#### DMCA

## M. HABIB Michel, Président

### Citations

14015 |
Computers and Intractability; A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
Citation Context ...eed some algorithms to decide SEPI comparability and compute SEPI glb/lub. However, the induced subgraph isomorphism problem, which is the decision problem related to SISO, is known to be NP-complete =-=[28]-=-. The decision problem related to EPI is also NP-complete [68]. To obtain a similar result for SEPI, we cannot use the pointed graph encoding of Prop. 3.38 and the NP-completeness result for EPI: inde... |

1472 | Exact stochastic simulation of coupled chemical reactions - Gillespie - 1977 |

1046 | The complexity of theorem-proving procedures
- Cook
- 1971
(Show Context)
Citation Context ...sking whether M ′ can be reached from M by vertex deletions is equivalent to asking whether there is a subgraph isomorphism (SISO) from M to M ′, and the SISO problem is a classic NP-complete problem =-=[16]-=-. Yet SISO is not satisfying, since it does not capture the omnipresent graph transformation underlying the Michaelis-Menten reduction in Fig.1.2. However, we observe that adding vertex merging is eno... |

350 |
Categories for the working mathematician, Graduate Texts
- Lane
- 1998
(Show Context)
Citation Context ...tices, but none surjective on arcs. In the second row, there is a morphism from G to G′ surjective on arcs, but none surjective on vertices. G G′ a b a b a1 b1 a2 b2 a b c In categorical lexicon (see =-=[41]-=-) an epi is an arrow h such that g1○h = g2○h⇒ g1 = g2 ; the meaning in our case is that through an epimorphism, the source graph should completely capture the structure of the target graph; every node... |

349 |
Graph minors. XIII. The disjoint paths problem
- Robertson, Seymour
- 1995
(Show Context)
Citation Context ...t of graphs such that if G ∉ S, then G reduces to some O ∈ O(S). 42 In turn, for every given graph O, there is a polynomial time algorithm AO which determines whether its input graph has O as a minor =-=[56]-=-, which means that for every family stable by the minor operations, there is a polynomial-time algorithm that determines membership. Is there such a property for SEPI? We will see that SEPI is not a W... |

226 |
A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks
- Schuster, Fell, et al.
- 2000
(Show Context)
Citation Context ...or each reaction. For instance, in [38], it is elaborated that structural information hidden in kinetic laws may affect the results obtained from structural analyses, such as elementary mode analysis =-=[59]-=-, flux balance analysis [67], chemical organization theory [18], deficiency analysis or chemical reaction network theory [25, 60]. Furthermore, the correct structure is mandatory when a reaction netwo... |

194 |
Ultrasensitivity in the mitogen-activated protein kinase cascade’,
- Huang, Ferrell
- 1996
(Show Context)
Citation Context ...Still, model 26 (with non-differentiated Mp) does not reduce to model 29 since that model indeed distinguishes MpY and MpT variants. Now, concerning 3-step MAPK cascade models, the models 9 and 11 of =-=[37]-=- and [48] respectively are detected as isomorphic. Indeed, they only differ by molecule names and parameter values. They do not reduce to 28 and 30, which are models that do not differentiate sites of... |

166 |
animating dynamical systems: a guide to XPPAUT for researchers and students
- Ermentrout, Simulating
(Show Context)
Citation Context ...s for both transient and steady-state analyses via numerical integration (for instance using MATLAB®, Copasi, . . . ), parameter sensitivity analyses, or bifurcation analyses, (with tools like XPPAUT =-=[21]-=- for instance), but only when kinetic information is available. In absence of knowledge on the kinetics of each reaction, various qualitative analyses can be performed on the structure of the reaction... |

161 | Graph minors. XX. Wagner’s conjecture
- Robertson, Seymour
- 2004
(Show Context)
Citation Context ..., but it is quite different. The graph minor theory has been extensively studied. The “minor of” binary relation between graphs, which we will write →minor, enjoys the well-quasi-order property (WQO) =-=[57]-=-. That property entails that for every set S of graphs stable by the operations considered, this set can be characterized by a finite obstruction set O(S), i.e., a set of graphs such that if G ∉ S, th... |

151 |
Graph minors. I. Excluding a forest.
- Robertson, Seymour
- 1983
(Show Context)
Citation Context ... that there may be several common graphs of maximum cardinality. 3.6 Comparison to graph minors SEPI is the relation defined by vertex deletion and vertex merging. It may look similar to graph minors =-=[55]-=-, which are defined by vertex deletion, arc deletion and merging vertices linked by an arc, but it is quite different. The graph minor theory has been extensively studied. The “minor of” binary relati... |

148 |
On a relation between graph edit distance and maximum common subgraph.
- Bunke
- 1997
(Show Context)
Citation Context ...perational way, by means of the minimum cost sequence of graph edit operations that should be performed to transform G into G′, i.e. by using the state graph induced by allowed edition operations. In =-=[9]-=-, Bunke has connected these two definitions in the context of edit operations that generalize deletion, by introducing a special cost function for the graph edit distance, and by showing that under th... |

127 |
Regulatory networks seen as asynchronous automata: A logical description
- Thomas
- 1991
(Show Context)
Citation Context ...k. This approach has rapidly developed in Systems Biology for reasoning on large interaction networks, with for instance, the analysis of qualitative attractors in a logical dynamics of gene networks =-=[65]-=-, reachability and temporal logic properties in reaction networks [20, 5, 12, 24, 10], structural invariants in the Petri net representation of the reactions [54, 71, 2, 14, 58, 63], or model reductio... |

117 | Biomodels database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Research, 34(suppl 1):D689–D691
- Novere, Bornstein, et al.
- 2006
(Show Context)
Citation Context ...ssification of Models by Model Reduction. When we have worked on a model M and obtained a model M ′, how can we relate M ′ to the mass of published models, collected in repositories such as BioModels =-=[43]-=-? Most results on model reduction only answer to the problem of preserving some behaviour of M and when simplifying to M ′. However, other questions are of interest: Is M ′ also a reduced version of a... |

106 |
Metabolic Flux Balancing: Basic Concepts, Scientific and Practical Use.
- Varma, Palsson
- 1994
(Show Context)
Citation Context ...ce, in [38], it is elaborated that structural information hidden in kinetic laws may affect the results obtained from structural analyses, such as elementary mode analysis [59], flux balance analysis =-=[67]-=-, chemical organization theory [18], deficiency analysis or chemical reaction network theory [25, 60]. Furthermore, the correct structure is mandatory when a reaction network must be interpreted as a ... |

103 |
A model for circadian oscillations in the Drosophila period protein (PER
- Goldbeter
- 1995
(Show Context)
Citation Context ...8_Bind 122_Fish 145_Wang Figure 10.3: Subgraph epimorphisms for models of Calcium Oscillations from BioModels. accordance with the fact those models were built on top of knowledge from the Drosophila =-=[34]-=- with a similar clock mechanism. Models 171 [45] presents a model for the Drosophila, including Per/Tim (with two levels of phosphorylation) and the complex. Model 21 [46] actually studies the same mo... |

102 |
Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades’,
- Markevich, Hoek, et al.
- 2004
(Show Context)
Citation Context ... GHz. These results where first published in [31]. 10.2.1 Mapk models The matchings found between the models of the MAPK cascade are depicted in Fig. 10.1. This class contains the family of models of =-=[51]-=- numbered 26 to 31. The reductions found automatically among these models are interesting for checking whether the formalism is faithful to biological reasoning, since the authors describe refinements... |

100 | Application of formal methods to biological regulatory networks: extending Thomas’ asynchronous logical approach with temporal logic.
- Bernot, Comet, et al.
- 2004
(Show Context)
Citation Context ...g on large interaction networks, with for instance, the analysis of qualitative attractors in a logical dynamics of gene networks [65], reachability and temporal logic properties in reaction networks =-=[20, 5, 12, 24, 10]-=-, structural invariants in the Petri net representation of the reactions [54, 71, 2, 14, 58, 63], or model reductions using graph theory concepts [31, 29]. These qualitative analysis tools do not rely... |

95 | M.L.: Petri Net Representations in Metabolic Pathways. In:
- Reddy, Mavrovouniotis, et al.
- 1993
(Show Context)
Citation Context ...n a logical dynamics of gene networks [65], reachability and temporal logic properties in reaction networks [20, 5, 12, 24, 10], structural invariants in the Petri net representation of the reactions =-=[54, 71, 2, 14, 58, 63]-=-, or model reductions using graph theory concepts [31, 29]. These qualitative analysis tools do not rely on kinetic information, but on the structure of the reaction network which has thus to be corre... |

90 |
Scaffold Proteins May Biphasically Affect the Levels of Mitogen-Activated Protein Kinase Signaling and Reduce Its Threshold Properties.
- Levchenko, Bruck, et al.
- 2000
(Show Context)
Citation Context ...del 26 (with non-differentiated Mp) does not reduce to model 29 since that model indeed distinguishes MpY and MpT variants. Now, concerning 3-step MAPK cascade models, the models 9 and 11 of [37] and =-=[48]-=- respectively are detected as isomorphic. Indeed, they only differ by molecule names and parameter values. They do not reduce to 28 and 30, which are models that do not differentiate sites of phosphor... |

88 |
A minimal cascade model for the mitotic oscillator involving cyclin and cdc2 kinase
- Goldbeter
- 1991
(Show Context)
Citation Context ...eactions scheme. This is the case for instance of model BIOMD0000000008.xml in BioModels, for the ODE model of [27]. This model adds a control mechanism to the cell-cycle model of Goldbeter et al. in =-=[33]-=- but with this transcription in SBML, the reaction graph is not even connected. Here are some of the reactions of this model which illustrate the problem: r4: (1+ -1*[M])*V1*(r4K1+(-1*[M]+1))^-1 for _... |

86 | Predicting learnt clauses quality in modern sat solvers
- Audemard, Simon
- 2009
(Show Context)
Citation Context ... caoscill mapk circ ccycle Figure 9.2: No-solutions in Glucose. 9.2 SEPI We implemented the CLP model of chapter 5 using GNU Prolog [17] 1.4.4, and the SAT model from chapter 6 is solved with Glucose =-=[3]-=- 2.2. In the experiments reported in Tab. 9.2, the computation time was limited with a timeout of 20 minutes. Performance has been evaluated on an Intel Core 2 Duo 2.4Ghz processor. The four macro-col... |

77 | N.: Modelling and querying interaction networks in the biochemical abstract machine biocham
- Fages, Soliman, et al.
- 2004
(Show Context)
Citation Context ...g on large interaction networks, with for instance, the analysis of qualitative attractors in a logical dynamics of gene networks [65], reachability and temporal logic properties in reaction networks =-=[20, 5, 12, 24, 10]-=-, structural invariants in the Petri net representation of the reactions [54, 71, 2, 14, 58, 63], or model reductions using graph theory concepts [31, 29]. These qualitative analysis tools do not rely... |

74 |
BIOCHAM: An environment for modeling biological systems and formalizing experimental knowledge
- Calzone, Fages, et al.
(Show Context)
Citation Context ...-coding ODEs into models make it so that extracting reaction graphs straightforwardly would yield incomplete structure from models. In this chapter, we explain the import algorithms used in Biocham ( =-=[23, 11]-=-) to deal with the gap between an intended reaction model and the given encoding. This preprocessing algorithm has been published in [22], the contribution of the author is mainly the hidden molecule ... |

74 | A.: Experimental validation of a predicted feedback loop in the multi-oscillator clock of Arabidopsis thaliana. Molecular systems biology 2(1)
- Locke, Kozma-Bognar, et al.
- 2006
(Show Context)
Citation Context ...ich explains why only 34 cannot be reduced to it. Model 22 [66] is a quite detailed model that focusses on the interlocked feedback loops, which can be mapped to 170 but not 34. Models 55 [50] and 89 =-=[49]-=- are both from Locke and others and about the circadian clock of Arabidopsis but include, in one case light induction, and in the other a new feedback loop. This explains why they do not give any matc... |

72 |
Toward a detailed computational model for the mammalian circadian clock
- Leloup, Goldbeter
- 2003
(Show Context)
Citation Context ...son were left out from the picture. Let us first have a look at the isomorphisms found. Models 73 and 78 are isomorphic. This is in accordance with the fact that these quite detailed models come from =-=[47]-=- and differ indeed by parameter values. Models 74 and 83 are isomorphic too. They also correspond to two versions of a second model from the same article, but this time with the addition of the Rev-Er... |

58 |
A model for circadian rhythms in Drosophila incorporating the formation of a complex between the PER and TIM proteins
- Leloup, Goldbeter
- 1998
(Show Context)
Citation Context ...pimorphisms for models of Calcium Oscillations from BioModels. accordance with the fact those models were built on top of knowledge from the Drosophila [34] with a similar clock mechanism. Models 171 =-=[45]-=- presents a model for the Drosophila, including Per/Tim (with two levels of phosphorylation) and the complex. Model 21 [46] actually studies the same model, unfortunately a different encoding in SBML ... |

45 |
Schuster S: Topological analysis of metabolic networks based on Petri net theory
- Zevedei-Oancea
(Show Context)
Citation Context ...n a logical dynamics of gene networks [65], reachability and temporal logic properties in reaction networks [20, 5, 12, 24, 10], structural invariants in the Petri net representation of the reactions =-=[54, 71, 2, 14, 58, 63]-=-, or model reductions using graph theory concepts [31, 29]. These qualitative analysis tools do not rely on kinetic information, but on the structure of the reaction network which has thus to be corre... |

44 |
Snoopy e a unifying Petri net framework to investigate biomolecular networks
- Rohr, Marwan, et al.
- 2010
(Show Context)
Citation Context ...n a logical dynamics of gene networks [65], reachability and temporal logic properties in reaction networks [20, 5, 12, 24, 10], structural invariants in the Petri net representation of the reactions =-=[54, 71, 2, 14, 58, 63]-=-, or model reductions using graph theory concepts [31, 29]. These qualitative analysis tools do not rely on kinetic information, but on the structure of the reaction network which has thus to be corre... |

43 | Extension of a genetic network model by iterative experimentation and mathematical analysis.
- Locke, Southern
- 2005
(Show Context)
Citation Context ...artments, which explains why only 34 cannot be reduced to it. Model 22 [66] is a quite detailed model that focusses on the interlocked feedback loops, which can be mapped to 170 but not 34. Models 55 =-=[50]-=- and 89 [49] are both from Locke and others and about the circadian clock of Arabidopsis but include, in one case light induction, and in the other a new feedback loop. This explains why they do not g... |

35 |
Structural sources of robustness in biochemical reaction networks,”
- Shinar, Feinberg
- 2010
(Show Context)
Citation Context ...esults obtained from structural analyses, such as elementary mode analysis [59], flux balance analysis [67], chemical organization theory [18], deficiency analysis or chemical reaction network theory =-=[25, 60]-=-. Furthermore, the correct structure is mandatory when a reaction network must be interpreted as a stochastic process à la Gillespie [32]. It is worth noticing that these structural analyses may also... |

33 |
Robust oscillations within the interlocked feedback model of Drosophila circadian rhythm
- Ueda, Hagiwara, et al.
- 2001
(Show Context)
Citation Context ... model 170 [4] which focusses on the positive feedback loop of the circadian cycle oscillator. It is quite small but has two compartments, which explains why only 34 cannot be reduced to it. Model 22 =-=[66]-=- is a quite detailed model that focusses on the interlocked feedback loops, which can be mapped to 170 but not 34. Models 55 [50] and 89 [49] are both from Locke and others and about the circadian clo... |

30 | 2003 Measuring the similarity of labeled graphs
- Champin, Solnon
(Show Context)
Citation Context ...the distance between two graphs not only by means of vertex insertion and deletion operations, but also by means of vertex merge and split operations, thus leading to the extended graph edit distance =-=[1, 13]-=-. Here we introduce a graph edit distance which also allows merge operations. This distance is a simplified case of the extended graph edit distance introduced in [1], which has been defined for label... |

26 |
Chaos and birhythmicity in a model for circadian oscillations of the PER
- Leloup, Goldbeter
- 1999
(Show Context)
Citation Context ...nowledge from the Drosophila [34] with a similar clock mechanism. Models 171 [45] presents a model for the Drosophila, including Per/Tim (with two levels of phosphorylation) and the complex. Model 21 =-=[46]-=- actually studies the same model, unfortunately a different encoding in SBML (variable parameters instead of species for instance) makes it impossible to find a matching. Many models map to model 170 ... |

25 |
Graph Edit Distance with Node Splitting and Merging, and Its Application to Diatom Identification.
- Ambauen, Fischer, et al.
- 2003
(Show Context)
Citation Context ...the distance between two graphs not only by means of vertex insertion and deletion operations, but also by means of vertex merge and split operations, thus leading to the extended graph edit distance =-=[1, 13]-=-. Here we introduce a graph edit distance which also allows merge operations. This distance is a simplified case of the extended graph edit distance introduced in [1], which has been defined for label... |

25 |
Modeling and querying biochemical interaction networks
- Chabrier-Rivier, Chiaverini, et al.
- 2004
(Show Context)
Citation Context ...g on large interaction networks, with for instance, the analysis of qualitative attractors in a logical dynamics of gene networks [65], reachability and temporal logic properties in reaction networks =-=[20, 5, 12, 24, 10]-=-, structural invariants in the Petri net representation of the reactions [54, 71, 2, 14, 58, 63], or model reductions using graph theory concepts [31, 29]. These qualitative analysis tools do not rely... |

24 | Symmetry breaking using value precedence.
- Walsh
- 2006
(Show Context)
Citation Context ...ce relation of the pairs (µ1, µ2). We can force the tuple (µ(1) . . . µ(n)) to be lexicographically minimal among all the possible σ ○ µ where σ is a permutation. The following scheme is described in =-=[69]-=-: associate a bounding function M ∶ Vi Ð→{1, . . . , ni}, with M(1) = 1, ∀v ∈ Viµi(v) ≤ M(v), and M(v + 1) = max(M(v), µi(v) + 1). This is called a precedence constraint. When listing the numbers that... |

23 |
Modularization of biochemical networks based on classification of Petri net t-invariants
- Grafahrend-Belau, Schreiber, et al.
- 2008
(Show Context)
Citation Context ...uces a structural persistence criterion, Petri net place invariants 83 reveal conservation laws in [62], while transition invariants can be used to identify fragile vertices and the core of a network =-=[35]-=-, or to determine steady state solutions [53]. We intend to try SEPI on real-life models repository BioModels ( [43]), however the expressivity allowed by the SBML format and the common practice of ha... |

21 |
Modeling feedback loops of the mammalian circadian oscillator
- Becker-Weimann
- 2004
(Show Context)
Citation Context ... actually studies the same model, unfortunately a different encoding in SBML (variable parameters instead of species for instance) makes it impossible to find a matching. Many models map to model 170 =-=[4]-=- which focusses on the positive feedback loop of the circadian cycle oscillator. It is quite small but has two compartments, which explains why only 34 cannot be reduced to it. Model 22 [66] is a quit... |

21 | A decompositional approach to parameter estimation in pathway modeling: a case study of the Akt and MAPK pathways and their crosstalk, Bioinformatics
- Koh
- 2006
(Show Context)
Citation Context ...when a reaction network must be interpreted as a stochastic process à la Gillespie [32]. It is worth noticing that these structural analyses may also directly support dynamic analyses. For instance, =-=[39]-=- applies network decomposition for a modular parameter estimation approach, [2] introduces a structural persistence criterion, Petri net place invariants 83 reveal conservation laws in [62], while tra... |

19 | Complex intracellular calcium oscillations. A theoretical exploration of possible mechanisms, Biophys
- Borghans, Dupont, et al.
- 1997
(Show Context)
Citation Context ... to the addition of a third species in this model where Ca2+ oscillations are seen as a mediator of genetic expression. Models 43, 44 and 45 all relate to three different models from the same article =-=[8]-=-. Model 43 is the “basic one pool” model and there is a match from 44, the “1-pool model with IP3 degradation” since the latter is indeed a refinement of the former. The morphisms from 43 and 44 to 16... |

17 | Decompositions of all different, global cardinality and related constraints
- Bessiere, Katsirelos, et al.
- 2009
(Show Context)
Citation Context ...o publications that describe how sorting networks can be implemented and what can be gained from them. For a full exposition, [19] compares different approaches to coding integers in boolean clauses, =-=[6]-=- uses such networks on decompositions of cardinality-related constraints, [15] shows that Parberry’s odd-even networks behave better than Batcher’s merge networks for this purpose, [40] efficiently so... |

17 |
Mathematical aspects of mass action kinetics
- Feinberg
- 1977
(Show Context)
Citation Context ...esults obtained from structural analyses, such as elementary mode analysis [59], flux balance analysis [67], chemical organization theory [18], deficiency analysis or chemical reaction network theory =-=[25, 60]-=-. Furthermore, the correct structure is mandatory when a reaction network must be interpreted as a stochastic process à la Gillespie [32]. It is worth noticing that these structural analyses may also... |

16 | Petri net modelling of biological regulatory networks.
- Chaouiya, Remy, et al.
- 2008
(Show Context)
Citation Context |

16 | Formal cell biology in Biocham
- Fages, Soliman
- 2008
(Show Context)
Citation Context ...-coding ODEs into models make it so that extracting reaction graphs straightforwardly would yield incomplete structure from models. In this chapter, we explain the import algorithms used in Biocham ( =-=[23, 11]-=-) to deal with the gap between an intended reaction model and the given encoding. This preprocessing algorithm has been published in [22], the contribution of the author is mainly the hidden molecule ... |

16 | Solving subgraph isomorphism problems with constraint programming, Constraints 15
- Zampelli, Deville, et al.
- 2010
(Show Context)
Citation Context ...nstraint satisfaction problems [42], and in this context, constraint programming has experimentally proven to be as competitive as, and in some cases to outperform, dedicated approaches such as Vflib =-=[70, 64]-=-. The model we present here is a refinement of the one used in our first publication about the subject in [31]. In the next chapter, we will present a SAT solver -based approach to the SEPI decision p... |

15 | A Petri net approach to persistence analysis in chemical reaction networks
- Angeli, Sontag
- 2007
(Show Context)
Citation Context |

14 | Simulation of drosophila circadian oscillations, mutations, and light responses by a model with vri, pdp-1, and clk
- Smolen
- 2004
(Show Context)
Citation Context ...nations, by merging the three new species (Rev-Erbα mRNA, protein in the cytoplasm and protein in the nucleus named Mr, Rc and Rn in model 74) to Bmal1 in the nucleus (named Bn in model 73). Model 34 =-=[61]-=- is a quite small model of the Drosophila’s circadian clock. The fact that its structure is included in that of the mammalian clock of the above models is in 105 039_Marh 098_Gold 115_Somo 117_Dupo 16... |

13 |
A theory for controlling cell cycle dynamics using a reversibly binding inhibitor
- Gardner, Dolnik, et al.
- 1998
(Show Context)
Citation Context ...nd play simulations, some ODE models have been transcribed in SBML using the artificial reactions scheme. This is the case for instance of model BIOMD0000000008.xml in BioModels, for the ODE model of =-=[27]-=-. This model adds a control mechanism to the cell-cycle model of Goldbeter et al. in [33] but with this transcription in SBML, the reaction graph is not even connected. Here are some of the reactions ... |

13 |
Using chemical organization theory for model checking
- Kaleta
- 2009
(Show Context)
Citation Context ...y Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 8.4.2 Global analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 8.4.3 Model inconsistencies studied in =-=[38]-=- . . . . . . . . . . . . . . . . . . . . 91 9 Performance Evaluation 93 9.1 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 9.2 SEPI . . . . . . . . . . .... |

12 | All different-based filtering for subgraph isomorphism
- Solnon
- 2010
(Show Context)
Citation Context ...nstraint satisfaction problems [42], and in this context, constraint programming has experimentally proven to be as competitive as, and in some cases to outperform, dedicated approaches such as Vflib =-=[70, 64]-=-. The model we present here is a refinement of the one used in our first publication about the subject in [31]. In the next chapter, we will present a SAT solver -based approach to the SEPI decision p... |

11 |
Sönmez. Pathway logic: Symbolic analysis of biological signaling
- Eker, Knapp, et al.
- 2002
(Show Context)
Citation Context |

11 |
Fages F. A graphical method for reducing and relating models in systems biology
- Gay, Soliman
(Show Context)
Citation Context ...ular order of the operations is not important, so we can use commutation properties 2.3, 2.7 and 2.8 to reduce the search space. These results were already used in our first publication about SEPI in =-=[31]-=-. Doing this amounts to changing formalisms: for each chain of operations, there is a corresponding notion of graph morphism. We first introduce classical notions of graph morphisms, and then introduc... |

10 | Pairwise cardinality networks
- Codish, Zazon-Ivry
- 2010
(Show Context)
Citation Context ... can be gained from them. For a full exposition, [19] compares different approaches to coding integers in boolean clauses, [6] uses such networks on decompositions of cardinality-related constraints, =-=[15]-=- shows that Parberry’s odd-even networks behave better than Batcher’s merge networks for this purpose, [40] efficiently solves MAXSAT by coding the cardinality constraints with sorting networks coded ... |

10 |
di Fenizio P. Chemical organisation theory
- Dittrich, Speroni
(Show Context)
Citation Context ...structural information hidden in kinetic laws may affect the results obtained from structural analyses, such as elementary mode analysis [59], flux balance analysis [67], chemical organization theory =-=[18]-=-, deficiency analysis or chemical reaction network theory [25, 60]. Furthermore, the correct structure is mandatory when a reaction network must be interpreted as a stochastic process à la Gillespie ... |

10 |
Invariants and other structural properties of biochemical models as a constraint satisfaction problem. Algorithms for Molecular Biology
- Soliman
- 2012
(Show Context)
Citation Context |

9 |
Computational complexity of graph compaction
- Vikas
- 1997
(Show Context)
Citation Context ...or the converse, if G′ has no arcs, then the arc codomain of an epimorphism on G′ is empty, since epimorphisms are defined everywhere, the domain must also be empty. The Ph.D. thesis of Narayan Vikas =-=[68]-=- provides an extensive study of graph epimorphisms, which are graph compaction in his nomenclature. 2.2.5 Subgraph Epimorphisms are merge/deletion strings There are notions of morphism corresponding t... |

6 | Finding minimal P/T-invariants as a CSP. In:
- Soliman
- 2008
(Show Context)
Citation Context ... instance, [39] applies network decomposition for a modular parameter estimation approach, [2] introduces a structural persistence criterion, Petri net place invariants 83 reveal conservation laws in =-=[62]-=-, while transition invariants can be used to identify fragile vertices and the core of a network [35], or to determine steady state solutions [53]. We intend to try SEPI on real-life models repository... |

5 |
Nfat and nfkappab activation in t lymphocytes: a model of differential activation of gene expression
- Fisher
- 2006
(Show Context)
Citation Context ...e eliminated by using annotations as further constraints, for instance by taking into account the references to UniProt/KEGG or ChEBI databases that are already present in some SBML models. Model 122 =-=[26]-=- is actually a big model of NFAT and NFκB with a side Calcium oscillator. It includes however many reversible reactions and thus structurally maps to all of the other models of this class. Model 58 is... |

5 |
Steady-state solution of biochemical systems, beyond SSystems via T-invariants
- Nabli, Soliman
- 2010
(Show Context)
Citation Context ...i net place invariants 83 reveal conservation laws in [62], while transition invariants can be used to identify fragile vertices and the core of a network [35], or to determine steady state solutions =-=[53]-=-. We intend to try SEPI on real-life models repository BioModels ( [43]), however the expressivity allowed by the SBML format and the common practice of hard-coding ODEs into models make it so that ex... |

4 |
François Fages, and Sylvain Soliman. Machine learning biochemical networks from temporal logic properties
- Calzone, Chabrier-Rivier
- 2006
(Show Context)
Citation Context |

4 |
On the implementation
- Diaz, Abreu, et al.
- 2012
(Show Context)
Citation Context ... 5 6 7 8 9 10 0 10 20 30 40 50 Timeout (s) N o -s o lu ti o n s (# ) caoscill mapk circ ccycle Figure 9.2: No-solutions in Glucose. 9.2 SEPI We implemented the CLP model of chapter 5 using GNU Prolog =-=[17]-=- 1.4.4, and the SAT model from chapter 6 is solved with Glucose [3] 2.2. In the experiments reported in Tab. 9.2, the computation time was limited with a timeout of 20 minutes. Performance has been ev... |

4 |
Solnon C: On the subgraph epimorphism problem
- Gay, Fages, et al.
(Show Context)
Citation Context ...parametrized by edit costs. Here we provide 25 a means to compute this distance using a notion akin to maximal subgraph computation, but in the SEPI setting. The result is one of the contributions of =-=[29]-=-. In the first part of this chapter, we will see that SEPI can also be used to formalize the notion of graph contained in both G and G′, and of graph containing both G and G′. In the second part of th... |

4 | Constraint-based graph matching
- Clément
- 2009
(Show Context)
Citation Context ...done in exponential time. In this chapter, we present a constraint programming approach to the SEPI decision problem. Graph matching problems can be easily modeled as constraint satisfaction problems =-=[42]-=-, and in this context, constraint programming has experimentally proven to be as competitive as, and in some cases to outperform, dedicated approaches such as Vflib [70, 64]. The model we present here... |

4 | A boolean model for enumerating minimal siphons and traps in petri-nets
- Nabli, Fages, et al.
- 2012
(Show Context)
Citation Context ...graphs, the decision problem for SEPI comparability is NP-complete. However, reaction graphs coming from real models usually have a particular structure, e.g. low degree, connectedness, low treewidth =-=[52]-=-. Are the problems we presented tractable for some interesting families of graphs? Constraint Model We used GNU-Prolog for our Constraint Programming model, because Biocham is coded with it. SWI-Prolo... |

2 | Inferring reaction models from odes
- Fages, Gay, et al.
- 2012
(Show Context)
Citation Context ...hapter, we explain the import algorithms used in Biocham ( [23, 11]) to deal with the gap between an intended reaction model and the given encoding. This preprocessing algorithm has been published in =-=[22]-=-, the contribution of the author is mainly the hidden molecule inferrence algorithm, which was actually already used in another form in [31]. 8.1 Issues Related to BioModels Encodings Any ODE model ca... |

2 | QMaxSAT: A partial max-SAT solver system description
- Koshimura, Zhang, et al.
(Show Context)
Citation Context ...oolean clauses, [6] uses such networks on decompositions of cardinality-related constraints, [15] shows that Parberry’s odd-even networks behave better than Batcher’s merge networks for this purpose, =-=[40]-=- efficiently solves MAXSAT by coding the cardinality constraints with sorting networks coded in boolean clauses. 6.2 SAT SEPI GLB model Since the SEPI decision problem is NP-complete, the SEPI glb dec... |

1 |
al Biere. Handbook of Satisfiability. Frontiers in artificial intelligence and applications
- et
- 2009
(Show Context)
Citation Context ...s a problem in practice. The coding above, so-called ladder encoding, achieved by using the order on ∣V ′ ∪ {}∣ to force the image of v ∈ V to be minimal, only has O(∣V ∣ ⋅ ∣V ′ ∪ {}∣) clauses. See =-=[7]-=- for general information on encodings. 6.1.2 Subgraph Epimorphism Coding Let us build on the previous part to constrain the function to represent a SEPI. Variables. Additional variables are used to co... |

1 |
François Fages. A constraint program for subgraph epimorphisms with application to identifying model reductions in systems biology
- Gay, Martinez, et al.
- 2011
(Show Context)
Citation Context ...nto SAT instances and using a SAT solver to find whether they are satisfiable or not is another successful approach to solve NP-complete problems. We presented this approach in a specialized workshop =-=[30]-=-. In this chapter, we present CNF (Conjunctive Normal Form) encodings of the SEPI problem and of the decision variants of the SEPI glb (resp. lub) problems, i.e. the existence of a graph of bounded si... |

1 |
le Novère et al. BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems
- Nicolas
- 2006
(Show Context)
Citation Context ...emains after automatic curation, in accordance with the earlier results. 91 92 Chapter 9 Performance Evaluation 9.1 Data The reaction graphs used for this benchmark come from the BioModels repository =-=[44]-=-, in particular, the same models adopted in [31]. These are real-life, curated models retranscribed from publications. The method used to extract a reaction graph from a BioModels file will be describ... |