A fast identification algorithm for Box-Cox transformation based radial basis function neural network

In this letter, a Box-Cox transformation-based radial basis function (RBF) neural network is introduced using the RBF neural network to represent the transformed system output. Initially a fixed and moderate sized RBF model base is derived based on a rank revealing orthogonal matrix triangularization (QR decomposition). Then a new fast identification algorithm is introduced using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator. The main contribution of this letter is to explore the special structure of the proposed RBF neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma. Finally, the Box-Cox transformation-based RBF neural network, with good generalization and sparsity, is identified based on the derived optimal Box-Cox transformation and a D-optimality-based orthogonal forward regression algorithm. The proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression.

On a Theorem by Van Vleck Regarding Sturm Sequences

In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences with pivot, and (b) incomplete Sturm sequences. Despite its importance, the Pell-Gordon Theorem for polynomials in Q[x] has been totally forgotten and, to our knowledge, it is referenced by us for the first time in the literature. In this paper we go over Van Vleck’s theorem and method, modify slightly the formula of the Pell-Gordon Theorem and present a general triangularization method, called the VanVleck-Pell-Gordon method, that correctly computes in Z[x] polynomial Sturm sequences, both complete and incomplete.

Sturm Sequences and Modified Subresultant Polynomial Remainder Sequences

ACM Computing Classification System (1998): F.2.1, G.1.5, I.1.2.

Transceiver designs and analysis for LTI, LTV and broadcast channels - new matrix decompositions and majorization theory

Signal processing techniques play important roles in the design of digital communication systems. These include information manipulation, transmitter signal processing, channel estimation, channel equalization and receiver signal processing. By interacting with communication theory and system implementing technologies, signal processing specialists develop efficient schemes for various communication problems by wisely exploiting various mathematical tools such as analysis, probability theory, matrix theory, optimization theory, and many others. In recent years, researchers realized that multiple-input multiple-output (MIMO) channel models are applicable to a wide range of different physical communications channels. Using the elegant matrix-vector notations, many MIMO transceiver (including the precoder and equalizer) design problems can be solved by matrix and optimization theory. Furthermore, the researchers showed that the majorization theory and matrix decompositions, such as singular value decomposition (SVD), geometric mean decomposition (GMD) and generalized triangular decomposition (GTD), provide unified frameworks for solving many of the point-to-point MIMO transceiver design problems.

In this thesis, we consider the transceiver design problems for linear time invariant (LTI) flat MIMO channels, linear time-varying narrowband MIMO channels, flat MIMO broadcast channels, and doubly selective scalar channels. Additionally, the channel estimation problem is also considered. The main contributions of this dissertation are the development of new matrix decompositions, and the uses of the matrix decompositions and majorization theory toward the practical transmit-receive scheme designs for transceiver optimization problems. Elegant solutions are obtained, novel transceiver structures are developed, ingenious algorithms are proposed, and performance analyses are derived.

The first part of the thesis focuses on transceiver design with LTI flat MIMO channels. We propose a novel matrix decomposition which decomposes a complex matrix as a product of several sets of semi-unitary matrices and upper triangular matrices in an iterative manner. The complexity of the new decomposition, generalized geometric mean decomposition (GGMD), is always less than or equal to that of geometric mean decomposition (GMD). The optimal GGMD parameters which yield the minimal complexity are derived. Based on the channel state information (CSI) at both the transmitter (CSIT) and receiver (CSIR), GGMD is used to design a butterfly structured decision feedback equalizer (DFE) MIMO transceiver which achieves the minimum average mean square error (MSE) under the total transmit power constraint. A novel iterative receiving detection algorithm for the specific receiver is also proposed. For the application to cyclic prefix (CP) systems in which the SVD of the equivalent channel matrix can be easily computed, the proposed GGMD transceiver has K/log_2(K) times complexity advantage over the GMD transceiver, where K is the number of data symbols per data block and is a power of 2. The performance analysis shows that the GGMD DFE transceiver can convert a MIMO channel into a set of parallel subchannels with the same bias and signal to interference plus noise ratios (SINRs). Hence, the average bit rate error (BER) is automatically minimized without the need for bit allocation. Moreover, the proposed transceiver can achieve the channel capacity simply by applying independent scalar Gaussian codes of the same rate at subchannels.

In the second part of the thesis, we focus on MIMO transceiver design for slowly time-varying MIMO channels with zero-forcing or MMSE criterion. Even though the GGMD/GMD DFE transceivers work for slowly time-varying MIMO channels by exploiting the instantaneous CSI at both ends, their performance is by no means optimal since the temporal diversity of the time-varying channels is not exploited. Based on the GTD, we develop space-time GTD (ST-GTD) for the decomposition of linear time-varying flat MIMO channels. Under the assumption that CSIT, CSIR and channel prediction are available, by using the proposed ST-GTD, we develop space-time geometric mean decomposition (ST-GMD) DFE transceivers under the zero-forcing or MMSE criterion. Under perfect channel prediction, the new system minimizes both the average MSE at the detector in each space-time (ST) block (which consists of several coherence blocks), and the average per ST-block BER in the moderate high SNR region. Moreover, the ST-GMD DFE transceiver designed under an MMSE criterion maximizes Gaussian mutual information over the equivalent channel seen by each ST-block. In general, the newly proposed transceivers perform better than the GGMD-based systems since the super-imposed temporal precoder is able to exploit the temporal diversity of time-varying channels. For practical applications, a novel ST-GTD based system which does not require channel prediction but shares the same asymptotic BER performance with the ST-GMD DFE transceiver is also proposed.

The third part of the thesis considers two quality of service (QoS) transceiver design problems for flat MIMO broadcast channels. The first one is the power minimization problem (min-power) with a total bitrate constraint and per-stream BER constraints. The second problem is the rate maximization problem (max-rate) with a total transmit power constraint and per-stream BER constraints. Exploiting a particular class of joint triangularization (JT), we are able to jointly optimize the bit allocation and the broadcast DFE transceiver for the min-power and max-rate problems. The resulting optimal designs are called the minimum power JT broadcast DFE transceiver (MPJT) and maximum rate JT broadcast DFE transceiver (MRJT), respectively. In addition to the optimal designs, two suboptimal designs based on QR decomposition are proposed. They are realizable for arbitrary number of users.

Finally, we investigate the design of a discrete Fourier transform (DFT) modulated filterbank transceiver (DFT-FBT) with LTV scalar channels. For both cases with known LTV channels and unknown wide sense stationary uncorrelated scattering (WSSUS) statistical channels, we show how to optimize the transmitting and receiving prototypes of a DFT-FBT such that the SINR at the receiver is maximized. Also, a novel pilot-aided subspace channel estimation algorithm is proposed for the orthogonal frequency division multiplexing (OFDM) systems with quasi-stationary multi-path Rayleigh fading channels. Using the concept of a difference co-array, the new technique can construct M^2 co-pilots from M physical pilot tones with alternating pilot placement. Subspace methods, such as MUSIC and ESPRIT, can be used to estimate the multipath delays and the number of identifiable paths is up to O(M^2), theoretically. With the delay information, a MMSE estimator for frequency response is derived. It is shown through simulations that the proposed method outperforms the conventional subspace channel estimator when the number of multipaths is greater than or equal to the number of physical pilots minus one.

Dynamic matrix control on wind-induced vibration of spatial latticed structures [Chinese title = 空间网壳结构风振抑制的动态矩阵预测控制分析]

Ameliorated strategies were put forward to improve the model predictive control in reducing the wind induced vibration of spatial latticed structures. The dynamic matrix control (DMC) predictive method was used and the reference trajectory which is called the decaying functions was suggested for the analysis of spatial latticed structure (SLS) under wind loads. The wind-induced vibration control model of SLS with improved DMC model predictive control was illustrated, then the different feedback strategies were investigated and a typical SLS was taken as example to investigate the reduction of wind-induced vibration. In addition, the robustness and reliability of DMC strategy were discussed by varying the model configurations.

Decision Matrix Compared with Partnering Principles

The ideas for this CRC research project are based directly on Sidwell, Kennedy and Chan (2002). That research examined a number of case studies to identify the characteristics of successful projects. The findings were used to construct a matrix of best practice project delivery strategies. The purpose of this literature review is to test the decision matrix against established theory and best practice in the subject of construction project management.

Report on the Development and Validation of the Best Practice Decision Matrix

The Co-operative Research Centre for Construction Innovation (CRC-CI) is funding a project known as Value Alignment Process for Project Delivery. The project consists of a study of best practice project delivery and the development of a suite of products, resources and services to guide project teams towards the best procurement approach for a specific project or group of projects. These resources will be focused on promoting the principles that underlie best practice project delivery rather than simply identifying an off-the-shelf procurement system. This project builds on earlier work by Sidwell, Kennedy and Chan (2002), on re-engineering the construction delivery process, which developed a procurement framework in the form of a Decision Matrix

Towards a rule-based matrix for evaluating distress mechanisms in bridges

The effective management of bridge stock involves making decisions as to when to repair, remedy, or do nothing, taking into account the financial and service life implications. Such decisions require a reliable diagnosis as to the cause of distress and an understanding of the likely future degradation. Such diagnoses are based on a combination of visual inspections, laboratory tests on samples and expert opinions. In addition, the choice of appropriate laboratory tests requires an understanding of the degradation mechanisms involved. Under these circumstances, the use of expert systems or evaluation tools developed from “realtime” case studies provides a promising solution in the absence of expert knowledge. This paper addresses the issues in bridge infrastructure management in Queensland, Australia. Bridges affected by alkali silica reaction and chloride induced corrosion have been investigated and the results presented using a mind mapping tool. The analysis highights that several levels of rules are required to assess the mechanism causing distress. The systematic development of a rule based approach is presented. An example of this application to a case study bridge has been used to demonstrate that preliminary results are satisfactory.

Towards a Rule-based matrix for evaluating distress mechanisms in bridges

One of the key issues facing public asset owners is the decision of refurbishing aged built assets. This decision requires an assessment of the “remaining service life” of the key components in a building. The remaining service life is significantly dependent upon the existing condition of the asset and future degradation patterns considering durability and functional obsolescence. Recently developed methods on Residual Service Life modelling, require sophisticated data that are not readily available. Most of the data available are in the form of reports prior to undertaking major repairs or in the form of sessional audit reports. Valuable information from these available sources can serve as bench marks for estimating the reference service life. The authors have acquired similar informations from a public asset building in Melbourne. Using these informations, the residual service life of a case study building façade has been estimated in this paper based on state-of-the-art approaches. These estimations have been evaluated against expert opinion. Though the results are encouraging it is clear that the state-of-the-art methodologies can only provide meaningful estimates provided the level and quality of data are available. This investigation resulted in the development of a new framework for maintenance that integrates the condition assessment procedures and factors influencing residual service life

Inducing shades of meaning by matrix methods : a first step towards thematic analysis of opinion

This article explores two matrix methods to induce the ``shades of meaning" (SoM) of a word. A matrix representation of a word is computed from a corpus of traces based on the given word. Non-negative Matrix Factorisation (NMF) and Singular Value Decomposition (SVD) compute a set of vectors corresponding to a potential shade of meaning. The two methods were evaluated based on loss of conditional entropy with respect to two sets of manually tagged data. One set reflects concepts generally appearing in text, and the second set comprises words used for investigations into word sense disambiguation. Results show that for NMF consistently outperforms SVD for inducing both SoM of general concepts as well as word senses. The problem of inducing the shades of meaning of a word is more subtle than that of word sense induction and hence relevant to thematic analysis of opinion where nuances of opinion can arise.

Addressing issues in sparseness, ecological bias and formulation of the adjacency matrix in Bayesian spatio-temporal analysis of disease counts

The main objective of this PhD was to further develop Bayesian spatio-temporal models (specifically the Conditional Autoregressive (CAR) class of models), for the analysis of sparse disease outcomes such as birth defects. The motivation for the thesis arose from problems encountered when analyzing a large birth defect registry in New South Wales. The specific components and related research objectives of the thesis were developed from gaps in the literature on current formulations of the CAR model, and health service planning requirements. Data from a large probabilistically-linked database from 1990 to 2004, consisting of fields from two separate registries: the Birth Defect Registry (BDR) and Midwives Data Collection (MDC) were used in the analyses in this thesis. The main objective was split into smaller goals. The first goal was to determine how the specification of the neighbourhood weight matrix will affect the smoothing properties of the CAR model, and this is the focus of chapter 6. Secondly, I hoped to evaluate the usefulness of incorporating a zero-inflated Poisson (ZIP) component as well as a shared-component model in terms of modeling a sparse outcome, and this is carried out in chapter 7. The third goal was to identify optimal sampling and sample size schemes designed to select individual level data for a hybrid ecological spatial model, and this is done in chapter 8. Finally, I wanted to put together the earlier improvements to the CAR model, and along with demographic projections, provide forecasts for birth defects at the SLA level. Chapter 9 describes how this is done. For the first objective, I examined a series of neighbourhood weight matrices, and showed how smoothing the relative risk estimates according to similarity by an important covariate (i.e. maternal age) helped improve the model’s ability to recover the underlying risk, as compared to the traditional adjacency (specifically the Queen) method of applying weights. Next, to address the sparseness and excess zeros commonly encountered in the analysis of rare outcomes such as birth defects, I compared a few models, including an extension of the usual Poisson model to encompass excess zeros in the data. This was achieved via a mixture model, which also encompassed the shared component model to improve on the estimation of sparse counts through borrowing strength across a shared component (e.g. latent risk factor/s) with the referent outcome (caesarean section was used in this example). Using the Deviance Information Criteria (DIC), I showed how the proposed model performed better than the usual models, but only when both outcomes shared a strong spatial correlation. The next objective involved identifying the optimal sampling and sample size strategy for incorporating individual-level data with areal covariates in a hybrid study design. I performed extensive simulation studies, evaluating thirteen different sampling schemes along with variations in sample size. This was done in the context of an ecological regression model that incorporated spatial correlation in the outcomes, as well as accommodating both individual and areal measures of covariates. Using the Average Mean Squared Error (AMSE), I showed how a simple random sample of 20% of the SLAs, followed by selecting all cases in the SLAs chosen, along with an equal number of controls, provided the lowest AMSE. The final objective involved combining the improved spatio-temporal CAR model with population (i.e. women) forecasts, to provide 30-year annual estimates of birth defects at the Statistical Local Area (SLA) level in New South Wales, Australia. The projections were illustrated using sixteen different SLAs, representing the various areal measures of socio-economic status and remoteness. A sensitivity analysis of the assumptions used in the projection was also undertaken. By the end of the thesis, I will show how challenges in the spatial analysis of rare diseases such as birth defects can be addressed, by specifically formulating the neighbourhood weight matrix to smooth according to a key covariate (i.e. maternal age), incorporating a ZIP component to model excess zeros in outcomes and borrowing strength from a referent outcome (i.e. caesarean counts). An efficient strategy to sample individual-level data and sample size considerations for rare disease will also be presented. Finally, projections in birth defect categories at the SLA level will be made.

Botanical matrix

Botanical matrix is a graphic map produced via a process involving an initial site installation (350 m contour transect), a botanical survey and photographic documentation of species. The site is a housing subdivision at Point Henry, on the SE coast of Western Australia which is a landscape which is host the most botanically diverse vegetation found worldwide - known locally as 'kwongan'. Notoriously difficult vegetation to measure and map, kwongan is a visual 'engima', for paradoxically it appears to the lay person as visually bland and highly homogenous. There is thus is a critical need for the development of new forms of representation which overcome the barriers between the perception and reality of this botanical condition. Botanical Matrix is one result of the author's research which seeks to address this important problem.

The osteogenic differentiation of adipose tissue-derived precursor cells in A 3D scaffold/matrix environment

Abstract: This paper details an in-vitro study using human adipose tissue-derived precursor/stem cells (ADSCs) in three-dimensional (3D) tissue culture systems. ADSCs from 3 donors were seeded onto NaOH-treated medical grade polycaprolactone-tricalcium phosphate (mPCL-TCP) scaffolds with two different matrix components; fibrin glue and lyophilized collagen. ADSCs within these scaffolds were then induced to differentiate along the osteogenic lineage for a 28-day period and various assays and imaging techniques were performed at Day 1, 7, 14, 21 and 28 to assess and compare the ADSC’s adhesion, viability, proliferation, metabolism and differentiation along the osteogenic lineage when cultured in the different scaffold/matrix systems. The ADSC cells were proliferative in both collagen and fibrin mPCL-TCP scaffold systems with a consistently higher cell number (by comparing DNA amounts) in the induced group over the non-induced groups for both scaffold systems. In response to osteogenic induction, these ADSCs expressed elevated osteocalcin, alkaline phosphatase and osteonectin levels. Cells were able to proliferate within the pores of the scaffolds and form dense cellular networks after 28 days of culture and induction. The successful cultivation of osteogenic by FDM process manufactured ADSCs within a 3D matrix comprising fibrin glue or collagen, immobilized within a robust synthetic scaffold is a promising technique which should enhance their potential usage in the regenerative medicine arena, such as bone tissue engineering.