Solving set-valued constraint satisfaction problems

Jaulin, Luc

doi:10.1007/s00607-011-0169-5

Cited by 11 publications

(5 citation statements)

References 21 publications

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“…Granvilliers and Benhamou [19] proposed an algorithm that prunes boxes using both constraint propagation techniques and the interval Newton method. Recently, Domes and Neumaier [15] proposed a constraint propagation method for linear and quadratic constraints and Jaulin [27] studied set-valued CSPs.…”

Section: Review Of Constraint Propagation Methodsmentioning

confidence: 99%

Reverse propagation of McCormick relaxations

et al. 2015

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Constraint propagation techniques have heavily utilized interval arithmetic while the application of convex and concave relaxations has been mostly restricted to the domain of global optimization. Here, reverse McCormick propagation, a method to construct and improve McCormick relaxations using a directed acyclic graph representation of the constraints, is proposed. In particular, this allows the interpretation of constraints as implicitly defining set-valued mappings between variables, and allows the construction and improvement of relaxations of these mappings. Reverse McCormick propagation yields potentially tighter enclosures of the solutions of constraint satisfaction problems than reverse interval propagation. Ultimately, the relaxations of the objective of a non-convex program can be improved by incorporating information about the constraints.

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Section: Review Of Constraint Propagation Methodsmentioning

confidence: 99%

Reverse propagation of McCormick relaxations

et al. 2015

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“…In this case, the location of the bifurcation points of the model in the bifurcation diagram must coincide with the location observed in the experimental dose response curves. To this aim we formulate next a constraint satisfaction problem [ 21 ] where a set of constraints impose the desired conditions on the decision variables.…”

Section: Resultsmentioning

confidence: 99%

A method for inverse bifurcation of biochemical switches: inferring parameters from dose response curves

2014

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BackgroundWithin cells, stimuli are transduced into cell responses by complex networks of biochemical reactions. In many cell decision processes the underlying networks behave as bistable switches, converting graded stimuli or inputs into all or none cell responses. Observing how systems respond to different perturbations, insight can be gained into the underlying molecular mechanisms by developing mathematical models. Emergent properties of systems, like bistability, can be exploited to this purpose. One of the main challenges in modeling intracellular processes, from signaling pathways to gene regulatory networks, is to deal with high structural and parametric uncertainty, due to the complexity of the systems and the difficulty to obtain experimental measurements. Formal methods that exploit structural properties of networks for parameter estimation can help to overcome these problems.ResultsWe here propose a novel method to infer the kinetic parameters of bistable biochemical network models. Bistable systems typically show hysteretic dose response curves, in which the so called bifurcation points can be located experimentally. We exploit the fact that, at the bifurcation points, a condition for multistationarity derived in the context of the Chemical Reaction Network Theory must be fulfilled. Chemical Reaction Network Theory has attracted attention from the (systems) biology community since it connects the structure of biochemical reaction networks to qualitative properties of the corresponding model of ordinary differential equations. The inverse bifurcation method developed here allows determining the parameters that produce the expected behavior of the dose response curves and, in particular, the observed location of the bifurcation points given by experimental data.ConclusionsOur inverse bifurcation method exploits inherent structural properties of bistable switches in order to estimate kinetic parameters of bistable biochemical networks, opening a promising route for developments in Chemical Reaction Network Theory towards kinetic model identification.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-014-0114-2) contains supplementary material, which is available to authorized users.

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“…This distinction is crucial for the proper handling of sets in computations. Thus a thick set, as a set of sets, is epistemic and represents an ill-known set, which is itself considered as ontic; for example, a physical area for which one wants to guarantee the coverage [14], for instance for making sure that a robot can pass in between two obstacles [15,16], is an ontic set.…”

Section: Epistemic Sets and Ontic Setsmentioning

confidence: 99%

Thick Sets, Multiple-Valued Mappings, and Possibility Theory

Dubois

Jaulin

Prade

2020

Statistical and Fuzzy Approaches to Data Processing, With Applications to Econometrics and Other Areas

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Carrying uncertain information via a multivalued function can be found in different settings, ranging from the computation of the image of a set by an inverse function to the Dempsterian transfer of a probabilistic space by a multivalued function. We then get upper and lower images. In each case one handles socalled "thick sets' in the sense of Jaulin, i.e., lower and upper bounded ill-known sets. Such ill-known sets can be found under different names in the literature, e.g., "interval sets" after Y. Y. Yao, "twofold fuzzy sets" in the sense of Dubois and Prade, or "interval-valued fuzzy sets", ... Various operations can then be defined on these sets, then understood in a disjunctive manner (epistemic uncertainty), rather than conjunctively. The intended purpose of this note is to propose a unified view of these formalisms in the setting of possibility theory, which should enable us to provide graded extensions to some of the considered calculi.

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Solving set-valued constraint satisfaction problems

Cited by 11 publications

References 21 publications

Reverse propagation of McCormick relaxations

Reverse propagation of McCormick relaxations

A method for inverse bifurcation of biochemical switches: inferring parameters from dose response curves

Thick Sets, Multiple-Valued Mappings, and Possibility Theory

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