Isobaric Reconstruction of the Baryonic Acoustic Oscillation

In this paper, we report a significant recovery of the linear baryonic acoustic oscillation (BAO) signature by applying the isobaric reconstruction algorithm to the non-linear matter density field. Assuming only the longitudinal component of the displacement being cosmologically relevant, this algorithm iteratively solves the coordinate transform between the Lagrangian and Eulerian frames without requiring any specific knowledge of the dynamics. For dark matter field, it produces the non-linear displacement potential with very high fidelity. The reconstruction error at the pixel level is within a few percent, and is caused only by the emergence of the transverse component after the shell-crossing. As it circumvents the strongest non-linearity of the density evolution, the reconstructed field is well-described by linear theory and immune from the bulk-flow smearing of the BAO signature. Therefore this algorithm could significantly improve the measurement accuracy of the sound horizon scale. For a perfect large-scale structure survey at redshift zero without Poisson or instrumental noise, the fractional error is reduced by a factor of 2.7, very close to the ideal limit with linear power spectrum and Gaussian covariance matrix.Comment: 5 pages, 3 figures, accepted versio

Approximate Closest Community Search in Networks

Recently, there has been significant interest in the study of the community search problem in social and information networks: given one or more query nodes, find densely connected communities containing the query nodes. However, most existing studies do not address the "free rider" issue, that is, nodes far away from query nodes and irrelevant to them are included in the detected community. Some state-of-the-art models have attempted to address this issue, but not only are their formulated problems NP-hard, they do not admit any approximations without restrictive assumptions, which may not always hold in practice. In this paper, given an undirected graph G and a set of query nodes Q, we study community search using the k-truss based community model. We formulate our problem of finding a closest truss community (CTC), as finding a connected k-truss subgraph with the largest k that contains Q, and has the minimum diameter among such subgraphs. We prove this problem is NP-hard. Furthermore, it is NP-hard to approximate the problem within a factor $(2-\varepsilon)$, for any $\varepsilon >0$. However, we develop a greedy algorithmic framework, which first finds a CTC containing Q, and then iteratively removes the furthest nodes from Q, from the graph. The method achieves 2-approximation to the optimal solution. To further improve the efficiency, we make use of a compact truss index and develop efficient algorithms for k-truss identification and maintenance as nodes get eliminated. In addition, using bulk deletion optimization and local exploration strategies, we propose two more efficient algorithms. One of them trades some approximation quality for efficiency while the other is a very efficient heuristic. Extensive experiments on 6 real-world networks show the effectiveness and efficiency of our community model and search algorithms

Exact penalty method for D-stationary point of nonlinear optimization

We consider the nonlinear optimization problem with least $\ell_1$-norm measure of constraint violations and introduce the concepts of the D-stationary point, the DL-stationary point and the DZ-stationary point with the help of exact penalty function. If the stationary point is feasible, they correspond to the Fritz-John stationary point, the KKT stationary point and the singular stationary point, respectively. In order to show the usefulness of the new stationary points, we propose a new exact penalty sequential quadratic programming (SQP) method with inner and outer iterations and analyze its global and local convergence. The proposed method admits convergence to a D-stationary point and rapid infeasibility detection without driving the penalty parameter to zero, which demonstrates the commentary given in [SIAM J. Optim., 20 (2010), 2281--2299] and can be thought to be a supplement of the theory of nonlinear optimization on rapid detection of infeasibility. Some illustrative examples and preliminary numerical results demonstrate that the proposed method is robust and efficient in solving infeasible nonlinear problems and a degenerate problem without LICQ in the literature.Comment: 24 page