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Gear composition and the stable set polytope

A. Galluccio, C. Gentile, P. Ventura
2008 Operations Research Letters  
We present a new graph composition that produces a graph G from a given graph H and a fixed graph B called gear and we study its polyhedral properties.  ...  This composition yields counterexamples to a conjecture on the facial structure of ST AB(G) when G is claw-free.  ...  The stable set polytope, denoted by ST AB(G), is the convex hull of the incidence vectors of the stable sets of G and it is known to be full-dimensional.  ... 
doi:10.1016/j.orl.2008.01.003 fatcat:ke2ytyaeurelzjuzuxr5umdqsy

2 -clique-bond of stable set polyhedra

Anna Galluccio, Claudio Gentile, Paolo Ventura
2013 Discrete Applied Mathematics  
We consider a graph G obtained as the 2-clique-bond of two graphs G 1 and G 2 and we study the polyhedral properties of the stable set polytope associated with this graph.  ...  In particular, we prove that a linear description of the stable set polytope of G is obtained by properly composing the linear inequalities describing the stable set polytopes of four graphs that are related  ...  The stable set polytope of G is the convex hull of the incidence vectors of the stable sets of G. This polytope has full dimension and it is usually denoted as ST AB(G).  ... 
doi:10.1016/j.dam.2013.02.022 fatcat:asiiqsjgv5hh3m6z6ypligan6q

Lovász-Schrijver PSD-operator on Claw-Free Graphs [article]

Silvia Bianchi, Mariana Escalante, Graciela Nasini, Annegret Wagler
2016 arXiv   pre-print
The subject of this work is the study of _+-perfect graphs defined as those graphs G for which the stable set polytope (G) is achieved in one iteration of Lovász-Schrijver PSD-operator _+, applied to its  ...  In particular, we look for a polyhedral relaxation of (G) that coincides with _+((G)) and (G) if and only if G is _+-perfect.  ...  the stable set polytope.  ... 
arXiv:1612.02670v1 fatcat:o6xiebog4jdxndzeyk63oaait4

Robust Oscillation Suppression Control of Electrified Powertrain System Considering Mechanical-Electric-Network Effects

Wei Li, Wei Zhu, Xiaoyuan Zhu, Jingang Guo
2020 IEEE Access  
In order to dealing with the coupling effects of network-induced delays and event-driven manner of the controller nodes, a delay-free discrete model is further built via polytopic inclusion approach and  ...  The stability of electrified powertrain control system is ensured by using Lyapunov theory, and the controller gain is obtained by solving a set of linear matrix inequalities (LMIs).  ...  J mg is the composite inertia of motor and gear box, ω m and ω w are the speed of motor and wheel respectively, while θ m and θ w are the output angles respectively.  ... 
doi:10.1109/access.2020.2982317 fatcat:as7bj76elnh4jmvtidmclmedji

Combinatorial hybrid systems

Jesper A. Larsen, Rafal Wisniewski, Jacob D. Grunnet
2008 2008 IEEE International Conference on Computer-Aided Control Systems  
affine system on which the possible flows to the polytopes facets can be expressed.  ...  In practice a discrete equivalent of the continuous dynamics is derived, by splitting the continuous state space into a polyhedra complex, and on each of its polytopes approximate the dynamics with an  ...  Driving the car along in 1 st gear, and the car has one specific dynamic. Changing the gear into 2 nd suddenly gives another and different dynamic.  ... 
doi:10.1109/cacsd.2008.4627367 dblp:conf/cacsd/LarsenWG08 fatcat:vj7eahc2ivdprd3mxgbp7i7ua4

Elementary Growth Modes provide a molecular description of cellular self-fabrication [article]

Daan H. de Groot, Josephus Hulshof, Bas Teusink, Frank J. Bruggeman, Robert Planqué
2019 bioRxiv   pre-print
, enzymes and ribosomes, in the proportions that exactly match its own compositionthe growth demand thus depends on the cellular composition.  ...  Simultaneously, the concentrations of these components should be tuned to accomplish this synthesis task – the cellular composition thus depends on the growth demand.  ...  For a given set of metabolite concentrations x and growth rate µ, let P x,µ ⊂ R n+1 be the corresponding convex polytope.  ... 
doi:10.1101/608083 fatcat:ccqiere7ovdoxi2twqm2cesv2u

Elementary Growth Modes provide a molecular description of cellular self-fabrication

Daan H. de Groot, Josephus Hulshof, Bas Teusink, Frank J. Bruggeman, Robert Planqué, Christoph Kaleta
2020 PLoS Computational Biology  
that match its own composition.  ...  Simultaneously, the concentrations of these components affect the rates of metabolism and biosynthesis, and hence the growth rate.  ...  We are grateful to our colleagues Douwe Molenaar and Sieze Douwenga for their helpful opinion and constructive feedback, and to students Thomas Rooijakkers and Martino Pitruzzella for providing insight  ... 
doi:10.1371/journal.pcbi.1007559 pmid:31986156 fatcat:mlh6simodrg7fiyaultm23uqju

Hybrid Dynamical Systems: An Introduction to Control and Verification

Lin Hai
2014 Foundations and Trends® in Systems and Control  
Acknowledgements We highly appreciate the constructive and helpful comments from four anonymous reviewers.  ...  The financial supports of NSF-CNS-1239222 and NSF-CAREER-1253488 for this work are greatly acknowledged.  ...  The vector n i is the normal vector of the facet F i , (i = 1, · · · , K), and, by convention, n i is of unit length and always points out of the polytope P .  ... 
doi:10.1561/2600000001 fatcat:kxr4yc3rjzet7kwzz7pcm6a2ri

Claw-free graphs, skeletal graphs, and a stronger conjecture on ω, Δ, and χ [article]

Andrew D. King, Bruce A. Reed
2012 arXiv   pre-print
In this paper we prove that the conjecture holds for all claw-free graphs. Our approach uses the structure theorem of Chudnovsky and Seymour.  ...  Along the way we discuss a stronger local conjecture, and prove that it holds for claw-free graphs with a three-colourable complement.  ...  Acknowledgements The authors are very grateful to Maria Chudnovsky, Anna Galluccio, and Bruce Shepherd for their extremely helpful input on this work.  ... 
arXiv:1212.3036v1 fatcat:oak65zthsnhvzpzodbnribdiv4

Parameter region for multistationarity in n-site phosphorylation networks [article]

Elisenda Feliu, Nidhi Kaihnsa, Timo de Wolff, Oğuzhan Yürük
2022 arXiv   pre-print
These conditions are derived by exploiting the structure of the polynomial, its Newton polytope, and employing circuit polynomials.  ...  The networks are indexed by a natural number n and for all n, we give sufficient conditions for the polynomial to be positive and hence, preclude multistationarity.  ...  EF acknowledges funding from the Independent Research Fund of Denmark.  ... 
arXiv:2206.08908v1 fatcat:csnfu2yahfc2plbo2jtaxjj2ym

Deformations of convex real projective manifolds and orbifolds [article]

Suhyoung Choi, Gye-Seon Lee, Ludovic Marquis
2016 arXiv   pre-print
We survey the basics of the theory of character varieties, geometric structures on orbifolds, and Hilbert geometry.  ...  The main examples of finitely generated groups for us will be Fuchsian groups, 3-manifold groups and Coxeter groups.  ...  Choose a polytope P and a Coxeter matrix M on the set S of facets of P such that if two facets s and t are not adjacent, 19 then M st = ∞.  ... 
arXiv:1605.02548v4 fatcat:obludy62xzgqbgwlz3x2svmjhe

Reduced Models in Chemical Kinetics via Nonlinear Data-Mining

Eliodoro Chiavazzo, Charles Gear, Carmeline Dsilva, Neta Rabin, Ioannis Kevrekidis
2014 Processes  
The scope of the proposed procedure is presented and discussed by means of an illustrative combustion example.  ...  Unfortunately, no generally applicable a priori recipe for selecting suitable parameterizations of the reduced model is available, and the choice of slow variables often relies upon intuition and experience  ...  , much faster stable eigenvalue; this indicates a separation of time scales and suggest a two-dimensional stable submanifold close to the equilibrium.  ... 
doi:10.3390/pr2010112 fatcat:2vwwotatbzcsfmafvpbqsespui

Holography, Matrix Factorizations and K-stability [article]

Marco Fazzi, Alessandro Tomasiello
2020 arXiv   pre-print
On the other hand, the algebraic technique of non-commutative crepant resolutions, involving matrix factorizations, has been developed to associate a quiver to a singularity.  ...  Recent progress in differential geometry has produced a technique (called K-stability) to recognize which singularities admit conical Calabi-Yau metrics.  ...  In our example, the candidate subsets would be three: one associated to the set of polytopes {∆ 2 , ∆ 3 } (obtained by forgetting ∆ 1 , which is associated to p 1 ), one associated to the set of polytopes  ... 
arXiv:1906.08272v2 fatcat:daznvyegrba5rjvtseofwwmviq

Holography, matrix factorizations and K-stability

Marco Fazzi, Alessandro Tomasiello
2020 Journal of High Energy Physics  
On the other hand, the algebraic technique of non-commutative crepant resolutions, involving matrix factorizations, has been developed to associate a quiver to a singularity.  ...  Recent progress in differential geometry has produced a technique (called K-stability) to recognize which singularities admit conical Calabi-Yau metrics.  ...  If n = m + 1 the quiver in figure 2 does not provide an NCCR,  ... 
doi:10.1007/jhep05(2020)119 fatcat:6eewjj2p5ffhhh3f2q4geep5nu

Full Ellipsoid Embeddings and Toric Mutations [article]

Roger Casals, Renato Vianna
2022 arXiv   pre-print
The construction uniformly recovers the full sequences for the Fibonacci Staircase of McDuff-Schlenk, the Pell Staircase of Frenkel-Muller and the Cristofaro-Gardiner-Kleinman's Staircase, and adds new  ...  This article introduces a new method to construct volume-filling symplectic embeddings of 4-dimensional ellipsoids by employing polytope mutations in toric and almost-toric varieties.  ...  We are grateful to Dan Cristofaro-Gardiner, Richard Hind, Liana Heuberger, Jeff Hicks, Tara Holm, Alessia Mandini, Dusa McDuff, Navid Nabijou, Ana Rita Pires, Laura Starkston and Weiwei Wu for valuable  ... 
arXiv:2004.13232v3 fatcat:bpj7yyghefgctm46wjcg7d7z74
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