Related papers: Preprocessing Ambiguous Imprecise Points
The reconstruction of an unknown quantity from noisy measurements is a mathematical problem relevant in most applied sciences, for example, in medical imaging, radar inverse scattering, or astronomy. This underlying mathematical problem is…
Real-life parallel machine scheduling problems can be characterized by: (i) limited information about the exact task duration at scheduling time, and (ii) an opportunity to reschedule the remaining tasks each time a task processing is…
We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…
Generative AI systems have revolutionized human interaction by enabling natural language-based coding and problem solving. However, the inherent ambiguity of natural language often leads to imprecise instructions, forcing users to…
The temporal analysis of products reactor provides a vast amount of transient kinetic information that may be used to describe a variety of chemical features including the residence time distribution, kinetic coefficients, number of active…
Neural networks used for multi-interaction trajectory reconstruction lack the ability to estimate the uncertainty in their outputs, which would be useful to better analyse and understand the systems they model. In this paper we extend the…
Given a set $P$ of $n$ uncertain points on the real line, each represented by its one-dimensional probability density function, we consider the problem of building data structures on $P$ to answer range queries of the following three types…
We preprocess the input subdivision with $n$ points on the plane in $O(n\sqrt{\log n})$ time to facilitate point location in constant time. Previously the preprocessing time is $O(n\log n)$ and point location takes $O(\log n)$ time.
Reinforcement Learning has applications in field of mechatronics, robotics, and other resource-constrained control system. Problem of resource allocation is primarily solved using traditional predefined techniques and modern deep learning…
Deep Learning systems excel in complex tasks but often lack transparency, limiting their use in critical applications. Counterfactual explanations, a core tool within eXplainable Artificial Intelligence (XAI), offer insights into model…
In this paper, using an optimal partition approach, we study the parametric analysis of a second-order conic optimization problem, where the objective function is perturbed along a fixed direction. We characterize the notions of so-called…
In 1972, Fredman proposes the problem of sorting under partial information: preprocess a directed acyclic graph $G$ with vertex set $X$ so that you can sort $X$ in $O(\log e(G))$ time, where $e(G)$ is the number of sorted orders compatible…
In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…
Preconditioning is a technique from numerical linear algebra that can accelerate algorithms to solve systems of equations. In this paper, we demonstrate how preconditioning can circumvent a stringent assumption for sign consistency in…
This paper analyzes the computational complexity of validated interval methods for uncertain nonlinear systems and steady-state enclosure. Interval analysis produces guaranteed enclosures that account for uncertainty and round-off, but its…
We propose and analyze a continuous-time robust reinforcement learning framework for optimal stopping under ambiguity. In this framework, an agent chooses a robust exploratory stopping time motivated by two objectives: robust…
Recoverable robust optimization is a multi-stage approach, where it is possible to adjust a first-stage solution after the uncertain cost scenario is revealed. We analyze this approach for a class of selection problems. The aim is to choose…
Quantifying the robustness of neural networks or verifying their safety properties against input uncertainties or adversarial attacks have become an important research area in learning-enabled systems. Most results concentrate around the…
A procedure and theoretical results are presented for the problem of determining a minimal robust positively invariant (RPI) set for a linear discrete-time system subject to unknown, bounded disturbances. The procedure computes, via the…
The linear subspaces of a multiresolution analysis (MRA) and the linear subspaces of the wavelet analysis induced by the MRA, together with the set inclusion relation, form a very special lattice of subspaces which herein is called a…