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Results for “Algorithmic Optimization”

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DOE OSTI2017

Fast optimization algorithms and the cosmological constant

Denef and Douglas have observed that in certain landscape models the problem of finding small values of the cosmological constant is a large instance of a problem that is hard for the complexity class NP (Nondeterministic Polynomial-time). The number of elementary operations (quantum gates) needed to solve this problem by brute force search exceeds the estimated computational capacity of the observable Universe. Here in this paper, we describe a way out of this puzzling circumstance: despite being NP-hard, the problem of finding a small cosmological constant can be attacked by more sophisticated algorithms whose performance vastly exceeds brute force search. In fact, in some parameter regimes the average-case complexity is polynomial. We demonstrate this by explicitly finding a cosmological constant of order 10 -120 in a randomly generated 10 9 -dimensional Arkani-Hamed–Dimopoulos–Kachru landscape.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

A 3D Voronoi+Gapper Galaxy Cluster Finder in Redshift Space to z ∼ 0.2 I: an Algorithm Optimized for the 2dFGRS

This paper is the first in a series, presenting a new galaxy cluster finder based on a three-dimensional Voronoi Tesselation plus a maximum likelihood estimator, followed by gapping-filtering in radial velocity(VoML+G). The scientific aim of the series is a reassessment of the diversity of optical clusters in the local universe. A mock galaxy database mimicking the southern strip of the magnitude(blue)-limited 2dF Galaxy Redshift Survey (2dFGRS), for the redshift range 0.009 < z < 0.22, is built on the basis of the Millennium Simulation of the LCDM cosmology and a reference catalog of “Millennium clusters,” spannning across the 1.0 × 10{sup 12}–1.0 × 10{sup 15} M {sub ⊙} h {sup −1} dark matter (DM) halo mass range, is recorded. The validation of VoML+G is performed through its application to the mock data and the ensuing determination of the completeness and purity of the cluster detections by comparison with the reference catalog. The execution of VoML+G over the 2dFGRS mock data identified 1614 clusters, 22% with N {sub g} ≥ 10, 64 percent with 10 > N {sub g} ≥ 5, and 14% with N {sub g} < 5. The ensemble of VoML+G clusters has a ∼59% completeness and a ∼66% purity, whereas the subsample with N {sub g} ≥ 10, to z ∼ 0.14, has greatly improved mean rates of ∼75% and ∼90%, respectively. The VoML+G cluster velocity dispersions are found to be compatible with those corresponding to “Millennium clusters” over the 300–1000 km s{sup −1} interval, i.e., for cluster halo masses in excess of ∼3.0 × 10{sup 13} M {sub ⊙} h {sup −1}.

79 ASTRONOMY AND ASTROPHYSICS↗