Generalized IBE in the exponent-inversion framework

The purpose of this chapter is to provide an abstraction for the class of Exponent-Inversion IBE exemplified by the [Bscr ][Bscr ]2 and [Sscr ][Kscr ] schemes, and, on the basis of that abstraction, to show that those schemes do support interesting and useful extensions such as HIBE and ABE. Our results narrow, if not entirely close, the “flexibility gap” between the Exponent-Inversion and Commutative-Blinding IBE concepts.

Permutation polynomials of the form (xp −x +δ)s +L(x)

Recently, several classes of permutation polynomials of the form (x2 + x + δ)s + x over F2m have been discovered. They are related to Kloosterman sums. In this paper, the permutation behavior of polynomials of the form (xp − x + δ)s + L(x) over Fpm is investigated, where L(x) is a linearized polynomial with coefficients in Fp. Six classes of permutation polynomials on F2m are derived. Three classes of permutation polynomials over F3m are also presented.

Generalized aggregate Quality of Service computation for composite services

This article addresses the problem of estimating the Quality of Service (QoS) of a composite service given the QoS of the services participating in the composition. Previous solutions to this problem impose restrictions on the topology of the orchestration models, limiting their applicability to well-structured orchestration models for example. This article lifts these restrictions by proposing a method for aggregate QoS computation that deals with more general types of unstructured orchestration models. The applicability and scalability of the proposed method are validated using a collection of models from industrial practice.

Non-linear refined finite element elastic analysis of steel frames with generalized transverse member loads

In the finite element modelling of steel frames, external loads usually act along the members rather than at the nodes only. Conventionally, when a member is subjected to these transverse loads, they are converted to nodal forces which act at the ends of the elements into which the member is discretised by either lumping or consistent nodal load approaches. For a contemporary geometrically non-linear analysis in which the axial force in the member is large, accurate solutions are achieved by discretising the member into many elements, which can produce unfavourable consequences on the efficacy of the method for analysing large steel frames. Herein, a numerical technique to include the transverse loading in the non-linear stiffness formulation for a single element is proposed, and which is able to predict the structural responses of steel frames involving the effects of first-order member loads as well as the second-order coupling effect between the transverse load and the axial force in the member. This allows for a minimal discretisation of a frame for second-order analysis. For those conventional analyses which do include transverse member loading, prescribed stiffness matrices must be used for the plethora of specific loading patterns encountered. This paper shows, however, that the principle of superposition can be applied to the equilibrium condition, so that the form of the stiffness matrix remains unchanged with only the magnitude of the loading being needed to be changed in the stiffness formulation. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. The results are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple structural frames.

Revisiting Polya's summation techniques using a spreadsheet : from addition tables to Bernoulli polynomials

Recurrence relations in mathematics form a very powerful and compact way of looking at a wide range of relationships. Traditionally, the concept of recurrence has often been a difficult one for the secondary teacher to convey to students. Closely related to the powerful proof technique of mathematical induction, recurrences are able to capture many relationships in formulas much simpler than so-called direct or closed formulas. In computer science, recursive coding often has a similar compactness property, and, perhaps not surprisingly, suffers from similar problems in the classroom as recurrences: the students often find both the basic concepts and practicalities elusive. Using models designed to illuminate the relevant principles for the students, we offer a range of examples which use the modern spreadsheet environment to powerfully illustrate the great expressive and computational power of recurrences.

Generalized azimuthal shear deformations in compressible isotropic elastic materials

In this article we study the azimuthal shear deformations in a compressible Isotropic elastic material. This class of deformations involves an azimuthal displacement as a function of the radial and axial coordinates. The equilibrium equations are formulated in terms of the Cauchy-Green strain tensors, which form an overdetermined system of partial differential equations for which solutions do not exist in general. By means of a Legendre transformation, necessary and sufficient conditions for the material to support this deformation are obtained explicitly, in the sense that every solution to the azimuthal equilibrium equation will satisfy the remaining two equations. Additionally, we show how these conditions are sufficient to support all currently known deformations that locally reduce to simple shear. These conditions are then expressed both in terms of the invariants of the Cauchy-Green strain and stretch tensors. Several classes of strain energy functions for which this deformation can be supported are studied. For certain boundary conditions, exact solutions to the equilibrium equations are obtained. © 2005 Society for Industrial and Applied Mathematics.

Identity in dialogue : identity as hyper-generalized personal sense

In this paper I propose that identity is momentary, fluid, and multiple while simultaneously providing us with a sense of sameness and continuity. Building on Valsiner’s ideas about human sense-making I suggest that we can reasonably deal with the multiplicity/unity paradox if we conceive of this process as resulting in the construction of a fuzzy field of hyper-generalized personal sense, which ordinarily functions as an implicit and unspeakable background of our everyday functioning, while being constantly re-created through momentary instances of foregrounded and explicit identity-dialogues. I illustrate the ideas put forward in the paper by analysing a case of a young woman experiencing a change in her being. Finally, in an attempt to illustrate and further develop the case I introduce a metaphor of carpet-weaving as an apposite image for thinking about identity as a process of a multiple and fragmented, yet also a united and constant being.

Generalized element load method for first- and second-order element solutions with element load effect

The finite element method in principle adaptively divides the continuous domain with complex geometry into discrete simple subdomain by using an approximate element function, and the continuous element loads are also converted into the nodal load by means of the traditional lumping and consistent load methods, which can standardise a plethora of element loads into a typical numerical procedure, but element load effect is restricted to the nodal solution. It in turn means the accurate continuous element solutions with the element load effects are merely restricted to element nodes discretely, and further limited to either displacement or force field depending on which type of approximate function is derived. On the other hand, the analytical stability functions can give the accurate continuous element solutions due to element loads. Unfortunately, the expressions of stability functions are very diverse and distinct when subjected to different element loads that deter the numerical routine for practical applications. To this end, this paper presents a displacement-based finite element function (generalised element load method) with a plethora of element load effects in the similar fashion that never be achieved by the stability function, as well as it can generate the continuous first- and second-order elastic displacement and force solutions along an element without loss of accuracy considerably as the analytical approach that never be achieved by neither the lumping nor consistent load methods. Hence, the salient and unique features of this paper (generalised element load method) embody its robustness, versatility and accuracy in continuous element solutions when subjected to the great diversity of transverse element loads.

Multiple stages classification of Alzheimer’s disease based on structural brain networks using generalized low rank approximations (GLRAM)

To classify each stage for a progressing disease such as Alzheimer’s disease is a key issue for the disease prevention and treatment. In this study, we derived structural brain networks from diffusion-weighted MRI using whole-brain tractography since there is growing interest in relating connectivity measures to clinical, cognitive, and genetic data. Relatively little work has usedmachine learning to make inferences about variations in brain networks in the progression of the Alzheimer’s disease. Here we developed a framework to utilize generalized low rank approximations of matrices (GLRAM) and modified linear discrimination analysis for unsupervised feature learning and classification of connectivity matrices. We apply the methods to brain networks derived from DWI scans of 41 people with Alzheimer’s disease, 73 people with EMCI, 38 people with LMCI, 47 elderly healthy controls and 221 young healthy controls. Our results show that this new framework can significantly improve classification accuracy when combining multiple datasets; this suggests the value of using data beyond the classification task at hand to model variations in brain connectivity.

Working covariance model selection for generalized estimating equations

We investigate methods for data-based selection of working covariance models in the analysis of correlated data with generalized estimating equations. We study two selection criteria: Gaussian pseudolikelihood and a geodesic distance based on discrepancy between model-sensitive and model-robust regression parameter covariance estimators. The Gaussian pseudolikelihood is found in simulation to be reasonably sensitive for several response distributions and noncanonical mean-variance relations for longitudinal data. Application is also made to a clinical dataset. Assessment of adequacy of both correlation and variance models for longitudinal data should be routine in applications, and we describe open-source software supporting this practice.

Discussion of “Generalized estimating equations: Notes on the choice of the working correlation matrix”

Objective To discuss generalized estimating equations as an extension of generalized linear models by commenting on the paper of Ziegler and Vens "Generalized Estimating Equations. Notes on the Choice of the Working Correlation Matrix". Methods Inviting an international group of experts to comment on this paper. Results Several perspectives have been taken by the discussants. Econometricians have established parallels to the generalized method of moments (GMM). Statisticians discussed model assumptions and the aspect of missing data Applied statisticians; commented on practical aspects in data analysis. Conclusions In general, careful modeling correlation is encouraged when considering estimation efficiency and other implications, and a comparison of choosing instruments in GMM and generalized estimating equations, (GEE) would be worthwhile. Some theoretical drawbacks of GEE need to be further addressed and require careful analysis of data This particularly applies to the situation when data are missing at random.

Working-correlation-structure identification in generalized estimating equations

Selecting an appropriate working correlation structure is pertinent to clustered data analysis using generalized estimating equations (GEE) because an inappropriate choice will lead to inefficient parameter estimation. We investigate the well-known criterion of QIC for selecting a working correlation Structure. and have found that performance of the QIC is deteriorated by a term that is theoretically independent of the correlation structures but has to be estimated with an error. This leads LIS to propose a correlation information criterion (CIC) that substantially improves the QIC performance. Extensive simulation studies indicate that the CIC has remarkable improvement in selecting the correct correlation structures. We also illustrate our findings using a data set from the Madras Longitudinal Schizophrenia Study.

A generalized estimating equations approach for analysis of the impact of new technology on a trawl fishery

The article describes a generalized estimating equations approach that was used to investigate the impact of technology on vessel performance in a trawl fishery during 1988-96, while accounting for spatial and temporal correlations in the catch-effort data. Robust estimation of parameters in the presence of several levels of clustering depended more on the choice of cluster definition than on the choice of correlation structure within the cluster. Models with smaller cluster sizes produced stable results, while models with larger cluster sizes, that may have had complex within-cluster correlation structures and that had within-cluster covariates, produced estimates sensitive to the correlation structure. The preferred model arising from this dataset assumed that catches from a vessel were correlated in the same years and the same areas, but independent in different years and areas. The model that assumed catches from a vessel were correlated in all years and areas, equivalent to a random effects term for vessel, produced spurious results. This was an unexpected finding that highlighted the need to adopt a systematic strategy for modelling. The article proposes a modelling strategy of selecting the best cluster definition first, and the working correlation structure (within clusters) second. The article discusses the selection and interpretation of the model in the light of background knowledge of the data and utility of the model, and the potential for this modelling approach to apply in similar statistical situations.

Generalized self-assembly of scalable two-dimensional transition metal oxide nanosheets

Two-dimensional (2D) transition metal oxide systems present exotic electronic properties and high specific surface areas, and also demonstrate promising applications ranging from electronics to energy storage. Yet, in contrast to other types of nanostructures, the question as to whether we could assemble 2D nanomaterials with an atomic thickness from molecules in a general way, which may give them some interesting properties such as those of graphene, still remains unresolved. Herein, we report a generalized and fundamental approach to molecular self-assembly synthesis of ultrathin 2D nanosheets of transition metal oxides by rationally employing lamellar reverse micelles. It is worth emphasizing that the synthesized crystallized ultrathin transition metal oxide nanosheets possess confined thickness, high specific surface area and chemically reactive facets, so that they could have promising applications in nanostructured electronics, photonics, sensors, and energy conversion and storage devices.