Related papers: High-dimensional dynamics in low-dimensional netwo…
Finding the global minimum in complex networks while avoiding local minima is challenging in many types of networks. We study the dynamics of complex human networks and observed that humans have different methods to avoid local minima than…
Modeling human dynamics responsible for the formation and evolution of the so-called social networks - structures comprised of individuals or organizations and indicating connectivities existing in a community - is a topic recently…
Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
Despite the huge interest in network resilience to stress, most of the studies have concentrated on internal stress damaging network structure (e.g., node removals). Here we study how networks respond to environmental stress deteriorating…
The need to build a link between the structure of a complex network and the dynamical properties of the corresponding complex system (comprised of multiple low dimensional systems) has recently become apparent. Several attempts to tackle…
In the study of reaction networks and the polynomial dynamical systems that they generate, special classes of networks with important properties have been identified. These include reversible, weakly reversible}, and, more recently,…
We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on…
We study systems of interacting reinforced stochastic processes, where agents' decisions evolve under reinforcement, network-mediated interactions, and environmental influences. In competitive environments with irreducible networks, we…
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…
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on…
Learning in neural systems arises from synaptic changes that reshape the representations underlying behavior. While low-rank recurrent neural networks (RNNs) have emerged as a powerful framework for linking connectivity to function, a…
A certain degree of inhibition is a common trait of dynamical networks in nature, ranging from neuronal and biochemical networks, to social and technological networks. We study here the role of inhibition in a representative dynamical…
Routing information through networks is a universal phenomenon in both natural and manmade complex systems. When each node has full knowledge of the global network connectivity, finding short communication paths is merely a matter of…
Time-discrete dynamical systems on a finite state space have been used with great success to model natural and engineered systems such as biological networks, social networks, and engineered control systems. They have the advantage of being…
There are many surprising and perhaps counter-intuitive properties of optimization of deep neural networks. We propose and experimentally verify a unified phenomenological model of the loss landscape that incorporates many of them. High…
Recent results from statistical physics show that large classes of complex networks, both man-made and of natural origin, are characterized by high clustering properties yet strikingly short path lengths between pairs of nodes. This class…
Networked systems are systems of interconnected components, in which the dynamics of each component are influenced by the behavior of neighboring components. Examples of networked systems include biological networks, critical…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…