An empirical study of process-related attributes in segmented software cost-estimation relationships

Parametric software effort estimation models consisting on a single mathematical relationship suffer from poor adjustment and predictive characteristics in cases in which the historical database considered contains data coming from projects of a heterogeneous nature. The segmentation of the input domain according to clusters obtained from the database of historical projects serves as a tool for more realistic models that use several local estimation relationships. Nonetheless, it may be hypothesized that using clustering algorithms without previous consideration of the influence of well-known project attributes misses the opportunity to obtain more realistic segments. In this paper, we describe the results of an empirical study using the ISBSG-8 database and the EM clustering algorithm that studies the influence of the consideration of two process-related attributes as drivers of the clustering process: the use of engineering methodologies and the use of CASE tools. The results provide evidence that such consideration conditions significantly the final model obtained, even though the resulting predictive quality is of a similar magnitude.

Perturbation, extraction and refinement of invariant pairs for matrix polynomials

Generalizing the notion of an eigenvector, invariant subspaces are frequently used in the context of linear eigenvalue problems, leading to conceptually elegant and numerically stable formulations in applications that require the computation of several eigenvalues and/or eigenvectors. Similar benefits can be expected for polynomial eigenvalue problems, for which the concept of an invariant subspace needs to be replaced by the concept of an invariant pair. Little has been known so far about numerical aspects of such invariant pairs. The aim of this paper is to fill this gap. The behavior of invariant pairs under perturbations of the matrix polynomial is studied and a first-order perturbation expansion is given. From a computational point of view, we investigate how to best extract invariant pairs from a linearization of the matrix polynomial. Moreover, we describe efficient refinement procedures directly based on the polynomial formulation. Numerical experiments with matrix polynomials from a number of applications demonstrate the effectiveness of our extraction and refinement procedures.

Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

Feedback design for a second-order control system leads to an eigenstructure assignment problem for a quadratic matrix polynomial. It is desirable that the feedback controller not only assigns specified eigenvalues to the second-order closed loop system but also that the system is robust, or insensitive to perturbations. We derive here new sensitivity measures, or condition numbers, for the eigenvalues of the quadratic matrix polynomial and define a measure of the robustness of the corresponding system. We then show that the robustness of the quadratic inverse eigenvalue problem can be achieved by solving a generalized linear eigenvalue assignment problem subject to structured perturbations. Numerically reliable methods for solving the structured generalized linear problem are developed that take advantage of the special properties of the system in order to minimize the computational work required. In this part of the work we treat the case where the leading coefficient matrix in the quadratic polynomial is nonsingular, which ensures that the polynomial is regular. In a second part, we will examine the case where the open loop matrix polynomial is not necessarily regular.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

Wavelets and the generalization of the variogram

The experimental variogram computed in the usual way by the method of moments and the Haar wavelet transform are similar in that they filter data and yield informative summaries that may be interpreted. The variogram filters out constant values; wavelets can filter variation at several spatial scales and thereby provide a richer repertoire for analysis and demand no assumptions other than that of finite variance. This paper compares the two functions, identifying that part of the Haar wavelet transform that gives it its advantages. It goes on to show that the generalized variogram of order k=1, 2, and 3 filters linear, quadratic, and cubic polynomials from the data, respectively, which correspond with more complex wavelets in Daubechies's family. The additional filter coefficients of the latter can reveal features of the data that are not evident in its usual form. Three examples in which data recorded at regular intervals on transects are analyzed illustrate the extended form of the variogram. The apparent periodicity of gilgais in Australia seems to be accentuated as filter coefficients are added, but otherwise the analysis provides no new insight. Analysis of hyerpsectral data with a strong linear trend showed that the wavelet-based variograms filtered it out. Adding filter coefficients in the analysis of the topsoil across the Jurassic scarplands of England changed the upper bound of the variogram; it then resembled the within-class variogram computed by the method of moments. To elucidate these results, we simulated several series of data to represent a random process with values fluctuating about a mean, data with long-range linear trend, data with local trend, and data with stepped transitions. The results suggest that the wavelet variogram can filter out the effects of long-range trend, but not local trend, and of transitions from one class to another, as across boundaries.

Geomorphological Map of Ribbed Moraines on the Dubawnt Lake Palaeo-Ice Stream Bed: A Signature of Ice Stream Shut-down?

The beds of active ice streams in Greenland and Antarctica are largely inaccessible, hindering a full understanding of the processes that initiate, sustain and inhibit fast ice flow in ice sheets. Detailed mapping of the glacial geomorphology of palaeo-ice stream tracks is, therefore, a valuable tool for exploring the basal processes that control their behaviour. In this paper we present a map that shows detailed glacial geomorphology from a part of the Dubawnt Lake Palaeo-Ice Stream bed on the north-western Canadian Shield (Northwest Territories), which operated at the end of the last glacial cycle. The map (centred on 63 degrees 55 '' 42'N, 102 degrees 29 '' 11'W, approximate scale 1:90,000) was compiled from digital Landsat Enhanced Thematic Mapper Plus satellite imagery and digital and hard-copy stereo-aerial photographs. The ice stream bed is dominated by parallel mega-scale glacial lineations (MGSL), whose lengths exceed several kilometres but the map also reveals that they have, in places, been superimposed with transverse ridges known as ribbed moraines. The ribbed moraines lie on top of the MSGL and appear to have segmented the individual lineaments. This indicates that formation of the ribbed moraines post-date the formation of the MSGL. The presence of ribbed moraine in the onset zone of another palaeo-ice stream has been linked to oscillations between cold and warm-based ice and/or a patchwork of cold-based areas which led to acceleration and deceleration of ice velocity. Our hypothesis is that the ribbed moraines on the Dubawnt Lake Ice Stream bed are a manifestation of the process that led to ice stream shut-down and may be associated with the process of basal freeze-on. The precise formation of ribbed moraines, however, remains open to debate and field observation of their structure will provide valuable data for formal testing of models of their formation.

A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.

A high-wavenumber boundary-element method for an acoustic scattering problem

In this paper we show stability and convergence for a novel Galerkin boundary element method approach to the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data. This problem models, for example, outdoor sound propagation over inhomogeneous flat terrain. To achieve a good approximation with a relatively low number of degrees of freedom we employ a graded mesh with smaller elements adjacent to discontinuities in impedance, and a special set of basis functions for the Galerkin method so that, on each element, the approximation space consists of polynomials (of degree $\nu$) multiplied by traces of plane waves on the boundary. In the case where the impedance is constant outside an interval $[a,b]$, which only requires the discretization of $[a,b]$, we show theoretically and experimentally that the $L_2$ error in computing the acoustic field on $[a,b]$ is ${\cal O}(\log^{\nu+3/2}|k(b-a)| M^{-(\nu+1)})$, where $M$ is the number of degrees of freedom and $k$ is the wavenumber. This indicates that the proposed method is especially commendable for large intervals or a high wavenumber. In a final section we sketch how the same methodology extends to more general scattering problems.

Variational calculations of rovibrational states: a precise high-energy potential surface for HCN [and discussion]

We report the results of variational calculations of the rovibrational energy levels of HCN for J = 0, 1 and 2, where we reproduce all the ca. 100 observed vibrational states for all observed isotopic species, with energies up to 18000 cm$^{-1}$, to about $\pm $1 cm$^{-1}$, and the corresponding rotational constants to about $\pm $0.001 cm$^{-1}$. We use a hamiltonian expressed in internal coordinates r$_{1}$, r$_{2}$ and $\theta $, using the exact expression for the kinetic energy operator T obtained by direct transformation from the cartesian representation. The potential energy V is expressed as a polynomial expansion in the Morse coordinates y$_{i}$ for the bond stretches and the interbond angle $\theta $. The basis functions are built as products of appropriately scaled Morse functions in the bond-stretches and Legendre or associated Legendre polynomials of cos $\theta $ in the angle bend, and we evaluate matrix elements by Gauss quadrature. The hamiltonian matripx is factorized using the full rovibrational symmetry, and the basis is contracted to an optimized form; the dimensions of the final hamiltonian matrix vary from 240 $\times $ 240 to 1000 $\times $ 1000.We believe that our calculation is converged to better than 1 cm$^{-1}$ at 18 000 cm$^{-1}$. Our potential surface is expressed in terms of 31 parameters, about half of which have been refined by least squares to optimize the fit to the experimental data. The advantages and disadvantages and the future potential of calculations of this type are discussed.

The influence of age and gender on food choice: a focus group exploration

With 25% of the UK population predicted to be obese by 2010, the costs to individuals and society are set to rise. Due to the extra economic and social pressures obesity causes, there is an increasing need to understand what motivates and prevents consumers from eating a healthy diet so as to be able to tailor policy interventions to specific groups in society. In so doing, it is important to explore potential variations in attitudes, motivation and behaviour as a function of age and gender. Both demographic factors are easily distinguished within society and a future intervention study which targets either, or both, of these would likely be both feasible and cost-effective for policy makers. As part of a preliminary study, six focus groups (total n = 43) were conducted at the University of Reading in November 2006, with groups segmented on the basis of age and gender. In order to gather more sensitive information, participants were also asked to fill out a short anonymous questionnaire before each focus group began, relating to healthy eating, alcohol consumption and body dissatisfaction. Making use of thematic content analysis, results suggested that most participants were aware of the type of foods that contribute to a healthy diet and the importance of achieving a healthy balance within a diet. However, they believed that healthy eating messages were often conflicting, and were uncertain about where to find information on the topic. Participants believed that the family has an important role in educating children about eating habits. Despite these similarities, there were a number of key differences among the groups in terms of their reasons for making food choices. Older participants (60+ years old) were more likely to make food choices based on health considerations. Participants between the ages of 18–30 were less concerned with this link, and instead focused on issues of food preparation and knowledge, prices and time. Younger female participants said they had more energy when they ate healthier diets; however, very often their food choices related to concern with their appearance. Older female participants also expressed this concern within the questionnaire, rather than in the group discussions. Overall, these results suggest that consumer motivations for healthy eating are diverse and that this must be considered by government, retailers and food producers.

Protochordate Zic genes define primitive somite compartments and highlight molecular changes underlying neural crest evolution

The vertebrate Zic gene family encodes C2H2 zinc finger transcription factors closely related to the Gli proteins. Zic genes are expressed in multiple areas of developing vertebrate embryos, including the dorsal neural tube where they act as potent neural crest inducers. Here we describe the characterization of a Zic ortholog from the amphioxus Branchiostoma floridae and further describe the expression of a Zic ortholog from the ascidian Ciona intestinalis. Molecular phylogenetic analysis and sequence comparisons suggest the gene duplications that formed the vertebrate Zic family were specific to the vertebrate lineage. In Ciona maternal CiZic/Ci-macho1 transcripts are localized during cleavage stages by asymmetric cell division, whereas zygotic expression by neural plate cells commences during neurulation. The amphioxus Zic ortholog AmphiZic is expressed in dorsal mesoderm and ectoderm during gastrulation, before being eliminated first from midline cells and then from all neurectoderm during neurulation. After neurulation, expression is reactivated in the dorsal neural tube and dorsolateral somite. Comparison of CiZic and AmphiZic expression with vertebrate Zic expression leads to two main conclusions. First, Zic expression allows us to define homologous compartments between vertebrate and amphioxus somites, showing primitive subdivision of vertebrate segmented mesoderm. Second, we show that neural Zic expression is a chordate synapomorphy, whereas the precise pattern of neural expression has evolved differently on the different chordate lineages. Based on these observations we suggest that a change in Zic regulation, specifically the evolution of a dorsal neural expression domain in vertebrate neurulae, was an important step in the evolution of the neural crest.

Characterisation of an amphioxus Fringe gene and the evolution of the vertebrate segmentation clock

In mouse and chick embryos, cyclic expression of lunatic fringe has an important role in the regulation of mesoderm segmentation. We have isolated a Fringe gene from the protochordate amphioxus. Amphioxus is the closest living relative of the vertebrates, and has mesoderm that is definitively segmented in a manner that is similar to, and probably homologous with, that of vertebrates. AmphiFringe is placed basal to vertebrate Fringe genes in molecular phylogenetic analyses, indicating that the duplications that formed radical-, manic- and lunatic fringe are specific to the vertebrate lineage. AmphiFringe expression was detected in the anterior neural plate of early neurulae, where it resolved into a series of segmental patches by the mid-neurulae stage. No AmphiFringe transcripts were detected in the mesoderm. Based on these observations, we propose a model depicting a successive recruitment of Fringe in the maintenance then regulation of segmentation during vertebrate evolution.