Related papers: Procedure to produce discretized path composed by …
In this paper, we consider the problem of generating inspection paths for robots. These paths should allow an attached measurement device to perform high-quality measurements. We formally show that generating robot paths, while maximizing…
We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as…
Path sums are a convenient symbolic formalism for quantum operations with applications to the simulation, optimization, and verification of quantum protocols. Unlike quantum circuits, path sums are not limited to unitary operations, but can…
We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This…
The theory of rough paths arose from a desire to establish continuity properties of ordinary differential equations involving terms of low regularity. While essentially an analytic theory, its main motivation and applications are in…
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of…
Diffusion models form an important class of generative models today, accounting for much of the state of the art in cutting edge AI research. While numerous extensions beyond image and video generation exist, few of such approaches address…
A directed graph is semi-transitive if and only if it is acyclic and for any directed path $u_1\rightarrow u_2\rightarrow \cdots \rightarrow u_t$, $t \geq 2$, either there is no edge from $u_1$ to $u_t$ or all edges $u_i\rightarrow u_j$…
Shape calculus concerns the calculation of directional derivatives of some quantity of interest, typically expressed as an integral. This article introduces a type of shape calculus based on localized dilation of boundary faces through…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
The design space of discrete-space diffusion or flow generative models are significantly less well-understood than their continuous-space counterparts, with many works focusing only on a simple masked construction. In this work, we aim to…
A bounded curvature path is a continuously differentiable piece-wise $C^2$ path with bounded absolute curvature connecting two points in the tangent bundle of a surface. These paths have been widely considered in computer science and…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
An application design is offered, which students of physics can use when authoring a solver for mechanical systems with constraints. A 'chainlist' concept is introduced to capture a constrained mechanical system configuration and to pass…
The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries:…
In this short note we show that for a Markovian open quantum system it is always possible to construct a unique set of perfectly consistent Schmidt paths, supporting quasi-classicality. Our Schmidt process, elaborated several years ago, is…
This article provides an overview of the performance and the theoretical complexity of approximate and exact methods for various versions of the shortest path problem. The proposed study aims to improve the resolution of a more general…
For electron transport in parallel-plane semiconducting structures, a model is developed that unifies ballistic and diffusive transport and thus generalizes the Drude model. The unified model is valid for arbitrary magnitude of the mean…
Directed paths have been used by several authors to describe concurrent executions of a program. Spaces of directed paths in an appropriate state space contain executions with all possible legal schedulings. It is interesting to investigate…
We consider the motion of a particle on a surface which is a small perturbation of the standard sphere. One may qualitatively describe the motion by means of a precessing great circle of the sphere. The observation is employed to derive a…