An analysis of geometric uncertainty calculations for prostate radiotherapy in clinical practice.

Margins are used in radiotherapy to assist in the calculation of planning target volumes. These margins can be determined by analysing the geometric uncertainties inherent to the radiotherapy planning and delivery process. An important part of this process is the study of electronic portal images collected throughout the course of treatment. Set-up uncertainties were determined for prostate radiotherapy treatments at our previous site and the new purpose-built centre, with margins determined using a number of different methods. In addition, the potential effect of reducing the action level from 5 mm to 3 mm for changing a patient set-up, based on off-line bony anatomy-based portal image analysis, was studied. Margins generated using different methodologies were comparable. It was found that set-up errors were reduced following relocation to the new centre. Although a significant increase in the number of corrections to a patient's set-up was predicted if the action level was reduced from 5 mm to 3 mm, minimal reduction in patient set-up uncertainties would be seen as a consequence. Prescriptive geometric uncertainty analysis not only supports calculation and justification of the margins used clinically to generate planning target volumes, but may also best be used to monitor trends in clinical practice or audit changes introduced by new equipment, technology or practice. Simulations on existing data showed that a 3 mm rather than a 5 mm action level during off-line, bony anatomy-based portal imaging would have had a minimal benefit for the patients studied in this work.

Uncertainty and Sensitivity Analysis in Aircraft Operating Costs in Structural Design Optimization

The paper focuses on the development of an aircraft design optimization methodology that models uncertainty and sensitivity analysis in the tradeoff between manufacturing cost, structural requirements, andaircraft direct operating cost.Specifically,ratherthanonlylooking atmanufacturingcost, direct operatingcost is also consideredintermsof the impact of weight on fuel burn, in addition to the acquisition cost to be borne by the operator. Ultimately, there is a tradeoff between driving design according to minimal weight and driving it according to reduced manufacturing cost. Theanalysis of cost is facilitated withagenetic-causal cost-modeling methodology,andthe structural analysis is driven by numerical expressions of appropriate failure modes that use ESDU International reference data. However, a key contribution of the paper is to investigate the modeling of uncertainty and to perform a sensitivity analysis to investigate the robustness of the optimization methodology. Stochastic distributions are used to characterize manufacturing cost distributions, andMonteCarlo analysis is performed in modeling the impact of uncertainty on the cost modeling. The results are then used in a sensitivity analysis that incorporates the optimization methodology. In addition to investigating manufacturing cost variance, the sensitivity of the optimization to fuel burn cost and structural loading are also investigated. It is found that the consideration of manufacturing cost does make an impact and results in a different optimal design configuration from that delivered by the minimal-weight method. However, it was shown that at lower applied loads there is a threshold fuel burn cost at which the optimization process needs to reduce weight, and this threshold decreases with increasing load. The new optimal solution results in lower direct operating cost with a predicted savings of 640=m2 of fuselage skin over the life, relating to a rough order-of-magnitude direct operating cost savings of $500,000 for the fuselage alone of a small regional jet. Moreover, it was found through the uncertainty analysis that the principle was not sensitive to cost variance, although the margins do change.

Uncertainty, learning and growth

The paper extends Blackburn and Galindev's (Economics Letters, Vol. 79 (2003), pp. 417-421) stochastic growth model in which productivity growth entails both external and internal learning behaviour with a constant relative risk aversion utility function and productivity shocks. Consequently, the relationship between long-term growth and short-term volatility depends not only on the relative importance of each learning mechanism but also on a parameter measuring individuals' attitude towards risk.

Robust Dynamic Pricing Over Infinite Horizon in The Presence of Model Uncertainty( 2* Journal)

This paper studies a problem of dynamic pricing faced by a retailer with limited inventory, uncertain about the demand rate model, aiming to maximize expected discounted revenue over an infinite time horizon. The retailer doubts his demand model which is generated by historical data and views it as an approximation. Uncertainty in the demand rate model is represented by a notion of generalized relative entropy process, and the robust pricing problem is formulated as a two-player zero-sum stochastic differential game. The pricing policy is obtained through the Hamilton-Jacobi-Isaacs (HJI) equation. The existence and uniqueness of the solution of the HJI equation is shown and a verification theorem is proved to show that the solution of the HJI equation is indeed the value function of the pricing problem. The results are illustrated by an example with exponential nominal demand rate.

The Uncertainty of Experience: On George Brecht's Event Scores

George Brecht, an artist best known for his associations with Fluxus, is considered to have made significant contributions to emerging traditions of conceptual art and experimental music in the early 1960s. His Event scores, brief verbal scores that comprised lists of terms or open-ended instructions, provided a signature model for indeterminate composition and were ‘used extensively by virtually every Fluxus artist’. This article revisits Brecht’s early writings and research to argue that, while Event scores were adopted within Fluxus performance, they were intended as much more than performance devices. Specifically, Brecht conceived of his works as ‘structures of experience’ that, by revealing the underlying connections between chanced forms, could enable a kind of enlightenment rooted within an experience of a ‘unified reality’.