A Mathematical Framework for Agent Based Models of Complex Biological Networks

Hinkelmann, Franziska; Murrugarra, David; Jarrah, Abdul Salam; Laubenbacher, Reinhard

doi:10.1007/s11538-010-9582-8

Cited by 67 publications

(46 citation statements)

References 12 publications

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“…We note here that there are many approaches to designing the SLM, including (but not limited to) time series models of transfer functions, difference equations (Oremland and Laubenbacher 2014b), ordinary, partial, and stochastic differential equations, polynomial dynamical systems (Hinkelmann et al. 2011), and Markov chains. Within each of these rough categories, many approaches to developing a model exist.…”

Section: Systems Analysis and Control For Agent-based Modelsmentioning

confidence: 99%

Optimization and Control of Agent-Based Models in Biology: A Perspective

Fitzpatrick

Christley

et al. 2016

Bull Math Biol

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Agent-based models (ABMs) have become an increasingly important mode of inquiry for the life sciences. They are particularly valuable for systems that are not understood well enough to build an equation-based model. These advantages, however, are counterbalanced by the difficulty of analyzing and using ABMs, due to the lack of the type of mathematical tools available for more traditional models, which leaves simulation as the primary approach. As models become large, simulation becomes challenging. This paper proposes a novel approach to two mathematical aspects of ABMs, optimization and control, and it presents a few first steps outlining how one might carry out this approach. Rather than viewing the ABM as a model, it is to be viewed as a surrogate for the actual system. For a given optimization or control problem (which may change over time), the surrogate system is modeled instead, using data from the ABM and a modeling framework for which ready-made mathematical tools exist, such as differential equations, or for which control strategies can explored more easily. Once the optimization problem is solved for the model of the surrogate, it is then lifted to the surrogate and tested. The final step is to lift the optimization solution from the surrogate system to the actual system. This program is illustrated with published work, using two relatively simple ABMs as a demonstration, Sugarscape and a consumer-resource ABM. Specific techniques discussed include dimension reduction and approximation of an ABM by difference equations as well systems of PDEs, related to certain specific control objectives. This demonstration illustrates the very challenging mathematical problems that need to be solved before this approach can be realistically applied to complex and large ABMs, current and future. The paper outlines a research program to address them.

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Section: Systems Analysis and Control For Agent-based Modelsmentioning

confidence: 99%

Optimization and Control of Agent-Based Models in Biology: A Perspective

Fitzpatrick

Christley

et al. 2016

Bull Math Biol

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“…A method that allows a researcher to look at the quotient of the model and predict the behavior of the bigger original model would be a desirable tool. There exist a framework that makes it possible to translate an agent-based model into a system of Boolean equations [3], and thus, at least in some cases, it can be translated to a Boolean CCN.…”

Section: Relationship With Agent-based Modelsmentioning

confidence: 99%

Coupled cell networks: Boolean perspective

Swirydowicz

2017

BIOMATH

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Abstract-In this paper we use Boolean framework to redefine coupled cell networkss, originally described in [2]. We also analyze some of the important properties of Boolean coupled cell networkss.In the second part of this paper we focus on properties of a quotient networks. We redefine the concept of a quotient to suit Boolean network framework. Next, we investigate in details the networks in which two-cell bidirectional ring and three-cell bidirectional ring arise as quotients.

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“…Furthermore, they do not use their formalism to prove properties of either kind of model or show how this could be done. Hinkelmann et al (2011) extend Grimm et al's (2006 Overview, Design Concepts, and Details (ODD) protocol by adding an algebraic field to describe agent behavior. First we review ODD then consider Hinkelmann et al's (2011) extension of it.…”

Section: Partial Recursive Functionsmentioning

confidence: 99%

A theoretical formalism for analyzing agent-based models

North

2014

Complex Adapt Syst Model

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Purpose: Following Holland, complex adaptive systems (CASs) are collections of interacting, autonomous, learning decision makers embedded in an interactive environment. Modeling CASs is challenging for a variety of reasons including the presence of heterogeneity, spatial relationships, nonlinearity, and, of course, adaptation. The challenges of modeling CASs can largely be overcome by using the individual-level focus of agent-based modeling. Agent-based modeling has been used successfully to model CASs in many disciplines. Many of these models were implemented using agent-based modeling software such as Swarm, Repast 3, Repast Simphony, Repast for High-Performance Computing, MASON, NetLogo, or StarLogo. All of these options use modular imperative architectures with factored agents, spaces, a scheduler, logs, and an interface. Many custom agent-based models also use this kind of architecture. This paper's contribution is to introduce and apply a theoretical formalism for analyzing modular imperative agent-based models of CASs. This paper includes an analysis of three example models to show how the formalism is useful for predicting the execution time and space requirements for representations of common CASs.Method: The paper details the formalism and then uses it to prove several new findings about modular imperative agent-based models.Results: It is proven that the asymptotic time and space performance of modular imperative agent-based modeling studies is computationally optimal for a common class of problems. Here 'optimal' means that no other technique can solve the same problem computationally using less asymptotic time or space. Modular imperative agent-based models are shown to be universal models, subject to the correctness of the Church-Turing thesis. Several other results are also proven about the time and space performance of modular imperative agent-based models. The formalism is then used to predict the performance of three models and the results are found to compare closely to the measured performance.Conclusions: This paper's contribution is to introduce, analyze, and apply a theoretical formalism for proving findings about agent-based models with modular agent scheduler architectures. Given that this kind of modeling is both computationally optimal and a natural structural match for many modeling problems, it follows that it is the best modeling method for such problems.

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A Mathematical Framework for Agent Based Models of Complex Biological Networks

Cited by 67 publications

References 12 publications

Optimization and Control of Agent-Based Models in Biology: A Perspective

Optimization and Control of Agent-Based Models in Biology: A Perspective

Coupled cell networks: Boolean perspective

A theoretical formalism for analyzing agent-based models

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