One algorithm is based on the idea of ``delays as durations'' | In the first part of the thesis we study different DSSAs. The first two algorithms we present treat delays by means of some scheduling policy. One algorithm is based on the idea of ''delays as durations'' approach (DDA), the other is based on a ''purely delayed'' |
| approach (DDA), the other is based on a ``purely delayed'' | |
| interpretation (PDA) of delays. We perform deterministic and stochastic analysis of a cell cycle model. Results suggest that the algorithms differ in the sense that the PDA, even in a naive definition, is more suitable than the DDA to model systems in which species involved in a delayed interaction can be involved at the same time in other interactions. We investigate the mathematical foundations of the algorithms by means of the associated Delay Chemical Master Equations (DCMEs). Result of the comparison is that both are correct with respect to their DCMEs, but they refer to systems ruled by different DCMEs. These results endorse our intuition on the difference between the algorithms. Improvements of the naive PDA lead to a definition of a more precise algorithm, the PDA with markings, which is finally combined with the DDA. | interpretation (PDA) of delays. We perform deterministic and stochastic analysis of a cell cycle model. Results suggest that the algorithms differ in the sense that the PDA, even in a naive definition, is more suitable than the DDA to model systems in which species involved in a delayed interaction can be involved at the same time in other interactions. We investigate the mathematical foundations of the algorithms by means of the associated Delay Chemical Master Equations (DCMEs). Result of the comparison is that both are correct with respect to their DCMEs, but they refer to systems ruled by different DCMEs. These results endorse our intuition on the difference between the algorithms. Improvements of the naive PDA lead to a definition of a more precise algorithm, the PDA with markings, which is finally combined with the DDA. |
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