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The aim of this paper is to provide a gradient clustering algorithm in its complete form, suitable for direct use without requiring a deeper statistical knowledge. The values of all parameters are effectively calculated using optimizing procedures. Moreover, an illustrative analysis of the meaning of particular parameters is shown, followed by the effects resulting from possible modifications with respect to their primarily assigned optimal values. The proposed algorithm does not demand strict assumptions...
A computational framework for testing the effects of cytotoxic molecules, specific to a
given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The
model is based on a cellular automaton to describe tumour cell states transitions from
proliferation to death. It is coupled with a model describing the tumour vasculature and
its adaptation to the blood rheological constraints when alterations are induced by VDAs
treatment....
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...
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....
We present a Monte Carlo technique for sampling from the
canonical distribution in molecular dynamics. The method is built upon
the Nosé-Hoover constant temperature formulation and the generalized
hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods
only the thermostat degree of freedom is stochastically resampled
during a Monte Carlo step.
A simple model of biological evolution of community food webs is introduced. This model
is based on the niche model, which is known to generate model food webs that are very
similar to empirical food webs. The networks evolve by speciation and extinction.
Co-extinctions due to the loss of all prey species are found to play a major role in
determining the longterm shape of the food webs. The central aim is to design the model
such that the characteristic...
The reduced basis element method is a new approach for approximating
the solution of problems described by partial differential equations.
The method takes its roots in domain decomposition methods and
reduced basis discretizations. The basic idea is to first decompose
the computational domain into a series of subdomains that are deformations
of a few reference domains (or generic computational parts).
Associated with each reference domain are precomputed solutions
corresponding to the same...
We present in this paper a stability study concerning finite volume schemes
applied to the two-dimensional Maxwell system, using rectangular or triangular
meshes. A stability condition is proved for the
first-order upwind scheme on a rectangular mesh. Stability comparisons
between the Yee scheme and the finite volume formulation are proposed.
We also compare the stability domains obtained when considering the
Maxwell system and the convection equation.
We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. Compt. Rend. Math. Anal. Num. 339 (2004) 667–672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, e.g. random variables obeying various probability distributions. A priori convergence analysis...
We introduce a new tool for obtaining efficient a posteriori estimates of errors of approximate solutions of differential equations the data of which depend linearly on random parameters. The solution method is the stochastic Galerkin method. Polynomial chaos expansion of the solution is considered and the approximation spaces are tensor products of univariate polynomials in random variables and of finite element basis functions. We derive a uniform upper bound to the strengthened Cauchy-Bunyakowski-Schwarz...
We propose two models of vessel impairment in the process of tumour angiogenesis and we consider three types of treatment: standard chemotherapy, antiangiogenic treatment and a combined treatment. The models are based on the idea of Hahnfeldt et al. that the carrying capacity for any solid tumour depends on its vessel density. In the models proposed the carrying capacity also depends on the process of vessel impairment. In the first model a logistic type equation is used to describe the neoplastic...
We give results for the approximation of a laminate with
varying volume fractions for multi-well energy minimization
problems modeling martensitic crystals that
can undergo either an orthorhombic
to monoclinic or a cubic to tetragonal transformation.
We construct energy minimizing sequences of deformations which satisfy
the corresponding boundary condition, and we
establish a series of error bounds in terms of the elastic energy
for the approximation of the limiting macroscopic
deformation and...
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