Relaxation-Corrected Bootstrap Algebraic Multigrid (rBAMG)

Bootstrap Algebraic Multigrid (BAMG) is a multigrid-based solver for matrix equations of the form Ax = b. Its aim is to automatically determine the interpolation weights used in algebraic multigrid (AMG) by locally fitting a set of test vectors that have been relaxed as solutions to the corresponding homogeneous equation, Ax = 0. This thesis introduces an indirect operator based interpolation scheme for BAMG that determines the interpolation weights indirectly by “collapsing” the unwanted connections in “operator interpolation”. Compared to BAMG, this indirect BAMG approach (iBAMG) is more in the spirit of classical AMG, which collapses unwanted connections in operator interpolation based on the (restrictive) assumption that smooth error is locally constant. This thesis also develops another form of BAMG, called rBAMG, that involves modifying the least-squares process by temporarily relaxing on the test vectors at the fine-grid interpolation points. The theory here shows that, under fairly general conditions, iBAMG and rBAMG are equivalent. Simplicity and potentially greater generality favor rBAMG, so this algorithm is at the focus of the numerical performance study here. The rBAMG setup process involves several components that are developed in this thesis. Besides the new least-squares principle involving the residuals of the test vectors, a simple extrapolation scheme is developed to accurately estimate the convergence factors of the evolving AMG solver. Such a capability is essential to effective development of a fast solver, and the approach introduced here proves to be much more effective than the conventional approach of just observing successive error reduction factors. Another component of the setup process is the use of the current V-cycle to ensure its effectiveness or, when poor convergence is observed, to expose error components that are not being properly attenuated. How we coordinate use of these evolving error components together with the original test vectors to direct the setup process is a critical issue to rBAMG’s effectiveness. Another related component is the scaling and recombination Ritz process that targets the so-called weak approximation property in an attempt to reveal the important elements of these evolving error and test vector spaces. The details of the components used here are spelled out in what follows. The study of rBAMG here is an attempt to systematically analyze the behavior of the algorithm in terms relative to several parameters. The focus here is on the number of test vectors, the number of relaxations applied to them, and the dimension of the matrix to which the scheme is applied. A large number of other parameters and options could also be considered, including different cycling strategies, other coarsening strategies (e. g., computing several eigenvector approximations on coarse levels), different numbers of relaxation sweeps on coarse levels, different possible strategies for combining test vectors and error components produced by the current cycles, and so on. Studying all of these options and parameters would not be feasible here. Instead, reasonable choices are made based on some sample studies (that, in the interest of space, we choose not to document here), with the hope that the rBAMG algorithm studied here is generally fairly effective and robust. Our analysis is thus able to focus on how this scheme behaves numerically in the face of increasing the numbers of test vectors and relaxation sweeps performed on them, as well as the problem sizes

Random Parameter Negative Binomial Model of Signalized Intersections

Factors affecting accident frequencies at 72 signalized intersections in the Gyeonggi-Do (province) over a four-year period (2007~2010) were explored using the random parameters negative binomial model. The empirical results from the comparison with fixed parameters binomial model show that the random parameters model outperforms its fixed parameters counterpart and provides a fuller understanding of the factors which determine accident frequencies at signalized intersections. In addition, elasticity and marginal effect were estimated to gain more insight into the effects of one-percent and one-unit changes in the dependent variable from changes in the independent variables

Identifying a new particle with jet substructures

We investigate a potential of measuring properties of a heavy resonance X, exploiting jet substructure techniques. Motivated by heavy higgs boson searches, we focus on the decays of X into a pair of (massive) electroweak gauge bosons. More specifically, we consider a hadronic Z boson, which makes it possible to determine properties of X at an earlier stage. For $m_X$ of O(1) TeV, two quarks from a Z boson would be captured as a "merged jet" in a significant fraction of events. The use of the merged jet enables us to consider a Z-induced jet as a reconstructed object without any combinatorial ambiguity. We apply a conventional jet substructure method to extract four-momenta of subjets from a merged jet. We find that jet substructure procedures may enhance features in some kinematic observables formed with subjets. Subjet momenta are fed into the matrix element associated with a given hypothesis on the nature of X, which is further processed to construct a matrix element method (MEM)-based observable. For both moderately and highly boosted Z bosons, we demonstrate that the MEM with current jet substructure techniques can be a very powerful discriminator in identifying the physics nature of X. We also discuss effects from choosing different jet sizes for merged jets and jet-grooming parameters upon the MEM analyses.Comment: 36 pages, 11 figures, published in JHE

Ammonia Imaging of the Disks in the NGC 1333 IRAS 4A Protobinary System

The NGC 1333 IRAS 4A protobinary was observed in the ammonia (2, 2) and (3, 3) lines and in the 1.3 cm continuum with a high resolution (about 1.0 arcsec). The ammonia maps show two compact sources, one for each protostar, and they are probably protostellar accretion disks. The disk associated with IRAS 4A2 is seen nearly edge-on and shows an indication of rotation. The A2 disk is brighter in the ammonia lines but dimmer in the dust continuum than its sibling disk, with the ammonia-to-dust flux ratios different by about an order of magnitude. This difference suggests that the twin disks have surprisingly dissimilar characters, one gas-rich and the other dusty. The A2 disk may be unusually active or hot, as indicated by its association with water vapor masers. The existence of two very dissimilar disks in a binary system suggests that the formation process of multiple systems has a controlling agent lacking in the isolated star formation process and that stars belonging to a multiple system do not necessarily evolve in phase with each other