Weighted entropy and optimal portfolios for risk-averse Kelly investments

Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are twofold: (A) under certain conditions, the logarithmic growth rate leads to a supermartingale, and (B) the optimal (martingale) investment strategy is a proportional betting. We focus on properties of the optimal portfolios and discuss a number of simple examples extending the well-known Kelly betting scheme. An important restriction is that the investment does not exceed the current capital value and allows the trader to cover the worst possible losses. The paper deals with a class of discrete-time models. A continuous-time extension is a topic of an ongoing study

Empirical study of correlated survival times for recurrent events with proportional hazards margins and the effect of correlation and censoring.

Background: In longitudinal studies where subjects experience recurrent incidents over a period of time, such as respiratory infections, fever or diarrhea, statistical methods are required to take into account the within-subject correlation. Methods: For repeated events data with censored failure, the independent increment (AG), marginal (WLW) and conditional (PWP) models are three multiple failure models that generalize Cox"s proportional hazard model. In this paper, we revise the efficiency, accuracy and robustness of all three models under simulated scenarios with varying degrees of within-subject correlation, censoring levels, maximum number of possible recurrences and sample size. We also study the methods performance on a real dataset from a cohort study with bronchial obstruction. Results: We find substantial differences between methods and there is not an optimal method. AG and PWP seem to be preferable to WLW for low correlation levels but the situation reverts for high correlations. Conclusions: All methods are stable in front of censoring, worsen with increasing recurrence levels and share a bias problem which, among other consequences, makes asymptotic normal confidence intervals not fully reliable, although they are well developed theoretically

Direct interaction between the Gulf Stream and the shelfbreak south of New England

© The Author(s), 2012. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Scientific Reports 2 (2012): 553, doi:10.1038/srep00553.Sea surface temperature imagery, satellite altimetry, and a surface drifter track reveal an unusual tilt in the Gulf Stream path that brought the Gulf Stream to 39.9°N near the Middle Atlantic Bight shelfbreak—200 km north of its mean position—in October 2011, while a large meander brought Gulf Stream water within 12 km of the shelfbreak in December 2011. Near-bottom temperature measurements from lobster traps on the outer continental shelf south of New England show distinct warming events (temperature increases exceeding 6°C) in November and December 2011. Moored profiler measurements over the continental slope show high salinities and temperatures, suggesting that the warm water on the continental shelf originated in the Gulf Stream. The combination of unusual water properties over the shelf and slope in late fall and the subsequent mild winter may affect seasonal stratification and habitat selection for marine life over the continental shelf in 2012.Profiler data were made available by the Ocean Observatory Initiative (OOI) during the construction phase of the project. The OOI is funded by the National Science Foundation and managed by the Consortium for Ocean Leadership. Drifter data were provided by Tim Shaw and David Calhoun at Cape Fear Community College.GGGwas supported by NSFGrant OCE-1129125. RET was supported by the Postdoctoral Scholar Program at the Woods Hole Oceanographic Institution, with funding provided by the Cooperative Institute for the North Atlantic Region. MA was supported by the Penzance Endowed Fund in Support of Assistant Scientists

Optimal leverage from non-ergodicity

In modern portfolio theory, the balancing of expected returns on investments against uncertainties in those returns is aided by the use of utility functions. The Kelly criterion offers another approach, rooted in information theory, that always implies logarithmic utility. The two approaches seem incompatible, too loosely or too tightly constraining investors' risk preferences, from their respective perspectives. The conflict can be understood on the basis that the multiplicative models used in both approaches are non-ergodic which leads to ensemble-average returns differing from time-average returns in single realizations. The classic treatments, from the very beginning of probability theory, use ensemble-averages, whereas the Kelly-result is obtained by considering time-averages. Maximizing the time-average growth rates for an investment defines an optimal leverage, whereas growth rates derived from ensemble-average returns depend linearly on leverage. The latter measure can thus incentivize investors to maximize leverage, which is detrimental to time-average growth and overall market stability. The Sharpe ratio is insensitive to leverage. Its relation to optimal leverage is discussed. A better understanding of the significance of time-irreversibility and non-ergodicity and the resulting bounds on leverage may help policy makers in reshaping financial risk controls.Comment: 17 pages, 3 figures. Updated figures and extended discussion of ergodicit

Optimal measurement of visual motion across spatial and temporal scales

Sensory systems use limited resources to mediate the perception of a great variety of objects and events. Here a normative framework is presented for exploring how the problem of efficient allocation of resources can be solved in visual perception. Starting with a basic property of every measurement, captured by Gabor's uncertainty relation about the location and frequency content of signals, prescriptions are developed for optimal allocation of sensors for reliable perception of visual motion. This study reveals that a large-scale characteristic of human vision (the spatiotemporal contrast sensitivity function) is similar to the optimal prescription, and it suggests that some previously puzzling phenomena of visual sensitivity, adaptation, and perceptual organization have simple principled explanations.Comment: 28 pages, 10 figures, 2 appendices; in press in Favorskaya MN and Jain LC (Eds), Computer Vision in Advanced Control Systems using Conventional and Intelligent Paradigms, Intelligent Systems Reference Library, Springer-Verlag, Berli

Increased Oxidative Burden Associated with Traffic Component of Ambient Particulate Matter at Roadside and Urban Background Schools Sites in London

As the incidence of respiratory and allergic symptoms has been reported to be increased in children attending schools in close proximity to busy roads, it was hypothesised that PM from roadside schools would display enhanced oxidative potential (OP). Two consecutive one-week air quality monitoring campaigns were conducted at seven school sampling sites, reflecting roadside and urban background in London. Chemical characteristics of size fractionated particulate matter (PM) samples were related to the capacity to drive biological oxidation reactions in a synthetic respiratory tract lining fluid. Contrary to hypothesised contrasts in particulate OP between school site types, no robust size-fractionated differences in OP were identified due high temporal variability in concentrations of PM components over the one-week sampling campaigns. For OP assessed both by ascorbate (OPAA m−3) and glutathione (OPGSH m−3) depletion, the highest OP per cubic metre of air was in the largest size fraction, PM1.9–10.2. However, when expressed per unit mass of particles OPAA µg−1 showed no significant dependence upon particle size, while OPGSH µg−1 had a tendency to increase with increasing particle size, paralleling increased concentrations of Fe, Ba and Cu. The two OP metrics were not significantly correlated with one another, suggesting that the glutathione and ascorbate depletion assays respond to different components of the particles. Ascorbate depletion per unit mass did not show the same dependence as for GSH and it is possible that other trace metals (Zn, Ni, V) or organic components which are enriched in the finer particle fractions, or the greater surface area of smaller particles, counter-balance the redox activity of Fe, Ba and Cu in the coarse particles. Further work with longer-term sampling and a larger suite of analytes is advised in order to better elucidate the determinants of oxidative potential, and to fuller explore the contrasts between site types.\ud \u

'Reaching the hard to reach' - lessons learned from the VCS (voluntary and community Sector). A qualitative study.

Background The notion 'hard to reach' is a contested and ambiguous term that is commonly used within the spheres of social care and health, especially in discourse around health and social inequalities. There is a need to address health inequalities and to engage in services the marginalized and socially excluded sectors of society. Methods This paper describes a pilot study involving interviews with representatives from eight Voluntary and Community Sector (VCS) organisations . The purpose of the study was to explore the notion of 'hard to reach' and perceptions of the barriers and facilitators to accessing services for 'hard to reach' groups from a voluntary and community sector perspective. Results The 'hard to reach' may include drug users, people living with HIV, people from sexual minority communities, asylum seekers, refugees, people from black and ethnic minority communities, and homeless people although defining the notion of the 'hard to reach' is not straight forward. It may be that certain groups resist engaging in treatment services and are deemed hard to reach by a particular service or from a societal stance. There are a number of potential barriers for people who may try and access services, including people having bad experiences in the past; location and opening times of services and how services are funded and managed. A number of areas of commonality are found in terms of how access to services for 'hard to reach' individuals and groups could be improved including: respectful treatment of service users, establishing trust with service users, offering service flexibility, partnership working with other organisations and harnessing service user involvement. Conclusions: If health services are to engage with groups that are deemed 'hard to reach' and marginalised from mainstream health services, the experiences and practices for engagement from within the VCS may serve as useful lessons for service improvement for statutory health services

Case Report: Disseminated, rifampicin resistant Mycobacterium bovis (BCG) infection in an immunocompromised child.

Background: Bacillus Calmette-Guérin (BCG) is a live-attenuated vaccine used world-wide for prevention of tuberculosis disease. In some immunocompromised hosts it has the potential to cause disease. As with other members of the M. tuberculosis complex it has the potential for acquiring drug resistance. Methods: We reviewed 10 years of paediatric clinical BCG strains referred to our clinical microbiology laboratory in Oxford where they underwent whole genome sequencing. We present a case series comparing clinical, pathogen genetic and pathogen phenotypic data, and consider the clinical implications. Results: We identified 15 BCG isolates from 8 children under 16 years old. Only one child had clinical disease with the other seven reported as local inoculation-site reactions. Case 1 suffered disseminated disease secondary to an undiagnosed IL-12/IFNγ receptor defect and the BCG isolates evolved two different rifampicin resistance mutations. Across all 15 isolates, phenotypic resistance to each first line drug was seen. Conclusions: BCG is a safe and effective vaccine in children. Most clinical specimens in our series were not related to disease. However, in the context of rare pathogen-specific immunocompromise, BCG can cause pathology and acquire drug resistance under selection from therapy