Project description:Variational approximations provide fast, deterministic alternatives to Markov Chain Monte Carlo for Bayesian inference on the parameters of complex, hierarchical models. Variational approximations are often limited in practicality in the absence of conjugate posterior distributions. Recent work has focused on the application of variational methods to models with only partial conjugacy, such as in semiparametric regression with heteroskedastic errors. Here, both the mean and log variance functions are modeled as smooth functions of covariates. For this problem, we derive a mean field variational approximation with an embedded Laplace approximation to account for the non-conjugate structure. Empirical results with simulated and real data show that our approximate method has significant computational advantages over traditional Markov Chain Monte Carlo; in this case, a delayed rejection adaptive Metropolis algorithm. The variational approximation is much faster and eliminates the need for tuning parameter selection, achieves good fits for both the mean and log variance functions, and reasonably reflects the posterior uncertainty. We apply the methods to log-intensity data from a small angle X-ray scattering experiment, in which properly accounting for the smooth heteroskedasticity leads to significant improvements in posterior inference for key physical characteristics of an organic molecule.
Project description:Time-domain diffuse optical measurement systems determine depth-resolved absorption changes by using the time of flight distribution of the detected photons. It is well known that certain feature data, such as the Laplace transform of the temporal point spread function, is sufficient for image reconstruction and diffuse optical sensing. Conventional time-domain systems require the acquisition of full temporal profiles of diffusive photons and then numerically compute the feature dataset, for example, Laplace transformed intensities for imaging applications. We have proposed a novel method for directly obtaining the Laplace transform data. Our approach can significantly improve the data acquisition speed for time-domain diffuse optical imaging. We also demonstrated that the use of negative Laplace parameters can provide enhanced sensitivity to perturbations located in deep regions.
Project description:As a perfect complement to conventional NMR that aims for chemical structure elucidation, Laplace NMR constitutes a powerful technique to study spin relaxation and diffusion, revealing information on molecular motions and spin interactions. Different from conventional NMR adopting Fourier transform to deal with the acquired data, Laplace NMR relies on specially designed signal processing and reconstruction algorithms resembling the inverse Laplace transform, and it generally faces severe challenges in cases where high spectral resolution and high spectral dimensionality are required. Herein, based on the tensor technique for high-dimensional problems and the sparsity assumption, we propose a general method for high-resolution reconstruction of multidimensional Laplace NMR data. We show that the proposed method can reconstruct multidimensional Laplace NMR spectra in a high-resolution manner for exponentially decaying relaxation and diffusion data acquired by commercial NMR instruments. Therefore, it would broaden the scope of multidimensional Laplace NMR applications.
Project description:Animal models are generalized linear mixed models used in evolutionary biology and animal breeding to identify the genetic part of traits. Integrated Nested Laplace Approximation (INLA) is a methodology for making fast, nonsampling-based Bayesian inference for hierarchical Gaussian Markov models. In this article, we demonstrate that the INLA methodology can be used for many versions of Bayesian animal models. We analyze animal models for both synthetic case studies and house sparrow (Passer domesticus) population case studies with Gaussian, binomial, and Poisson likelihoods using INLA. Inference results are compared with results using Markov Chain Monte Carlo methods. For model choice we use difference in deviance information criteria (DIC). We suggest and show how to evaluate differences in DIC by comparing them with sampling results from simulation studies. We also introduce an R package, AnimalINLA, for easy and fast inference for Bayesian Animal models using INLA.
Project description:Antibodies are important immune molecules with high commercial value and therapeutic interest because of their ability to bind diverse antigens. Computational prediction of antibody structure can quickly reveal valuable information about the nature of these antigen-binding interactions, but only if the models are of sufficient quality. To achieve high model quality during complementarity-determining region (CDR) structural prediction, one must account for the VL-VH orientation. We developed a novel four-metric VL-VH orientation coordinate frame. Additionally, we extended the CDR grafting protocol in RosettaAntibody with a new method that diversifies VL-VH orientation by using 10 VL-VH orientation templates rather than a single one. We tested the multiple-template grafting protocol on two datasets of known antibody crystal structures. During the template-grafting phase, the new protocol improved the fraction of accurate VL-VH orientation predictions from only 26% (12/46) to 72% (33/46) of targets. After the full RosettaAntibody protocol, including CDR H3 remodeling and VL-VH re-orientation, the new protocol produced more candidate structures with accurate VL-VH orientation than the standard protocol in 43/46 targets (93%). The improved ability to predict VL-VH orientation will bolster predictions of other parts of the paratope, including the conformation of CDR H3, a grand challenge of antibody homology modeling.
Project description:Using molecular dynamics (MD) simulations, a new approach based on the behavior of pressurized water out of a nanopore (1.3-2.7 nm) in a flat plate is developed to calculate the relationship between the water surface curvature and the pressure difference across water surface. It is found that the water surface curvature is inversely proportional to the pressure difference across surface at nanoscale, and this relationship will be effective for different pore size, temperature, and even for electrolyte solutions. Based on the present results, we cannot only effectively determine the surface tension of water and the effects of temperature or electrolyte ions on the surface tension, but also show that the Young-Laplace (Y-L) equation is valid at nanoscale. In addition, the contact angle of water with the hydrophilic material can be further calculated by the relationship between the critical instable pressure of water surface (burst pressure) and nanopore size. Combining with the infiltration behavior of water into hydrophobic microchannels, the contact angle of water at nanoscale can be more accurately determined by measuring the critical pressure causing the instability of water surface, based on which the uncertainty of measuring the contact angle of water at nanoscale is highly reduced.
Project description:Conformational sampling of biomolecules using molecular dynamics simulations often produces a large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here, we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE), that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscape of protein folding with highly separated clusters that correspond to the metastable states during folding. Since GMVAE uses a mixture of Gaussians as its prior, it can directly acknowledge the multi-basin nature of the protein folding free energy landscape. To make the model end-to-end differentiable, we use a Gumbel-softmax distribution. We test the model on three long-timescale protein folding trajectories and show that GMVAE embedding resembles the folding funnel with folded states down the funnel and unfolded states outside the funnel path. Additionally, we show that the latent space of GMVAE can be used for kinetic analysis and Markov state models built on this embedding produce folding and unfolding timescales that are in close agreement with other rigorous dynamical embeddings such as time independent component analysis.
Project description:Variational autoencoders (VAEs) employ Bayesian inference to interpret sensory inputs, mirroring processes that occur in primate vision across both ventral [1] and dorsal [2] pathways. Despite their success, traditional VAEs rely on continuous latent variables, which deviates sharply from the discrete nature of biological neurons. Here, we developed the Poisson VAE ( 𝒫 -VAE), a novel architecture that combines principles of predictive coding with a VAE that encodes inputs into discrete spike counts. Combining Poisson-distributed latent variables with predictive coding introduces a metabolic cost term in the model loss function, suggesting a relationship with sparse coding which we verify empirically. Additionally, we analyze the geometry of learned representations, contrasting the 𝒫 -VAE to alternative VAE models. We find that the 𝒫 -VAE encodes its inputs in relatively higher dimensions, facilitating linear separability of categories in a downstream classification task with a much better (5×) sample efficiency. Our work provides an interpretable computational framework to study brain-like sensory processing and paves the way for a deeper understanding of perception as an inferential process.
Project description:BackgroundCOVID-19 has largely impacted the management of Visceral leishmaniasis (VL), like several other Neglected Tropical Diseases. The impact was particularly evident in Lower and Middle-Income countries where the already inadequate healthcare resources were diverted to managing the COVID-19 pandemic. Bangladesh achieved the elimination target for VL in 2016. To sustain this success, early diagnosis and treatment, effective vector control, and periodic surveillance are paramount. However, the specific control measures for VL in Bangladesh that were hampered during COVID-19 and their extent are unknown.MethodsThis study aimed at identifying the gaps and challenges in the follow-up of treated VL patients by interviewing both the treated VL cases and their health service providers. We followed VL cases treated between 2019 and 2020 in five VL endemic subdistricts (upazilas) both retrospectively and prospectively to monitor clinical improvement, relapse, or other consequences. Moreover, interviews were conducted with the health service providers to assess the impact of COVID-19 on VL case detection, treatment, reporting, vector control operations, and logistic supply chain management.ResultsThere was no added delay for VL diagnosis; however, VL treatment initiation and reporting time increased almost two-fold due to COVID-19. Indoor Residual Spraying activity was significantly hampered due to a shortage of insecticides. Out of 44 enrolled and treated VL patients, two relapsed (4.5 %), two developed Para Kala-Azar Dermal Leishmaniasis (4.5 %), and three (6.8 %) Post Kala-Azar Dermal Leishmaniasis (PKDL). The health service providers highlighted patients` unwillingness to visit the hospital, financial constraints, and distance from the hospitals as the main reasons for missed follow-up visits (20.5 %). Building good communication in the community, awareness schemes, and incentive-based approaches were suggested as possible solutions to mitigate these problems.ConclusionLong-term follow-up is required for the early detection and management of VL relapse and PKDL cases. Effective vector control measures, capacity development, and identification of new VL hotspots are pivotal in the VL endemic regions to sustain the elimination goal.