5,736 research outputs found
Non trivial examples of coupled equations for K\"ahler metrics and Yang-Mills connections
We provide non trivial examples of solutions to the system of coupled
equations introduced by M. Garc\'ia-Fern\'andez for the uniformization problem
of a triple where is a holomorphic vector bundle over a polarized
complex manifold , generalizing the notions of both constant scalar
curvature K\"ahler metric and Hermitian-Einstein metric.Comment: 17 page
MAX-consensus in open multi-agent systems with gossip interactions
We study the problem of distributed maximum computation in an open
multi-agent system, where agents can leave and arrive during the execution of
the algorithm. The main challenge comes from the possibility that the agent
holding the largest value leaves the system, which changes the value to be
computed. The algorithms must as a result be endowed with mechanisms allowing
to forget outdated information. The focus is on systems in which interactions
are pairwise gossips between randomly selected agents. We consider situations
where leaving agents can send a last message, and situations where they cannot.
For both cases, we provide algorithms able to eventually compute the maximum of
the values held by agents.Comment: To appear in the proceedings of the 56th IEEE Conference on Decision
and Control (CDC 17). 8 pages, 3 figure
On the capacity achieving covariance matrix for Rician MIMO channels: an asymptotic approach
The capacity-achieving input covariance matrices for coherent block-fading
correlated MIMO Rician channels are determined. In this case, no closed-form
expressions for the eigenvectors of the optimum input covariance matrix are
available. An approximation of the average mutual information is evaluated in
this paper in the asymptotic regime where the number of transmit and receive
antennas converge to . New results related to the accuracy of the
corresponding large system approximation are provided. An attractive
optimization algorithm of this approximation is proposed and we establish that
it yields an effective way to compute the capacity achieving covariance matrix
for the average mutual information. Finally, numerical simulation results show
that, even for a moderate number of transmit and receive antennas, the new
approach provides the same results as direct maximization approaches of the
average mutual information, while being much more computationally attractive.Comment: 56 pp. Extended version of the published article in IEEE Inf. Th.
(march 2010) with more proof
The Stackelberg equilibrium as a consistent conjectural equilibrium
We consider a static game with conjectural variations where some firms make conjectures while others do not. Two propositions are proved. We first show that there exists a continuum of conjectural variations such that the conjectural equilibrium locally coincides with the Stackelberg equilibrium (Proposition 1). Second, we define the conditions under which a conjectural equilibrium is a locally consistent equilibrium (i.e. such that conjectures are fulfilled). The concept of (local) consistency is restricted to firms making conjectures. Two conditions on consistency are featured: consistency within a cohort and consistency among cohorts. The Stackelberg equilibrium fulfills only the latter condition (Proposition 2). An example is provided.Consistent conjectural variations, reaction functions, Stackelberg competition
Do followers really matter in Stackelberg competition?
In this note, we consider a generalized T−stage Stackelberg oligopoly. We provide a proof and an interpretation that under the two necessary and sufficient conditions of linear aggregate demand and identical constant marginal costs, followers do not matter for leaders. Leaders act as rational myopic agents, voluntarily ignoring the number of followers and remaining stages, thereby behaving as Cournotian oligopolists. Strategies of incumbent firms are invariant to entry of new cohorts. Their profits can be studied by the way of two discount factors: the first impacting markup and the second impacting output supply. Some implications in terms of welfare and convergence toward competitive equilibrium are derived.Leader’s markup discount factor, linear economy, follower’s output discount factor, myopic behavior
Experimental hydrodynamics of the accelerated turbulent boundary layer with and without mass injection
Hydrodynamics of accelerated turbulent boundary layer with and without mass injectio
- …