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A possible alternative which brings together computational portability with mathematical tractability is represented by neuron astrocyte mass modeling of dynamical interactions between neurons and astrocytes populations.
In this appendix, we would like to show that the approach proposed in details for ZF can be also applied for MSE criterion; however, the mathematical tractability is highly demanding in that case.
The unconstrained multiplicative model, often used in theoretical studies because of its mathematical tractability, is not a realistic model.
The simplest, and one of the first and most widely used mathematical models for the HIV epidemic, because of its relative mathematical tractability, is the "Anderson-May" model[ 23- 25].
Importantly, we show that the unconstrained multiplicative (Risch) model, often used in theoretical studies because of its mathematical tractability, is not a realistic model as impossible probabilities of disease are implied.
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Building on this, let us define P Int as the probability that an arrival of a PU interrupts the analyzed call.5 As an approximation and for the sake of mathematical tractability, it is considered that the interruption probability is independent for each individual user.6 As shown below, with this approximation, the call interruption process of SUs due the arrival of PUs is a Poisson process.
Mathematical tractability, which is undoubtedly a good in itself, should not lead us to overlook this fact.
Stochastic leaky integrate-and-fire (LIF) neuronal models are a good compromise between biophysical realism and mathematical tractability, and are commonly applied as theoretical tools to study properties of real neuronal systems.
Second, tractability is not an issue.
Assuming (p = 0) for mathematical tractability, the IS scheme is expressed as overline{u_{rho ( i,l ) }} = textstylebegin{cases} u_{i}& ( mbox{if } exp ( p_{i,l} ) u_{i} - u_{rho ( i,l ) } ge 0 ) u_{rho ( i,l ) }& ( mathrm{otherwise} ).
This model, which has been chosen partly because of mathematical tractability, has also been used by Bartoszyński et al. [ 17] and Plevritis et al. [ 18].
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