Related papers: Indirect Influences on Directed Manifolds

Many real-world networks are intrinsically directed. Such networks include activation of genes, hyperlinks on the internet, and the network of followers on Twitter among many others. The challenge, however, is to create a network model that…

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…

In this work we study the dynamics of systems composed of numerous interacting elements interconnected through a random weighted directed graph, such as models of random neural networks. We develop an original theoretical approach based on…

Efficient networking has a substantial economic and societal impact in a broad range of areas including transportation systems, wired and wireless communications and a range of Internet applications. As transportation and communication…

Asymmetric relational data is increasingly prevalent across diverse fields, underscoring the need for directed network models to address the complex challenges posed by their unique structures. Unlike undirected models, directed models can…

A new characteristic of paired nodes in a directed weight complex network is considered. A method (named as K-method) of the characteristics calculation for complex networks is proposed. The method is based on transforming the initial…

Manifolds discovered by machine learning models provide a compact representation of the underlying data. Geodesics on these manifolds define locally length-minimising curves and provide a notion of distance, which are key for reduced-order…

Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a class of ' cellular networks'…

Spatially embedded networks are shaped by a combination of purely topological (space-independent) and space-dependent formation rules. While it is quite easy to artificially generate networks where the relative importance of these two…

We combine Riemannian geometry with the mean field theory of high dimensional chaos to study the nature of signal propagation in generic, deep neural networks with random weights. Our results reveal an order-to-chaos expressivity phase…

Transport and mixing processes in fluid flows can be studied directly from Lagrangian trajectory data, such as obtained from particle tracking experiments. Recent work in this context highlights the application of graph-based approaches,…

Distributions of the resilience of transport networks are studied numerically, in particular the large-deviation tails. Thus, not only typical quantities like average or variance but the distributions over the (almost) full support can be…

Starting from the working hypothesis that both physics and the corresponding mathematics have to be described by means of discrete concepts on the Planck scale, one of the many problems one has to face in this enterprise is to find the…

The goals of this paper are two-fold. The first goal is to serve as an expository tutorial on the working of deep learning models which emphasizes geometrical intuition about the reasons for success of deep learning. The second goal is to…

Influence propagation in social networks has recently received large interest. In fact, the understanding of how influence propagates among subjects in a social network opens the way to a growing number of applications. Many efforts have…

Network theory has unveiled the underlying structure of complex systems such as the Internet or the biological networks in the cell. It has identified universal properties of complex networks, and the interplay between their structure and…

Metric networks are network-shaped, one-dimensional structures on which one can solve differential equations to simulate a wide range of physical systems including conjugated molecules, photonic crystals, quantum mechanics in waveguide…

Compositionality is a key strategy for addressing combinatorial complexity and the curse of dimensionality. Recent work has shown that compositional solutions can be learned and offer substantial gains across a variety of domains, including…

Despite significant advances in the field of deep learning in ap-plications to various areas, an explanation of the learning pro-cess of neural network models remains an important open ques-tion. The purpose of this paper is a comprehensive…

This paper presents a methodological approach based on the use of complex networks to analyze the structure and content of curricula. We analyze the concept network built from the final year of a particular high school Physics curriculum,…