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Cultivating oleaginous microalgae in specific culturing devices such as raceways is seen as a future way to produce biofuel. The complexity of this process coupling non linear biological activity to hydrodynamics makes the optimization problem very delicate. The large amount of parameters to be taken into account paves the way for a useful mathematical modeling. Due to the heterogeneity of raceways along the depth dimension regarding temperature, light intensity or nutrients availability, we adopt...
We address the issue of parameter variations in POD approximations of time-dependent problems, without any specific restriction on the form of parameter dependence. Considering a parabolic model problem, we propose a POD construction strategy allowing us to obtain some a priori error estimates controlled by the POD remainder – in the construction procedure – and some parameter-wise interpolation errors for the model solutions. We provide a thorough numerical assessment of this strategy with the...
We consider initial boundary problems of a two-chemical substances chemotaxis system. In the four-dimensional setting, it was shown that solutions exist globally in time and remain bounded if the total mass is less than , whereas the solution emanating from some initial data of large magnitude may blows up. This result can be regarded as a generalization of the well-known problem in the Keller–Segel system to higher dimensions. We will compare mathematical structures of the Keller–Segel system...
The invasive capability is fundamental in determining the malignancy of a solid tumor.
Revealing biomedical strategies that are able to partially decrease cancer invasiveness is
therefore an important approach in the treatment of the disease and has given rise to
multiple in vitro and in silico models. We here develop
a hybrid computational framework, whose aim is to characterize the effects of the
different cellular and subcellular mechanisms involved...
In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation. Moreover our scheme is able to yield a correct approximation of the effects of the source term at equilibrium. Several numerical tests are presented to show the...
There is evidence that cancer develops when cells acquire a sequence of mutations that
alter normal cell characteristics. This sequence determines a hierarchy among the cells,
based on how many more mutations they need to accumulate in order to become cancerous.
When cells divide, they exhibit telomere loss and differentiate, which defines another
cell hierarchy, on top of which is the stem cell. We propose a mutation-generation model,
which combines...
In this article we propose a model to describe the inflammatory process which occurs
during ischemic stroke. First, an introduction to some basic concepts about the biological
phenomenon is given. Then, a detailed derivation of the model and the numerical scheme
used are presented. Finally, the studies of the model robustness and sensitivity are
showed and some numerical results on the time and space evolution of the process are
presented and discussed....
The existence of a positive solution for the generalized predator-prey model for two species
are investigated. The techniques used in the paper are the elliptic theory, upper-lower solutions, maximum principles and spectrum estimates. The arguments also rely on some detailed properties of the solution of logistic equations.
An optimal control problem is studied for a predator-prey system of PDE, with a logistic
growth rate of the prey and a general functional response of the predator. The control
function has two components. The purpose is to maximize a mean density of the two species
in their habitat. The existence of the optimal solution is analyzed and some necessary
optimality conditions are established. The form of the optimal control is found in some
particular...
In this paper we deal with a model describing the evolution in time of the density of a
neural population in a state space, where the state is given by Izhikevich’s two -
dimensional single neuron model. The main goal is to mathematically describe the
occurrence of a significant phenomenon observed in neurons populations, the
synchronization. To this end, we are making the transition to phase
density population, and use Malkin theorem to calculate...
In this paper the Sigma-if artificial neural network model is considered, which is a generalization of an MLP network with sigmoidal neurons. It was found to be a potentially universal tool for automatic creation of distributed classification and selective attention systems. To overcome the high nonlinearity of the aggregation function of Sigma-if neurons, the training process of the Sigma-if network combines an error backpropagation algorithm with the self-consistency paradigm widely used in physics....
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