Numerical integration for high order pyramidal finite elements

We examine the effect of numerical integration on the convergence of high order pyramidal finite element methods. Rational functions are indispensable to the construction of pyramidal interpolants so the conventional treatment of numerical integration, which requires that the finite element approximation space is piecewise polynomial, cannot be applied. We develop an analysis that allows the finite element approximation space to include rational functions and show that despite this complication, conventional rules of thumb can still be used to select appropriate quadrature methods on pyramids. Along the way, we present a new family of high order pyramidal finite elements for each of the spaces of the de Rham complex.Comment: 28 page

High-order finite elements on pyramids: approximation spaces, unisolvency and exactness

We present a family of high-order finite element approximation spaces on a pyramid, and associated unisolvent degrees of freedom. These spaces consist of rational basis functions. We establish conforming, exactness and polynomial approximation properties.Comment: 37 pages, 3 figures. This work was originally in one paper, then split into two; it has now been recombined into one paper, with substantial changes from both of its previous form

Comparing Mid Lumbar Interbody Fusion (MIDLF) with Traditional Posterior Lumbar Interbody Fusion (PLIF)

Mid-lumbar interbody fusion (MIDLF) uses a novel cortical bone trajectory (CBT) screw that provides robust fixation that is less dependent on cancellous bone quality than a traditional pedicle screw. MIDLF also allows for decompression and instrumentation through a smaller central surgical window. The aim of this study is to compare MIDLF with posterior lumbar interbody fusion (PLIF) with regards to perioperative complications, operative time, blood loss, length in hospital, radiographic outcomes and post-operative patient functional scores. A retrospective review of our institutional database was performed of patients undergoing MIDLF. Matched PLIF controls were then selected from the same database for comparison. 20 MIDLF patients were identified as were 20 matched PLIF controls. Primary outcomes included perioperative clinical and radiographic measures as well as postoperative patient self-reported function. Results demonstrated no significant difference between the two groups with respect to all clinical, radiographic and patient self-reported measures

Environmental Fate and Effects of Bacillus thuringiensis (Bt) Proteins from Transgenic Crops: a Review

This paper reviews the scientific literature addressing the environmental fate and nontarget effects of the Cry protein toxins from Bacillus thuringiensis (Bt), specifically resulting from their expression in transgenic crops. Published literature on analytical methodologies for the detection and quantification of the Cry proteins in environmental matrices is also reviewed, with discussion of the adequacy of the techniques for determining the persistence and mobility of the Bt proteins. In general, assessment of the nontarget effects of Bt protein toxins indicates that there is a low level of hazard to most groups of nontarget organisms, although some investigations are of limited ecological relevance. Some published reports on the persistence of the proteins in soil show short half-lives, whereas others show low-level residues lasting for many months. Improvements in analytical methods will allow a more complete understanding of the fate and significance of Bt proteins in the environment

Breaking down bias

What is bias? A review of the library literature reveals no attempts to define the concept. Nor does it reveal systematic attempts to develop interventions that teach the identification and evaluation of bias. Current pedagogical approaches (checklists and bias charts) tend to assume a self-evident definition that categorises bias as unquestioningly bad and disqualifying. Current approaches, however, fail to recognise the cognitive complexity of decoding bias within a source. A decoding process includes identifying the type of bias, determining an objective baseline, recognising biased features, and analysing bias’s impact. Based on work done from several fields—argumentation theory, media bias, media literacy, and history education—this paper proposes an operational definition of bias and a practical framework for conceptualising a process to identify and evaluate bias. This paper will explore the limitations of this framework, as well as existing source evaluation paradigms. If librarians want to prepare individuals to participate in a post-truth society, where disinformation weaponises bias by appealing to emotions and beliefs rather than facts, an inclusive and nuanced conception of bias is a necessary component of library instruction

Task Scheduling in Networks

Scheduling a set of tasks on a set of machines so as to yield an efficient schedule is a basic problem in computer science and operations research. Most of the research on this problem incorporates the potentially unrealistic assumption that communication between the different machines is instantaneous. In this paper we remove this assumption and study the problem of network scheduling, where each job originates at some node of a network, and in order to be processed at another node must take the time to travel through the network to that node. Our main contribution is to give approximation algorithms and hardness proofs for fully general forms of the fundamental problems in network scheduling. We consider two basic scheduling objectives: minimizing the makespan and minimizing the average completion time. For the makespan, we prove small constant factor hardness-to-approximate and approximation results. For the average completion time, we give a log-squared approximation algorithm for the most general form of the problem. The techniques used in this approximation are fairly general and have several other applications. For example, we give the first nontrivial approximation algorithm to minimize the average weighted completion time of a set of jobs on related or unrelated machines, with or without a network