Posterior Distribution Research Articles

Inferring stellar parameters and their uncertainties from high-resolution spectroscopy using invertible neural networks

New spectroscopic surveys will increase the number of astronomical objects in need of characterisation by more than an order of magnitude. Machine learning tools are required to address this data deluge in a fast and accurate fashion. Most machine learning algorithms cannot directly estimate error, making them unsuitable for reliable science. We aim to train a supervised deep-learning algorithm tailored for high-resolution observational stellar spectra. This algorithm accurately infers precise estimates while providing coherent estimates of uncertainties by leveraging information from both the neural network and the spectra. We trained a conditional invertible neural network (cINN) on observational spectroscopic data obtained from the GIRAFFE spectrograph (HR10 and HR21 setups) within the Gaia-ESO survey. A key feature of cINN is its ability to produce the Bayesian posterior distribution of parameters for each spectrum. By analysing this distribution, we inferred stellar parameters and their corresponding uncertainties. We carried out several tests to investigate how parameters are inferred and errors are estimated. We achieved an accuracy of 28K in $T_ eff $, 0.06 dex in $ g$, 0.03 dex in Fe/H $, and between 0.05 dex and 0.17 dex for the other abundances for high-quality spectra. Accuracy remains stable with low signal-to-noise ratio (between 5 and 25) spectra, with an accuracy of 39K in $T_ eff $, 0.08 dex in $ g$, and 0.05 dex in Fe/H $. The uncertainties obtained are well within the same order of magnitude. The network accurately reproduces astrophysical relationships both on the scale of the Milky Way and within smaller star clusters. We created a table containing the new parameters generated by our cINN. This neural network represents a compelling proposition for future astronomical surveys. These derived uncertainties are coherent and can therefore be reused in future works as Bayesian priors.

Exploiting the diversity of modeling methods to probe systematic biases in strong lensing analyses

Challenges inherent to high-resolution and high signal-to-noise data as well as model degeneracies can cause systematic biases in analyses of strong lens systems. In the past decade, the number of lens modeling methods has significantly increased, from purely analytical methods, to pixelated and non-parametric ones, or ones based on deep learning. We embraced this diversity by selecting different software packages and use them to blindly model independently simulated Hubble Space Telescope (HST) imaging data. To overcome the difficulties arising from using different codes and conventions, we used the COde-independent Organized LEns STandard (COOLEST) to store, compare, and release all models in a self-consistent and human-readable manner. From an ensemble of six modeling methods, we studied the recovery of the lens potential parameters and properties of the reconstructed source. In particular, we simulated and inferred parameters of an elliptical power-law mass distribution embedded in a shear field for the lens, while each modeling method reconstructs the source differently. We find that, overall, both lens and source properties are recovered reasonably well, but systematic biases arise in all methods. Interestingly, we do not observe that a single method is significantly more accurate than others, and the amount of bias largely depends on the specific lens or source property of interest. By combining posterior distributions from individual methods using equal weights, the maximal systematic biases on lens model parameters inferred from individual models are reduced by a factor of 5.4 on average. We investigated a selection of modeling effects that partly explain the observed biases, such as the cuspy nature of the background source and the accuracy of the point spread function. This work introduces, for the first time, a generic framework to compare and ease the combination of models obtained from different codes and methods, which will be key to retain accuracy in future strong lensing analyses.

Morphological and molecular analysis of Propanagrolaimus siweyae sp. n. (Nematoda: Panagrolaimidae) from Molepo dam, Limpopo Province, South Africa, and its relationship with water parameters

AbstractPanagrolaimidae members are bacterivorous with global distribution. There is no information on this species' morphology and molecular characterization in South Africa. During a survey of Molepo dam, Limpopo Province, a population of Propanagrolaimus nematodes belonging to the family Panagrolaimidae was recovered and determined utilizing conventional and molecular characters. Propanagrolaimus siweyae sp. n., was confirmed by morphological and molecular informations. Propanagrolaimus siweyae sp. n. is characterized by a body length 1026–1258 µm (a = 39.4–45.5, b = 5.4–6.5, c = 8.1–10.0, c’ = 6.9–7.8, V = 53–57), post vulval uterine sac 25–53 µm, and tail length 108–158 µm long. The scan electron microscopy (SEM) photographs revealed a tessellated cuticle and six slightly separated lips. The discriminant analysis placed populations of P. siweyae sp. n. close to P. hygrophilus with clear separation from the mentioned species. Partial sequences of the 18S and 28S regions of the ribosomal DNA gene were amplified for P. siweyae sp. n. The phylogenetic analysis grouped P. siweyae sp. n. in a clade with 1.00 and 0.87 posterior probability values together with other Propanagrolaimus and Halicephalobus based on 18S and 28S rDNA, respectively. Principal component analysis revealed no correlation between Propanagrolaimus and water parameters. However, the result showed a high correlation with diatoms (r = 0.937) in Molepo dam (site MD-6). In contrast, The PCA showed salinity, pH, and temperature with no significant effect on nematodes in Molepo dam, Limpopo Province, South Africa. In conclusion, the usefulness of free-living nematodes as bioindicators is an advantage to studying pollution in aquatic systems. Limpopo Province is facing pollution in the river and dam systems. Therefore, finding a bioindicator is critical to examine the ecological role of free-living nematodes such as Propanagrolaimus.

Binocular integration of chromatic and luminance signals.

Much progress has been made in understanding how the brain combines signals from the two eyes. However, most of this work has involved achromatic (black and white) stimuli, and it is not clear if the same processes apply in color-sensitive pathways. In our first experiment, we measured contrast discrimination ("dipper") functions for four key ocular configurations (monocular, binocular, half-binocular, and dichoptic), for achromatic, isoluminant L-M and isoluminant S-(L+M) sine-wave grating stimuli (L: long-, M: medium-, S: short-wavelength). We find a similar pattern of results across stimuli, implying equivalently strong interocular suppression within each pathway. Our second experiment measured dichoptic masking within and between pathways using the method of constant stimuli. Masking was strongest within-pathway and weakest between S-(L+M) and achromatic mechanisms. Finally, we repeated the dipper experiment using temporal luminance modulations, which produced slightly weaker interocular suppression than for spatially modulated stimuli. We interpret our results in the context of a contemporary two-stage model of binocular contrast gain control, implemented here using a hierarchical Bayesian framework. Posterior distributions of the weight of interocular suppression overlapped with a value of 1 for all dipper data sets, and the model captured well the pattern of thresholds from all three experiments.

Deciphering the genetic underpinnings of neuroticism: A Mendelian randomization study of druggable gene targets

BackgroundNeuroticism, known for its association with a greater risk of psychiatric conditions such as depression and anxiety, is a critical focus of research. MethodsCis-expression quantitative trait loci (eQTLs) from 31,684 whole blood samples provided by the eQTLGen Consortium, alongside data from a large neuroticism cohort, were analyzed to identify genes causally linked to neuroticism. To further explore the influence of gene expression changes on neuroticism, colocalization analysis was conducted. Identified drug targets were assessed for potential side effects using a phenome-wide association study (PheWAS). Additionally, we utilized multiple databases to explore the interactions between drugs and genes for drug prediction and assess the current medications for drug repurposing. ResultsThe analysis involved a total of 4473 druggable genes, with two-sample Mendelian randomization (MR) identifying 186 genes that are causally linked to neuroticism. Colocalization analysis highlighted 11 genes (TLR4, MMRN1, EP300, BRAF, ORM1, ACVR1B, LRRC17, NOS2, ADAMTS6, GPX1, and VCL) with a posterior probability of colocalization (PPH4) >0.8. PheWAS revealed that drugs targeting BRAF, LRRC17, ADAMTS6, and GPX1 were also associated with other traits. Notably, six of these genes (TLR4, MMRN1, BRAF, ACVR1B, NOS2, and GPX1) are already being explored for drug development in psychiatric and other diseases. ConclusionThis study pinpointed six genes as promising therapeutic targets for neuroticism. The repurposing and development of drugs targeting these genes hold potential for managing neuroticism and associated psychiatric disorders.

Failure rate of D-dimer testing in patients with high clinical probability of pulmonary embolism: Ancillary analysis of three European studies.

In patients with a high clinical probability of pulmonary embolism (PE), the high prevalence can lower the D-dimer negative predictive value and increase the risk of diagnostic failure. It is therefore recommended that these high-risk patients should undergo chest imaging without D-dimer testing although no evidence supports this recommendation. The objective was to evaluate the safety of ruling out PE based on D-dimer testing among patients with a high clinical probability of PE. This was a post hoc analysis of three European studies (PROPER, MODIGLIANI, and TRYSPEED). Patients were included if they presented a high clinical probability of PE (according to either the Wells or the revised Geneva score) and underwent D-dimer testing. The D-dimer-based strategy ruled out PE if the D-dimer level was below the age-adjusted threshold (i.e., <500 ng/mL in patients aged less than 50 and age × 10 ng/mL in patients older than 50). The primary endpoint was a thromboembolic event in patients with negative D-dimer either at index visit or at 3-month follow-up. A Bayesian approach estimated the probability that the failure rate of the D-dimer-based strategy was below 2% given observed data. Among the 12,300 patients included in the PROPER, MODIGLIANI, and TRYSPEED studies, 651 patients (median age 68 years, 60% female) had D-dimer testing and a high clinical probability of PE and were included in the study. PE prevalence was 31.3%. Seventy patients had D-dimer levels under the age-adjusted threshold, and none of them had a PE after follow-up (failure rate 0.0% [95% CI 0.0%-6.5%]). Bayesian analysis reported a credible interval of 0.0%-4.1%, with a 76.2% posterior probability of a failure rate below 2%. In this study, ruling out PE in high-risk patients based on D-dimer below the age-adjusted threshold was safe, with no missed PE. However, the large CI of the primary endpoint precludes a definitive conclusion.

Integrating Factor Models Using Bayesian Model Averaging: Evidence from Korea

This study applies the Bayesian model averaging approach to the Korean stock market data to yield an integrated factor model that can address model uncertainty. During the period from 2004 to 2022, we choose 14 factors and 10 macro predictors and generate a total of 10,485,760 candidate factor models by considering all possible combinations of each variable and whether to allow for model mispricing. The integrated model estimates the expected return and covariance matrix by combining the predictions of all the candidate models using Bayesian posterior probabilities as weights. In the Korean stock market, there is no clear winner model with dominant posterior probabilities, implying that model uncertainty is substantial. The optimal portfolio of the integrated model has a higher out-of-sample Sharpe ratio and lower downside risk than benchmark factor models. Model uncertainty has a significant impact on the estimation of the covariance matrix of the integrated model, and model disagreement about expected returns is particularly acute during periods of sharp market declines. In the presence of model uncertainty, Bayesian investors perceive equities to be riskier than historical volatility.

A probabilistic assessment of ship blackout incident with Fault Tree Analysis into (FTA) Bayesian Network (BN)

Blackouts in maritime activities can cause propulsion loss and dangerous maritime conditions. Bayesian risk analysis is applied to ship blackout incidents in this study to improve understanding and reduce risks. Using Fault Tree Analysis (FTA), a Bayesian Network (BN) model incorporates fuel quality, lubricating oil quality, sensor error, injector error, and mechanical defects to estimate blackout probability. The model analyses how hazards and their interactions affect this situation using probabilistic inference. Sensitivity analysis identifies variables that affect blackout probabilities and prioritises risk mitigation solutions. Based on prior and posterior probabilities, ‘Automatic Voltage Regulator Failure’ (0.03 prior, 0.17 posterior), ‘Rotor Mechanical Fault’ (0.03 prior, 0.15 posterior), and ‘High Cooling Water Temperature’ (0.03 prior, 0.13 posterior) are the top three blackout causes. Other significant variables include ‘Switchboard Line Failure,’ ‘Faulty Fuel Pump,’ ‘Rotor Open Circuit,’ and ‘Temperature Sensor Failure’ in relative amounts. Bayesian risk analysis can identify and minimise marine blackout concerns, giving decision-makers a comprehensive framework for informed decision-making and proactive risk management. This research emphasises blackout accidents’ importance, improving maritime transportation safety and reliability.

Rapid Parameter Estimation for Merging Massive Black Hole Binaries Using Continuous Normalizing Flows

Abstract Detecting the coalescences of massive black hole binaries (MBHBs) is one of the primary targets for space-based gravitational wave observatories such as LISA, Taiji, and Tianqin. &amp;#xD;The fast and accurate parameter estimation of merging MBHBs is of great significance for the global fitting of all resolvable sources, as well as the astrophysical interpretation of gravitational wave signals.&amp;#xD;However, such analyses usually entail significant computational costs.&amp;#xD;To address these challenges, inspired by the latest progress in generative models, we explore the application of continuous normalizing flows (CNFs) on the parameter estimation of MBHBs. &amp;#xD;Specifically, we employ linear interpolation and trig interpolation methods to construct transport paths for training CNFs. &amp;#xD;Additionally, we creatively introduce a parameter transformation method based on the symmetry in the detector's response function. This transformation is integrated within CNFs, allowing us to train the model using a simplified dataset, and then perform parameter estimation on more general data, hence also acting as a crucial factor in improving the training speed.&amp;#xD;In conclusion, for the first time, within a comprehensive and reasonable parameter range, we have achieved a complete and unbiased 11-dimensional rapid inference for MBHBs in the presence of astrophysical confusion noise using CNFs. In the experiments based on simulated data, our model produces posterior distributions comparable to those obtained by nested sampling.

Probabilistic geophysical inversion of complex resistivity measurements using the Hamiltonian Monte Carlo method

Summary In this work, we introduce the probabilistic inversion of tomographic complex resistivity (CR) measurements using the Hamiltonian Monte Carlo (HMC) method. The posterior model distribution on which our approach operates accounts for the underlying complex-valued nature of the CR imaging problem accurately by including the individual errors of the measured impedance magnitude and phase, allowing for the application of independent regularization on the inferred subsurface conductivity magnitude and phase, and incorporating the effects of cross-sensitivities. As the tomographic CR inverse problem is non-linear, of high dimension and features strong correlations between model parameters, efficiently sampling from the posterior model distribution is challenging. To meet this challenge we use HMC, a Markov-chain Monte Carlo method that incorporates gradient information to achieve efficient model updates. To maximize the benefit of a given number of forward calculations, we use the No-U-Turn sampler (NUTS) as a variant of HMC. We demonstrate the probabilistic inversion approach on a synthetic CR tomography measurement. The NUTS succeeds in creating a sample of the posterior model distribution that provides us with the ability to analyze correlations between model parameters and to calculate statistical estimators of interest, such as the mean model and the covariance matrix. Our results provide a strong basis for the characterization of the posterior model distribution and uncertainty quantification in the context of the tomographic CR inverse problem.

Mediating role of systemic inflammation in the association between volatile organic compounds exposure and periodontitis: NHANES 2011–2014

BackgroundVolatile organic compounds (VOCs) are ubiquitous environmental pollutants which have been suggested to have adverse effects on human health. While the influence of environmental pollutant exposures on periodontitis has attracted elevating attention in recent years, the epidemiological evidence on the association between VOCs exposure and periodontitis was scarce. This study aimed to investigate the potential mediating role of systemic inflammation factors in the complex association between VOCs exposure and periodontitis.MethodsUtilizing data from the National Health and Nutrition Examination Survey (NHANES) 2011–2014, we examined the impacts of VOCs exposure on periodontitis. Concentrations of urinary metabolites of VOCs (mVOCs) were measured using electrospray tandem mass spectrometry to evaluate internal VOCs exposure. Multivariable logistic regression, restricted cubic spline regression (RCS), Bayesian kernel machine regression (BKMR) and Quantile g-computation (QGC) models were performed to investigate the impacts of VOCs exposure on periodontitis. Mediation models were applied to assess the mediated effects of systemic inflammation on the association between mixed VOCs exposure and periodontitis. Besides, we analyzed the association between mixed VOCs exposure and periodontitis in stratified age, gender, and smoking status subgroups.Results1,551 participants were ultimately included for further analyses, of whom 45.20% suffering from periodontitis. Multivariable logistic regression and RCS identified positive associations between single urinary mVOCs and periodontitis (P < 0.05). Notably, BKMR and QGC models suggested that mixed VOCs exposure was significantly associated with periodontitis, with 2-Aminothiazoline-4-carboxylic acid (ATCA) contributing the most (conditional posterior inclusion probability = 0.997). Moreover, systemic inflammation markers (leukocyte and lymphocyte counts) were found to partly mediate the association between VOCs exposure and periodontitis (P < 0.05). No interaction effect was identified between mixed VOCs exposure and periodontitis in age, gender and smoking status subgroups (P > 0.05).ConclusionThis study demonstrated a positive association between VOCs exposure and periodontitis, which was potentially mediated by systemic inflammation factors. Further longitudinal researches are demanded to clarify the underlying mechanisms.

Plasma metabolites as mediators in the relationship between inflammation-related proteins and benign prostatic hyperplasia: insights from mendelian randomization

Benign prostatic hyperplasia (BPH) is a condition commonly observed in aging males. Inflammatory and metabolic factors are pivotal in the development and progression of BPH. The degree to which the effects of 91 inflammation-related proteins on BPH are mediated by 1400 plasma metabolites remains ambiguous. Our research analyzed the impact of these traits utilizing genetic evidence.Two-sample Mendelian randomization (MR) and multivariable MR (MVMR) were utilized in our study to infer the genetic causal effect of inflammation-related proteins on BPH, with metabolites serving as mediators. Increased levels of IL-2 were linked to a heightened incidence of BPH (β = 0.071, OR:1.074, 95% CI [1.002–1.152], p = 0.045), whereas lower concentrations of N6,N6-dimethyllysine were associated with decreased risk (β1=-0.127, p = 0.02; β2=-0.039, p = 0.008). The mediation effect was 0.005 (95% CI [0.0004, 0.012], OR: 1.005, 95% CI [1.000, 1.012]), accounting for 7.04% of the total effect. subsequently, we examined the phenotypic co-localization of the two pairings independently, revealing that the posterior probability of rs145516501 associated with IL-2 and BPH was 80.7%, whereas the posterior likelihood of rs4917820 linked to N6,N6-dimethyllysine levels and BPH was 95.9%. The research indicated that N6,N6-dimethyllysine levels seem to influence the causative relationship between IL-2 and BPH. These results elucidate the complex interplay between inflammation-related proteins and metabolism in the context of BPH, offering novel diagnostic and therapeutic avenues and enhancing our comprehension of the disease’s etiology for prospective research.

Updating probability of pathogenicity for RYR1 and CACNA1S exon variants in individuals without malignant hyperthermia after exposure to triggering anesthetics

Objectives We aimed to classify genetic variants in RYR1 and CACNA1S associated with malignant hyperthermia using biobank genotyping data in patients exposed to triggering anesthetics without malignant hyperthermia phenotype. Methods We identified individuals who underwent surgery and were exposed to triggering anesthetics without malignant hyperthermia phenotype and who had RYR1 or CACNA1S genotyping data available in our biobank. We classified all variants in the cohort using a Bayesian framework of the American College of Medical Genetics and Genomics and the Association of Molecular Pathologists guidelines for variant classification and updated the posterior probabilities from this model with the new information from our biobank cohort. Results We identified 253 patients with 95 RYR1 variants and 12 CACNA1S variants. After applying a Bayesian framework, we classified 17 variants as benign (B), 31 as likely benign (LB), 57 as uncertain (VUS), and 2 as likely pathogenic (LP). When we incorporated evidence about unique exposures to malignant hyperthermia triggering anesthetic agents, 48 of 107 (45%) variants were downgraded (9 to B, 37 to LB, and 2 to VUS). Notably, 41 (72%) of 57 VUSs were downgraded to B or LB. When repeat anesthetics in the same individual were counted as one exposure, 42 of 107 (39%) of variants were downgraded (5 to B, 35 to LB, and 2 to VUS). Specifically, 37 (65%) of 57 VUSs were downgraded to LB. Conclusion Deidentified biorepositories linked with anesthetic data offer a new method of integrating clinical evidence into the assessment of variant probability of pathogenicity.

Learning probability distributions of sensory inputs with Monte Carlo predictive coding.

It has been suggested that the brain employs probabilistic generative models to optimally interpret sensory information. This hypothesis has been formalised in distinct frameworks, focusing on explaining separate phenomena. On one hand, classic predictive coding theory proposed how the probabilistic models can be learned by networks of neurons employing local synaptic plasticity. On the other hand, neural sampling theories have demonstrated how stochastic dynamics enable neural circuits to represent the posterior distributions of latent states of the environment. These frameworks were brought together by variational filtering that introduced neural sampling to predictive coding. Here, we consider a variant of variational filtering for static inputs, to which we refer as Monte Carlo predictive coding (MCPC). We demonstrate that the integration of predictive coding with neural sampling results in a neural network that learns precise generative models using local computation and plasticity. The neural dynamics of MCPC infer the posterior distributions of the latent states in the presence of sensory inputs, and can generate likely inputs in their absence. Furthermore, MCPC captures the experimental observations on the variability of neural activity during perceptual tasks. By combining predictive coding and neural sampling, MCPC can account for both sets of neural data that previously had been explained by these individual frameworks.

Estimating the Sampling Distribution of Posterior Decision Summaries in Bayesian Clinical Trials.

Bayesian inference and the use of posterior or posterior predictive probabilities for decision making have become increasingly popular in clinical trials. The current practice in Bayesian clinical trials relies on a hybrid Bayesian-frequentist approach where the design and decision criteria are assessed with respect to frequentist operating characteristics such as power and type I error rate conditioning on a given set of parameters. These operating characteristics are commonly obtained via simulation studies. The utility of Bayesian measures, such as "assurance," that incorporate uncertainty about model parameters in estimating the probabilities of various decisions in trials has been demonstrated. However, the computational burden remains an obstacle toward wider use of such criteria. In this article, we propose methodology which utilizes large sample theory of the posterior distribution to define parametric models for the sampling distribution of the posterior summaries used for decision making. The parameters of these models are estimated using a small number of simulation scenarios, thereby refining these models to capture the sampling distribution for small to moderate sample size. The proposed approach toward the assessment of conditional and marginal operating characteristics and sample size determination can be considered as simulation-assisted rather than simulation-based. It enables formal incorporation of uncertainty about the trial assumptions via a design prior and significantly reduces the computational burden for the design of Bayesian trials ingeneral.

Estimation of HIV prevalence at the ZIP code-level in Atlanta, Georgia: Bayesian prediction modeling using passive surveillance data and social determinants of disease spreading

ObjectiveThis study aims to predict the number of undiagnosed HIV cases at the ZIP Code-level in Atlanta, Georgia, based on publicly available information. Study designStatistical modeling. MethodsWe fitted a Bayesian hierarchical Binomial model to county-level estimates of the passive-surveillance-system. The denominator was the true total HIV cases arising from a Negative Binomial distribution. The trial probability, known as ascertainment probability, depended on socio-economic determinants of HIV, retained via feature-selection algorithms. Data were obtained from CDC's HIV report for End of the HIV Epidemic and the American Community Survey. The prediction model was assessed out-of-sample in Georgia counties. We combined socio-economic data with the posterior predictive distribution of the coefficients to predict the mean ascertainment probability and total HIV cases at the ZIP Code-level. These estimates were spatially smoothed and aggregated at the county-level for secondary validations. ResultsThe county-level model showed good mixing properties and predictive accuracy. The mean ascertainment probability calibrated to the ZIP Code-level varied from 78.4% (95% credible interval: 24.4%–99.3%) to 93.8% (95%CI: 80.6%–99.8%). Further, the predicted undiagnosed HIV cases ranged between 12 (95%CI: 6–19; ZIP Code 30322) to 1603 (95%CI 1209–1968; ZIP Code 30318). ConclusionsOur findings provide a more complete picture of the relative burden of HIV across ZIP codes. Such information can be used by Local Health Departments to identify underserved areas and allocate resources accordingly. Furthermore, our methodological approach can be applied to complement the information obtained from passive surveillance, especially when more resource-intensive approaches are not available or are unfeasible to employ.

Within-chain parallelization-Giving Stan Jet Fuel for population modeling in pharmacometrics.

Stan is a powerful probabilistic programming language designed mainly for Bayesian data analysis. Torsten is a collection of Stan functions that handles the events (e.g., dosing events) and solves the ODE systems that are frequently present in pharmacometric models. To perform a Bayesian data analysis, most models in pharmacometrics require Markov Chain Monte Carlo (MCMC) methods to sample from the posterior distribution. However, MCMC is computationally expensive and can be time-consuming, enough so that people will often forgo Bayesian methods for a more traditional approach. This paper shows how to speed up the sampling process in Stan by within-chain parallelization through both multi-threading using Stan's reduce_sum() function and multi-processing using Torsten's group ODE solver. Both methods show substantial reductions in the time necessary to sufficiently sample from the posterior distribution compared with a basic approach with no within-chain parallelization.

Bayesian quantum phase estimation with fixed photon states

We consider a two-mode bosonic state with fixed photon number n∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n \\in \\mathbb {N}$$\\end{document}, whose upper and lower modes pick up a phase ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} and -ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$-\\phi $$\\end{document}, respectively. We compute the optimal Fock coefficients of the input state, such that the mean square error (MSE) for estimating ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} is minimized, while the minimum MSE is always attainable by a measurement. Our setting is Bayesian, i.e., we consider ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} to be a random variable that follows a prior probability distribution function (PDF). Initially, we consider the flat prior PDF and we discuss the well-known fact that the MSE is not an informative tool for estimating a phase when the variance of the prior PDF is large. Therefore, we move on to study truncated versions of the flat prior in both single-shot and adaptive approaches. For our adaptive technique, we consider n=1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n=1$$\\end{document} and truncated prior PDFs. Each subsequent step utilizes as prior PDF the posterior probability of the previous step, and at the same time we update the optimal state and optimal measurement.

Prospective comparison of temporal myocardial function in men vs women after anterior ST-elevation myocardial infarction

Abstract Background Compared to men, women have been reported to have increased morbidity and mortality after ST-elevation myocardial infarction (STEMI), but sex differences in cardiac function in the acute and subacute phases of STEMI are incompletely understood. Objective To prospectively compare changes in cardiac function over the acute and subacute phases after anterior STEMI with timely reperfusion in women versus men. Methods The Stunning in Takotsubo versus Acute Myocardial Infarction (STAMI) study prospectively enrolled 94 men and 36 women with anterior STEMI. Echocardiography and blood sampling were performed within 4 hours of admission and at 1, 2, 3, 7, 14 and 30 days after admission. The primary outcome was akinesia recovery, defined as the difference in the per cent akinesia observed at baseline versus follow-up. Secondary outcomes included wall motion score index (WMSI), left ventricular ejection fraction (LVEF) and global longitudinal strain (GLS). Mixed effects linear regression or zero-inflated tobit models with random intercepts were used to model echocardiographic parameters over time. Results Baseline patient characteristics were similar in both groups. The difference between women and men in akinesia recovery at 30 days was 8.4% (95% confidence interval [CI] 1.23-14.99). The covariate-adjusted Bayesian posterior probability that akinesia recovery and WMSI improvement at 30 days are more significant in women than men were 95% and 99%, respectively. Similar but less pronounced trends towards greater improvement in women than men were observed for LVEF and GLS. Conclusions After anterior STEMI with timely reperfusion, cardiac dysfunction recovered to a greater extent in women than in men.

Sex estimation using metrics of the innominate: A test of the DSP2 method.

Sex estimation is a critical component of the biological profile, and forensic anthropologists may use a variety of sex estimation methods depending upon the degree of completeness and state of preservation of the skeletal remains being analyzed. The innominate is widely accepted to be the most sexually dimorphic skeletal element. The Diagnose Sexuelle Probabiliste (DSP) method, which uses 10 measurements of the innominate, was introduced in 2005 and updated as DSP2 in 2017. While DSP2 has been reported to have high classification accuracy rates in studies of South American and European populations, the method has not been widely tested in US samples, and few US practitioners incorporate this method into their casework. The goal of this study was to test the reliability and accuracy of DSP2 using a large, modern sample from the US (n = 174). Two observers, blinded from demographic information associated with each specimen, collected the DSP2 metrics. Intra- and interobserver error analyses showed acceptable levels of agreement for all measurements, except for IIMT. Classification accuracies exceeded 95%, with minimal sex bias, for both observers and using various measurement combinations; however, an inclusivity sex bias occurred with more males reaching the 0.95 posterior probability threshold required by DSP2 to provide a sex classification estimate. Based on its high accuracy, forensic anthropologists in the US may consider incorporating DSP2 into their casework, although we recommend excluding IIMT and using SPU with caution. Additional methods will continue to be needed when the posterior probability threshold is not reached.