Epidemics on Static and Adaptive Networks

The COVID-19 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...

Formal Abstraction of General Stochastic Systems via Noise Partitioning

Verifying the performance of safety-critical, 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., non-affine, non-symmetric, non-unimodal) noise distributions for verification purposes. The method uses a finite...

Migration-aware Network Services with Edge Computing

The development of Multi-access 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...

Conditioning continuous-time Markov processes by guiding

A continuous-time Markov process X can be conditioned to be in a given state at a fixed time T>0 using Doob's h-transform. This transform requires the typically intractable transition density of X. The effect of the h-transform can be described as introducing a guiding force on the process. Replacing this force with an approximation...

Event-Based Communication in Distributed Q-Learning

We present an approach to reduce the communication of information needed on a Distributed Q-Learning system inspired by Event Triggered Control (ETC) techniques. We consider a baseline scenario of a Distributed Q-Learning problem on a Markov Decision Process (MDP). Following an event-based approach, N agents sharing a value function explore the...

Active particles in one dimension: Asymptotic behaviour and collective dynamics

In this thesis, we study the asymptotic behaviour and the dynamics of a one-dimensional active particle model with excluded volume interactions. The model is a version of run-and-tumble motion, where a particle performs both symmetric random walks and active transport. The direction and the speed of the transport are governed by an internal...

Modeling the Spread of Epidemics: Visualizing the Spread of COVID-19 and Applying a Markov-Modulated Process Model to Mobility Processes

This thesis consists of two parts which are connected by the central theme of epidemics. In the first part, a website is designed for forecasting the number of cases of COVID-19 in the Netherlands. The forecasting is performed using the Network-Inference-Based Prediction Algorithm (NIPA). The first part of the thesis documents the design process...

Developing a Markov-Modulated Process Model for Mobility Processes

A major factor in the spreading of viruses is human-to-human transmission, and human mobility is clearly linked to the spreading process of epidemics. If we hope to understand the evolution of an epidemic, then we must also understand the underlying mobility process and the interaction between the two.<br/><br/>We propose the Markov modulated...

Distinguishing level-1 phylogenetic networks on the basis of data generated by Markov processes

Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, introgression, and lateral gene transfer. Recently, network-based Markov models of DNA sequence evolution have been introduced along with model...

The exponential resolvent of a markov process and large deviations for markov processes via hamilton-jacobi equations

We study the Hamilton-Jacobi equation f − λHf = h, where Hf = e^−f Ae^f and where A is an operator that corresponds to a well-posed martingale problem. We identify an operator that gives viscosity solutions to the Hamilton-Jacobi equa-tion, and which can therefore be interpreted as the resolvent of H. The operator is given...

Symmetric interacting particle systems: Self-duality and hydrodynamics in dynamic random environment

In this thesis, we study scaling and detailed properties of a class of conservative interacting particle systems. In particular, in the first part we derive the hydrodynamic equation for the symmetric exclusion process in presence of dynamic random environment. The second part of the thesis focuses on a detailed property of conservative particle...

Diffusive behaviour and large deviations of one-dimensional active particles with drift

In this thesis a simple model of an active particle was taken, one including a drift according to its internal state. For this model a diffusion coefficient was determined as well as a rate function for the large deviations. This same model is also applied to electrons, although these particles are not active a diffusion coefficient was also...

Reservoir Lithology Determination by Hidden Markov Random Fields Based on a Gaussian Mixture Model

In this paper, geological prior information is incorporated in the classification of reservoir lithologies after the adoption of Markov random fields (MRFs). The prediction of hidden lithologies is based on measured observations, such as seismic inversion results, which are associated with the latent categorical variables, based on the...

Reservoir lithology determination from seismic inversion results using markov processes

For reservoir characterization, the subsurface heterogeneity needs to be qualified in which the distribution of lithologies is an essential part since it determines the location and migration paths of hydrocarbons. Preliminary analysis of well-log data could help to identify various lithologies in a one-dimensional direction (depth), while the...

Sign Language Recognition by Combining Statistical DTW and Independent Classification

To recognize speech, handwriting, or sign language, many hybrid approaches have been proposed that combine Dynamic Time Warping (DTW) or Hidden Markov Models (HMMs) with discriminative classifiers. However, all methods rely directly on the likelihood models of DTW/HMM. We hypothesize that time warping and classification should be separated...

Bayesian estimation for decision-directed stochastic control

Stochastic processes with a decision-directed control are considered as controlled Markov processes, the state space of which is hybrid; i.e. a product of a discrete set and a Euclidean space. This approach yields a mathematical model for many problems of decision-directed stochastic control. In general, the observations made from the "past" and...

Data compression in computational fluid dynamics

Computations in numerical fluid dynamics create large sets of data. Transmission of these datasets requires a high speed communication link or, alternatively, the use of data compression techniques. This report describes the results of a study to the applicability of data compression techniques. An algorithm is designed that yields favourable...

Detection-filter representations for Markov jump diffusions

The problem considered is filtering for Gaussian observations of linear differential systems that are driven by both Wiener processes and marked Poisson point processes. Well-known representations of the MMSE-filter for such a Markov jump-diffusion are a differential for the evolution of its conditional density or differentials for all its...