相关论文: Edge anisotropy and the geometric perspective on f…

Quantification of the stationary points and the associated basins of attraction of neural network loss surfaces is an important step towards a better understanding of neural network loss surfaces at large. This work proposes a novel method…

Given a smooth compact surface without focal points and of higher genus, it is shown that its geodesic flow is semi-conjugate to a continuous expansive flow with a local product structure such that the semi-conjugation preserves…

Network models with latent geometry have been used successfully in many applications in network science and other disciplines, yet it is usually impossible to tell if a given real network is geometric, meaning if it is a typical element in…

Many realistic systems such as infrastructures are characterized by spatial structure and anisotropic alignment. Here we propose and study a model for dealing with such characteristics by introducing a parameter that controls the strength…

The edge-degeneracy model is an exponential random graph model that uses the graph degeneracy, a measure of the graph's connection density, and number of edges in a graph as its sufficient statistics. We show this model is relatively…

Physical Flow Networks are different infrastructure networks that allow the flow of physical commodities through edges between its constituent nodes. These include power grid, natural gas transmission network, water pipelines etc. In such…

We present an approach to learning features that represent the local geometry around a point in an unstructured point cloud. Such features play a central role in geometric registration, which supports diverse applications in robotics and 3D…

We introduce a description of a minimal surface in a space with boundary, as the world-hypersurface that the entangling surface traces. It does so by evolving from the boundary to the interior of the bulk under an appropriate geometric…

We study spatial embeddings of random graphs in which nodes are randomly distributed in geographical space. We let the edge probability between any two nodes to be dependent on the spatial distance between them and demonstrate that this…

Many complex networks in the real world have community structures -- groups of well-connected nodes with important functional roles. It has been well recognized that the identification of communities bears numerous practical applications.…

The stationary isotropic Poisson line process was used to derive upper bounds on mean excess network geodesic length in Aldous and Kendall [Adv. in Appl. Probab. 40 (2008) 1-21]. The current paper presents a study of the geometry and…

A network-based analysis of a turbulent channel flow numerically solved at $Re_\tau=180$ is proposed as an innovative perspective for the spatial characterization of the flow field. Two spatial networks corresponding to the streamwise and…

The shortest path problem is related to many dynamic processes on networks, ranging from routing in communication networks to signaling in molecular interaction networks. When the network is fully known, the shortest path problem can be…

Many applications in traffic, civil engineering, or electrical engineering revolve around edge-level signals. Such signals can be categorized as inherently directed, for example, the water flow in a pipe network, and undirected, like the…

Most complex systems can be captured by graphs or networks. Networks connect nodes (e.g.\ neurons) through edges (synapses), thus summarizing the system's structure. A popular way of interrogating graphs is community detection, which…

Biological networks, such as cellular metabolic pathways or networks of corticocortical connections in the brain, are intricately organized, yet remarkably robust toward structural damage. Whereas many studies have investigated specific…

In this work we propose the use of a hirarchical extension of the polygonality index as a means to characterize and model geographical networks: each node is associated with the spatial position of the nodes, while the edges of the network…

The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…

This work contributes to the analysis of linear geometric polygon transformations with the aim to force a desired shape by an iterative procedure.

Temporal networks, defined as sequences of time-aggregated adjacency matrices, sample latent graph dynamics and trace trajectories in graph space. By interpreting each adjacency matrix as a different time snapshot of a scalar field,…