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Observable dynamics, such as waves propagating on a surface, are generally governed by partial differential equations (PDEs), which are determined by the physical properties of the propagation media. The spatial variations of these properties lead to spatially dependent PDEs. It is useful in many fields to recover the variations from the observations of dynamical behaviors on the material. A method is proposed to form a map of the physical properties' spatial variations for a material via data-driven spatially dependent PDE identification and applied to recover acoustical properties (viscosity, attenuation, and phase speeds) for propagating waves. The proposed data-driven PDE identification scheme is based on ℓ1-norm minimization. It does not require any PDE term that is assumed active from the prior knowledge and is the first approach that is capable of identifying spatially dependent PDEs from measurements of phenomena. In addition, the method is efficient as a result of its non-iterative nature and can be robust against noise if used with an integration transformation technique. It is demonstrated in multiple experimental settings, including real laser measurements of a vibrating aluminum plate. Codes and data are available online at https://tinyurl.com/4wza8vxs.

Inspired by recent developments in data-driven methods for partial differential equation (PDE) estimation, we use sparse modeling techniques to automatically estimate PDEs from data. A dictionary consisting of hypothetical PDE terms is constructed using numerical differentiation. Given data, PDE terms are selected assuming a parsimonious representation, which is enforced using a sparsity constraint. Unlike previous PDE identification schemes, we make no assumptions about which PDE terms are responsible for a given field. The approach is demonstrated on synthetic and real video data, with physical phenomena governed by wave, Burgers, and Helmholtz equations. Codes are available at https://github.com/NoiseLab-RLiu/Automate-PDE-identification.

We use a machine learning-based tomography method to obtain high-resolution subsurface geophysical structure in Long Beach, CA, from seismic noise recorded on a "large-N" array with 5204 geophones (~13.5 million travel times). This method, called locally sparse travel time tomography (LST) uses unsupervised machine learning to exploit the dense sampling obtained by ambient noise processing on large arrays. Dense sampling permits the LST method to learn directly from the data a dictionary of local, or small-scale, geophysical features. The features are the small scale patterns of Earth structure most relevant to the given tomographic imaging scenario. Using LST, we obtain a high-resolution 1 Hz Rayleigh wave phase speed map of Long Beach. Among the geophysical features shown in the map, the important Silverado aquifer is well isolated relative to previous surface wave tomography studies. Our results show promise for LST in obtaining detailed geophysical structure in travel time tomography studies.

UNAIDS has identified the Danish HIV epidemic in men who have sex with men (MSM) as a priority for elimination. Incidence is close to the elimination threshold of one new infection per year per 1,000 individuals. However, surveillance data show that HIV strains are being imported into Denmark, mainly due to travel. We use a transmission model to predict (from 2018 to 2030) the impact of pre-exposure prophylaxis (PrEP) on incidence. Our model reflects the current epidemic and diagnosis rates in the Danish MSM community. We conduct a sensitivity analysis based on 20,000 simulations, and assume that PrEP coverage could range from zero to 50% and diagnosis rates increase up to three-fold. We predict that incidence will fall below the elimination threshold, even without the introduction of PrEP, reaching 0.87 (median, 95% Confidence Interval: 0.65-1.23) new infections per 1,000 MSM by 2030. PrEP could reduce incidence to well below the threshold, if it results in a significant increase in diagnosis rates and reduces the number of infections occurring abroad. The Danish Medicine Agency and Danish Health Authority have recommended introducing PrEP. Our study provides strong support for this recommendation, and shows the importance of Danish MSM using PrEP when abroad.

The multi-snapshot, multi-frequency sparse Bayesian learning (SBL) processor is derived and its performance compared to the Bartlett, minimum variance distortionless response, and white noise constraint processors for the matched field processing application. The two-source model and data scenario of interest includes realistic mismatch implemented in the form of array tilt and data snapshots not exactly corresponding to the range-depth grid of the replica vectors. Results demonstrate that SBL behaves similar to an adaptive processor when localizing a weaker source in the presence of a stronger source, is robust to mismatch, and exhibits improved localization performance when compared to the other processors. Unlike the basis or matching pursuit methods, SBL automatically determines sparsity and its solution can be interpreted as an ambiguity surface. Because of its computational efficiency and performance, SBL is practical for applications requiring adaptive and robust processing.

BackgroundWorldwide, approximately 35 million individuals are infected with HIV; about 25 million of these live in sub-Saharan Africa. WHO proposes using treatment as prevention (TasP) to eliminate HIV. Treatment suppresses viral load, decreasing the probability an individual transmits HIV. The elimination threshold is one new HIV infection per 1000 individuals. Here, we test the hypothesis that TasP can substantially reduce epidemics and eliminate HIV. We estimate the impact of TasP, between 1996 and 2013, on the Danish HIV epidemic in men who have sex with men (MSM), an epidemic UNAIDS has identified as a priority for elimination.MethodsWe use a CD4-staged Bayesian back-calculation approach to estimate incidence, and the hidden epidemic (the number of HIV-infected undiagnosed MSM). To develop the back-calculation model, we use data from an ongoing nationwide population-based study: the Danish HIV Cohort Study.FindingsIncidence, and the hidden epidemic, decreased substantially after treatment was introduced in 1996. By 2013, incidence was close to the elimination threshold: 1·4 (median, 95% Bayesian credible interval [BCI] 0·4-2·1) new HIV infections per 1000 MSM and there were only 617 (264-858) undiagnosed MSM. Decreasing incidence and increasing treatment coverage were highly correlated; a treatment threshold effect was apparent.InterpretationOur study is the first to show that TasP can substantially reduce a country's HIV epidemic, and bring it close to elimination. However, we have shown the effectiveness of TasP under optimal conditions: very high treatment coverage, and exceptionally high (98%) viral suppression rate. Unless these extremely challenging conditions can be met in sub-Saharan Africa, the WHO's global elimination strategy is unlikely to succeed.FundingNational Institute of Allergy and Infectious Diseases.

[1] This paper addresses the problem of estimating the lower atmospheric refractivity ( M profile) under nonstandard propagation conditions frequently encountered in low-altitude maritime radar applications. This is done by statistically estimating the duct strength (range- and height-dependent atmospheric index of refraction) from the sea surface reflected radar clutter. These environmental statistics can then be used to predict the radar performance. In previous work, genetic algorithms (GA) and Markov chain Monte Carlo (MCMC) samplers were used to calculate the atmospheric refractivity from returned radar clutter. Although GA is fast and estimates the maximum a posteriori ( MAP) solution well, it poorly calculates the multidimensional integrals required to obtain the means, variances, and underlying posterior probability distribution functions of the estimated parameters. More accurate distributions and integral calculations can be obtained using MCMC samplers, such as the Metropolis-Hastings and Gibbs sampling (GS) algorithms. Their drawback is that they require a large number of samples relative to the global optimization techniques such as GA and become impractical with an increasing number of unknowns. A hybrid GA-MCMC method based on the nearest neighborhood algorithm is implemented in this paper. It is an improved GA method which improves integral calculation accuracy through hybridization with a MCMC sampler. Since the number of forward models is determined by GA, it requires fewer forward model samples than a MCMC, enabling inversion of atmospheric models with a larger number of unknowns.

BackgroundPoor adherence is the main barrier to the effectiveness of HIV medication. The objective of this study was to explore and conceptualize patterns and difficulties in physicians' work with patients' adherence to HIV medication. No previous studies on this subject have directly observed physicians' behavior.MethodsThis is a qualitative, cross-sectional study. We used a Grounded Theory approach to let the main issues in physicians' work with patients' adherence emerge without preconceiving the focus of the study. We included physicians from HIV clinics in San Francisco, U.S.A. as well as from Copenhagen, Denmark. Physicians were observed during their clinical work and subsequently interviewed with a semi-structured interview guide. Notes on observations and transcribed interviews were analyzed with NVivo software.ResultsWe enrolled 16 physicians from San Francisco and 18 from Copenhagen. When we discovered that physicians and patients seldom discussed adherence issues in depth, we made adherence communication and its barriers the focus of the study. The main patterns in physicians' communication with patients about adherence were similar in both settings. An important barrier to in-depth adherence communication was that some physicians felt it was awkward to explore the possibility of non-adherence if there were no objective signs of treatment failure, because patients could feel "accused." To overcome this awkwardness, some physicians consciously tried to "de-shame" patients regarding non-adherence. However, a recurring theme was that physicians often suspected non-adherence even when patients did not admit to have missed any doses, and physicians had difficulties handling this low believability of patient statements. We here develop a simple four-step, three-factor model of physicians' adherence communication. The four steps are: deciding whether to ask about adherence or not, pre-questioning preparations, phrasing the question, and responding to the patient's answer. The three factors/determinants are: physicians' perceptions of adherence, awkwardness, and believability.ConclusionCommunication difficulties were a main barrier in physicians' work with patients' adherence to HIV medication. The proposed model of physicians' communication with patients about adherence--and the identification of awkwardness and believability as key issues--may aid thinking on the subject for use in clinical practice and future research.

BackgroundPoor adherence is the main barrier to the effectiveness of HIV medication. The objective of this study was to explore and conceptualize patterns and difficulties in physicians' work with patients' adherence to HIV medication. No previous studies on this subject have directly observed physicians' behavior.MethodsThis is a qualitative, cross-sectional study. We used a Grounded Theory approach to let the main issues in physicians' work with patients' adherence emerge without preconceiving the focus of the study. We included physicians from HIV clinics in San Francisco, U.S.A. as well as from Copenhagen, Denmark. Physicians were observed during their clinical work and subsequently interviewed with a semi-structured interview guide. Notes on observations and transcribed interviews were analyzed with NVivo software.ResultsWe enrolled 16 physicians from San Francisco and 18 from Copenhagen. When we discovered that physicians and patients seldom discussed adherence issues in depth, we made adherence communication and its barriers the focus of the study. The main patterns in physicians' communication with patients about adherence were similar in both settings. An important barrier to in-depth adherence communication was that some physicians felt it was awkward to explore the possibility of non-adherence if there were no objective signs of treatment failure, because patients could feel "accused." To overcome this awkwardness, some physicians consciously tried to "de-shame" patients regarding non-adherence. However, a recurring theme was that physicians often suspected non-adherence even when patients did not admit to have missed any doses, and physicians had difficulties handling this low believability of patient statements. We here develop a simple four-step, three-factor model of physicians' adherence communication. The four steps are: deciding whether to ask about adherence or not, pre-questioning preparations, phrasing the question, and responding to the patient's answer. The three factors/determinants are: physicians' perceptions of adherence, awkwardness, and believability.ConclusionCommunication difficulties were a main barrier in physicians' work with patients' adherence to HIV medication. The proposed model of physicians' communication with patients about adherence--and the identification of awkwardness and believability as key issues--may aid thinking on the subject for use in clinical practice and future research.

This paper describes a Markov chain Monte Carlo (MCMC) sampling approach for the estimation of not only the radio refractivity profiles from radar clutter but also the uncertainties in these estimates. This is done by treating the refractivity from clutter (RFC) problem in a Bayesian framework. It uses unbiased MCMC sampling techniques, such as Metropolis and Gibbs sampling algorithms, to gather more accurate information about the uncertainties. Application of these sampling techniques using an electromagnetic split-step fast Fourier transform parabolic equation propagation model within a Bayesian inversion framework can provide accurate posterior probability distributions of the estimated refractivity parameters. Then these distributions can be used to estimate the uncertainties in the parameters of interest. Two different MCMC samplers (Metropolis and Gibbs) are analyzed and the results compared not only with the exhaustive search results but also with the genetic algorithm results and helicopter refractivity profile measurements. Although it is slower than global optimizers, the probability densities obtained by this method are closer to the true distributions.

Quantifying uncertainty for parameter estimates obtained from matched-field geoacoustic inversions using a Bayesian approach requires estimation of the uncertainties in the data due to ambient noise as well as modeling errors. In this study, the variance parameter of the Gaussian error model, hereafter called error variance, is assumed to describe the data uncertainty. In practice, this parameter is not known a priori, and choosing a particular value is often difficult. Hence, to account for the uncertainty in error variance, several methods are introduced for implementing both the full and empirical Bayesian approaches. A full Bayesian approach that permits uncertainty of the error variance to propagate through the parameter estimation processes is a natural way of incorporating the uncertainty of error variance. Due to the large number of unknown parameters in the full Bayesian uncertainty analysis, an alternative, the empirical Bayesian approach is developed, in which the posterior distributions of model parameters are conditioned on a point estimate of the error variance. Comparisons between the full and empirical Bayesian inferences of model parameters are presented using both synthetic and experimental data. (c) 2006 Acoustical Society of America.