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Electrohydrodynamics is a discipline that studies the interaction between fluid motion and electric field. Finite element method, finite difference method and other numerical simulations are effective numerical calculation methods for electrofluid dynamics models. In this paper, the finite element format of the electrofluid dynamics model is established, and the second-order convergence accuracy of the format is achieved through time filtering method. Finally, a numerical example is given to verify the convergence.

Existing statistical methods for the analysis of micro-randomized trials (MRTs) are designed to estimate causal excursion effects using data from a single MRT. In practice, however, researchers can often find previous MRTs that employ similar interventions. In this paper, we develop data integration methods that capitalize on this additional information, leading to statistical efficiency gains. To further increase efficiency, we demonstrate how to combine these approaches according to a generalization of multivariate precision weighting that allows for correlation between estimates, and we show that the resulting meta-estimator possesses an asymptotic optimality property. We illustrate our methods in simulation and in a case study involving two MRTs in the area of smoking cessation.

The subject of this work is an adaptive stochastic Galerkin finite element method for parametric or random elliptic partial differential equations, which generates sparse product polynomial expansions with respect to the parametric variables of solutions. For the corresponding spatial approximations, an independently refined finite element mesh is used for each polynomial coefficient. The method relies on multilevel expansions of input random fields and achieves error reduction with uniform rate. In particular, the saturation property for the refinement process is ensured by the algorithm. The results are illustrated by numerical experiments, including cases with random fields of low regularity.

We propose a material design method via gradient-based optimization on compositions, overcoming the limitations of traditional methods: exhaustive database searches and conditional generation models. It optimizes inputs via backpropagation, aligning the model's output closely with the target property and facilitating the discovery of unlisted materials and precise property determination. Our method is also capable of adaptive optimization under new conditions without retraining. Applying to exploring high-Tc superconductors, we identified potential compositions beyond existing databases and discovered new hydrogen superconductors via conditional optimization. This method is versatile and significantly advances material design by enabling efficient, extensive searches and adaptability to new constraints.

We present the design and implementation of a tool for semi-automatic verification of functional specifications of operating system modules. Such verification tasks are traditionally done in interactive theorem provers, where the functionalities of the module are specified at abstract and concrete levels using data such as structures, algebraic datatypes, arrays, maps and so on. In this work, we provide encodings to SMT for these commonly occurring data types. This allows verification conditions to be reduced into a form suitable for SMT solvers. The use of SMT solvers combined with a tactic language allows semi-automatic verification of the specification. We apply the tool to verify functional specification for key parts of the uC-OS/II operating system, based on earlier work giving full verification of the system in Coq. We demonstrate a large reduction in the amount of human effort due to increased level of automation.

We present a finite element approach for diffusion problems with thermal fluctuations based on a fluctuating hydrodynamics model. The governing transport equations are stochastic partial differential equations with a fluctuating forcing term. We propose a discrete formulation of the stochastic forcing term that has the correct covariance matrix up to a standard discretization error. Furthermore, to obtain a numerical solution with spatial correlations that converge to those of the continuum equation, we derive a linear mapping to transform the finite element solution into an equivalent discrete solution that is free from the artificial correlations introduced by the spatial discretization. The method is validated by applying it to two diffusion problems: a second-order diffusion equation and a fourth-order diffusion equation. The theoretical (continuum) solution to the first case presents spatially decorrelated fluctuations, while the second case presents fluctuations correlated over a finite length. In both cases, the numerical solution presents a structure factor that approximates well the continuum one.

Conformal inference is a fundamental and versatile tool that provides distribution-free guarantees for many machine learning tasks. We consider the transductive setting, where decisions are made on a test sample of $m$ new points, giving rise to $m$ conformal $p$-values. While classical results only concern their marginal distribution, we show that their joint distribution follows a P\'olya urn model, and establish a concentration inequality for their empirical distribution function. The results hold for arbitrary exchangeable scores, including adaptive ones that can use the covariates of the test+calibration samples at training stage for increased accuracy. We demonstrate the usefulness of these theoretical results through uniform, in-probability guarantees for two machine learning tasks of current interest: interval prediction for transductive transfer learning and novelty detection based on two-class classification.

We combine the recent relaxation approach with multiderivative Runge-Kutta methods to preserve conservation or dissipation of entropy functionals for ordinary and partial differential equations. Relaxation methods are minor modifications of explicit and implicit schemes, requiring only the solution of a single scalar equation per time step in addition to the baseline scheme. We demonstrate the robustness of the resulting methods for a range of test problems including the 3D compressible Euler equations. In particular, we point out improved error growth rates for certain entropy-conservative problems including nonlinear dispersive wave equations.

Image information is restricted by the dynamic range of the detector, which can be addressed using multi-exposure image fusion (MEF). The conventional MEF approach employed in ptychography is often inadequate under conditions of low signal-to-noise ratio (SNR) or variations in illumination intensity. To address this, we developed a Bayesian approach for MEF based on a modified Poisson noise model that considers the background and saturation. Our method outperforms conventional MEF under challenging experimental conditions, as demonstrated by the synthetic and experimental data. Furthermore, this method is versatile and applicable to any imaging scheme requiring high dynamic range (HDR).

The use of discretized variables in the development of prediction models is a common practice, in part because the decision-making process is more natural when it is based on rules created from segmented models. Although this practice is perhaps more common in medicine, it is extensible to any area of knowledge where a predictive model helps in decision-making. Therefore, providing researchers with a useful and valid categorization method could be a relevant issue when developing prediction models. In this paper, we propose a new general methodology that can be applied to categorize a predictor variable in any regression model where the response variable belongs to the exponential family distribution. Furthermore, it can be applied in any multivariate context, allowing to categorize more than one continuous covariate simultaneously. In addition, a computationally very efficient method is proposed to obtain the optimal number of categories, based on a pseudo-BIC proposal. Several simulation studies have been conducted in which the efficiency of the method with respect to both the location and the number of estimated cut-off points is shown. Finally, the categorization proposal has been applied to a real data set of 543 patients with chronic obstructive pulmonary disease from Galdakao Hospital's five outpatient respiratory clinics, who were followed up for 10 years. We applied the proposed methodology to jointly categorize the continuous variables six-minute walking test and forced expiratory volume in one second in a multiple Poisson generalized additive model for the response variable rate of the number of hospital admissions by years of follow-up. The location and number of cut-off points obtained were clinically validated as being in line with the categorizations used in the literature.