1,872 research outputs found
Deep redshift topological lensing: strategies for the T^3 candidate
The 3-torus (T^3) FLRW model better fits the nearly zero large-scale
auto-correlation of the WMAP CMB sky maps than the infinite flat model. The T^3
model's WMAP parameters imply approximately equal-redshift topological lensing
at z \sim 6. We investigate observational strategies for rejecting the T^3
solution or providing candidate topologically lensed galaxy pairs. T^3
holonomies are applied to (i) existing z \sim 6 observations and (ii) simulated
observations, creating multiply connected catalogues. Corresponding simply
connected catalogues are generated. Each catalogue is analysed using a
successive filter method and collecting matched quadruples. Quadruple
statistics between the multiply and simply connected catalogues are compared.
The expected rejection of the hypothesis, or detection of candidate
topologically lensed galaxies, is possible at a significance of 5% for a pair
of T^3 axis-centred northern and southern surveys if photometric redshift
accuracy is \sigma(\zphot) < 0.01 for a pair of nearly complete 100 deg^2
surveys with a total of > 500 galaxies over 4.3 < z < 6.6, or for a pair of 196
deg^2 surveys with > 400 galaxies and \sigma(\zphot) < 0.02 over 4<z<7.
Dropping the maximum time interval in a pair from \Delta t =1 Gyr/h to \Delta t
=0.1 Gyr/h yields a requirement of \sigma(\zphot) < 0.005 or \sigma(\zphot) <
0.01, respectively. Millions of z \sim 6 galaxies will be observed over fields
of these sizes during the coming decades, implying much stronger constraints.
The question is not if the hypothesis will be rejected or confirmed, it is
when.Comment: 13 pages, 9 figures, 5 tables, MNRAS, accepte
Entanglement witnesses for a class of bipartite states of n x n qubits
We characterize the positive maps detecting the entangled bipartite states of
n x n qubits that are diagonal with respect to the orthonormal basis
constructed by tensor products of Pauli matrices acting on the totally
symmetric state. We then discuss the case n=2 for a class of states completely
determined by the geometric patterns of subsets of a 16 point lattice.Comment: 25 page
Counting real rational functions with all real critical values
We study the number of real rational degree n functions (considered up to
linear fractional transformations of the independent variable) with a given set
of 2n-2 distinct real critical values. We present a combinatorial reformulation
of this number and pose several related questions.Comment: 12 pages (AMSTEX), 3 picture
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