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Achterberg, M.A. (author)The COVID19 pandemic has had a disruptive impact on healthcare systems and everyday life of the majority of the people around the globe. Despite many years of research on network epidemiology, many key aspects of disease transmission and in particular the response of people to the spread of a disease, remain poorly understood. On the basis of...doctoral thesis 2024
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Pengel, A.L. (author), Bierkens, G.N.J.C. (author)Strong invariance principles describe the error term of a Brownian approximation to the partial sums of a stochastic process. While these strong approximation results have many applications, results for continuoustime settings have been limited. In this paper, we obtain strong invariance principles for a broad class of ergodic Markov...journal article 2024
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Blom, H.A.P. (author)Abstract.: The transition kernel of an ℝ<sup>n</sup>valued diffusion or jump diffusion process {X<sub>t</sub>} is known to satisfy the Feller property if {X<sub>t</sub>} is the solution of an SDE whose coefficients are Lipschitz continuous. This Lipschitz route to Feller falls short if {X<sub>t</sub>} is the solution of an SDE whose...journal article 2024
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Della Corte, S. (author), Kraaij, R.C. (author)We consider the context of molecular motors modelled by a diffusion process driven by the gradient of a weakly periodic potential that depends on an internal degree of freedom. The switch of the internal state, that can freely be interpreted as a molecular switch, is modelled as a Markov jump process that depends on the location of the motor....journal article 2024
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Bertazzi, A. (author)This thesis studies methods to improve the applicability and the performance of Markov Chain Monte Carlo (MCMC) algorithms based on Piecewise Deterministic Markov processes (PDMPs). First, we discuss the key ideas that lay the foundations of the field of MCMC, spanning from the MetropolisHastings algorithm to PDMC methods, emphasising a common...doctoral thesis 2023
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Skovbekk, John (author), Laurenti, L. (author), Frew, Eric (author), Lahijanian, Morteza (author)Verifying the performance of safetycritical, stochastic systems with complex noise distributions is difficult. We introduce a general procedure for the finite abstraction of nonlinear stochastic systems with nonstandard (e.g., nonaffine, nonsymmetric, nonunimodal) noise distributions for verification purposes. The method uses a finite...journal article 2023
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Bierkens, G.N.J.C. (author), Grazzi, S. (author), van der Meulen, F.H. (author), Schauer, M.R. (author)We construct a new class of efficient Monte Carlo methods based on continuoustime piecewise deterministic Markov processes (PDMPs) suitable for inference in high dimensional sparse models, i.e. models for which there is prior knowledge that many coordinates are likely to be exactly 0. This is achieved with the fairly simple idea of endowing...journal article 2023
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Dobson, P. (author), Bierkens, G.N.J.C. (author)In this paper we aim to construct infinite dimensional versions of well established Piecewise Deterministic Monte Carlo methods, such as the Bouncy Particle Sampler, the ZigZag Sampler and the Boomerang Sampler. In order to do so we provide an abstract infinite dimensional framework for Piecewise Deterministic Markov Processes (PDMPs) with...journal article 2023
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Floreani, S. (author)Interacting particle systems (IPS) is a subfield of probability theory that provided a fruitful framework in which several questions of physical interests have been answered with mathematical rigor. An interacting particle system is a stochastic system consisting of a very large number of particles interacting with each other. The class of IPS...doctoral thesis 2022
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Bierkens, G.N.J.C. (author), Kamatani, Kengo (author), Roberts, Gareth O. (author)Piecewise deterministic Markov processes are an important new tool in the design of Markov chain Monte Carlo algorithms. Two examples of fundamental importance are the bouncy particle sampler (BPS) and the zig–zag process (ZZ). In this paper scaling limits for both algorithms are determined. Here the dimensionality of the space tends towards...journal article 2022
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Crul, Thomas (author)Even though the abaility to recommend items in the long tail is one of the main strengths of recommendation systems, modern models still show decreased performance when recommending these niche items. Various bipartite and tripartite graphbased models have been proposed that are specifically tailored to solving this long tail issue. This study...bachelor thesis 2022
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Mukhopadhyay, Atri (author), Iosifidis, G. (author), Ruffini, Marco (author)The development of Multiaccess edge computing (MEC) has resulted from the requirement for supporting next generation mobile services, which need high capacity, high reliability and low latency. The key issue in such MEC architectures is to decide which edge nodes will be employed for serving the needs of the different end users. Here, we...journal article 2022
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Corstanje, M.A. (author), van der Meulen, F.H. (author), Schauer, M.R. (author)A continuoustime Markov process X can be conditioned to be in a given state at a fixed time T>0 using Doob's htransform. This transform requires the typically intractable transition density of X. The effect of the htransform can be described as introducing a guiding force on the process. Replacing this force with an approximation...journal article 2022
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Nain, Philippe (author), Vardoyan, G.S. (author), Guha, Saikat (author), Towsley, Don (author)We study a quantum switch that distributes tripartite entangled states to sets of users. The entanglement switching process requires two steps: First, each user attempts to generate bipartite entanglement between itself and the switch, and second, the switch performs local operations and a measurement to create multipartite entanglement for a...journal article 2022
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Bertazzi, A. (author), Bierkens, G.N.J.C. (author), Dobson, P. (author)Piecewise deterministic Markov processes (PDMPs) are a class of stochastic processes with applications in several fields of applied mathematics spanning from mathematical modelling of physical phenomena to computational methods. A PDMP is specified by three characteristic quantities: the deterministic motion, the law of the random event times...journal article 2022
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Bertazzi, A. (author), Bierkens, G.N.J.C. (author)The Bouncy Particle sampler (BPS) and the ZigZag sampler (ZZS) are continuous time, nonreversible Monte Carlo methods based on piecewise deterministic Markov processes. Experiments show that the speed of convergence of these samplers can be affected by the shape of the target distribution, as for instance in the case of anisotropic targets....journal article 2022
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Bierkens, G.N.J.C. (author), Verduyn Lunel, Sjoerd M. (author)The zigzag process is a variant of the telegraph process with position dependent switching intensities. A characterization of the L2spectrum for the generator of the onedimensional zigzag process is obtained in the case where the marginal stationary distribution on R is unimodal and the refreshment intensity is zero. Sufficient conditions...journal article 2022
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Jarne Ornia, D. (author), Mazo, M. (author)We present an approach to reduce the communication of information needed on a Distributed QLearning system inspired by Event Triggered Control (ETC) techniques. We consider a baseline scenario of a Distributed QLearning problem on a Markov Decision Process (MDP). Following an eventbased approach, N agents sharing a value function explore the...conference paper 2022
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Wiarda, Sjoerd (author)In this thesis, we analyse the spectrum of the generator of the onedimensional ZigZag process defined on the torus $\mathbb{T}$. This is a piecewise deterministic Markov process (PDMP) used in Monte Carlo Markov chain methods (MCMC) for sampling from a probability distribution and calculating integrals \cite{Rejectionfree}, \cite{ZigZag}, ...master thesis 2021
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van Tol, Berend (author)In this thesis we study criticality in the context of the dissipative Abelian sandpile model. The model is linked to a simple trapped random walk, giving a practical method to determine criticality for certain landscapes of dissipative sites. The main results concern the lifetime of the random walk, especially the divergence of its first moment...bachelor thesis 2021