The supply and movement of Denarii in Roman Britain

Hoards of denarii are common in Britain and the number which have been recorded in detail means that it is now possible to suggest reasonably accurately what a ‘normal’ hoard of a particular date should look like. That being the case, we can then look for variation around that norm and both investigate and speculate what that variation means. A methodology is developed which suggests periods of faster and less rapid coin circulation which has implications for consideration of monetisation. The model also enables us to view where denarii entered circulation; unsurprisingly the army looms large in this picture. The methodology is directly transferable to other provinces and other periods where there are longlived, relatively stable monetary systems.

A radial basis function network classifier to maximise leave-one-out mutual information

tWe develop an orthogonal forward selection (OFS) approach to construct radial basis function (RBF)network classifiers for two-class problems. Our approach integrates several concepts in probabilisticmodelling, including cross validation, mutual information and Bayesian hyperparameter fitting. At eachstage of the OFS procedure, one model term is selected by maximising the leave-one-out mutual infor-mation (LOOMI) between the classifier’s predicted class labels and the true class labels. We derive theformula of LOOMI within the OFS framework so that the LOOMI can be evaluated efficiently for modelterm selection. Furthermore, a Bayesian procedure of hyperparameter fitting is also integrated into theeach stage of the OFS to infer the l2-norm based local regularisation parameter from the data. Since eachforward stage is effectively fitting of a one-variable model, this task is very fast. The classifier construc-tion procedure is automatically terminated without the need of using additional stopping criterion toyield very sparse RBF classifiers with excellent classification generalisation performance, which is par-ticular useful for the noisy data sets with highly overlapping class distribution. A number of benchmarkexamples are employed to demonstrate the effectiveness of our proposed approach.

Interpolation of Hilbert and Sobolev spaces: quantitative estimates and counterexamples

This paper provides an overview of interpolation of Banach and Hilbert spaces, with a focus on establishing when equivalence of norms is in fact equality of norms in the key results of the theory. (In brief, our conclusion for the Hilbert space case is that, with the right normalisations, all the key results hold with equality of norms.) In the final section we apply the Hilbert space results to the Sobolev spaces Hs(Ω) and tildeHs(Ω), for s in R and an open Ω in R^n. We exhibit examples in one and two dimensions of sets Ω for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if Ω is Lipschitz) we exhibit examples that show that, in general, the interpolation norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio of these two norms can be arbitrarily large.

Unpaid work and conformity: why care?

We study the supply of unpaid eldercare (in particular caring for parents) in the UK, focusing on both the division of care and caring tasks by gender and the effect of conformity to social norms in relation to caring. We then investigate the effect of the amount of care on the well-being of caregivers and whether agreeing with the care norm enhances their well-being. Our results suggest that the eldercare reform neglects important aspects underlying the distribution of care hours and care tasks between caregivers and may potentially worsen intrahousehold inequality in earnings and well-being, in particular, between men and women.

Application of complex extreme learning machine to multiclass classification problems with high dimensionality: a THz spectra classification problem

We extend extreme learning machine (ELM) classifiers to complex Reproducing Kernel Hilbert Spaces (RKHS) where the input/output variables as well as the optimization variables are complex-valued. A new family of classifiers, called complex-valued ELM (CELM) suitable for complex-valued multiple-input–multiple-output processing is introduced. In the proposed method, the associated Lagrangian is computed using induced RKHS kernels, adopting a Wirtinger calculus approach formulated as a constrained optimization problem similarly to the conventional ELM classifier formulation. When training the CELM, the Karush–Khun–Tuker (KKT) theorem is used to solve the dual optimization problem that consists of satisfying simultaneously smallest training error as well as smallest norm of output weights criteria. The proposed formulation also addresses aspects of quaternary classification within a Clifford algebra context. For 2D complex-valued inputs, user-defined complex-coupled hyper-planes divide the classifier input space into four partitions. For 3D complex-valued inputs, the formulation generates three pairs of complex-coupled hyper-planes through orthogonal projections. The six hyper-planes then divide the 3D space into eight partitions. It is shown that the CELM problem formulation is equivalent to solving six real-valued ELM tasks, which are induced by projecting the chosen complex kernel across the different user-defined coordinate planes. A classification example of powdered samples on the basis of their terahertz spectral signatures is used to demonstrate the advantages of the CELM classifiers compared to their SVM counterparts. The proposed classifiers retain the advantages of their ELM counterparts, in that they can perform multiclass classification with lower computational complexity than SVM classifiers. Furthermore, because of their ability to perform classification tasks fast, the proposed formulations are of interest to real-time applications.

A comparison of duality and energy a posteriori estimates for $\mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ in parabolic problems

We use the elliptic reconstruction technique in combination with a duality approach to prove a posteriori error estimates for fully discrete backward Euler scheme for linear parabolic equations. As an application, we combine our result with the residual based estimators from the a posteriori estimation for elliptic problems to derive space-error indicators and thus a fully practical version of the estimators bounding the error in the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$ norm. These estimators, which are of optimal order, extend those introduced by Eriksson and Johnson in 1991 by taking into account the error induced by the mesh changes and allowing for a more flexible use of the elliptic estimators. For comparison with previous results we derive also an energy-based a posteriori estimate for the $ \mathrm {L}_{\infty }(0,T;\mathrm {L}_2(\varOmega ))$-error which simplifies a previous one given by Lakkis and Makridakis in 2006. We then compare both estimators (duality vs. energy) in practical situations and draw conclusions.

Psychological contracts and independent sales contractors: an examination of the predictors of contractor-level outcomes

Over the past decade, the independent sales contractor (ISC) has emerged as both an important distribution channel and a management challenge. This study makes two contributions to this evolving field. First, it explores the interrelations of the psychological contract with sales performance, voluntary turnover and organisational advocacy of ISCs, which have hitherto been largely unexplored. Second, it examines differences between high- and low-performing sales contractors on these linkages, due to findings in the literature that a small number of sales contractors often achieve a majority of sales. Based on survey data as well as 7 years of contractor-level data related to sales performance and voluntary turnover (n = 189), results indicate that psychological contract fulfilment and perceived dependency are important determinants of subsequent sales performance, voluntary turnover and organisational advocacy, with significant differences reported between high- and low-performing ISCs. A notable finding pertinent for sales managers responsible for managing ISCs is that high-performing sales contractors are motivated by psychological contract fulfilment and a low perception of dependency, while low-performing sales contractors are more likely to act as advocates for the firm due to perceived dependency, but may concurrently engage in organisational advocacy as a means to leave the firm.

Standing on the shoulders of giants: an examination of the interdisciplinary foundation of relationship marketing

In the 20th century, the scholarly study of human relationships both grew dramatically and simultaneously fragmented into various disciplines and subdisciplines. Although diversity of thought is generally considered helpful for the evolution of scientific fields, the value accrued from interdisciplinary discourse depends on the ability of scholars to integrate multiple perspectives and synthesize foundational works in a systematic manner. The goal of this study is to synthesize foundational theories from social and behavioral sciences that have contributed to an understanding of relationship marketing. In seeking to provide a holistic understanding of the field, we incorporate contributions from the disciplines of marketing, management, psychology, and sociology. In building on our analysis, we synthesize our findings into a conceptual model that examines the systematic dimensions of relationship marketing. The article concludes by identifying key themes for contributors to the Journal of Relationship Marketing to consider going forward.

Conversion in late antiquity: Christianity, Islam, and beyond

The papers in this volume were presented at a Mellon-Sawyer Seminar held at the University of Oxford in 2009-2010, which sought to investigate side by side the two important movements of conversion that frame late antiquity: to Christianity at its start, and to Islam at the other end. Challenging the opposition between the two stereotypes of Islamic conversion as an intrinsically violent process, and Christian conversion as a fundamentally spiritual one, the papers seek to isolate the behaviours and circumstances that made conversion both such a common and such a contested phenomenon. The spread of Buddhism in Asia in broadly the same period serves as an external comparator that was not caught in the net of the Abrahamic religions. The volume is organised around several themes, reflecting the concerns of the initial project with the articulation between norm and practice, the role of authorities and institutions, and the social and individual fluidity on the ground. Debates, discussions, and the expression of norms and principles about conversion conversion are not rare in societies experiencing religious change, and the first section of the book examines some of the main issues brought up by surviving sources. This is followed by three sections examining different aspects of how those principles were - or were not - put into practice: how conversion was handled by the state, how it was continuously redefined by individual ambivalence and cultural fluidity, and how it was enshrined through different forms of institutionalization. Finally, a topographical coda examines the effects of religious change on the iconic holy city of Jerusalem.

Written Cypriot Greek in online chat: Usage and attitudes

This paper investigates the attitudes of Greek-Cypriot internet users towards written Cypriot Greek (CG) in online chat. CG does not have a standard official orthography and it is only used in informal oral communication. With the emergence of computer-mediated communication (CMC), a novel Romanized form of CG is used instead of Standard Greek (SG) in online environments (Themistocleous 2005). To investigate language attitudes, an online questionnaire was distributed electronically to Greek-Cypriot internet users. The results show that the majority of the informants have positive attitudes towards written CG, a practice that goes against the results of previous attitudinal surveys. In this paper, I demonstrate how the internet can influence and change the attitudes of Greek-Cypriots towards their regional variety. It is argued that the unconventional and norm-free character of CMC allows internet users to use their non-standard variety in a domain where the standard would be expected to be used.

Responsibility effects in decision making under risk

We systematically explore decision situations in which a decision maker bears responsibility for somebody else's outcomes as well as for her own in situations of payoff equality. In the gain domain we confirm the intuition that being responsible for somebody else's payoffs increases risk aversion. This is however not attributable to a 'cautious shift' as often thought. Indeed, looking at risk attitudes in the loss domain, we find an increase in risk seeking under responsibility. This raises issues about the nature of various decision biases under risk, and to what extent changed behavior under responsibility may depend on a social norm of caution in situations of responsibility versus naive corrections from perceived biases. To further explore this issue, we designed a second experiment to explore risk-taking behavior for gain prospects offering very small or very large probabilities of winning. For large probabilities, we find increased risk aversion, thus confirming our earlier finding. For small probabilities however, we find an increase of risk seeking under conditions of responsibility. The latter finding thus discredits hypotheses of a social rule dictating caution under responsibility, and can be explained through flexible self-correction models predicting an accentuation of the fourfold pattern of risk attitudes predicted by prospect theory. An additional accountability mechanism does not change risk behavior, except for mixed prospects, in which it reduces loss aversion. This indicates that loss aversion is of a fundamentally different nature than probability weighting or utility curvature. Implications for debiasing are discussed.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

On the structure of infinity-harmonic maps

Let H ∈ C 2(ℝ N×n ), H ≥ 0. The PDE system arises as the Euler-Lagrange PDE of vectorial variational problems for the functional E ∞(u, Ω) = ‖H(Du)‖ L ∞(Ω) defined on maps u: Ω ⊆ ℝ n → ℝ N . (1) first appeared in the author's recent work. The scalar case though has a long history initiated by Aronsson. Herein we study the solutions of (1) with emphasis on the case of n = 2 ≤ N with H the Euclidean norm on ℝ N×n , which we call the “∞-Laplacian”. By establishing a rigidity theorem for rank-one maps of independent interest, we analyse a phenomenon of separation of the solutions to phases with qualitatively different behaviour. As a corollary, we extend to N ≥ 2 the Aronsson-Evans-Yu theorem regarding non existence of zeros of |Du| and prove a maximum principle. We further characterise all H for which (1) is elliptic and also study the initial value problem for the ODE system arising for n = 1 but with H(·, u, u′) depending on all the arguments.

Antecedents of travellers' electronic word-of-mouth communication

Electronic word-of-mouth (eWOM) is recognised as a means of interpersonal communication and a powerful marketing tool. However, previous studies have focussed on related motivations, and limited attention has been given to understanding the antecedents of eWOM communication behaviour in the travel industry. This study proposes a full and partial mediation model, which brings together for the first time three key antecedents: adoption of electronic communication technology, consumer dis/satisfaction with travel consumption experience, and subjective norm. The model aims to understand the impact of these antecedents on travellers' attitude towards eWOM communication and intention to use eWOM communication media. The data were collected from international travellers (n = 524), and structural equation modelling is used to test the conceptual framework. The findings of the study suggest that overall attitude towards eWOM communication partially mediates the impact of the traveller's adoption of electronic communication technology and subjective norm, and fully mediates the impact of consumer dis/satisfaction with travel consumption experience on travellers' intention to use eWOM communication media.

Symbolic consumption of tourism destination brands

Electronic word-of-mouth (eWOM) is recognised as a means of interpersonal communication and a powerful marketing tool. However, previous studies have focussed on related motivations, and limited attention has been given to understanding the antecedents of eWOM communication behaviour in the travel industry. This study proposes a full and partial mediation model, which brings together for the first time three key antecedents: adoption of electronic communication technology, consumer dis/satisfaction with travel consumption experience, and subjective norm. The model aims to understand the impact of these antecedents on travellers' attitude towards eWOM communication and intention to use eWOM communication media. The data were collected from international travellers (n = 524), and structural equation modelling is used to test the conceptual framework. The findings of the study suggest that overall attitude towards eWOM communication partially mediates the impact of the traveller's adoption of electronic communication technology and subjective norm, and fully mediates the impact of consumer dis/satisfaction with travel consumption experience on travellers' intention to use eWOM communication media.