Solving tri-diagonal linear systems using field programmable gate arrays

In this paper, we present the outcomes of a project on the exploration of the use of Field Programmable Gate Arrays (FPGAs) as co-processors for scientific computation. We designed a custom circuit for the pipelined solving of multiple tri-diagonal linear systems. The design is well suited for applications that require many independent tri-diagonal system solves, such as finite difference methods for solving PDEs or applications utilising cubic spline interpolation. The selected solver algorithm was the Tri-Diagonal Matrix Algorithm (TDMA or Thomas Algorithm). Our solver supports user specified precision thought the use of a custom floating point VHDL library supporting addition, subtraction, multiplication and division. The variable precision TDMA solver was tested for correctness in simulation mode. The TDMA pipeline was tested successfully in hardware using a simplified solver model. The details of implementation, the limitations, and future work are also discussed.

Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

Linear adaptive channel equalization for multiuser MIMO-OFDM systems

Linear adaptive channel equalization using the least mean square (LMS) algorithm and the recursive least-squares(RLS) algorithm for an innovative multi-user (MU) MIMOOFDM wireless broadband communications system is proposed. The proposed equalization method adaptively compensates the channel impairments caused by frequency selectivity in the propagation environment. Simulations for the proposed adaptive equalizer are conducted using a training sequence method to determine optimal performance through a comparative analysis. Results show an improvement of 0.15 in BER (at a SNR of 16 dB) when using Adaptive Equalization and RLS algorithm compared to the case in which no equalization is employed. In general, adaptive equalization using LMS and RLS algorithms showed to be significantly beneficial for MU-MIMO-OFDM systems.

A non-linear dynamic analysis of heavy haul track line sleepers under wheel flat

Significant wheel-rail dynamic forces occur because of imperfections in the wheels and/or rail. One of the key responses to the transmission of these forces down through the track is impact force on the sleepers. Dynamic analysis of nonlinear systems is very complicated and does not lend itself easily to a classical solution of multiple equations. Trying to deduce the behaviour of track components from experimental data is very difficult because such data is hard to obtain and applies to only the particular conditions of the track being tested. The finite element method can be the best solution to this dilemma. This paper describes a finite element model using the software package ANSYS for various sized flat defects in the tread of a wheel rolling at a typical speed on heavy haul track. The paper explores the dynamic response of a prestressed concrete sleeper to these defects.

RcppArmadillo : accelerating R with high-performance C++ linear algebra

The R statistical environment and language has demonstrated particular strengths for interactive development of statistical algorithms, as well as data modelling and visualisation. Its current implementation has an interpreter at its core which may result in a performance penalty in comparison to directly executing user algorithms in the native machine code of the host CPU. In contrast, the C++ language has no built-in visualisation capabilities, handling of linear algebra or even basic statistical algorithms; however, user programs are converted to high-performance machine code, ahead of execution. A new method avoids possible speed penalties in R by using the Rcpp extension package in conjunction with the Armadillo C++ matrix library. In addition to the inherent performance advantages of compiled code, Armadillo provides an easy-to-use template-based meta-programming framework, allowing the automatic pooling of several linear algebra operations into one, which in turn can lead to further speedups. With the aid of Rcpp and Armadillo, conversion of linear algebra centered algorithms from R to C++ becomes straightforward. The algorithms retains the overall structure as well as readability, all while maintaining a bidirectional link with the host R environment. Empirical timing comparisons of R and C++ implementations of a Kalman filtering algorithm indicate a speedup of several orders of magnitude.

Anomalous Seebeck coefficient in boron carbides

Boron carbides exhibit an anomalously large Seebeck coefficient with a temperature coefficient that is characteristic of polaronic hopping between inequivalent sites. The inequivalence in the sites is associated with disorder in the solid. The temperature dependence of the Seebeck coefficient for materials prepared by different techniques provides insight into the nature of the disorder.

Analytical Solution of a Walters’ Liquid B Flow Over a Linear Stretching Sheet in a Porous Medium

This chapter represents the analytical solution of two-dimensional linear stretching sheet problem involving a non-Newtonian liquid and suction by (a) invoking the boundary layer approximation and (b) using this result to solve the stretching sheet problem without using boundary layer approximation. The basic boundary layer equations for momentum, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The results reveal a new analytical procedure for solving the boundary layer equations arising in a linear stretching sheet problem involving a non-Newtonian liquid (Walters’ liquid B). The present study throws light on the analytical solution of a class of boundary layer equations arising in the stretching sheet problem.

V1-inspired features induce a weighted margin in SVMs

Image representations derived from simplified models of the primary visual cortex (V1), such as HOG and SIFT, elicit good performance in a myriad of visual classification tasks including object recognition/detection, pedestrian detection and facial expression classification. A central question in the vision, learning and neuroscience communities regards why these architectures perform so well. In this paper, we offer a unique perspective to this question by subsuming the role of V1-inspired features directly within a linear support vector machine (SVM). We demonstrate that a specific class of such features in conjunction with a linear SVM can be reinterpreted as inducing a weighted margin on the Kronecker basis expansion of an image. This new viewpoint on the role of V1-inspired features allows us to answer fundamental questions on the uniqueness and redundancies of these features, and offer substantial improvements in terms of computational and storage efficiency.

Effect of family relatedness on characteristics of estimated IBD probabilities in relation to precision of QTL estimates

Background: A random QTL effects model uses a function of probabilities that two alleles in the same or in different animals at a particular genomic position are identical by descent (IBD). Estimates of such IBD probabilities and therefore, modeling and estimating QTL variances, depend on marker polymorphism, strength of linkage and linkage disequilibrium of markers and QTL, and the relatedness of animals in the pedigree. The effect of relatedness of animals in a pedigree on IBD probabilities and their characteristics was examined in a simulation study. Results: The study based on nine multi-generational family structures, similar to a pedigree structure of a real dairy population, distinguished by an increased level of inbreeding from zero to 28 % across the studied population. Highest inbreeding level in the pedigree, connected with highest relatedness, was accompanied by highest IBD probabilities of two alleles at the same locus, and by lower relative variation coefficients. Profiles of correlation coefficients of IBD probabilities along the marked chromosomal segment with those at the true QTL position were steepest when the inbreeding coefficient in the pedigree was highest. Precision of estimated QTL location increased with increasing inbreeding and pedigree relatedness. A method to assess the optimum level of inbreeding for QTL detection is proposed, depending on population parameters. Conclusions: An increased overall relationship in a QTL mapping design has positive effects on precision of QTL position estimates. But the relationship of inbreeding level and the capacity for QTL detection depending on the recombination rate of QTL and adjacent informative marker is not linear. © 2010 Freyer et al., licensee BioMed Central Ltd.

Transmission system expansion planning considering combined operation of wind farms and energy storage systems

An energy storage system (ESS) can provide ancillary services such as frequency regulation and reserves, as well as smooth the fluctuations of wind power outputs, and hence improve the security and economics of the power system concerned. The combined operation of a wind farm and an ESS has become a widely accepted operating mode. Hence, it appears necessary to consider this operating mode in transmission system expansion planning, and this is an issue to be systematically addressed in this work. Firstly, the relationship between the cost of the NaS based ESS and its discharging cycle life is analyzed. A strategy for the combined operation of a wind farm and an ESS is next presented, so as to have a good compromise between the operating cost of the ESS and the smoothing effect of the fluctuation of wind power outputs. Then, a transmission system expansion planning model is developed with the sum of the transmission investment costs, the investment and operating costs of ESSs and the punishment cost of lost wind energy as the objective function to be minimized. An improved particle swarm optimization algorithm is employed to solve the developed planning model. Finally, the essential features of the developed model and adopted algorithm are demonstrated by 18-bus and 46-bus test systems.

Multi-scale numerical simulations of thermal expansion properties of CNT-reinforced nanocomposites

In this work, the thermal expansion properties of carbon nanotube (CNT)-reinforced nanocomposites with CNT content ranging from 1 to 15 wt% were evaluated using a multi-scale numerical approach, in which the effects of two parameters, i.e., temperature and CNT content, were investigated extensively. For all CNT contents, the obtained results clearly revealed that within a wide low-temperature range (30°C ~ 62°C), thermal contraction is observed, while thermal expansion occurs in a high-temperature range (62°C ~ 120°C). It was found that at any specified CNT content, the thermal expansion properties vary with temperature - as temperature increases, the thermal expansion rate increases linearly. However, at a specified temperature, the absolute value of the thermal expansion rate decreases nonlinearly as the CNT content increases. Moreover, the results provided by the present multi-scale numerical model were in good agreement with those obtained from the corresponding theoretical analyses and experimental measurements in this work, which indicates that this multi-scale numerical approach provides a powerful tool to evaluate the thermal expansion properties of any type of CNT/polymer nanocomposites and therefore promotes the understanding on the thermal behaviors of CNT/polymer nanocomposites for their applications in temperature sensors, nanoelectronics devices, etc.

An entry mode decision-making model for the international expansion of construction enterprises

Purpose – The purpose of this paper is to provide a new type of entry mode decision-making model for construction enterprises involved in international business. Design/methodology/approach – A hybrid method combining analytic hierarchy process (AHP) with preference ranking organization method for enrichment evaluations (PROMETHEE) is used to aid entry mode decisions. The AHP is used to decompose the entry mode problem into several dimensions and determine the weight of each criterion. In addition, PROMETHEE method is used to rank candidate entry modes and carry out sensitivity analyses. Findings – The proposed decision-making method is demonstrated to be a suitable approach to resolve the entry mode selection decision problem. Practical implications – The research provides practitioners with a more systematic decision framework and a more precise decision method. Originality/value – The paper sheds light on the further development of entry strategies for international construction markets. It not only introduces a new decision-making model for entry mode decision making, but also provides a conceptual framework with five determinants for a construction company entry mode selection based on the unique properties of the construction industry.

Heteroscedastic probabilistic linear discriminant analysis for manifold learning in video-based face recognition

To recognize faces in video, face appearances have been widely modeled as piece-wise local linear models which linearly approximate the smooth yet non-linear low dimensional face appearance manifolds. The choice of representations of the local models is crucial. Most of the existing methods learn each local model individually meaning that they only anticipate variations within each class. In this work, we propose to represent local models as Gaussian distributions which are learned simultaneously using the heteroscedastic probabilistic linear discriminant analysis (PLDA). Each gallery video is therefore represented as a collection of such distributions. With the PLDA, not only the within-class variations are estimated during the training, the separability between classes is also maximized leading to an improved discrimination. The heteroscedastic PLDA itself is adapted from the standard PLDA to approximate face appearance manifolds more accurately. Instead of assuming a single global within-class covariance, the heteroscedastic PLDA learns different within-class covariances specific to each local model. In the recognition phase, a probe video is matched against gallery samples through the fusion of point-to-model distances. Experiments on the Honda and MoBo datasets have shown the merit of the proposed method which achieves better performance than the state-of-the-art technique.

Image based visual servo control for fixed wing UAVs tracking linear infrastructure in wind

This paper presents an Image Based Visual Servo control design for Fixed Wing Unmanned Aerial Vehicles tracking locally linear infrastructure in the presence of wind using a body fixed imaging sensor. Visual servoing offers improved data collection by posing the tracking task as one of controlling a feature as viewed by the inspection sensor, although is complicated by the introduction of wind as aircraft heading and course angle no longer align. In this work it is shown that the effects of wind alter the desired line angle required for continuous tracking to equal the wind correction angle as would be calculated to set a desired course. A control solution is then sort by linearizing the interaction matrix about the new feature pose such that kinematics of the feature can be augmented with the lateral dynamics of the aircraft, from which a state feedback control design is developed. Simulation results are presented comparing no compensation, integral control and the proposed controller using the wind correction angle, followed by an assessment of response to atmospheric disturbances in the form of turbulence and wind gusts

Board age and gender diversity : a test of competing linear and curvilinear predictions

We test competing linear and curvilinear predictions between board diversity and performance. The predictions were tested using archival data on 288 organizations listed on the Australian Securities Exchange. The findings provide additional evidence on the business case for board gender diversity and refine the business case for board age diversity.