相关论文: Measuring the Hierarchy of Feedforward Networks

Network motifs are characteristic patterns which occur in the networks essentially more frequently than the other patterns. For five motifs found in S. Itzkovitz, U. Alon, Phys. Rev.~E, 2005, 71, 026117-1, hierarchical random graphs are…

Causal networks offer an intuitive framework to understand influence structures within time series systems. However, the presence of cycles can obscure dynamic relationships and hinder hierarchical analysis. These networks are typically…

Hierarchy seems to pervade complexity in both living and artificial systems. Despite its relevance, no general theory that captures all features of hierarchy and its origins has been proposed yet. Here we present a formal approach resulting…

Interconnected networks describe the dynamics of important systems in a wide range such as biological systems and electrical power grids. Some important features of these systems were successfully studied and understood through simplified…

When solving ill-posed inverse problems, one often desires to explore the space of potential solutions rather than be presented with a single plausible reconstruction. Valuable insights into these feasible solutions and their associated…

In this paper we investigate a relaxed concept of controllability, known in the literature as herdability, namely the capability of a system to be driven towards the(interior of the) positive orthant. Specifically, we investigate…

Identifying the effect of a treatment from observational data typically requires assuming a fully specified causal diagram. However, such diagrams are rarely known in practice, especially in complex or high-dimensional settings. To overcome…

Entropic causal inference is a recent framework for learning the causal graph between two variables from observational data by finding the information-theoretically simplest structural explanation of the data, i.e., the model with smallest…

As intelligent systems are developed across diverse substrates - from machine learning models and neuromorphic hardware to in vitro neural cultures - understanding what gives a system agency has become increasingly important. Existing…

Identifying latent variables and causal structures from observational data is essential to many real-world applications involving biological data, medical data, and unstructured data such as images and languages. However, this task can be…

An important task for any large-scale organization is to prepare forecasts of key performance metrics. Often these organizations are structured in a hierarchical manner and for operational reasons, projections of these metrics may have been…

We study core-periphery structure in networks using inference methods based on a flexible network model that allows for traditional onion-like cores within cores, but also for hierarchical tree-like structures and more general non-nested…

Modular and hierarchical community structures are pervasive in real-world complex systems. A great deal of effort has gone into trying to detect and study these structures. Important theoretical advances in the detection of modular have…

Causal discovery, the task of automatically constructing a causal model from data, is of major significance across the sciences. Evaluating the performance of causal discovery algorithms should ideally involve comparing the inferred models…

The information conveyed by a hierarchical attractor neural network is examined. The network learns sets of correlated patterns (the examples) in the lowest level of the hierarchical tree and can categorize them at the upper levels. A way…

Understanding the structural complexity and predictability of complex networks is a central challenge in network science. Although recent studies have revealed a relationship between compression-based entropy and link prediction…

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…

The outputs of non-linear feed-forward neural network are positive, which could be treated as probability when they are normalized to one. If we take Entropy-Based Principle into consideration, the outputs for each sample could be…

The entities in directed networks arising from real-world interactions are often naturally organized under some hierarchical structure. Given a directed, weighted, graph with edges and node labels, we introduce ranking problem where the…

Imitation is a basic updating mechanism for strategy evolution in structured populations, determining how individuals sample social information and translate it into behavioral changes. Higher-order networks, such as hypergraphs, generalize…