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We propose a stochastic Model Predictive Control (MPC) framework that ensures closed-loop chance constraint satisfaction for linear systems with general sub-Gaussian process and measurement noise. By considering sub-Gaussian noise, we can…
Gibbs sampling is a common procedure used to fit finite mixture models. However, it is known to be slow to converge when exploring correlated regions of a parameter space and so blocking correlated parameters is sometimes implemented in…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
Probabilistic Cellular Automata are extended stochastic systems, widely used for modelling phenomena in many disciplines. The possibility of controlling their behaviour is therefore an important topic. We shall present here an approach to…
Universality classes of Ising-like phase transitions are investigated in series of two-dimensional synchronously updated probabilistic cellular automata (PCAs), whose time evolution rules are either of Glauber type or of majority-vote type,…
Using the linear Gaussian latent variable model as a starting point we relax some of the constraints it imposes by deriving a nonparametric latent feature Gaussian variable model. This model introduces additional discrete latent variables…
We aim this paper to develop the classical lattice models with unbounded spin to the case of non-quadratic polynomial interaction. We demonstrate that the distinct relation between the growths of potentials leads to the uniqueness and the…
We build a quantum cellular automaton (QCA) which coincides with 1+1 QED on its known continuum limits. It consists in a circuit of unitary gates driving the evolution of particles on a one dimensional lattice, and having them interact with…
Gaussian process (GP) regression has been widely used in supervised machine learning due to its flexibility and inherent ability to describe uncertainty in function estimation. In the context of control, it is seeing increasing use for…
From the perspective of the large deviations theory of occupational measures, the paper considers Probabilistic Cellular Automata (PCA) as Markov chains on infinite dimensional space. It turns out that for a wide range of PCA, the…
In this dissertation, we study temporally stochasticity in cellular automata and the behavior of such cellular automata. The work also explores the computational ability of such cellular automaton that illustrates the computability of…
We investigate the density classification task (DCT) -- determining the majority bit in a one-dimensional binary lattice -- within a quantum cellular automaton (CA) framework. While there is no one-dimensional two-state, radius $r \geq 1$,…
On the space of $\pm 1$ spin configurations on the 3$d$-square lattice, we consider the \emph{shaken dynamics}, a parallel Markovian dynamics that can be interpreted in terms of Probabilistic Cellular Automata. The transition probabilities…
We study a class of Gibbs measures of classical particle spin systems with spin space $S=\mathbb{R}^{m}$ and unbounded pair interaction, living on a metric graph given by a typical realization $\gamma $ of a random point process in…
The phase diagram of the coupled sine circle map lattice shows spatio-temporal intermittency of two distinct types: spatio-temporal intermittency of the directed percolation (DP) class, and spatial intermittency which does not belong to…
Instances of discrete quantum systems coupled to a continuum of oscillators are ubiquitous in physics. Often the continua are approximated by a discrete set of modes. We derive analytical error bounds on expectation values of system…
Certain fermionic quantum field theories are equivalent to probabilistic cellular automata, with fermionic occupation numbers associated to bits. We construct an automaton that represents a discrete model of spinor gravity in four…
We present a novel decentralized algorithm for coverage control in unknown spatial environments modeled by Gaussian Processes (GPs). To trade-off between exploration and exploitation, each agent autonomously determines its trajectory by…
We exhibit a Probabilistic Cellular Automaton (PCA) on the integers with an alphabet and a neighborhood of size 2 which is non-ergodic although it has a unique invariant measure. This answers by the negative an old open question on whether…
Gaussian process classification (GPC) provides a flexible and powerful statistical framework describing joint distributions over function space. Conventional GPCs however suffer from (i) poor scalability for big data due to the full kernel…