Trading spaces : on the lore and limitations of latent semantic analysis

Two decades after its inception, Latent Semantic Analysis(LSA) has become part and parcel of every modern introduction to Information Retrieval. For any tool that matures so quickly, it is important to check its lore and limitations, or else stagnation will set in. We focus here on the three main aspects of LSA that are well accepted, and the gist of which can be summarized as follows: (1) that LSA recovers latent semantic factors underlying the document space, (2) that such can be accomplished through lossy compression of the document space by eliminating lexical noise, and (3) that the latter can best be achieved by Singular Value Decomposition. For each aspect we performed experiments analogous to those reported in the LSA literature and compared the evidence brought to bear in each case. On the negative side, we show that the above claims about LSA are much more limited than commonly believed. Even a simple example may show that LSA does not recover the optimal semantic factors as intended in the pedagogical example used in many LSA publications. Additionally, and remarkably deviating from LSA lore, LSA does not scale up well: the larger the document space, the more unlikely that LSA recovers an optimal set of semantic factors. On the positive side, we describe new algorithms to replace LSA (and more recent alternatives as pLSA, LDA, and kernel methods) by trading its l2 space for an l1 space, thereby guaranteeing an optimal set of semantic factors. These algorithms seem to salvage the spirit of LSA as we think it was initially conceived.

Models of collective cell motion for cell populations with different aspect ratio : diffusion, proliferation and travelling waves

Continuum, partial differential equation models are often used to describe the collective motion of cell populations, with various types of motility represented by the choice of diffusion coefficient, and cell proliferation captured by the source terms. Previously, the choice of diffusion coefficient has been largely arbitrary, with the decision to choose a particular linear or nonlinear form generally based on calibration arguments rather than making any physical connection with the underlying individual-level properties of the cell motility mechanism. In this work we provide a new link between individual-level models, which account for important cell properties such as varying cell shape and volume exclusion, and population-level partial differential equation models. We work in an exclusion process framework, considering aligned, elongated cells that may occupy more than one lattice site, in order to represent populations of agents with different sizes. Three different idealizations of the individual-level mechanism are proposed, and these are connected to three different partial differential equations, each with a different diffusion coefficient; one linear, one nonlinear and degenerate and one nonlinear and nondegenerate. We test the ability of these three models to predict the population level response of a cell spreading problem for both proliferative and nonproliferative cases. We also explore the potential of our models to predict long time travelling wave invasion rates and extend our results to two dimensional spreading and invasion. Our results show that each model can accurately predict density data for nonproliferative systems, but that only one does so for proliferative systems. Hence great care must be taken to predict density data for with varying cell shape.

Diffusion determinants for passive building technologies

This summary is based on an international review of leading peer reviewed journals, in both technical and management fields. It draws on highly cited articles published between 2000 and 2009 to investigate the research question, "What are the diffusion determinants for passive building technologies in Australia?". Using a conceptual framework drawn from the innovation systems literature, this paper synthesises and interprets the literature to map the current state of passive building technologies in Australia and to analyse the drivers for, and obstacles to, their optimal diffusion. The paper concludes that the government has a key role to play through its influence over the specification of building codes.

Time limitations in NAPLAN numeracy tests

The article discusses evidence that time prevented many students from showing what they could do in the 2010 Year 7 and 9 NAPLAN numeracy tests. In addition to analysing the available data, the article discusses some NAPLAN numeracy questions that contribute to this problem. It is suggested that schools should investigate whether time limitation is a problem for their own students. The article discusses the implications of these findings for teachers preparing students for NAPLAN tests and for the developers of the tests.

Computationally efficient methods for solving time-variable-order time-space fractional reaction-diffusion equation

Fractional differential equations are becoming more widely accepted as a powerful tool in modelling anomalous diffusion, which is exhibited by various materials and processes. Recently, researchers have suggested that rather than using constant order fractional operators, some processes are more accurately modelled using fractional orders that vary with time and/or space. In this paper we develop computationally efficient techniques for solving time-variable-order time-space fractional reaction-diffusion equations (tsfrde) using the finite difference scheme. We adopt the Coimbra variable order time fractional operator and variable order fractional Laplacian operator in space where both orders are functions of time. Because the fractional operator is nonlocal, it is challenging to efficiently deal with its long range dependence when using classical numerical techniques to solve such equations. The novelty of our method is that the numerical solution of the time-variable-order tsfrde is written in terms of a matrix function vector product at each time step. This product is approximated efficiently by the Lanczos method, which is a powerful iterative technique for approximating the action of a matrix function by projecting onto a Krylov subspace. Furthermore an adaptive preconditioner is constructed that dramatically reduces the size of the required Krylov subspaces and hence the overall computational cost. Numerical examples, including the variable-order fractional Fisher equation, are presented to demonstrate the accuracy and efficiency of the approach.

Efficient preconditioning of the method of lines for solving nonlinear two-sided space-fractional diffusion equations

A standard method for the numerical solution of partial differential equations (PDEs) is the method of lines. In this approach the PDE is discretised in space using �finite di�fferences or similar techniques, and the resulting semidiscrete problem in time is integrated using an initial value problem solver. A significant challenge when applying the method of lines to fractional PDEs is that the non-local nature of the fractional derivatives results in a discretised system where each equation involves contributions from many (possibly every) spatial node(s). This has important consequences for the effi�ciency of the numerical solver. First, since the cost of evaluating the discrete equations is high, it is essential to minimise the number of evaluations required to advance the solution in time. Second, since the Jacobian matrix of the system is dense (partially or fully), methods that avoid the need to form and factorise this matrix are preferred. In this paper, we consider a nonlinear two-sided space-fractional di�ffusion equation in one spatial dimension. A key contribution of this paper is to demonstrate how an eff�ective preconditioner is crucial for improving the effi�ciency of the method of lines for solving this equation. In particular, we show how to construct suitable banded approximations to the system Jacobian for preconditioning purposes that permit high orders and large stepsizes to be used in the temporal integration, without requiring dense matrices to be formed. The results of numerical experiments are presented that demonstrate the effectiveness of this approach.

Numerical methods for solving the multi-term time-fractional wave-diffusion equations

In this paper, the multi-term time-fractional wave diffusion equations are considered. The multiterm time fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0,1], [1,2), [0,2), [0,3), [2,3) and [2,4), respectively. Some computationally effective numerical methods are proposed for simulating the multi-term time-fractional wave-diffusion equations. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and techniques can also be extended to other kinds of the multi-term fractional time-space models with fractional Laplacian.

Analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations on a finite domain

Generalized fractional partial differential equations have now found wide application for describing important physical phenomena, such as subdiffusive and superdiffusive processes. However, studies of generalized multi-term time and space fractional partial differential equations are still under development. In this paper, the multi-term time-space Caputo-Riesz fractional advection diffusion equations (MT-TSCR-FADE) with Dirichlet nonhomogeneous boundary conditions are considered. The multi-term time-fractional derivatives are defined in the Caputo sense, whose orders belong to the intervals [0, 1], [1, 2] and [0, 2], respectively. These are called respectively the multi-term time-fractional diffusion terms, the multi-term time-fractional wave terms and the multi-term time-fractional mixed diffusion-wave terms. The space fractional derivatives are defined as Riesz fractional derivatives. Analytical solutions of three types of the MT-TSCR-FADE are derived with Dirichlet boundary conditions. By using Luchko's Theorem (Acta Math. Vietnam., 1999), we proposed some new techniques, such as a spectral representation of the fractional Laplacian operator and the equivalent relationship between fractional Laplacian operator and Riesz fractional derivative, that enabled the derivation of the analytical solutions for the multi-term time-space Caputo-Riesz fractional advection-diffusion equations. © 2012.

Numerical techniques for the variable order time fractional diffusion equation

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Solution methods for advection-diffusion-reaction equations on growing domains and subdomains, with application to modelling skin substitutes

Problems involving the solution of advection-diffusion-reaction equations on domains and subdomains whose growth affects and is affected by these equations, commonly arise in developmental biology. Here, a mathematical framework for these situations, together with methods for obtaining spatio-temporal solutions and steady states of models built from this framework, is presented. The framework and methods are applied to a recently published model of epidermal skin substitutes. Despite the use of Eulerian schemes, excellent agreement is obtained between the numerical spatio-temporal, numerical steady state, and analytical solutions of the model.

Langevin dynamics modeling of the water diffusion tensor in partially aligned collagen networks

In this work, a Langevin dynamics model of the diffusion of water in articular cartilage was developed. Numerical simulations of the translational dynamics of water molecules and their interaction with collagen fibers were used to study the quantitative relationship between the organization of the collagen fiber network and the diffusion tensor of water in model cartilage. Langevin dynamics was used to simulate water diffusion in both ordered and partially disordered cartilage models. In addition, an analytical approach was developed to estimate the diffusion tensor for a network comprising a given distribution of fiber orientations. The key findings are that (1) an approximately linear relationship was observed between collagen volume fraction and the fractional anisotropy of the diffusion tensor in fiber networks of a given degree of alignment, (2) for any given fiber volume fraction, fractional anisotropy follows a fiber alignment dependency similar to the square of the second Legendre polynomial of cos(θ), with the minimum anisotropy occurring at approximately the magic angle (θMA), and (3) a decrease in the principal eigenvalue and an increase in the transverse eigenvalues is observed as the fiber orientation angle θ progresses from 0◦ to 90◦. The corresponding diffusion ellipsoids are prolate for θ < θMA, spherical for θ ≈ θMA, and oblate for θ > θMA. Expansion of the model to include discrimination between the combined effects of alignment disorder and collagen fiber volume fraction on the diffusion tensor is discussed.

Studies on bending limitations for the optimal fit of orthopaedic bone plates

Distal tibial fractures are now commonly treated via intermedullary plate fixation due to higher rates of union and lower rates of postoperative complications. However, patient specific bone morphology demands manual deformation of the plate to ensure appropriate fit along the bone Distal tibial fractures are now commonly treated via intermedullary plate fixation due to higher rates of union and lower rates of postoperative complications. However, patient specific bone morphology demands manual deformation of the plate to ensure appropriate fit along the bone contours, and depending on the material of the plate, different outcomes have been reported along with postoperative complications. A comparative analysis of Stainless Steel 316L and Ti-6Al-4V alloys was carried to estimate the safe bending limit for appropriate fits. The results from the ANSYS FEA simulations were validated with experiments based on ASTM F382-99. It is found that SS316L is better suited for large deformations (up to 16˚ in proximal tip and 7.5˚ in distal end) and Ti for smaller deformation contours (up to 3˚ in proximal tip and 1.8˚ in distal end). The results of this study have profound implications for the choice of plates based on preliminary radiographical fracture examinations to ensure better fixation and higher rates of union of distal tibial fractures.

Valuation of family firms : the limitations of accounting information

This conceptual paper explores the extent to which reported accounting information captures unique family firm decision-making and intangible asset factors that impact financial value. We review the family firm valuation-relevant literature and identify that this body of research is predicated on the assumption that accounting information reflects the underlying reality of family firms. This research, however, fails to recognise that current accounting technology does not fully recognise the family firm factors in the book value of the firm or the implications for long run persistence of earnings. Thus, valuation models underpinning the extant empirical research, which are predicated on reported accounting information, may not fully reflect the intrinsic value of family firms. We present propositions on the interaction between accounting information, family factors and valuation as a road map for future empirical research with a discussion of appropriate methodologies.