Mesopic rod and S-cone interactions revealed by modulation thresholds

We analyzed mesopic rod and S-cone interactions in terms of their contributions to the blue-yellow opponent pathway. Stimuli were generated using a 4-primary colorimeter. Mixed rod and S-cone modulation thresholds (constant L-, M-cone excitation) were measured as a function of their phase difference. Modulation amplitude was equated using threshold units and contrast ratios. This study identified three interaction types: (1) A linear and antagonistic rod:S-cone interaction, (2) probability summation (3) and a previously unidentified mutual nonlinear reinforcement. Linear rod:S-cone interactions occur within the blue-yellow opponent pathway. Probability summation involves signaling by different post-receptoral pathways. The origin of the nonlinear reinforcement is possibly at the photoreceptors.

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.

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.

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.

The Glenn A. Fry award lecture 2011 : peripheral optics of the human eye

There has been a low level of interest in peripheral aberrations and corresponding image quality for over 200 years. Most work has been concerned with the second-order aberrations of defocus and astigmatism that can be corrected with conventional lenses. Studies have found high levels of aberration, often amounting to several dioptres, even in eyes with only small central defocus and astigmatism. My investigations have contributed to understanding shape changes in the eye with increases in myopia, changes in eye optics with ageing, and how surgical interventions intended to correct central refractive errors have unintended effects on peripheral optics. My research group has measured peripheral second- and higher-order aberrations over a 42° horizontal × 32° vertical diameter visual field. There is substantial variation in individual aberrations with age and pathology. While the higher-order aberrations in the periphery are usually small compared with second-order aberrations, they can be substantial and change considerably after refractive surgery. The thrust of my research in the next few years is to understand more about the peripheral aberrations of the human eye, to measure visual performance in the periphery and determine whether this can be improved by adaptive optics correction, to use measurements of peripheral aberrations to learn more about the optics of the eye and in particular the gradient index structure of the lens, and to investigate ways of increasing the size of the field of good retinal image quality.

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.

Improved earthwork allocation planning for fuel consumption and emissions reduction in linear infrastructure construction – case study data

This document provides data for the case study presented in our recent earthwork planning papers. Some results are also provided in a graphical format using Excel.

Very sensitive fiber Bragg grating accelerometer using transverse forces with an easy over-range protection and low cross axial sensitivity

The first fiber Bragg grating (FBG) accelerometer using direct transverse forces is demonstrated by fixing the FBG by its two ends and placing a transversely moving inertial object at its middle. It is very sensitive because a lightly stretched FBG is more sensitive to transverse forces than axial forces. Its resonant frequency and static sensitivity are analyzed by the classic spring-mass theory, assuming the axial force changes little. The experiments show that the theory can be modified for cases where the assumption does not hold. The resonant frequency can be modified by a linear relationship experimentally achieved, and the static sensitivity by an alternative method proposed. The principles of the over-range protection and low cross axial sensitivity are achieved by limiting the movement of the FBG and were validated experimentally. The sensitivities 1.333 and 0.634 nm/g were experimentally achieved by 5.29 and 2.83 gram inertial objects at 10 Hz from 0.1 to 0.4 g (g = 9.8 m/s 2), respectively, and their resonant frequencies were around 25 Hz. Their theoretical static sensitivities and resonant frequencies found by the modifications are 1.188 nm/g and 26.81 Hz for the 5.29 gram one and 0.784 nm/g and 29.04 Hz for the 2.83 gram one, respectively.

A class B switch-mode assisted linear amplifier

A switch-mode assisted linear amplifier (SMALA) combining a linear (Class B) and a switch-mode (Class D) amplifier is presented. The usual single hysteretic controlled half-bridge current dumping stage is replaced by two parallel buck converter stages, in a parallel voltage controlled topology. These operate independently: one buck converter sources current to assist the upper Class B output device, and a complementary converter sinks current to assist the lower device. This topology lends itself to a novel control approach of a dead-band at low power levels where neither class D amplifier assists, allowing the class B amplifier to supply the load without interference, ensuring high fidelity. A 20 W implementation demonstrates 85% efficiency, with distortion below 0.08% measured across the full audio bandwidth at 15 W. The class D amplifier begins assisting at 2 W, and below this value, the distortion was below 0.03%. Complete circuitry is given, showing the simplicity of the additional class D amplifier and its corresponding control circuitry.