Antoine Spicher

Declarative mesh subdivision using topological rewriting in MGS

Mesh subdivision algorithms are usually specified informally using graphical schemes defining local mesh refinements. These algorithms are then implemented efficiently in an imperative framework. The implementation is cumbersome and implies some tricky indices management. Smith et al. (2004) asks the question of the declarative programming of such algorithms in an index-free way. In this paper, we positively answer this question by presenting a rewriting framework where mesh refinements are described by simple rules. This framework is based on a notion of topological chain rewriting. Topological chains generalize the notion of labeled graph to higher dimensional objects. This framework has been implemented in the domain specific language MGS. The same generic approach has been used to implement Loop as well as Butterfly, Catmull-Clark and Kobbelt subdivision schemes.

Rule-based programming for integrative biological modeling

Systems biology aims at integrating processes at various time and spatial scales into a single and coherent formal description to allow computer modeling. In this context, we focus on rule-based modeling and its integration in the domain-specific language MGS. Through the notions of topological collections and transformations, MGS allows the modeling of biological processes at various levels of description. We validate our approach through the description of various models of the genetic switch of the λ phage, from a very simple biochemical description of the process to an individual-based model on a Delaunay graph topology. This approach is a first step into providing the requirements for the emerging field of spatial systems biology which integrates spatial properties into systems biology.

Building topological spaces for musical objects

The development of spatial representations of musical objects allows for a reformulation of algorithmic problems arising in musical theory, fosters novel classifications and provides new computational tools. In this paper, we show how a topological representation for n-note chords associated with the degrees of the diatonic scale and for the All-Interval Series (AIS) can be automatically built using MGS, a rule-based spatial programming language. Then, we suggest a new categorization for AIS based on their spatial construction.

Interaction-Based Simulations for Integrative Spatial Systems Biology

Systems biology aims at integrating processes at various time and spatial scales into a single and coherent formal description to allow analysis and computer simulation. In this context, we focus on rule-based modeling and its integration in the domain-specific language MGS. Through the notions of topological collections and transformations, MGS allows the modeling of biological processes at various levels of description. We validate our approach through the description of various models of a synthetic bacteria designed in the context of the International Genetically Engineered Machine Competition, from a very simple biochemical description of the process to an individual-based model on a Delaunay graph topology. This approach is a first step into providing the requirements for the emerging field of spatial systems biology which integrates spatial properties into systems biology.

Computation and Visualization of Musical Structures in Chord-Based Simplicial Complexes

We represent chord collections by simplicial complexes. A temporal organization of the chords corresponds to a path in the complex. A set of n-note chords equivalent up to transposition and inversion is represented by a complex related by its 1-skeleton to a generalized Tonnetz. Complexes are computed with MGS, a spatial computing language, and analyzed and visualized in Hexachord, a computer-aided music analysis environment. We introduce the notion of compliance, a measure of the ability of a chord-based simplicial complex to represent a musical object compactly. Some examples illustrate the use of this notion to characterize musical pieces and styles.

Translating Discrete Multi-Agents Systems into Cellular Automata: Application to Diffusion-Limited Aggregation

This paper deals with the synchronous implementation of situated Multi-Agent Systems (MAS) in order to have no execution bias and to ease their programming on massively parallel computing devices. For this purpose we investigate the translation of discrete MAS into Cellular Automata (CA). Contrarily to the sequential scheduling generally used in MAS simulations, CA are a model for massively parallel computing where the updating of the components is synchronous.

Spatial Organization of the Chemical Paradigm and the Specification of Autonomic Systems

The chemical paradigm is an unconventional programming paradigm well fitted to the high-level specification of parallel systems . Based on the fixed point iterations of local rules, its use has been advocated for the programming of autonomic and amorphous systems . However, this model lacks an explicit handling of spatial relationships . n nIn this contribution, we first show how the chemical paradigm can be extended beyond multisets to arbitrary topological collections . Topological collections handle in a uniform way sophisticated data structures required in algorithmics as well as distributed data structures needed for the programming of autonomic or amorphous systems. Then we adapt a well-known result on multiset ordering to the more general case of topological collections. Well-founded ordering on topological collection can be used to prove the termination of the fixed point iteration of local rules.

Gardening cyber-physical systems

Todays artefacts, from small devices to buildings and cities, are, or are becoming, cyber-physical socio-technical systems, with tightly interwoven material and computational parts. Currently, we have to laboriously build such systems, component by component, and the results are often difficult to maintain, adapt, and reconfigure. Even soft ware is brittle and non-trivial to adapt and change.

Representation of musical structures and processes in simplicial chord spaces

In this article, we present a set of musical transformations based on the representations of chord spaces derived from the Tonnetz. These chord spaces are formalized as simplicial complexes. A musical composition is represented in such a space by a trajectory. Spatial transformations are applied on these trajectories and induce a transformation of the original composition. These concepts are implemented in two applications, the software HexaChord and the Max object bach.tonnetz, dedicated to music analysis and composition, respectively.

Interaction-Based Modeling of Morphogenesis in MGS

In this chapter, we advocate a domain specific language (DSL) approach to overcome the difficulties of modeling and simulating morphogenetic processes. A careful discussion of the design goals of a DSL leads to the development of an experimental programming language called MGS. Its declarative approach is based on the notion of topological collection originating from algebraic topology. Topological collections arise naturally when modeling a “dynamical system with a dynamic structure”, or (ds) (^2), as the state of the system. The evolution function of the system is specified by a transformation, which is a set of rewriting rules where each rule defines a local interaction. We illustrate these notions through different models of the same morphogenetic process: the growth of a T-shaped structure. The objective is to show how a variety of models can be consistently handled within the MGS framework.