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Traditional centralized stability analysis struggles with scalability in large complex modern power grids. This two-part paper proposes a compositional and equilibrium-free approach to analyzing power system stability. In Part I, we prove…
We study feature selection in high-dimensional regression under two distinct sources of instability: sampling variability and measurement error in the design matrix. Stability Selection addresses the former through sub-sampling and…
High-throughput screening of large hypothetical databases of metal-organic frameworks (MOFs) can uncover new materials, but their stability in real-world applications is often unknown. We leverage community knowledge and machine learning…
The assignment game models a housing market where buyers and sellers are matched, and transaction prices are set so that the resulting allocation is stable. Shapley and Shubik showed that every stable allocation is necessarily built on a…
Inferring step-wise actions to assemble 3D objects with primitive bricks from images is a challenging task due to complex constraints and the vast number of possible combinations. Recent studies have demonstrated promising results on…
Decision trees and logistic regression are one of the most popular and well-known machine learning algorithms, frequently used to solve a variety of real-world problems. Stability of learning algorithms is a powerful tool to analyze their…
We study stable matchings that are robust to preference changes in the two-sided stable matching setting of Gale and Shapley [GS62]. Given two instances $A$ and $B$ on the same set of agents, a matching is said to be robust if it is stable…
Voltage stability in modern power systems involves coupled dynamics across multiple time scales. Conventional methods based on time-scale separation or static stability margins may overlook instabilities caused by the coupling of slow and…
Reinforcement learning has received significant interest in recent years, due primarily to the successes of deep reinforcement learning at solving many challenging tasks such as playing Chess, Go and online computer games. However, with the…
Fractional derivative and delay are important tools in modeling memory properties in the natural system. This work deals with the stability analysis of a fractional order delay differential equation \begin{equation*} D^\alpha x(t)=\delta…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
In this paper we consider the stability issue for the inverse problem of determining an unknown inclusion contained in an elastic body by all the pairs of measurements of displacement and traction taken at the boundary of the body. Both the…
Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content…
Many safety-critical scientific and engineering systems evolve according to differential-algebraic equations (DAEs), where dynamical behavior is constrained by physical laws and admissibility conditions. In practice, these systems operate…
We develop an automated computational modeling framework for rapid gradient-based design of multistable soft mechanical structures composed of non-identical bistable unit cells with appropriate geometric parameterization. This framework…
As machine learning black boxes are increasingly being deployed in real-world applications, there has been a growing interest in developing post hoc explanations that summarize the behaviors of these black boxes. However, existing…
The field of complex self-assembly is moving toward the design of multi-particle structures consisting of thousands of distinct building blocks. To exploit the potential benefits of structures with such `addressable complexity,' we need to…
Lego is a well-known platform for prototyping pixelized objects. However, robotic Lego prototyping (i.e., manipulating Lego bricks) is challenging due to the tight connections and accuracy requirements. This paper investigates safe and…
This paper studies stability analysis of DC microgrids with uncertain constant power loads (CPLs). It is well known that CPLs have negative impedance effects, which may cause instability in a DC microgrid. Existing works often study the…
Owing to their inherently interpretable structure, decision trees are commonly used in applications where interpretability is essential. Recent work has focused on improving various aspects of decision trees, including their predictive…