3,109 research outputs found
Oscillations in I/O monotone systems under negative feedback
Oscillatory behavior is a key property of many biological systems. The
Small-Gain Theorem (SGT) for input/output monotone systems provides a
sufficient condition for global asymptotic stability of an equilibrium and
hence its violation is a necessary condition for the existence of periodic
solutions. One advantage of the use of the monotone SGT technique is its
robustness with respect to all perturbations that preserve monotonicity and
stability properties of a very low-dimensional (in many interesting examples,
just one-dimensional) model reduction. This robustness makes the technique
useful in the analysis of molecular biological models in which there is large
uncertainty regarding the values of kinetic and other parameters. However,
verifying the conditions needed in order to apply the SGT is not always easy.
This paper provides an approach to the verification of the needed properties,
and illustrates the approach through an application to a classical model of
circadian oscillations, as a nontrivial ``case study,'' and also provides a
theorem in the converse direction of predicting oscillations when the SGT
conditions fail.Comment: Related work can be retrieved from second author's websit
Multi-Stability in Monotone Input/Output Systems
This paper studies the emergence of multi-stability and hysteresis in those
systems that arise, under positive feedback, starting from monotone systems
with well-defined steady-state responses. Such feedback configurations appear
routinely in several fields of application, and especially in biology.
Characterizations of global stability behavior are stated in terms of easily
checkable graphical conditions. An example of a signaling cascade under
positive feedback is presented.Comment: See http://www.math.rutgers.edu/~sontag for related work; to appear
in Systems and Control Letter
Monotone Control Systems
Monotone systems constitute one of the most important classes of dynamical
systems used in mathematical biology modeling.
The objective of this paper is to extend the notion of monotonicity to
systems with inputs and outputs, a necessary first step in trying to understand
interconnections, especially including feedback loops, built up out of monotone
components.
Basic definitions and theorems are provided, as well as an application to the
study of a model of one of the cell's most important subsystems.Comment: See http://www.math.rutgers.edu/~sontag/ for related wor
Structural instability in an autophosphorylating kinase switch
We analyse a simple kinase model that exhibits bistability when there is no protein turnover, and show analytically that the property of being bistable is not necessarily conserved when degradation and synthesis of the kinase are taken into account
A large annotated corpus for learning natural language inference
Understanding entailment and contradiction is fundamental to understanding
natural language, and inference about entailment and contradiction is a
valuable testing ground for the development of semantic representations.
However, machine learning research in this area has been dramatically limited
by the lack of large-scale resources. To address this, we introduce the
Stanford Natural Language Inference corpus, a new, freely available collection
of labeled sentence pairs, written by humans doing a novel grounded task based
on image captioning. At 570K pairs, it is two orders of magnitude larger than
all other resources of its type. This increase in scale allows lexicalized
classifiers to outperform some sophisticated existing entailment models, and it
allows a neural network-based model to perform competitively on natural
language inference benchmarks for the first time.Comment: To appear at EMNLP 2015. The data will be posted shortly before the
conference (the week of 14 Sep) at http://nlp.stanford.edu/projects/snli
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