Colour by numbers in Excel 2007 : solving algebraic equations without algebra

This is an update of an earlier paper, and is written for Excel 2007. A series of Excel 2007 models is described. The more advanced versions allow solution of f(x)=0 by examining change of sign of function values. The function is graphed and change of sign easily detected by a change of colour. Relevant features of Excel 2007 used are Names, Scatter Chart and Conditional Formatting. Several sample Excel 2007 models are available for download, and the paper is intended to be used as a lesson plan for students having some familiarity with derivatives. For comparison and reference purposes, the paper also presents a brief outline of several common equation-solving strategies as an Appendix.

The Number Crunch game : a simple vehicle for building algebraic reasoning skills

A newspaper numbers game based on simple arithmetic relationships is discussed. Its potential to give students of elementary algebra practice in semi-ad hoc reasoning and to build general arithmetic reasoning skills is explored.

Algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering

This paper presents algebraic attacks on SOBER-t32 and SOBER-t16 without stuttering. For unstuttered SOBER-t32, two different attacks are implemented. In the first attack, we obtain multivariate equations of degree 10. Then, an algebraic attack is developed using a collection of output bits whose relation to the initial state of the LFSR can be described by low-degree equations. The resulting system of equations contains 2^69 equations and monomials, which can be solved using the Gaussian elimination with the complexity of 2^196.5. For the second attack, we build a multivariate equation of degree 14. We focus on the property of the equation that the monomials which are combined with output bit are linear. By applying the Berlekamp-Massey algorithm, we can obtain a system of linear equations and the initial states of the LFSR can be recovered. The complexity of attack is around O(2^100) with 2^92 keystream observations. The second algebraic attack is applicable to SOBER-t16 without stuttering. The attack takes around O(2^85) CPU clocks with 2^78 keystream observations.

The path to stoichiometric composition of III–V binary quantum dots through plasma/ion-assisted self-assembly

Semiconductor III-V quantum dots (QDs) are particularly enticing components for the integration of optically promising III-V materials with the silicon technology prevalent in the microelectronics industry. However, defects due to deviations from a stoichiometric composition [group III: group V = 1] may lead to impaired device performance. This paper investigates the initial stages of formation of InSb and GaAs QDs on Si(1 0 0) through hybrid numerical simulations. Three situations are considered: a neutral gas environment (NG), and two ionized gas environments, namely a localized ion source (LIS) and a background plasma (BP) case. It is shown that when the growth is conducted in an ionized gas environment, a stoichiometric composition may be obtained earlier in the QD as compared to a NG. Moreover, the stoichiometrization time, tst, is shorter for the BP case compared to the LIS scenario. A discussion of the effect of ion/plasma-based tools as well as a range of process conditions on the final island size distribution is also included. Our results suggest a way to obtain a deterministic level of control over nanostructure properties (in particular, elemental composition and size) during the initial stages of growth which is a crucial step towards achieving highly tailored QDs suitable for implementation in advanced technological devices.

On algebraic immunity and annihilators

Algebraic immunity AI(f) defined for a boolean function f measures the resistance of the function against algebraic attacks. Currently known algorithms for computing the optimal annihilator of f and AI(f) are inefficient. This work consists of two parts. In the first part, we extend the concept of algebraic immunity. In particular, we argue that a function f may be replaced by another boolean function f^c called the algebraic complement of f. This motivates us to examine AI(f ^c ). We define the extended algebraic immunity of f as AI *(f)= min {AI(f), AI(f^c )}. We prove that 0≤AI(f)–AI *(f)≤1. Since AI(f)–AI *(f)= 1 holds for a large number of cases, the difference between AI(f) and AI *(f) cannot be ignored in algebraic attacks. In the second part, we link boolean functions to hypergraphs so that we can apply known results in hypergraph theory to boolean functions. This not only allows us to find annihilators in a fast and simple way but also provides a good estimation of the upper bound on AI *(f).

Aligning off-balance sheet risk, on-balance sheet risk and audit fees: a PLS path modelling analysis

This study focuses on using the partial least squares (PLS) path modelling technique in archival auditing research by replicating the data and research questions from prior bank audit fee studies. PLS path modelling allows for inter-correlations among audit fee determinants by establishing latent constructs and multiple relationship paths in one simultaneous PLS path model. Endogeneity concerns about auditor choice can also be addressed with PLS path modelling. With a sample of US bank holding companies for the period 2003-2009, we examine the associations among on-balance sheet financial risks, off-balance sheet risks and audit fees, and also address the pervasive client size effect, and the effect of the self-selection of auditors. The results endorse the dominating effect of size on audit fees, both directly and indirectly via its impacts on other audit fee determinants. By simultaneously considering the self-selection of auditors, we still find audit fee premiums on Big N auditors, which is the second important factor on audit fee determination. On-balance-sheet financial risk measures in terms of capital adequacy, loan composition, earnings and asset quality performance have positive impacts on audit fees. After allowing for the positive influence of on-balance sheet financial risks and entity size on off-balance sheet risk, the off-balance sheet risk measure, SECRISK, is still positively associated with bank audit fees, both before and after the onset of the financial crisis. The consistent results from this study compared with prior literature provide supporting evidence and enhance confidence on the application of this new research technique in archival accounting studies.

Aligning off-balance sheet risk, on-balance sheet risk and audit fees: a PLS path modelling analysis

This study focuses on using the partial least squares (PLS) path modelling methodology in archival auditing research by replicating the data and research questions from prior bank audit fee studies. PLS path modelling allows for inter-correlations among audit fee determinants by establishing latent constructs and multiple relationship paths in one simultaneous PLS path model. Endogeneity concerns about auditor choice can also be addressed with PLS path modelling. With a sample of US bank holding companies for the period 2003-2009, we examine the associations among on-balance sheet financial risks, off-balance sheet risks and audit fees, and also address the pervasive client size effect, and the effect of the self-selection of auditors. The results endorse the dominating effect of size on audit fees, both directly and indirectly via its impacts on other audit fee determinants. By simultaneously considering the self-selection of auditors, we still find audit fee premiums on Big N auditors, which is the second important factor on audit fee determination. On-balance-sheet financial risk measures in terms of capital adequacy, loan composition, earnings and asset quality performance have positive impacts on audit fees. After allowing for the positive influence of on-balance sheet financial risks and entity size on off-balance sheet risk, the off-balance sheet risk measure, SECRISK, is still positively associated with bank audit fees, both before and after the onset of the financial crisis. The consistent results from this study compared with prior literature provide supporting evidence and enhance confidence on the application of this new research technique in archival accounting studies.

Mission path planning of aerial survey tasks using hybrid game evolutionary algorithm

The work presented in this report is aimed to implement a cost-effective offline mission path planner for aerial inspection tasks of large linear infrastructures. Like most real-world optimisation problems, mission path planning involves a number of objectives which ideally should be minimised simultaneously. Understandably, the objectives of a practical optimisation problem are conflicting each other and the minimisation of one of them necessarily implies the impossibility to minimise the other ones. This leads to the need to find a set of optimal solutions for the problem; once such a set of available options is produced, the mission planning problem is reduced to a decision making problem for the mission specialists, who will choose the solution which best fit the requirements of the mission. The goal of this work is then to develop a Multi-Objective optimisation tool able to provide the mission specialists a set of optimal solutions for the inspection task amongst which the final trajectory will be chosen, given the environment data, the mission requirements and the definition of the objectives to minimise. All the possible optimal solutions of a Multi-Objective optimisation problem are said to form the Pareto-optimal front of the problem. For any of the Pareto-optimal solutions, it is impossible to improve one objective without worsening at least another one. Amongst a set of Pareto-optimal solutions, no solution is absolutely better than another and the final choice must be a trade-off of the objectives of the problem. Multi-Objective Evolutionary Algorithms (MOEAs) are recognised to be a convenient method for exploring the Pareto-optimal front of Multi-Objective optimization problems. Their efficiency is due to their parallelism architecture which allows to find several optimal solutions at each time

Homing by path integration when a locomotion trajectory crosses itself

Path integration is a process with which navigators derive their current position and orientation by integrating self-motion signals along a locomotion trajectory. It has been suggested that path integration becomes disproportionately erroneous when the trajectory crosses itself. However, there is a possibility that this previous finding was confounded by effects of the length of a traveled path and the amount of turns experienced along the path, two factors that are known to affect path integration performance. The present study was designed to investigate whether the crossover of a locomotion trajectory truly increases errors of path integration. In an experiment, blindfolded human navigators were guided along four paths that varied in their lengths and turns, and attempted to walk directly back to the beginning of the paths. Only one of the four paths contained a crossover. Results showed that errors yielded from the path containing the crossover were not always larger than those observed in other paths, and the errors were attributed solely to the effects of longer path lengths or greater degrees of turns. These results demonstrated that path crossover does not always cause significant disruption in path integration processes. Implications of the present findings for models of path integration are discussed.

Creative arts research : a long path to acceptance

The majority of tertiary practice-led creative arts disciplines became part of the Australian university system as a result of the creation of the Unified National System of tertiary education in 1988. Over the past two decades, research has grown as the yardstick by which academic performance in the Australian university sector is recognised and rewarded. Academics in artistic disciplines, who struggled to adapt to a culture and workload expectations different from their previous, predominantly teaching based, employment, continue to see their research under-valued within the established evaluation framework. Despite a late 1990s Australian government funded inquiry, many of the inequities remain. While the Excellence in Research in Australia (ERA) exercise has acknowledged the non-text outputs of artist-academics in its evaluation of 'research outcomes', much of the process remains resolutely framed by measures that work against creative arts researchers.

A new study on binder performance and formulation modification of anti-corrosive primer based on ethyl silicate resin

Zinc-rich ethyl silicate coatings are quite successful in protecting steel against corrosion under severe exposing conditions. In spite of providing excellent cathodic protection to steel structure after film curing, two-component zinc-rich ethyl silicate coatings have some limitations, one of which is inadequate shelf life as a result of in-can binder gelation. In this work, the preparation steps of ethyl silicate such as pre-hydrolysis, dehydration and organometallic reactions were surveyed and herein an approach towards understanding the cause and effect relationship of the use of ingredients is presented. The effects of water and catalytic acid dosages on gel time under accelerated conditions and the effect of alcoholic solvent order on the rate of the hydrolysis and dehydration reactions were studied via Karl-Fischer test determining the water content of hydrolysate. A thriving optimization in shelf life without any loss in physical–mechanical characteristics of the final film (e.g. hardness, adhesion, solvent and salt spray resistance) was obtained.

Identifying weak linear features with the "coalescing shortest path image transform"

The detection of line-like features in images finds many applications in microanalysis. Actin fibers, microtubules, neurites, pilis, DNA, and other biological structures all come up as tenuous curved lines in microscopy images. A reliable tracing method that preserves the integrity and details of these structures is particularly important for quantitative analyses. We have developed a new image transform called the "Coalescing Shortest Path Image Transform" with very encouraging properties. Our scheme efficiently combines information from an extensive collection of shortest paths in the image to delineate even very weak linear features. © Copyright Microscopy Society of America 2011.

Tubule detection in testis images using boundary weighting and circular shortest path

In studies of germ cell transplantation, measureing tubule diameters and counting cells from different populations using antibodies as markers are very important. Manual measurement of tubule sizes and cell counts is a tedious and sanity grinding work. In this paper, we propose a new boundary weighting based tubule detection method. We first enhance the linear features of the input image and detect the approximate centers of tubules. Next, a boundary weighting transform is applied to the polar transformed image of each tubule region and a circular shortest path is used for the boundary detection. Then, ellipse fitting is carried out for tubule selection and measurement. The algorithm has been tested on a dataset consisting of 20 images, each having about 20 tubules. Experiments show that the detection results of our algorithm are very close to the results obtained manually. © 2013 IEEE.