Smoothness for Simultaneous Composition of Mechanisms with Admission

We study social welfare of learning outcomes in mechanisms with admission. In our repeated game there are $n$ bidders and $m$ mechanisms, and in each round each mechanism is available for each bidder only with a certain probability. Our scenario is an elementary case of simple mechanism design with incomplete information, where availabilities are bidder types. It captures natural applications in online markets with limited supply and can be used to model access of unreliable channels in wireless networks. If mechanisms satisfy a smoothness guarantee, existing results show that learning outcomes recover a significant fraction of the optimal social welfare. These approaches, however, have serious drawbacks in terms of plausibility and computational complexity. Also, the guarantees apply only when availabilities are stochastically independent among bidders. In contrast, we propose an alternative approach where each bidder uses a single no-regret learning algorithm and applies it in all rounds. This results in what we call availability-oblivious coarse correlated equilibria. It exponentially decreases the learning burden, simplifies implementation (e.g., as a method for channel access in wireless devices), and thereby addresses some of the concerns about Bayes-Nash equilibria and learning outcomes in Bayesian settings. Our main results are general composition theorems for smooth mechanisms when valuation functions of bidders are lattice-submodular. They rely on an interesting connection to the notion of correlation gap of submodular functions over product lattices.Comment: Full version of WINE 2016 pape

A Striking Confluence Between Theory and Observations of High-Mass X-ray Binary Pulsars

We analyse the most powerful X-ray outbursts from neutron stars in ten Magellanic high-mass X-ray binaries and three pulsating ultraluminous X-ray sources. Most of the outbursts rise to $L_{max}$ which is about the level of the Eddington luminosity, while the rest and more powerful outbursts also appear to recognize that limit when their emissions are assumed to be anisotropic and beamed toward our direction. We use the measurements of pulsar spin periods $P_S$ and their derivatives $\dot{P_S}$ to calculate the X-ray luminosities $L_p$ in their faintest accreting ("propeller") states. In four cases with unknown $\dot{P_S}$, we use the lowest observed X-ray luminosities, which only adds to the heterogeneity of the sample. Then we calculate the ratios $L_p/L_{max}$ and we obtain an outstanding confluence of theory and observations from which we conclude that work done on both fronts is accurate and the results are trustworthy: sources known to reside on the lowest Magellanic propeller line are all located on/near that line, whereas other sources jump higher and reach higher-lying propeller lines. These jumps can be interpreted in only one way, higher-lying pulsars have stronger surface magnetic fields in agreement with empirical results in which $\dot{P_S}$ and $L_p$ values were not used.Comment: Added LMC X-4 and commented on the cyclotron absorption line of SMC X-2. 4 pages, 1 figure, 2 tables, submitted to MNRAS

Spherically symmetric perfect fluid in area-radial coordinates

We study the spherically symmetric collapse of a perfect fluid using area-radial coordinates. We show that analytic mass functions describe a static regular centre in these coordinates. In this case, a central singularity can not be realized without an infinite discontinuity in the central density. We construct mass functions involving fluid dynamics at the centre and investigate the relationship between those and the nature of the singularities.Comment: Accepted by CQG. LaTex file, 14 pages, no figure

On static shells and the Buchdahl inequality for the spherically symmetric Einstein-Vlasov system

In a previous work \cite{An1} matter models such that the energy density $\rho\geq 0,$ and the radial- and tangential pressures $p\geq 0$ and $q,$ satisfy $p+q\leq\Omega\rho, \Omega\geq 1,$ were considered in the context of Buchdahl's inequality. It was proved that static shell solutions of the spherically symmetric Einstein equations obey a Buchdahl type inequality whenever the support of the shell, $[R_0,R_1], R_0>0,$ satisfies $R_1/R_0<1/4.$ Moreover, given a sequence of solutions such that $R_1/R_0\to 1,$ then the limit supremum of $2M/R_1$ was shown to be bounded by $((2\Omega+1)^2-1)/(2\Omega+1)^2.$ In this paper we show that the hypothesis that $R_1/R_0\to 1,$ can be realized for Vlasov matter, by constructing a sequence of static shells of the spherically symmetric Einstein-Vlasov system with this property. We also prove that for this sequence not only the limit supremum of $2M/R_1$ is bounded, but that the limit is $((2\Omega+1)^2-1)/(2\Omega+1)^2=8/9,$ since $\Omega=1$ for Vlasov matter. Thus, static shells of Vlasov matter can have $2M/R_1$ arbitrary close to $8/9,$ which is interesting in view of \cite{AR2}, where numerical evidence is presented that 8/9 is an upper bound of $2M/R_1$ of any static solution of the spherically symmetric Einstein-Vlasov system.Comment: 20 pages, Late

Exact solution for scalar field collapse

We give an exact spherically symmetric solution for the Einstein-scalar field system. The solution may be interpreted as an inhomogeneous dynamical scalar field cosmology. The spacetime has a timelike conformal Killing vector field and is asymptotically conformally flat. It also has black or white hole-like regions containing trapped surfaces. We describe the properties of the apparent horizon and comment on the relevance of the solution to the recently discovered critical behaviour in scalar field collapse.Comment: 10 pages(Latex) (2 figures available upon request), Alberta-Thy-4-9

The Great Pretenders Among the ULX Class

The recent discoveries of pulsed X-ray emission from three ultraluminous X-ray (ULX) sources have finally enabled us to recognize a subclass within the ULX class: the great pretenders, neutron stars (NSs) that appear to emit X-ray radiation at isotropic luminosities $L_X = 7\times 10^{39}$~erg~s$^{-1}-1\times 10^{41}$~erg~s$^{-1}$ only because their emissions are strongly beamed toward our direction and our sight lines are offset by only a few degrees from their magnetic-dipole axes. The three known pretenders appear to be stronger emitters than the presumed black holes of the ULX class, such as Holmberg II \& IX X-1, IC10 X-1, and NGC300 X-1. For these three NSs, we have adopted a single reasonable assumption, that their brightest observed outbursts unfold at the Eddington rate, and we have calculated both their propeller states and their surface magnetic-field magnitudes. We find that the results are not at all different from those recently obtained for the Magellanic Be/X-ray pulsars: the three NSs reveal modest magnetic fields of about 0.3-0.4~TG and beamed propeller-line X-ray luminosities of $\sim 10^{36-37}$~erg~s$^{-1}$, substantially below the Eddington limit.Comment: To appear in Research in Astronomy and Astrophysic

How Formal and Informal Institutions of Middle Eastern Countries Influence Managerial Discretion: An Empirical Investigation

Managerial discretion is the focal theme bridging the clash between two schools of thoughts; whether executives have greater influence on their firms’ outcomes or other factors restrain their actions (Hambrick & Finkelstein, 1987). It is argued that constraints come from inertial, normative and environmental forces (e.g. DiMaggio & Powell, 1983). Of these restraints is the institutional environment in which a firm is headquartered. Our paper falls within this research stream and provides an extension for Crossland and Hambrick (2007, 2011) work. We investigate the national level of discretion in new cross-cultural contexts, provide deeper understanding of its concept, and shed the light on undiscovered discretion’s antecedents and consequences. We adopt a quantitative approach in which questionnaires represent our data collection instrument. We anticipate that in high discretion countries firms tend to follow what Miles & Snow (1978) labeled ‘Prospector’ strategy as opposed to low discretion countries in which firms incline to implement a ‘Defender’ strategy

Generic Cosmic Censorship Violation in anti de Sitter Space

We consider (four dimensional) gravity coupled to a scalar field with potential V(\phi). The potential satisfies the positive energy theorem for solutions that asymptotically tend to a negative local minimum. We show that for a large class of such potentials, there is an open set of smooth initial data that evolve to naked singularities. Hence cosmic censorship does not hold for certain reasonable matter theories in asymptotically anti de Sitter spacetimes. The asymptotically flat case is more subtle. We suspect that potentials with a local Minkowski minimum may similarly lead to violations of cosmic censorship in asymptotically flat spacetimes, but we do not have definite results.Comment: 4 pages, v2: minor change

Improving the Price of Anarchy for Selfish Routing via Coordination Mechanisms

We reconsider the well-studied Selfish Routing game with affine latency functions. The Price of Anarchy for this class of games takes maximum value 4/3; this maximum is attained already for a simple network of two parallel links, known as Pigou's network. We improve upon the value 4/3 by means of Coordination Mechanisms. We increase the latency functions of the edges in the network, i.e., if $\ell_e(x)$ is the latency function of an edge $e$, we replace it by $\hat{\ell}_e(x)$ with $\ell_e(x) \le \hat{\ell}_e(x)$ for all $x$. Then an adversary fixes a demand rate as input. The engineered Price of Anarchy of the mechanism is defined as the worst-case ratio of the Nash social cost in the modified network over the optimal social cost in the original network. Formally, if \CM(r) denotes the cost of the worst Nash flow in the modified network for rate $r$ and \Copt(r) denotes the cost of the optimal flow in the original network for the same rate then [\ePoA = \max_{r \ge 0} \frac{\CM(r)}{\Copt(r)}.] We first exhibit a simple coordination mechanism that achieves for any network of parallel links an engineered Price of Anarchy strictly less than 4/3. For the case of two parallel links our basic mechanism gives 5/4 = 1.25. Then, for the case of two parallel links, we describe an optimal mechanism; its engineered Price of Anarchy lies between 1.191 and 1.192.Comment: 17 pages, 2 figures, preliminary version appeared at ESA 201