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In the context of network dynamics, the complexity of systems increases possible evolutionary paths that often are not deterministic. Occasionally, some map routs form over the course of time which guide systems towards some particular…
Several natural phenomena exhibit long-range conditional dependencies. High-order mixture transition distribution (MTD) are parsimonious non-parametric models to study these phenomena. An MTD is a Markov chain in which the transition…
We consider a second-order linear system of ordinary differential equations (ODEs) including random variables. A stochastic Galerkin method yields a larger deterministic linear system of ODEs. We apply a model order reduction (MOR) of this…
State-space models (SSMs) are a class of networks for sequence learning that benefit from fixed state size and linear complexity with respect to sequence length, contrasting the quadratic scaling of typical attention mechanisms. Inspired…
In this paper, a sampling-based Stochastic Model Predictive Control algorithm is proposed for discrete-time linear systems subject to both parametric uncertainties and additive disturbances. One of the main drivers for the development of…
Statistical shape models enhance machine learning algorithms providing prior information about deformation. A Point Distribution Model (PDM) is a popular landmark-based statistical shape model for segmentation. It requires choosing a model…
Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
In this contribution to the VIEWS 2023 prediction challenge, we propose using an observed Markov model for making predictions of densities of fatalities from armed conflicts. The observed Markov model can be conceptualized as a two-stage…
The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which…
We present a unified dynamical mean-field theory for stochastic self-organized critical models. We use a single site approximation and we include the details of different models by using effective parameters and constraints. We identify the…
We investigate different emergent dynamics namely oscillation quenching and revival of oscillation in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
It is a common belief that the order of a Boolean network is mainly determined by its attractors, including fixed points and cycles. Using semi-tensor product (STP) of matrices and the algebraic state-space representation (ASSR) of Boolean…
In this paper, we present a methodology to identify discrete-time state-space switched linear systems (SLSs) from input-output measurements. Continuous-state is not assumed to be measured. The key step is a deadbeat observer based…
Autonomous robots operating in complex, unstructured environments face significant challenges due to latent, unobserved factors that obscure their understanding of both their internal state and the external world. Addressing this challenge…
Time series modeling is a well-established problem, which often requires that methods (1) expressively represent complicated dependencies, (2) forecast long horizons, and (3) efficiently train over long sequences. State-space models (SSMs)…
Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…