A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure

Lepton Acceleration in Pulsar Wind Nebulae

Pulsar Wind Nebulae (PWNe) act as calorimeters for the relativistic pair winds emanating from within the pulsar light cylinder. Their radiative dissipation in various wavebands is significantly different from that of their pulsar central engines: the broadband spectra of PWNe possess characteristics distinct from those of pulsars, thereby demanding a site of lepton acceleration remote from the pulsar magnetosphere. A principal candidate for this locale is the pulsar wind termination shock, a putatively highly-oblique, ultra-relativistic MHD discontinuity. This paper summarizes key characteristics of relativistic shock acceleration germane to PWNe, using predominantly Monte Carlo simulation techniques that compare well with semi-analytic solutions of the diffusion-convection equation. The array of potential spectral indices for the pair distribution function is explored, defining how these depend critically on the parameters of the turbulent plasma in the shock environs. Injection efficiencies into the acceleration process are also addressed. Informative constraints on the frequency of particle scattering and the level of field turbulence are identified using the multiwavelength observations of selected PWNe. These suggest that the termination shock can be comfortably invoked as a principal injector of energetic leptons into PWNe without resorting to unrealistic properties for the shock layer turbulence or MHD structure.Comment: 19 pages, 5 figures, invited review to appear in Proc. of the inaugural ICREA Workshop on "The High-Energy Emission from Pulsars and their Systems" (2010), eds. N. Rea and D. Torres, (Springer Astrophysics and Space Science series

Associations between HIV-RNA-based indicators and virological and clinical outcomes

OBJECTIVES: To evaluate and compare the performance of six HIV-RNA-based quality of care indicators for predicting short-term and long-term outcomes. DESIGN: Multinational cohort study. METHODS: We included EuroSIDA patients on antiretroviral therapy (ART) with ≥3viral load (VL) measurements after baseline (the latest of 01/01/2001 or entry into EuroSIDA). Using multivariate Poisson regression we modelled the association between short-term (resistance, triple-class failure) and long-term (all-cause mortality, any AIDS/non-AIDS clinical event) outcomes and the indicators: (i)viraemia copy years (VCY), (ii) Consecutive months with VL ≥50 copies/mL, (iii) percentage of time on ART spent fully suppressed (%FS), (iv) stable on ART, (v)48 weeks snapshot, and (vi) current VL. Indicators were compared using area under the ROC curve (AUC) and different measures of model fit. RESULTS: Adjusted incidence rate ratios for all outcomes tended to increase with increasing VCY, number of consecutive months with VL ≥50 copies/mL, current VL and with lower %FS, but the gradient of increased risk was weak across strata. None of the indicators reliably identified those at risk of long-term outcomes (AUC 0.54-0.58), but performed consistently better with short-term outcomes (triple class failure [AUC 0.67-0.76]) and resistance [AUC 0.64-0.79]). Goodness of fitvariedwith the outcome evaluated, but differences between indicators were small. CONCLUSIONS: Differences between quality of care indicators were small and no indicator performed consistently better than current VL. Given the simplicity in assessing and interpreting this indicator, wepropose to use current VL when HIV-RNA-based indicators are used to evaluate the efficacy of ART programs

Evaluation of a standard provision versus an autonomy promotive exercise referral programme: rationale and study design

Background The National Institute of Clinical Excellence in the UK has recommended that the effectiveness of ongoing exercise referral schemes to promote physical activity should be examined in research trials. Recent empirical evidence in health care and physical activity promotion contexts provides a foundation for testing the utility of a Self Determination Theory (SDT) -based exercise referral consultation. Methods/Design Design: An exploratory cluster randomised controlled trial comparing standard provision exercise on prescription with a Self Determination Theory-based (SDT) exercise on prescription intervention. Participants: 347 people referred to the Birmingham Exercise on Prescription scheme between November 2007 and July 2008. The 13 exercise on prescription sites in Birmingham were randomised to current practice (n=7) or to the SDT-based intervention (n=6). Outcomes measured at 3 and 6-months: Minutes of moderate or vigorous physical activity per week assessed using the 7-day Physical Activity Recall; physical health: blood pressure and weight; health status measured using the Dartmouth CO-OP charts; anxiety and depression measured by the Hospital Anxiety and Depression Scale and vitality measured by the subjective vitality score; motivation and processes of change: perceptions of autonomy support from the advisor, satisfaction of the needs for competence, autonomy, and relatedness via physical activity, and motivational regulations for exercise. Discussion This trial will determine whether an exercise referral programme based on Self Determination Theory increases physical activity and other health outcomes compared to a standard programme and will test the underlying SDT-based process model (perceived autonomy support, need satisfaction, motivation regulations, outcomes) via structural equation modelling. Trial registration The trial is registered as Current Controlled trials ISRCTN07682833

Collective Animal Behavior from Bayesian Estimation and Probability Matching

Animals living in groups make movement decisions that depend, among other factors, on social interactions with other group members. Our present understanding of social rules in animal collectives is based on empirical fits to observations and we lack first-principles approaches that allow their derivation. Here we show that patterns of collective decisions can be derived from the basic ability of animals to make probabilistic estimations in the presence of uncertainty. We build a decision-making model with two stages: Bayesian estimation and probabilistic matching.
In the first stage, each animal makes a Bayesian estimation of which behavior is best to perform taking into account personal information about the environment and social information collected by observing the behaviors of other animals. In the probability matching stage, each animal chooses a behavior with a probability given by the Bayesian estimation that this behavior is the most appropriate one. This model derives very simple rules of interaction in animal collectives that depend only on two types of reliability parameters, one that each animal assigns to the other animals and another given by the quality of the non-social information. We test our model by obtaining theoretically a rich set of observed collective patterns of decisions in three-spined sticklebacks, Gasterosteus aculeatus, a shoaling fish species. The quantitative link shown between probabilistic estimation and collective rules of behavior allows a better contact with other fields such as foraging, mate selection, neurobiology and psychology, and gives predictions for experiments directly testing the relationship between estimation and collective behavior

Effectiveness of vocational interventions for gaining paid work for people living with mild to moderate mental health conditions: Systematic review and meta-analysis

Objectives: To evaluate the effectiveness of vocational interventions to help people living with mild to moderate mental health conditions gain paid work. Methods: Systematic review of international, peer-reviewed literature. Development of the prepublished protocol and search strategy was done in consultation with stakeholder reference groups consisting of people with lived experience of long-term conditions, advocates and clinicians. We searched academic databases MEDLINE, EMBASE, PsychINFO, AMED, CINAHL, Proquest Dissertations and Theses database, and Business Source Complete for controlled trials comparing a specific vocational intervention against a control intervention or usual care, published between 1 January 2004 and 1 August 2019. Two authors independently screened search results, extracted data and appraised studies using the Cochrane risk of bias tool. Results: Eleven studies met inclusion criteria. Seven studies investigated Individual Placement and Support (IPS) modified for people who were not in intensive mental health treatment services. These studies occurred settings such as community vocational rehabilitation services, a housing programme and community mental health services. The studies provided very low quality evidence that people who receive IPS-style vocational rehabilitation are more likely to gain competitive employment than people who receive usual care (risk ratio 1.70, 95% CI 1.23 to 2.34, seven studies, 1611 participants). The remaining four studies considered cognitive behavioural therapy or specific vocational rehabilitation interventions designed to fit a unique context. There was insufficient evidence from these studies to draw conclusions regarding the effectiveness of non-IPS forms of vocational rehabilitation for people with mild to moderate mental health conditions. Discussion: The meta-analysis showed a clear intervention effect but low precision, and more high-quality studies are needed in this field. There is currently very low quality evidence that IPS-style intervention results in more participants in competitive employment compared with &lsquo;usual care&rsquo; control groups in populations with mild to moderate mental health conditions.</jats:sec

Emergent dynamic chirality in a thermally driven artificial spin ratchet

Modern nanofabrication techniques have opened the possibility to create novel functional materials, whose properties transcend those of their constituent elements. In particular, tuning the magnetostatic interactions in geometrically frustrated arrangements of nanoelements called artificial spin ice1, 2 can lead to specific collective behaviour3, including emergent magnetic monopoles4, 5, charge screening6, 7 and transport8, 9, as well as magnonic response10, 11, 12. Here, we demonstrate a spin-ice-based active material in which energy is converted into unidirectional dynamics. Using X-ray photoemission electron microscopy we show that the collective rotation of the average magnetization proceeds in a unique sense during thermal relaxation. Our simulations demonstrate that this emergent chiral behaviour is driven by the topology of the magnetostatic field at the edges of the nanomagnet array, resulting in an asymmetric energy landscape. In addition, a bias field can be used to modify the sense of rotation of the average magnetization. This opens the possibility of implementing a magnetic Brownian ratchet13, 14, which may find applications in novel nanoscale devices, such as magnetic nanomotors, actuators, sensors or memory cells

Calibration of myocardial T2 and T1 against iron concentration.

BACKGROUND: The assessment of myocardial iron using T2* cardiovascular magnetic resonance (CMR) has been validated and calibrated, and is in clinical use. However, there is very limited data assessing the relaxation parameters T1 and T2 for measurement of human myocardial iron. METHODS: Twelve hearts were examined from transfusion-dependent patients: 11 with end-stage heart failure, either following death (n=7) or cardiac transplantation (n=4), and 1 heart from a patient who died from a stroke with no cardiac iron loading. Ex-vivo R1 and R2 measurements (R1=1/T1 and R2=1/T2) at 1.5 Tesla were compared with myocardial iron concentration measured using inductively coupled plasma atomic emission spectroscopy. RESULTS: From a single myocardial slice in formalin which was repeatedly examined, a modest decrease in T2 was observed with time, from mean (± SD) 23.7 ± 0.93 ms at baseline (13 days after death and formalin fixation) to 18.5 ± 1.41 ms at day 566 (p<0.001). Raw T2 values were therefore adjusted to correct for this fall over time. Myocardial R2 was correlated with iron concentration [Fe] (R2 0.566, p<0.001), but the correlation was stronger between LnR2 and Ln[Fe] (R2 0.790, p<0.001). The relation was [Fe] = 5081•(T2)-2.22 between T2 (ms) and myocardial iron (mg/g dry weight). Analysis of T1 proved challenging with a dichotomous distribution of T1, with very short T1 (mean 72.3 ± 25.8 ms) that was independent of iron concentration in all hearts stored in formalin for greater than 12 months. In the remaining hearts stored for <10 weeks prior to scanning, LnR1 and iron concentration were correlated but with marked scatter (R2 0.517, p<0.001). A linear relationship was present between T1 and T2 in the hearts stored for a short period (R2 0.657, p<0.001). CONCLUSION: Myocardial T2 correlates well with myocardial iron concentration, which raises the possibility that T2 may provide additive information to T2* for patients with myocardial siderosis. However, ex-vivo T1 measurements are less reliable due to the severe chemical effects of formalin on T1 shortening, and therefore T1 calibration may only be practical from in-vivo human studies

Observation of associated near-side and away-side long-range correlations in √sNN=5.02 TeV proton-lead collisions with the ATLAS detector

Two-particle correlations in relative azimuthal angle (Δϕ) and pseudorapidity (Δη) are measured in √sNN=5.02  TeV p+Pb collisions using the ATLAS detector at the LHC. The measurements are performed using approximately 1  μb-1 of data as a function of transverse momentum (pT) and the transverse energy (ΣETPb) summed over 3.1<η<4.9 in the direction of the Pb beam. The correlation function, constructed from charged particles, exhibits a long-range (2<|Δη|<5) “near-side” (Δϕ∼0) correlation that grows rapidly with increasing ΣETPb. A long-range “away-side” (Δϕ∼π) correlation, obtained by subtracting the expected contributions from recoiling dijets and other sources estimated using events with small ΣETPb, is found to match the near-side correlation in magnitude, shape (in Δη and Δϕ) and ΣETPb dependence. The resultant Δϕ correlation is approximately symmetric about π/2, and is consistent with a dominant cos⁡2Δϕ modulation for all ΣETPb ranges and particle pT

Search for new phenomena in final states with an energetic jet and large missing transverse momentum in pp collisions at √ s = 8 TeV with the ATLAS detector

Results of a search for new phenomena in final states with an energetic jet and large missing transverse momentum are reported. The search uses 20.3 fb−1 of √ s = 8 TeV data collected in 2012 with the ATLAS detector at the LHC. Events are required to have at least one jet with pT > 120 GeV and no leptons. Nine signal regions are considered with increasing missing transverse momentum requirements between Emiss T > 150 GeV and Emiss T > 700 GeV. Good agreement is observed between the number of events in data and Standard Model expectations. The results are translated into exclusion limits on models with either large extra spatial dimensions, pair production of weakly interacting dark matter candidates, or production of very light gravitinos in a gauge-mediated supersymmetric model. In addition, limits on the production of an invisibly decaying Higgs-like boson leading to similar topologies in the final state are presente