1,720,995 research outputs found
Representation of equilibrium solutions to the table problem for growing sandpiles
Full text linkIn the dynamical theory of granular matter the so-called table problem consists in studying the evolution of a heap of matter poured continuously onto a bounded domain Omega subset of R-2. The mathematical description of the table problem, at an equilibrium configuration, can be reduced to a boundary value problem for a system of partial differential equations. The analysis of such a system, also connected with other mathematical models such as the Monge-Kantorovich problem, is the object of this paper. Our main result is an integral representation formula for the solution, in terms of the boundary curvature and of the normal distance to the cut locus of Omega
Regularity of the eikonal equation with Neumann boundary conditions in the plane: application to fronts with nonlocal terms
Full text linkThe first part of the paper is devoted to length estimates of the boundary of the reachable set for the plane and state constrained controlled system x'(t) = c(t, x(t)) b(t) (where |b(t)| <= 1 a.e.). This study is motivated in the second part by the analysis of dislocation dynamics, which can be modeled as a curve G( t) moving in an open set O subset of R-2 according to some nonlocal law with Neumann boundary conditions on partial derivative O. The length estimates of the first part play a crucial role in the proof of the existence and uniqueness of a viscosity solution for this model
An introduction to mean field game theory
No full textThese notes are an introduction to Mean Field Game (MFG) theory, which models differential games involving infinitely many interacting players. We focus here on the Partial Differential Equations (PDEs) approach to MFGs. The two main parts of the text correspond to the two emblematic equations in MFG theory: the first part is dedicated to the MFG system, while the second part is devoted to the master equation. The MFG system describes Nash equilibrium configurations in the mean field approach to differential games with infinitely many players. It consists in the coupling between a backward Hamilton-Jacobi equation (for the value function of a single player) and a forward Fokker-Planck equation (for the distribution law of the individual states). We discuss the existence and the uniqueness of the solution to the MFG system in several frameworks, depending on the presence or not of a diffusion term and on the nature of the interactions between the players (local or nonlocal coupling). We also explain how these different frameworks are related to each other. As an application, we show how to use the MFG system to find approximate Nash equilibria in games with a finite number of players and we discuss the asymptotic behavior of the MFG system. The master equation is a PDE in infinite space dimension: more precisely it is a kind of transport equation in the space of measures. The interest of this equation is that it allows to handle more complex MFG problems as, for instance, MFG problems involving a randomness affecting all the players. To analyse this equation, we first discuss the notion of derivative of maps defined on the space of measures; then we present the master equation in several frameworks (classical form, case of finite state space and case with common noise); finally we explain how to use the master equation to prove the convergence of Nash equilibria of games with finitely many players as the number of players tends to infinity. As the works on MFGs are largely inspired by P.L. Lions’ courses held at the Collège de France in the years 2007–2012, we complete the text with an appendix describing the organization of these courses
Regularity properties of attainable sets under state constraints
Full text linkThe Maximum principle in control theory provides necessary optimality conditions for a given trajectory in terms of the co-state, which is the solution of a suitable adjoint system. For constrained problems the adjoint system contains a measure supported at the boundary of the constraint set. In this paper we give a representation formula for such a measure for smooth constraint sets and nice Hamiltonians. As an application, we obtain a perimeter estimate for constrained attainable sets
"Supremal Representation of L^{infty} Functionals"
No full textWe study the weak* lower semicontinuity properties of functionals of the form
F(u)=\supess_{x \in \Og} f(x,Du (x))
where \Og is a bounded open set of and
Without a continuity assumption on we show that the {\sl supremal} functional is weakly* lower semicontinuous if and only if it is a level convex functional (i.e. it has convex sub-levels). In particular if is weakly* lower semicontinuous, then it can be represented through a level convex function. Finally a counterexample shows that in general it is not possible to represent through the level convex envelope of
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
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