Related papers: High-dimensional dynamics in low-dimensional netwo…
We consider a dynamic social network model in which agents play repeated games in pairings determined by a stochastically evolving social network. Individual agents begin to interact at random, with the interactions modeled as games. The…
Symmetries naturally occur in real-world networks and can significantly influence the observed dynamics. For instance, many synchronization patterns result from the underlying network symmetries, and high symmetries are known to increase…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent…
Elastic structures can be designed to exhibit precise, complex, and exotic functions. While recent work has focused on the quasistatic limit governed by force balance, the mechanics at a finite driving rate are governed by Newton's…
We study matrix completion via deep matrix factorization (a.k.a. deep linear neural networks) as a simplified testbed to examine how network depth influences training dynamics. Despite the simplicity and importance of the problem, prior…
Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the system's units and inter-unit interactions. Understanding how physical rules shape the topological structure…
Dynamics of arbitrary communication system is analysed as unreduced interaction process. The applied generalised, universally nonperturbative method of effective potential reveals the phenomenon of dynamic multivaluedness of competing…
Deep neural networks have achieved great success in many data processing applications. However, the high computational complexity and storage cost makes deep learning hard to be used on resource-constrained devices, and it is not…
Empirical and theoretical works show that the input weights of two-layer neural networks, when initialized with small values, converge towards isolated orientations. This phenomenon, referred to as condensation, indicates that the gradient…
Experimental fMRI studies have shown that spontaneous brain activity i.e. in the absence of any external input, exhibit complex spatial and temporal patterns of co-activity between segregated brain regions. These so-called large-scale…
Network structure has a large impact on constant-selection evolutionary dynamics, with which multiple types of fitness (i.e., strength) compete on the network. Here we study constant-selection dynamics on two-layer networks in which the…
Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of…
Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…
We study a generic family of nonlinear dynamics on undirected networks generalising linear consensus. We find a compact expression for its equilibrium points in terms of the topology of the network and classify their stability using the…
We present a data-driven dimensionality reduction method that is well-suited for physics-based data representing hyperbolic wave propagation. The method utilizes a specialized neural network architecture called low rank neural…
Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic…
Over the last decade, random hyperbolic graphs have proved successful in providing geometric explanations for many key properties of real-world networks, including strong clustering, high navigability, and heterogeneous degree…
Controlling complex networked systems to a desired state is a key research goal in contemporary science. Despite recent advances in studying the impact of network topology on controllability, a comprehensive understanding of the synergistic…