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In linear regression, the least squares (LS) estimator has certain optimality properties if the errors are normally distributed. This assumption is often violated in practice, partly caused by data outliers. Robust estimators can cope with…
Time series analysis plays a critical role in numerous applications, supporting tasks such as forecasting, classification, anomaly detection, and imputation. In this work, we present the time series pattern machine (TSPM), a model designed…
The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improving the efficiency of such solvers is careful design of…
Fine-tuning pre-trained language models (PLMs) has become a dominant paradigm in applying PLMs to downstream tasks. However, with limited fine-tuning, PLMs still struggle with the discrepancies between the representation obtained from the…
Digital pathology based on whole slide images (WSIs) plays a key role in cancer diagnosis and clinical practice. Due to the high resolution of the WSI and the unavailability of patch-level annotations, WSI classification is usually…
Material discovery is a critical area of research with the potential to revolutionize various fields, including carbon capture, renewable energy, and electronics. However, the immense scale of the chemical space makes it challenging to…
In this paper, phase correction and amplitude compensation are introduced to a previously developed mixed domain method (MDM), which is only accurate for modeling wave propagation in weakly heterogeneous media. Multiple reflections are also…
We present describe a new computer code that solves the radiative transfer problem on multi-resolution grids. If the cloud model is from an MHD simulation on a regular cartesian grid, criteria based for example on local density or velocity…
We discuss parallel (additive) and sequential (multiplicative) variants of overlapping Schwarz methods for the Helmholtz equation in $\mathbb{R}^d$, with large real wavenumber and smooth variable wave speed. The radiation condition is…
Extreme-mass-ratio inspirals are one of the most exciting and promising target sources for space-based interferometers (such as LISA, TianQin). The observation of their emitted gravitational waves will offer stringent tests on general…
Modal phase matching (MPM) is a widely used phase matching technique in Al$_x$Ga$_{1-x}$As and other $\chi^{(2)}$ nonlinear waveguides for efficient wavelength conversions. The use of a non-fundamental spatial mode compensates the material…
To what extent can particulate random media be characterised using direct wave backscattering from a single receiver/source? Here, in a two dimensional setting, we show using a machine learning approach that both the particle radius and…
Due to it's simplicity the diffuse mismatch model (DMM) remains a popular description of phonon transmission across solid-solid boundaries. However, it remains unclear in which situations the DMM should be expected to be a valid model of…
This work studies optimal detection for communication over diffusion-based molecular timing (DBMT) channels. The transmitter simultaneously releases multiple information particles, where the information is encoded in the time of release.…
Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model…
We study the fundamental problem of \emph{moduli selection} in the Robust Chinese Remainder Theorem (RCRT), where each residue may be perturbed by a bounded error. Consider $L$ moduli of the form $m_i = \Gamma_i m$ ($1 \le i \le L$), where…
Full-waveform inversion (FWI) is an effective method for imaging subsurface properties using sparsely recorded data. It involves solving a wave propagation problem to estimate model parameters that accurately reproduce the data. Recent…
Multiscale problems are computationally costly to solve by direct simulation because the smallest scales must be represented over a domain determined by the largest scales of the problem. We have developed and analyzed new numerical methods…
Large language models (LLMs) are pretrained by minimizing the cross-entropy loss for next-token prediction. In this paper, we study whether this optimization strategy can induce geometric structure in the learned model weights and context…
Assimilation of data into a fire-spread model is formulated as an optimization problem. The level set equation, which relates the fire arrival time and the rate of spread, is allowed to be satisfied only approximately, and we minimize a…