Related papers: The low-rank hypothesis of complex systems
Recent evidence indicates that the abundance of recurring elementary interaction patterns in complex networks, often called subgraphs or motifs, carry significant information about their function and overall organization. Yet, the…
We study the structural complexity of bimatrix games, formalized via rank, from an empirical perspective. We consider a setting where we have data on player behavior in diverse strategic situations, but where we do not observe the relevant…
Various hypotheses exist about the paths used for communication between the nodes of complex networks. Most studies simply suppose that communication goes via shortest paths, while others have more explicit assumptions about how routing…
Network coherence generally refers to the emergence of simple aggregated dynamical behaviours, despite heterogeneity in the dynamics of the subsystems that constitute the network. In this paper, we develop a general frequency domain…
Many dynamical processes of complex systems can be understood as the dynamics of a group of nodes interacting on a given network structure. However, finding such interaction structure and node dynamics from time series of node behaviours is…
It is common to use networks to encode the architecture of interactions between entities in complex systems in the physical, biological, social, and information sciences. To study the large-scale behavior of complex systems, it is useful to…
The heterogeneous structure implies that a very few nodes may play the critical role in maintaining structural and functional properties of a large-scale network. Identifying these vital nodes is one of the most important tasks in network…
In spite of a few attempts in understanding the dynamical robustness of complex networks, this extremely important subject of research is still in its dawn as compared to the other dynamical processes on networks. We hereby consider the…
Networks are ubiquitous throughout science and engineering. A number of methods, including some from our own group, have explored how one goes about computing or predicting the dynamics of networks given information about internal models of…
Many decision-making algorithms draw inspiration from the inner workings of individual biological systems. However, it remains unclear whether collective behavior among biological species can also lead to solutions for computational tasks.…
Biologists and physicists have a rich tradition of modeling living systems with simple models composed of a few interacting components. Despite the remarkable success of this approach, it remains unclear how to use such finely tuned models…
Even in times of deep learning, low-rank approximations by factorizing a matrix into user and item latent factors continue to be a method of choice for collaborative filtering tasks due to their great performance. While deep learning based…
We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…
The interactions between individuals play a pivotal role in shaping the structure and dynamics of social systems. Complex network models have proven invaluable in uncovering the underlying mechanisms that govern the formation and evolution…
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…
Studies of the dynamics of nonlinear recurrent neural networks often assume independent and identically distributed couplings, but large-scale connectomics data indicate that biological neural circuits exhibit markedly different…
Correlations and other collective phenomena in a schematic model of heterogeneous binary agents (individual spin-glass samples) are considered on the complete graph and also on 2d and 3d regular lattices. The system's stochastic dynamics is…
In many real world networks agents are initially unsure of each other's qualities and must learn about each other over time via repeated interactions. This paper is the first to provide a methodology for studying the dynamics of such…
The recent discovery of universal principles underlying many complex networks occurring across a wide range of length scales in the biological world has spurred physicists in trying to understand such features using techniques from…
Graphons offer a powerful framework for modeling large-scale networks, yet estimation remains challenging. We propose a novel approach that leverages a low-rank additive representation, yielding both a low-rank connection probability matrix…