466 research outputs found
Petri Net Languages and Infinite Subsets of Nm
No full textAbstractFamilies of Petri net languages are usually defined by varying the type of transition labeling and the class of subsets of Nm to be used as sets of final markings (m is the number of places). So far three main classes of subsets have been studied: the trivial class containing as single element Nm, the class of finite subsets of Nm, and the class of ideals (or covering subsets) of Nm. In this paper we extend the known hierarchy of Petri net languages by considering the classes of semi-cylindrical, star-free, recognizable, rational (or semilinear) subsets of Nm. We compare the related Petri net languages. For arbitrarily labeled and for λ-free labeled Petri net languages, the above hierarchy collapses: one does not increase the generality by considering semilinear accepting sets instead of the usual finite ones. However, for free-labeled and for deterministic Petri net languages, we show that one gets new distinct subclasses of languages, for which several decidability problems become solvable. We establish as intermediate results some properties of star-free subsets of general monoids
Nonlinear perron-probenius theory and dynamics of cone maps
No full textIn this paper several recent results concerning the dynamics of order preserving (sub) homogeneous maps on polyhedral cones are reviewed. These results were obtained by the author in collaboration with Marianne Akian, Stephane Gaubert, Roger Nussbaum, Michael Scheutzow and Colin Sparrow in [2], [13] and [15] and are new nonlinear extensions of the Perron-Frobenius theory
Stephane Mallarme: A synthesis of romanticism and parnassianism, 1970
No full textThe purpose of this paper is to analyse works of Stephane Mallarme, father of Symbolism, pointing out romantic and parnassian elements. Symbolism, like Romanticism, attempted to express the interior thoughts of man. The symbolist movement then, was not only a revolt against Parnassianism but also a return to Romanticism. On the other hand, one would not be incorrect in saying that Romanticism reached its culmination in the works of the symbolists poets. For this reason, an attempt will be made to show that the works of Mallarme, father of Symbolism, can be considered as a synthesis of Romanticism and Parnassianism. This thesis contains three chapters. The first chapter is devoted to a discussion of Romanticism and of Parnassianism. Special attention is given to the origin, development, characteristics and influences of each school. The relationship of one School with the other is also pointed out. The second chapter consists of a biographical sketch of Stephane Mallarme. Special emphasis is placed on factors and events in his life which may have influenced or determined the elements of Romanticism and Parnassianism in his poetry. The third chapter is devoted to an analysis of some of the poems of Stephane Mallarme", "Les Fenetres," V Apparition," "L'Azur," "Toast Funebre," "Le Vierge," "L'Apres-Midi d'un Faune." In these analyses special attention is given to the romantic and parnassian tendencies of the poems. Since these romantic-parnaassian elements occur frequently throughout his works, it has been concluded that Mallarme's poetry can be considered as a synthesis of the two poetic schools
Linear algebra over T-pairs
No full textThis paper treats linear algebra over a semiring pair, in a wide range of
applications to tropical algebra and related areas such as hyperrings and fuzzy
rings. First we present a more general category of ``pairs'' with their
morphisms, called ``weak morphisms,'' paying special attention to supertropical
pairs, hyperpairs, and the doubling functor. Then we turn to matrices and the
question of whether the row rank, column rank, and submatrix rank of a matrix
are equal. Often the submatrix rank is less than or equal to the row rank and
the column rank, but there is a counterexample to equality, discovered some
time ago by the second author, which we provide in a more general setting
(``pairs of the second kind'') that includes the hyperfield of signs.
Additional positive results include a version of Cramer's rule, and we find
situations when equality holds, encompassing results by Akian, Gaubert,
Guterman, Izhakian, Knebusch, and Rowen. We pay special attention to the
question of whether vectors of length need be dependent. At the end,
we introduce a category with stronger morphisms, that preserve a surpassing
relation.Comment: 46 p
Obama's visit to Korea : an unwavering US-ROC alliance amidst regional tensions
No full textFor more about the East-West Center, see http://www.eastwestcenter.org/Stephane Mot, Independent Author and Blogger living in Seoul, explains that "Obama's visit did not change the opinion of the vast majority of South Koreans who consider the US-ROK alliance to be unequal, but it did further confirm the importance of South Korea for US engagement towards Asia.
Solving multichain stochastic games with mean payoff by policy iteration
No full textInternational audienceZero-sum stochastic games with finite state and action spaces, perfect information, and mean payoff criteria arise in particular from the monotone discretization of mean-payoff pursuit-evasion deterministic differential games. In that case no irreducibility assumption on the Markov chains associated to strategies are satisfied (multichain games). The value of such a game can be characterized by a system of nonlinear equations, involving the mean payoff vector and an auxiliary vector (relative value or bias). Cochet-Terrasson and Gaubert proposed in (C. R. Math. Acad. Sci. Paris, 2006) a policy iteration algorithm relying on a notion of nonlinear spectral projection (Akian and Gaubert, Nonlinear Analysis TMA, 2003), which allows one to avoid cycling in degenerate iterations. We give here a complete presentation of the algorithm, with details of implementation in particular of the nonlinear projection. This has led to the software PIGAMES and allowed us to present numerical results on pursuit-evasion games
Iteration of order preserving subhomogeneous maps on a cone
No full textWe investigate the iterative behaviour of continuous order preserving subhomogeneous maps , where is a polyhedral cone in a finite dimensional vector space. We show that each bounded orbit of converges to a periodic orbit and, moreover, the period of each periodic point of is bounded by where is the number of facets of the polyhedral cone. By constructing examples on the standard positive cone in , we show that the upper bound is asymptotically sharp
Tropical Cramer Determinants Revisited
No full textSee also arXiv:1309.6298International audienceWe prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness results, which extend or refine earlier results of Gondran and Minoux (1978), Plus (1990), Gaubert (1992), Richter-Gebert, Sturmfels and Theobald (2005) and Izhakian and Rowen (2009). Computational issues are also discussed; in particular, some of our proofs lead to Jacobi and Gauss-Seidel type algorithms to solve linear systems in suitably extended tropical semirings
De la convexité tropicale aux jeux à somme nulle
No full textConférence plénièreInternational audienc
Rational Series over Dioids and Discrete Event Systems
No full textthis paper is obviously too short for such a program, we have chosen to propose an introductive guided tour. A more detailed exposition will be found in our references and in a more complete paper to appear elsewhere. 1 Rational Series in a Single Indeterminat
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