Preprint Series 2014

2014:08
J. Zhao and
Q. Wang
In the late stage of the mitotic cycle of eukaryotic cells , cytokinesis ensues where a parent cell replicates its nucleus with the necessary genetical substances (i.e., DNAs and chromosomes) and splits into two similar offspring cells. This mitotic process involves complex chemical, biophysical and mechanical processes whose details are ...
[Full Abstract] 
2014:07
J. Zhao and
Q. Wang
Biofilms are known to be more persistent to antimicrobial treatment than planktonic bacterial cells. In addition to the protective extracellular matrix formed primarily by expopolysaccharides (EPS), one of the current point of views on this issue is that there may exist a small portion of phenotypic bacterial variants, known as ...
[Full Abstract] 
2014:06
J. Zhao and
Q. Wang
Biofilms are microorganisms, where bacteria are embedded in networks formed by bacteriaproduced expopolysacharrides, also known as extracellular polymeric substances (EPS). Bacteria in biofilms communicate and cooperate with each other by sensing the density of signalling molecules that bacteria excrete. This phenomenon is known as quorum sensing (QS). In this paper ...
[Full Abstract] 
2014:05
V. Temlyakov
Applications of the Incremental Algorithm, which was developed in the theory of greedy algorithms in Banach spaces, to approximation and numerical integration are discussed. In particular, it is shown that the Incremental Algorithm provides an efficient way for deterministic construction of cubature formulas with equal weights, which give good rate ...
[Full Abstract] 
2014:04
S. Dekel,
G. Kerkyacharian,
G. Kyriazis, and
P. Petrushev
A new proof is given of the atomic decomposition of Hardy spaces $H^p$, $0<p\le 1$, in the classical setting on $\mathbb{R}^n$. The new method can be used to establish atomic decomposition of maximal Hardy spaces in general and nonclassical settings.
[Full Abstract] 
2014:03
S. Dekel,
G. Kerkyacharian,
G. Kyriazis, and
P. Petrushev
Maximal and atomic Hardy spaces $H^p$ and $H^p _ A$, $0<p\le 1$, are considered in the setting of a doubling metric measure space in the presence of a nonnegative selfadjoint operator whose heat kernel has Gaussian localization and the Markov property. It is shown that $H ...
[Full Abstract] 
2014:02
D. Bazarkhanov and
V. Temlyakov
We are interested in approximation of a multivariate function $f(x _ 1,\dots,x _ d)$ by linear combinations of products $u^1(x _ 1)\cdots u^d(x _ d)$ of univariate functions $u^i(x _ i)$, $i=1,\dots,d$. In the case $d=2 ...
[Full Abstract] 
2014:01
R. DeVore and
V. Temlyakov
Greedy algorithms which use only function evaluations are applied to convex optimization in a general Banach space X. Along with algorithms that use exact evaluations, algorithms with approximate evaluations are treated. A priori upper bounds for the convergence rate of the proposed algorithms are given. These bounds depend on the ...
[Full Abstract]