Verena Wolf

• Prof
• Professor (Associate) at Saarland University

Generating molecular graphs is a challenging task due to their discrete nature and the competitive objectives involved. Diffusion models have emerged as SOTA approaches in data generation across various modalities. For molecular graphs, graph neural networks (GNNs) as a diffusion backbone have achieved impressive results. Latent space diffusion, wh...

Deep reinforcement learning (DRL) has succeeded tremendously in many complex decision-making tasks. However, for many real-world applications standard DRL training results in agents with brittle performance because, in particular for safety-critical problems, the discovery of both, safe and successful strategies is very challenging. Various explora...

Motion planning for autonomous vehicles is commonly implemented via graph-search methods, which pose limitations to the model accuracy and environmental complexity that can be handled under real-time constraints. In contrast, reinforcement learning, specifically the deep Q-learning (DQL) algorithm, provides an interesting alternative for real-time...

In recent years, a wide variety of graph neural network (GNN) architectures have emerged, each with its own strengths, weaknesses, and complexities. Various techniques, including rewiring, lifting, and node annotation with centrality values, have been employed as pre-processing steps to enhance GNN performance. However, there are no universally acc...

We propose an extension of the reinforcement learning architecture that enables moral decision-making of reinforcement learning agents based on normative reasons. Central to this approach is a reason-based shield generator yielding a moral shield that binds the agent to actions that conform with recognized normative reasons so that our overall arch...

Drug discovery pipelines nowadays rely on machine learning models to explore and evaluate large chemical spaces. While including 3D structural information is considered beneficial, structural models are hindered by the availability of protein-ligand complex structures. Exemplified for kinase drug discovery, we address this issue by generating kinas...

Transformers and Graph Neural Networks (GNNs) represent state-of-the-art models for their respective modalities, namely sequences and graphs. While they are conceptually similar and can both be viewed as instances of the message passing (MP) paradigm, their parallel historical development has birthed distinct concepts, design choices, and practices...

The increasing prevalence of artificial intelligence (AI) systems has led to a growing consensus on the importance of the explainability of such systems. This is often emphasized with respect to societal and developmental contexts, but it is also crucial within the context of business processes, including manufacturing and production. While this is...

Neural networks (NN) are gaining importance in sequential decision-making. Deep reinforcement learning (DRL), in particular, is extremely successful in learning action policies in complex and dynamic environments. Despite this success, however, DRL technology is not without its failures, especially in safety-critical applications: (i) the training...

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 learnin...

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 (represent...

Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates based on the statistical moments of the process to reduce the estimators’ variances. We develop an algorithm that...

MoGym, is an integrated toolbox enabling the training and verification of machine-learned decision-making agents based on formal models, for the purpose of sound use in the real world. Given a formal representation of a decision-making problem in the JANI format and a reach-avoid objective, MoGym (a) enables training a decision-making agent with re...

A precise understanding of DNA methylation dynamics is of great importance for a variety of biological processes including cellular reprogramming and differentiation. To date, complex integration of multiple and distinct genome-wide datasets is required to realize this task. We present GwEEP (genome-wide epigenetic efficiency profiling) a versatile...

Monte Carlo estimation in plays a crucial role in stochastic reaction networks. However, reducing the statistical uncertainty of the corresponding estimators requires sampling a large number of trajectories. We propose control variates based on the statistical moments of the process to reduce the estimators' variances. We develop an algorithm that...

Neural networks (NN) are gaining importance in sequential de-cision-making. Deep reinforcement learning (DRL), in particular, is extremely successful in learning action policies in complex and dynamic environments. Despite this success however, DRL technology is not without its failures, especially in safety-critical applications: (i) the training...

To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating states in a grid structure. The resulting approximate stationary distribution is used to iteratively refine releva...

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...

Dynamical systems in which local interactions among agents 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)....

To understand the long-run behavior of Markov population models, the computation of the stationary distribution is often a crucial part. We propose a truncation-based approximation that employs a state-space lumping scheme, aggregating states in a grid structure. The resulting approximate stationary distribution is used to iteratively refine releva...

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...

Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme...

Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely large. Therefore hybrid models, in which protein counts are replaced by average protein concentrations, have beco...

Human mobility is the fuel of global pandemics. In this simulation study, we analyze how mobility restrictions mitigate epidemic processes and how this mitigation is influenced by the epidemic's degree of dispersion. We find that (even imperfect) mobility restrictions are generally efficient in mitigating epidemic spreading. Notably, the effectiv...

We address the problem of reducing the spread of an epidemic over a contact network by vaccinating a limited number of nodes that represent individuals or agents. We propose a Simulation based vaccine allocation method (Simba), a combination of (i) numerous repetitions of an efficient Monte-Carlo simulation , (ii) a PageRank-type influence analysis...

In the recent COVID-19 pandemic, computer simulations are used to predict the evolution of the virus propagation and to evaluate the prospective effectiveness of non-pharmaceutical interventions. As such, the corresponding mathematical models and their simulations are central tools to guide political decision-making. Typically, ODE-based models are...

Learning-based approaches for solving large sequential decision making problems have become popular in recent years. The resulting agents perform differently and their characteristics depend on those of the underlying learning approach. Here, we consider a benchmark planning problem from the reinforcement learning domain, the Racetrack, to investig...

We consider the problem of bounding mean first passage times and reachability probabilities for the class of population continuous-time Markov chains, which capture stochastic interactions between groups of identical agents. The quantitative analysis of such models is notoriously difficult since typically neither state-based numerical approaches no...

We study continuous-time multi-agent models, where agents interact according to a network topology. At any point in time, each agent occupies a specific local node state. Agents change their state at random through interactions with neighboring agents. The time until a transition happens can follow an arbitrary probability density. Stochastic (Mont...

Many probabilistic inference problems such as stochastic filtering or the computation of rare event probabilities require model analysis under initial and terminal constraints. We propose a solution to this bridging problem for the widely used class of population-structured Markov jump processes. The method is based on a state-space lumping scheme...

We address the problem of reducing the spread of an epidemic over a contact network by vaccinating a limited number of nodes that represent individuals or agents. We propose a Simulation based vaccine allocation method (Simba), a combination of (i) numerous repetitions of an efficient Monte-Carlo simulation , (ii) a PageRank-type influence analys...

Background DNA methylation is an essential epigenetic modification which is set and maintained by DNA methyl transferases (Dnmts) and removed via active and passive mechanisms involving Tet mediated oxidation. While the molecular mechanisms of these enzymes are well studied, their interplay on shaping cell specific methylomes remains less well unde...

Learning-based approaches for solving large sequential decision making problems have become popular in recent years. The resulting agents perform differently and their characteristics depend on those of the underlying learning approach. Here, we consider a benchmark planning problem from the reinforcement learning domain, the Racetrack, to investig...

In the recent COVID-19 pandemic, computer simulations are used to predict the evolution of the virus propagation and to evaluate the prospective effectiveness of non-pharmaceutical interventions. As such, the corresponding mathematical models and their simulations are central tools to guide political decision-making. Typically, ODE-based models are...

DNA methylation is an important biological mechanism to regulate gene expression and control cell development. Mechanistic modeling has become a popular approach to enhance our understanding of the dynamics of methylation pattern formation in living cells. Recent findings suggest that the methylation state of a cytosine base can be influenced by it...

This book constitutes the refereed proceedings of the 18th International Conference on Computational Methods in Systems Biology, CMSB 2020, held in Konstanz, Germany, in September 2020.* The 17 full papers and 5 tool papers were carefully reviewed and selected from 30 submissions. In addition 3 abstracts of invited talks and 2 tutorials have been i...

With recent advances in sequencing technologies, large amounts of epigenomic data have become available and computational methods are contributing significantly to the progress of epigenetic research. As an orthogonal approach to methods based on machine learning, mechanistic modeling aims at a description of the mechanisms underlying epigenetic ch...

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—sometimes the only feasible—way to investigate such systems. Previous research focused primarily...

We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population models is notoriously difficult since typically neither state-based numerical approaches nor methods based on s...

DNA methylation is an important biological mechanism to regulate gene expression and control cell development. Mechanistic modeling has become a popular approach to enhance our understanding of the dynamics of methylation pattern formation in living cells. Recent findings suggest that the methylation state of a cytosine base can be influenced by it...

Chemical reaction networks describe the interaction of different molecular species in a well-stirred reactor.

Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires the generation of a large number of simulation runs, which is computationally expensive. To reduce the number o...

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-sometimes the only feasible-way to investigate such systems. Previous research focused primarily...

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest. In this work we consider the wide-spread compartment model where each node is in one of several states (or co...

The understanding of mechanisms that control epigenetic changes is an important research area in modern functional biology. Epigenetic modifications such as DNA methylation are in general very stable over many cell divisions. DNA methylation can however be subject to specific and fast changes over a short time scale even in non-dividing (i.e. not-r...

Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires the generation of a large number of simulation runs, which is computationally expensive. To reduce the number o...

Stochastic simulation is a widely used method for estimating quantities in models of chemical reaction networks where uncertainty plays a crucial role. However, reducing the statistical uncertainty of the corresponding estimators requires the generation of a large number of simulation runs, which is computationally expensive. To reduce the number o...

DNA methylation is an epigenetic mark whose important role in development has been widely recognized. This epigenetic modification results in heritable information not encoded by the DNA sequence. The underlying mechanisms controlling DNA methylation are only partly understood. Several mechanistic models of enzyme activities responsible for DNA met...

The understanding of mechanisms that control epigenetic changes is an important research area in modern functional biology. Epigenetic modifications such as DNA methylation are in general very stable over many cell divisions. DNA methylation can however be subject to specific and fast changes over a short time scale even in non-dividing (i.e. not-r...

This book constitutes the proceedings of the 16th International Conference on Quantitative Evaluation Systems, QEST 2019, held in Glasgow, UK, in September 2019. The 17 full papers presented together with 2 short papers were carefully reviewed and selected from 40 submissions. The papers cover topics in the field of Probabilistic Verification; Lear...

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest. In this work we consider the wide-spread compartment model where each node is in one of several states (or co...

Discrete-state stochastic models are a popular approach to describe the inherent stochasticity of gene expression in single cells. The analysis of such models is hindered by the fact that the underlying discrete state space is extremely large. Therefore hybrid models, in which protein counts are replaced by average protein concentrations, have beco...

A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models is extremely challenging due to their large discrete state space. We therefore propose a hybrid approximation...

Complex networks play an important role in human society and in nature. Stochastic multistate processes provide a powerful framework to model a variety of emerging phenomena such as the dynamics of an epidemic or the spreading of information on complex networks. In recent years, mean-field type approximations gained widespread attention as a tool t...

The dramatically decreasing costs of DNA sequencing have triggered more than a million humans to have their genotypes sequenced. Moreover, these individuals increasingly make their genomic data publicly available, thereby creating privacy threats for themselves and their relatives because of their DNA similarities. More generally, an entity that ga...

Course selection can be a daunting task, especially for first-year students. Sub-optimal selection can lead to bad performance of students and increase the dropout rate. Given the availability of historic data about student performances, it is possible to aid students in the selection of appropriate courses. Here, we propose a method to compose a p...

The controlled and stepwise oxidation of 5mC to 5hmC, 5fC and 5caC by Tet enzymes is influencing the chemical and biological properties of cytosine. Besides direct effects on gene regulation, oxidised forms influence the dynamics of demethylation and re-methylation processes. So far, no combined methods exist which allow to precisely determine the...

We consider the approximation of transient (time dependent) probability distributions of discrete-state continuous-time Markov chains on large, possibly infinite state spaces. A framework for approximate adaptive uniformization is provided, which generalizes the well-known uniformization technique and many of its variants. Based on a birth process...

Complex networks play an important role in human society and in nature. Stochastic multistate processes provide a powerful framework to model a variety of emerging phenomena such as the dynamics of an epidemic or the spreading of information on complex networks. In recent years, mean-field type approximations gained widespread attention as a tool t...

A widely used approach to describe the dynamics of gene regulatory networks is based on the chemical master equation, which considers probability distributions over all possible combinations of molecular counts. The analysis of such models is extremely challenging due to their large discrete state space. We therefore propose a hybrid approximation...

Improving the performance of students is an important challenge for higher education institutions. At most European universities, duration and completion rate of degrees are highly varying and consulting services are offered to increase student achievement. Here, we propose a data analytics approach to determine optimal choices for the courses of t...

Calibrating parameters is a crucial problem within quantitative modeling approaches to reaction networks. Existing methods for stochastic models rely either on statistical sampling or can only be applied to small systems. Here we present an inference procedure for stochastic models in equilibrium that is based on a moment matching scheme with optim...

DNA methylation is an epigenetic mechanism whose important role in development has been widely recognized. This epigenetic modification results in heritable changes in gene expression not encoded by the DNA sequence. The underlying mechanisms controlling DNA methylation are only partly understood and recently different mechanistic models of enzyme...

DNA methylation is an epigenetic mechanism whose important role in development has been widely recognized. This epigenetic modification results in heritable changes in gene expression not encoded by the DNA sequence. The underlying mechanisms controlling DNA methylation are only partly understood and recently different mechanistic models of enzyme...

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information spreading. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One...

Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information spreading. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One...

The stochastic nature of chemical reactions has resulted in an increasing research interest in discrete-state stochastic models and their analysis. A widely used approach is the description of the temporal evolution of such systems in terms of a chemical master equation (CME). In this paper we study two approaches for approximating the underlying p...

Calibrating parameters is a crucial problem within quantitative modeling approaches to reaction networks. Existing methods for stochastic models rely either on statistical sampling or can only be applied to small systems. Here we present an inference procedure for stochastic models in equilibrium that is based on a moment matching scheme with optim...

Discrete-state stochastic models have become a well-established approach to describe biochemical reac- tion networks that are influenced by the inherent randomness of cellular events. In the last years several methods for accurately approximating the statistical moments of such models have become very popular since they allow an efficient analysis...

Motivation: Methylation and hydroxylation of cytosines to form 5-methylcytosine (5mC) and 5-hydroxymethylcytosine (5hmC) belong to the most important epigenetic modifications and their vital role in the regulation of gene expression has been widely recognized. Recent experimental techniques allow to infer methylation and hydroxylation levels at Cp...

Methylation and hydroxylation of cytosines to form 5-methylcytosine (5mC) and 5-droxymethylcytosine (5hmC) belong to the most important epigenetic modifications and their vital role in the regulation of gene expression has been widely recognized. Recent experimental techniques allow to infer methylation and hydroxylation levels at CpG dinucleotides...

DNA methylation and demethylation are opposing processes that when in balance create stable patterns of epigenetic memory. The control of DNA methylation pattern formation by replication dependent and independent demethylation processes has been suggested to be influenced by Tet mediated oxidation of 5mC. Several alternative mechanisms have been pr...

Details on the theoretical model, the parameter estimation, the statistical analysis of the results and the experimental procedure. (PDF)

Comparison of model prediction and data for IAP, L1mdA, MuERVL, Ttc25 and Snrpn. Plotted according to Fig 5. (PDF)

(Hydroxy-)methylation levels for each single CpG dyad of repetitive elements IAP, L1mdA, L1mdT, mSat, MuERVL and single copy genes Afp, Ttc25, Zim3 and Snrpn over time. The colormap is the same as in Fig 6. (PDF)

Estimated coefficients of the functions μd(t), μm(t) and η(t) and their approximate standard deviations. The p-values have been taken conducting a hypothesis test H0: β1 = 0 using the Wald statistic. (PDF)

BS and oxBS data, Conversion Errors (repetitive elements). (PDF)

Results for loci IAP, L1mdA, MuERVL, Ttc25 and Snrpn. Left: Probabilities of the hidden states. Plotted according to Fig 6. Right: Estimated efficiencies and standard deviations over time. Plotted according to Fig 7 (PDF)

Estimated efficiencies and standard deviations for each single CpG dyad of repetitive elements IAP, L1mdA, L1mdT, mSat, MuERVL and single copy genes Afp, Ttc25, Zim3 and Snrpn over time. In the case of IAP we cover six CpG positions. However, during evolution CpG one and five underwent a transition resulting in a loss of the CpG positions in this p...

BS and oxBS data, Conversion Errors (single copy genes). (PDF)

Test error: Linear vs Constant Assumption. Computed Kullback-Leibler divergence and Bhattacharya distance values given by LOOCV data to compare the test error for assuming linear vs constant efficiencies. (PDF)

Bs and oxBS data for single CpGs. The dataset contains the BS and oxBS data of each single CpG and loci after processing of the sequencing data; error rates are included as separate files. Raw sequencing data are available on request. (ZIP)

Estimated coefficients of the function λ(t) and their approximate standard deviations. The p-values have been taken conducting a hypothesis test H0:β1λ=0∧β2λ=0 using the Wald statistic. (PDF)

Discrete-state stochastic models have become a well-established approach to describe biochemical reaction networks that are influenced by the inherent randomness of cellular events. In the last years severalmethods for accurately approximating the statistical moments of such models have become very popular since they allow an efficient analysis of...

The stochastic nature of chemical reactions involving randomly fluctuating population sizes has lead to a growing research interest in discrete-state stochastic models and their analysis. A widely-used approach is the description of the temporal evolution of the system in terms of a chemical master equation (CME). In this paper we study two approac...

We consider the problem of understanding how DNA methylation fidelity, i.e. the preservation of methylated sites in the genome, varies across the genome and across different cell types. Our approach uses a stochastic model of DNA methylation across generations and trains it using data obtained through next generation sequencing. By training the mod...

We consider rule-based models extended with time-dependent reaction rates, a suitable formalism to describe the effect of drug administration on biochemical systems. In the paper, we provide a novel and efficient rejection-based simulation algorithm that samples exactly the trajectory space of such models. Furthermore, we investigate a model of dru...

Wet-lab experiments, in which the dynamics within living cells are observed, are usually costly and time consuming. This is particularly true if single-cell measurements are obtained using experimental techniques such as flow-cytometry or fluorescence microscopy. It is therefore important to optimize experiments with respect to the information they...

The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state space, analysis techniques based on an exploration of the state space are often not feasible and the integrat...

Based on the theory of stochastic chemical kinetics, the inherent randomness and stochasticity of biochemical reaction networks can be accurately described by discrete-state continuous-time Markov chains. The analysis of such processes is, however, computationally expensive and sophisticated numerical methods are required. Here, we propose an analy...

The classical problem of moments is addressed by the maximum entropy approach for one-dimensional discrete distributions. The numerical technique of adaptive support approximation is proposed to reconstruct the distributions in the region where the main part of probability mass is located.

We consider continuous-time Markov chains (CTMC) with very large or infinite state spaces which are, for instance, used to model biological processes or to evaluate the performance of computer and communication networks. We propose a numerical integration algorithm to approximate the probability that a process conforms to a specification that belon...

In stochastic biochemically reacting systems, certain rare events can cause serious consequences, which makes their probabilities important to analyze. We solve the chemical master equation using a four-stage fourth order Runge-Kutta integration scheme in combination with a guided state space exploration and a dynamical state space truncation in or...

The time-evolution of continuous-time discrete-state biochemical processes is governed by the Chemical Master Equation (CME), which describes the probability of the molecular counts of each chemical species. As the corresponding number of discrete states is, for most processes, large, a direct numerical simulation of the CME is in general infeasibl...

In this paper we deal with transient analysis of networks of queues. These systems most often have enormous state space and the exact computation of their transient behavior is not possible. We propose to apply an approximate technique based on assumptions on the structure of the transient probabilities. In particular, we assume that the transient...