359 research outputs found
Molecular Distributions in Gene Regulatory Dynamics
We show how one may analytically compute the stationary density of the
distribution of molecular constituents in populations of cells in the presence
of noise arising from either bursting transcription or translation, or noise in
degradation rates arising from low numbers of molecules. We have compared our
results with an analysis of the same model systems (either inducible or
repressible operons) in the absence of any stochastic effects, and shown the
correspondence between behaviour in the deterministic system and the stochastic
analogs. We have identified key dimensionless parameters that control the
appearance of one or two steady states in the deterministic case, or unimodal
and bimodal densities in the stochastic systems, and detailed the analytic
requirements for the occurrence of different behaviours. This approach
provides, in some situations, an alternative to computationally intensive
stochastic simulations. Our results indicate that, within the context of the
simple models we have examined, bursting and degradation noise cannot be
distinguished analytically when present alone.Comment: 14 pages, 12 figures. Conferences: "2010 Annual Meeting of The
Society of Mathematical Biology", Rio de Janeiro (Brazil), 24-29/07/2010.
"First International workshop on Differential and Integral Equations with
Applications in Biology and Medicine", Aegean University, Karlovassi, Samos
island (Greece), 6-10/09/201
Quantum-assisted finite-element design optimization
Quantum annealing devices such as the ones produced by D-Wave systems are typically used for solving optimization and sampling tasks, and in both academia and industry the characterization of their usefulness is subject to active research. Any problem that can naturally be described as a weighted, undirected graph may be a particularly interesting candidate, since such a problem may be formulated a as quadratic unconstrained binary optimization (QUBO) instance, which is solvable on D-Wave's Chimera graph architecture. In this paper, we introduce a quantum-assisted finite-element method for design optimization. We show that we can minimize a shape-specific quantity, in our case a ray approximation of sound pressure at a specific position around an object, by manipulating the shape of this object. Our algorithm belongs to the class of quantum-assisted algorithms, as the optimization task runs iteratively on a D-Wave 2000Q quantum processing unit (QPU), whereby the evaluation and interpretation of the results happens classically. Our first and foremost aim is to explain how to represent and solve parts of these problems with the help of a QPU, and not to prove supremacy over existing classical finite-element algorithms for design optimization.Algorithms and the Foundations of Software technolog
Mathematical description of bacterial traveling pulses
The Keller-Segel system has been widely proposed as a model for bacterial
waves driven by chemotactic processes. Current experiments on {\em E. coli}
have shown precise structure of traveling pulses. We present here an
alternative mathematical description of traveling pulses at a macroscopic
scale. This modeling task is complemented with numerical simulations in
accordance with the experimental observations. Our model is derived from an
accurate kinetic description of the mesoscopic run-and-tumble process performed
by bacteria. This model can account for recent experimental observations with
{\em E. coli}. Qualitative agreements include the asymmetry of the pulse and
transition in the collective behaviour (clustered motion versus dispersion). In
addition we can capture quantitatively the main characteristics of the pulse
such as the speed and the relative size of tails. This work opens several
experimental and theoretical perspectives. Coefficients at the macroscopic
level are derived from considerations at the cellular scale. For instance the
stiffness of the signal integration process turns out to have a strong effect
on collective motion. Furthermore the bottom-up scaling allows to perform
preliminary mathematical analysis and write efficient numerical schemes. This
model is intended as a predictive tool for the investigation of bacterial
collective motion
Trail formation based on directed pheromone deposition
We propose an Individual-Based Model of ant-trail formation. The ants are
modeled as self-propelled particles which deposit directed pheromones and
interact with them through alignment interaction. The directed pheromones
intend to model pieces of trails, while the alignment interaction translates
the tendency for an ant to follow a trail when it meets it. Thanks to adequate
quantitative descriptors of the trail patterns, the existence of a phase
transition as the ant-pheromone interaction frequency is increased can be
evidenced. Finally, we propose both kinetic and fluid descriptions of this
model and analyze the capabilities of the fluid model to develop trail
patterns. We observe that the development of patterns by fluid models require
extra trail amplification mechanisms that are not needed at the
Individual-Based Model level
Survey of coherent ∼1 Hz waves in Mercury's inner magnetosphere from MESSENGER observations
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95559/1/jgra22073.pd
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