Introduction to the Maple Power Tool Intpakx

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Operator-splitting finite element algorithms for computations of high-dimensional parabolic problems

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, are presented. Both the quadrature and the nodal point based operator-splitting algorithms are validated using a three-dimensional (3D) test problem. The numerical results obtained with the full 3D computations and the operator-split 2D + 1D computations are found to be in a good agreement with the analytical solution. Further, the optimal order of convergence is obtained in both variants of the operator-splitting algorithms. (C) 2012 Elsevier Inc. All rights reserved.

Development of numerical techniques for near-field aeroacoustic computations

This work is concerned with the development of a numerical scheme capable of producing accurate simulations of sound propagation in the presence of a mean flow field. The method is based on the concept of variable decomposition, which leads to two separate sets of equations. These equations are the linearised Euler equations and the Reynolds-averaged Navier–Stokes equations. This paper concentrates on the development of numerical schemes for the linearised Euler equations that leads to a computational aeroacoustics (CAA) code. The resulting CAA code is a non-diffusive, time- and space-staggered finite volume code for the acoustic perturbation, and it is validated against analytic results for pure 1D sound propagation and 2D benchmark problems involving sound scattering from a cylindrical obstacle. Predictions are also given for the case of prescribed source sound propagation in a laminar boundary layer as an illustration of the effects of mean convection. Copyright © 1999 John Wiley & Sons, Ltd.

Molecular computations for reactions and phase transitions: applications to protein stabilization, hydrates and catalysis

In this work we have made significant contributions in three different areas of interest: therapeutic protein stabilization, thermodynamics of natural gas clathrate-hydrates, and zeolite catalysis. In all three fields, using our various computational techniques, we have been able to elucidate phenomena that are difficult or impossible to explain experimentally. More specifically, in mixed solvent systems for proteins we developed a statistical-mechanical method to model the thermodynamic effects of additives in molecular-level detail. It was the first method demonstrated to have truly predictive (no adjustable parameters) capability for real protein systems. We also describe a novel mechanism that slows protein association reactions, called the “gap effect.” We developed a comprehensive picture of methioine oxidation by hydrogen peroxide that allows for accurate prediction of protein oxidation and provides a rationale for developing strategies to control oxidation. The method of solvent accessible area (SAA) was shown not to correlate well with oxidation rates. A new property, averaged two-shell water coordination number (2SWCN) was identified and shown to correlate well with oxidation rates. Reference parameters for the van der Waals Platteeuw model of clathrate-hydrates were found for structure I and structure II. These reference parameters are independent of the potential form (unlike the commonly used parameters) and have been validated by calculating phase behavior and structural transitions for mixed hydrate systems. These calculations are validated with experimental data for both structures and for systems that undergo transitions from one structure to another. This is the first method of calculating hydrate thermodynamics to demonstrate predictive capability for phase equilibria, structural changes, and occupancy in pure and mixed hydrate systems. We have computed a new mechanism for the methanol coupling reaction to form ethanol and water in the zeolite chabazite. The mechanism at 400°C proceeds via stable intermediates of water, methane, and protonated formaldehyde.

Empirically validated interventions for adult disorders

The movement toward evidence-based practice in psychology and medicine should offer few problems in cognitive-behavior therapies because it is consistent with the principles by which they have been developed and disseminated. However, the criteria for assessing empirical status, including the heavy emphasis on manualized treatments, need close examination. A possible outcome of the evidence-based movement would be to focus on the application of manualized treatments in both training and clinical practice; problems with that approach are discussed. Commitment to evidence-based treatment should also include comparisons between psychological and pharmacological interventions, so that rational health care decisions can be made. Psychologists should not be afraid of following the evidence, even when it supports treatments that are not cognitive-behavioral in stated orientation. Such results should be taken as an opportunity for theoretical development and new empirical inquiry rather than be a cause for concern.

Australian pelvic floor questionnaire : a validated interviewer-administered pelvic floor questionnaire for routine clinic and research

The aim of this study was to design and validate an interviewer-administered pelvic floor questionnaire that integrates bladder, bowel and sexual function, pelvic organ prolapse, severity, bothersomeness and condition-specific quality of life. Validation testing of the questionnaire was performed using data from 106 urogynaecological patients and a separately sampled community cohort of 49 women. Missing data did not exceed 2% for any question. It distinguished community and urogynaecological populations regarding pelvic floor dysfunction. The bladder domain correlated with the short version of the Urogenital Distress Inventory, bowel function with an established bowel questionnaire and prolapse symptoms with the International Continence Society prolapse quantification. Sexual function assessment reflected scores on the McCoy Female Sexuality Questionnaire. Cronbach’s α coefficients were acceptable in all domains. Kappa coefficients of agreement for the test–retest analyses varied from 0.5 to 1.0. The interviewer-administered pelvic floor questionnaire assessed pelvic floor function in a reproducible and valid fashion in a typical urogynaecological clinic.

Creation of a validated 3D finite element model of an ovine tibia

Introduction Ovine models are widely used in orthopaedic research. To better understand the impact of orthopaedic procedures computer simulations are necessary. 3D finite element (FE) models of bones allow implant designs to be investigated mechanically, thereby reducing mechanical testing. Hypothesis We present the development and validation of an ovine tibia FE model for use in the analysis of tibia fracture fixation plates. Material & Methods Mechanical testing of the tibia consisted of an offset 3-pt bend test with three repetitions of loading to 350N and return to 50N. Tri-axial stacked strain gauges were applied to the anterior and posterior surfaces of the bone and two rigid bodies – consisting of eight infrared active markers, were attached to the ends of the tibia. Positional measurements were taken with a FARO arm 3D digitiser. The FE model was constructed with both geometry and material properties derived from CT images of the bone. The elasticity-density relationship used for material property determination was validated separately using mechanical testing. This model was then transformed to the same coordinate system as the in vitro mechanical test and loads applied. Results Comparison between the mechanical testing and the FE model showed good correlation in surface strains (difference: anterior 2.3%, posterior 3.2%). Discussion & Conclusion This method of model creation provides a simple method for generating subject specific FE models from CT scans. The use of the CT data set for both the geometry and the material properties ensures a more accurate representation of the specific bone. This is reflected in the similarity of the surface strain results.

Avoiding full extension field arithmetic in pairing computations

The most costly operations encountered in pairing computations are those that take place in the full extension field Fpk . At high levels of security, the complexity of operations in Fpk dominates the complexity of the operations that occur in the lower degree subfields. Consequently, full extension field operations have the greatest effect on the runtime of Miller’s algorithm. Many recent optimizations in the literature have focussed on improving the overall operation count by presenting new explicit formulas that reduce the number of subfield operations encountered throughout an iteration of Miller’s algorithm. Unfortunately, almost all of these improvements tend to suffer for larger embedding degrees where the expensive extension field operations far outweigh the operations in the smaller subfields. In this paper, we propose a new way of carrying out Miller’s algorithm that involves new explicit formulas which reduce the number of full extension field operations that occur in an iteration of the Miller loop, resulting in significant speed ups in most practical situations of between 5 and 30 percent.

Faster pairing computations on curves with high-degree twists

Research on efficient pairing implementation has focussed on reducing the loop length and on using high-degree twists. Existence of twists of degree larger than 2 is a very restrictive criterion but luckily constructions for pairing-friendly elliptic curves with such twists exist. In fact, Freeman, Scott and Teske showed in their overview paper that often the best known methods of constructing pairing-friendly elliptic curves over fields of large prime characteristic produce curves that admit twists of degree 3, 4 or 6. A few papers have presented explicit formulas for the doubling and the addition step in Miller’s algorithm, but the optimizations were all done for the Tate pairing with degree-2 twists, so the main usage of the high- degree twists remained incompatible with more efficient formulas. In this paper we present efficient formulas for curves with twists of degree 2, 3, 4 or 6. These formulas are significantly faster than their predecessors. We show how these faster formulas can be applied to Tate and ate pairing variants, thereby speeding up all practical suggestions for efficient pairing implementations over fields of large characteristic.

Delaying mismatched field multiplications in pairing computations

Miller’s algorithm for computing pairings involves perform- ing multiplications between elements that belong to different finite fields. Namely, elements in the full extension field Fpk are multiplied by elements contained in proper subfields F pk/d , and by elements in the base field Fp . We show that significant speedups in pairing computations can be achieved by delaying these “mismatched” multiplications for an optimal number of iterations. Importantly, we show that our technique can be easily integrated into traditional pairing algorithms; implementers can exploit the computational savings herein by applying only minor changes to existing pairing code.

A validated self-administered female pelvic floor questionnaire

Introduction and hypothesis: The aim of this study was to validate a self-administered version of the already validated interviewer-administered Australian pelvic floor questionnaire. Methods: The questionnaire was completed by 163 women attending an urogynecological clinic. Face and convergent validity was assessed. Reliability testing and comparison with the interviewer-administered version was performed in a subset of 105 patients. Responsiveness was evaluated in a subset of 73 women. Results: Missing data did not exceed 4% for any question. Cronbach’s alpha coefficients were acceptable in all domains. Kappa coefficients for the test–retest analyses varied from 0.64–1.0. Prolapse symptoms correlated significantly with the pelvic organ prolapse quantification. Urodynamics confirmed the reported symptom stress incontinence in 70%. The self and interviewer administered questionnaires demonstrated equivalence. Effect sizes ranged from 0.6 to 1.4. Conclusions: This self-administered pelvic floor questionnaire assessed pelvic floor function in a reproducible and valid fashion and due to its responsiveness, can be used for routine clinical assessment and outcome research.

Group law computations on Jacobians of hyperelliptic Curves

We derive an explicit method of computing the composition step in Cantor’s algorithm for group operations on Jacobians of hyperelliptic curves. Our technique is inspired by the geometric description of the group law and applies to hyperelliptic curves of arbitrary genus. While Cantor’s general composition involves arithmetic in the polynomial ring F_q[x], the algorithm we propose solves a linear system over the base field which can be written down directly from the Mumford coordinates of the group elements. We apply this method to give more efficient formulas for group operations in both affine and projective coordinates for cryptographic systems based on Jacobians of genus 2 hyperelliptic curves in general form.

Malnutrition screening tools : comparison against two validated nutrition assessment methods in older medical inpatients

Objective Although several validated nutritional screening tools have been developed to “triage” inpatients for malnutrition diagnosis and intervention, there continues to be debate in the literature as to which tool/tools clinicians should use in practice. This study compared the accuracy of seven validated screening tools in older medical inpatients against two validated nutritional assessment methods. Methods This was a prospective cohort study of medical inpatients at least 65 y old. Malnutrition screening was conducted using seven tools recommended in evidence-based guidelines. Nutritional status was assessed by an accredited practicing dietitian using the Subjective Global Assessment (SGA) and the Mini-Nutritional Assessment (MNA). Energy intake was observed on a single day during first week of hospitalization. Results In this sample of 134 participants (80 ± 8 y old, 50% women), there was fair agreement between the SGA and MNA (κ = 0.53), with MNA identifying more “at-risk” patients and the SGA better identifying existing malnutrition. Most tools were accurate in identifying patients with malnutrition as determined by the SGA, in particular the Malnutrition Screening Tool and the Nutritional Risk Screening 2002. The MNA Short Form was most accurate at identifying nutritional risk according to the MNA. No tool accurately predicted patients with inadequate energy intake in the hospital. Conclusion Because all tools generally performed well, clinicians should consider choosing a screening tool that best aligns with their chosen nutritional assessment and is easiest to implement in practice. This study confirmed the importance of rescreening and monitoring food intake to allow the early identification and prevention of nutritional decline in patients with a poor intake during hospitalization.