Related papers: Belyi map verification using certified path tracki…
Control architectures are often implemented in a layered fashion, combining independently designed blocks to achieve complex tasks. Providing guarantees for such hierarchical frameworks requires considering the capabilities and limitations…
In the field of robotics, researchers face a critical challenge in ensuring reliable and efficient task planning. Verifying high-level task plans before execution significantly reduces errors and enhance the overall performance of these…
Drawing network maps automatically comprises two challenging steps, namely laying out the map and placing non-overlapping labels. In this paper we tackle the problem of labeling an already existing network map considering the application of…
Formal modelling is a powerful tool for developing complex systems. At MongoDB, we use TLA+ to model and verify multiple aspects of several systems. Ensuring conformance between a specification and its implementation can add value to any…
In a previous paper we classified the homotopy classes of proper Fredholm maps from an infinite dimensional Hilbert manifold to its model space in terms of a suitable version of framed cobordism. We explicitly computed these homotopy…
This paper describes our work on demonstrating verification technologies on a flight-critical system of realistic functionality, size, and complexity. Our work targeted a commercial aircraft control system named Transport Class Model (TCM),…
We classify projective plane nonsingular curves admitting a 3-term presentation; they exist in any degree, generally constitute 5 birational families and are defined over rational numbers. The Belyi functions on all these curves are…
For isolated complex hypersurface singularities with real defining equation we show the existence of a monodromy vector field such that complex conjugation intertwines the local monodromy diffeomorphism with its inverse. In particular, it…
We prove that a proper holomorphic map on the unit disk in the complex plane is uniquely determined up to post-composition with a Moebius transformation by its critical points.
An \emph{s-graph} is a graph with two kinds of edges: \emph{subdivisible} edges and \emph{real} edges. A \emph{realisation} of an s-graph $B$ is any graph obtained by subdividing subdivisible edges of $B$ into paths of arbitrary length (at…
We prove the existence and the essential uniqueness of canonical models for the forward (resp. backward) iteration of a holomorphic self-map $f$ of a cocompact Kobayashi hyperbolic complex manifold, such as the ball $\mathbb{B}^q$ or the…
Let $\Hol_{x_0}^{{\bf n}} (\C\P^1, X)$ be the space of based holomorphic maps of degree ${\bf n}$ from $\C\P^1$ into a simply connected algebraic variety $X$. Under some condition we prove that the map $\map \Hol_{x_0}^{{\bf n}} (\C\P^1,…
We present a reusable formally verified safety net that provides end-to-end safety and liveness guarantees for 2D waypoint-following of Dubins-type ground robots with tolerances and acceleration. We: i) Model a robot in differential dynamic…
The logarithmic connections studied in the paper are direct images of regular connections on line bundles over genus-2 double covers of the elliptic curve. We give an explicit parametrization of all such connections, determine their…
Real-world reinforcement learning is often \emph{nonstationary}: rewards and dynamics drift, accelerate, oscillate, and trigger abrupt switches in the optimal action. Existing theory often represents nonstationarity with coarse-scale models…
In this work, we describe a method for large-scale 3D cell-tracking through a segmentation selection approach. The proposed method is effective at tracking cells across large microscopy datasets on two fronts: (i) It can solve problems…
We present in this position paper a methodology to validate legal governance regulatory models from an empirical approach, as illustrated by means of three diagrams: (i) a scheme drawing the rule and meta-rule of law; (ii) a metamodel for…
The monotonicity of entropy is investigated for real quadratic rational maps on the real circle $\mathbb{R}\cup\{\infty\}$ based on the natural partition of the corresponding moduli space $\mathcal{M}_2(\mathbb{R})$ into its monotonic,…
On the one hand, ordered completion is a fundamental technique in equational theorem proving that is employed by automated tools. On the other hand, their complexity makes such tools inherently error prone. As a remedy to this situation we…
We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system $x' = f(x,y,\epsilon), y' = \epsilon g(x,y,\epsilon)$ with…