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.

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.

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.

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.

Spatial learning ability of rats following differing levels of exposure to alcohol during early postnatal life

Rats exposed to a relatively high dose (7.5 g/kg body weight) of alcohol on either the fifth or tenth postnatal day of age have been reported to have long-lasting deficits in spatial learning ability as tested on the Morris water maze task. The question arises concerning the level of alcohol required to achieve this effect. Wistar rats were exposed to either 2, 4 or 6 g/kg body weight of ethanol administered as a 10% solution. This ethanol was given over an 8-h period on the fifth postnatal day of age by means of an intragastric cannula. Gastrostomy controls received a 5% sucrose solution substituted isocalorically for the ethanol. Another set of pups raised by their mother were used as suckle controls. All surgical procedures were carried out under halothane vapour anaesthesia. After the artificial feeding regimes all pups were returned to lactating dams and weaned at 21 days of age. The spatial learning ability of these rats was tested in the Morris water maze when they were between 61-64 days of age. This task requires the rats to swim in a pool containing water made opaque and locate and climb onto a submerged platform. The time taken to accomplish this is known as the escape latency. Each rat was subjected to 24 trials over 3 days of the test period. Statistical analysis of the escape latency data revealed that the rats given 6 g/kg body weight of ethanol had significant deficits in their spatial learning ability compared with their control groups. However, there was no significant difference in spatial learning ability for the rats given either 2 or 4 g/kg body weight of ethanol compared with their respective gastrostomy or suckle control animals. We concluded that ethanol exposure greater than 4 g/kg over an 8-h period to 5-day-old rats is required for them to develop long-term deficits in spatial learning behaviour. (C) 1998 Elsevier Science Inc.