Global well-posedness and scattering of the (4+1)-dimensional Maxwell-Klein-Gordon equation

This article constitutes the final and main part of a three-paper sequence, whose goal is to prove global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon equation (MKG) on $\mathbb{R}^{1+4}$ for arbitrary finite energy initial data. Using the successively stronger continuation/scattering criteria established in the previous two papers, we carry out a blow-up analysis and deduce that the failure of global well-posedness and scattering implies the existence of a nontrivial stationary or self-similar solution to MKG. Then, by establishing that such solutions do not exist, we complete the proof.Comment: 64 page

Local well-posedness of the (4+1)-dimensional Maxwell-Klein-Gordon equation at energy regularity

This paper is the first part of a trilogy dedicated to a proof of global well-posedness and scattering of the (4+1)-dimensional mass-less Maxwell-Klein-Gordon equation (MKG) for any finite energy initial data. The main result of the present paper is a large energy local well-posedness theorem for MKG in the global Coulomb gauge, where the lifespan is bounded from below by the energy concentration scale of the data. Hence the proof of global well-posedness is reduced to establishing non-concentration of energy. To deal with non-local features of MKG we develop initial data excision and gluing techniques at critical regularity, which might be of independent interest.Comment: 59 page

Energy dispersed solutions for the (4+1)-dimensional Maxwell-Klein-Gordon equation

This article is devoted to the mass-less energy critical Maxwell-Klein-Gordon system in 4+1 dimensions. In earlier work of the second author, joint with Krieger and Sterbenz, we have proved that this problem has global well-posedness and scattering in the Coulomb gauge for small initial data. This article is the second of a sequence of three papers of the authors, whose goal is to show that the same result holds for data with arbitrarily large energy. Our aim here is to show that large data solutions persist for as long as one has small energy dispersion; hence failure of global well-posedness must be accompanied with a non-trivial energy dispersion.Comment: 63 page

Two-Layered Superposition of Broadcast/Multicast and Unicast Signals in Multiuser OFDMA Systems

We study optimal delivery strategies of one common and $K$ independent messages from a source to multiple users in wireless environments. In particular, two-layered superposition of broadcast/multicast and unicast signals is considered in a downlink multiuser OFDMA system. In the literature and industry, the two-layer superposition is often considered as a pragmatic approach to make a compromise between the simple but suboptimal orthogonal multiplexing (OM) and the optimal but complex fully-layered non-orthogonal multiplexing. In this work, we show that only two-layers are necessary to achieve the maximum sum-rate when the common message has higher priority than the $K$ individual unicast messages, and OM cannot be sum-rate optimal in general. We develop an algorithm that finds the optimal power allocation over the two-layers and across the OFDMA radio resources in static channels and a class of fading channels. Two main use-cases are considered: i) Multicast and unicast multiplexing when $K$ users with uplink capabilities request both common and independent messages, and ii) broadcast and unicast multiplexing when the common message targets receive-only devices and $K$ users with uplink capabilities additionally request independent messages. Finally, we develop a transceiver design for broadcast/multicast and unicast superposition transmission based on LTE-A-Pro physical layer and show with numerical evaluations in mobile environments with multipath propagation that the capacity improvements can be translated into significant practical performance gains compared to the orthogonal schemes in the 3GPP specifications. We also analyze the impact of real channel estimation and show that significant gains in terms of spectral efficiency or coverage area are still available even with estimation errors and imperfect interference cancellation for the two-layered superposition system

Does "Grease Money" Speed Up the Wheels of Commerce?

In an environment in which bureaucratic burden and delay are exogenous, an individual firm may find bribes helpful to reduce the effective red tape it faces. The efficient grease' hypothesis asserts therefore that corruption can improve economic efficiency and that fighting bribery would be counter-productive. This need not be the case. In a general equilibrium in which regulatory burden and delay can be endogenously chosen by rent-seeking bureaucrats, the effective (not just nominal) red tape and bribery may be positively correlated across firms. Using data from three worldwide firm-level surveys, we examine the relationship between bribe payment, management time wasted with bureaucrats, and cost of capital. Contrary to the efficient grease' theory, we find that firms that pay more bribes are also likely to spend more, not less, management time with bureaucrats negotiating regulations, and face higher, not lower, cost of capital.