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This paper extends an a posteriori error estimator for the elastic, Frank-Oseen model of liquid crystals, derived in [9], to include electric and flexoelectric effects. The problem involves a nonlinear coupled system of equations with a local unit-length constraint imposed via a penalty method. The proposed estimator is proven to be a reliable estimate of global approximation error. The performance of the coupled error estimator as a guide for adaptive refinement is shown in the numerical results, where the adapted grids successfully yield substantial reductions in computational work and comparable or better conformance to important physical laws., Comment: 10 Pages, 2 Figures, Conference: LSSC 2023. arXiv admin note: substantial text overlap with arXiv:1806.06248

Deep models trained through maximum likelihood have achieved state-of-the-art results for survival analysis. Despite this training scheme, practitioners evaluate models under other criteria, such as binary classification losses at a chosen set of time horizons, e.g. Brier score (BS) and Bernoulli log likelihood (BLL). Models trained with maximum likelihood may have poor BS or BLL since maximum likelihood does not directly optimize these criteria. Directly optimizing criteria like BS requires inverse-weighting by the censoring distribution. However, estimating the censoring model under these metrics requires inverse-weighting by the failure distribution. The objective for each model requires the other, but neither are known. To resolve this dilemma, we introduce Inverse-Weighted Survival Games. In these games, objectives for each model are built from re-weighted estimates featuring the other model, where the latter is held fixed during training. When the loss is proper, we show that the games always have the true failure and censoring distributions as a stationary point. This means models in the game do not leave the correct distributions once reached. We construct one case where this stationary point is unique. We show that these games optimize BS on simulations and then apply these principles on real world cancer and critically-ill patient data., Comment: Neurips 2021

Causal inference relies on two fundamental assumptions: ignorability and positivity. We study causal inference when the true confounder value can be expressed as a function of the observed data; we call this setting estimation with functional confounders (EFC). In this setting, ignorability is satisfied, however positivity is violated, and causal inference is impossible in general. We consider two scenarios where causal effects are estimable. First, we discuss interventions on a part of the treatment called functional interventions and a sufficient condition for effect estimation of these interventions called functional positivity. Second, we develop conditions for nonparametric effect estimation based on the gradient fields of the functional confounder and the true outcome function. To estimate effects under these conditions, we develop Level-set Orthogonal Descent Estimation (LODE). Further, we prove error bounds on LODE's effect estimates, evaluate our methods on simulated and real data, and empirically demonstrate the value of EFC., Comment: 17 pages, 7 figures, 2 tables

Survival analysis models the distribution of time until an event of interest, such as discharge from the hospital or admission to the ICU. When a model's predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model's calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows practitioners to directly optimize calibration and strike a desired balance between predictive power and calibration. In our experiments, we fit a variety of shallow and deep models on simulated data, a survival dataset based on MNIST, on length-of-stay prediction using MIMIC-III data, and on brain cancer data from The Cancer Genome Atlas. We show that the models we study can be miscalibrated. We give experimental evidence on these datasets that X-CAL improves D-CALIBRATION without a large decrease in concordance or likelihood.

The magnetohydrodynamics (MHD) equations model a wide range of plasma physics applications and are characterized by a nonlinear system of partial differential equations that strongly couples a charged fluid with the evolution of electromagnetic fields. After discretization and linearization, the resulting system of equations is generally difficult to solve due to the coupling between variables, and the heterogeneous coefficients induced by the linearization process. In this paper, we investigate multigrid preconditioners for this system based on specialized relaxation schemes that properly address the system structure and coupling. Three extensions of Vanka relaxation are proposed and applied to problems with up to 170 million degrees of freedom and fluid and magnetic Reynolds numbers up to 400 for stationary problems and up to 20,000 for time-dependent problems.

Causal inference often relies on the counterfactual framework, which requires that treatment assignment is independent of the outcome, known as strong ignorability. Approaches to enforcing strong ignorability in causal analyses of observational data include weighting and matching methods. Effect estimates, such as the average treatment effect (ATE), are then estimated as expectations under the reweighted or matched distribution, P . The choice of P is important and can impact the interpretation of the effect estimate and the variance of effect estimates. In this work, instead of specifying P, we learn a distribution that simultaneously maximizes coverage and minimizes variance of ATE estimates. In order to learn this distribution, this research proposes a generative adversarial network (GAN)-based model called the Counterfactual $\chi$-GAN (cGAN), which also learns feature-balancing weights and supports unbiased causal estimation in the absence of unobserved confounding. Our model minimizes the Pearson $\chi^2$ divergence, which we show simultaneously maximizes coverage and minimizes the variance of importance sampling estimates. To our knowledge, this is the first such application of the Pearson $\chi^2$ divergence. We demonstrate the effectiveness of cGAN in achieving feature balance relative to established weighting methods in simulation and with real-world medical data., Comment: 9 pages; 3 figures; See peer-reviewed work at Journal of Biomedical Informatics

This paper analyzes the discrete energy laws associated with first-order system least-squares (FOSLS) discretizations of time-dependent partial differential equations. Using the heat equation and the time-dependent Stokes' equation as examples, we discuss how accurately a FOSLS finite-element formulation adheres to the underlying energy law associated with the physical system. Using regularity arguments involving the initial condition of the system, we are able to give bounds on the convergence of the discrete energy law to its expected value (zero in the examples presented here). Numerical experiments are performed, showing that the discrete energy laws hold with order $\mathcal O\left(h^{2p}\right)$, where $h$ is the mesh spacing and $p$ is the order of the finite-element space. Thus, the energy law conformance is held with a higher order than the expected, $\mathcal{O}\left(h^p\right)$, convergence of the finite-element approximation. Finally, we introduce an abstract framework for analyzing the energy laws of general FOSLS discretizations.

Multiple equilibrium states arise in many physical systems, including various types of liquid crystal structures. Having the ability to reliably compute such states enables more accurate physical analysis and understanding of experimental behavior. This paper adapts and extends a deflation technique for the computation of multiple distinct solutions arising in the context of modeling equilibrium configurations of nematic and cholesteric liquid crystals. The deflation method is applied as part of an overall free-energy variational approach and is modified to fit the framework of optimization of a functional with pointwise constraints. It is shown that multigrid methods designed for the undeflated systems may be applied to efficiently solve the linear systems arising in the application of deflation. For the numerical algorithm, the deflation approach is interwoven with nested iteration, creating a dynamic and efficient method that further enables the discovery of distinct solutions. Finally, four numerical experiments are performed demonstrating the efficacy and accuracy of the algorithm in detecting important physical phenomena, including bifurcation and disclination behaviors. The final numerical experiment expands the algorithm to model cholesteric liquid crystals and illustrates the full discovery power of the deflation process., Comment: 22 Pages, 6 Figures, 5 Tables

A multi-cell He gas-scintillator active target, designed for the measurement of photoreaction cross sections, is described. The target has four main chambers, giving an overall thickness of 0.103 $\mathrm{g/cm^{2}}$ at an operating pressure of 2 MPa. Scintillations are read out by photomultiplier tubes and the addition of small amounts of $\mathrm{N}_{2}$ to the He, to shift the scintillation emission from UV to visible, is discussed. First results of measurements at the MAX IV Laboratory tagged-photon facility show that the target has good timing resolution and can cope well with a high-flux photon beam. The determination of reaction cross sections from target yields relies on a Monte Carlo simulation, which considers scintillation light transport, photodisintegration processes in $^{4}\mathrm{He}$, background photon interactions in target windows and interactions of the reaction-product particles in the gas and target container. The predictions of this simulation are compared to the measured target response., Comment: 24 pages, 15 figures

This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these methods when the necessary unit-length constraint is enforced by either continuous Lagrange multipliers or a penalty functional. Building on previous work in [1,2], the penalty method is derived and the linearizations within the nonlinear iteration are shown to be well-posed under certain assumptions. In addition, the paper discusses the effects of tailored trust-region methods and nested iteration for both formulations. Such methods are aimed at increasing the efficiency and robustness of each algorithms' nonlinear iterations. Three representative, free-elastic, equilibrium problems are considered to examine each method's performance. The first two configurations have analytical solutions and, therefore, convergence to the true solution is considered. The third problem considers more complicated boundary conditions, relevant in ongoing research, simulating surface nano-patterning. A multigrid approach is introduced and tested for a flexoelectrically coupled model to establish scalability for highly complicated applications. The Lagrange multiplier method is found to outperform the penalty method in a number of measures, trust regions are shown to improve robustness, and nested iteration proves highly effective at reducing computational costs., Comment: 28 Pages, 8 Figures, 15 Tables, 5 Procedures. Added and removed references, as well as some minor figure rearrangement

This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system free energy based on the electrically and flexoelectrically augmented Frank-Oseen free energy models. The Hessian, resulting from the linearization of the first-order optimality conditions, is shown to be invertible for both models when discretized by a mixed finite-element method under certain assumptions. This implies that the intermediate discrete linearizations are well-posed. A coupled multigrid solver with Vanka-type relaxation is proposed and numerically vetted for approximation of the solution to the linear systems arising in the linearizations. Two electric model numerical experiments are performed with the proposed iterative solver. The first compares the algorithm's solution of a classical Freedericksz transition problem to the known analytical solution and demonstrates the convergence of the algorithm to the true solution. The second experiment targets a problem with more complicated boundary conditions, simulating a nano-patterned surface. In addition, numerical simulations incorporating these nano-patterned boundaries for a flexoelectric model are run with the iterative solver. These simulations verify expected physical behavior predicted by a perturbation model. The algorithm accurately handles heterogeneous coefficients and efficiently resolves configurations resulting from classical and complicated boundary conditions relevant in ongoing research., Comment: 24 Pages, 10 Figures, 4 tables. arXiv admin note: substantial text overlap with arXiv:1402.3310

This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy based on the Frank-Oseen free-energy model. Solutions to the intermediate discretized free elastic linearizations are shown to exist generally and are unique under certain assumptions. This requires proving continuity, coercivity, and weak coercivity for the accompanying appropriate bilinear forms within a mixed finite-element framework. Error analysis demonstrates that the method constitutes a convergent scheme. Numerical experiments are performed for problems with a range of physical parameters as well as simple and patterned boundary conditions. The resulting algorithm accurately handles heterogeneous constant coefficients and effectively resolves configurations resulting from complicated boundary conditions relevant in ongoing research., Comment: 31 pages, 3 figures, 3 tables

This paper develops a first-order system least-squares (FOSLS) formulation for equations of two-phase flow. The main goal is to show that this discretization, along with numerical techniques such as nested iteration, algebraic multigrid, and adaptive local refinement, can be used to solve these types of complex fluid flow problems. In addition, from an energetic variational approach, it can be shown that an important quantity to preserve in a given simulation is the energy law. We discuss the energy law and inherent structure for two-phase flow using the Allen-Cahn interface model and indicate how it is related to other complex fluid models, such as magnetohydrodynamics. Finally, we show that, using the FOSLS framework, one can still satisfy the appropriate energy law globally while using well-known numerical techniques., Comment: 22 pages, 8 figures submitted to Journal of Computational Physics

The two-body photodisintegration of 3He has been investigated using tagged photons with energies from 14 -- 31 MeV at MAX-lab in Lund, Sweden. The two-body breakup channel was unambiguously identified by the (nonsimultaneous) detection of both protons and deuterons. This approach was made feasible by the over-determined kinematic situation afforded by the tagged-photon technique. Proton- and deuteron-energy spectra were measured using four silicon surface-barrier detector telescopes located at a laboratory angle of 90deg with respect to the incident photon-beam direction. Average statistical and systematic uncertainties of 5.7% and 6.6% in the differential cross section were obtained for 11 photon-energy bins with an average width of 1.2 MeV. The results are compared to previous experimental data measured at comparable photon energies as well as to the results of two recent Faddeev calculations which employ realistic potential models and take into account three-nucleon forces and final-state interactions. Both the accuracy and precision of the present data are improved over the previous measurements. The data are in good agreement with most of the previous results, and favor the inclusion of three-nucleon forces in the calculations., Comment: 12 pages, 13 figures; further Referee comments addressed

Differential cross sections for Compton scattering from the deuteron were measured at MAX-lab for incident photon energies of 55 MeV and 66 MeV at nominal laboratory angles of $45^\circ$, $125^\circ$, and $135^\circ$. Tagged photons were scattered from liquid deuterium and detected in three NaI spectrometers. By comparing the data with theoretical calculations in the framework of a one-boson-exchange potential model, the sum and difference of the isospin-averaged nucleon polarizabilities, $\alpha_N + \beta_N = 17.4 \pm 3.7$ and $\alpha_N - \beta_N = 6.4 \pm 2.4$ (in units of $10^{-4}$ fm$^3$), have been determined. By combining the latter with the global-averaged value for $\alpha_p - \beta_p$ and using the predictions of the Baldin sum rule for the sum of the nucleon polarizabilities, we have obtained values for the neutron electric and magnetic polarizabilities of $\alpha_n= 8.8 \pm 2.4$(total) $\pm 3.0$(model) and $\beta_n = 6.5 \mp 2.4$(total) $\mp 3.0$(model), respectively., Comment: 4 pages, 2 figures, revtex. The text is substantially revised. The cross sections are slightly different due to improvements in the analysis

A broad excited state was observed in 6-He with energy E_x = 5 +/- 1 MeV and width Gamma = 3 +/- 1 MeV, following the reaction Li-7(gamma,p)He-6. The state is consistent with a number of broad resonances predicted by recent cluster model calculations. The well-established reaction mechanism, combined with a simple and transparent analysis procedure confers considerable validity to this observation., Comment: 3 pages of LaTeX, 3 figures in PostScript, approved for publication in Phys. Rev. C, August, 2001

Differential cross sections for elastic scattering of photons have been measured for $^{40}$Ca at energies of 58 and 74 MeV and for $^{16}$O and $^4$He at 61 MeV, in the angular range from 45$^o$ to 150$^o$. Evidence is obtained that there are no significant in-medium modifications of the electromagnetic polarizabilities except for those originating from meson exchange currents., Comment: 20 pages including 5 Figures

Although there is now a good measure of agreement between Monte Carlo and high-temperature series expansion estimates for Ising ($n=1$) models, published results for the critical temperature from series expansions up to 12{\em th} order for the three-dimensional classical Heisenberg ($n=3$) and XY ($n=2$) model do not agree very well with recent high-precision Monte Carlo estimates. In order to clarify this discrepancy we have analyzed extended high-temperature series expansions of the susceptibility, the second correlation moment, and the second field derivative of the susceptibility, which have been derived a few years ago by L\"uscher and Weisz for general $O(n)$ vector spin models on $D$-dimensional hypercubic lattices up to 14{\em th} order in $K \equiv J/k_B T$. By analyzing these series expansions in three dimensions with two different methods that allow for confluent correction terms, we obtain good agreement with the standard field theory exponent estimates and with the critical temperature estimates from the new high-precision MC simulations. Furthermore, for the Heisenberg model we reanalyze existing series for the susceptibility on the BCC lattice up to 11{\em th} order and on the FCC lattice up to 12{\em th} order., Comment: 15 pages, Latex, 2 PS figures not included. FUB-HEP 18/92 and HLRZ 76/92