Constructing good deals in discrete time arbitrage-free dynamic pricing models

Recent literature has proved that many classical pricing models (Black and Scholes, Heston, etc.) and risk measures (V aR, CV aR, etc.) may lead to “pathological meaningless situations”, since traders can build sequences of portfolios whose risk leveltends to −infinity and whose expected return tends to +infinity, i.e., (risk = −infinity, return = +infinity). Such a sequence of strategies may be called “good deal”. This paper focuses on the risk measures V aR and CV aR and analyzes this caveat in a discrete time complete pricing model. Under quite general conditions the explicit expression of a good deal is given, and its sensitivity with respect to some possible measurement errors is provided too. We point out that a critical property is the absence of short sales. In such a case we first construct a “shadow riskless asset” (SRA) without short sales and then the good deal is given by borrowing more and more money so as to invest in the SRA. It is also shown that the SRA is interested by itself, even if there are short selling restrictions.

OPTIMAX 2014 - Radiation dose and image quality optimisation in medical imaging

Medical imaging is a powerful diagnostic tool. Consequently, the number of medical images taken has increased vastly over the past few decades. The most common medical imaging techniques use X-radiation as the primary investigative tool. The main limitation of using X-radiation is associated with the risk of developing cancers. Alongside this, technology has advanced and more centres now use CT scanners; these can incur significant radiation burdens compared with traditional X-ray imaging systems. The net effect is that the population radiation burden is rising steadily. Risk arising from X-radiation for diagnostic medical purposes needs minimising and one way to achieve this is through reducing radiation dose whilst optimising image quality. All ages are affected by risk from X-radiation however the increasing population age highlights the elderly as a new group that may require consideration. Of greatest concern are paediatric patients: firstly they are more sensitive to radiation; secondly their younger age means that the potential detriment to this group is greater. Containment of radiation exposure falls to a number of professionals within medical fields, from those who request imaging to those who produce the image. These staff are supported in their radiation protection role by engineers, physicists and technicians. It is important to realise that radiation protection is currently a major European focus of interest and minimum competence levels in radiation protection for radiographers have been defined through the integrated activities of the EU consortium called MEDRAPET. The outcomes of this project have been used by the European Federation of Radiographer Societies to describe the European Qualifications Framework levels for radiographers in radiation protection. Though variations exist between European countries radiographers and nuclear medicine technologists are normally the professional groups who are responsible for exposing screening populations and patients to X-radiation. As part of their training they learn fundamental principles of radiation protection and theoretical and practical approaches to dose minimisation. However dose minimisation is complex – it is not simply about reducing X-radiation without taking into account major contextual factors. These factors relate to the real world of clinical imaging and include the need to measure clinical image quality and lesion visibility when applying X-radiation dose reduction strategies. This requires the use of validated psychological and physics techniques to measure clinical image quality and lesion perceptibility.

Equilibrium distributions of discrete non-autonomous graphs

We introduce the notions of equilibrium distribution and time of convergence in discrete non-autonomous graphs. Under some conditions we give an estimate to the convergence time to the equilibrium distribution using the second largest eigenvalue of some matrices associated with the system.

Optimisation of exposure parameters for spinal curvature measurements in paediatric radiography

This review aims to identify strategies to optimise radiography practice using digital technologies, for full spine studies on paediatrics focusing particularly on methods used to diagnose and measure severity of spinal curvatures. The literature search was performed on different databases (PubMed, Google Scholar and ScienceDirect) and relevant websites (e.g., American College of Radiology and International Commission on Radiological Protection) to identify guidelines and recent studies focused on dose optimisation in paediatrics using digital technologies. Plain radiography was identified as the most accurate method. The American College of Radiology (ACR) and European Commission (EC) provided two guidelines that were identified as the most relevant to the subject. The ACR guidelines were updated in 2014; however these guidelines do not provide detailed guidance on technical exposure parameters. The EC guidelines are more complete but are dedicated to screen film systems. Other studies provided reviews on the several exposure parameters that should be included for optimisation, such as tube current, tube voltage and source-to-image distance; however, only explored few of these parameters and not all of them together. One publication explored all parameters together but this was for adults only. Due to lack of literature on exposure parameters for paediatrics, more research is required to guide and harmonise practice.

Optimisation of paediatrics computed radiography for full spine curvature measurements using a phantom: a pilot study

Aim: Optimise a set of exposure factors, with the lowest effective dose, to delineate spinal curvature with the modified Cobb method in a full spine using computed radiography (CR) for a 5-year-old paediatric anthropomorphic phantom. Methods: Images were acquired by varying a set of parameters: positions (antero-posterior (AP), posteroanterior (PA) and lateral), kilo-voltage peak (kVp) (66-90), source-to-image distance (SID) (150 to 200cm), broad focus and the use of a grid (grid in/out) to analyse the impact on E and image quality (IQ). IQ was analysed applying two approaches: objective [contrast-to-noise-ratio/(CNR] and perceptual, using 5 observers. Monte-Carlo modelling was used for dose estimation. Cohen’s Kappa coefficient was used to calculate inter-observer-variability. The angle was measured using Cobb’s method on lateral projections under different imaging conditions. Results: PA promoted the lowest effective dose (0.013 mSv) compared to AP (0.048 mSv) and lateral (0.025 mSv). The exposure parameters that allowed lower dose were 200cm SID, 90 kVp, broad focus and grid out for paediatrics using an Agfa CR system. Thirty-seven images were assessed for IQ and thirty-two were classified adequate. Cobb angle measurements varied between 16°±2.9 and 19.9°±0.9. Conclusion: Cobb angle measurements can be performed using the lowest dose with a low contrast-tonoise ratio. The variation on measurements for this was ±2.9° and this is within the range of acceptable clinical error without impact on clinical diagnosis. Further work is recommended on improvement to the sample size and a more robust perceptual IQ assessment protocol for observers.

Spectral invariants of periodic nonautonomous discrete dynamical systems

For an interval map, the poles of the Artin-Mazur zeta function provide topological invariants which are closely connected to topological entropy. It is known that for a time-periodic nonautonomous dynamical system F with period p, the p-th power [zeta(F) (z)](p) of its zeta function is meromorphic in the unit disk. Unlike in the autonomous case, where the zeta function zeta(f)(z) only has poles in the unit disk, in the p-periodic nonautonomous case [zeta(F)(z)](p) may have zeros. In this paper we introduce the concept of spectral invariants of p-periodic nonautonomous discrete dynamical systems and study the role played by the zeros of [zeta(F)(z)](p) in this context. As we will see, these zeros play an important role in the spectral classification of these systems.

Exploiting the bin-class histograms for feature selection on discrete data

In machine learning and pattern recognition tasks, the use of feature discretization techniques may have several advantages. The discretized features may hold enough information for the learning task at hand, while ignoring minor fluctuations that are irrelevant or harmful for that task. The discretized features have more compact representations that may yield both better accuracy and lower training time, as compared to the use of the original features. However, in many cases, mainly with medium and high-dimensional data, the large number of features usually implies that there is some redundancy among them. Thus, we may further apply feature selection (FS) techniques on the discrete data, keeping the most relevant features, while discarding the irrelevant and redundant ones. In this paper, we propose relevance and redundancy criteria for supervised feature selection techniques on discrete data. These criteria are applied to the bin-class histograms of the discrete features. The experimental results, on public benchmark data, show that the proposed criteria can achieve better accuracy than widely used relevance and redundancy criteria, such as mutual information and the Fisher ratio.