Quantile mechanics II: changes of variables in Monte Carlo methods and GPU-optimised normal quantiles

With financial modelling requiring a better understanding of model risk, it is helpful to be able to vary assumptions about underlying probability distributions in an efficient manner, preferably without the noise induced by resampling distributions managed by Monte Carlo methods. This paper presents differential equations and solution methods for the functions of the form Q(x) = F −1(G(x)), where F and G are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples from one distribution into samples from another. The method may be developed analytically for certain special cases, and illuminate the idea that it is a more precise form of the traditional Cornish–Fisher expansion. In this manner the model risk of distributional risk may be assessed free of the Monte Carlo noise associated with resampling. The method may also be regarded as providing both analytical and numerical bases for doing more precise Cornish–Fisher transformations. Examples are given of equations for converting normal samples to Student t, and converting exponential to normal. In the case of the normal distribution, the change of variables employed allows the sampling to take place to good accuracy based on a single rational approximation over a very wide range of sample space. The avoidance of branching statements is of use in optimal graphics processing unit (GPU) computations as it avoids the effect of branch divergence. We give a branch-free normal quantile that offers performance improvements in a GPU environment while retaining the best precision characteristics of well-known methods. We also offer models with low probability branch divergence. Comparisons of new and existing forms are made on Nvidia GeForce GTX Titan and Tesla C2050 GPUs. We argue that in both single- and double-precisions, the change-of-variables approach offers the most GPU-optimal Gaussian quantile yet, working faster than the Cuda 5.5 built-in function

Phase Control of Trapped Ion Quantum Gates

There are several known schemes for entangling trapped ion quantum bits for large-scale quantum computation. Most are based on an interaction between the ions and external optical fields, coupling internal qubit states of trapped-ions to their Coulomb-coupled motion. In this paper, we examine the sensitivity of these motional gate schemes to phase fluctuations introduced through noisy external control fields, and suggest techniques to suppress the resulting phase decoherence.Comment: 21 pages 12 figure

Notes about the Caratheodory number

In this paper we give sufficient conditions for a compactum in $\mathbb R^n$ to have Carath\'{e}odory number less than $n+1$, generalizing an old result of Fenchel. Then we prove the corresponding versions of the colorful Carath\'{e}odory theorem and give a Tverberg type theorem for families of convex compacta

Happiness and life satisfaction in Rwanda

This study investigated predictors of happiness and life satisfaction in Rwanda. Data from the World Values Survey and gathered from 3 030 Rwandese (age ranging 16 to 90 years, mean age = 34.2, SD = 12.7; females = 50.5%) were pooled for the analysis. For the comparison, international World Values Survey data were utilised. A fixed effects multilevel regression model was used to predict happiness and life satisfaction from gender, health, socio-economic, and some subjective measures. Males had greater self-rated happiness and life satisfaction scores than females. State of health and sense of freedom of choice predicted both happiness and life satisfaction. Valuing of friends, weekly religious attendance, and national pride positively predicted happiness, whereas household’s financial satisfaction, full-time employment, high-income group, being a student, and sense of trust predicted life satisfaction. This study suggests that health status, household’s financial satisfaction and emancipative values could maximise subjective well-being in Rwanda

Precautionary Regulation in Europe and the United States: A Quantitative Comparison

Much attention has been addressed to the question of whether Europe or the United States adopts a more precautionary stance to the regulation of potential environmental, health, and safety risks. Some commentators suggest that Europe is more risk-averse and precautionary, whereas the US is seen as more risk-taking and optimistic about the prospects for new technology. Others suggest that the US is more precautionary because its regulatory process is more legalistic and adversarial, while Europe is more lax and corporatist in its regulations. The flip-flop hypothesis claims that the US was more precautionary than Europe in the 1970s and early 1980s, and that Europe has become more precautionary since then. We examine the levels and trends in regulation of environmental, health, and safety risks since 1970. Unlike previous research, which has studied only a small set of prominent cases selected non-randomly, we develop a comprehensive list of almost 3,000 risks and code the relative stringency of regulation in Europe and the US for each of 100 risks randomly selected from that list for each year from 1970 through 2004. Our results suggest that: (a) averaging over risks, there is no significant difference in relative precaution over the period, (b) weakly consistent with the flip-flop hypothesis, there is some evidence of a modest shift toward greater relative precaution of European regulation since about 1990, although (c) there is a diversity of trends across risks, of which the most common is no change in relative precaution (including cases where Europe and the US are equally precautionary and where Europe or the US has been consistently more precautionary). The overall finding is of a mixed and diverse pattern of relative transatlantic precaution over the period

Early Changes in Cortical Emotion Processing Circuits after Mild Traumatic Brain Injury from Motor Vehicle Collision

Mild traumatic brain injury (mTBI) patients frequently experience emotion dysregulation symptoms, including post-traumatic stress. Although mTBI likely affects cortical activation and structure, resulting in cognitive symptoms after mTBI, early effects of mTBI on cortical emotion processing circuits have rarely been examined. To assess early mTBI effects on cortical functional and structural components of emotion processing, we assessed cortical activation to fearful faces within the first 2 weeks after motor vehicle collision (MVC) in survivors who did and did not experience mTBI. We also examined the thicknesses of cortical regions with altered activation. MVC survivors with mTBI (n = 21) had significantly less activation in left superior parietal gyrus (SPG) (−5.9, −81.8, 33.8; p = 10−3.623), left medial orbitofrontal gyrus (mOFG) (−4.7, 36.1, −19.3; p = 10−3.231), and left and right lateral orbitofrontal gyri (lOFG) (left: −16.0, 41.4, −16.6; p = 10−2.573; right: 18.7, 22.7, −17.7; p = 10−2.764) than MVC survivors without mTBI (n = 23). SPG activation in mTBI survivors within 2 weeks after MVC was negatively correlated with subsequent post-traumatic stress symptom severity at 3 months (r = −0.68, p = 0.03). Finally, the SPG region was thinner in the mTBI survivors than in the non-mTBI survivors (F = 11.07, p = 0.002). These results suggest that early differences in activation and structure in cortical emotion processing circuits in trauma survivors who sustain mTBI may contribute to the development of emotion-related symptoms

Export of functional Streptomyces coelicolor alditol oxidase to the periplasm or cell surface of Escherichia coli and its application in whole-cell biocatalysis

Streptomyces coelicolor A3(2) alditol oxidase (AldO) is a soluble monomeric flavoprotein in which the flavin cofactor is covalently linked to the polypeptide chain. AldO displays high reactivity towards different polyols such as xylitol and sorbitol. These characteristics make AldO industrially relevant, but full biotechnological exploitation of this enzyme is at present restricted by laborious and costly purification steps. To eliminate the need for enzyme purification, this study describes a whole-cell AldO biocatalyst system. To this end, we have directed AldO to the periplasm or cell surface of Escherichia coli. For periplasmic export, AldO was fused to endogenous E. coli signal sequences known to direct their passenger proteins into the SecB, signal recognition particle (SRP), or Twin-arginine translocation (Tat) pathway. In addition, AldO was fused to an ice nucleation protein (INP)-based anchoring motif for surface display. The results show that Tat-exported AldO and INP-surface-displayed AldO are active. The Tat-based system was successfully employed in converting xylitol by whole cells, whereas the use of the INP-based system was most likely restricted by lipopolysaccharide LPS in wild-type cells. It is anticipated that these whole-cell systems will be a valuable tool for further biological and industrial exploitation of AldO and other cofactor-containing enzymes.

Post-mortem brain analyses of the Lothian Birth Cohort 1936:Extending lifetime cognitive and brain phenotyping to the level of the synapse

INTRODUCTION: Non-pathological, age-related cognitive decline varies markedly between individuals andplaces significant financial and emotional strain on people, their families and society as a whole.Understanding the differential age-related decline in brain function is critical not only for the development oftherapeutics to prolong cognitive health into old age, but also to gain insight into pathological ageing suchas Alzheimer’s disease. The Lothian Birth Cohort of 1936 (LBC1936) comprises a rare group of people forwhom there are childhood cognitive test scores and longitudinal cognitive data during older age, detailedstructural brain MRI, genome-wide genotyping, and a multitude of other biological, psycho-social, andepidemiological data. Synaptic integrity is a strong indicator of cognitive health in the human brain;however, until recently, it was prohibitively difficult to perform detailed analyses of synaptic and axonalstructure in human tissue sections. We have adapted a novel method of tissue preparation at autopsy toallow the study of human synapses from the LBC1936 cohort in unprecedented morphological andmolecular detail, using the high-resolution imaging techniques of array tomography and electronmicroscopy. This allows us to analyze the brain at sub-micron resolution to assess density, proteincomposition and health of synapses. Here we present data from the first donated LBC1936 brain andcompare our findings to Alzheimer’s diseased tissue to highlight the differences between healthy andpathological brain ageing. RESULTS: Our data indicates that compared to an Alzheimer’s disease patient, the cognitively normalLBC1936 participant had a remarkable degree of preservation of synaptic structures. However,morphological and molecular markers of degeneration in areas of the brain associated with cognition(prefrontal cortex, anterior cingulate cortex, and superior temporal gyrus) were observed. CONCLUSIONS: Our novel post-mortem protocol facilitates high-resolution neuropathological analysis of the well-characterized LBC1936 cohort, extending phenotyping beyond cognition and in vivo imaging to nowinclude neuropathological changes, at the level of single synapses. This approach offers an unprecedentedopportunity to study synaptic and axonal integrity during ageing and how it contributes to differences in agerelatedcognitive change. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s40478-015-0232-0) contains supplementary material, which is available to authorized users