Related papers: Successive Continuation for Locating Connecting Or…
It is often unnoticed that the predominant way to use collocation methods is fundamentally flawed when applied to optimal control in robotics. Such methods assume that the system dynamics is given by a first order ODE, whereas robots are…
In autonomous differential equations where a single first integral is present, periodic orbits are well-known to belong to one-parameter families, parameterized by the first integral's values. This paper shows that this characteristic…
Positioning systems in self-organizing networks generally rely on measurements such as delay and received signal strength, which may be difficult to obtain and often require dedicated equipment. An alternative to such approaches is to use…
Topological bases of behaviour of trajectories for autonomous differential systems of the second order on sphere are stated. Stereographic atlas of trajectories is constructed. Differential connections between trajectories of…
In this paper, we will describe a combinatorial object to list the orbits in the ${\mathbb Z}$-graded Lie algebra, their Jordan bloc decomposition, their dimension, their dimension, the partial order and the equivariant local system (up to…
Order dependencies (ODs) capture relationships between ordered domains of attributes. Approximate ODs (AODs) capture such relationships even when there exist exceptions in the data. During automated discovery of ODs, validation is the…
Reliable robot pose estimation is a key building block of many robot autonomy pipelines, with LiDAR localization being an active research domain. In this work, a versatile self-supervised LiDAR odometry estimation method is presented, in…
While topology given by a linear order has been extensively studied, this cannot be said about the case when the order is given only locally. The aim of this paper is to fill this gap. We consider relation between local orderability and…
Certain solutions of autonomous PDEs without any boundary conditions describing the spatiotemporal evolution of a dependent variable in an unbounded spatial domain can be characterised as a travelling wave moving with constant speed. In the…
We consider an autonomous differential system in $\mathbb{R}^n$ with a periodic orbit and we give a new method for computing the characteristic multipliers associated to it. Our method works when the periodic orbit is given by the…
In this paper, convergent, multi-infinite, series solutions are derived for the homoclinic orbits of a canonical fourth-order ODE system, in both reversible and non-reversible cases. This ODE includes traveling-wave reductions of many…
In this work we extend the framework of monotone dynamical systems to a broad and important class of stochastic equations, namely cooperative McKean-Vlasov SDEs with multiplicative noise. Under a locally dissipative assumption, our main…
The present work considers the localization problem in wireless sensor networks formed by fixed nodes. Each node seeks to estimate its own position based on noisy measurements of the relative distance to other nodes. In a centralized batch…
A method of embedding partially ordered sets into linear spaces is presented. The problem of finding all orthocomplementations in a finite lattice is reduced to a linear programming problem.
Locating each node in a wireless sensor network is essential for starting the monitoring job and sending information about the area. One method that has been used in hard and inaccessible environments is randomly scattering each node in the…
This paper explores the state of the art on to methods to verify and validate navigation algorithms for autonomous surface ships. We perform a systematic mapping study to find research works published in the last 10 years proposing new…
Starting from a semiclassical quantization condition based on the trace formula, we derive a periodic-orbit formula for the distribution of spacings of eigenvalues with k intermediate levels. Numerical tests verify the validity of this…
Low earth orbit (LEO) satellite constellation-enabled communication networks are expected to be an important part of many Internet of Things (IoT) deployments due to their unique advantage of providing seamless global coverage. In this…
We extend the use of piecewise orthogonal collocation to computing periodic solutions of renewal equations, which are particularly important in modeling population dynamics. We prove convergence through a rigorous error analysis. Finally,…
Potts models, which can be used to analyze dependent observations on a lattice, have seen widespread application in a variety of areas, including statistical mechanics, neuroscience, and quantum computing. To address the intractability of…