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Abstract BackgroundRoughly a quarter of the US population suffers from moderate to severe chronic pain for at least six months in any given year. The complexity of managing chronic pain has encouraged providers to use innovative methods to address it. Research has shown that problem lists are potential tools that support the care of patients with diabetes and chronic kidney disease. ObjectivesTo examine the extent to which the inclusion of chronic pain in a problem list is associated with follow-up specialty pain care. MethodsThe association between chronic pain documentation on the problem list and specialty pain care was investigated in this retrospective cohort study using 4531 patient records. ResultsChronic pain documentation in the problem list was associated with higher odds of receiving specialty pain care. The most common diagnosis was chronic pain (69.7%). A migraine diagnosis was associated with decreased odds of receiving specialty care, and chronic pain syndrome was associated with increased odds of receiving specialty care compared with the other chronic pain groups. ConclusionDocumenting chronic pain on the problem list was associated with a higher likelihood of patients receiving specialty pain care. 

Abstract Incorporating external data, such as external controls, holds the promise of improving the efficiency of traditional randomized controlled trials especially when treating rare diseases or diseases with unmet needs. To this end, we propose novel weighting estimators grounded in the causal inference framework. As an alternative framework, Bayesian methods are also discussed. From trial design perspective, operating characteristics including Type I error and power are particularly important and are assessed in our realistic simulation studies representing a variety of practical scenarios. Our proposed weighting estimators achieve significant power gain, while maintaining Type I error close to the nominal value of 0.05. An empirical application of the methods is demonstrated through a Phase III clinical trial in rare disease. 

Abstract The stein variational gradient descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational Gradient Flow) only provides a constant-order approximation to the Wasserstein gradient flow corresponding to the KL-divergence minimization. In this work, we propose the Regularized Stein Variational Gradient Flow, which interpolates between the Stein Variational Gradient Flow and the Wasserstein gradient flow. We establish various theoretical properties of the Regularized Stein Variational Gradient Flow (and its time-discretization) including convergence to equilibrium, existence and uniqueness of weak solutions, and stability of the solutions. We provide preliminary numerical evidence of the improved performance offered by the regularization. 

Abstract BackgroundCOVID-19 mitigation strategies such as masking, social distancing, avoiding group gatherings, and vaccination uptake are crucial interventions to preventing the spread of COVID-19. At present, COVID-19 data are aggregated and fail to identify subgroup variation in Asian American communities such as Hmong Americans. To understand the acceptance, adoption, and adherence to COVID-19 mitigation behaviors, an investigation of Hmong Americans’ contextual and personal characteristics was conducted. MethodsThis study aims to describe COVID-19 mitigation behaviors among Hmong Americans and the contextual and personal characteristics that influence these behaviors. A cross-sectional online survey was conducted from April 8 till June 1, 2021, with Hmong Americans aged 18 and over. Descriptive statistics were used to summarize the overall characteristics and COVID-19 related behaviors of Hmong Americans. Chi-square and Fisher’s Exact Test were computed to describe COVID-19 mitigation behaviors by gender and generational status (a marker of acculturation). ResultsThe sample included 507 participants who completed the survey. A majority of the Hmong American participants in our study reported masking (449/505, 88.9%), social distancing (270/496, 55.3%), avoiding group gatherings (345/505, 68.3%), avoiding public spaces (366/506, 72.3%), and obtaining the COVID-19 vaccination (350/506, 69.2%) to stay safe from COVID-19. Women were more likely to socially distance (P = .005), and avoid family (P = .005), and social gatherings (P = .009) compared to men. Social influence patterns related to mitigation behaviors varied by sex. Men were more likely compared to women to be influenced by Hmong community leaders to participate in family and group gatherings (P = .026), masking (P = .029), social distancing (P = .022), and vaccination uptake (P = .037), whereas healthcare providers and government officials were social influencers for social distancing and masking for women. Patterns of social distancing and group gatherings were also influenced by generational status. ConclusionContextual and personal characteristics influence COVID-19 mitigation behaviors among English speaking Hmong Americans. These findings have implications for identifying and implementing culturally appropriate health messages, future public health interventions, policy development, and ongoing research with this population. 

Abstract Without imposing prior distributional knowledge underlying multivariate time series of interest, we propose a nonparametric change-point detection approach to estimate the number of change points and their locations along the temporal axis. We develop a structural subsampling procedure such that the observations are encoded into multiple sequences of Bernoulli variables. A maximum likelihood approach in conjunction with a newly developed searching algorithm is implemented to detect change points on each Bernoulli process separately. Then, aggregation statistics are proposed to collectively synthesize change-point results from all individual univariate time series into consistent and stable location estimations. We also study a weighting strategy to measure the degree of relevance for different subsampled groups. Simulation studies are conducted and shown that the proposed change-point methodology for multivariate time series has favorable performance comparing with currently available state-of-the-art nonparametric methods under various settings with different degrees of complexity. Real data analyses are finally performed on categorical, ordinal, and continuous time series taken from fields of genetics, climate, and finance. 

Abstract Based on polymer scaling theory and numerical evidence, Orlandini, Tesi, Janse van Rensburg and Whittington conjectured in 1996 that the limiting entropy of knot-typeKlattice polygons is the same as that for unknot polygons, and that the entropic critical exponent increases by one for each prime knot in the knot decomposition ofK. This Knot Entropy (KE) conjecture is consistent with the idea that for unconfined polymers, knots occur in a localized way (the knotted part is relatively small compared to polymer length). For full confinement (to a sphere or box), numerical evidence suggests that knots are much less localized. Numerical evidence for nanochannel or tube confinement is mixed, depending on how the size of a knot is measured. Here we outline the proof that the KE conjecture holds for polygons in the $\mathrm{\infty }\times 2\times 1$lattice tube and show that knotting is localized when a connected-sum measure of knot size is used. Similar results are established for linked polygons. This is the first model for which the knot entropy conjecture has been proved. 

Abstract Recent progress in solving macromolecular structures and assemblies by cryogenic electron microscopy techniques enables sampling of their conformations in different states that are relevant to their biological function. Knowing the transition path between these conformations would provide new avenues for drug discovery. While the experimental study of transition paths is intrinsically difficult, in-silico methods can be used to generate an initial guess for those paths. The Elastic Network Model (ENM), along with a coarse-grained representation (CG) of the structures are among the most popular models to explore such possible paths. Here we propose an update to our software platform MinActionPath that generates non-linear transition paths based on ENM and CG models, using action minimization to solve the equations of motion. The new website enables the study of large structures such as ribosomes or entire virus envelopes. It provides direct visualization of the trajectories along with quantitative analyses of their behaviors at http://dynstr.pasteur.fr/servers/minactionpath/minactionpath2_submission. 

Abstract A conjecture of Milena Mihail and Umesh Vazirani (Proc. 24th Annu. ACM Symp. Theory Comput., ACM, Victoria, BC, 1992, pp. 26–38.) states that the edge expansion of the graph of every polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used to generate an element from a set of combinatorial objects uniformly at random. A weaker form of the conjecture of Mihail and Vazirani says that the edge expansion of the graph of a polytope in is greater than one over some polynomial function of . This weaker version of the conjecture would suffice for all applications. Our main result is that the edge expansion of the graph of arandompolytope in is at least with high probability. 

Abstract This paper develops uniqueness theory for 3D phase retrieval with finite, discrete measurement data for strong phase objects and weak phase objects, including: (i)Unique determination of (phase) projections from diffraction patterns—General measurement schemes with coded and uncoded apertures are proposed and shown to ensure unique reduction of diffraction patterns to the phase projection for a strong phase object (respectively, the projection for a weak phase object) in each direction separately without the knowledge of relative orientations and locations. (ii)Uniqueness for 3D phase unwrapping—General conditions for unique determination of a 3D strong phase object from its phase projection data are established, including, but not limited to, random tilt schemes densely sampled from a spherical triangle of vertexes in three orthogonal directions and other deterministic tilt schemes. (iii)Uniqueness for projection tomography—Unique 

Abstract Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex—but very common—machine learning tasks such as clustering or classification. In this paper we overcome some of these limitations. Working with metric privacy, a powerful generalization of differential privacy, we develop a polynomial-time algorithm that creates aprivate measurefrom a data set. This private measure allows us to efficiently construct private synthetic data that are accurate for a wide range of statistical analysis tools. Moreover, we prove an asymptotically sharp min-max result for private measures and synthetic data in general compact metric spaces, for any fixed privacy budget$$\varepsilon $$ $\epsilon$bounded away from zero. A key ingredient in our construction is a newsuperregular random walk, whose joint distribution of steps is as regular as that of independent random variables, yet which deviates from the origin logarithmically slowly.