Mathematical Models for Cellular Interactions in Development

By A. Lindenmayer. 1968

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Citations in the corpus

Deep learning in neural networks: An overview (2014, background): “, through Lindenmeyer Systems (Jacob, Lindenmayer, & Rozenberg, 1994; Lindenmayer, 1968), graph rewriting (Kitano, 1990), Cellular Encoding (Gruau, Whitley, & Pyeatt, 1996), HyperNEAT (Clune, Stanley, Pennock, & Ofria, 2011; D’Ambrosio & Stanley, 2007; Stanley, D’Ambrosio, & Gauci, 2009; van den Ber”
Generating Purkinje networks in the human heart (2015, methodology): “Under similar conditions, our algorithm generates a network with 1219761 branches, three times more than a conventional algorithm with 4197107 branches.”
A Survey on Procedural Modelling for Virtual Worlds (2014, background): “Lindenmayer described a linear cellular subdivision mechanism as a rewriting system of terminal and non-terminal symbols of a grammar [Lin68].”
Finite element tree crown hydrodynamics model (FETCH) using porous media flow within branching elements: A new representation of tree hydrodynamics (2005, methodology): “One of the popular models for branching-tree systems is based on the so-called L-system [Lindenmayer, 1968, 1971].”
Evolutionary Computation for Reinforcement Learning (2012, methodology): “For example, L-systems (Lindenmayer, 1968), which are formal grammars for describing complex recursive structures, have been used to evolve both the morphology and control system for autonomous robots, greatly outperforming direct encodings (Hornby and Pollack, 2002).”
Designing Neural Networks Using Genetic Algorithms with Graph Generation System (1990, methodology): “The graph generation grammar is augmentation of Lindenmayer's L-system, which is designed to describe morphogenesis [13] [12].”
Evolutionary computation: a unified approach (2018, unknown): “A well-known example of this are “L-systems”, a parallel rule system interpreter which has been used to model the growth process in many biological systems (Lindenmayer, 1968).”
3D Architectural Modelling of Aerial Photomorphogenesis in White Clover (Trifolium repens L.) using L-systems (2000, methodology): “…(Prusinkiewicz et al., 2000), which describes constituent elements of a compound module: M t; thM !d I t; thI K t; thK B t; thB 7 The square brackets indicate that the leaf primordium and the bud are positioned laterally (as branches) with respect to their supporting internode (Lindenmayer, 1968).”
Grammar-based codes: A new class of universal lossless source codes (2000, background): “First, we need to define the concept of unnormalized entropy, which will be needed in this section and in subsequent parts of the paper.”
Procedural Modeling Using Autoencoder Networks (2015, background): “[21] mark the first use of procedural models and targets biological modeling.”
Advances in Computational Intelligence (2003, unknown): “L-systems were intended to model cellular division; nowadays they are popular in many areas, including computer graphics and theoretical computer science [59, 110].”
In search of intelligence: evolving a developmental neuron capable of learning (2014, background): “Lindenmayer (1968) systems though introduced for modelling plant branching structures, its application to develop neural morphologies was also successful (Ascoli, Krichmar, Scorcioni, Nasuto, & Senft, 2001).”
Evolving 3D Morphology and Behavior by Competition (1994, methodology): “This approach is related to Lsystems, graftal grammars, and object instancing techniques [8,11,13,15,23].”