arXiv subjects

Johannes Müller

Publications and source records attributed to Johannes Müller.

At least 37 records · Page 2Linked to original sources

arXiv2024

Opinion models, data, and politics

We investigate the connection between Potts (Curie-Weiss) models and stochastic opinion models in the view of the Boltzmann distribution and stochastic Glauber dynamics. We particularly find that the q-voter model can be considered as a natural extension of the Zealot model which is adapted by Lagrangian parameters. We also discuss weak and strong effects continuum limits for the models. We then fit four models (Curie-Weiss, strong and weak effects limit for the q-voter model, and the reinforcement model) to election data from United States, United Kingdom, France and Germany. We find that particularly the weak effects models are able to fit the data (Kolmogorov-Smirnov test), where the weak effects reinforcement model performs best (AIC). The resulting estimates are interpreted in the view of political sciences, and also the importance of this kind of model-based approaches to election data for the political sciences is discussed.

physics.soc-ph↗

arXiv2023

A Golden-Free Formal Method for Trojan Detection in Non-Interfering Accelerators

The threat of hardware Trojans (HTs) in security-critical IPs like cryptographic accelerators poses severe security risks. The HT detection methods available today mostly rely on golden models and detailed circuit specifications. Often they are specific to certain HT payload types, making pre-silicon verification difficult and leading to security gaps. We propose a novel formal verification method for HT detection in non-interfering accelerators at the Register Transfer Level (RTL), employing standard formal property checking. Our method guarantees the exhaustive detection of any sequential HT independently of its payload behavior, including physical side channels. It does not require a golden model or a functional specification of the design. The experimental results demonstrate efficient and effective detection of all sequential HTs in accelerators available on Trust-Hub, including those with complex triggers and payloads.

cs.CR↗

arXiv2023

Parameter estimation for contact tracing in graph-based models

We adopt a maximum-likelihood framework to estimate parameters of a stochastic susceptible-infected-recovered (SIR) model with contact tracing on a rooted random tree. Given the number of detectees per index case, our estimator allows to determine the degree distribution of the random tree as well as the tracing probability. Since we do not discover all infectees via contact tracing, this estimation is non-trivial. To keep things simple and stable, we develop an approximation suited for realistic situations (contract tracing probability small, or the probability for the detection of index cases small). In this approximation, the only epidemiological parameter entering the estimator is $R_0$. The estimator is tested in a simulation study and is furthermore applied to covid-19 contact tracing data from India. The simulation study underlines the efficiency of the method. For the empirical covid-19 data, we compare different degree distributions and perform a sensitivity analysis. We find that particularly a power-law and a negative binomial degree distribution fit the data well and that the tracing probability is rather large. The sensitivity analysis shows no strong dependency of the estimates on the reproduction number. Finally, we discuss the relevance of our findings.

math.DS↗

arXiv2023

Lossy Compression of Electron Diffraction Patterns for Ptychography via Change of Basis

Ptychography is a computational imaging technique that has risen in popularity in the x-ray and electron microscopy communities in the past half decade. One of the reasons for this success is the development of new high performance electron detectors with increased dynamic range and readout speed, both of which are necessary for a successful application of this technique. Despite the advances made in computing power, processing the recorded data remains a challenging task, and the growth in data rate has made the size of the resulting datasets a bottleneck for the whole process. Here we present an investigation into lossy compression methods for electron diffraction patterns that retain the necessary information for ptychographic reconstructions, yet lead to a decrease in data set size by three or four orders of magnitude. We apply several compression methods to both simulated and experimental data - all with promising results.

physics.comp-ph↗

arXiv2023

Decorative coating or corrosion product? TEM and SEM Study on a Late Neolithic Axe to find origins of silver metal on the surface

Here we report on the analysis of a metallic Late Neolithic copper axe by means of Scanning Electron Microscopy (SEM) and Transmission Electron Microscopy (TEM). The axe was found at Eskilstorp, south-west Scania during archaeological excavations in autumn of 2015. It showed a hint of silver en-richment on the surface which is unusual for Late Neolithic axes from Pile type hoard. To identify the origin of the silver content, we extracted a thin lamella of the axe interior using Focused Ion Beam (FIB) technology to reach the internal structure to keep the process extremely minimally invasive. The results revealed the presence of porous external layer of copper oxide enriched with silver particles. It is shown with the corrosion test performed on copper-silver experimental replica that the silver en-richment is attributed to the selective dissolution of copper metal as a resut of corrosion process on the axe. The corrosion experiment is performed in the presence of an organic electrolyte such as Hemic Acid (HA) which replicates soil and natural water environment. In the scope of this research work, we found a strong evidence that the silver on the surface of the axe was not decrative layer and instead remained on the surface due to its more noble character while copper leached out into the soil due to corrosion.

physics.chem-ph↗

arXiv2023

Achieving High Accuracy with PINNs via Energy Natural Gradients

We propose energy natural gradient descent, a natural gradient method with respect to a Hessian-induced Riemannian metric as an optimization algorithm for physics-informed neural networks (PINNs) and the deep Ritz method. As a main motivation we show that the update direction in function space resulting from the energy natural gradient corresponds to the Newton direction modulo an orthogonal projection onto the model's tangent space. We demonstrate experimentally that energy natural gradient descent yields highly accurate solutions with errors several orders of magnitude smaller than what is obtained when training PINNs with standard optimizers like gradient descent or Adam, even when those are allowed significantly more computation time.

cs.LG↗

arXiv2023

A Protocol for Cast-as-Intended Verifiability with a Second Device

Numerous institutions, such as companies, universities, or non-governmental organizations, employ Internet voting for remote elections. Since the main purpose of an election is to determine the voters' will, it is fundamentally important to ensure that the final election result correctly reflects the voters' votes. To this end, modern secure Internet voting schemes aim for what is called end-to-end verifiability. This fundamental security property ensures that the correctness of the final result can be verified, even if some of the computers or parties involved are malfunctioning or corrupted. A standard component in this approach is so called cast-as-intended verifiability which enables individual voters to verify that the ballots cast on their behalf contain their intended choices. Numerous approaches for cast-as-intended verifiability have been proposed in the literature, some of which have also been employed in real-life Internet elections. One of the well established approaches for cast-as-intended verifiability is to employ a second device which can be used by voters to audit their submitted ballots. This approach offers several advantages - including support for flexible ballot/election types and intuitive user experience - and it has been used in real-life elections, for instance in Estonia. In this work, we improve the existing solutions for cast-as-intended verifiability based on the use of a second device. We propose a solution which, while preserving the advantageous practical properties sketched above, provides tighter security guarantees. Our method does not increase the risk of vote-selling when compared to the underlying voting protocol being augmented and, to achieve this, it requires only comparatively weak trust assumptions. It can be combined with various voting protocols, including commitment-based systems offering everlasting privacy.

cs.CR↗

arXiv2022

Age structure, replicator equation, and the prisoner's dilemma

We investigate the evolutionary dynamics of an age-structured population under weak frequency-dependent selection. It turns out that the weak selection is affected in a non-trivial way by the life-history trait. We can disentangle the dynamics, based on the appearance of different time scales. These time scales, which seem to form a universal structure in the interplay of weak selection and life-history traits, allow us to reduce the infinite dimensional model to a one-dimensional modified replicator equation. The modified replicator equation is then used to investigate cooperation (the prisoner's dilemma) by means of adaptive dynamics. We identify conditions under which age structure is able to promote cooperation. At the end we discuss the relevance of our findings.

q-bio.PE↗

arXiv2022

Geometry and convergence of natural policy gradient methods

We study the convergence of several natural policy gradient (NPG) methods in infinite-horizon discounted Markov decision processes with regular policy parametrizations. For a variety of NPGs and reward functions we show that the trajectories in state-action space are solutions of gradient flows with respect to Hessian geometries, based on which we obtain global convergence guarantees and convergence rates. In particular, we show linear convergence for unregularized and regularized NPG flows with the metrics proposed by Kakade and Morimura and co-authors by observing that these arise from the Hessian geometries of conditional entropy and entropy respectively. Further, we obtain sublinear convergence rates for Hessian geometries arising from other convex functions like log-barriers. Finally, we interpret the discrete-time NPG methods with regularized rewards as inexact Newton methods if the NPG is defined with respect to the Hessian geometry of the regularizer. This yields local quadratic convergence rates of these methods for step size equal to the penalization strength.

math.OC↗

arXiv2022

Error Estimates for the Deep Ritz Method with Boundary Penalty

We estimate the error of the Deep Ritz Method for linear elliptic equations. For Dirichlet boundary conditions, we estimate the error when the boundary values are imposed through the boundary penalty method. Our results apply to arbitrary sets of ansatz functions and estimate the error in dependence of the optimization accuracy, the approximation capabilities of the ansatz class and -- in the case of Dirichlet boundary values -- the penalization strength $λ$. To the best of our knowledge, our results are presently the only ones in the literature that treat the case of Dirichlet boundary conditions in full generality, i.e., without a lower order term that leads to coercivity on all of $H^1(Ω)$. Further, we discuss the implications of our results for ansatz classes which are given through ReLU networks and the relation to existing estimates for finite element functions. For high dimensional problems our results show that the favourable approximation capabilities of neural networks for smooth functions are inherited by the Deep Ritz Method.

math.NA↗

arXiv2022

Notes on Exact Boundary Values in Residual Minimisation

We analyse the difference in convergence mode using exact versus penalised boundary values for the residual minimisation of PDEs with neural network type ansatz functions, as is commonly done in the context of physics informed neural networks. It is known that using an $L^2$ boundary penalty leads to a loss of regularity of $3/2$ meaning that approximation in $H^2$ yields a priori estimates in $H^{1/2}$. These notes demonstrate how this loss of regularity can be circumvented if the functions in the ansatz class satisfy the boundary values exactly. Furthermore, it is shown that in this case, the loss function provides a consistent a posteriori error estimator in $H^2$ norm made by the residual minimisation method. We provide analogue results for linear time dependent problems and discuss the implications of measuring the residual in Sobolev norms.

math.NA↗

arXiv2022

Extrinsic Camera Calibration with Semantic Segmentation

Monocular camera sensors are vital to intelligent vehicle operation and automated driving assistance and are also heavily employed in traffic control infrastructure. Calibrating the monocular camera, though, is time-consuming and often requires significant manual intervention. In this work, we present an extrinsic camera calibration approach that automatizes the parameter estimation by utilizing semantic segmentation information from images and point clouds. Our approach relies on a coarse initial measurement of the camera pose and builds on lidar sensors mounted on a vehicle with high-precision localization to capture a point cloud of the camera environment. Afterward, a mapping between the camera and world coordinate spaces is obtained by performing a lidar-to-camera registration of the semantically segmented sensor data. We evaluate our method on simulated and real-world data to demonstrate low error measurements in the calibration results. Our approach is suitable for infrastructure sensors as well as vehicle sensors, while it does not require motion of the camera platform.

cs.CV↗

arXiv2022

Invariance Properties of the Natural Gradient in Overparametrised Systems

The natural gradient field is a vector field that lives on a model equipped with a distinguished Riemannian metric, e.g. the Fisher-Rao metric, and represents the direction of steepest ascent of an objective function on the model with respect to this metric. In practice, one tries to obtain the corresponding direction on the parameter space by multiplying the ordinary gradient by the inverse of the Gram matrix associated with the metric. We refer to this vector on the parameter space as the natural parameter gradient. In this paper we study when the pushforward of the natural parameter gradient is equal to the natural gradient. Furthermore we investigate the invariance properties of the natural parameter gradient. Both questions are addressed in an overparametrised setting.

cs.LG↗

arXiv2022

Self-Assessment for Single-Object Tracking in Clutter Using Subjective Logic

Reliable tracking algorithms are essential for automated driving. However, the existing consistency measures are not sufficient to meet the increasing safety demands in the automotive sector. Therefore, this work presents a novel method for self-assessment of single-object tracking in clutter based on Kalman filtering and subjective logic. A key feature of the approach is that it additionally provides a measure of the collected statistical evidence in its online reliability scores. In this way, various aspects of reliability, such as the correctness of the assumed measurement noise, detection probability, and clutter rate, can be monitored in addition to the overall assessment based on the available evidence. Here, we present a mathematical derivation of the reference distribution used in our self-assessment module for our studied problem. Moreover, we introduce a formula that describes how a threshold should be chosen for the degree of conflict, the subjective logic comparison measure used for the reliability decision making. Our approach is evaluated in a challenging simulation scenario designed to model adverse weather conditions. The simulations show that our method can significantly improve the reliability checking of single-object tracking in clutter in several aspects.

eess.SP↗

arXiv2022

Solving infinite-horizon POMDPs with memoryless stochastic policies in state-action space

Reward optimization in fully observable Markov decision processes is equivalent to a linear program over the polytope of state-action frequencies. Taking a similar perspective in the case of partially observable Markov decision processes with memoryless stochastic policies, the problem was recently formulated as the optimization of a linear objective subject to polynomial constraints. Based on this we present an approach for Reward Optimization in State-Action space (ROSA). We test this approach experimentally in maze navigation tasks. We find that ROSA is computationally efficient and can yield stability improvements over other existing methods.

cs.LG↗

arXiv2022

The Geometry of Memoryless Stochastic Policy Optimization in Infinite-Horizon POMDPs

We consider the problem of finding the best memoryless stochastic policy for an infinite-horizon partially observable Markov decision process (POMDP) with finite state and action spaces with respect to either the discounted or mean reward criterion. We show that the (discounted) state-action frequencies and the expected cumulative reward are rational functions of the policy, whereby the degree is determined by the degree of partial observability. We then describe the optimization problem as a linear optimization problem in the space of feasible state-action frequencies subject to polynomial constraints that we characterize explicitly. This allows us to address the combinatorial and geometric complexity of the optimization problem using recent tools from polynomial optimization. In particular, we estimate the number of critical points and use the polynomial programming description of reward maximization to solve a navigation problem in a grid world.

math.OC↗

arXiv2022

Situation-Aware Environment Perception Using a Multi-Layer Attention Map

Within the field of automated driving, a clear trend in environment perception tends towards more sensors, higher redundancy, and overall increase in computational power. This is mainly driven by the paradigm to perceive the entire environment as best as possible at all times. However, due to the ongoing rise in functional complexity, compromises have to be considered to ensure real-time capabilities of the perception system. In this work, we introduce a concept for situation-aware environment perception to control the resource allocation towards processing relevant areas within the data as well as towards employing only a subset of functional modules for environment perception, if sufficient for the current driving task. Specifically, we propose to evaluate the context of an automated vehicle to derive a multi-layer attention map (MLAM) that defines relevant areas. Using this MLAM, the optimum of active functional modules is dynamically configured and intra-module processing of only relevant data is enforced. We outline the feasibility of application of our concept using real-world data in a straight-forward implementation for our system at hand. While retaining overall functionality, we achieve a reduction of accumulated processing time of 59%.

cs.RO↗

arXiv2022

Deep Reinforcement Learning for Data-Driven Adaptive Scanning in Ptychography

We present a method that lowers the dose required for a ptychographic reconstruction by adaptively scanning the specimen, thereby providing the required spatial information redundancy in the regions of highest importance. The proposed method is built upon a deep learning model that is trained by reinforcement learning (RL), using prior knowledge of the specimen structure from training data sets. We show that equivalent low-dose experiments using adaptive scanning outperform conventional ptychography experiments in terms of reconstruction resolution.

physics.comp-ph↗