Magnification bias in the shear-ratio test: a viable mitigation strategy

Using the same lens galaxies, the ratios of tangential shears for different source galaxy redshifts is equal to the ratios of their corresponding angular-diameter distances. This is the so-called shear-ratio test (SRT) and it is valid when effects induced by the intervening large-scale structure (LSS) can be neglected. The dominant LSS effect is magnification bias which, on the one hand, induces an additional shear, and on the other hand, causes a magnification of the lens population. Our objective is to quantify the magnification bias for the SRT and show an easy-to-apply mitigation strategy that does not rely on additional observations. We use ray-tracing data through the Millennium simulation to measure the influence of magnification on the SRT and test our mitigation strategy. Using the SRT as a null-test we find deviations from zero up to $10 \%$ for a flux-limited sample of lens galaxies, which is a strong function of lens redshift and the lens-source line-of-sight separation. Using our mitigation strategy we can improve the null-test by a factor of $\sim \!100$.Comment: 9 pages, 7 figure

A Satisfiability Algorithm for Sparse Depth Two Threshold Circuits

We give a nontrivial algorithm for the satisfiability problem for cn-wire threshold circuits of depth two which is better than exhaustive search by a factor 2^{sn} where s= 1/c^{O(c^2)}. We believe that this is the first nontrivial satisfiability algorithm for cn-wire threshold circuits of depth two. The independently interesting problem of the feasibility of sparse 0-1 integer linear programs is a special case. To our knowledge, our algorithm is the first to achieve constant savings even for the special case of Integer Linear Programming. The key idea is to reduce the satisfiability problem to the Vector Domination Problem, the problem of checking whether there are two vectors in a given collection of vectors such that one dominates the other component-wise. We also provide a satisfiability algorithm with constant savings for depth two circuits with symmetric gates where the total weighted fan-in is at most cn. One of our motivations is proving strong lower bounds for TC^0 circuits, exploiting the connection (established by Williams) between satisfiability algorithms and lower bounds. Our second motivation is to explore the connection between the expressive power of the circuits and the complexity of the corresponding circuit satisfiability problem

Quantum Populations in Zeno Regions inside Black Holes

Schwarzschild black-hole interiors border on space-like singularities representing classical information leaks. We show that local quantum physics is decoupled from these leaks due to dynamically generated boundaries, called Zeno borders. Beyond Zeno borders black-hole interiors become asymptotically silent, and quantum fields evolve freely towards the geodesic singularity with vanishing probability measure for populating the geodesic boundary. Thus Zeno borders represent a probabilistic completion of Schwarzschild black holes within the semiclassical framework.Comment: 5 pages, 2 figures, more pedagogical presentation of our unchanged results including an introduction to Zeno region