Quantum fluids in nanopores

We describe calculations of the properties of quantum fluids inside nanotubes of various sizes. Very small radius ($R$) pores confine the gases to a line, so that a one-dimensional (1D) approximation is applicable; the low temperature behavior of 1D $^4$He is discussed. Somewhat larger pores permit the particles to move off axis, resulting eventually in a transition to a cylindrical shell phase--a thin film near the tube wall; we explored this behavior for H$_2$. At even larger $R\sim 1$ nm, both the shell phase and an axial phase are present. Results showing strong binding of cylindrical liquids $^4$He and $^3$He are discussed.Comment: 8 pages, 4 figures, uses ws-ijmpb, graphicx, xspace; minor revisions from version published in Proc. 13th Intl. Conference on Recent Progress in Many-Body Theories (QMBT13), Buenos Aires, 200

Upscaling fluxes from towers to regions, continents and global scales using datadriven approaches

Quantifying the current carbon cycle of terrestrial ecosystems requires that we translate spatially sparse measurements into consistent, gridded flux estimates at the regional scale. This is particularly challenging in heterogeneous regions such as the northern forests of the United States. We use a network of 17 eddy covariance flux towers deployed across the Upper Midwest region of northern Wisconsin and Michigan and upscale flux observations from towers to the regional scale. This region is densely instrumented and provides a unique test bed for regional upscaling. We develop a simple Diagnostic Carbon Flux Model (DCFM) and use flux observations and a data assimilation approach to estimate the model parameters. We then use the optimized model to produce gridded flux estimates across the region. We find that model parameters vary not only across plant functional types (PFT) but also within a given PFT. Our results show that the parameter estimates from a single site are not representative of the parameter values of a given PFT; cross-site (or joint) optimization using observations from multiple sites encompassing a range of site and climate conditions considerably improves the representativeness and robustness of parameter estimates. Parameter variability within a PFT can result in substantial variability in regional flux estimates. We also find that land cover representation including land cover heterogeneity and the spatial resolution and accuracy of land cover maps can lead to considerable uncertainty in regional flux estimates. In heterogeneous, complex regions, detailed and accurate land cover maps are essential for accurate estimation of regional fluxes

Upscaling carbon fluxes from towers to the regional scale: Influence of parameter variability and land cover representation on regional flux estimates

Quantifying the current carbon cycle of terrestrial ecosystems requires that we translate spatially sparse measurements into consistent, gridded flux estimates at the regional scale. This is particularly challenging in heterogeneous regions such as the northern forests of the United States. We use a network of 17 eddy covariance flux towers deployed across the Upper Midwest region of northern Wisconsin and Michigan and upscale flux observations from towers to the regional scale. This region is densely instrumented and provides a unique test bed for regional upscaling. We develop a simple Diagnostic Carbon Flux Model (DCFM) and use flux observations and a data assimilation approach to estimate the model parameters. We then use the optimized model to produce gridded flux estimates across the region. We find that model parameters vary not only across plant functional types (PFT) but also within a given PFT. Our results show that the parameter estimates from a single site are not representative of the parameter values of a given PFT; cross-site (or joint) optimization using observations from multiple sites encompassing a range of site and climate conditions considerably improves the representativeness and robustness of parameter estimates. Parameter variability within a PFT can result in substantial variability in regional flux estimates. We also find that land cover representation including land cover heterogeneity and the spatial resolution and accuracy of land cover maps can lead to considerable uncertainty in regional flux estimates. In heterogeneous, complex regions, detailed and accurate land cover maps are essential for accurate estimation of regional fluxes

Learning Active Subspaces for Effective and Scalable Uncertainty Quantification in Deep Neural Networks

Bayesian inference for neural networks, or Bayesian deep learning, has the potential to provide well-calibrated predictions with quantified uncertainty and robustness. However, the main hurdle for Bayesian deep learning is its computational complexity due to the high dimensionality of the parameter space. In this work, we propose a novel scheme that addresses this limitation by constructing a low-dimensional subspace of the neural network parameters-referred to as an active subspace-by identifying the parameter directions that have the most significant influence on the output of the neural network. We demonstrate that the significantly reduced active subspace enables effective and scalable Bayesian inference via either Monte Carlo (MC) sampling methods, otherwise computationally intractable, or variational inference. Empirically, our approach provides reliable predictions with robust uncertainty estimates for various regression tasks

Identifying Bayesian Optimal Experiments for Uncertain Biochemical Pathway Models

Pharmacodynamic (PD) models are mathematical models of cellular reaction networks that include drug mechanisms of action. These models are useful for studying predictive therapeutic outcomes of novel drug therapies in silico. However, PD models are known to possess significant uncertainty with respect to constituent parameter data, leading to uncertainty in the model predictions. Furthermore, experimental data to calibrate these models is often limited or unavailable for novel pathways. In this study, we present a Bayesian optimal experimental design approach for improving PD model prediction accuracy. We then apply our method using simulated experimental data to account for uncertainty in hypothetical laboratory measurements. This leads to a probabilistic prediction of drug performance and a quantitative measure of which prospective laboratory experiment will optimally reduce prediction uncertainty in the PD model. The methods proposed here provide a way forward for uncertainty quantification and guided experimental design for models of novel biological pathways