Buy low, sell high

We consider online trading in a single security with the objective of getting rich when its price ever exhibits a large upcrossing, without risking bankruptcy. We investigate payoff guarantees that are expressed in terms of the extremity of the upcrossings. We obtain an exact and elegant characterisation of the guarantees that can be achieved. Moreover, we derive a simple canonical strategy for each attainable guarantee.

Evaluative decision-making for high-quality professional development: Cultivating an evaluative stance

Unprecedented policy attention to early childhood education internationally has highlighted the crucial need for a skilled early years workforce. Consequently, professional development of early years educators has become a global policy imperative. At the same time, many maintain that professional development research has reached an impasse. In this paper, we offer a new approach to addressing this impasse. In contrast to calls for a redesign of comparative studies of professional development programs, or for the refinement of researcher-constructed professional development evaluation frameworks, we argue the need to cultivate what we refer to as an ‘evaluative stance’ amongst all involved in making decisions about professional development in the early years – from senior bureaucrats with responsibilities for funding professional development programs to individual educators with choices about which professional development opportunities to take up. Drawing on three bodies of literature -- evaluation capacity building, personal epistemology, and co-production -- that, for the most part, have been overlooked with respect to early years professional learning this paper proposes a conceptual framework to explain why cultivating an evaluative stance in professional development decision-making has rich possibilities for systemic, sustainable, and transformative change in early years education.

High order unconditionally stable difference schemes for the Riesz space-fractional telegraph equation

In this paper, a class of unconditionally stable difference schemes based on the Pad´e approximation is presented for the Riesz space-fractional telegraph equation. Firstly, we introduce a new variable to transform the original dfferential equation to an equivalent differential equation system. Then, we apply a second order fractional central difference scheme to discretise the Riesz space-fractional operator. Finally, we use (1, 1), (2, 2) and (3, 3) Pad´e approximations to give a fully discrete difference scheme for the resulting linear system of ordinary differential equations. Matrix analysis is used to show the unconditional stability of the proposed algorithms. Two examples with known exact solutions are chosen to assess the proposed difference schemes. Numerical results demonstrate that these schemes provide accurate and efficient methods for solving a space-fractional hyperbolic equation.

Model refinement through high-performance computing: an agent-based HIV example

Background Recent advances in Immunology highlighted the importance of local properties on the overall progression of HIV infection. In particular, the gastrointestinal tract is seen as a key area during early infection, and the massive cell depletion associated with it may influence subsequent disease progression. This motivated the development of a large-scale agent-based model. Results Lymph nodes are explicitly implemented, and considerations on parallel computing permit large simulations and the inclusion of local features. The results obtained show that GI tract inclusion in the model leads to an accelerated disease progression, during both the early stages and the long-term evolution, compared to a theoretical, uniform model. Conclusions These results confirm the potential of treatment policies currently under investigation, which focus on this region. They also highlight the potential of this modelling framework, incorporating both agent-based and network-based components, in the context of complex systems where scaling-up alone does not result in models providing additional insights.

Complexity and high-end computing in biology and medicine

Biomedical systems involve a large number of entities and intricate interactions between these. Their direct analysis is, therefore, difficult, and it is often necessary to rely on computational models. These models require significant resources and parallel computing solutions. These approaches are particularly suited, given parallel aspects in the nature of biomedical systems. Model hybridisation also permits the integration and simultaneous study of multiple aspects and scales of these systems, thus providing an efficient platform for multidisciplinary research.