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This paper proposes a novel approach to improve the performance of distributed nonlinear control systems while preserving stability by leveraging Deep Neural Networks (DNNs). We build upon the Neural System Level Synthesis (Neur-SLS)…
Threshold-linear networks consist of simple units interacting in the presence of a threshold nonlinearity. Competitive threshold-linear networks have long been known to exhibit multistability, where the activity of the network settles into…
We study distributed computation in synchronous dynamic networks where an omniscient adversary controls the unidirectional communication links. Its behavior is modeled as a sequence of directed graphs representing the active (i.e. timely)…
We study the collective dynamics of a population of particles/organisms subject to self-consistent attraction-repulsion interactions and an external velocity field. The starting point of our analysis is a mean-field kinetic model and we…
If we have a system of binary variables and we measure the pairwise correlations among these variables, then the least structured or maximum entropy model for their joint distribution is an Ising model with pairwise interactions among the…
We consider the problem of rational decision making in the presence of nonlinear constraints. By using tools borrowed from spin glass and random matrix theory, we focus on the portfolio optimisation problem. We show that the number of…
Small-world networks, known for high local clustering and short path lengths, are a fundamental structure in many real-world systems, including social, biological, and technological networks. We apply the theory of (marked) local…
In this paper, we unroll the dynamics of the dual ascent (DA) algorithm in two coupled graph neural networks (GNNs) to solve constrained optimization problems. The two networks interact with each other at the layer level to find a saddle…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
Energy landscapes are high-dimensional surfaces representing the dependence of system energy on variable configurations, which determine crucially the system's emergent behavior but are difficult to be analyzed due to their high-dimensional…
We study the dynamics of a population subject to selective pressures, evolving either on RNA neutral networks or in toy fitness landscapes. We discuss the spread and the neutrality of the population in the steady state. Different limits…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
Despite prior advances in PINNs, significant challenges remain in localized solid mechanics problems because of the limitations of single network formulations in simultaneous resolution of smooth global responses and near-tip singularities,…
We study the large-population limit of interacting particle systems evolving on adaptive dynamical networks, motivated in particular by models of opinion dynamics. In such systems, agents interact through weighted graphs whose structure…
Randomly connected neural networks have long served as a theoretical tool for studying collective dynamics in neural populations, yet quantitative comparisons to experiments remain limited. Recent technological advances have made it…
We establish central and non-central limit theorems for sequences of functionals of the Gaussian output of an infinitely-wide random neural network on the d-dimensional sphere . We show that the asymptotic behaviour of these functionals as…
The inverse statistical problem of finding direct interactions in complex networks is difficult. In the natural sciences, well-controlled perturbation experiments are widely used to probe the structure of complex networks. However, our…
The nonequilibrium Ising model on a restricted scale-free network has been studied with one- and two-spin flip competing dynamics employing Monte Carlo simulations. The dynamics present in the system can be defined by the probability $q$ in…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
Reconstructing the states of the nodes of a dynamical network is a problem of fundamental importance in the study of neuronal and genetic networks. An underlying related problem is that of observability, i.e., identifying the conditions…