Effect of patient age on management decisions in breast cancer: consensus from a national consultation

This qualitative study investigated the attitudes, perceptions, and practices of breast cancer specialists with reference to the effect of patient age on management decisions in breast cancer, and attempted to identify national consensus on this issue. One hundred thirty-three relevant specialists, including 75 surgeons and 43 oncologists, participated in a virtual consultation using e-mailed questionnaires and open-ended discussion documents, culminating in the development of proposed consensus statements sent to participants for validation. A strong consensus was seen in favor of incorporating minimum standards of diagnostic services, treatment, and care for older patients with breast cancer into relevant national guidance, endorsed by professional bodies. Similarly, an overwhelming majority of participants agreed that simple, evidence-based protocols or guidelines on standardizing assessment of biological and chronological age should be produced by the National Institute for Health and Clinical Excellence and the Scottish Medicines Consortium, developed in collaboration with specialist oncogeriatricians, and endorsed by professional bodies. A further recommendation that all breast cancer patient treatment and diagnostic procedures be undertaken in light of up-to-date, relevant scientific data met with majority support. This study was successful in gauging national specialist opinion regarding the effect of patient age on management decisions in breast cancer in the U.K.

Operator space structure of JC*-triples and TROs, I

We embark upon a systematic investigation of operator space structure of JC*-triples via a study of the TROs (ternary rings of operators) they generate. Our approach is to introduce and develop a variety of universal objects, including universal TROs, by which means we are able to describe all possible operator space structures of a JC*-triple. Via the concept of reversibility we obtain characterisations of universal TROs over a wide range of examples. We apply our results to obtain explicit descriptions of operator space structures of Cartan factors regardless of dimension

On the operator space structure of Hilbert spaces

Operator spaces of Hilbertian JC∗ -triples E are considered in the light of the universal ternary ring of operators (TRO) introduced in recent work. For these operator spaces, it is shown that their triple envelope (in the sense of Hamana) is the TRO they generate, that a complete isometry between any two of them is always the restriction of a TRO isomorphism and that distinct operator space structures on a fixed E are never completely isometric. In the infinite-dimensional cases, operator space structure is shown to be characterized by severe and definite restrictions upon finite-dimensional subspaces. Injective envelopes are explicitly computed.

Universally reversible JC*-triples and operator spaces

Abstract. We prove that the vast majority of JC∗-triples satisfy the condition of universal reversibility. Our characterisation is that a JC∗-triple is universally reversible if and only if it has no triple homomorphisms onto Hilbert spaces of dimension greater than two nor onto spin factors of dimension greater than four. We establish corresponding characterisations in the cases of JW∗-triples and of TROs (regarded as JC∗-triples). We show that the distinct natural operator space structures on a universally reversible JC∗-triple E are in bijective correspondence with a distinguished class of ideals in its universal TRO, identify the Shilov boundaries of these operator spaces and prove that E has a unique natural operator space structure precisely when E contains no ideal isometric to a nonabelian TRO. We deduce some decomposition and completely contractive properties of triple homomorphisms on TROs.

Accounting for the economic risk, caused by variation in disease severity, in fungicide dose decisions: exemplified for Mycosphaerella graminicola on winter wheat

A method is presented to calculate economic optimum fungicide doses accounting for the risk-aversion of growers responding to variability in disease severity between crops. Simple dose-response and disease-yield loss functions are used to estimate net disease-related costs (fungicide cost, plus disease-induced yield loss) as a function of dose and untreated severity. With fairly general assumptions about the shapes of the probability distribution of disease severity and the other functions involved, we show that a choice of fungicide dose which minimises net costs on average across seasons results in occasional large net costs caused by inadequate control in high disease seasons. This may be unacceptable to a grower with limited capital. A risk-averse grower can choose to reduce the size and frequency of such losses by applying a higher dose as insurance. For example, a grower may decide to accept ‘high loss’ years one year in ten or one year in twenty (i.e. specifying a proportion of years in which disease severity and net costs will be above a specified level). Our analysis shows that taking into account disease severity variation and risk-aversion will usually increase the dose applied by an economically rational grower. The analysis is illustrated with data on septoria tritici leaf blotch of wheat caused by Mycosphaerella graminicola. Observations from untreated field plots at sites across England over three years were used to estimate the probability distribution of disease severities at mid-grain filling. In the absence of a fully reliable disease forecasting scheme, reducing the frequency of ‘high loss’ years requires substantially higher doses to be applied to all crops. Disease resistant cultivars reduce both the optimal dose at all levels of risk and the disease-related costs at all doses.

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

First order k-th moment finite element analysis of nonlinear operator equations with stochastic data

We develop and analyze a class of efficient Galerkin approximation methods for uncertainty quantification of nonlinear operator equations. The algorithms are based on sparse Galerkin discretizations of tensorized linearizations at nominal parameters. Specifically, we consider abstract, nonlinear, parametric operator equations J(\alpha ,u)=0 for random input \alpha (\omega ) with almost sure realizations in a neighborhood of a nominal input parameter \alpha _0. Under some structural assumptions on the parameter dependence, we prove existence and uniqueness of a random solution, u(\omega ) = S(\alpha (\omega )). We derive a multilinear, tensorized operator equation for the deterministic computation of k-th order statistical moments of the random solution's fluctuations u(\omega ) - S(\alpha _0). We introduce and analyse sparse tensor Galerkin discretization schemes for the efficient, deterministic computation of the k-th statistical moment equation. We prove a shift theorem for the k-point correlation equation in anisotropic smoothness scales and deduce that sparse tensor Galerkin discretizations of this equation converge in accuracy vs. complexity which equals, up to logarithmic terms, that of the Galerkin discretization of a single instance of the mean field problem. We illustrate the abstract theory for nonstationary diffusion problems in random domains.

Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

The influence of environmental policy on the decisions of managers to adopt G-SCM practices

This article explores the reasons that affect the decisions of managers of firms to adopt management practices in order to green their supply chain management. Under the context of environmental policy, the relationship between policy instruments (‘command and control’, market-based, and self-regulated) and the decisions of managers to adopt green supply chain management (G-SCM) practices is examined. The results show that in some cases the environmental legislation, market-based instruments and self-regulated incentives could play a critical role in the decisions of managers to adopt some specific G-SCM practices, while in other cases environmental policy instruments have not seemed to affect the decisions of managers regarding some other G-SCM practices.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Eigenvalues of a one-dimensional Dirac operator pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.

Risk allocation in a public–private partnership: a case study of construction and operation of kindergartens in Kazakhstan

In Kazakhstan, a transitional nation in Central Asia, the development of public–private partnerships (PPPs) is at its early stage and increasingly of strategic importance. This case study investigates risk allocation in an ongoing project: the construction and operation of 11 kindergartens in the city of Karaganda in the concession form for 14 years. Drawing on a conceptual framework of effective risk allocation, the study identifies principal PPP risks, provides a critical assessment of how and in what way each partner bears a certain risk, highlights the reasons underpinning risk allocation decisions and delineates the lessons learned. The findings show that the government has effectively transferred most risks to the private sector partner, whilst both partners share the demand risk of childcare services and the project default risk. The strong elements of risk allocation include clear assignment of parties’ responsibilities, streamlined financing schemes and incentives to complete the main project phases on time. However, risk allocation has missed an opportunity to create incentives for service quality improvements and take advantage of economies of scale. The most controversial element of risk allocation, as the study finds, is a revenue stream that an operator is supposed to receive from the provision of services unrelated to childcare, as neither partner is able to mitigate this revenue risk. The article concludes that in the kindergartens’ PPP, the government has achieved almost complete transfer of risks to the private sector partner. However, the costs of transfer are extensive government financial outlays that seriously compromise the PPP value for money.

The mediating effect of environmental and ethical behaviour on supply chain partnership decisions and management appreciation of supplier partnership risks

Green supply chain management and environmental and ethical behaviour (EEB), a major component of corporate responsibility (CR), are rapidly developing fields in research and practice. The influence and effect of EEB at the functional level, however, is under-researched. Similarly, the management of risk in the supply chain has become a practical concern for many firms. It is important that managers have a good understanding of the risks associated with supplier partnerships. This paper examines the effect of firms’ investment in EEB as part of corporate social responsibility in mediating the relationship between supply chain partnership (SCP) and management appreciation of the risk of partnering. We hypothesise that simply entering into a SCP does not facilitate an appreciation of the risk of partnering and may even hamper such awareness. However, such an appreciation of the risk is facilitated through CR’s environmental and stakeholder management ethos. The study contributes further by separating risk into distinct relational and performance components. The results of a firm-level survey confirm the mediation effect, highlighting the value to supply chain strategy and design of investing in EEB on three fronts: building internal awareness, monitoring and sharing best practice.