Related papers: On weighted two-mode network projections

We introduce new clustering coefficients for weighted networks. They are continuous and robust against edge weight changes. Recently, generalized clustering coefficients for weighted and directed networks have been proposed. These…

A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…

Recent work has shown that topological enhancements to recurrent neural networks (RNNs) can increase their expressiveness and representational capacity. Two popular enhancements are stacked RNNs, which increases the capacity for learning…

Recent theoretical and empirical studies have focused on the structural properties of complex relational networks in social, biological and technological systems. Here we study the basic properties of twenty 1-square-mile samples of street…

Transferability of learned features between tasks can massively reduce the cost of training a neural network on a novel task. We investigate the effect of network width on learned features using activation atlases --- a visualization…

Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…

Neural networks with random hidden nodes have gained increasing interest from researchers and practical applications. This is due to their unique features such as very fast training and universal approximation property. In these networks…

Topology and weights are closely related in weighted complex networks and this is reflected in their modular structure. We present a simple network model where the weights are generated dynamically and they shape the developing topology. By…

Convolutional neural networks are state-of-the-art for various segmentation tasks. While for 2D images these networks are also computationally efficient, 3D convolutions have huge storage requirements and require long training time. To…

Assortativity measures the tendency of a vertex in a network being connected by other vertexes with respect to some vertex-specific features. Classical assortativity coefficients are defined for unweighted and undirected networks with…

We introduce a generalization of the Stirling numbers via symmetric functions involving two weight functions. The resulting extension unifies previously known Stirling-type sequences with known symmetric function forms, as well as other…

Our ability to control complex systems is a fundamental challenge of contemporary science. Recently introduced tools to identify the driver nodes, nodes through which we can achieve full control, predict the existence of multiple control…

In this paper, we study the local spectral properties for both unilateral and bilateral weighted shift operators.

Neural networks have seen an explosion of usage and research in the past decade, particularly within the domains of computer vision and natural language processing. However, only recently have advancements in neural networks yielded…

Modularity is one of the most prominent properties of real-world complex networks. Here, we address the issue of module identification in two important classes of networks: bipartite networks and directed unipartite networks. Nodes in…

We prove sufficient conditions for the two-weight boundedness of the Bergman projection on the unit ball. The first condition is in terms of Orlicz averages of the weights, while the second condition is in terms of the mixed…

Techniques for feedforward networks (FFNs) and convolutional networks (CNNs) are frequently reused across families, but the relationship between the underlying model classes is rarely made explicit. We introduce a unified node-level…

We investigate local and global weighted heights a-la Weil for weighted projective spaces via Cartier and Weil divisors and extend the definition of weighted heights on weighted projective spaces from arXiv:1902.06563 to weighted varieties…

We discuss several interesting random network models which exhibit (provable) explosive transitions and their applications.

In this study, we investigate whether the representations learned by neural networks possess a privileged and convergent basis. Specifically, we examine the significance of feature directions represented by individual neurons. First, we…