Numerical Methods for Transport-Resistance Source–Sink Allocation Models

Prusinkiewicz, Przemysław; Allen, Mitch; Escobar‐Gutiérrez, Abraham J.; DeJong, Theodore M.

doi:10.1007/1-4020-6034-3_11

Cited by 33 publications

(33 citation statements)

References 10 publications

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“…Thus, instead of expressing a structure using a matrix, and applying general methods for dealing with sparse matrices, it is better to operate directly on cell complexes [4,29,30]. The appropriate numerical methods have been devised in some contexts [12,[31][32][33], but a more complete toolbox of numerical methods designed for dynamic cell complexes is needed.…”

Section: Discussionmentioning

confidence: 99%

Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems

Prusinkiewicz

Lane

2012

Springer Proceedings in Mathematics

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We consider computational modeling of biological systems that consist of discrete components arranged into linear structures. As time advances, these components may process information, communicate and divide. We show that: (1) the topological notion of cell complexes provides a useful framework for simulating information processing and flow between components; (2) an index-free notation exploiting topological adjacencies in the structure is needed to conveniently model structures in which the number of components changes (for example, due to cell division); and (3) Lindenmayer systems operating on cell complexes combine the above elements in the case of linear structures. These observations provide guidance for constructing L-systems and explain their modeling power. L-systems operating on cell complexes are illustrated by revisiting models of heterocyst formation in Anabaena and by presenting a simple model of leaf development focused on the morphogenetic role of the leaf margin.

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Section: Discussionmentioning

confidence: 99%

Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems

Prusinkiewicz

Lane

2012

Springer Proceedings in Mathematics

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“…A potentially more efficient alternative is to store and manipulate quantities at their geometrically meaningful location [3]; in other words, to reformulate numerical methods so that they operate directly on the dynamic data structures that represent the system topology [27,28]. Examples include a method for solving systems of linear equations in growing tree structures directly using L-systems [4,17], based on an adaptation of Gaussian elimination to tree graphs [15].…”

Section: Extensions Of Developmental Computing To Surfaces and Volumesmentioning

confidence: 99%

Developmental Computing

Prusinkiewicz

2009

Lecture Notes in Computer Science

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Abstract. Since their inception over forty years ago, L-systems have proven to be a useful conceptual and programming framework for modeling the development of plants at different levels of abstraction and different spatial scales. Formally, L-systems offer a means of defining cell complexes with changing topology and geometry. Associated with these complexes are self-configuring systems of equations that represent functional aspects of the models. The close coupling of topology, geometry and computation constitutes a computing paradigm inspired by nature, termed developmental computing. We analyze distinctive features of this paradigm within and outside the realm of biological models.

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“…This specific feature of L-systems was used in the last decade to develop computational models for which the flow of information propagates in a natural way over the plant structure from component to component, e.g. [1] for the transport of carbon, [15] for the transport of water, and [10,5] for the reaction of plants to gravity. All these algorithms use finite di↵erence methods (FDM) for which the plant is decomposed into a finite number of elements and quantities of interest (water content, sugar concentration, forces, displacements, etc.)…”

Section: Introductionmentioning

confidence: 99%

Combining Finite Element Method and L-Systems Using Natural Information Flow Propagation to Simulate Growing Dynamical Systems

Bernard

Gilles

Godin

2014

Theory and Practice of Natural Computing

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Abstract. This paper shows how to solve a system of di↵erential equations controlling the development of a dynamical system based on finite element method and L-Systems. Our methods leads to solve a linear system of equations by propagating the flow of information throughout the structure of the developing system in a natural way. The method is illustrated on the growth of a branching system whose axes bend under their own weight.

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Numerical Methods for Transport-Resistance Source–Sink Allocation Models

Cited by 33 publications

References 10 publications

Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems

Modeling Morphogenesis in Multicellular Structures with Cell Complexes and L-systems

Developmental Computing

Combining Finite Element Method and L-Systems Using Natural Information Flow Propagation to Simulate Growing Dynamical Systems

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