113,936 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
Probabilistic Guarded P Systems, A New Formal Modelling Framework
Multienvironment P systems constitute a general, formal
framework for modelling the dynamics of population biology, which consists
of two main approaches: stochastic and probabilistic. The framework
has been successfully used to model biologic systems at both micro (e.g.
bacteria colony) and macro (e.g. real ecosystems) levels, respectively.
In this paper, we extend the general framework in order to include
a new case study related to P. Oleracea species. The extension is made
by a new variant within the probabilistic approach, called Probabilistic
Guarded P systems (in short, PGP systems). We provide a formal definition,
a simulation algorithm to capture the dynamics, and a survey of
the associated software.Ministerio de EconomĂa y Competitividad TIN2012- 37434Junta de AndalucĂa P08-TIC-0420
Bayesian Updating, Model Class Selection and Robust Stochastic Predictions of Structural Response
A fundamental issue when predicting structural response by using mathematical models is how to treat both modeling and excitation uncertainty. A general framework for this is presented which uses probability as a multi-valued
conditional logic for quantitative plausible reasoning in the presence of uncertainty due to incomplete information. The
fundamental probability models that represent the structureâs uncertain behavior are specified by the choice of a stochastic
system model class: a set of input-output probability models for the structure and a prior probability distribution over this set
that quantifies the relative plausibility of each model. A model class can be constructed from a parameterized deterministic
structural model by stochastic embedding utilizing Jaynesâ Principle of Maximum Information Entropy. Robust predictive
analyses use the entire model class with the probabilistic predictions of each model being weighted by its prior probability, or if
structural response data is available, by its posterior probability from Bayesâ Theorem for the model class. Additional robustness
to modeling uncertainty comes from combining the robust predictions of each model class in a set of competing candidates
weighted by the prior or posterior probability of the model class, the latter being computed from Bayesâ Theorem. This higherlevel application of Bayesâ Theorem automatically applies a quantitative Ockham razor that penalizes the data-fit of more
complex model classes that extract more information from the data. Robust predictive analyses involve integrals over highdimensional spaces that usually must be evaluated numerically. Published applications have used Laplace's method of
asymptotic approximation or Markov Chain Monte Carlo algorithms
Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems
Development of robust dynamical systems and networks such as autonomous
aircraft systems capable of accomplishing complex missions faces challenges due
to the dynamically evolving uncertainties coming from model uncertainties,
necessity to operate in a hostile cluttered urban environment, and the
distributed and dynamic nature of the communication and computation resources.
Model-based robust design is difficult because of the complexity of the hybrid
dynamic models including continuous vehicle dynamics, the discrete models of
computations and communications, and the size of the problem. We will overview
recent advances in methodology and tools to model, analyze, and design robust
autonomous aerospace systems operating in uncertain environment, with stress on
efficient uncertainty quantification and robust design using the case studies
of the mission including model-based target tracking and search, and trajectory
planning in uncertain urban environment. To show that the methodology is
generally applicable to uncertain dynamical systems, we will also show examples
of application of the new methods to efficient uncertainty quantification of
energy usage in buildings, and stability assessment of interconnected power
networks
Bridging the Gap between Probabilistic and Deterministic Models: A Simulation Study on a Variational Bayes Predictive Coding Recurrent Neural Network Model
The current paper proposes a novel variational Bayes predictive coding RNN
model, which can learn to generate fluctuated temporal patterns from exemplars.
The model learns to maximize the lower bound of the weighted sum of the
regularization and reconstruction error terms. We examined how this weighting
can affect development of different types of information processing while
learning fluctuated temporal patterns. Simulation results show that strong
weighting of the reconstruction term causes the development of deterministic
chaos for imitating the randomness observed in target sequences, while strong
weighting of the regularization term causes the development of stochastic
dynamics imitating probabilistic processes observed in targets. Moreover,
results indicate that the most generalized learning emerges between these two
extremes. The paper concludes with implications in terms of the underlying
neuronal mechanisms for autism spectrum disorder and for free action.Comment: This paper is accepted the 24th International Conference On Neural
Information Processing (ICONIP 2017). The previous submission to arXiv is
replaced by this version because there was an error in Equation
Probabilistic model checking of complex biological pathways
Probabilistic model checking is a formal verification technique that has been successfully applied to the analysis of systems from a broad range of domains, including security and communication protocols, distributed algorithms and power management. In this paper we illustrate its applicability to a complex biological system: the FGF (Fibroblast Growth Factor) signalling pathway. We give a detailed description of how this case study can be modelled in the probabilistic model checker PRISM, discussing some of the issues that arise in doing so, and show how we can thus examine a rich selection of quantitative properties of this model. We present experimental results for the case study under several different scenarios and provide a detailed analysis, illustrating how this approach can be used to yield a better understanding of the dynamics of the pathway
A probabilistic approach to model-based adaptive control for damping of interarea oscillations
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