Half-tapering strategy for conditional simulation with large datasets

Gaussian conditional realizations are routinely used for risk assessment and planning in a variety of Earth sciences applications. Conditional realizations can be obtained by first creating unconditional realizations that are then post-conditioned by kriging. Many efficient algorithms are available for the first step, so the bottleneck resides in the second step. Instead of doing the conditional simulations with the desired covariance (F approach) or with a tapered covariance (T approach), we propose to use the taper covariance only in the conditioning step (Half-Taper or HT approach). This enables to speed up the computations and to reduce memory requirements for the conditioning step but also to keep the right short scale variations in the realizations. A criterion based on mean square error of the simulation is derived to help anticipate the similarity of HT to F. Moreover, an index is used to predict the sparsity of the kriging matrix for the conditioning step. Some guides for the choice of the taper function are discussed. The distributions of a series of 1D, 2D and 3D scalar response functions are compared for F, T and HT approaches. The distributions obtained indicate a much better similarity to F with HT than with T.Comment: 39 pages, 2 Tables and 11 Figure

An Efficient Linear Programming Algorithm to Generate the Densest Lattice Sphere Packings

Finding the densest sphere packing in $d$-dimensional Euclidean space $\mathbb{R}^d$ is an outstanding fundamental problem with relevance in many fields, including the ground states of molecular systems, colloidal crystal structures, coding theory, discrete geometry, number theory, and biological systems. Numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations, even for the restricted problem of finding the densest lattice sphere packings. In this paper, we apply the Torquato-Jiao packing algorithm, which is a method based on solving a sequence of linear programs, to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19. We show that the TJ algorithm is appreciably more efficient at solving these problems than previously published methods. Indeed, in some dimensions, the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones. We also study the suboptimal local density-maxima solutions (inherent structures or "extreme" lattices) to gain insight about the nature of the topography of the "density" landscape.Comment: 23 pages, 3 figure

Exit Exams and High School Dropout

In this paper, I consider the impact of the expansion of exams students must pass in order to graduate high school on dropout rates. "Exit exams," as these tests are known, have become more common, and more difficult. These exams are controversial, with opponents claiming they drive marginal students out of school, and proponents arguing they align student interests with those of the school and encourage teachers and administrators to provide effort and resources on the students' behalf. I make use of the fact that when states implement exit exams, they first affect a specific graduating class. So in some states, some students in high school are required to pass these exams, while students in the grade above are not. Using a state-grade panel constructed from the Common Core of Data I find evidence that the recent expansion of exit exams has resulted in a modest increase in high school dropout rates in the aggregate, but a large increase among students in 12th grade, where additional attempts to pass exams are not possible. I also find that a policy often used to limit the impacts of exit exams on high school completion has only limited effect: Dropout rates in states where students can earn a diploma or credential even when unable to pass exit exams, dropout increases in 12th grade at about the same rate as in other states without such alternative pathways. This suggests that at least some of the impact is due to stop-out on the part of students.high school dropout, exit exams, accountability, attainment

Tangle Solutions for a Family of DNA-Rearranging Proteins

We study two systems of tangle equations that arise when modeling the action of the Integrase family of proteins on DNA. These two systems--direct and inverted repeats--correspond to two different possibilities for the initial DNA sequence. We present one new class of solutions to the tangle equations. In the case of inverted repeats we prove that any solution not in these, or 2 previously known classes, would have to belong to one specific class. In the case of direct repeats we prove that the three classes are are the only solutions possible.Comment: 26 pages, 9 figures, Appendix. To appear in Mathematical Proceedings of the Cambridge Philosophical Societ

Importance of Cultural Intelligence: cross-cultural examination and analysis

Globalization requires collaboration, partnerships, alliances, trade agreements, and business conduct across both borders and cultures. Growth in international business necessitates corporations and employees to be culturally intelligent. Cultural intelligence has proved to be an instrumental skill that will be a major determinant in the success of cross-cultural collaborations. We examine cross-cultural situations of financial and social problems caused by a lack of cultural intelligence and compare them to situations of effective collaborations. We conclude with practical suggestions and five recommendations that can help improve cultural intelligence levels

Jammed lattice sphere packings

We generate and study an ensemble of isostatic jammed hard-sphere lattices. These lattices are obtained by compression of a periodic system with an adaptive unit cell containing a single sphere until the point of mechanical stability. We present detailed numerical data about the densities, pair correlations, force distributions, and structure factors of such lattices. We show that this model retains many of the crucial structural features of the classical hard-sphere model and propose it as a model for the jamming and glass transitions that enables exploration of much higher dimensions than are usually accessible.Comment: 8 pages, 2 tables, 8 figures, final submitted manuscrip