11,092 research outputs found
Development of modularity in the neural activity of children's brains
We study how modularity of the human brain changes as children develop into
adults. Theory suggests that modularity can enhance the response function of a
networked system subject to changing external stimuli. Thus, greater cognitive
performance might be achieved for more modular neural activity, and modularity
might likely increase as children develop. The value of modularity calculated
from fMRI data is observed to increase during childhood development and peak in
young adulthood. Head motion is deconvolved from the fMRI data, and it is shown
that the dependence of modularity on age is independent of the magnitude of
head motion. A model is presented to illustrate how modularity can provide
greater cognitive performance at short times, i.e.\ task switching. A fitness
function is extracted from the model. Quasispecies theory is used to predict
how the average modularity evolves with age, illustrating the increase of
modularity during development from children to adults that arises from
selection for rapid cognitive function in young adults. Experiments exploring
the effect of modularity on cognitive performance are suggested. Modularity may
be a potential biomarker for injury, rehabilitation, or disease.Comment: 29 pages, 11 figure
Hierarchy of Gene Expression Data is Predictive of Future Breast Cancer Outcome
We calculate measures of hierarchy in gene and tissue networks of breast
cancer patients. We find that the likelihood of metastasis in the future is
correlated with increased values of network hierarchy for expression networks
of cancer-associated genes, due to correlated expression of cancer-specific
pathways. Conversely, future metastasis and quick relapse times are negatively
correlated with values of network hierarchy in the expression network of all
genes, due to dedifferentiation of gene pathways and circuits. These results
suggest that hierarchy of gene expression may be useful as an additional
biomarker for breast cancer prognosis.Comment: 14 pages, 5 figure
Modularity Enhances the Rate of Evolution in a Rugged Fitness Landscape
Biological systems are modular, and this modularity affects the evolution of
biological systems over time and in different environments. We here develop a
theory for the dynamics of evolution in a rugged, modular fitness landscape. We
show analytically how horizontal gene transfer couples to the modularity in the
system and leads to more rapid rates of evolution at short times. The model, in
general, analytically demonstrates a selective pressure for the prevalence of
modularity in biology. We use this model to show how the evolution of the
influenza virus is affected by the modularity of the proteins that are
recognized by the human immune system. Approximately 25\% of the observed rate
of fitness increase of the virus could be ascribed to a modular viral
landscape.Comment: 45 pages; 7 figure
Normal approximation for nonlinear statistics using a concentration inequality approach
Let be a general sampling statistic that can be written as a linear
statistic plus an error term. Uniform and non-uniform Berry--Esseen type bounds
for are obtained. The bounds are the best possible for many known
statistics. Applications to U-statistics, multisample U-statistics,
L-statistics, random sums and functions of nonlinear statistics are discussed.Comment: Published at http://dx.doi.org/10.3150/07-BEJ5164 in the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Residual-Based A Posteriori Error Estimates for Symmetric Conforming Mixed Finite Elements for Linear Elasticity Problems
A posteriori error estimators for the symmetric mixed finite element methods
for linear elasticity problems of Dirichlet and mixed boundary conditions are
proposed. Stability and efficiency of the estimators are proved. Finally, we
provide numerical examples to verify the theoretical results
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