46,755 research outputs found
Moment-based analysis of biochemical networks in a heterogeneous population of communicating cells
Cells can utilize chemical communication to exchange information and
coordinate their behavior in the presence of noise. Communication can reduce
noise to shape a collective response, or amplify noise to generate distinct
phenotypic subpopulations. Here we discuss a moment-based approach to study how
cell-cell communication affects noise in biochemical networks that arises from
both intrinsic and extrinsic sources. We derive a system of approximate
differential equations that captures lower-order moments of a population of
cells, which communicate by secreting and sensing a diffusing molecule. Since
the number of obtained equations grows combinatorially with number of
considered cells, we employ a previously proposed model reduction technique,
which exploits symmetries in the underlying moment dynamics. Importantly, the
number of equations obtained in this way is independent of the number of
considered cells such that the method scales to arbitrary population sizes.
Based on this approach, we study how cell-cell communication affects population
variability in several biochemical networks. Moreover, we analyze the accuracy
and computational efficiency of the moment-based approximation by comparing it
with moments obtained from stochastic simulations.Comment: 6 pages, 5 Figure
Low-rank approximate inverse for preconditioning tensor-structured linear systems
In this paper, we propose an algorithm for the construction of low-rank
approximations of the inverse of an operator given in low-rank tensor format.
The construction relies on an updated greedy algorithm for the minimization of
a suitable distance to the inverse operator. It provides a sequence of
approximations that are defined as the projections of the inverse operator in
an increasing sequence of linear subspaces of operators. These subspaces are
obtained by the tensorization of bases of operators that are constructed from
successive rank-one corrections. In order to handle high-order tensors,
approximate projections are computed in low-rank Hierarchical Tucker subsets of
the successive subspaces of operators. Some desired properties such as symmetry
or sparsity can be imposed on the approximate inverse operator during the
correction step, where an optimal rank-one correction is searched as the tensor
product of operators with the desired properties. Numerical examples illustrate
the ability of this algorithm to provide efficient preconditioners for linear
systems in tensor format that improve the convergence of iterative solvers and
also the quality of the resulting low-rank approximations of the solution
A discrete approach to stochastic parametrization and dimensional reduction in nonlinear dynamics
Many physical systems are described by nonlinear differential equations that
are too complicated to solve in full. A natural way to proceed is to divide the
variables into those that are of direct interest and those that are not,
formulate solvable approximate equations for the variables of greater interest,
and use data and statistical methods to account for the impact of the other
variables. In the present paper the problem is considered in a fully
discrete-time setting, which simplifies both the analysis of the data and the
numerical algorithms. The resulting time series are identified by a NARMAX
(nonlinear autoregression moving average with exogenous input) representation
familiar from engineering practice. The connections with the Mori-Zwanzig
formalism of statistical physics are discussed, as well as an application to
the Lorenz 96 system.Comment: 12 page, includes 2 figure
Extended Differential Aggregations in Process Algebra for Performance and Biology
We study aggregations for ordinary differential equations induced by fluid
semantics for Markovian process algebra which can capture the dynamics of
performance models and chemical reaction networks. Whilst previous work has
required perfect symmetry for exact aggregation, we present approximate fluid
lumpability, which makes nearby processes perfectly symmetric after a
perturbation of their parameters. We prove that small perturbations yield
nearby differential trajectories. Numerically, we show that many heterogeneous
processes can be aggregated with negligible errors.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Study of the risk-adjusted pricing methodology model with methods of Geometrical Analysis
Families of exact solutions are found to a nonlinear modification of the
Black-Scholes equation. This risk-adjusted pricing methodology model (RAPM)
incorporates both transaction costs and the risk from a volatile portfolio.
Using the Lie group analysis we obtain the Lie algebra admitted by the RAPM
equation. It gives us the possibility to describe an optimal system of
subalgebras and correspondingly the set of invariant solutions to the model. In
this way we can describe the complete set of possible reductions of the
nonlinear RAPM model. Reductions are given in the form of different second
order ordinary differential equations. In all cases we provide solutions to
these equations in an exact or parametric form. We discuss the properties of
these reductions and the corresponding invariant solutions.Comment: larger version with exact solutions, corrected typos, 13 pages,
Symposium on Optimal Stopping in Abo/Turku 200
Non-equilibrium phase transitions in biomolecular signal transduction
We study a mechanism for reliable switching in biomolecular
signal-transduction cascades. Steady bistable states are created by system-size
cooperative effects in populations of proteins, in spite of the fact that the
phosphorylation-state transitions of any molecule, by means of which the switch
is implemented, are highly stochastic. The emergence of switching is a
nonequilibrium phase transition in an energetically driven, dissipative system
described by a master equation. We use operator and functional integral methods
from reaction-diffusion theory to solve for the phase structure, noise
spectrum, and escape trajectories and first-passage times of a class of minimal
models of switches, showing how all critical properties for switch behavior can
be computed within a unified framework
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