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49 results on '"Maignan, Aude"'

1. Optimal Communication Unbalanced Private Set Union

Author

Dumas, Jean-Guillaume, Galan, Alexis, Grenet, Bruno, Maignan, Aude, and Roche, Daniel S.

Subjects
Computer Science - Cryptography and Security, Computer Science - Symbolic Computation
Abstract

We present new two-party protocols for the Unbalanced Private Set Union (UPSU) problem.Here, the Sender holds a set of data points, and the Receiver holds another (possibly much larger) set, and they would like for the Receiver to learn the union of the two sets and nothing else. Furthermore, the Sender's computational cost, along with the communication complexity, should be smaller when the Sender has a smaller set.While the UPSU problem has numerous applications and has seen considerable recent attention in the literature, our protocols are the first where the Sender's computational cost and communication volume are linear in the size of the Sender's set only, and do not depend on the size of the Receiver's set.Our constructions combine linearly homomorphic encryption (LHE) withfully homomorphic encryption (FHE). The first construction uses multi-point polynomial evaluation (MEv) on FHE, and achieves optimal linear cost for the Sender, but has higher quadratic computational cost for the Receiver. In the second construction we explore another trade-off: the Receiver computes fast polynomial Euclidean remainder in FHE while the Sender computes a fast MEv, in LHE only. This reduces the Receiver's cost to quasi-linear, with a modest increase in the computational cost for the Sender.Preliminary experimental results using HElib indicate that, for example, a Sender holding 1000 elements can complete our first protocol using less than 2s of computation time and less than 10MB of communication volume, independently of the Receiver's set size.

Published
2024

2. Organic Structures Emerging From Bio-Inspired Graph-Rewriting Automata

Author

Cousin, Paul and Maignan, Aude

Subjects
Mathematics - Dynamical Systems
Abstract

Graph-Rewriting Automata (GRA) are an extension of Cellular Automata to a dynamic structure using local graph-rewriting rules. This work introduces linear algebra based tools that allow for a practical investigation of their behavior in deeply extended time scales. A natural subset of GRA is explored in different ways thereby demonstrating the benefits of this method. Some elements of the subset were discovered to create chaotic patterns of growth and others to generate organic-looking graph structures. These phenomena suggest a strong relevance of GRA in the modeling natural complex systems. The approach presented here can be easily adapted to a wide range of GRA beyond the chosen subset.

Published
2022
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3. VESPo: Verified Evaluation of Secret Polynomials

Author

Dumas, Jean-Guillaume, Maignan, Aude, Pernet, Clément, and Roche, Daniel S.

Subjects
Computer Science - Cryptography and Security, Computer Science - Symbolic Computation
Abstract

Proofs of Retrievability are protocols which allow a Client to store data remotely and to efficiently ensure, via audits, that the entirety of that data is still intact. Dynamic Proofs of Retrievability (DPoR) also support efficient retrieval and update of any small portion of the data.We propose a novel protocol for arbitrary outsourced data storage that achieves both low remote storage size and audit complexity.A key ingredient, that can be also of intrinsic interest, reduces to efficiently evaluating a secret polynomial at given public points, when the (encrypted) polynomial is stored on an untrusted Server.The Server performs the evaluations and also returns associated certificates. A Client can check that the evaluations are correct using the certificates and some pre-computed keys, more efficiently than re-evaluating the polynomial.Our protocols support two important features: the polynomial itself can be encrypted on the Server, and it can be dynamically updated by changing individual coefficients cheaply without redoing the entire setup.Our methods rely on linearly homomorphic encryption and pairings, and our implementation shows good performance for polynomial evaluations with millions of coefficients, and efficient DPoR with terabytes of data.For instance, for a 1TB database, compared to the state of art, we can reduce the Client storage by 5000x, communication size by 20x, and client-side audit time by 2x, at the cost of one order of magnitude increase in server-side audit time.

Published
2021

4. Dynamic proofs of retrievability with low server storage

Author

Anthoine, Gaspard, Dumas, Jean-Guillaume, Hanling, Michael, de Jonghe, Mélanie, Maignan, Aude, Pernet, Clément, and Roche, Daniel

Subjects
Computer Science - Cryptography and Security
Abstract

Proofs of Retrievability (PoRs) are protocols which allow a client to store data remotely and to efficiently ensure, via audits, that the entirety of that data is still intact. A dynamic PoR system also supports efficient retrieval and update of any small portion of the data. We propose new, simple protocols for dynamic PoR that are designed for practical efficiency, trading decreased persistent storage for increased server computation, and show in fact that this tradeoff is inherent via a lower bound proof of time-space for any PoR scheme. Notably, ours is the first dynamic PoR which does not require any special encoding of the data stored on the server, meaning it can be trivially composed with any database service or with existing techniques for encryption or redundancy. Our implementation and deployment on Google Cloud Platform demonstrates our solution is scalable: for example, auditing a 1TB file takes just less than 5 minutes and costs less than $0.08 USD. We also present several further enhancements, reducing the amount of client storage, or the communication bandwidth, or allowing public verifiability, wherein any untrusted third party may conduct an audit.

Published
2020

5. Parallel Graph Rewriting with Overlapping Rules

Author

Echahed, Rachid and Maignan, Aude

Subjects
Computer Science - Formal Languages and Automata Theory, Computer Science - Logic in Computer Science, F.4.2
Abstract

We tackle the problem of simultaneous transformations of networks represented as graphs. Roughly speaking, one may distinguish two kinds of simultaneous or parallel rewrite relations over complex structures such as graphs: (i) those which transform disjoint subgraphs in parallel and hence can be simulated by successive mere sequential and local transformations and (ii) those which transform overlapping subgraphs simultaneously. In the latter situations, parallel transformations cannot be simulated in general by means of successive local rewrite steps. We investigate this last problem in the framework of overlapping graph transformation systems. As parallel transformation of a graph does not produce a graph in general, we propose first some sufficient conditions that ensure the closure of graphs by parallel rewrite relations. Then we mainly introduce and discuss two parallel rewrite relations over graphs. One relation is functional and thus deterministic, the other one is not functional for which we propose sufficient conditions which ensure its confluence., Comment: 26 pages

Published
2017

6. On the Planar Split Thickness of Graphs

Author

Eppstein, David, Kindermann, Philipp, Kobourov, Stephen, Liotta, Giuseppe, Lubiw, Anna, Maignan, Aude, Mondal, Debajyoti, Vosoughpour, Hamideh, Whitesides, Sue, and Wismath, Stephen

Subjects
Mathematics - Combinatorics
Abstract

Motivated by applications in graph drawing and information visualization, we examine the planar split thickness of a graph, that is, the smallest $k$ such that the graph is $k$-splittable into a planar graph. A $k$-split operation substitutes a vertex $v$ by at most $k$ new vertices such that each neighbor of $v$ is connected to at least one of the new vertices. We first examine the planar split thickness of complete graphs, complete bipartite graphs, multipartite graphs, bounded degree graphs, and genus-1 graphs. We then prove that it is NP-hard to recognize graphs that are $2$-splittable into a planar graph, and show that one can approximate the planar split thickness of a graph within a constant factor. If the treewidth is bounded, then we can even verify $k$-splittability in linear time, for a constant $k$.

Published
2015
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7. Communication Optimal Unbalanced Private Set Union

Author

Dumas, Jean-Guillaume, Galan, Alexis, Grenet, Bruno, Maignan, Aude, Roche, Daniel S., Dumas, Jean-Guillaume, Galan, Alexis, Grenet, Bruno, Maignan, Aude, and Roche, Daniel S.

Abstract

We consider the private set union (PSU) problem, where two parties each hold a private set of elements, and they want one of the parties (the receiver) to learn the union of the two sets and nothing else. Our protocols are targeted for the unbalanced case where the receiver's set size is larger than the sender's set size, with the goal of minimizing the costs for the sender both in terms of communication volume and local computation time. This setting is motivated by applications where the receiver has significantly more data (input set size) and computational resources than the sender which might be realized on a small, low-power device. Asymptotically, we achieve communication cost linear in the sender's (smaller) set size, and computation costs for sender and receiver which are nearly-linear in their respective set sizes. To our knowledge, ours is the first algorithm to achieve nearly-linear communication and computation for PSU in this unbalanced setting. Our protocols utilize fully homomorphic encryption (FHE) and, optionally, linearly homomorphic encryption (LHE) to perform the necessary computations while preserving privacy. The underlying computations are based on univariate polynomial arithmetic realized within homomorphic encryption, namely fast multiplication, modular reduction, and multi-point evaluation. These asymptotically fast HE polynomial arithmetic algorithms may be of independent interest.

Published
2024

8. Random Chromatin Neighborhoods in 2n=40 Mus m. domesticus Meiotic Cells: P-Percolation and Image Segmentation

Author

Berríos, Soledad, Fenner, Julio López, Maignan, Aude, Hutchison, David, Editorial Board Member, Kanade, Takeo, Editorial Board Member, Kittler, Josef, Editorial Board Member, Kleinberg, Jon M., Editorial Board Member, Mattern, Friedemann, Editorial Board Member, Mitchell, John C., Editorial Board Member, Naor, Moni, Editorial Board Member, Pandu Rangan, C., Editorial Board Member, Steffen, Bernhard, Editorial Board Member, Terzopoulos, Demetri, Editorial Board Member, Tygar, Doug, Editorial Board Member, Goos, Gerhard, Founding Editor, Hartmanis, Juris, Founding Editor, Chaves, Madalena, editor, and Martins, Manuel A., editor

Published
2019
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12. On the Planar Split Thickness of Graphs

Author

Eppstein, David, Kindermann, Philipp, Kobourov, Stephen, Liotta, Giuseppe, Lubiw, Anna, Maignan, Aude, Mondal, Debajyoti, Vosoughpour, Hamideh, Whitesides, Sue, Wismath, Stephen, Hutchison, David, Series editor, Kanade, Takeo, Series editor, Kittler, Josef, Series editor, Kleinberg, Jon M., Series editor, Mattern, Friedemann, Series editor, Mitchell, John C., Series editor, Naor, Moni, Series editor, Pandu Rangan, C., Series editor, Steffen, Bernhard, Series editor, Terzopoulos, Demetri, Series editor, Tygar, Doug, Series editor, Weikum, Gerhard, Series editor, Kranakis, Evangelos, editor, Navarro, Gonzalo, editor, and Chávez, Edgar, editor

Published
2016
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15. Complex Self-Reproducing Systems

Author

Edwards, Roderick, Maignan, Aude, Zelinka, Ivan, Series editor, Adamatzky, Andrew, Series editor, Chen, Guanrong, Series editor, Sanayei, Ali, editor, and Rössler, Otto E., editor

Published
2014
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18. Comments on and Extensions to Criteria of Keiper and Li for the Riemann Hypothesis

Author

Mcphedran, Ross, Scott, Tony, Maignan, Aude, School of Physics [Sydney], The University of Sydney, Institute of Physical Chemistry [Aachen] (IPC), Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH), Calcul Algébrique et Symbolique, Sécurité, Systèmes Complexes, Codes et Cryptologie (CASC), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), and Maignan, Aude

Subjects
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [PHYS.MPHY] Physics [physics]/Mathematical Physics [math-ph]
Abstract

Keiper and Li published independent investigations of the connection between the Riemann hypothesis and the properties of sums over powers of zeros of the Riemann zeta function. Here we comment on these papers, and propose some extensions of their results. Key results are obtained using generalised Lambert functions.

Published
2022

20. On the Planar Split Thickness of Graphs

Author

Eppstein, David, primary, Kindermann, Philipp, additional, Kobourov, Stephen, additional, Liotta, Giuseppe, additional, Lubiw, Anna, additional, Maignan, Aude, additional, Mondal, Debajyoti, additional, Vosoughpour, Hamideh, additional, Whitesides, Sue, additional, and Wismath, Stephen, additional

Published
2016
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21. Quantum clustering analysis: Minima of the potential energy function

Author

Maignan, Aude, Scott, Tony, Calcul Algébrique et Symbolique, Sécurité, Systèmes Complexes, Codes et Cryptologie (CASC), Laboratoire Jean Kuntzmann (LJK), Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP ), Université Grenoble Alpes (UGA), Institute of Physical Chemistry [Aachen] (IPC), Rheinisch-Westfälische Technische Hochschule Aachen (RWTH), Maignan, Aude, and Rheinisch-Westfälische Technische Hochschule Aachen University (RWTH)

Subjects
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], energy function, Quantum clustering, exponential polynomial, [MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph], Data clustering, optimization
Abstract

International audience; Quantum clustering (QC), is a data clustering algorithm based on quantum mechanics which is accomplished by substituting each point in a given dataset with a Gaussian. The width of the Gaussian is a value, a hyper-parameter which can be manually defined and manipulated to suit the application. Numerical methods are used to find all the minima of the quantum potential as they correspond to cluster centers. Herein, we investigate the mathematical task of expressing and finding all the roots of the exponential polynomial corresponding to the minima of a twodimensional quantum potential. This is an outstanding task because normally such expressions are impossible to solve analytically. However, we prove that if the points are all included in a square region of size , there is only one minimum. This bound is not only useful in the number of solutions to look for, by numerical means, it allows to to propose a new numerical approach "per block". This technique decreases the number of particles (or samples) by approximating some groups of particles to weighted particles. These findings are not only useful to the quantum clustering problem but also for the exponential polynomials encountered in quantum chemistry, Solid-state Physics and other applications.

Published
2020

27. GPaR

Author

Despréaux, Stéphane, Maignan, Aude, Maignan, Aude, and Laboratoires d'excellence - Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique - - PERSYVAL-lab2011 - ANR-11-LABX-0025 - LABX - VALID

Subjects
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-MS] Computer Science [cs]/Mathematical Software [cs.MS]
Published
2018

29. Poster

Author

Hanling, Michael, primary, Anthoine, Gaspard, additional, Dumas, Jean-Guillaume, additional, Maignan, Aude, additional, Pernet, Clément, additional, and Roche, Daniel S., additional

Published
2019
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31. DEM-Systems: a new type of adaptive system

Author

Edwards, Roderick, Maignan, Aude, Department of Mathematics and Statistics [Melbourne], University of Melbourne, Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), and Maignan, Aude

Subjects
[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM], self-organizing systems, self-reproducing systems, cellular automata, [INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation
Abstract

International audience; A generic adaptive network called a DEM-system is presented. Deeply influenced bycellular automata (CA) and L-Systems, it has the structural flexibility of an L-system but canexpand to higher dimensions and inherits algebraic properties of CA. The behavior of DEM-systems are discussed here in the case of a linear ring or chain. For the additive case, a partialpartition into three finiteness classes is given. Interesting behaviors, such as reproduction, areexhibited.

Published
2016

32. Discrete stochastic graph dynamics for the nuclear architecture of mouse meiotic prophase spermatocytes

Author

López fenner, Julio, Maignan, Aude, Echahed, Rachid, Berríos, Soledad, Universidad de La Frontera, Temuco, Chile, Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019])-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Laboratoire d'Informatique de Grenoble (LIG ), Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes [2016-2019] (UGA [2016-2019]), Universidad de Chile, ANR-11-LABX-0025,PERSYVAL-lab,Systemes et Algorithmes Pervasifs au confluent des mondes physique et numérique(2011), and Universidad de Chile = University of Chile [Santiago] (UCHILE)

Subjects
[SDV.BC]Life Sciences [q-bio]/Cellular Biology, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [INFO.INFO-MO]Computer Science [cs]/Modeling and Simulation, ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2017

33. A class of discrete dynamical systems with properties of both cellular automata and L-systems.

Author

Edwards, Roderick and Maignan, Aude

Subjects
*CELLULAR automata, *DYNAMICAL systems, *DISCRETE systems, *ENTROPY (Information theory), *DEFINITIONS
Abstract

We introduce and explore a type of discrete dynamic system inheriting some properties of both cellular automata (CA) and L-systems. Originally suggested by Jean Della Dora, and thus called DEM-systems after him and the two current authors, these systems can have the structural flexibility of an L-system as well as algebraic properties of CA. They are defined as sequences on a one-dimensional loop with rules governing dynamics in which new sites can be created, depending on the states of a neighbourhood of sites, and complex behaviour can be generated. Although the definition of DEM-systems is quite broad, we define some subclasses, for which more complete results can be obtained. For example, we define an additive subclass, for which algebraic results on asymptotic growth are possible, and an elementary class of particularly simple rules, for which nevertheless impressive complexity is achievable. Unlike for CA, finite initial sequences can produce positive spatial entropy over time. However, even in cases where the entropy is zero, considerable complexity is possible, especially when the sequence length grows to infinity, and we demonstrate and study behaviours of DEM-systems including fragmentation of sequences, self-reproducing patterns, self-similar but irregular patterns, patterns that not only produce new sites but produce producers of new sites, and sequences whose growth rate is sublinear, linear, quadratic, cubic, or exponential. The most complex behaviour from small finite initial conditions and the simplest class of rules appear to have positive entropy, a suggestion for which we have so far only stong numerical evidence, though we present a proof for these 'elementary' DEM-systems that entropy cannot reach the theoretical maximum of 1. [ABSTRACT FROM AUTHOR]

Published
2020
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36. Modélisation des systèmes dynamiques évolutifs

Author

Maignan, Aude, Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), région Rhônes-Alpes, and Maignan, Aude

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]
Published
2009

38. On the Planar Split Thickness of Graphs.

Author

Eppstein, David, Kindermann, Philipp, Kobourov, Stephen, Liotta, Giuseppe, Lubiw, Anna, Maignan, Aude, Mondal, Debajyoti, Vosoughpour, Hamideh, Whitesides, Sue, and Wismath, Stephen

Subjects
BIPARTITE graphs, GEOMETRIC vertices, APPROXIMATION theory, COMPLETE graphs, VISUALIZATION
Abstract

Motivated by applications in graph drawing and information visualization, we examine the planar split thickness of a graph, that is, the smallest k such that the graph is k-splittable into a planar graph. A k-split operation substitutes a vertex v by at most k new vertices such that each neighbor of v is connected to at least one of the new vertices. We first examine the planar split thickness of complete graphs, complete bipartite graphs, multipartite graphs, bounded degree graphs, and genus-1 graphs. We then prove that it is NP-hard to recognize graphs that are 2-splittable into a planar graph, and show that one can approximate the planar split thickness of a graph within a constant factor. If the treewidth is bounded, then we can even verify k-splittability in linear time, for a constant k. [ABSTRACT FROM AUTHOR]

Published
2018
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39. A short tutorial for DynSys: A program for dynamical systems based on dynamic graphs

Author

Despréaux, Stéphane, Maignan, Aude, Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Calculs Algébriques et Systèmes Dynamiques (CASYS), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), and Bidégaray-Fesquet, Brigitte

Subjects
InformationSystems_MODELSANDPRINCIPLES, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], ComputingMilieux_MISCELLANEOUS, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

Rapport technique; International audience

Published
2009

40. Dynamical systems based on dynamic graphs

Author

Despréaux, Stéphane, Maignan, Aude, Bidégaray-Fesquet, Brigitte, Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Calculs Algébriques et Systèmes Dynamiques (CASYS), and Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2009

41. Dynamic systems: an algorithmic point of view

Author

Della Dora, Jean, Maignan, Aude, Tournier, Laurent, Laboratoire de Modélisation et Calcul (LMC - IMAG), Université Joseph Fourier - Grenoble 1 (UJF)-Institut National Polytechnique de Grenoble (INPG)-Centre National de la Recherche Scientifique (CNRS), and Bidegaray-Fesquet, Brigitte

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], ComputingMilieux_MISCELLANEOUS
Abstract

International audience

Published
2006

45. Hybrid computation

Author

Dora, Jean Della, primary, Maignan, Aude, additional, Mirica-Ruse, Mihaela, additional, and Yovine, Sergio, additional

Published
2001
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49. Complex Self-reproducing Systems

Author

Roderick Edwards, Aude Maignan, Department of Mathematics and Statistics [Melbourne], University of Melbourne, Calculs Algébriques et Systèmes Dynamiques (CASYS), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Ali Sanayei, Ivan Zelinka, and Otto E. Rössler, Department of Mathematics and Statistics, University of Victoria, Canada, UPMF, and Maignan, Aude

Subjects
Physics, Self-organization, Pure mathematics, Class (set theory), Dynamical systems theory, cellular automata, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], 0102 computer and information sciences, 01 natural sciences, Cellular automaton, Prime (order theory), 010305 fluids & plasmas, Set (abstract data type), self-organizing systems, 010201 computation theory & mathematics, self-reproducing systems, 0103 physical sciences, Line (geometry), L-Systems, Algebraic number, substitution systems, ComputingMilieux_MISCELLANEOUS, F42
Abstract

Cellular automata and L-Systems are well-known formal models to describe the behaviour of biological processes. They are discrete dynamical systems, each of which can have complex and varied behaviour. Here, we study a class of substitutive systems incorporating properties of both cellular automata and L-systems, that exhibits self-reproducing behaviour. A one-dimensional array of cells is considered, each cell has a set of modes or states which are determined by a number from \(\mathbb {Z}/\mathbf{{n}}\mathbb {Z}^*\) (\(n\) prime). The behaviour of a cell depends on the states of its neighbours and obeys an additive rule. It has also a cell-division mode, which allows the line of cells to grow. The behaviour of such a model can be complex, but, using algebraic techniques, we prove that it can describe a reproducing system.

Published
2014

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