32,730 research outputs found
Mutual information for stochastic differential equations
Mutual information is calculated for processes described by stochastic differential equations. The expression for the mutual information has an interpretation in filtering theory.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/33555/1/0000056.pd
Capacity of Control for Stochastic Dynamical Systems Perturbed by Mixed Fractional Brownian Motion with Delay in Control
In this paper, we discuss the relationships between capacity of control in
entropy theory and intrinsic properties in control theory for a class of finite
dimensional stochastic dynamical systems described by a linear stochastic
differential equations driven by mixed fractional Brownian motion with delay in
control. Stochastic dynamical systems can be described as an information
channel between the space of control signals and the state space. We study this
control to state information capacity of this channel in continuous time. We
turned out that, the capacity of control depends on the time of final state in
dynamical systems. By using the analysis and representation of fractional
Gaussian process, the closed form of continuous optimal control law is derived.
The reached optimal control law maximizes the mutual information between
control signals and future state over a finite time horizon. The results
obtained here are motivated by control to state information capacity for linear
systems in both types deterministic and stochastic models that are widely used
to understand information flows in wireless network information theory.
The contribution of this paper is that we propose some new relationships
between control theory and entropy theoretic properties of stochastic dynamical
systems with delay in control. Finally, we present an example that serve to
illustrate the relationships between capacity of control and intrinsic
properties in control theory.Comment: 17 pages, 2 example
Path mutual information for a class of biochemical reaction networks
Living cells encode and transmit information in the temporal dynamics of
biochemical components. Gaining a detailed understanding of the input-output
relationship in biological systems therefore requires quantitative measures
that capture the interdependence between complete time trajectories of
biochemical components. Mutual information provides such a measure but its
calculation in the context of stochastic reaction networks is associated with
mathematical challenges. Here we show how to estimate the mutual information
between complete paths of two molecular species that interact with each other
through biochemical reactions. We demonstrate our approach using three simple
case studies.Comment: 6 pages, 2 figure
A non-adapted sparse approximation of PDEs with stochastic inputs
We propose a method for the approximation of solutions of PDEs with
stochastic coefficients based on the direct, i.e., non-adapted, sampling of
solutions. This sampling can be done by using any legacy code for the
deterministic problem as a black box. The method converges in probability (with
probabilistic error bounds) as a consequence of sparsity and a concentration of
measure phenomenon on the empirical correlation between samples. We show that
the method is well suited for truly high-dimensional problems (with slow decay
in the spectrum)
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