Bounds on the entanglement of two-qutrit systems from fixed marginals

We discuss the problem of characterizing upper bounds on entanglement in a bipartite quantum system when only the reduced density matrices (marginals) are known. In particular, starting from the known two-qubit case, we propose a family of candidates for maximally entangled mixed states with respect to fixed marginals for two qutrits. These states are extremal in the convex set of two-qutrit states with fixed marginals. Moreover, it is shown that they are always quasidistillable. As a by-product we prove that any maximally correlated state that is quasidistillable must be pure. Our observations for two qutrits are supported by numerical analysis

Bayesian regression discontinuity designs: Incorporating clinical knowledge in the causal analysis of primary care data

The regression discontinuity (RD) design is a quasi-experimental design that estimates the causal effects of a treatment by exploiting naturally occurring treatment rules. It can be applied in any context where a particular treatment or intervention is administered according to a pre-specified rule linked to a continuous variable. Such thresholds are common in primary care drug prescription where the RD design can be used to estimate the causal effect of medication in the general population. Such results can then be contrasted to those obtained from randomised controlled trials (RCTs) and inform prescription policy and guidelines based on a more realistic and less expensive context. In this paper we focus on statins, a class of cholesterol-lowering drugs, however, the methodology can be applied to many other drugs provided these are prescribed in accordance to pre-determined guidelines. NHS guidelines state that statins should be prescribed to patients with 10 year cardiovascular disease risk scores in excess of 20%. If we consider patients whose scores are close to this threshold we find that there is an element of random variation in both the risk score itself and its measurement. We can thus consider the threshold a randomising device assigning the prescription to units just above the threshold and withholds it from those just below. Thus we are effectively replicating the conditions of an RCT in the area around the threshold, removing or at least mitigating confounding. We frame the RD design in the language of conditional independence which clarifies the assumptions necessary to apply it to data, and which makes the links with instrumental variables clear. We also have context specific knowledge about the expected sizes of the effects of statin prescription and are thus able to incorporate this into Bayesian models by formulating informative priors on our causal parameters.Comment: 21 pages, 5 figures, 2 table

Bayesian hierarchical model for the prediction of football results

The problem of modelling football data has become increasingly popular in the last few years and many different models have been proposed with the aim of estimating the characteristics that bring a team to lose or win a game, or to predict the score of a particular match. We propose a Bayesian hierarchical model to fulfil both these aims and test its predictive strength based on data about the Italian Serie A 1991-1992 championship. To overcome the issue of overshrinkage produced by the Bayesian hierarchical model, we specify a more complex mixture model that results in a better fit to the observed data. We test its performance using an example of the Italian Serie A 2007-2008 championship

Estimating the Expected Value of Partial Perfect Information in Health Economic Evaluations using Integrated Nested Laplace Approximation

The Expected Value of Perfect Partial Information (EVPPI) is a decision-theoretic measure of the "cost" of parametric uncertainty in decision making used principally in health economic decision making. Despite this decision-theoretic grounding, the uptake of EVPPI calculations in practice has been slow. This is in part due to the prohibitive computational time required to estimate the EVPPI via Monte Carlo simulations. However, recent developments have demonstrated that the EVPPI can be estimated by non-parametric regression methods, which have significantly decreased the computation time required to approximate the EVPPI. Under certain circumstances, high-dimensional Gaussian Process regression is suggested, but this can still be prohibitively expensive. Applying fast computation methods developed in spatial statistics using Integrated Nested Laplace Approximations (INLA) and projecting from a high-dimensional into a low-dimensional input space allows us to decrease the computation time for fitting these high-dimensional Gaussian Processes, often substantially. We demonstrate that the EVPPI calculated using our method for Gaussian Process regression is in line with the standard Gaussian Process regression method and that despite the apparent methodological complexity of this new method, R functions are available in the package BCEA to implement it simply and efficiently

Calculating the Expected Value of Sample Information in Practice: Considerations from Three Case Studies

Investing efficiently in future research to improve policy decisions is an important goal. Expected Value of Sample Information (EVSI) can be used to select the specific design and sample size of a proposed study by assessing the benefit of a range of different studies. Estimating EVSI with the standard nested Monte Carlo algorithm has a notoriously high computational burden, especially when using a complex decision model or when optimizing over study sample sizes and designs. Therefore, a number of more efficient EVSI approximation methods have been developed. However, these approximation methods have not been compared and therefore their relative advantages and disadvantages are not clear. A consortium of EVSI researchers, including the developers of several approximation methods, compared four EVSI methods using three previously published health economic models. The examples were chosen to represent a range of real-world contexts, including situations with multiple study outcomes, missing data, and data from an observational rather than a randomized study. The computational speed and accuracy of each method were compared, and the relative advantages and implementation challenges of the methods were highlighted. In each example, the approximation methods took minutes or hours to achieve reasonably accurate EVSI estimates, whereas the traditional Monte Carlo method took weeks. Specific methods are particularly suited to problems where we wish to compare multiple proposed sample sizes, when the proposed sample size is large, or when the health economic model is computationally expensive. All the evaluated methods gave estimates similar to those given by traditional Monte Carlo, suggesting that EVSI can now be efficiently computed with confidence in realistic examples.Comment: 11 pages, 3 figure

A Virtual Conversational Agent for Teens with Autism: Experimental Results and Design Lessons

We present the design of an online social skills development interface for teenagers with autism spectrum disorder (ASD). The interface is intended to enable private conversation practice anywhere, anytime using a web-browser. Users converse informally with a virtual agent, receiving feedback on nonverbal cues in real-time, and summary feedback. The prototype was developed in consultation with an expert UX designer, two psychologists, and a pediatrician. Using the data from 47 individuals, feedback and dialogue generation were automated using a hidden Markov model and a schema-driven dialogue manager capable of handling multi-topic conversations. We conducted a study with nine high-functioning ASD teenagers. Through a thematic analysis of post-experiment interviews, identified several key design considerations, notably: 1) Users should be fully briefed at the outset about the purpose and limitations of the system, to avoid unrealistic expectations. 2) An interface should incorporate positive acknowledgment of behavior change. 3) Realistic appearance of a virtual agent and responsiveness are important in engaging users. 4) Conversation personalization, for instance in prompting laconic users for more input and reciprocal questions, would help the teenagers engage for longer terms and increase the system's utility

Five questions to consider before conducting a stepped wedge trial.

Researchers should consider five questions before starting a stepped wedge trial. Why are you planning one? Researchers sometimes think that stepped wedge trials are useful when there is little doubt about the benefit of the intervention being tested. However, if the primary reason for an intervention is to measure its effect, without equipoise there is no ethical justification for delaying implementation in some clusters. By contrast, if you are undertaking pragmatic research, where the primary reason for rolling out the intervention is for it to exert its benefits, and if phased implementation is inevitable, a stepped wedge trial is a valid option and provides better evidence than most non-randomized evaluations. What design will you use? Two common stepped wedge designs are based on the recruitment of a closed or open cohort. In both, individuals may experience both control and intervention conditions and you should be concerned about carry-over effects. In a third, continuous-recruitment, short-exposure design, individuals are recruited as they become eligible and experience either control or intervention condition, but not both. How will you conduct the primary analysis? In stepped wedge trials, control of confounding factors through secular variation is essential. 'Vertical' approaches preserve randomization and compare outcomes between randomized groups within periods. 'Horizontal' approaches compare outcomes before and after crossover to the intervention condition. Most analysis models used in practice combine both types of comparison. The appropriate analytic strategy should be considered on a case-by-case basis. How large will your trial be? Standard sample size calculations for cluster randomized trials do not accommodate the specific features of stepped wedge trials. Methods exist for many stepped wedge designs, but simulation-based calculations provide the greatest flexibility. In some scenarios, such as when the intracluster correlation coefficient is moderate or high, or the cluster size is large, a stepped wedge trial may require fewer clusters than a parallel cluster trial. How will you report your trial? Stepped wedge trials are currently challenging to report using CONSORT principles. Researchers should consider how to demonstrate balance achieved by randomization and how to describe trends for outcomes in both intervention and control clusters

A novel method for measuring bowel motility and velocity with dynamic magnetic resonance imaging in two and three dimensions

Increasingly, dynamic magnetic resonance imaging (MRI) has potential as a noninvasive and accessible tool for diagnosing and monitoring gastrointestinal motility in healthy and diseased bowel. However, current MRI methods of measuring bowel motility have limitations: requiring bowel preparation or long acquisition times; providing mainly surrogate measures of motion; and estimating bowel-wall movement in just two dimensions. In this proof-of-concept study we apply a method that provides a quantitative measure of motion within the bowel, in both two and three dimensions, using existing, vendor-implemented MRI pulse sequences with minimal bowel preparation. This method uses a minimised cost function to fit linear vectors in the spatial and temporal domains. It is sensitised to the spatial scale of the bowel and aims to address issues relating to the low signal-to-noise in high-temporal resolution dynamic MRI scans, previously compensated for by performing thick-slice (10-mm) two-dimensional (2D) coronal scans. We applied both 2D and three-dimensional (3D) scanning protocols in two healthy volunteers. For 2D scanning, analysis yielded bi-modal velocity peaks, with a mean antegrade motion of 5.5 mm/s and an additional peak at similar to 9 mm/s corresponding to longitudinal peristalsis, as supported by intraoperative data from the literature. Furthermore, 3D scans indicated a mean forward motion of 4.7 mm/s, and degrees of antegrade and retrograde motion were also established. These measures show promise for the noninvasive assessment of bowel motility, and have the potential to be tuned to particular regions of interest and behaviours within the bowel.Radiolog

Relating ASD symptoms to well-being:Moving across different construct levels

BACKGROUND: Little is known about the specific factors that contribute to the well-being (WB) of individuals with autism spectrum disorder (ASD). A plausible hypothesis is that ASD symptomatology has a direct negative effect on WB. In the current study, the emerging tools of network analysis allow to explore the functional interdependencies between specific symptoms of ASD and domains of WB in a multivariate framework. We illustrate how studying both higher-order (total score) and lower-order (subscale) representations of ASD symptomatology can clarify the interrelations of factors relevant for domains of WB. METHODS: We estimated network structures on three different construct levels for ASD symptomatology, as assessed with the Adult Social Behavior Questionnaire (item, subscale, total score), relating them to daily functioning (DF) and subjective WB in 323 adult individuals with clinically identified ASD (aged 17-70 years). For these networks, we assessed the importance of specific factors in the network structure. RESULTS: When focusing on the highest representation level of ASD symptomatology (i.e. a total score), we found a negative connection between ASD symptom severity and domains of WB. However, zooming in on lower representation levels of ASD symptomatology revealed that this connection was mainly funnelled by ASD symptoms related to insistence on sameness and experiencing reduced contact and that those symptom scales, in turn, impact different domains of WB. CONCLUSIONS: Zooming in across construct levels of ASD symptom severity into subscales of ASD symptoms can provide us with important insights into how specific domains of ASD symptoms relate to specific domains of DF and WB