3,013 research outputs found
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Background: Many biological systems are modeled qualitatively with discrete
models, such as probabilistic Boolean networks, logical models, Petri nets, and
agent-based models, with the goal to gain a better understanding of the system.
The computational complexity to analyze the complete dynamics of these models
grows exponentially in the number of variables, which impedes working with
complex models. Although there exist sophisticated algorithms to determine the
dynamics of discrete models, their implementations usually require
labor-intensive formatting of the model formulation, and they are oftentimes
not accessible to users without programming skills. Efficient analysis methods
are needed that are accessible to modelers and easy to use. Method: By
converting discrete models into algebraic models, tools from computational
algebra can be used to analyze their dynamics. Specifically, we propose a
method to identify attractors of a discrete model that is equivalent to solving
a system of polynomial equations, a long-studied problem in computer algebra.
Results: A method for efficiently identifying attractors, and the web-based
tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other
analysis methods for discrete models. ADAM converts several discrete model
types automatically into polynomial dynamical systems and analyzes their
dynamics using tools from computer algebra. Based on extensive experimentation
with both discrete models arising in systems biology and randomly generated
networks, we found that the algebraic algorithms presented in this manuscript
are fast for systems with the structure maintained by most biological systems,
namely sparseness, i.e., while the number of nodes in a biological network may
be quite large, each node is affected only by a small number of other nodes,
and robustness, i.e., small number of attractors
Entropy of complex relevant components of Boolean networks
Boolean network models of strongly connected modules are capable of capturing
the high regulatory complexity of many biological gene regulatory circuits. We
study numerically the previously introduced basin entropy, a parameter for the
dynamical uncertainty or information storage capacity of a network as well as
the average transient time in random relevant components as a function of their
connectivity. We also demonstrate that basin entropy can be estimated from
time-series data and is therefore also applicable to non-deterministic networks
models.Comment: 8 pages, 6 figure
A micropower centroiding vision processor
Published versio
Compositionality, stochasticity and cooperativity in dynamic models of gene regulation
We present an approach for constructing dynamic models for the simulation of
gene regulatory networks from simple computational elements. Each element is
called a ``gene gate'' and defines an input/output-relationship corresponding
to the binding and production of transcription factors. The proposed reaction
kinetics of the gene gates can be mapped onto stochastic processes and the
standard ode-description. While the ode-approach requires fixing the system's
topology before its correct implementation, expressing them in stochastic
pi-calculus leads to a fully compositional scheme: network elements become
autonomous and only the input/output relationships fix their wiring. The
modularity of our approach allows to pass easily from a basic first-level
description to refined models which capture more details of the biological
system. As an illustrative application we present the stochastic repressilator,
an artificial cellular clock, which oscillates readily without any cooperative
effects.Comment: 15 pages, 8 figures. Accepted by the HFSP journal (13/09/07
Assessing Random Dynamical Network Architectures for Nanoelectronics
Independent of the technology, it is generally expected that future nanoscale
devices will be built from vast numbers of densely arranged devices that
exhibit high failure rates. Other than that, there is little consensus on what
type of technology and computing architecture holds most promises to go far
beyond today's top-down engineered silicon devices. Cellular automata (CA) have
been proposed in the past as a possible class of architectures to the von
Neumann computing architecture, which is not generally well suited for future
parallel and fine-grained nanoscale electronics. While the top-down engineered
semi-conducting technology favors regular and locally interconnected
structures, future bottom-up self-assembled devices tend to have irregular
structures because of the current lack precise control over these processes. In
this paper, we will assess random dynamical networks, namely Random Boolean
Networks (RBNs) and Random Threshold Networks (RTNs), as alternative computing
architectures and models for future information processing devices. We will
illustrate that--from a theoretical perspective--they offer superior properties
over classical CA-based architectures, such as inherent robustness as the
system scales up, more efficient information processing capabilities, and
manufacturing benefits for bottom-up designed devices, which motivates this
investigation. We will present recent results on the dynamic behavior and
robustness of such random dynamical networks while also including manufacturing
issues in the assessment.Comment: 8 pages, 6 figures, IEEE/ACM Symposium on Nanoscale Architectures,
NANOARCH 2008, Anaheim, CA, USA, Jun 12-13, 200
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