796,470 research outputs found
Model Creation and Equivalence Proofs of Cellular Automata and Artificial Neural Networks
Computational methods and mathematical models have invaded arguably every
scientific discipline forming its own field of research called computational
science. Mathematical models are the theoretical foundation of computational
science. Since Newton's time, differential equations in mathematical models
have been widely and successfully used to describe the macroscopic or global
behaviour of systems. With spatially inhomogeneous, time-varying, local
element-specific, and often non-linear interactions, the dynamics of complex
systems is in contrast more efficiently described by local rules and thus in an
algorithmic and local or microscopic manner. The theory of mathematical
modelling taking into account these characteristics of complex systems has to
be established still. We recently presented a so-called allagmatic method
including a system metamodel to provide a framework for describing, modelling,
simulating, and interpreting complex systems. Implementations of cellular
automata and artificial neural networks were described and created with that
method. Guidance from philosophy were helpful in these first studies focusing
on programming and feasibility. A rigorous mathematical formalism, however, is
still missing. This would not only more precisely describe and define the
system metamodel, it would also further generalise it and with that extend its
reach to formal treatment in applied mathematics and theoretical aspects of
computational science as well as extend its applicability to other mathematical
and computational models such as agent-based models. Here, a mathematical
definition of the system metamodel is provided. Based on the presented
formalism, model creation and equivalence of cellular automata and artificial
neural networks are proved. It thus provides a formal approach for studying the
creation of mathematical models as well as their structural and operational
comparison.Comment: 13 pages, 1 tabl
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Artificial Immune Systems - Models, algorithms and applications
Copyright © 2010 Academic Research Publishing Agency.This article has been made available through the Brunel Open Access Publishing Fund.Artificial Immune Systems (AIS) are computational paradigms that belong to the computational intelligence family and are inspired by the biological immune system. During the past decade, they have attracted a lot of interest from researchers aiming to develop immune-based models and techniques to solve complex computational or engineering problems. This work presents a survey of existing AIS models and algorithms with a focus on the last five years.This article is available through the Brunel Open Access Publishing Fun
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
Stochasticity is a key characteristic of intracellular processes such as gene
regulation and chemical signalling. Therefore, characterising stochastic
effects in biochemical systems is essential to understand the complex dynamics
of living things. Mathematical idealisations of biochemically reacting systems
must be able to capture stochastic phenomena. While robust theory exists to
describe such stochastic models, the computational challenges in exploring
these models can be a significant burden in practice since realistic models are
analytically intractable. Determining the expected behaviour and variability of
a stochastic biochemical reaction network requires many probabilistic
simulations of its evolution. Using a biochemical reaction network model to
assist in the interpretation of time course data from a biological experiment
is an even greater challenge due to the intractability of the likelihood
function for determining observation probabilities. These computational
challenges have been subjects of active research for over four decades. In this
review, we present an accessible discussion of the major historical
developments and state-of-the-art computational techniques relevant to
simulation and inference problems for stochastic biochemical reaction network
models. Detailed algorithms for particularly important methods are described
and complemented with MATLAB implementations. As a result, this review provides
a practical and accessible introduction to computational methods for stochastic
models within the life sciences community
Instantaneous modelling and reverse engineering of data-consistent prime models in seconds!
A theoretical framework that supports automated construction of dynamic prime models purely from experimental time series data has been invented and developed, which can automatically generate (construct) data-driven models of any time series data in seconds. This has resulted in the formulation and formalisation of new reverse engineering and dynamic methods for automated systems modelling of complex systems, including complex biological, financial, control, and artificial neural network systems. The systems/model theory behind the invention has been formalised as a new, effective and robust system identification strategy complementary to process-based modelling. The proposed dynamic modelling and network inference solutions often involve tackling extremely difficult parameter estimation challenges, inferring unknown underlying network structures, and unsupervised formulation and construction of smart and intelligent ODE models of complex systems. In underdetermined conditions, i.e., cases of dealing with how best to instantaneously and rapidly construct data-consistent prime models of unknown (or well-studied) complex system from small-sized time series data, inference of unknown underlying network of interaction is more challenging. This article reports a robust step-by-step mathematical and computational analysis of the entire prime model construction process that determines a model from data in less than a minute
Developmental motifs reveal complex structure in cell lineages
Many natural and technological systems are complex, with organisational structures that exhibit characteristic patterns, but defy concise description. One effective approach to analysing such systems is in terms of repeated topological motifs. Here, we extend the motif concept to characterise the dynamic behaviour of complex systems by introducing developmental motifs, which capture patterns of system growth. As a proof of concept, we use developmental motifs to analyse the developmental cell lineage of the nematode Caenorhabditis elegans, revealing a new perspective on its complex structure. We use a family of computational models to explore how biases arising from the dynamics of the developmental gene network, as well as spatial and temporal constraints acting on development, contribute to this complex organisation
Nature-Inspired Coordination Models: Current Status and Future Trends
Coordination models and languages are meant to provide abstractions and mechanisms to harness the space of interaction as one of the foremost sources of complexity in computational systems. Nature-inspired computing aims at understanding the mechanisms and patterns of complex natural systems in order to bring their most desirable features to computational systems. Thus, the promise of nature-inspired coordination models is to prove themselves fundamental in the design of complex computational systems|such as intelligent, knowledge-intensive, pervasive, adaptive, and self-organising ones. In this paper, we survey the most relevant nature-inspired coordination models in the literature, focussing in particular on tuple-based models, and foresee the most interesting research trends in the field
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
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