Related papers: Discrete Gliding Along Principal Curves

The rotating nuclei represent one of most interesting subjects for theoretical and experimental studies. They open a new dimension of nuclear landscape, namely, spin direction. Contrary to the majority of nuclear systems, their properties…

Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…

We study a rolling model from the perspective of probability. More precisely, we consider a Riemannian manifold rolling against Euclidean space, where the rolling is coupled with random slipping and twisting. The system is modelled by a…

Human social interactions are typically recorded as time-specific dyadic interactions, and represented as evolving (temporal) networks, where links are activated/deactivated over time. However, individuals can interact in groups of more…

We define general rotational surfaces of elliptic and hyperbolic type in the pseudo-Euclidean 4-space with neutral metric which are analogous to the general rotational surfaces of C. Moore in the Euclidean 4-space. We study Lorentz general…

Recently it was shown that slowly rotating neutron stars exhibit an interesting correlation between their moment of inertia $I$, their quadrupole moment $Q$, and their tidal deformation Love number $\lambda$ (the I-Love-Q relations),…

Real networks often form interacting parts of larger and more complex systems. Examples can be found in different domains, ranging from the Internet to structural and functional brain networks. Here, we show that these multiplex systems are…

Spatially embedded networks have attracted increasing attention in the last decade. In this context, new types of network characteristics have been introduced which explicitly take spatial information into account. Among others, edge…

Rotation curves of interacting galaxies often show that velocities are either rising or falling in the direction of the companion galaxy. We seek to reproduce and analyse these features in the rotation curves of simulated equal-mass…

The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally…

We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…

We study the problem of determining optimal coordinated motions for two disc robots in an otherwise obstacle-free plane. Using the total path length traced by the two disc centres as a measure of distance, we give an exact characterization…

We study random graph models for directed acyclic graphs, an important class of networks that includes citation networks, food webs, and feed-forward neural networks among others. We propose two specific models, roughly analogous to the…

Weight matrices in deep networks exhibit geometric continuity -- principal singular vectors of adjacent layers point in similar directions. While this property has been widely observed, its origin remains unexplained. Through experiments on…

Connecting curves have been shown to organize the rotational structure of strange attractors in three-dimensional dynamical systems. We extend the description of connecting curves and their properties to higher dimensions within the special…

We report in experiment and simulation the spontaneous formation of dynamically bound pairs of shape changing robots undergoing locally repulsive collisions. These physical `gliders' robustly emerge from an ensemble of individually…

Connections on principal bundles play a fundamental role in expressing the equations of motion for mechanical systems with symmetry in an intrinsic fashion. A discrete theory of connections on principal bundles is constructed by introducing…

Attention mechanisms are developing into a viable alternative to convolutional layers as elementary building block of NNs. Their main advantage is that they are not restricted to capture local dependencies in the input, but can draw…

In this paper, we present a principled method to model general planar sliding motion with distributed convex contact patch. The effect of contact patch with indeterminate pressure distribution can be equivalently modeled as the contact…

This paper is a continuation and an extension of our recent work [3] on the geometric structures of Laplacian eigenfunctions and their applications to inverse scattering problems. In [3], the analytic behaviour of the Laplacian…