Robust development of biological organisms in the presence of genetic and epi-genetic
perturbations is important for time spans short relative to evolutionary time. Gradients of receptor
bound signaling morphogens are responsible for patterning formation and development. A
variety of inhibitors for reducing ectopic signaling activities are known to exist and their specific
role in down-regulating the undesirable ectopic activities reasonably well understood. However,
how a developing organism manages to adjust inhibition/stimulation in response to genetic and/or
environmental changes remains to be uncovered. The need to adjust for ectopic signaling activities
requires the presence of one or more feedback mechanisms to stimulate the needed adjustment.
As the ultimate effect of many inhibitors (including those of the nonreceptor type) is to reduce the
availability of signaling morphogens for binding with signaling receptors, a negative feedback on
signaling morphogen synthesis rate based on a root-mean-square measure of the spatial distribution
of signaling concentration offers a simple approach to robusness and has been demonstrated
to be effective in a proof-of-concept implementation. In this paper, we complement the previous
investigation of feedback in steady state by examining the effect of one or more feedback
adjustments during the transient phase of the biological development.
An arbitrary resolution video coding method based on compressive sampling is pro-posed.
In this method, a video is coded using compressive measurements. The compressive
measurements are made on videos of high resolution. The measurements may be used to reconstruct
the video at the same resolution as the original video, and any subset of the measurements
can be used to reconstruct video at lower resolution with a lower complexity. Video coding with
arbitrary solution has important application in mobile video transmission.
We propose a mathematical model and immersed boundary method for the growth
and breakup of diatom chains. Diatom chains are treated as zero thickness open curves thanks to
their small aspect ratio. The growth of the chain is modelled by adding small pieces of diatoms
at the two end points while the breakup is done by removing a small piece in the middle of the
chain. Numerical experiments are carried out to investigate the effects of growth and breakup
on the sedimentation rate of diatom chains. Simulations of multiple diatom chains show that
sedimentation rate is highly dependent on diatoms' spatial distribution. The results can be used
to explain the observations that diatoms often form chain-like structures in natural habitats.
Since the successful construction of the so-called double negative metamaterials in
2000, there has been a growing interest in studying metamaterials across many disciplinaries. In
this paper, we present a survey of recent progress in metamaterials and its applications from the
mathematical point of view. Due to the great amount of papers published in this area, here we
mainly discuss those issues interested to us. Our main goal is to attract more mathematicians to
study this fascinating subject.
This paper is devoted to the presentation and analysis of some linear and quadratic
finite volume (FV) schemes for elliptic problems with singular solutions due to the non-smoothness
of the domain. Our FV schemes are constructed over specially-designed graded triangular meshes.
We provide sharp parameter selection criteria for the graded mesh, such that both the linear and
quadratic FV schemes achieve the optimal convergence rate approximating singular solutions in
H¹. In addition, we show that on the same mesh, a linear FV scheme obtains the optimal rate of
convergence in L². Numerical tests are provided to verify the analysis.
In this paper, we discuss the time optimal control problems governed by heat equation.
The variational discretization concept is introduced for the approximation of the control, and the
semi-discrete finite element method is applied for the controlled heat equation. We prove optimal
a priori error estimate for the optimal time T, and quasi-optimal estimates for the optimal control
u, the related state y and adjoint state p.
MRICE-E model is a new integrated assessment model (IAM) applied on evaluating
climate change and the loss of economic welfare. Its economic module for China adopts a dynamic,
nonlinear and multi-sectional CGE model. In this paper, we are concerned with the effects of
perturbations in input-output coefficients in the CGE model. In the analytical framework, some
concepts such as the Lyapunov exponent and the condition number from dynamic system and
numerical linear algebra are employed to measure the errors brought by perturbations of the
I-O coefficients. We finally derive the upper bound estimation of errors growth through time.
To reduce the effects of the possible perturbations, some suggestions about categorization of the
industrial sectors are given in the end.
Convection-diffusion equations provide the basis for describing heat and mass transfer
phenomena as well as processes of continuum mechanics. An unsteady problem is considered
for a convection and a space-fractional diffusion equation in a bounded domain. A first-order
evolutionary equation containing a fractional power of an elliptic operator of second order is
studied for general boundary conditions of Robin type. Finite element approximation in space
is employed. To construct approximation in time, regularized two-level schemes are used. The
numerical implementation is based on solving the equation with the fractional power of the elliptic
operator using an auxiliary Cauchy problem for a pseudo-parabolic equation. The results of
numerical experiments are presented for a model two-dimensional problem.
In this paper we design a modified version of FVCOM by adopting hybrid meshes and
shifting the placement of velocity variables from the centroids of elements to the middle points of
edges. A simplified version of geostrophic equation is solved to test the new scheme, and illustrates
a nearly uniform error distribution.
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