1,662 research outputs found
An ISS Small-Gain Theorem for General Networks
We provide a generalized version of the nonlinear small-gain theorem for the
case of more than two coupled input-to-state stable (ISS) systems. For this
result the interconnection gains are described in a nonlinear gain matrix and
the small-gain condition requires bounds on the image of this gain matrix. The
condition may be interpreted as a nonlinear generalization of the requirement
that the spectral radius of the gain matrix is less than one. We give some
interpretations of the condition in special cases covering two subsystems,
linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals,
and Systems (MCSS
Global entrainment of transcriptional systems to periodic inputs
This paper addresses the problem of giving conditions for transcriptional
systems to be globally entrained to external periodic inputs. By using
contraction theory, a powerful tool from dynamical systems theory, it is shown
that certain systems driven by external periodic signals have the property that
all solutions converge to a fixed limit cycle. General results are proved, and
the properties are verified in the specific case of some models of
transcriptional systems. The basic mathematical results needed from contraction
theory are proved in the paper, making it self-contained
Singularly Perturbed Monotone Systems and an Application to Double Phosphorylation Cycles
The theory of monotone dynamical systems has been found very useful in the
modeling of some gene, protein, and signaling networks. In monotone systems,
every net feedback loop is positive. On the other hand, negative feedback loops
are important features of many systems, since they are required for adaptation
and precision. This paper shows that, provided that these negative loops act at
a comparatively fast time scale, the main dynamical property of (strongly)
monotone systems, convergence to steady states, is still valid. An application
is worked out to a double-phosphorylation ``futile cycle'' motif which plays a
central role in eukaryotic cell signaling.Comment: 21 pages, 3 figures, corrected typos, references remove
Alterations of nocturnal activity in rats following subchronic oral administration of the neurotoxin 1-trichloromethyl-1,2,3,4-tetrahydro-β-carboline
1-Trichloromethyl-1,2,3,4-tetrahydro-β-carboline (TaClo) is neurotoxic when administered to the brain and alters motor behaviour following intraperitoneal administration. We have assessed the long-term effects of oral TaClo administration on nocturnal motor behaviour in rats. Two groups of rats received TaClo orally at a dose of either 0.2 or 0.4 mg/kg twice daily for 7 weeks. The control group was given saline. No change in locomotor activity was observed 4–9 days after the end of the 7-week administration of TaClo. In addition, the spontaneous motor activity was altered dose-dependently 9 months after oral TaClo administration, with an increase in the low-dose TaClo group and a decrease in the high-dose group. Oral administration of TaClo in rats may be useful in investigating the hypothesis that in Parkinson’s disease, an unknown pathogenic factor crossing the intestinal mucosa barrier can induce neurodegenerative processes eventually affecting the entire brain
Early childhood lung function is a stronger predictor of adolescent lung function in cystic fibrosis than early Pseudomonas aeruginosa infection
Pseudomonas aeruginosa has been suggested as a major determinant of poor pulmonary outcomes in cystic fibrosis (CF), although other factors play a role. Our objective was to investigate the association of early childhood Pseudomonas infection on differences in lung function in adolescence with CF
Stability of quantized time-delay nonlinear systems: A Lyapunov-Krasowskii-functional approach
Lyapunov-Krasowskii functionals are used to design quantized control laws for
nonlinear continuous-time systems in the presence of constant delays in the
input. The quantized control law is implemented via hysteresis to prevent
chattering. Under appropriate conditions, our analysis applies to stabilizable
nonlinear systems for any value of the quantization density. The resulting
quantized feedback is parametrized with respect to the quantization density.
Moreover, the maximal allowable delay tolerated by the system is characterized
as a function of the quantization density.Comment: 31 pages, 3 figures, to appear in Mathematics of Control, Signals,
and System
A Characterization of Scale Invariant Responses in Enzymatic Networks
An ubiquitous property of biological sensory systems is adaptation: a step
increase in stimulus triggers an initial change in a biochemical or
physiological response, followed by a more gradual relaxation toward a basal,
pre-stimulus level. Adaptation helps maintain essential variables within
acceptable bounds and allows organisms to readjust themselves to an optimum and
non-saturating sensitivity range when faced with a prolonged change in their
environment. Recently, it was shown theoretically and experimentally that many
adapting systems, both at the organism and single-cell level, enjoy a
remarkable additional feature: scale invariance, meaning that the initial,
transient behavior remains (approximately) the same even when the background
signal level is scaled. In this work, we set out to investigate under what
conditions a broadly used model of biochemical enzymatic networks will exhibit
scale-invariant behavior. An exhaustive computational study led us to discover
a new property of surprising simplicity and generality, uniform linearizations
with fast output (ULFO), whose validity we show is both necessary and
sufficient for scale invariance of enzymatic networks. Based on this study, we
go on to develop a mathematical explanation of how ULFO results in scale
invariance. Our work provides a surprisingly consistent, simple, and general
framework for understanding this phenomenon, and results in concrete
experimental predictions
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