Related papers: Universal limit theorem for rough differential equ…
Fourier normal ordering \cite{Unt09bis} is a new algorithm to construct explicit rough paths over arbitrary H\"older-continuous multidimensional paths. We apply in this article the Fourier normal ordering ordering algorithm to the…
This article presents a formal model and formal safety proofs for the ABZ'25 case study in differential dynamic logic (dL). The case study considers an autonomous car driving on a highway avoiding collisions with neighbouring cars. Using…
The performance of search algorithms for grid-based pathfinding, e.g. A*, critically depends on the heuristic function that is used to focus the search. Recent studies have shown that informed heuristics that take the positions/shapes of…
A stable and fast path linking two arbitrary states of a quantum system is generally required for state-engineering protocols, such as stimulated Raman adiabatic passage, shortcuts to adiabaticity, and holonomic transformation. Such a path…
In this note we construct solutions to rough differential equations ${\rm d} Y = f(Y) \,{\rm d} X$ with a driver $X \in C^\alpha([0,T];\mathbb{R}^d)$, $\frac13 < \alpha \le \frac12$, using a splitting-up scheme. We show convergence of our…
Universal definitions of irredundance for X-set parameters are presented using blocking sets. This approach is modeled on (domination) irredundance (which uses closed neighborhoods as blocking sets) and zero forcing irredundance (which uses…
In this article, we address the control problem of unicycle path following, using a rigidly attached target point. The initial path following problem has been transformed into a reference trajectory following problem, using saturated…
We characterize generalized derivatives of the solution operator of the obstacle problem. This precise characterization requires the usage of the theory of so-called capacitary measures and the associated solution operators of relaxed…
The need to control the residual of a potentially nonlinear function $\mathcal{F}$ arises in several situations in mathematics. For example, computing the zeros of a given map, or the reduction of some cost function during an optimization…
Motivated by the recent advances in the theory of stochastic partial differential equations involving nonlinear functions of distributions, like the Kardar-Parisi-Zhang (KPZ) equation, we reconsider the unique solvability of one-dimensional…
With recently developed tools, we prove a homogenisation theorem for a random ODE with short and long-range dependent fractional noise. The effective dynamics are not necessarily diffusions, they are given by stochastic differential…
We bring a control perspective to the problem of identifying paths of measures for sampling via dynamic measure transport (DMT). We highlight the fact that commonly used paths may be poor choices for DMT and connect existing methods for…
We consider exact and averaged control problem for a system of quasi-linear ODEs and SDEs with a non-negative definite symmetric matrix of the system. The strategy of the proof is the standard linearization of the system by fixing the…
We consider the generic discrete open mappings in ${\mathbb R}^n$ under which the perturbation of extremal lengths of curve collections is controlled integrally via $\int Q(x)\eta^p(|x-x_0|) dm(x)$ with $n-1<p<n$, where $Q$ is a measurable…
We consider the problem of enumerating Dyck paths staying weakly above the x-axis with a limit to the number of consecutive up steps, or a limit to the number of consecutive down steps. We use Finite Operator Calculus to obtain formulas for…
In the long paper "Family Blowup formula, Admissible Graphs and the Enumeration of Singular Curves (I)" (appearing in JDG), the author solved the enumeration problem of nodal (or general singular) curve counting on algebraic surfaces by…
We prove two universal approximation theorems for a range of dropout neural networks. These are feed-forward neural networks in which each edge is given a random $\{0,1\}$-valued filter, that have two modes of operation: in the first each…
In this paper we propose distributed dual gradient algorithms for linearly constrained separable convex problems and analyze their rate of convergence under different assumptions. Under the strong convexity assumption on the primal…
The empirical mean of $n$ independent and identically distributed (i.i.d.) random variables $(X_1,\dots,X_n)$ can be viewed as a suitably normalized scalar projection of the $n$-dimensional random vector $X^{(n)}\doteq(X_1,\dots,X_n)$ in…
Sampling-based motion planners have proven to be efficient solutions to a variety of high-dimensional, geometrically complex motion planning problems with applications in several domains. The traditional view of these approaches is that…