543 research outputs found
Low-lying bifurcations in cavity quantum electrodynamics
The interplay of quantum fluctuations with nonlinear dynamics is a central
topic in the study of open quantum systems, connected to fundamental issues
(such as decoherence and the quantum-classical transition) and practical
applications (such as coherent information processing and the development of
mesoscopic sensors/amplifiers). With this context in mind, we here present a
computational study of some elementary bifurcations that occur in a driven and
damped cavity quantum electrodynamics (cavity QED) model at low intracavity
photon number. In particular, we utilize the single-atom cavity QED Master
Equation and associated Stochastic Schrodinger Equations to characterize the
equilibrium distribution and dynamical behavior of the quantized intracavity
optical field in parameter regimes near points in the semiclassical
(mean-field, Maxwell-Bloch) bifurcation set. Our numerical results show that
the semiclassical limit sets are qualitatively preserved in the quantum
stationary states, although quantum fluctuations apparently induce phase
diffusion within periodic orbits and stochastic transitions between attractors.
We restrict our attention to an experimentally realistic parameter regime.Comment: 13 pages, 10 figures, submitted to PR
Microscopic/stochastic timesteppers and coarse control: a kinetic Monte Carlo example
Coarse timesteppers provide a bridge between microscopic / stochastic system
descriptions and macroscopic tasks such as coarse stability/bifurcation
computations. Exploiting this computational enabling technology, we present a
framework for designing observers and controllers based on microscopic
simulations, that can be used for their coarse control. The proposed
methodology provides a bridge between traditional numerical analysis and
control theory on the one hand and microscopic simulation on the other
Stochastic analysis of nonlinear dynamics and feedback control for gene regulatory networks with applications to synthetic biology
The focus of the thesis is the investigation of the generalized repressilator model
(repressing genes ordered in a ring structure). Using nonlinear bifurcation analysis
stable and quasi-stable periodic orbits in this genetic network are characterized
and a design for a switchable and controllable genetic oscillator is proposed. The
oscillator operates around a quasi-stable periodic orbit using the classical engineering
idea of read-out based control. Previous genetic oscillators have been
designed around stable periodic orbits, however we explore the possibility of
quasi-stable periodic orbit expecting better controllability.
The ring topology of the generalized repressilator model has spatio-temporal
symmetries that can be understood as propagating perturbations in discrete lattices.
Network topology is a universal cross-discipline transferable concept and
based on it analytical conditions for the emergence of stable and quasi-stable
periodic orbits are derived. Also the length and distribution of quasi-stable oscillations
are obtained. The findings suggest that long-lived transient dynamics
due to feedback loops can dominate gene network dynamics.
Taking the stochastic nature of gene expression into account a master equation
for the generalized repressilator is derived. The stochasticity is shown to influence
the onset of bifurcations and quality of oscillations. Internal noise is shown to
have an overall stabilizing effect on the oscillating transients emerging from the
quasi-stable periodic orbits.
The insights from the read-out based control scheme for the genetic oscillator
lead us to the idea to implement an algorithmic controller, which would direct
any genetic circuit to a desired state. The algorithm operates model-free, i.e. in
principle it is applicable to any genetic network and the input information is a
data matrix of measured time series from the network dynamics. The application
areas for readout-based control in genetic networks range from classical tissue
engineering to stem cells specification, whenever a quantitatively and temporarily
targeted intervention is required
Coarse Bifurcation Diagrams via Microscopic Simulators: A State-Feedback Control-Based Approach
The arc-length continuation framework is used for the design of state
feedback control laws that enable a microscopic simulator trace its own
open-loop coarse bifurcation diagram. The steering of the system along solution
branches is achieved through the manipulation of the bifurcation parameter,
which becomes our actuator. The design approach is based on the assumption that
the eigenvalues of the linearized system can be decomposed into two well
separated clusters: one containing eigenvalues with large negative real parts
and one containing (possibly unstable) eigenvalues close to the origin
Tutorial of numerical continuation and bifurcation theory for systems and synthetic biology
Mathematical modelling allows us to concisely describe fundamental principles
in biology. Analysis of models can help to both explain known phenomena, and
predict the existence of new, unseen behaviours. Model analysis is often a
complex task, such that we have little choice but to approach the problem with
computational methods. Numerical continuation is a computational method for
analysing the dynamics of nonlinear models by algorithmically detecting
bifurcations. Here we aim to promote the use of numerical continuation tools by
providing an introduction to nonlinear dynamics and numerical bifurcation
analysis. Many numerical continuation packages are available, covering a wide
range of system classes; a review of these packages is provided, to help both
new and experienced practitioners in choosing the appropriate software tools
for their needs.Comment: 14 pages, 2 figures, 2 table
Optimization of synthetic oscillatory biological networks through Reinforcement Learning
In the expanding realm of computational biology, Reinforcement Learning (RL) emerges as a novel and promising approach, especially for designing and optimizing complex synthetic biological circuits. This study explores the application of RL in controlling Hopf bifurcations within ODE-based systems, particularly under the influence of molecular noise. Through two case studies, we demonstrate RL’s capabilities in navigating biological systems’ inherent non-linearity and high dimensionality. Our findings reveal that RL effectively identifies the onset of Hopf bifurcations and preserves biological plausibility within the optimized networks. However, challenges were encountered in achieving persistent oscillations and matching traditional algorithms’ computational speed. Despite these limitations, the study highlights RL’s significant potential as an instrumental tool in computational biology, offering a novel perspective for exploring and optimizing oscillatory dynamics within complex biological systems. Our research establishes RL as a promising strategy for manipulating and designing intricate behaviors in biological networks
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