Construction of more reliable complex metabolic models without repeated solution of their constituent differential equations

A method is described for constructing metabolic models composed of many nonlinear stiff differential equations. The system being modeled is divided into subunits (where such division is impractical, forcing functions are used), and algebraic relationships for their behavior at an instant in time are derived. Most of the usual searches for correct model structure and parameter sets are then done with the set of these algebraic relationships at different time points, relatively few expensive differential equation solutions being required. The software used, the application to several models of cardiac metabolism, and the significance of models of this type are discussed.     

Optimization of tool change timing in a nut forming process using genetic algorithms

In this study, we consider an optimization problem arising from tool change scheduling of a nut forming process. The process has nine punches with different life spans. The objective of the study is to optimize the tool change timing of the nine punches in order to maximize the production yield. The punch life spans can be extended by means of Ti coating, but coated punches are more expensive. We also evaluate whether it is worth using coated punches. A cost model is developed for the nut forming process. In the developed cost model, we consider the reliability of the nine punches, the periods taken for changing punches, scrap cost and production yield. The cost function for the process is complex, and is difficult to be solved using conventional optimization methods. Therefore, genetic algorithms are used to solve the problems. We have developed our own genetic algorithms using Java programs and applied the developed genetic algorithms to provide solutions to the optimization problem.     

Efficient monolithic simulation techniques for the stationary Lattice Boltzmann equation on general meshes

In this paper, we present special discretization and solution techniques for the numerical simulation of the Lattice Boltzmann equation (LBE). In Hübner and Turek (Computing, 81:281–296, 2007), the concept of the generalized mean intensity had been proposed for radiative transfer equations which we adapt here to the LBE, treating it as an analogous (semi-discretized) integro-differential equation with constant characteristics. Thus, we combine an efficient finite difference-like discretization based on short-characteristic upwinding techniques on unstructured, locally adapted grids with fast iterative solvers. The fully implicit treatment of the LBE leads to nonlinear systems which can be efficiently solved with the Newton method, even for a direct solution of the stationary LBE. With special exact preconditioning by the transport part due to the short-characteristic upwinding, we obtain an efficient linear solver for transport dominated configurations (macroscopic Stokes regime), while collision dominated cases (Navier-Stokes regime for larger Re numbers) are treated with a special block-diagonal preconditioning. Due to the new generalized equilibrium formulation (GEF) we can combine the advantages of both preconditioners, i.e. independence of the number of unknowns for convection-dominated cases with robustness for stiff configurations. We further improve the GEF approach by using hierarchical multigrid algorithms to obtain grid-independent convergence rates for a wide range of problem parameters, and provide representative results for various benchmark problems. Finally, we present quantitative comparisons between a highly optimized CFD-solver based on the Navier-Stokes equation (FeatFlow) and our new LBE solver (FeatLBE).     

Split-step Adams–Moulton Milstein methods for systems of stiff stochastic differential equations

In this paper we discuss new split-step methods for solving systems of Itô stochastic differential equations (SDEs). The methods are based on a L-stable (strongly stable) second-order split Adams–Moulton Formula for stiff ordinary differential equations in collusion with Milstein methods for use on SDEs which are stiff in both the deterministic and stochastic components. The L-stability property is particularly useful when the drift components are stiff and contain widely varying decay constants. For SDEs wherein the diffusion is especially stiff, we consider balanced and modified balanced split-step methods which posses larger regions of mean-square stability. Strong order convergence one is established and stability regions are displayed. The methods are tested on problems with one and two noise channels. Numerical results show the effectiveness of the methods in the pathwise approximation of stiff SDEs when compared to some existing split-step methods.     

An electric-analog simulation of elliptic partial differential equations using finite element theory

Elliptic partial differential equations can be solved using the Galerkin-finite element method to generate the approximating algebraic equations, and an electrical network to solve the resulting matrices. Some element configurations require the use of networks containing negative resistances which, while physically realizable, are more expensive and time-consuming to construct.     

Weld sequence optimization: The use of surrogate models for solving sequential combinatorial problems

The solution of combinatorial optimization problems usually involves the consideration of many possible design configurations. This often makes such approaches computationally expensive, especially when dealing with complex finite element models. Here a surrogate model is proposed that can be used to reduce substantially the computational expense of sequential combinatorial finite element problems. The model is illustrated by application to a weld path planning problem.     

Multicriteria optimization of lightweight bridge structures with a constrained force density method

This paper deals with the preliminary shape design of three-dimensional bridge structures. For crossing wide spans, lightweight truss structures are well-suited. Due to their complex equilibrium state involving a geometrically nonlinear behaviour, the generation of an equilibrated system requires numerical form finding methods, namely the force density method for truss structures. To enforce geometric restrictions, a constrained force density method is developed. Then, the scope of the form finding method is extended to the search of optimal configurations by combining the force density method with multiobjective genetic algorithms within an integrated design process. Large scale applications illustrate the proposed strategy.     

An integrated approach for optimum design of bridge decks using genetic algorithms and artificial neural networks

The objective of this paper is to develop an integrated approach using artificial neural networks (ANN) and genetic algorithms (GA) for cost optimization of bridge deck configurations. In the present work, ANN is used to predict the structural design responses which are used further in evaluation of fitness and constraint violation in GA process. A multilayer back-propagation neural network is trained with the results obtained using grillage analysis program for different bridge deck configurations and the correlation between sectional parameters and design responses has been established. Subsequently, GA is employed for arriving at optimum configuration of the bridge deck system by minimizing the total cost. By integrating ANN with GA, the computational time required for obtaining optimal solution could be reduced substantially. The efficacy of this approach is demonstrated by carrying out studies on cost optimization of T-girder bridge deck system for different spans. The method presented in this paper, would greatly reduce the computational effort required to find the optimum solution and guarantees bridge engineers to arrive at the near-optimal solution that could not be easily obtained using general modeling programs or by trial-and-error.     

CP/NET: control program for a microcomputer network

The purpose of the CP/NET software system is to support network technology by allowing independent microcomputers access to common, and often expensive, facilities such as peripherals, programs and databases. It is designed for adaptation to a wide range of network hardware, operating with CP/M and MP/M to support the many CP/M-compatible products available. This article considers aspects of this operating system and some of the network configurations possible.     

The construction of digital terrain models on small computers

The construction of digital terrain models on small computers has been expensive in terms of computation time especially in the context of local and hybrid interpolation procedures. This problem arises because a set of sampled height observations must be searched repeatedly for every height estimated in the terrain model. An algorithm is described which enables relatively rapid construction of digital terrain representations by local methods and hence enables effective surface mapping even on low-cost microcomputer configurations.     

A note on convergence concepts for stiff problems

Most convergence concepts for discretizations of nonlinear stiff initial value problems are based on one-sided Lipschitz continuity. Therefore only those stiff problems that admit moderately sized one-sided Lipschitz constants are covered in a satisfactory way by the respective theory. In the present note we show that the assumption of moderately sized one-sided Lipschitz constants is violated for many stiff problems. We recall some convergence results that are not based on one-sided Lipschitz constants; the concept of singular perturbations is one of the key issues. Numerical experience with stiff problems that are not covered by available convergence results is reported.     

Performance-based constraints for multidimensional networks

A stochastic analysis of multidimensional networks with unidirectional or bidirectional links between nodes is presented. The analysis allows the development of an accurate model for examining the performance and cost trade-offs of different network configurations. The model is validated through simulation and does not rely on the simplifying assumptions of previous models. In addition, the model is valid for the hypercube network. Two new performance-based design constraints are introduced: constant maximum throughput and constant unity queue. These new constraints are fundamentally different than previous constraints, which are based on some characterization of hardware implementation costs. Both of the new constraints allow performance and cost comparisons of different network configurations to be made on the basis of an equal ability to handle a range of traffic load. Results under the new constraints clearly show that a low dimensional network, while offering the lowest message latency, must be significantly more expensive than a comparable high dimensional network and, in some cases, may be impractical to implement. In addition, the constraints demonstrate that performance is highly dependent on offered load     

The evaluation of numerical techniques for solution of stiff ordinary differential equations arising from chemical kinetic problems

Ordinary differential equations with widely scattered eigenvalues (stiff O.D.E.'s) occur often in the studies of reaction network problems. Five numerical methods, including two methods based on Backward differentiation formulas, a modified Runge-Kutta-Fehlberg method, a method based on PECE Adams formulas, and an improved semi-implicit Euler method are evaluated by comparing their performance when applied to test systems. The test systems represent different combinations of linearity and nonlinearity, small and large dimension, real and complex eigenvalues, and slightly stiff and very stiff problems. The relative merits and dificiencies of the methods are discussed.     

Dynamic optimization of a sandwich beam

Analytical procedure for the determination of the least weight design sandwich beam which satisfies a specific frequency requirement is presented. The approach is to modify an initial design by varying the thickness of each of its different layers. This is accomplished using gradient equations to first obtain the correct beam fundamental frequency and then, while this frequency is held constant, to minimize the weight. The gradient equations are derived in matrix notation suitable for the use of digital computers. For practical as well as other considerations, imposing lower bounds on layers' thicknesses have been found necessary. The equations of motion used include all the higher order effects like inertia, extension and shear of all the layers. Hence the procedure is applicable for short as well as long, soft or stiff cored beams. The design procedure has been completely automated in a computer program. Results of numerical examples show that the method is convergent and that optimized configurations can be determined in a few redesign cycles.     

Skeleton-Sectional Structural Analysis for 3D Printing

3D printing has become popular and has been widely used in various applications in recent years. More and more home users have motivation to design their own models and then fabricate them using 3D printers. However, the printed objects may have some structural or stress defects as the users may be lack of knowledge on stress analysis on 3D models. In this paper, we present an approach to help users analyze a model’s structural strength while designing its shape. We adopt sectional structural analysis instead of conventional FEM (Finite Element Method) analysis which is computationally expensive. Based on sectional structural analysis, our approach imports skeletons to assist in integrating mesh designing, strength computing and mesh correction well. Skeletons can also guide sections building and load calculation for analysis. For weak regions with high stress over a threshold value in the model from analysis result, our system corrects them by scaling the corresponding bones of skeleton so as to make these regions stiff enough. A number of experiments have demonstrated the applicability and practicability of our approach.     

Some algebraic laws for spans (and their connections with multirelations)

This paper investigates some key algebraic properties of the categories of spans and cospans (up to isomorphic supports) over the category Set of (small) sets and functions, analyzing the monoidal structures induced over both spans and cospans by cartesian product and disjoint union of sets. Our results find analogous counterparts in (and are partly inspired by) the theory of relational algebras, thus our paper also sheds some light on the relationship between (co)spans and the categories of (multi)relations and of equivalence relations. And, since (co)spans yield an intuitive presentation of dynamical systems with input and output interfaces, our results introduce an expressive, two-fold algebra that can serve as a specification formalism for rewriting systems and for composing software modules.     

State space models of remote manipulation tasks

A state variable formulation of the remote manipulation problem is presented, applicable to human-supervised or autonomous computer-manipulators. A discrete state vector, containing position variables for the manipulator and relevant objects, spans a quantized state space comprising many static configurations of objects and hand. A manipulation task is a desired new state. State transitions are assigned costs and are accomplished by commands: hand motions plus grasp, release, push, twist, etc. In control theory terms the problem is to find the cheapest control history (if any) from present to desired state. A method similar to dynamic programming is used to determine the optimal history. The system is capable of obstacle avoidance, grasp rendezvous, incorporation of new sensor data, remembering results of previous tasks, and so on.     

Adaptable cache service and application to grid caching

Caching is an important element to tackle performance issues in largely distributed data management. However, caches are efficient only if they are well configured according to the context of use. As a consequence, they are usually built from scratch. Such an approach appears to be expensive and time consuming in grids where the various characteristics lead to many heterogeneous cache requirements. This paper proposes a framework facilitating the construction of sophisticated and dynamically adaptable caches for heterogeneous applications. Such a framework has enabled the evaluation of several configurations for distributed data querying systems and leads us to propose innovative approaches for semantic and cooperative caching. This paper also reports the results obtained in bioinformatics data management on grids showing the relevance of our proposals. Copyright © 2009 John Wiley & Sons, Ltd.