5,828 research outputs found
J-holomorphic curves in a nef class
Taubes established fundamental properties of holomorphic subvarieties in
dimension 4 in \cite{T1}. In this paper, we further investigate properties of
reducible holomorphic subvarieties. We offer an upper bound of the total
genus of a subvariety when the class of the subvariety is nef. For a
spherical class, it has particularly strong consequences. It is shown that, for
any tamed , each irreducible component is a smooth rational curve. We also
completely classify configurations of maximal dimension. To prove these results
we treat subvarieties as weighted graphs and introduce several combinatorial
moves.Comment: 30 pages. v2 Section 4.3 revised; minor changes elsewhere. v3
mistakes correcte
Coupled Reversible and Irreversible Bistable Switches Underlying TGF-\beta-induced Epithelial to Mesenchymal Transition
Epithelial to mesenchymal transition (EMT) plays important roles in embryonic
development, tissue regeneration and cancer metastasis. While several feedback
loops have been shown to regulate EMT, it remains elusive how they coordinately
modulate EMT response to TGF-\beta treatment. We construct a mathematical model
for the core regulatory network controlling TGF-\beta-induced EMT. Through
deterministic analyses and stochastic simulations, we show that EMT is a
sequential two-step program that an epithelial cell first transits to partial
EMT then to the mesenchymal state, depending on the strength and duration of
TGF-\beta stimulation. Mechanistically the system is governed by coupled
reversible and irreversible bistable switches. The SNAIL1/miR-34 double
negative feedback loop is responsible for the reversible switch and regulates
the initiation of EMT, while the ZEB/miR-200 feedback loop is accountable for
the irreversible switch and controls the establishment of the mesenchymal
state. Furthermore, an autocrine TGF-\beta/miR-200 feedback loop makes the
second switch irreversible, modulating the maintenance of EMT. Such coupled
bistable switches are robust to parameter variation and molecular noise. We
provide a mechanistic explanation on multiple experimental observations. The
model makes several explicit predictions on hysteretic dynamic behaviors,
system response to pulsed stimulation and various perturbations, which can be
straightforwardly tested.Comment: 32 pages, 8 figures, accepted by Biophysical Journa
Jointly Modeling Topics and Intents with Global Order Structure
Modeling document structure is of great importance for discourse analysis and
related applications. The goal of this research is to capture the document
intent structure by modeling documents as a mixture of topic words and
rhetorical words. While the topics are relatively unchanged through one
document, the rhetorical functions of sentences usually change following
certain orders in discourse. We propose GMM-LDA, a topic modeling based
Bayesian unsupervised model, to analyze the document intent structure
cooperated with order information. Our model is flexible that has the ability
to combine the annotations and do supervised learning. Additionally, entropic
regularization can be introduced to model the significant divergence between
topics and intents. We perform experiments in both unsupervised and supervised
settings, results show the superiority of our model over several
state-of-the-art baselines.Comment: Accepted by AAAI 201
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