Related papers: Validated numerics for algebraic path tracking
A novel prize-winner algorithm designed for a path following problem within the Unmanned Aerial Vehicle (UAV) field is presented in this paper. The proposed approach exploits the advantages offered by the pure pursuing algorithm to set up…
Verification of C++ programs has seen considerable progress in several areas, but not for programs that use these languages' mathematical libraries. The reason is that all libraries in widespread use come with no guarantees about the…
We offer a digital signature scheme using Boolean automorphisms of a multivariate polynomial algebra over integers. Verification part of this scheme is based on the approximation of the number of zeros of a multivariate Boolean function.
In this paper, we review the problem of matrix completion and expose its intimate relations with algebraic geometry, combinatorics and graph theory. We present the first necessary and sufficient combinatorial conditions for matrices of…
This article presents a validation of a recently proposed strongly polynomial-time algorithm for the general linear programming problem. The proposed algorithm is an implicit reduction procedure that combines primal and dual linear…
Uncertainty quantification is essential in decision-making, especially when joint distributions of random variables are involved. While conformal prediction provides distribution-free prediction sets with valid coverage guarantees, it…
The identification of continuous-time (CT) systems from discrete-time (DT) input and output signals, i.e., the sampled data, has received considerable attention for half a century. The state-of-the-art methods are parametric methods and…
This paper proposes the Parallel WiSARD Object Tracker (PWOT), a new object tracker based on the WiSARD weightless neural network that is robust against quantization errors. Object tracking in video is an important and challenging task in…
Binary classification is widely used in ML production systems. Monitoring classifiers in a constrained event space is well known. However, real world production systems often lack the ground truth these methods require. Privacy concerns may…
Roundoff errors cannot be avoided when implementing numerical programs with finite precision. The ability to reason about rounding is especially important if one wants to explore a range of potential representations, for instance for FPGAs…
This paper investigates the application of probabilistic prediction methodologies in route planning within a road network context. Specifically, we introduce the Conformalized Quantile Regression for Graph Autoencoders (CQR-GAE), which…
This paper presents a numerical solver for computing continuous trajectories in non-convex environments. Our approach relies on a customized implementation of the Alternating Direction Method of Multipliers (ADMM) built upon two key…
Models for long-term point tracking are typically trained on large synthetic datasets. The performance of these models degrades in real-world videos due to different characteristics and the absence of dense ground-truth annotations.…
The aim of this paper is to present a symbolic computational algorithm that will allow us to deal with the feedback stabilization problem for continuous nonlinear polynomial systems. The overall approach is based on a methodology that…
We present an effective criterion for determining whether a (augmented) vertically parametrized polynomial system admits multiple positive zeros for some choice of parameter values. Our method builds on previous algorithms from chemical…
The physical coupling between robots has the potential to improve the capabilities of multi-robot systems in challenging manufacturing processes. However, the path tracking accuracy of physically coupled robots is not studied adequately,…
Path signatures have been proposed as a powerful representation of paths that efficiently captures the path's analytic and geometric characteristics, having useful algebraic properties including fast concatenation of paths through tensor…
In this paper we present a technique that improves rendering performance for real-time scenes with ray traced lighting in the presence of dynamic lights and objects. In particular we verify photon paths from the previous frame against…
This paper is about solving polynomial systems. It first recalls how to do that efficiently with a very high probability of correctness by reconstructing a rational univariate representation (rur) using Groebner revlex computation,…
This paper addresses the trajectory-tracking problem for discrete-time linear time-invariant systems with bounded parametric uncertainty, subject to hard constraints on system states, control inputs, and input rates. Unlike existing…