A numerical code for a three-dimensional magnetospheric MHD equilibrium model

Two dimensional and three dimensional MHD equilibrium models were begun for Earth's magnetosphere. The original proposal was motivated by realizing that global, purely data based models of Earth's magnetosphere are inadequate for studying the underlying plasma physical principles according to which the magnetosphere evolves on the quasi-static convection time scale. Complex numerical grid generation schemes were established for a 3-D Poisson solver, and a robust Grad-Shafranov solver was coded for high beta MHD equilibria. Thus, the effects were calculated of both the magnetopause geometry and boundary conditions on the magnetotail current distribution

Where are the parallel algorithms?

Four paradigms that can be useful in developing parallel algorithms are discussed. These include computational complexity analysis, changing the order of computation, asynchronous computation, and divide and conquer. Each is illustrated with an example from scientific computation, and it is shown that computational complexity must be used with great care or an inefficient algorithm may be selected

A methodology for exploiting parallelism in the finite element process

A methodology is described for developing a parallel system using a top down approach taking into account the requirements of the user. Substructuring, a popular technique in structural analysis, is used to illustrate this approach

PriPeARL: A Framework for Privacy-Preserving Analytics and Reporting at LinkedIn

Preserving privacy of users is a key requirement of web-scale analytics and reporting applications, and has witnessed a renewed focus in light of recent data breaches and new regulations such as GDPR. We focus on the problem of computing robust, reliable analytics in a privacy-preserving manner, while satisfying product requirements. We present PriPeARL, a framework for privacy-preserving analytics and reporting, inspired by differential privacy. We describe the overall design and architecture, and the key modeling components, focusing on the unique challenges associated with privacy, coverage, utility, and consistency. We perform an experimental study in the context of ads analytics and reporting at LinkedIn, thereby demonstrating the tradeoffs between privacy and utility needs, and the applicability of privacy-preserving mechanisms to real-world data. We also highlight the lessons learned from the production deployment of our system at LinkedIn.Comment: Conference information: ACM International Conference on Information and Knowledge Management (CIKM 2018

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

A variant of nested dissection for solving n by n grid problems

Nested dissection orderings are known to be very effective for solving the sparse positive definite linear systems which arise from n by n grid problems. In this paper nested dissection is shown to be the final step of incomplete nested dissection, an ordering which corresponds to the premature termination of dissection. Analyses of the arithmetic and storage requirements for incomplete nested dissection are given, and the ordering is shown to be competitive with nested dissection under certain conditions

Maximally Entangled Mixed-State Generation via Local Operations

We present a general theoretical method to generate maximally entangled mixed states of a pair of photons initially prepared in the singlet polarization state. This method requires only local operations upon a single photon of the pair and exploits spatial degrees of freedom to induce decoherence. We report also experimental confirmation of these theoretical results.Comment: 5 pages, 2 figures, to be published in Physical Review

The Speaking Christ in His Royal Office

One might argue as to whether the doctrine of the threefold office of Christ is really usable for a comprehensive description of the work of Christ. There are expositions of Christian doctrine enough which do not follow this pattern at all. There are those who fear that this pattern may do violence to the content: the fullness of the Biblical proclamation concerning the office and the work of Christ may be lost if one seeks to reduce or confine the Biblical titles of honor applied to Christ and the Biblical designations of His office to the triplex munus. Among them is Werner Elert, who is intent upon letting the Biblical proclamation speak in all its multiplicity