Related papers: The Geometry of Continuous Latent Space Models for…
Understanding network functionality requires integrating structure and dynamics, and emergent latent geometry induced by network-driven processes captures the low-dimensional spaces governing this interplay. Here, we focus on…
Turing patterns, arising from the interplay between competing species of diffusive particles, has long been an important concept for describing non-equilibrium self-organization in nature, and has been extensively investigated in many…
Mechanistic statistical models are commonly used to study the flow of biological processes. For example, in landscape genetics, the aim is to infer spatial mechanisms that govern gene flow in populations. Existing statistical approaches in…
Multidimensional network data can have different levels of complexity, as nodes may be characterized by heterogeneous individual-specific features, which may vary across the networks. This paper introduces a class of models for…
Despite the abundance of bipartite networked systems, their organizing principles are less studied, compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result…
Geometric constraints impact the formation of a broad range of spatial networks, from amino acid chains folding to proteins structures to rearranging particle aggregates. How the network of interactions dynamically self-organizes in such…
Complex systems, ranging from soft materials to wireless communication, are often organised as random geometric networks in which nodes and edges evenly fill up the volume of some space. Studying such networks is difficult because they…
The increasing prevalence of relational data describing interactions among a target population has motivated a wide literature on statistical network analysis. In many applications, interactions may involve more than two members of the…
Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…
The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected. Besides of providing a natural geometrical interpretation of…
In the framework of on nonassociative geometry, we introduce a new effective model that extends the statistical treatment of complex networks with hidden geometry. The small-world property of the network is controlled by nonlocal curvature…
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…
Latent space geometry provides a rigorous and empirically valuable framework for interacting with the latent variables of deep generative models. This approach reinterprets Euclidean latent spaces as Riemannian through a pull-back metric,…
Describing networks geometrically through low-dimensional latent metric spaces has helped design efficient learning algorithms, unveil network symmetries and study dynamical network processes. However, latent space embeddings are limited to…
Optically active networks show feature-rich emission that depends on the fine details of their geometry, and find diverse applications in random lasers, sensing devices and photonics processors. In these and other systems, a thorough and…
Network data is ubiquitous in various scientific disciplines, including sociology, economics, and neuroscience. Latent space models are often employed in network data analysis, but the geometric effect of latent space curvature remains a…
Neural computation in biological and artificial networks relies on the nonlinear summation of many inputs. The structural connectivity matrix of synaptic weights between neurons is a critical determinant of overall network function, but…
We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this…
Many types of data from fields including natural language processing, computer vision, and bioinformatics, are well represented by discrete, compositional structures such as trees, sequences, or matchings. Latent structure models are a…
The analytical characterization of coverage probability in finite three-dimensional wireless networks has long remained an open problem, hindered by the loss of spatial independence in finite-node settings and the coupling between link…