Related papers: Connecting Curves in Higher Dimensions

We construct a connection and a curving on a bundle gerbe associated with lifting a structure group of a principal bundle to a central extension. The construction is based on certain structures on the bundle, i.e. connections and…

Hilbert's two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that…

We study complex analytic projective connections on surfaces in projective n-spaces in terms of the "second" neighborhood of the surface in the ambient space, and in terms of the osculating behavior of the integral curves. We also…

The transport properties of nanostructured systems are deeply affected by the geometry of the effective connections to metallic leads. In this work we derive a conductance expression for interacting systems whose connectivity geometries do…

The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.

The dynamical systems found in Nature are rarely isolated. Instead they interact and influence each other. The coupling functions that connect them contain detailed information about the functional mechanisms underlying the interactions and…

Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how…

We show that many of the unusual properties of the one-dimensional random quantum Ising model are shared also by dilute quantum Ising systems in the vicinity of a certain quantum transition in {\em any} dimension $d > 1$. Thus, while these…

Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…

We study the propagation in three dimensions of internal waves using ray tracing methods and traditional dynamical systems theory. The wave propagation on a cone that generalizes the Saint Andrew's cross justifies the introduction of an…

For a more general notion of Cartan connection we define characteristic classes, we investigate their relation to usual characteristic classes.

The curves of scaling behavior is a significant concept in fractal dimension analysis of complex systems. However, the underlying rationale of this kind of curves for fractal cities is not yet clear. The aim of this paper is at researching…

In this note we make use of some properties of vector fields on a manifold to give an alternate proof to [3] for the equivalence between connections and parallel transport on vector bundles over manifolds. Out of the proof will emerge a new…

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an…

Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of…

We generalize the array orthogonality property for perfect autocorrelation sequences to $n$-dimensional arrays. The generalized array orthogonality property is used to derive a number of $n$-dimensional perfect array constructions.

In functionally complex systems, higher-order connectivity is often revealed in the underlying geometry of networked units. Furthermore, such systems often show signatures of self-organized criticality, a specific type of non-equilibrium…

We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph…

Based on both qualitative method and numerical tests for a series of particular cases in the parameter region, a=1, 0<b <1, it is shown that the three-dimensional system (2) may have a series of interesting phenomena on the non-trivial…

We use stable maps, and their stable lifts to the Semple bundle variety of second-order curvilinear data, to calculate certain characteristic numbers for rational plane curves. These characteristic numbers involve first-order (tangency) and…