1,909 research outputs found
Homology Hopf surfaces. Non-abelian Seiberg-Witten-Theory
No full textCette thèse comporte deux chapitres. Le premier traite des transformations logarithmiques généralisées sur la surface de Hopf. Nous démontrons que toute quatre-variété que l'on obtient par transformations logarithmiques sur deux fibres de la surface de Hopf et qui possède le même type d'homologie que la surface de Hopf est difféomorphe à la surface de Hopf. En d'autres termes, on n'obtient pas de "structure exotique" par cette procédure contrairement à de nombreux exemples de quatre-variétés où cette opération donne lieu à des structures différentiables exotiques. Le deuxième chapitre traite une généralisation de la théorie de Seiberg-Witten à des groupes structuraux PU(N). Le cas des PU(2)-monopoles a déjà été étudié intensivement depuis plus de dix ans avec le but de démontrer la conjecture de Witten : pour certaines quatre-variétés (dites de SW-type simple) les invariants de Donaldson, associés à des PU(2)-connexions anti-autoduales, s'expriment par les variants de Seiberg-Witten. En 2004, Kronheimer a introduit des généralisations des invariants de Donaldson, associés à des PU(N)-connexions anti-autoduales. Nous adaptons les stratégies de Pidstrigach-Tyurin, Okonek-Teleman et Teleman avec le but de démontrer une généralisation de la conjecture de Witten pour les PU(N)-ASD invariants. Nous obtenons deux résultats, l'un de portée générale, l'autre sur des surfaces kähleriennes, qui semblent indiquer que cette conjecture devrait être vraieAIX-MARSEILLE1-Inst.Médit.tech (130552107) / SudocSudocFranceF
Multi-Agent Reinforcement Learning using Centralized Critics in Collaborative Environments
No full textAgents trained through single-agent reinforcement learning methods such as self-play can provide a good level of performance in multi-agent settings and even in fully cooperative environments. However, most of the time, training multiple agents together using single-agent self-play yields poor results as each agent tries to learn how to perform their task while their teammates are also learning. Thus, training models to reach an optimal behaviour in such situations becomes a challenging, if not impossible issue to overcome. One possible solution to deal with this problem is to facilitate a centralized training process in which the policies of all agents are evaluated by a centralized critic that has access to the observations and actions of all the agents in the environment. By using this approach, the environment becomes stationary and the agents learn in a similar way to using a single-agent algorithm in settings where only one agent needs to be trained. In this paper, we test whether by using a multi-agent reinforcement learning algorithm with centralized critics, as opposed to single-agent ones, we would obtain an agent that generalizes better to new partners in a collaborative environment such as Overcooked, where coordination is critical for good performance. The results display a similar performance between the two algorithms when evaluated through self-play and slightly better or worse results when paired with the human model, representing a mediocre agent, depending on the map. Thus, the multi-agent, centralized critics algorithm used in this study did not train agents that generalize better to new partners. However, the training metrics clearly indicate that the centralized critics method makes the agents learn and converge twice as fast as its single-agent version.https://github.com/andrei-07/rp-overcooked-centralized-critics Link to GitHub repositoryCSE3000 Research ProjectComputer Science and Engineerin
Andrei Tarkovsky:
No full textThe author studies the originality of the film language of Andrei Tarkovsky, one of the great filmmakers of the twentieth century. For this purpose he considers the symbolic, poetic, technical and mystical elements of Tarkovsky’s seven films. Beyond the standard critics, he builds an unitary language for the interpretation of a work reputedly tight.El autor estudia la originalidad del lenguaje cinematográfico de Andrei Tarkovsky, uno de los grandes directores de cine del siglo XX. Para este propósito considera los aspectos simbólicos, poéticos, técnicos y místicos de sus siete películas. Desecha el formato de ficha crítica y construye un lenguaje unitario para la interpretación de una obra reputada como hermética
História e Documentário no Cinema de Andrei Tarkóvski
No full textIn the article, the author discuses the Cinematic history and documentary of Andrei Tarkóvski
Curves on class VII surfaces. A gauge theoretical approach for proving existence of a cycle
No full textInternational audienceWe explain our general program to prove the existence of a cycle of curves on minimal class VII surfaces with b_2>0 and the recent progress obtained by the author in this direction
The Godbillon-Vey characteristic class
No full textNational audienceLet M be a (not necessarily paracompact) smooth manifold, F a 1-codimensional foliation on it, {U_i} an open cover of M and ω_i one-forms defining F|_{U_i}. The author defines a cohomology class in H^∗(Ω^∗) (the hypercohomology of the de Rham sheaf complex of M) and proves that in the paracompact case it coincides with the Godbillon-Vey class. In the paracompact case the new definition can be made even simpler and one obtains a cohomology class in the real Čech cohomology of M. No Riemannian metrics or connections are used. The holomorphic and algebraic cases are also discussed
Instantons and holomorphic curves on class VII surfaces
No full text55 pagesWe develop a general strategy, based on gauge theoretical methods, to prove existence of curves on class VII surfaces. We prove that, for b_2=2, every minimal class VII surface has a cycle of rational curves hence, by a result of Nakamura, is a global deformation of a one parameter family of blown up primary Hopf surfaces. The case b_2=1 was solved in a previous article. The fundamental object intervening in our strategy is the moduli space M^{pst}(0,K) of polystable bundles E with c_2(E)=0, det(E)=K. For large b_2 the geometry of this moduli space becomes very complicated. The case b_2=2 treated here in detail requires new ideas and difficult techniques of both complex geometric and gauge theoretical nature. We explain the substantial obstacles which must be overcome in order to extend our methods to the case b_2≥3
A variation formula for the determinant line bundle. Compact subspaces of moduli spaces of stable bundles over class VII surfaces
No full textProceedings of the Conference in honor of J. M. Bismut, Progress in Mathematics, BirkhäuserInternational audienceThis article deals with two topics: the first, which has a general character, is a variation formula for the the determinant line bundle in non-K\"ahlerian geometry. This formula, which is a consequence of the non-K\"ahlerian version of the Grothendieck-Riemann Roch theorem proved recently by Bismut, gives the variation of the determinant line bundle corresponding to a perturbation of a Fourier-Mukai kernel on a product B×X by a unitary flat line bundle on the fiber X. When this fiber is a complex surface and is a holomorphic 2-bundle, the result can be interpreted as a Donaldson invariant. The second topic concerns a geometric application of our variation formula, namely we will study compact complex subspaces of the moduli spaces of stable bundles considered in our program for proving existence of curves on minimal class VII surfaces. Such a moduli space comes with a distinguished point a=[\mathcal{A}] corresponding to the canonical extension of X. The compact subspaces containing this distinguished point play an important role in our program. We will prove a non-existence result: there exists no compact complex subspace of positive dimension containing a with an open neighborhood such that consists only of non-filtrable bundles. In other words, within any compact complex subspace of positive dimension containing a, the point a can be approached by filtrable bundles. Specializing to the case we obtain a new way to complete the proof of a theorem in a previous article: any minimal class VII surface with has a cycle of curves. Applications to class VII surfaces with higher will be be discussed in a forthcoming article
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