Generalised Mixability, Constant Regret, and Bayesian Updating

Mixability of a loss is known to characterise when constant regret bounds are achievable in games of prediction with expert advice through the use of Vovk's aggregating algorithm. We provide a new interpretation of mixability via convex analysis that highlights the role of the Kullback-Leibler divergence in its definition. This naturally generalises to what we call $\Phi$-mixability where the Bregman divergence $D_\Phi$ replaces the KL divergence. We prove that losses that are $\Phi$-mixable also enjoy constant regret bounds via a generalised aggregating algorithm that is similar to mirror descent.Comment: 12 page

Generalized Mixability via Entropic Duality

Mixability is a property of a loss which characterizes when fast convergence is possible in the game of prediction with expert advice. We show that a key property of mixability generalizes, and the exp and log operations present in the usual theory are not as special as one might have thought. In doing this we introduce a more general notion of $\Phi$-mixability where $\Phi$ is a general entropy (\ie, any convex function on probabilities). We show how a property shared by the convex dual of any such entropy yields a natural algorithm (the minimizer of a regret bound) which, analogous to the classical aggregating algorithm, is guaranteed a constant regret when used with $\Phi$-mixable losses. We characterize precisely which $\Phi$ have $\Phi$-mixable losses and put forward a number of conjectures about the optimality and relationships between different choices of entropy.Comment: 20 pages, 1 figure. Supersedes the work in arXiv:1403.2433 [cs.LG

Correlation induced non-Abelian quantum holonomies

In the context of two-particle interferometry, we construct a parallel transport condition that is based on the maximization of coincidence intensity with respect to local unitary operations on one of the subsystems. The dependence on correlation is investigated and it is found that the holonomy group is generally non-Abelian, but Abelian for uncorrelated systems. It is found that our framework contains the L\'{e}vay geometric phase [2004 {\it J. Phys. A: Math. Gen.} {\bf 37} 1821] in the case of two-qubit systems undergoing local SU(2) evolutions.Comment: Minor corrections; journal reference adde

Early warning signals of tipping points in periodically forced systems

This is the final version of the article. Available from the European Geosciences Union via the DOI in this record.The prospect of finding generic early warning signals of an approaching tipping point in a complex system has generated much interest recently. Existing methods are predicated on a separation of timescales between the system studied and its forcing. However, many systems, including several candidate tipping elements in the climate system, are forced periodically at a timescale comparable to their internal dynamics. Here we use alternative early warning signals of tipping points due to local bifurcations in systems subjected to periodic forcing whose timescale is similar to the period of the forcing. These systems are not in, or close to, a fixed point. Instead their steady state is described by a periodic attractor. For these systems, phase lag and amplification of the system response can provide early warning signals, based on a linear dynamics approximation. Furthermore, the Fourier spectrum of the system's time series reveals harmonics of the forcing period in the system response whose amplitude is related to how nonlinear the system's response is becoming with nonlinear effects becoming more prominent closer to a bifurcation. We apply these indicators as well as a return map analysis to a simple conceptual system and satellite observations of Arctic sea ice area, the latter conjectured to have a bifurcation type tipping point. We find no detectable signal of the Arctic sea ice approaching a local bifurcation.The research leading to these results has received funding from the European Union Seventh Framework Programme FP7/2007-2013 under grant agreement no. 603864 (HELIX). We are grateful to Peter Ashwin, Peter Cox, Michel Crucifix, Vasilis Dakos, Henk Dijkstra, Jan Sieber, Marten Scheffer and Appy Sluijs for the fruitful discussions over beers and balls

Does a monetary incentive improve the response to a postal questionnaire in a randomised controlled trial? : the MINT incentive study

Background: Sending a monetary incentive with postal questionnaires has been found to improve the proportion of responders, in research in non-healthcare settings. However, there is little research on use of incentives to improve follow-up rates in clinical trials, and existing studies are inconclusive. We conducted a randomised trial among participants in the Managing Injuries of the Neck Trial (MINT) to investigate the effects on the proportion of questionnaires returned and overall non-response of sending a £5 gift voucher with a follow-up questionnaire. Methods: Participants in MINT were randomised to receive either: (a) a £5 gift voucher (incentive group) or (b) no gift voucher (no incentive group), with their 4 month or 8 month follow-up questionnaire. We recorded, for each group, the number of questionnaires returned, the number returned without any chasing from the study office, the overall number of non-responders (after all chasing efforts by the study office), and the costs of following up each group. Results: 2144 participants were randomised, 1070 to the incentive group and 1074 to the no incentive group. The proportion of questionnaires returned (RR 1.10 (95% CI 1.05, 1.16)) and the proportion returned without chasing (RR 1.14 (95% CI 1.05, 1.24) were higher in the incentive group, and the overall non-response rate was lower (RR 0.68 (95% CI 0.53, 0.87)). Adjustment for injury severity and hospital of recruitment to MINT made no difference to these results, and there were no differences in results between the 4-month and 8-month follow up questionnaires. Analysis of costs suggested a cost of £67.29 per additional questionnaire returned. Conclusion: Monetary incentives may be an effective way to increase the proportion of postal questionnaires returned and minimise loss to follow-up in clinical trials

Decadal global temperature variability increases strongly with climate sensitivity

Climate-related risks are dependent not only on the warming trend from GHGs, but also on the variability about the trend. However, assessment of the impacts of climate change tends to focus on the ultimate level of global warming1, only occasionally on the rate of global warming, and rarely on variability about the trend. Here we show that models that are more sensitive to GHGs emissions (that is, higher equilibrium climate sensitivity (ECS)) also have higher temperature variability on timescales of several years to several decades2. Counter-intuitively, high-sensitivity climates, as well as having a higher chance of rapid decadal warming, are also more likely to have had historical ‘hiatus’ periods than lower-sensitivity climates. Cooling or hiatus decades over the historical period, which have been relatively uncommon, are more than twice as likely in a high-ECS world (ECS = 4.5 K) compared with a low-ECS world (ECS = 1.5 K). As ECS also affects the background warming rate under future scenarios with unmitigated anthropogenic forcing, the probability of a hyper-warming decade—over ten times the mean rate of global warming for the twentieth century—is even more sensitive to ECS

Cardiovascular disease biomarkers are associated with declining renal function in type 2 diabetes

Aims/hypothesis: We investigated whether biochemical cardiovascular risk factors and/or markers of subclinical cardiovascular disease were associated with the development of reduced renal function in people with type 2 diabetes. Methods: A cohort of 1066 Scottish men and women aged 60–74 years with type 2 diabetes from the Edinburgh Type 2 Diabetes Study were followed up for a median of 6.7 years. New-onset reduced renal function was defined as two eGFRs <60 ml−1 min−1 (1.73 m)−2 at least 3 months apart with a > 25% decline from baseline eGFR. Ankle brachial pressure index (ABI), N-terminal pro-B-type natriuretic peptide (NT-proBNP) and high-sensitivity troponin T (hsTnT) were measured at baseline. Pulse wave velocity (PWV) and carotid intima media thickness were measured 1 year into follow-up. Data were analysed using Cox proportional hazards models. Results: A total of 119 participants developed reduced renal function during follow-up. ABI, PWV, NT-proBNP and hsTnT were all associated with onset of decline in renal function following adjustment for age and sex. These associations were attenuated after adjustment for additional diabetes renal disease risk factors (systolic BP, baseline eGFR, albumin:creatinine ratio and smoking pack-years), with the exception of hsTnT which remained independently associated (HR 1.51 [95% CI 1.22, 1.87]). Inclusion of hsTnT in a predictive model improved the continuous net reclassification index by 0.165 (0.008, 0.286). Conclusions/interpretation: Our findings demonstrate an association between hsTnT, a marker of subclinical cardiac ischaemia, and subsequent renal function decline. Further research is required to establish the predictive value of hsTnT and response to intervention

A national survey of clinical practice for the management of whiplash-associated disorders in UK emergency departments

Objective: To undertake a national survey to determine current practice for the management of whiplash injuries in UK emergency departments (ED). Methods: Postal questionnaire survey. 316 lead consultants from all UK ED with annual new attendances of over 50 000 people were asked to indicate the use of a range of treatments and the frequency with which these treatments were used. Samples of written advice were requested and content analysis was conducted and compared with survey responses. Results: The response rate was 79% (251/316). The intervention most frequently used was verbal advice to exercise, reported by 84% of respondents for most or all cases, and advice against the use of a collar (83%). Other treatments reported as being used frequently were written advice and anti-inflammatory medication. 106 consultants (42%) provided a sample of written materials. Reference to expected recovery and encouragement for early return to activities were included in less than 6%. Nearly 50% of written materials contained information on how to use a soft collar and 61% contained information on solicitors and pursuing a personal injury claim. There were important differences between reported verbal behaviours and written advice. Conclusion: Verbal advice is the primary method for managing whiplash injuries in ED and is usually supplemented by written advice. Within individual hospitals there is a lack of consistency between verbal and written advice. The promotion of personal injury claims is a common feature of written advice. Research is required to develop effective and consistent models of advice