Stochastic spreading on complex networks

Complex interacting systems are ubiquitous in nature and society. Computational modeling of these systems is, therefore, of great relevance for science and engineering. Complex networks are common representations of these systems (e.g., friendship networks or road networks). Dynamical processes (e.g., virus spreading, traffic jams) that evolve on these networks are shaped and constrained by the underlying connectivity. This thesis provides numerical methods to study stochastic spreading processes on complex networks. We consider the processes as inherently probabilistic and analyze their behavior through the lens of probability theory. While powerful theoretical frameworks (like the SIS-epidemic model and continuous-time Markov chains) already exist, their analysis is computationally challenging. A key contribution of the thesis is to ease the computational burden of these methods. Particularly, we provide novel methods for the efficient stochastic simulation of these processes. Based on different simulation studies, we investigate techniques for optimal vaccine distribution and critically address the usage of mathematical models during the Covid-19 pandemic. We also provide model-reduction techniques that translate complicated models into simpler ones that can be solved without resorting to simulations. Lastly, we show how to infer the underlying contact data from node-level observations.Komplexe, interagierende Systeme sind in Natur und Gesellschaft allgegenwärtig. Die computergestützte Modellierung dieser Systeme ist daher von immenser Bedeutung für Wissenschaft und Technik. Netzwerke sind eine gängige Art, diese Systeme zu repräsentieren (z. B. Freundschaftsnetzwerke, Straßennetze). Dynamische Prozesse (z. B. Epidemien, Staus), die sich auf diesen Netzwerken ausbreiten, werden durch die spezifische Konnektivität geformt. In dieser Arbeit werden numerische Methoden zur Untersuchung stochastischer Ausbreitungsprozesse in komplexen Netzwerken entwickelt. Wir betrachten die Prozesse als inhärent probabilistisch und analysieren ihr Verhalten nach wahrscheinlichkeitstheoretischen Fragestellungen. Zwar gibt es bereits theoretische Grundlagen und Paradigmen (wie das SIS-Epidemiemodell und zeitkontinuierliche Markov-Ketten), aber ihre Analyse ist rechnerisch aufwändig. Ein wesentlicher Beitrag dieser Arbeit besteht darin, die Rechenlast dieser Methoden zu verringern. Wir erforschen Methoden zur effizienten Simulation dieser Prozesse. Anhand von Simulationsstudien untersuchen wir außerdem Techniken für optimale Impfstoffverteilung und setzen uns kritisch mit der Verwendung mathematischer Modelle bei der Covid-19-Pandemie auseinander. Des Weiteren führen wir Modellreduktionen ein, mit denen komplizierte Modelle in einfachere umgewandelt werden können. Abschließend zeigen wir, wie man von Beobachtungen einzelner Knoten auf die zugrunde liegende Netzwerkstruktur schließt

Heterogeneity matters: Contact structure and individual variation shape epidemic dynamics

In the recent COVID-19 pandemic, mathematical modeling constitutes an important tool to evaluate the prospective effectiveness of non-pharmaceutical interventions (NPIs) and to guide policy-making. Most research is, however, centered around characterizing the epidemic based on point estimates like the average infectiousness or the average number of contacts. In this work, we use stochastic simulations to investigate the consequences of a population’s heterogeneity regarding connectivity and individual viral load levels. Therefore, we translate a COVID-19 ODE model to a stochastic multi-agent system. We use contact networks to model complex interaction structures and a probabilistic infection rate to model individual viral load variation. We observe a large dependency of the dispersion and dynamical evolution on the population’s heterogeneity that is not adequately captured by point estimates, for instance, used in ODE models. In particular, models that assume the same clinical and transmission parameters may lead to different conclusions, depending on different types of heterogeneity in the population. For instance, the existence of hubs in the contact network leads to an initial increase of dispersion and the effective reproduction number, but to a lower herd immunity threshold (HIT) compared to homogeneous populations or a population where the heterogeneity stems solely from individual infectivity variations

Unsupervised relational inference using masked reconstruction

Problem setting: Stochastic dynamical systems in which local interactions give rise to complex emerging phenomena are ubiquitous in nature and society. This work explores the problem of inferring the unknown interaction structure (represented as a graph) of such a system from measurements of its constituent agents or individual components (represented as nodes). We consider a setting where the underlying dynamical model is unknown and where diferent measurements (i.e., snapshots) may be independent (e.g., may stem from diferent experiments). Method: Our method is based on the observation that the temporal stochastic evolution manifests itself in local patterns. We show that we can exploit these patterns to infer the underlying graph by formulating a masked reconstruction task. Therefore, we propose GINA (Graph Inference Network Architecture), a machine learning approach to simultaneously learn the latent interaction graph and, conditioned on the interaction graph, the prediction of the (masked) state of a node based only on adjacent vertices. Our method is based on the hypothesis that the ground truth interaction graph—among all other potential graphs—allows us to predict the state of a node, given the states of its neighbors, with the highest accuracy. Results: We test this hypothesis and demonstrate GINA’s efectiveness on a wide range of interaction graphs and dynamical processes. We fnd that our paradigm allows to reconstruct the ground truth interaction graph in many cases and that GINA outperforms statistical and machine learning baseline on independent snapshots as well as on time series data

TeachOpenCADD goes Deep Learning: Open-source Teaching Platform Exploring Molecular DL Applications

TeachOpenCADD is a free online platform that offers solutions to common computer-aided drug design (CADD) tasks using Python programming and open-source data and packages. The material is presented through interactive Jupyter notebooks, accommodating users from various backgrounds and programming levels. Due to the tremendous impact of deep learning (DL) methods in drug design, the TeachOpenCADD platform has been expanded to include an introduction to molecular DL tasks. This edition provides an overview of DL and its application in drug design, highlighting the usage of diverse molecular representations in this field. The platform introduces various neural network architectures, including graph neural networks (GNNs), equivariant graph neural networks (EGNNs), and recurrent neural networks (RNNs). It demonstrates how to use these architectures for developing predictive models for molecular property and activity prediction, exemplified by the Quantum Machine 9 (QM9), ChEMBL, and Kinase Inhibitor BioActivity (KiBA) data sets. The DL edition covers methods for evaluating the performance of neural networks using uncertainty estimation. Furthermore, it introduces an application of GNNs for protein-ligand interaction predictions, incorporating protein structure and ligand information. The TeachOpenCADD platform is continuously updated with new content and is open to contributions, bug reports, and questions from the community through its GitHub repository (https://github.com/volkamerlab/teachopencadd). It can be used for self-study, classroom instruction, and research applications, accommodating users from beginners to advanced levels

Rejection-Based Simulation of Non-Markovian Agents on Complex Networks

Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often the preferred\u2014sometimes the only feasible\u2014way to investigate such systems. Previous research focused primarily on Markovian models where the random time until an interaction happens follows an exponential distribution. In this work, we study a general framework to model systems where each agent is in one of several states. Agents can change their state at random, influenced by their complete neighborhood, while the time to the next event can follow an arbitrary probability distribution. Classically, these simulations are hindered by high computational costs of updating the rates of interconnected agents and sampling the random residence times from arbitrary distributions. We propose a rejection-based, event-driven simulation algorithm to overcome these limitations. Our method over-approximates the instantaneous rates corresponding to inter-event times while rejection events counter-balance these over-approximations. We demonstrate the effectiveness of our approach on models of epidemic and information spreading