arXiv subjects

Johannes Müller

Publications and source records attributed to Johannes Müller.

At least 55 records · Page 3Linked to original sources

arXiv2021

A model of opinion dynamics with echo chambers explains the spatial distribution of vaccine hesitancy

Vaccination hesitancy is a major obstacle to achieving and maintaining herd immunity. It is therefore of prime importance for public health authorities to understand the dynamics of an anti-vaccine opinion in the population. We introduce a novel mathematical model of opinion dynamics with spatial reinforcement, which can generate echo chambers, i.e. opinion bubbles in which information that is incompatible with one's entrenched worldview, is likely disregarded. In a first mathematical part, we scale the model both to a deterministic limit and to a weak-effects limit, and obtain bifurcations, phase transitions, and the invariant measure. In a second part, we fit our model to measles and meningococci vaccination coverage across 413 districts in Germany. We reveal that strong echo chambers explain the occurrence and persistence of the anti-vaccination opinion. We predict and compare the effectiveness of different policies aimed at influencing opinion dynamics in order to increase vaccination uptake.

q-bio.PE↗

arXiv2021

Life-History traits and the replicator equation

Due to the relevance for conservation biology, there is an increasing interest to extend evolutionary genomics models to plant, animal or microbial species. However, this requires to understand the effect of life-history traits absent in humans on genomic evolution. In this context, it is fundamentally of interest to generalize the replicator equation, which is at the heart of most population genomics models. However, as the inclusion of life-history traits generates models with a large state space, the analysis becomes involving. We focus, here, on quiescence and seed banks, two features common to many plant, invertebrate and microbial species. We develop a method to obtain a low-dimensional replicator equation in the context of evolutionary game theory, based on two assumptions: (1) the life-history traits are {\it per se} neutral, and (2) frequency-dependent selection is weak. We use the results to investigate the evolution and maintenance of cooperation based on the Prisoner's dilemma. We first consider the generalized replicator equation, and then refine the investigation using adaptive dynamics. It turns out that, depending on the structure and timing of the quiescence/dormancy life-history trait, cooperation in a homogeneous population can be stabilized. We finally discuss and highlight the relevance of these results for plant, invertebrate and microbial communities.

q-bio.PE↗

arXiv2021

Uniform Convergence Guarantees for the Deep Ritz Method for Nonlinear Problems

We provide convergence guarantees for the Deep Ritz Method for abstract variational energies. Our results cover non-linear variational problems such as the $p$-Laplace equation or the Modica-Mortola energy with essential or natural boundary conditions. Under additional assumptions, we show that the convergence is uniform across % bounded families of right-hand sides.

math.NA↗

arXiv2021

Motion Planning for Connected Automated Vehicles at Occluded Intersections With Infrastructure Sensors

Motion planning at urban intersections that accounts for the situation context, handles occlusions, and deals with measurement and prediction uncertainty is a major challenge on the way to urban automated driving. In this work, we address this challenge with a sampling-based optimization approach. For this, we formulate an optimal control problem that optimizes for low risk and high passenger comfort. The risk is calculated on the basis of the perception information and the respective uncertainty using a risk model. The risk model combines set-based methods and probabilistic approaches. Thus, the approach provides safety guarantees in a probabilistic sense, while for a vanishing risk, the formal safety guarantees of the set-based methods are inherited. By exploring all available behavior options, our approach solves decision making and longitudinal trajectory planning in one step. The available behavior options are provided by a formal representation of the situation context, which is also used to reduce calculation efforts. Occlusions are resolved using the external perception of infrastructure-mounted sensors. Yet, instead of merging external and ego perception with track-to-track fusion, the information is used in parallel. The motion planning scheme is validated through real-world experiments.

cs.RO↗

arXiv2021

Contact Tracing & Super-Spreaders in the Branching-Process Model

In recent years, it became clear that super-spreader events play an important role, particularly in the spread of airborne infections. We investigate a novel model for super-spreader events, not based on a heterogeneous contact graph but on a random contact rate: Many individuals become infected synchronously in single contact events. We use the branching-process approach for contact tracing to analyze the impact of super-spreader events on the effect of contact tracing. Here we neglect a tracing delay. Roughly speaking, we find that contact tracing is more efficient in the presence of super-spreaders if the fraction of symptomatics is small, the tracing probability is high, or the latency period is distinctively larger than the incubation period. In other cases, the effect of contact tracing can be decreased by super-spreaders. Numerical analysis with parameters suited for SARS-CoV-2 indicates that super-spreaders do not decrease the effect of contact tracing crucially in case of that infection.

q-bio.PE↗

arXiv2020

LMB Filter Based Tracking Allowing for Multiple Hypotheses in Object Reference Point Association*

Autonomous vehicles need precise knowledge on dynamic objects in their surroundings. Especially in urban areas with many objects and possible occlusions, an infrastructure system based on a multi-sensor setup can provide the required environment model for the vehicles. Previously, we have published a concept of object reference points (e.g. the corners of an object), which allows for generic sensor "plug and play" interfaces and relatively cheap sensors. This paper describes a novel method to additionally incorporate multiple hypotheses for fusing the measurements of the object reference points using an extension to the previously presented Labeled Multi-Bernoulli (LMB) filter. In contrast to the previous work, this approach improves the tracking quality in the cases where the correct association of the measurement and the object reference point is unknown. Furthermore, this paper identifies options based on physical models to sort out inconsistent and unfeasible associations at an early stage in order to keep the method computationally tractable for real-time applications. The method is evaluated on simulations as well as on real scenarios. In comparison to comparable methods, the proposed approach shows a considerable performance increase, especially the number of non-continuous tracks is decreased significantly.

cs.RO↗

arXiv2020

Contact Tracing -- Old Models and New Challenges

Contact tracing is an effective method to control emerging diseases. Since the 1980's, mathematical modelers are developing a consistent theory for contact tracing, with the aim to find effective and efficient implementations of contact tracing, and to assess the effects of contact tracing on the spread of an infectious disease. Despite the progress made in the area, there remain important open questions. In addition, technological developments, especially in the field of molecular biology (genetic sequencing of pathogens) and modern communication (digital contact tracing), have posed new challenges for the modeling community. In the present paper, we discuss modeling approaches for contact tracing and identify some of the current challenges for the field.

q-bio.PE↗

arXiv2020

Filter Bubbles, Echo Chambers, and Reinforcement: Tracing Populism in Election Data

We present a novel model for the effect of echo chambers, filter bubbles, and reinforcement on election results. Our model extends the well known voter model with zealots to include reinforcement. We analyze the behaviour of the model, determine the invariant measure, and show that reinforcement may 1) shift the distribution of votes compared to the voter model, and 2) lead to phase transitions. We test whether the model with reinforcement fit better than under its absence in election data from US presidential elections, the Brexit referendum, and parliamentary elections in France, The Netherlands, and Germany. We find in many cases that populist parties and candidates can be clearly identified by a high level of reinforcement. Furthermore, we find the phase transition predicted by the model back in data. We finally discuss the implications and relevance of our findings and possible origins of the reinforcement behaviour in modern societies.

physics.soc-ph↗

arXiv2020

Kalman Filter Meets Subjective Logic: A Self-Assessing Kalman Filter Using Subjective Logic

Self-assessment is a key to safety and robustness in automated driving. In order to design safer and more robust automated driving functions, the goal is to self-assess the performance of each module in a whole automated driving system. One crucial component in automated driving systems is the tracking of surrounding objects, where the Kalman filter is the most fundamental tracking algorithm. For Kalman filters, some classical online consistency measures exist for self-assessment, which are based on classical probability theory. However, these classical approaches lack the ability to measure the explicit statistical uncertainty within the self-assessment, which is an important quality measure, particularly, if only a small number of samples is available for the self-assessment. In this work, we propose a novel online self-assessment method using subjective logic, which is a modern extension of probabilistic logic that explicitly models the statistical uncertainty. Thus, by embedding classical Kalman filtering into subjective logic, our method additionally features an explicit measure for statistical uncertainty in the self-assessment.

eess.SY↗

arXiv2020

On the space-time expressivity of ResNets

Residual networks (ResNets) are a deep learning architecture that substantially improved the state of the art performance in certain supervised learning tasks. Since then, they have received continuously growing attention. ResNets have a recursive structure $x_{k+1} = x_k + R_k(x_k)$ where $R_k$ is a neural network called a residual block. This structure can be seen as the Euler discretisation of an associated ordinary differential equation (ODE) which is called a neural ODE. Recently, ResNets were proposed as the space-time approximation of ODEs which are not of this neural type. To elaborate this connection we show that by increasing the number of residual blocks as well as their expressivity the solution of an arbitrary ODE can be approximated in space and time simultaneously by deep ReLU ResNets. Further, we derive estimates on the complexity of the residual blocks required to obtain a prescribed accuracy under certain regularity assumptions.

cs.LG↗

arXiv2020

Exact and approximate formulas for contact tracing on random trees

We consider a stochastic susceptible-infected-recovered (SIR) model with contact tracing on random trees and on the configuration model. On a rooted tree, where initially all individuals are susceptible apart from the root which is infected, we are able to find exact formulas for the distribution of the infectious period. Thereto, we show how to extend the existing theory for contact tracing in homogeneously mixing populations to trees. Based on these formulas, we discuss the influence of randomness in the tree and the basic reproduction. We find the well known results for the homogeneously mixing case as a limit of the present model (tree-shaped contact graph). Furthermore, we develop approximate mean field equations for the dynamics on trees, and - using the message passing method - also for the configuration model. The interpretation and implications of the results are discussed.

q-bio.PE↗

arXiv2020

Deep Ritz revisited

Recently, progress has been made in the application of neural networks to the numerical analysis of partial differential equations (PDEs). In the latter the variational formulation of the Poisson problem is used in order to obtain an objective function - a regularised Dirichlet energy - that was used for the optimisation of some neural networks. In this notes we use the notion of $Γ$-convergence to show that ReLU networks of growing architecture that are trained with respect to suitably regularised Dirichlet energies converge to the true solution of the Poisson problem. We discuss how this approach generalises to arbitrary variational problems under certain universality assumptions of neural networks and see that this covers some nonlinear stationary PDEs like the $p$-Laplace.

math.NA↗

arXiv2019

Subjective Logic-based Identification of Markov Chains and Its Application to CAV's Safety

A reliable estimation of the communication chan-nel which connects automated vehicles is an important steptowards the safety of connected and automated vehicles. The communication channel is usually modeled as Markov chain with slowly time-varying transition rates and is identifiedthrough statistics on the observed state transitions. However, the classical identification approach lacks a measure on how reliable the identification results, and thus the channel, are. In this work, we propose an identification method, based onthe subjective logic theory, which features such a reliability measure in terms of statistical uncertainty. We demonstrate through simulations that the proposed method is capable of quickly responding to parameter changes. Furthermore, it is shown that the transition rates of the Markov chain are tracked with high accuracy. Finally, we validate our results by a real-world experiment.

eess.SP↗

arXiv2019

A Risk and Comfort Optimizing Motion Planning Scheme for Merging Scenarios

Motion planning for merging scenarios accounting for measurement and prediction uncertainties is a major challenge on the way to autonomous driving. Classical methods subdivide the motion planning into behavior and trajectory planning, thus narrowing down the solution set. Hence, incomplex merging scenarios, no suitable solution might be found. In this work, we present a planning scheme that solves behavior and trajectory planning together by exploring all possible decision options. A safety strategy is implemented and the risk of violating a safety constraint is minimized as well as the jerk to feature a risk and comfort optimal trajectory. To mitigate the injection of noise into the actual trajectory, a new analytical trajectory generation method is derived and its optimality is proven. The decision capability is evaluated through Monte-Carlo simulation. Furthermore, the calculation time is evaluated showing the real-time capability of our approach.

eess.SY↗

arXiv2019

LACI: Low-effort Automatic Calibration of Infrastructure Sensors

Sensor calibration usually is a time consuming yet important task. While classical approaches are sensor-specific and often need calibration targets as well as a widely overlapping field of view (FOV), within this work, a cooperative intelligent vehicle is used as callibration target. The vehicleis detected in the sensor frame and then matched with the information received from the cooperative awareness messagessend by the coperative intelligent vehicle. The presented algorithm is fully automated as well as sensor-independent, relying only on a very common set of assumptions. Due to the direct registration on the world frame, no overlapping FOV is necessary. The algorithm is evaluated through experiment for four laserscanners as well as one pair of stereo cameras showing a repetition error within the measurement uncertainty of the sensors. A plausibility check rules out systematic errors that might not have been covered by evaluating the repetition error.

eess.SP↗

arXiv2019

Multi-scale Convolutional Neural Networks for Inverse Problems

Inverse problems exist in many domains such as phase imaging, image processing, and computer vision. These problems are often solved with application-specific algorithms, even though their nature remains the same: mapping input image(s) to output image(s). Deep convolutional neural networks have shown great potential for highly variable tasks across many image-based domains, but are usually difficult to train due to their inner high non-linearities. We propose a novel neural network architecture highlighting fast convergence as a generic solution addressing image(s)-to-image(s) inverse problems of different domains. Here we show that this approach is effective at predicting phases from direct intensity measurements, imaging objects from diffused reflections and denoising scanning transmission electron microscopy images, with just different training datasets. This opens a way to solve problems statistically through big data, in contrast to implementing explicit inversion algorithms from their mathematical formulas. Previous works have targeted much more on \textit{how} can we reconstruct rather than \textit{what} can be reconstructed. Our strategy offers a paradigm shift.

physics.comp-ph↗

arXiv2019

Environment Modeling Based on Generic Infrastructure Sensor Interfaces Using a Centralized Labeled-Multi-Bernoulli Filter

Urban intersections put high demands on fully automated vehicles, in particular, if occlusion occurs. In order to resolve such and support vehicles in unclear situations, a popular approach is the utilization of additional information from infrastructure-based sensing systems. However, a widespread use of such systems is circumvented by their complexity and thus, high costs. Within this paper, a generic interface is proposed, which enables a huge variety of sensors to be connected. The sensors are only required to measure very few features of the objects, if multiple distributed sensors with different viewing directions are available. Furthermore, a Labeled Multi-Bernoulli (LMB) filter is presented, which can not only handle such measurements, but also infers missing object information about the objects' extents. The approach is evaluated on simulations and demonstrated on a real-world infrastructure setup.

eess.SP↗

arXiv2019

A Subjective-Logic-based Reliability Estimation Mechanism for Cooperative Information with Application to IV's Safety

Use of cooperative information, distributed by road-side units, offers large potential for intelligent vehicles (IVs). As vehicle automation progresses and cooperative perception is used to fill the blind spots of onboard sensors, the question of reliability of the data becomes increasingly important in safety considerations (SOTIF, Safety of the Intended Functionality). This paper addresses the problem to estimate the reliability of cooperative information for in-vehicle use. We propose a novel method to infer the reliability of received data based on the theory of Subjective Logic (SL). Using SL, we fuse multiple information sources, which individually only provide mild cues of the reliability, into a holistic estimate, which is statistically sound through an end-to-end modeling within the theory of SL. Using the proposed scheme for probabilistic SL-based fusion, IVs are able to separate faulty from correct data samples with a large margin of safety. Real world experiments show the applicability and effectiveness of our approach.

eess.SP↗