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Global spectral analysis (GSA) is used as a tool to test the accuracy of numerical methods with the help of canonical problems of convection and convection-diffusion equation which admit exact solutions. Similarly, events in turbulent flows…
Scientific machine learning reports predictive performance. It does not report whether the same prediction would survive a different draw of training data. Across $9$ chemistry benchmarks, two classifiers trained on independent bootstraps…
We study heterogeneous $k$-facility location games. In this model there are $k$ facilities where each facility serves a different purpose. Thus, the preferences of the agents over the facilities can vary arbitrarily. Our goal is to design…
This paper addresses patient heterogeneity associated with prediction problems in biomedical applications. We propose a systematic hypothesis testing approach to determine the existence of patient subgroup structure and the number of…
In Part I of this paper we have presented a simple model capable of describing the localized failure of a massive structure. In this part, we discuss the identification of the model parameters from two kinds of experiments: a uniaxial…
Current Lagrangian (particle-tracking) algorithms used to simulate diffusion-reaction equations must employ a certain number of particles to properly emulate the system dynamics---particularly for imperfectly-mixed systems. The number of…
We consider Heterogeneous Transfer Learning (HTL) from a source to a new target domain for high-dimensional regression with differing feature sets. Most homogeneous TL methods assume that target and source domains share the same feature…
Comparing two groups under different conditions is ubiquitous in the biomedical sciences. In many cases, samples from the two groups can be naturally paired; for example a pair of samples may come from the same individual under the two…
Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial…
Regularized regression models are well studied and, under appropriate conditions, offer fast and statistically interpretable results. However, large data in many applications are heterogeneous in the sense of harboring distributional…
We classify Keller maps $x + H$ in dimension $n$ over fields with $\tfrac16$, for which $H$ is homogeneous, and (1) deg $H = 3$ and rk $JH \le 2$; (2) deg $H = 3$ and $n \le 4$; (3) deg $H = 4$ and $n \le 3$; (4) deg $H = 4 = n$ and $H_1,…
Ordinal regression falls between discrete-valued classification and continuous-valued regression. Ordinal target variables can be associated with ranked random variables. These random variables are known as order statistics and they are…
We investigate the dynamics of cohesive particles in homogeneous isotropic turbulence, based on one-way coupled simulations that include Stokes drag, lubrication, cohesive and direct contact forces. We observe a transient flocculation phase…
For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…
Clustered data is ubiquitous in a variety of scientific fields. In this paper, we propose a flexible and interpretable modeling approach, called grouped heterogenous mixture modeling, for clustered data, which models cluster-wise…
We analyze the problem of comparing unitary transformations. The task is to decide, with minimal resources and maximal reliability, whether two given unitary transformations are identical or different. It is possible to make such…
We study the Non-Homogeneous Sequential Hypothesis Testing (NHSHT), where a single active Decision-Maker (DM) selects actions with heterogeneous positive costs to identify the true hypothesis under an average error constraint \(\delta\),…
Stochastic patrol routing is known to be advantageous in adversarial settings; however, the optimal choice of stochastic routing strategy is dependent on a model of the adversary. We adopt a worst-case omniscient adversary model from the…
In this paper, a subgroup least squares and a convex clustering are introduced for inferring a partially heterogenous linear regression that has potential application in the areas of precision marketing and precision medicine. The…
In recent years, significant advancements have been made in computational methods for analyzing masonry structures. Within the Finite Element Method, two primary approaches have gained traction: Micro and Macro Scale modeling, and their…