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We study the pointwise decay properties of solutions to the incompressible Navier-Stokes equations, both in the space and time variables. It is well known that generic global solutions on $\mathbb{R}^n$ do not decay faster at infinity than…
Spatial functional data arise in many settings, such as particulate matter curves observed at monitoring stations and age population curves at each areal unit. Most existing functional regression models have limited applicability because…
Treatment effects in a wide range of economic, environmental, and epidemiological applications often vary across space, and understanding the heterogeneity of causal effects across space and outcome quantiles is a critical challenge in…
We derive a continuum sharp-interface model for moving contact lines with soluble surfactants in a thermodynamically consistent framework. The model consists of the isothermal two-phase incompressible Navier-Stokes equations for the fluid…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
We consider spatially dependent functional data collected under a geostatistics setting, where locations are sampled from a spatial point process. The functional response is the sum of a spatially dependent functional effect and a spatially…
Statistical models used to estimate the spatio-temporal pattern in disease risk from areal unit data represent the risk surface for each time period with known covariates and a set of spatially smooth random effects. The latter act as a…
Modeling the interference effect is an important issue in the field of causal inference. Existing studies rely on explicit and often homogeneous assumptions regarding interference structures. In this paper, we introduce a low-rank and…
Nonlinear dynamical stochastic models are ubiquitous in different areas. Excitable media models are typical examples with large state dimensions. Their statistical properties are often of great interest but are also very challenging to…
We model longitudinal macular thickness measurements to monitor the course of glaucoma and prevent vision loss due to disease progression. The macular thickness varies over a 6$\times$6 grid of locations on the retina with additional…
Instrumental variables (IVs) are often continuous, arising in diverse fields such as economics, epidemiology, and the social sciences. Existing approaches for continuous IVs typically impose strong parametric models or assume homogeneous…
We consider the time-dependent Navier-Stokes equations in a half-space with boundary data on the line $(x,y)=(x_0,y)$ assumed to be time-periodic (or stationary) with a fixed asymptotic velocity ${\bf u}_{\infty}=(1,0)$ at infinity. We show…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
Spatial confounding is how is called the confounding between fixed and spatial random effects. It has been widely studied and it gained attention in the past years in the spatial statistics literature, as it may generate unexpected results…
The Navier-Stokes equations for viscous, incompressible fluids are studied in the three-dimensional periodic domains, with the body force having an asymptotic expansion, when time goes to infinity, in terms of power-decaying functions in a…
This paper studies the identification of causal effects of a continuous treatment using a new difference-in-difference strategy. Our approach allows for endogeneity of the treatment, and employs repeated cross-sections. It requires an…
We propose the spatial-temporal aggregated predictor (STAP) modeling framework to address measurement and estimation issues that arise when assessing the relationship between built environment features (BEF) and health outcomes. Many BEFs…
Proximal causal learning is a promising framework for identifying the causal effect under the existence of unmeasured confounders. Within this framework, the doubly robust (DR) estimator was derived and has shown its effectiveness in…
The dominant paradigm in computational materials discovery relies on heavily parameterized deep architectures, including message-passing graph networks and equivariant models, that require millions of DFT-labeled training structures and…
Per- and polyfluoroalkyl substances (PFAS) are typically encountered as mixtures of distinct chemicals with distinct effects on multiple health outcomes. Estimating joint causal effects using spatially-dependent observed data is…