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GAbased learning algorithms to identify fuzzy rules for fuzzy neural networksIdentification of fuzzy rules is an important issue in designing of a fuzzy neural network (FNN). However, there is no systematic design procedure at present. In this paper we present a genetic algorithm (GA) based learning algorithm to make use of the known membership function to identify the fuzzy rules form a large set of all possible rules. The proposed learning algorithm initially considers all possible rules then uses the training data and the fitness function to perform ruleselection. The proposed GA based learning algorithm has been tested with two different sets of training data. The results obtained from the experiments are promising and demonstrate that the proposed GA based learning algorithm can provide a reliable mechanism for fuzzy rule selection.

A GAbased technique for the scheduling of storage tanksThis paper proposes the application of a genetic algorithm based methodology for the scheduling of storage tanks. The proposed approach is an integration of GA and heuristic rulebased techniques, which decomposes the complex mixed integer optimisation problem into integer and real number subproblems. The GA string considers the integer problem, and the heuristic approach solves the real number problems within the GA framework. The algorithm is demonstrated for a test problem related to a water treatment facility at a port, and has been found to give a significantly better schedule than those generated using a heuristicbased approach.

GA/SAbased hybrid techniques for the scheduling of generator maintenance in power systemsProposes the application of a genetic algorithm (GA) and simulated annealing (SA) based hybrid approach for the scheduling of generator maintenance in power systems using an integer representation. The adapted approach uses the probabilistic acceptance criterion of simulated annealing within the genetic algorithm framework. A case study is formulated in this paper as an integer programming problem using a reliabilitybased objective function and typical problem constraints. The implementation and performance of the solution technique are discussed. The results in this paper demonstrate that the technique is more effective than approaches based solely on genetic algorithms or solely on simulated annealing. It therefore proves to be a valid approach for the solution of generator maintenance scheduling problems

Gait Alterations Negotiating A Raised Surface Induced by Monocular BlurFalls in the elderly are a major cause of serious injury and mortality. Impaired and absent stereopsis may be a significant risk factor for falls or hip fracture, although data from epidemiological studies are not consistent. Previous laboratory based studies, however, do suggest that stereoacuity is an important factor in adaptive gait. The present study investigates how acute impairment of stereopsis, through monocular blur of differing levels, ranging from 0.50 diopter (D) to a monovision correction affected gait when negotiating a raised surface in elderly subjects. Eleven elderly subjects (73.3 3.6 years) walked up to and negotiated a raised surface under nine visual conditions, binocular vision, one eye occluded and 0.50 D, 1.00 D and monovision correction (mean 2.50 D 0.20 D) with blur and occlusion either over the dominant or nondominant eye. Analysis focused on foot positioning and toe clearance parameters. There was no effect of ocular dominance on any parameters. Monocular blur impaired stereopsis (p 0.01), with more minor effects on high and low contrast acuity. Vertical and horizontal lead limb toe clearance both increased under all levels of monocular blur including the lowest level of 0.50 DBlur (p 0.03) and monovision correction led to toe clearance levels similar to that found with occlusion of one eye. Findings demonstrated that even small amounts of monocular blur can lead to a change in gait when negotiating a raised surface, suggesting acute monocular blur affected the ability to accurately judge the height of a step in the travel path. Further work is required to investigate if similar adaptations are used by patients with chronic monocular blur.

Gait termination on a declined surface in transfemoral amputees: Impact of using microprocessorcontrolled limb systemBackground: Walking down ramps is a demanding task for transfemoralamputees and terminating gait on ramps is even more challenging because of the requirement to maintain a stable limb so that it can do the necessary negative mechanical work on the centreofmass in order to arrest (dissipate) forward/downward velocity. We determined how the use of a microprocessorcontrolled limb system (simultaneous control over hydraulic resistances at ankle and knee) affected the negative mechanical work done by each limb when transfemoralamputees terminated gait during ramp descent. Methods: Eight transfemoralamputees completed planned gait terminations (stopping on prosthesis) on a 5degree ramp from slow and customary walking speeds, with the limb's microprocessor active or inactive. When active the limb operated in its ‘rampdescent’ mode and when inactive the knee and ankle devices functioned at constant default levels. Negative limb work, determined as the integral of the negative mechanical (external) limb power during the braking phase, was compared across speeds and microprocessor conditions. Findings: Negative work done by each limb increased with speed (p < 0.001), and on the prosthetic limb it was greater when the microprocessor was active compared to inactive (p = 0.004). There was no change in work done across microprocessor conditions on the intact limb (p = 0.35). Interpretation: Greater involvement of the prosthetic limb when the limb system was active indicates its rampdescent mode effectively altered the hydraulic resistances at the ankle and knee. Findings highlight participants became more assured using their prosthetic limb to arrest centreofmass velocity.

Gait termination on declined compared to level surface; contribution of terminating and trailing limb work in arresting centre of mass velocityTo terminate gait, the mechanical workdone by the lowerlimbs is likely to be predominantly negative but how such work is produced/completed has not previously been investigated. The aim of this study was to determine the amount of negative mechanical (external) workdone by the lowerlimbs, along with the associated joints (muscle) work, to terminate gait and how these work contributions were affected by a change in surface angle. Eight males completed terminations on the level floor and a declined ramp. Negative mechanical limbwork (limbW(−ve)) was computed (each orthogonal direction) as the dotproduct of the groundreactionforce and centreofmass (CoM) velocity. Inverse dynamics was used to calculate ankle, knee and hip negative joints (muscle) work (Wj(−ve)). Measures were determined for each limb for the twolocomotor steps of gait termination. The trailinglimb did 67% (−0.386 J/kg) of the overall limbW(−ve) to terminate gait on the level; and this increased to 74% (−0.451 J/kg) for ramp trials. Wj(−ve) was greater for the trailing (ankle −0.315; knee −0.357; hip −0.054 J/kg) compared to terminating limb (ankle, −0.063; knee −0.051; hip −0.014 J/kg), with the increases in ankle Wj(−ve) being temporally associated with increases in perpendicular limbW(−ve). Wj(−ve) increased on both limbs for declined compared to level surface, particularly at the knee (declined −0.357, level −0.096 J/kg), with such increases being temporally associated with increases in parallel limbW(−ve). These findings provide new perspectives on how the limbs do work on the CoM to terminate gait, and may be helpful in designing prosthetic limbs to facilitate walking on ramps.

Galois quantum systemsA finite quantum system in which the position and momentum take values in the Galois field GF(p¿l) is constructed from a smaller quantum system in which the position and momentum take values in Zp , using field extension. The Galois trace is used in the definition of the Fourier transform. The Heisenberg¿Weyl group of displacements and the Sp(2, GF(p¿l)) group of symplectic transformations are studied. A class of transformations inspired by the Frobenius maps in Galois fields is introduced. The relationship of this 'Galois quantum system' with its subsystems in which the position and momentum take values in subfields of GF(p¿l) is discussed.

Galois quantum systems, irreducible polynomials and Riemann surfacesFinite quantum systems in which the position and momentum take values in the Galois field GF(p), are studied. Ideas from the subject of field extension are transferred in the context of quantum mechanics. The Frobenius automorphisms in Galois fields lead naturally to the "Frobenius formalism" in a quantum context. The Hilbert space splits into "Frobenius subspaces" which are labeled with the irreducible polynomials associated with the yp¿y. The Frobenius maps transform unitarily the states of a Galois quantum system and leave fixed all states in some of its Galois subsystems (where the position and momentum take values in subfields of GF(p)). An analytic representation of these systems in the sheeted complex plane shows deeper links between Galois theory and Riemann surfaces. ©2006 American Institute of Physics

The GAMESSUK electronic structure package: algorithms, developments and applications.A description of the ab initio quantum chemistry package GAMESSUK is presented. The package offers a wide range of quantum mechanical wavefunctions, capable of treating systems ranging from closedshell molecules through to the species involved in complex reaction mechanisms. The availability of a wide variety of correlation methods provides the necessary functionality to tackle a number of chemically important tasks, ranging from geometry optimization and transitionstate location to the treatment of solvation effects and the prediction of excited state spectra. With the availability of relativistic ECPs and the development of ZORA, such calculations may be performed on the entire Periodic Table, including the lanthanides. Emphasis is given to the DFT module, which has been extensively developed in recent years, and a number of other, novel features of the program. The parallelization strategy used in the program is outlined, and detailed speedup results are given. Applications of the code in the areas of enzyme and zeolite catalysis and in spectroscopy are described.

Gateopening criterion for generating dambreak flow in nonrectangular wet bed channelsA sudden dam failure is usually simulated by the rapid removal of a gate in laboratory tests and numerical simulations. The gateopening time is often determined according to the Lauber and Hager instantaneous collapse criterion (referred to as LauberHager criterion) established for a rectangular open channel with a dry bed. However, this criterion is not suitable for nonrectangular channels or initial wetbed conditions. In this study, the effect of the gateopening time on the wave evolution is investigated by using the large eddy simulation (LES) model. The instantaneous dam break, namely the dam break without a gate, is simulated for comparison. A gateopening criterion for generating dambreak flow in nonrectangular wet bed channel is proposed in this study, which can be used as an extension of the LauberHager criterion and provides a more comprehensive and reasonable estimate of the gate opening time.

GazeauKlauder coherent states in onemode systems with periodic potential.GazeauKlauder coherent states for a onemode system with sinusoidal potential, are introduced. Their quantum statistical properties and their uncertainties are studied. The effect of dissipation on these states is estimated. The evolution of the ordinary (Glauber) coherent states in this system, is also studied. It is shown that these states evolve into superpositions of many macroscopically distinguishable states (`multiSchrödinger cats').

Gender and smile dynamicsThis chapter is concerned with the discussion of a computational framework to aid with gender classification in an automated fashion using the dynamics of a smile. The computational smile dynamics framework we discuss here uses the spatiotemporal changes on the face during a smile. Specifically, it uses a set of spatial and temporal features on the overall face. These include the changes in the area of the mouth, the geometric flow around facial features and a set of intrinsic features over the face. These features are explicitly derived from the dynamics of the smile. Based on it, a number of distinct dynamic smile parameters can be extracted which can then be fed to a machine learning algorithm for gender classification.

A General 4thOrder PDE Method to Generate Bézier Surfaces from the BoundaryIn this paper we present a method for generating Bézier surfaces from the boundary information based on a general 4thorder PDE. This is a generalisation of our previous work on harmonic and biharmonic Bézier surfaces whereby we studied the Bézier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bézier solutions of the Euler¿Lagrange equation associated with the most general quadratic functional. We show that there is a large class of fourthorder operators for which Bézier solutions exist and hence we show that such operators can be utilised to generate Bézier surfaces from the boundary information. As part of this work we present a general method for generating these Bézier surfaces. Furthermore, we show that some of the existing techniques for boundary based surface design, such as Coons patches and Bloor¿Wilson PDE method, are indeed particular cases of the generalised framework we present here.

General discriminative optimization for point set registrationPoint set registration has been actively studied in computer vision and graphics. Optimization algorithms are at the core of solving registration problems. Traditional optimization approaches are mainly based on the gradient of objective functions. The derivation of objective functions makes it challenging to find optimal solutions for complex optimization models, especially for those applications where accuracy is critical. Learningbased optimization is a novel approach to address this problem, which learns the gradient direction from datasets. However, many learningbased optimization algorithms learn gradient directions via a single feature extracted from the dataset, which will cause the updating direction to be vulnerable to perturbations around the data, thus falling into a bad stationary point. This paper proposes the General Discriminative Optimization (GDO) method that updates a gradient path automatically through the tradeoff among contributions of different features on updating gradients. We illustrate the benefits of GDO with tasks of 3D point set registrations and show that GDO outperforms the stateoftheart registration methods in terms of accuracy and robustness to perturbations.

The generalized Hamiltonian model for the shafting transient analysis of the hydro turbine generating sets.Traditional rotor dynamics mainly focuses on the steady state behavior of the rotor and shafting. However, for systems such as hydro turbine generating sets (HTGS) where the control and regulation is frequently applied, the shafting safety and stabilization in transient state is then a key factor. The shafting transient state inevitably involves multiparameter domain, multifield coupling, and coupling dynamics. In this paper, the relative value form of the Lagrange function and its equations have been established by defining the base value system of the shafting. Takingthe rotation angle and the angular speed of the shafting as a link, the shafting lateral vibration and generator equations are integrated into the framework of generalized Hamiltonian system. The generalized Hamiltonian control model is thus established. To make the model more general, additional forces of the shafting are taken as the input excitation in proposed model. The control system of the HTGS can be easily connected with the shafting model to form the whole simulation system of the HTGS. It is expected that this study will build a foundation for the coupling dynamics theory using the generalized Hamiltonian theory to investigate coupling dynamic mechanism among the shafting vibration, transient of hydro turbine generating sets, and additional forces of the shafting.

Generalized partial differential equations for interactive designThis paper presents a method for interactive design by means of extending the PDE based approach for surface generation. The governing partial differential equation is generalized to arbitrary order allowing complex shapes to be designed as single patch PDE surfaces. Using this technique a designer has the flexibility of creating and manipulating the geometry of shape that satisfying an arbitrary set of boundary conditions. Both the boundary conditions which are defined as curves in 3space and the spine of the corresponding PDE are utilized as interactive design tools for creating and manipulating geometry intuitively. In order to facilitate interactive design in real time, a compact analytic solution for the chosen arbitrary order PDE is formulated. This solution scheme even in the case of general boundary conditions satisfies exactly the boundary conditions where the resulting surface has an closed form representation allowing real time shape manipulation. In order to enable users to appreciate the powerful shape design and manipulation capability of the method, we present a set of practical examples.

Generation of discrete first and secondorder sensitivities for single shootingIn this work, an approach to the forward generation of discrete first and secondorder sensitivities is proposed. For this purpose, an algorithm has been developed, which can basically be applied to general implicit differentialalgebraic equation (DAE) systems. Moreover, the approach has been tailored to both the generation of directional derivatives and sensitivities with respect to discontinuous control trajectories. The implementation of the method is discussed here for the orthogonal collocation method based on Legendre–Gauss–Radau points and considering the linear implicit DAE type, which arises in problems related to chemical engineering. Lastly, the approach has been applied to three case studies of different complexities. The corresponding performance for the generation of Jacobian and Hessian information is discussed in detail.

Generation scheduling using genetic algorithm based hybrid techniquesThe solution of generation scheduling (GS) problems involves the determination of the unit commitment (UC) and economic dispatch (ED) for each generator in a power system at each time interval in the scheduling period. The solution procedure requires the simultaneous consideration of these two decisions. In recent years researchers have focused much attention on new solution techniques to GS. This paper proposes the application of a variety of genetic algorithm (GA) based approaches and investigates how these techniques may be improved in order to more quickly obtain the optimum or near optimum solution for the GS problem. The results obtained show that the GAbased hybrid approach offers an effective alternative for solving realistic GS problems within a realistic timeframe.

Generational and steady state genetic algorithms for generator maintenance scheduling problemsThe aim of generator maintenance scheduling (GMS) in an electric power system is to allocate a proper maintenance timetable for generators while maintaining a high system reliability, reducing total production cost, extending generator life time etc. In order to solve this complex problem a genetic algorithm technique is proposed here. The paper discusses the implementation of GAs to GMS problems with two approaches: generational and steady state. The results of applying these GAs to a test GMS problem based on a practical power system scenario are presented and analysed. The effect of different GA parameters is also studied

Generator maintenance scheduling in power systems using metaheuristicbased hybrid approachesThe effective maintenance scheduling of power system generators is very important for the economical and reliable operation of a power system. This represents a tough scheduling problem which continues to present a challenge for efficient optimization solution techniques. This paper presents the application of metaheuristic approaches, such as a genetic algorithm (GA), simulated annealing (SA) and their hybrid for generator maintenance scheduling (GMS) in power systems using an integer representation. This paper mainly focuses on the application of GA/SA and GA/SA/heuristic hybrid approaches. GA/SA hybrid uses the probabilistic acceptance criterion of SA within the GA framework. GA/SA/heuristic hybrid combines heuristic approaches within the GA/SA hybrid to seed the initial population. A case study is formulated in this paper as an integer programming problem using a reliabilitybased objective function and typical problem constraints. The implementation and performance of the metaheuristic approaches and their hybrid for the test case study are discussed. The results obtained are promising and show that the hybrid approaches are less sensitive to the variations of technique parameters and offer an effective alternative for solving the generator maintenance scheduling problem.