Iterative subspace analysis based on feature line distance

Nearest feature line-based subspace analysis is first proposed in this paper. Compared with conventional methods, the newly proposed one brings better generalization performance and incremental analysis. The projection point and feature line distance are expressed as a function of a subspace, which is obtained by minimizing the mean square feature line distance. Moreover, by adopting stochastic approximation rule to minimize the objective function in a gradient manner, the new method can be performed in an incremental mode, which makes it working well upon future data. Experimental results on the FERET face database and the UCI satellite image database demonstrate the effectiveness.

Relaxation procedures for an iterative MFS algorithm for the stable reconstruction of elastic fields from Cauchy data in two-dimensional isotropic linear elasticity

We investigate two numerical procedures for the Cauchy problem in linear elasticity, involving the relaxation of either the given boundary displacements (Dirichlet data) or the prescribed boundary tractions (Neumann data) on the over-specified boundary, in the alternating iterative algorithm of Kozlov et al. (1991). The two mixed direct (well-posed) problems associated with each iteration are solved using the method of fundamental solutions (MFS), in conjunction with the Tikhonov regularization method, while the optimal value of the regularization parameter is chosen via the generalized cross-validation (GCV) criterion. An efficient regularizing stopping criterion which ceases the iterative procedure at the point where the accumulation of noise becomes dominant and the errors in predicting the exact solutions increase, is also presented. The MFS-based iterative algorithms with relaxation are tested for Cauchy problems for isotropic linear elastic materials in various geometries to confirm the numerical convergence, stability, accuracy and computational efficiency of the proposed method.

A fuzzy levelised energy cost method for renewable energy technology assessment

Renewable energy project development is highly complex and success is by no means guaranteed. Decisions are often made with approximate or uncertain information yet the current methods employed by decision-makers do not necessarily accommodate this. Levelised energy costs (LEC) are one such commonly applied measure utilised within the energy industry to assess the viability of potential projects and inform policy. The research proposes a method for achieving this by enhancing the traditional discounting LEC measure with fuzzy set theory. Furthermore, the research develops the fuzzy LEC (F-LEC) methodology to incorporate the cost of financing a project from debt and equity sources. Applied to an example bioenergy project, the research demonstrates the benefit of incorporating fuzziness for project viability, optimal capital structure and key variable sensitivity analysis decision-making. The proposed method contributes by incorporating uncertain and approximate information to the widely utilised LEC measure and by being applicable to a wide range of energy project viability decisions. © 2013 Elsevier Ltd. All rights reserved.

Relaxation of alternating iterative algorithms for the Cauchy problem associated with the modified Helmholtz equation

We propose two algorithms involving the relaxation of either the given Dirichlet data or the prescribed Neumann data on the over-specified boundary, in the case of the alternating iterative algorithm of ` 12 ` 12 `$12 `&12 `#12 `^12 `_12 `%12 `~12 *Kozlov91 applied to Cauchy problems for the modified Helmholtz equation. A convergence proof of these relaxation methods is given, along with a stopping criterion. The numerical results obtained using these procedures, in conjunction with the boundary element method (BEM), show the numerical stability, convergence, consistency and computational efficiency of the proposed methods.

A method of fundamental solutions for transient heat conduction in layered materials

In this paper we investigate an application of the method of fundamental solutions (MFS) to transient heat conduction in layered materials, where the thermal diffusivity is piecewise constant. Recently, in Johansson and Lesnic [A method of fundamental solutions for transient heat conduction. Eng Anal Boundary Elem 2008;32:697–703], a MFS was proposed with the sources placed outside the space domain of interest, and we extend that technique to numerically approximate the heat flow in layered materials. Theoretical properties of the method, as well as numerical investigations are included.

Reconstruction of a stationary flow from boundary data using iterative methods

In this paper, three iterative procedures (Landweber-Fridman, conjugate gradient and minimal error methods) for obtaining a stable solution to the Cauchy problem in slow viscous flows are presented and compared. A section is devoted to the numerical investigations of these algorithms. There, we use the boundary element method together with efficient stopping criteria for ceasing the iteration process in order to obtain stable solutions.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

Towards the in silico identification of class II restricted T-cell epitopes:a partial least squares iterative self-consistent algorithm for affinity prediction

Motivation: The immunogenicity of peptides depends on their ability to bind to MHC molecules. MHC binding affinity prediction methods can save significant amounts of experimental work. The class II MHC binding site is open at both ends, making epitope prediction difficult because of the multiple binding ability of long peptides. Results: An iterative self-consistent partial least squares (PLS)-based additive method was applied to a set of 66 pep- tides no longer than 16 amino acids, binding to DRB1*0401. A regression equation containing the quantitative contributions of the amino acids at each of the nine positions was generated. Its predictability was tested using two external test sets which gave r pred =0.593 and r pred=0.655, respectively. Furthermore, it was benchmarked using 25 known T-cell epitopes restricted by DRB1*0401 and we compared our results with four other online predictive methods. The additive method showed the best result finding 24 of the 25 T-cell epitopes. Availability: Peptides used in the study are available from http://www.jenner.ac.uk/JenPep. The PLS method is available commercially in the SYBYL molecular modelling software package. The final model for affinity prediction of peptides binding to DRB1*0401 molecule is available at http://www.jenner.ac.uk/MHCPred. Models developed for DRB1*0101 and DRB1*0701 also are available in MHC- Pred

Solving Ratio-Dependent Predator-Prey System with Constant Effort Harvesting using Variational Iteration Method

Due to wide range of interest in use of bio-economic models to gain insight into the scientific management of renewable resources like fisheries and forestry,variational iteration method (VIM) is employed to approximate the solution of the ratio-dependent predator-prey system with constant effort prey harvesting.The results are compared with the results obtained by Adomian decomposition method and reveal that VIM is very effective and convenient for solving nonlinear differential equations.

Approximate Model Checking of Real-Time Systems for Linear Duration Invariants

Real-time systems are usually modelled with timed automata and real-time requirements relating to the state durations of the system are often specifiable using Linear Duration Invariants, which is a decidable subclass of Duration Calculus formulas. Various algorithms have been developed to check timed automata or real-time automata for linear duration invariants, but each needs complicated preprocessing and exponential calculation. To the best of our knowledge, these algorithms have not been implemented. In this paper, we present an approximate model checking technique based on a genetic algorithm to check real-time automata for linear durration invariants in reasonable times. Genetic algorithm is a good optimization method when a problem needs massive computation and it works particularly well in our case because the fitness function which is derived from the linear duration invariant is linear. ACM Computing Classification System (1998): D.2.4, C.3.

On Modified Method of Simplest Equation for Obtaining Exact Solutions of Nonlinear PDEs: Case of Elliptic Simplest Equation

2010 Mathematics Subject Classification: 74J30, 34L30.

Approximate axial symmetries from continuous time quantum walks

The analysis of complex networks is usually based on key properties such as small-worldness and vertex degree distribution. The presence of symmetric motifs on the other hand has been related to redundancy and thus robustness of the networks. In this paper we propose a method for detecting approximate axial symmetries in networks. For each pair of nodes, we define a continuous-time quantum walk which is evolved through time. By measuring the probability that the quantum walker to visits each node of the network in this time frame, we are able to determine whether the two vertices are symmetrical with respect to any axis of the graph. Moreover, we show that we are able to successfully detect approximate axial symmetries too. We show the efficacy of our approach by analysing both synthetic and real-world data. © 2012 Springer-Verlag Berlin Heidelberg.

An Iterative Procedure for Solving Nonsmooth Generalized Equation

2000 Mathematics Subject Classification: 47H04, 65K10.

Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.