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

A randomised trial of adaptive pacing therapy, cognitive behaviour therapy, graded exercise, and specialist medical care for chronic fatigue syndrome (PACE): statistical analysis plan

BACKGROUND: The publication of protocols by medical journals is increasingly becoming an accepted means for promoting good quality research and maximising transparency. Recently, Finfer and Bellomo have suggested the publication of statistical analysis plans (SAPs).The aim of this paper is to make public and to report in detail the planned analyses that were approved by the Trial Steering Committee in May 2010 for the principal papers of the PACE (Pacing, graded Activity, and Cognitive behaviour therapy: a randomised Evaluation) trial, a treatment trial for chronic fatigue syndrome. It illustrates planned analyses of a complex intervention trial that allows for the impact of clustering by care providers, where multiple care-providers are present for each patient in some but not all arms of the trial. RESULTS: The trial design, objectives and data collection are reported. Considerations relating to blinding, samples, adherence to the protocol, stratification, centre and other clustering effects, missing data, multiplicity and compliance are described. Descriptive, interim and final analyses of the primary and secondary outcomes are then outlined. CONCLUSIONS: This SAP maximises transparency, providing a record of all planned analyses, and it may be a resource for those who are developing SAPs, acting as an illustrative example for teaching and methodological research. It is not the sum of the statistical analysis sections of the principal papers, being completed well before individual papers were drafted. TRIAL REGISTRATION: ISRCTN54285094 assigned 22 May 2003; First participant was randomised on 18 March 2005

Individual Eigenvalue Distributions for the Wilson Dirac Operator

We derive the distributions of individual eigenvalues for the Hermitian Wilson Dirac Operator D5 as well as for real eigenvalues of the Wilson Dirac Operator DW. The framework we provide is valid in the epsilon regime of chiral perturbation theory for any number of flavours Nf and for non-zero low energy constants W6, W7, W8. It is given as a perturbative expansion in terms of the k-point spectral density correlation functions and integrals thereof, which in some cases reduces to a Fredholm Pfaffian. For the real eigenvalues of DW at fixed chirality nu this expansion truncates after at most nu terms for small lattice spacing "a". Explicit examples for the distribution of the first and second eigenvalue are given in the microscopic domain as a truncated expansion of the Fredholm Pfaffian for quenched D5, where all k-point densities are explicitly known from random matrix theory. For the real eigenvalues of quenched DW at small "a" we illustrate our method by the finite expansion of the corresponding Fredholm determinant of size nu.Comment: 20 pages, 5 figures; v2: typos corrected, refs added and discussion of W6 and W7 extende

Outcomes following kidney transplantation in patients with sickle cell disease: The impact of automated exchange blood transfusion

There are over 12,000 people with sickle cell disease (SCD) in the UK, and 4–12% of patients who develop Sickle Cell Nephropathy (SCN) progress to End Stage Renal Disease (ESRD). Renal transplantation offers the best outcomes for these patients with but their access to transplantation is often limited. Regular automated exchange blood transfusions (EBT) reduce the complications of SCD and may improve outcomes. However, concerns over alloimmunisation limit its widespread implementation. In this retrospective multicenter study, data were collected on 34 SCD patients who received a kidney transplant across 6 London Hospitals between 1997 and 2017. 20/34 patients were on an EBT program, pre or post renal transplantation. Overall patient and graft survival were inferior to contemporaneous UK data in the ESRD population as a whole, a finding which is well-recognised. However, patient survival (CI 95%, p = 0.0032), graft survival and graft function were superior at all time-points in those who received EBT versus those who did not. 4/20 patients (20%) on EBT developed de novo donor specific antibodies (DSAs). 3/14 patients (21%) not on EBT developed de novo DSAs. The incidence of rejection in those on EBT was 5/18 (28%), as compared with 7/13 (54%) not on EBT. In conclusion, our data, while limited by an inevitably small sample size and differences in the date of transplantation, do suggest that long-term automated EBT post renal transplant is effective and safe, with improvement in graft and patient outcomes and no increase in antibody formation or graft rejection

Incidence and drug treatment of emotional distress after cancer diagnosis : a matched primary care case-control study

Notes This work is published under the standard license to publish agreement. After 12 months the work will become freely available and the license terms will switch to a Creative Commons Attribution-NonCommercial-Share Alike 3.0 Unported License.Peer reviewedPublisher PD

Combustion in thermonuclear supernova explosions

Type Ia supernovae are associated with thermonuclear explosions of white dwarf stars. Combustion processes convert material in nuclear reactions and release the energy required to explode the stars. At the same time, they produce the radioactive species that power radiation and give rise to the formation of the observables. Therefore, the physical mechanism of the combustion processes, as reviewed here, is the key to understand these astrophysical events. Theory establishes two distinct modes of propagation for combustion fronts: subsonic deflagrations and supersonic detonations. Both are assumed to play an important role in thermonuclear supernovae. The physical nature and theoretical models of deflagrations and detonations are discussed together with numerical implementations. A particular challenge arises due to the wide range of spatial scales involved in these phenomena. Neither the combustion waves nor their interaction with fluid flow and instabilities can be directly resolved in simulations. Substantial modeling effort is required to consistently capture such effects and the corresponding techniques are discussed in detail. They form the basis of modern multidimensional hydrodynamical simulations of thermonuclear supernova explosions. The problem of deflagration-to-detonation transitions in thermonuclear supernova explosions is briefly mentioned.Comment: Author version of chapter for 'Handbook of Supernovae,' edited by A. Alsabti and P. Murdin, Springer. 24 pages, 4 figure

The science of clinical practice: disease diagnosis or patient prognosis? Evidence about "what is likely to happen" should shape clinical practice.

BACKGROUND: Diagnosis is the traditional basis for decision-making in clinical practice. Evidence is often lacking about future benefits and harms of these decisions for patients diagnosed with and without disease. We propose that a model of clinical practice focused on patient prognosis and predicting the likelihood of future outcomes may be more useful. DISCUSSION: Disease diagnosis can provide crucial information for clinical decisions that influence outcome in serious acute illness. However, the central role of diagnosis in clinical practice is challenged by evidence that it does not always benefit patients and that factors other than disease are important in determining patient outcome. The concept of disease as a dichotomous 'yes' or 'no' is challenged by the frequent use of diagnostic indicators with continuous distributions, such as blood sugar, which are better understood as contributing information about the probability of a patient's future outcome. Moreover, many illnesses, such as chronic fatigue, cannot usefully be labelled from a disease-diagnosis perspective. In such cases, a prognostic model provides an alternative framework for clinical practice that extends beyond disease and diagnosis and incorporates a wide range of information to predict future patient outcomes and to guide decisions to improve them. Such information embraces non-disease factors and genetic and other biomarkers which influence outcome. SUMMARY: Patient prognosis can provide the framework for modern clinical practice to integrate information from the expanding biological, social, and clinical database for more effective and efficient care

The Effect of N-nitrosodimethylamine (NDMA) on Bax and Mcl-1 Expression in Human Neutrophils

In the present study we examined a role of pro-apoptotic Bax and anti-apoptotic Mcl-1 proteins, participating in the regulation of intrinsic apoptosis pathway in human neutrophils (PMNs) exposed to N-nitrosodimethylamine (NDMA), the environmental xenobiotic. For the purpose comparison, the same studies were conducted in autologous peripheral blood mononuclear cells (PBMCs). The production of cytochrome c by PMNs was also determined. A deficit of anti-apoptotic Mcl-1 and overexpression of the pro-apoptotic protein Bax suggest that the apoptosis process in human neutrophils exposed to NDMA is dependent on changes in the expression of these proteins. PMNs were more sensitive to NDMA than PBMCs

Singular values of the Dirac operator in dense QCD-like theories

We study the singular values of the Dirac operator in dense QCD-like theories at zero temperature. The Dirac singular values are real and nonnegative at any nonzero quark density. The scale of their spectrum is set by the diquark condensate, in contrast to the complex Dirac eigenvalues whose scale is set by the chiral condensate at low density and by the BCS gap at high density. We identify three different low-energy effective theories with diquark sources applicable at low, intermediate, and high density, together with their overlapping domains of validity. We derive a number of exact formulas for the Dirac singular values, including Banks-Casher-type relations for the diquark condensate, Smilga-Stern-type relations for the slope of the singular value density, and Leutwyler-Smilga-type sum rules for the inverse singular values. We construct random matrix theories and determine the form of the microscopic spectral correlation functions of the singular values for all nonzero quark densities. We also derive a rigorous index theorem for non-Hermitian Dirac operators. Our results can in principle be tested in lattice simulations.Comment: 3 references added, version published in JHE

Branch Mode Selection during Early Lung Development

Many organs of higher organisms, such as the vascular system, lung, kidney, pancreas, liver and glands, are heavily branched structures. The branching process during lung development has been studied in great detail and is remarkably stereotyped. The branched tree is generated by the sequential, non-random use of three geometrically simple modes of branching (domain branching, planar and orthogonal bifurcation). While many regulatory components and local interactions have been defined an integrated understanding of the regulatory network that controls the branching process is lacking. We have developed a deterministic, spatio-temporal differential-equation based model of the core signaling network that governs lung branching morphogenesis. The model focuses on the two key signaling factors that have been identified in experiments, fibroblast growth factor (FGF10) and sonic hedgehog (SHH) as well as the SHH receptor patched (Ptc). We show that the reported biochemical interactions give rise to a Schnakenberg-type Turing patterning mechanisms that allows us to reproduce experimental observations in wildtype and mutant mice. The kinetic parameters as well as the domain shape are based on experimental data where available. The developed model is robust to small absolute and large relative changes in the parameter values. At the same time there is a strong regulatory potential in that the switching between branching modes can be achieved by targeted changes in the parameter values. We note that the sequence of different branching events may also be the result of different growth speeds: fast growth triggers lateral branching while slow growth favours bifurcations in our model. We conclude that the FGF10-SHH-Ptc1 module is sufficient to generate pattern that correspond to the observed branching modesComment: Initially published at PLoS Comput Bio