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Within data-driven artificial intelligence (AI) systems for industrial applications, ensuring the reliability of the incoming data streams is an integral part of trustworthy decision-making. An approach to assess data validity is data…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…
We present a novel framework for deriving integral constraints for correlators on conformal line defects. These constraints emerge from the non-linearly realized ambient-space conformal symmetry. To validate our approach, we examine several…
Model-free and data-driven prediction of tipping point transitions in nonlinear dynamical systems is a challenging and outstanding task in complex systems science. We propose a novel, fully data-driven machine learning algorithm based on…
Machine learning methods rely on data. However, gathering suitable data can be challenging due to availability constraints, cost, or the need for domain expertise. Expanding datasets with additional sources is a common response to limited…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
Concurrent separation logics have helped to significantly simplify correctness proofs for concurrent data structures. However, a recurring problem in such proofs is that data structure abstractions that work well in the sequential setting…
In this paper, we introduce a compositional method for the construction of finite abstractions of interconnected discrete-time switched systems. Particularly, we use a notion of so-called alternating simulation function as a relation…
Bounce-averaged theories provide a framework for simulating relatively slow processes, such as collisional transport and quasilinear diffusion, by averaging these processes over the fast periodic motions of a particle on a closed orbit.…
Recent deep learning methods for object detection rely on a large amount of bounding box annotations. Collecting these annotations is laborious and costly, yet supervised models do not generalize well when testing on images from a different…
Frequency-domain unsteady lifting-line theory is better developed than its time-domain counterpart. To take advantage of this, this paper transforms time-domain kinematics to the frequency domain, performs a convolution and then returns the…
ion is one of the most promising approaches to improve the performance of problem solvers. In several domains abstraction by dropping sentences of a domain description -- as used in most hierarchical planners -- has proven useful. In this…
We derive a numerical method, based on operator splitting, to abstract parabolic semilinear boundary coupled systems. The method decouples the linear components which describe the coupling and the dynamics in the bulk and on the surface,…
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which…
We study the problem of semi-supervised anomaly detection with domain adaptation. Given a set of normal data from a source domain and a limited amount of normal examples from a target domain, the goal is to have a well-performing anomaly…
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…
This paper deals with bounding the error on the estimation of quantities of interest obtained by finite element and domain decomposition methods. The proposed bounds are written in order to separate the two errors involved in the resolution…
Abstracting Gradual Typing (AGT) is a systematic approach to designing gradually-typed languages. Languages developed using AGT automatically satisfy the formal semantic criteria for gradual languages identified by Siek et al. [2015].…
This paper proposes a novel approach for designing functional observers for nonlinear systems, with linear error dynamics and assignable poles. Sufficient conditions for functional observability are first derived, leading to functional…
A restrictive assumption in change point analysis is "stationarity under the null hypothesis of no change-point", which is crucial for asymptotic theory but not very realistic from a practical point of view. For example, if change point…