Convergence Hypotheses are Ill-Posed:Non-stationarity of Cross-Country Income Distribution D

The recent literature on “convergence� of cross-country per capita incomes has been dominated by two competing hypotheses: “global convergence� and “club-convergence�. This debate has recently relied on the study of limiting distributions of estimated income distribution dynamics. Utilizing new measures of “stochastic stability�, we establish two stylized facts that question the fruitfulness of the literature’s focus on asymptotic income distributions. The first stylized fact is non-stationarity of transition dynamics, in the sense of changing transition kernels, which renders all “convergence� hypotheses that make long-term predictions on income distribution, based on relatively short time series, less meaningful. The second stylized fact is the periodic emergence, disappearance, and re-emergence of a “stochastically stable� middle-income group. We show that the probability of escaping a low-income poverty-trap depends on the existence of such a stable middle income group. While this does not answer the perennial questions about long-term effects of globalization on the cross-country income distribution, it does shed some light on the types of environments that are conducive to narrowing/global income distribution; convergence clubs; transition kernel; stochastic stability

When Does an Ensemble of Matrices with Randomly Scaled Rows Lose Rank?

We consider the problem of determining rank loss conditions for a concatenation of full-rank matrices, such that each row of the composing matrices is scaled by a random coefficient. This problem has applications in wireless interference management and recommendation systems. We determine necessary and sufficient conditions for the design of each matrix, such that the random ensemble will almost surely lose rank by a certain amount. The result is proved by converting the problem to determining rank loss conditions for the union of some specific matroids, and then using tools from matroid and graph theories to derive the necessary and sufficient conditions. As an application, we discuss how this result can be applied to the problem of topological interference management, and characterize the linear symmetric degrees of freedom for a class of network topologies.Comment: submitted to IEEE Transactions on Information Theory; shorter version to appear at IEEE International Symposium on Information Theory (ISIT 2015

The 3XMM/SDSS Stripe 82 Galaxy Cluster Survey: Cluster catalogue and discovery of two merging cluster candidates

We present a galaxy cluster survey based on XMM-Newton observations that are located in Stripe 82 of the Sloan Digital Sky Survey (SDSS). The survey covers an area of 11.25 deg$^2$. The X-ray cluster candidates were selected as serendipitously extended detected sources from the third XMM-Newton serendipitous source catalogue (3XMM-DR5). A cross-correlation of the candidate list that comprises 94 objects with recently published X-ray and optically selected cluster catalogues provided optical confirmations and redshift estimates for about half of the candidate sample. We present a catalogue of X-ray cluster candidates previously known in X-ray and/or optical bands from the matched catalogues or NED. The catalogue consists of 54 systems with redshift measurements in the range of 0.05-1.19 with a median of 0.36. Of these, 45 clusters have spectroscopic confirmations as stated in the matched catalogues. We spectroscopically confirmed another 6 clusters from the available spectroscopic redshifts in the SDSS-DR12. The cluster catalogue includes 17 newly X-ray discovered clusters, while the remainder were detected in previous XMM-Newton and/or ROSAT cluster surveys. Based on the available redshifts and fluxes given in the 3XMM-DR5 catalogue, we estimated the X-ray luminosities and masses for the cluster sample. We also present the list of the remaining X-ray cluster candidates (40 objects) that have no redshift information yet in the literature. Of these candidates, 25 sources are considered as distant cluster candidates beyond a redshift of 0.6. We also searched for galaxy cluster mergers in our cluster sample and found two strong candidates for newly discovered cluster mergers at redshifts of 0.11 and 0.26. The X-ray and optical properties of these systems are presented.Comment: 17 pages, 12 figures, accepted for publication in A&A, revised version after language editin

The Deterministic Capacity of Relay Networks with Relay Private Messages

We study the capacity region of a deterministic 4-node network, where 3 nodes can only communicate via the fourth one. However, the fourth node is not merely a relay since it can exchange private messages with all other nodes. This situation resembles the case where a base station relays messages between users and delivers messages between the backbone system and the users. We assume an asymmetric scenario where the channel between any two nodes is not reciprocal. First, an upper bound on the capacity region is obtained based on the notion of single sided genie. Subsequently, we construct an achievable scheme that achieves this upper bound using a superposition of broadcasting node 4 messages and an achievable "detour" scheme for a reduced 3-user relay network.Comment: 3 figures, accepted at ITW 201