A Deterministic Theory for Exact Non-Convex Phase Retrieval

In this paper, we analyze the non-convex framework of Wirtinger Flow (WF) for phase retrieval and identify a novel sufficient condition for universal exact recovery through the lens of low rank matrix recovery theory. Via a perspective in the lifted domain, we show that the convergence of the WF iterates to a true solution is attained geometrically under a single condition on the lifted forward model. As a result, a deterministic relationship between the accuracy of spectral initialization and the validity of {the regularity condition} is derived. In particular, we determine that a certain concentration property on the spectral matrix must hold uniformly with a sufficiently tight constant. This culminates into a sufficient condition that is equivalent to a restricted isometry-type property over rank-1, positive semi-definite matrices, and amounts to a less stringent requirement on the lifted forward model than those of prominent low-rank-matrix-recovery methods in the literature. We characterize the performance limits of our framework in terms of the tightness of the concentration property via novel bounds on the convergence rate and on the signal-to-noise ratio such that the theoretical guarantees are valid using the spectral initialization at the proper sample complexity.Comment: In Revision for IEEE Transactions on Signal Processin

Spatial Distribution of Housing Investment and Perception of Earthquake Risk in Istanbul Metropolitan Area

Istanbul, the largest metropolitan area in Turkey with a population of over 15 million inhabitants, lies close to major and active fault lines and has been previously hit by fatal earthquakes several times. Facing a high seismic risk as forecasted in a number of studies; Istanbul is particularly vulnerable due to the high density of old housing areas in the city center. Although there is a great body of knowledge in the literature focusing on the seismic risk of Istanbul and possible scenarios to strengthen the capacity for emergency preparedness in the event of future earthquakes, the attitudes and perceptions of housing investors living under the threat of the earthquake is yet to be explored. This study is an attempt to address this gap and aims to investigate the relationship between the location of the housing investment and perception of earthquake risk of the investors. Data was collected by means of a questionnaire from 117 participants, who made an investment in housing in Istanbul since 1999 Kocaeli earthquake. ArcGIS is used to indicate the spatial distribution of investment and the results provide empirical evidence of how spatial distribution of housing investment differs depending on the earthquake risk perception of the investors.

Medicaid Expansions and The Crowding Out of Private Health Insurance

In this paper, we re-examine the question of crowd out among children. Our primary contribution is the use of longitudinal data. These data allow us to identify several groups of children depending on whether their eligibility for Medicaid was affected by the eligibility expansions, and to investigate whether changes in insurance coverage of children affected by the expansions differed from changes in insurance coverage of children unaffected by the expansions. For example, we directly measure whether children who became eligible for Medicaid due to the expansions decreased their enrollment in private insurance plans faster than children whose eligibility for Medicaid was unaffected by the expansions. Our results suggest that there was relatively little crowd out among children. We estimate that 14.5 percent of the recent increase in Medicaid enrollment came from private insurance.

BcBcJ/ψ B_c B_c J/\psi Vertex Form Factor at Finite Temperature in the Framework of QCD Sum Rules Approach

The strong form factor of the $B_{c} B_{c}J/\Psi$ vertex is calculated in the framework of the QCD sum rules method at finite temperature. Taking into account additional operators appearing at finite temperature, thermal Wilson expansion is obtained and QCD sum rules are derived. While increasing temperature, the strong form factor remains unchanged up to $T\simeq100~MeV$ but slightly increases after this point. After $T\simeq160~MeV$, the form factor suddenly decreases up to $T\simeq170~MeV$. The obtained result of the coupling constant by fitting the form factor at $Q^2=-m^2_{offshell}$ at $T=0$ is in a very good agreement with the QCD sum rules calculations at vacuum. Our prediction can be checked in the future experiments.Comment: 8 pages, 7 figure