46,362 research outputs found
Transversality Properties: Primal Sufficient Conditions
The paper studies 'good arrangements' (transversality properties) of
collections of sets in a normed vector space near a given point in their
intersection. We target primal (metric and slope) characterizations of
transversality properties in the nonlinear setting. The Holder case is given a
special attention. Our main objective is not formally extending our earlier
results from the Holder to a more general nonlinear setting, but rather to
develop a general framework for quantitative analysis of transversality
properties. The nonlinearity is just a simple setting, which allows us to unify
the existing results on the topic. Unlike the well-studied subtransversality
property, not many characterizations of the other two important properties:
semitransversality and transversality have been known even in the linear case.
Quantitative relations between nonlinear transversality properties and the
corresponding regularity properties of set-valued mappings as well as nonlinear
extensions of the new transversality properties of a set-valued mapping to a
set in the range space due to Ioffe are also discussed.Comment: 33 page
About [q]-regularity properties of collections of sets
We examine three primal space local Hoelder type regularity properties of
finite collections of sets, namely, [q]-semiregularity, [q]-subregularity, and
uniform [q]-regularity as well as their quantitative characterizations.
Equivalent metric characterizations of the three mentioned regularity
properties as well as a sufficient condition of [q]-subregularity in terms of
Frechet normals are established. The relationships between [q]-regularity
properties of collections of sets and the corresponding regularity properties
of set-valued mappings are discussed.Comment: arXiv admin note: substantial text overlap with arXiv:1309.700
On a nonlinear heat equation associated with Dirichlet -- Robin conditions
This paper is devoted to the study of a nonlinear heat equation associated
with Dirichlet-Robin conditions. At first, we use the Faedo -- Galerkin and the
compactness method to prove existence and uniqueness results. Next, we consider
the properties of solutions. We obtain that if the initial condition is bounded
then so is the solution and we also get asymptotic behavior of solutions as.
Finally, we give numerical resultsComment: 20 page
An induction theorem and nonlinear regularity models
A general nonlinear regularity model for a set-valued mapping , where and are metric spaces, is considered
using special iteration procedures, going back to Banach, Schauder, Lusternik
and Graves. Namely, we revise the induction theorem from Khanh, J. Math. Anal.
Appl., 118 (1986) and employ it to obtain basic estimates for studying
regularity/openness properties. We also show that it can serve as a
substitution of the Ekeland variational principle when establishing other
regularity criteria. Then, we apply the induction theorem and the mentioned
estimates to establish criteria for both global and local versions of
regularity/openness properties for our model and demonstrate how the
definitions and criteria translate into the conventional setting of a
set-valued mapping .Comment: 28 page
Integrated signaling pathway and gene expression regulatory model to dissect dynamics of <em>Escherichia coli </em>challenged mammary epithelial cells
AbstractCells transform external stimuli, through the activation of signaling pathways, which in turn activate gene regulatory networks, in gene expression. As more omics data are generated from experiments, eliciting the integrated relationship between the external stimuli, the signaling process in the cell and the subsequent gene expression is a major challenge in systems biology. The complex system of non-linear dynamic protein interactions in signaling pathways and gene networks regulates gene expression.The complexity and non-linear aspects have resulted in the study of the signaling pathway or the gene network regulation in isolation. However, this limits the analysis of the interaction between the two components and the identification of the source of the mechanism differentiating the gene expression profiles. Here, we present a study of a model of the combined signaling pathway and gene network to highlight the importance of integrated modeling.Based on the experimental findings we developed a compartmental model and conducted several simulation experiments. The model simulates the mRNA expression of three different cytokines (RANTES, IL8 and TNFα) regulated by the transcription factor NFκB in mammary epithelial cells challenged with E. coli. The analysis of the gene network regulation identifies a lack of robustness and therefore sensitivity for the transcription factor regulation. However, analysis of the integrated signaling and gene network regulation model reveals distinctly different underlying mechanisms in the signaling pathway responsible for the variation between the three cytokine's mRNA expression levels. Our key findings reveal the importance of integrating the signaling pathway and gene expression dynamics in modeling. Modeling infers valid research questions which need to be verified experimentally and can assist in the design of future biological experiments
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