Related papers: Network Models
Our world produces massive data every day; they exist in diverse forms, from pairwise data and matrix to time series and trajectories. Meanwhile, we have access to the versatile toolkit of network analysis. Networks also have different…
Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…
We present two different approaches to model power grids as interconnected networks of networks. Both models are derived from a model for spatially embedded mono-layer networks and are generalised to handle an arbitrary number of network…
Multiplex networks allow us to study a variety of complex systems where nodes connect to each other in multiple ways, for example friend, family, and co-worker relations in social networks. Link prediction is the branch of network analysis…
It is often the case that the performance of a neural network can be improved by adding layers. In real-world practices, we always train dozens of neural network architectures in parallel which is a wasteful process. We explored $CompNet$,…
Network analysis is often focused on characterizing the dependencies between network relations and node-level attributes. Potential relationships are typically explored by modeling the network as a function of the nodal attributes or by…
Given a valued graph, where both the nodes and the edges of the graph are associated with one or several values, any network function for a given node must be defined in terms of that node and its connected nodes in the graph. Generally,…
A general notion of operad is given, which includes as instances, the operads originally conceived to study loop spaces, as well as the higher operads that arise in the globular approach to higher dimensional algebra. In the framework of…
We construct a novel class of stochastic blockmodels using Bayesian nonparametric mixtures. These model allows us to jointly estimate the structure of multiple networks and explicitly compare the community structures underlying them, while…
Monolithic neural networks that make use of a single set of weights to learn useful representations for downstream tasks explicitly dismiss the compositional nature of data generation processes. This characteristic exists in data where…
Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most…
This work presents a detailed analysis of the combinatorics of modular operads. These are operad-like structures that admit a contraction operation as well as an operadic multiplication. Their combinatorics are governed by graphs that admit…
From interacting cellular components to networks of neurons and neural systems, interconnected units comprise a fundamental organizing principle of the nervous system. Understanding how their patterns of connections and interactions give…
We study mixing patterns in networks, meaning the propensity for nodes of different kinds to connect to one another. The phenomenon of assortative mixing, whereby nodes prefer to connect to others that are similar to themselves, has been…
We endow categories of non-symmetric operads with natural model structures. We work with no restriction on our operads and only assume the usual hypotheses for model categories with a symmetric monoidal structure. We also study categories…
By leveraging information technologies, organizations now have the ability to design their communication networks and crowdsourcing platforms to pursue various performance goals, but existing research on network design does not account for…
Network-structured data becomes ubiquitous in daily life and is growing at a rapid pace. It presents great challenges to feature engineering due to the high non-linearity and sparsity of the data. The local and global structure of the…
We introduce a new operad-like structure that we call a reconnectad; the ``input'' of an element of a reconnectad is a finite simple graph, rather than a finite set, and ``compositions'' of elements are performed according to the notion of…
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…
We generalize the construction of multitildes in the aim to provide multitilde operators for regular languages. We show that the underliying algebraic structure involves the action of some operads. An operad is an algebraic structure that…