A new algorithm and refined bounds for extended gcd computation

Extended gcd computation is interesting itself. It also plays a fundamental role in other calculations. We present a new algorithm for solving the extended gcd problem. This algorithm has a particularly simple description and is practical. It also provides refined bounds on the size of the multipliers obtained.

The Qu-Prolog unification algorithm: Formalisation and correctness

Qu-Prolog is an extension of Prolog which performs meta-level computations over object languages, such as predicate calculi and lambda-calculi, which have object-level variables, and quantifier or binding symbols creating local scopes for those variables. As in Prolog, the instantiable (meta-level) variables of Qu-Prolog range over object-level terms, and in addition other Qu-Prolog syntax denotes the various components of the object-level syntax, including object-level variables. Further, the meta-level operation of substitution into object-level terms is directly represented by appropriate Qu-Prolog syntax. Again as in Prolog, the driving mechanism in Qu-Prolog computation is a form of unification, but this is substantially more complex than for Prolog because of Qu-Prolog's greater generality, and especially because substitution operations are evaluated during unification. In this paper, the Qu-Prolog unification algorithm is specified, formalised and proved correct. Further, the analysis of the algorithm is carried out in a frame-work which straightforwardly allows the 'completeness' of the algorithm to be proved: though fully explicit answers to unification problems are not always provided, no information is lost in the unification process.

Dynamic strain measurement using piezoelectric polymer film

Piezoelectric polymers have been used to form the basis of dynamic strain gauges for the detection of stress waves. The linearity of response was tested using a split Hopkinson pressure bar arrangement. The results obtained illustrate the effectiveness of piezoelectric film strain gauges in the measurement of axial stress waves.

Analysis of dynamic process models for structural insight and model reduction .1. Structural identification measures

An important consideration in the development of mathematical models for dynamic simulation, is the identification of the appropriate mathematical structure. By building models with an efficient structure which is devoid of redundancy, it is possible to create simple, accurate and functional models. This leads not only to efficient simulation, but to a deeper understanding of the important dynamic relationships within the process. In this paper, a method is proposed for systematic model development for startup and shutdown simulation which is based on the identification of the essential process structure. The key tool in this analysis is the method of nonlinear perturbations for structural identification and model reduction. Starting from a detailed mathematical process description both singular and regular structural perturbations are detected. These techniques are then used to give insight into the system structure and where appropriate to eliminate superfluous model equations or reduce them to other forms. This process retains the ability to interpret the reduced order model in terms of the physico-chemical phenomena. Using this model reduction technique it is possible to attribute observable dynamics to particular unit operations within the process. This relationship then highlights the unit operations which must be accurately modelled in order to develop a robust plant model. The technique generates detailed insight into the dynamic structure of the models providing a basis for system re-design and dynamic analysis. The technique is illustrated on the modelling for an evaporator startup. Copyright (C) 1996 Elsevier Science Ltd

Analysis of dynamic models for structural insight and model reduction .2. A multi-stage compressor shutdown case-study

In this second paper, the three structural measures which have been developed are used in the modelling of a three stage centrifugal synthesis gas compressor. The goal of this case study is to determine the essential mathematical structure which must be incorporated into the compressor model to accurately model the shutdown of this system. A simple, accurate and functional model of the system is created via three structural measures. It was found that the model can be correctly reduced into its basic modes and that the order of the differential system can be reduced from 51(st) to 20(th). Of the 31 differential equational 21 reduce to algebraic relations, 8 become constants and 2 can be deleted thereby increasing the algebraic set from 70 to 91 equations. An interpretation is also obtained as to which physical phenomena are dominating the dynamics of the compressor add whether the compressor will enter surge during the shutdown. Comparisons of the reduced model performance against the full model are given, showing the accuracy and applicability of the approach. Copyright (C) 1996 Elsevier Science Ltd

Analysis and implementation of a new constant acceleration subcycling algorithm

An algorithm for explicit integration of structural dynamics problems with multiple time steps is proposed that averages accelerations to obtain subcycle states at a nodal interface between regions integrated with different time steps. With integer time step ratios, the resulting subcycle updates at the interface sum to give the same effect as a central difference update over a major cycle. The algorithm is shown to have good accuracy, and stability properties in linear elastic analysis similar to those of constant velocity subcycling algorithms. The implementation of a generalised form of the algorithm with non-integer time step ratios is presented. (C) 1997 by John Wiley & Sons, Ltd.

A Dynamic Model of Hand-and-Foot Syndrome in Patients Receiving Capecitabine

For the purpose of developing a longitudinal model to predict hand-and-foot syndrome (HFS) dynamics in patients receiving capecitabine, data from two large phase III studies were used. Of 595 patients in the capecitabine arms, 400 patients were randomly selected to build the model, and the other 195 were assigned for model validation. A score for risk of developing HFS was modeled using the proportional odds model, a sigmoidal maximum effect model driven by capecitabine accumulation as estimated through a kinetic-pharmacodynamic model and a Markov process. The lower the calculated creatinine clearance value at inclusion, the higher was the risk of HFS. Model validation was performed by visual and statistical predictive checks. The predictive dynamic model of HFS in patients receiving capecitabine allows the prediction of toxicity risk based on cumulative capecitabine dose and previous HFS grade. This dose-toxicity model will be useful in developing Bayesian individual treatment adaptations and may be of use in the clinic.

The subcycled Newmark algorithm

The popular Newmark algorithm, used for implicit direct integration of structural dynamics, is extended by means of a nodal partition to permit use of different timesteps in different regions of a structural model. The algorithm developed has as a special case an explicit-explicit subcycling algorithm previously reported by Belytschko, Yen and Mullen. That algorithm has been shown, in the absence of damping or other energy dissipation, to exhibit instability over narrow timestep ranges that become narrower as the number of degrees of freedom increases, making them unlikely to be encountered in practice. The present algorithm avoids such instabilities in the case of a one to two timestep ratio (two subcycles), achieving unconditional stability in an exponential sense for a linear problem. However, with three or more subcycles, the trapezoidal rule exhibits stability that becomes conditional, falling towards that of the central difference method as the number of subcycles increases. Instabilities over narrow timestep ranges, that become narrower as the model size increases, also appear with three or more subcycles. However by moving the partition between timesteps one row of elements into the region suitable for integration with the larger timestep these the unstable timestep ranges become extremely narrow, even in simple systems with a few degrees of freedom. As well, accuracy is improved. Use of a version of the Newmark algorithm that dissipates high frequencies minimises or eliminates these narrow bands of instability. Viscous damping is also shown to remove these instabilities, at the expense of having more effect on the low frequency response.

Physical function interfering with pain and symptoms in fibromyalgia patients

Objectives. The aim of this study was to assess the relationship between variables of physical assessment - muscular strength, flexibility and dynamic balance - with pain, pain threshold, and fibromyalgia symptoms (FM). Methods. Our sample consists of 55 women, with age ranging from 30 to 55 years (mean of 46.5, (standard deviation, SD=6.6)), mean body mass index (BMI) of 28.7(3.8) and diagnosed for FM according to the American College of Rheumatology criteria. Pain intensity was measured using a visual analogue scale (VAS) and pain threshold (PT) using Fisher`s dolorimeter. FM symptoms were assessed by the Fibromyalgia Impact Questionnaire (FIQ); flexibility by the third finger to floor test (3FF); the muscular strength index (MSI) by the maximum volunteer isometric contraction at flexion and extension of right knee and elbow using a force transducer, dynamic balance by the time to get up and go (TUG) test and the functional reach test (FRT). Data were analysed using Pearson`s correlation, as well as simple and multivariate regression tests, with significance level of 5%. Results. PT and FIQ were weakly but significantly correlated with the TUG, MSI and 3FF as well as VAS with the TUG and MSI (p<0.05). VAS, PT and FIQ was not correlated with FRT. Simple regression suggests that, alone, TUG, FR, MSI and 3FF are low predictors of VAS, PT and FIQ. For the VAS, the best predictive model includes TUG and MSI, explaining 12.6% of pain. variability. For TP and total symptoms, as obtained by the FIQ, most predictive model includes 3FF and MSI, which respectively respond by 30% and 21% of the variability. Conclusion. Muscular strength, flexibility and balance are associated with pain, pain threshold, and symptoms in FM patients.

Simulated-annealing-based genetic algorithm for modeling the optical constants of solids

We propose a simulated-annealing-based genetic algorithm for solving model parameter estimation problems. The algorithm incorporates advantages of both genetic algorithms and simulated annealing. Tests on computer-generated synthetic data that closely resemble optical constants of a metal were performed to compare the efficiency of plain genetic algorithms against the simulated-annealing-based genetic algorithms. These tests assess the ability of the algorithms to and the global minimum and the accuracy of values obtained for model parameters. Finally, the algorithm with the best performance is used to fit the model dielectric function to data for platinum and aluminum. (C) 1997 Optical Society of America.

Assessment of immediate conservative breast surgery reconstruction: A classification system of defects revisited and an algorithm for selecting the appropriate technique

Background: Although various techniques have been used for breast conservation surgery reconstruction, there are few studies describing a logical approach to reconstruction of these defects. The objectives of this study were to establish a classification system for partial breast defects and to develop a reconstructive algorithm. Methods: The authors reviewed a 7-year experience with 209 immediate breast conservation surgery reconstructions. Mean follow-up was 31 months. Type I defects include tissue resection in smaller breasts (bra size A/B), including type IA, which involves minimal defects that do not cause distortion; type III, which involves moderate defects that cause moderate distortion; and type IC, which involves large defects that cause significant deformities. Type II includes tissue resection in medium-sized breasts with or without ptosis (bra size C), and type III includes tissue resection in large breasts with ptosis (bra size D). Results: Eighteen percent of patients presented type I, where a lateral thoracodorsal flap and a latissimus dorsi flap were performed in 68 percent. Forty-five percent presented type II defects, where bilateral mastopexy was performed in 52 percent. Thirty-seven percent of patients presented type III distortion, where bilateral reduction mammaplasty was performed in 67 percent. Thirty-five percent of patients presented complications, and most were minor. Conclusions: An algorithm based on breast size in relation to tumor location and extension of resection can be followed to determine the best approach to reconstruction. The authors` results have demonstrated that the complications were similar to those in other clinical series. Success depends on patient selection, coordinated planning with the oncologic surgeon, and careful intraoperative management.

Systemic lupus erythematosus exhibits a dynamic and continuum spectrum of effector/regulatory T cells

Objective: The identification of regulatory T cells (Treg cells) as CD4(+)CD25(high) cells may be upset by the increased frequency of activated effector T cells (Teff cells) in inflammatory diseases such as systemic lupus erythematosus (SLE). This study aimed to evaluate the frequency of T-cell subsets according to the expression of CD25 and CD127 in active (A-SLE) and inactive SLE (I-SLE). Methods: Peripheral blood mononuclear cells (PBMCs) from 26 A-SLE patients (SLE Disease Activity Index (SLEDAI) = 10.17 +/- 3.7), 31 I-SLE patients (SLEDAI = 0), and 26 healthy controls (HC) were analysed by multicolour flow. cytometry. Results: CD25(high) cell frequency was increased in A-SLE (5.2 +/- 5.7%) compared to I-SLE (3.4 +/- 3.4%) and HC (1.73 +/- 0.8%) (p < 0.01). However, the percentage of FoxP3(+) cells in the CD25(high) subset was decreased in A-SLE (24.6 +/- 16.4%) compared to I-SLE (33.7 +/- 16) and HC (45 +/- 25.1%) (p < 0.01). This was partly due to the increased frequency of Teff cells (CD25(high)CD127(+)FoxP3(empty set)) in A-SLE (10.7 +/- 7.3%) compared to I-SLE (8.5 +/- 6.5) and HC (6.1 +/- 1.8%) (p = 0.02). Hence the frequency of Treg cells (CD25(+/high)CD127(low/empty set)FoxP3(+)) was equivalent in A-SLE (1.4 +/- 0.8%), I-SLE (1.37 +/- 1.0%), and HC (1.13 +/- 0.59%) (p = 0.42). A-SLE presented an increased frequency of CD25(+)CD127(+)FoxP3(+) and CD25(empty set)FoxP3(+)CD127(low/empty set) T cells, which may represent intermediate phenotypes between Treg and Teff cells. Conclusions: The present study has provided data supporting normal Treg cell frequency in A-SLE and I-SLE as well as increased frequency of Teff cells in A-SLE. This scenario reflects a Treg/Teff ratio imbalance that may favour the inflammatory phenotype of the disease. In addition, the increased frequency of T cells with putative intermediate phenotypes may be compatible with a highly dynamic immune system in SLE.

POISSON DISTRIBUTION TO ANALYZE NEAR-THRESHOLD MOTOR EVOKED POTENTIALS

Motor unit action potentials (MUAPs) evoked by repetitive, low-intensity transcranial magnetic stimulation can be modeled as a Poisson process. A mathematical consequence of such a model is that the ratio of the variance to the mean of the amplitudes of motor evoked potentials (MEPs) should provide an estimate of the mean size of the individual MUAPs that summate to generate each MEP. We found that this is, in fact, the case. Our finding thus supports the use of the Poisson distribution to model MEP generation and indicates that this model enables characterization of the motor unit population that contributes to near-threshold MEPs. Muscle Nerve 42: 825-828, 2010