Related papers: Frenetic steering in a nonequilibrium graph

We explain the steering of slow degrees of freedom by coupling them to driven components for which the time-symmetric reactivities are manipulated. We present the strategy and main principle that make that sort of navigation feasible. For…

We introduce the concept of pattern graphs--directed acyclic graphs representing how response patterns are associated. A pattern graph represents an identifying restriction that is nonparametrically identified/saturated and is often a…

We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume…

We review the concept of dynamical ensembles in nonequilibrium statistical mechanics as specified from an action functional or Lagrangian on spacetime. There, under local detailed balance, the breaking of time-reversal invariance is…

We consider biased random walks on random networks constituted by a random comb comprising a backbone with quenched-disordered random-length branches. The backbone and the branches run in the direction of the bias. For the bare model as…

We consider a discrete-time nonatomic routing game with variable demand and uncertain costs. Given a routing network with single origin and destination, the cost function of each edge depends on some uncertain persistent state parameter. At…

A recurrent neural network is considered that can retrieve a collection of patterns, as well as slightly perturbed versions of this `pure' set of patterns via fixed points of its dynamics. By replacing the set of dynamical constraints,…

We consider a random walker whose motion is tethered around a focal point. We use two models that exhibit the same spatial dependence in the steady state but widely different dynamics. In one case, the walker is subject to a deterministic…

Fractional revival occurs between two vertices in a graph if a continuous-time quantum walk unitarily maps the characteristic vector of one vertex to a superposition of the characteristic vectors of the two vertices. This phenomenon is…

Graphs are ubiquitous in modelling relational structures. Recent endeavours in machine learning for graph-structured data have led to many architectures and learning algorithms. However, the graph used by these algorithms is often…

We consider the traffic assignment problem in nonatomic routing games where the players' cost functions may be subject to random fluctuations (e.g., weather disturbances, perturbations in the underlying network, etc.). We tackle this…

It is well known that a sparsely coded network in which the activity level is extremely low has intriguing equilibrium properties. In the present work, we study the dynamical properties of a neural network designed to store sparsely coded…

Many machine learning methods operate by inverting a neural network at inference time, which has become a popular technique for solving inverse problems in computer vision, robotics, and graphics. However, these methods often involve…

In a random linear graph, vertices are points on a line, and pairs of vertices are connected, independently, with a link probability that decreases with distance. We study the problem of reconstructing the linear embedding from the graph,…

Continuous attractors have been used to understand recent neuroscience experiments where persistent activity patterns encode internal representations of external attributes like head direction or spatial location. However, the conditions…

The statistical properties of the length of the cycles and of the weights of the attraction basins in fully asymmetric neural networks (i.e. with completely uncorrelated synapses) are computed in the framework of the annealed approximation…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

Information processing in the brain is coordinated by the dynamic activity of neurons and neural populations at a range of spatiotemporal scales. These dynamics, captured in the form of electrophysiological recordings and neuroimaging, show…

For nonequilibrium steady states, we identify observables whose fluctuations satisfy a general symmetry and for which a new reciprocity relation can be shown. Unlike the situation in recently discussed fluctuation theorems, these…

We introduce the "NoBackTrack" algorithm to train the parameters of dynamical systems such as recurrent neural networks. This algorithm works in an online, memoryless setting, thus requiring no backpropagation through time, and is scalable,…