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Spreading processes are often modelled as a stochastic dynamics occurring on top of a given network with edge weights corresponding to the transmission probabilities. Knowledge of veracious transmission probabilities is essential for…
This article presents several results establishing connections be- tween Markov chains and dynamical systems, from the point of view of open systems in physics. We show how all Markov chains can be understood as the information on one…
We present a new method to solve the dynamics of disordered spin systems on finite time-scales. It involves a closed driven diffusion equation for the joint spin-field distribution, with time-dependent coefficients described by a dynamical…
The spontaneous supersymmetry-breaking that takes place in certain spin-glass models signals a particular fragility in the structure of metastable states of such systems. This fragility is due to the presence of at least one marginal mode…
Using methods of statistical physics, we analyse the error of learning couplings in large Ising models from independent data (the inverse Ising problem). We concentrate on learning based on local cost functions, such as the…
Coordination of dynamical routes can alleviate traffic congestion and is essential for the coming era of autonomous self-driving cars. However, dynamical route coordination is difficult and many existing routing protocols are either static…
Causal Graph Dynamics extend Cellular Automata to arbitrary, bounded-degree, time-varying graphs. The whole graph evolves in discrete time steps, and this global evolution is required to have a number of physics-like symmetries:…
Non-prehensile manipulation such as pushing is typically subject to uncertain, non-smooth dynamics. However, modeling the uncertainty of the dynamics typically results in intractable belief dynamics, making data-efficient planning under…
A dynamical system may be defined by a simple transition law - such as a map or a vector field. The objective of most learning techniques is to reconstruct this dynamic transition law. This is a major shortcoming, as most dynamic properties…
An Ising model with local Glauber dynamics is studied under the influence of additional kinetic restrictions for the spin-flip rates depending on the orientation of neighboring spins. Even when the static interaction between the spins is…
We consider the inverse Ising problem, i.e. the inference of network couplings from observed spin trajectories for a model with continuous time Glauber dynamics. By introducing two sets of auxiliary latent random variables we render the…
We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact…
In these two lectures we shall discuss how the cavity approach can be used efficiently to study optimization problems with global (topological) constraints and how the same techniques can be generalized to study inverse problems in…
In this work, a strategy to estimate the information transfer between the elements of a complex system, from the time series associated to the evolution of this elements, is presented. By using the nearest neighbors of each state, the local…
This paper introduces a probabilistic approach for tracking the dynamics of unweighted and directed graphs using state-space models (SSMs). Unlike conventional topology inference methods that assume static graphs and generate point-wise…
We perform a numerical investigation of the \emph{shaken dynamics}, a parallel Markovian dynamics for spin systems with local interaction and whose transition probabilities depend on two parameters, $q$ and $J$, that tune the geometry of…
We consider data-driven reachability analysis of discrete-time stochastic dynamical systems using conformal inference. We assume that we are not provided with a symbolic representation of the stochastic system, but instead have access to a…
Many real-world systems studied are governed by complex, nonlinear dynamics. By modeling these dynamics, we can gain insight into how these systems work, make predictions about how they will behave, and develop strategies for controlling…
We introduce a quantum Monte Carlo method to simulate the reversible dynamics of correlated many-body systems. Our method is based on the Laplace transform of the time-evolution operator which, as opposed to most quantum Monte Carlo…
We study the dynamics of bond-disordered Ising spin systems on random graphs with finite connectivity, using generating functional analysis. Rather than disorder-averaged correlation and response functions (as for fully connected systems),…