arXiv subjects

Andreas Weber

Publications and source records attributed to Andreas Weber.

At least 19 recordsLinked to original sources

arXiv2023

Semantic Map Learning of Traffic Light to Lane Assignment based on Motion Data

Understanding which traffic light controls which lane is crucial to navigate intersections safely. Autonomous vehicles commonly rely on High Definition (HD) maps that contain information about the assignment of traffic lights to lanes. The manual provisioning of this information is tedious, expensive, and not scalable. To remedy these issues, our novel approach derives the assignments from traffic light states and the corresponding motion patterns of vehicle traffic. This works in an automated way and independently of the geometric arrangement. We show the effectiveness of basic statistical approaches for this task by implementing and evaluating a pattern-based contribution method. In addition, our novel rejection method includes accompanying safety considerations by leveraging statistical hypothesis testing. Finally, we propose a dataset transformation to re-purpose available motion prediction datasets for semantic map learning. Our publicly available API for the Lyft Level 5 dataset enables researchers to develop and evaluate their own approaches.

cs.CV↗

arXiv2022

Localization of Invariable Sparse Errors in Dynamic Systems

Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult to comprehend. Such a data-mismatch can be caused by endogenous model errors including misspecified interactions and inaccurate parameter values. These are often difficult to distinguish from unmodelled process influencing the real system like unknown inputs or faults. Localizing the root cause of these errors or faults and reconstructing their dynamics is only possible if the measured outputs of the system are sufficiently informative. Here, we present criteria for the measurements required to localize the position of error sources in large dynamic networks. We assume that faults or errors occur at a limited number of positions in the network. This invariable sparsity differs from previous sparsity definitions for inputs to dynamic systems. We provide an exact criterion for the recovery of invariable sparse inputs to nonlinear systems and formulate an optimization criterion for invariable sparse input reconstruction. For linear systems we can provide exact error bounds for this reconstruction method.

math.OC↗

arXiv2020

Sparse Error Localization in Complex Dynamic Networks

Understanding the dynamics of complex systems is a central task in many different areas ranging form biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even systems failure is sometimes difficult to comprehend. Such unexpected dynamics can be caused by systematic model errors, unknown inputs from the environment and systems faults. Localizing the root cause of these errors or faults and reconstructing their dynamics is only possible if the measured outputs of the system are sufficiently informative. Here, we present a mathematical theory for the measurements required to localize the position of error sources in large dynamic networks. We assume, that faults or errors occur at a limited number of positions in the network. This sparsity assumption facilitates the accurate reconstruction of the dynamic timecourses of the errors by solving a convex optimal control problem. For cases, where the sensor measurements are not sufficiently informative to pinpoint the error position exactly, we provide methods to restrict the error location to a smaller subset of network nodes. We also suggest strategies to efficiently select additional measurements for narrowing down the error location.

math.OC↗

arXiv2020

Efficiently and Effectively Recognizing Toricity of Steady State Varieties

We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, we study the notion of shifted toric varieties which generalizes the notion of toric varieties. This requires a geometric view on the varieties rather than an algebraic view on the ideals. We present algorithms and computations on 129 models from the BioModels repository testing for group and coset structures over both the complex numbers and the real numbers. Our methods over the complex numbers are based on Gröbner basis techniques and binomiality tests. Over the real numbers we use first-order characterizations and employ real quantifier elimination. In combination with suitable prime decompositions and restrictions to subspaces it turns out that almost all models show coset structure. Beyond our practical computations, we give upper bounds on the asymptotic worst-case complexity of the corresponding problems by proposing single exponential algorithms that test complex or real varieties for toricity or shifted toricity. In the positive case, these algorithms produce generating binomials. In addition, we propose an asymptotically fast algorithm for testing membership in a binomial variety over the algebraic closure of the rational numbers.

q-bio.MN↗

arXiv2019

Human Motion Anticipation with Symbolic Label

Anticipating human motion depends on two factors: the past motion and the person's intention. While the first factor has been extensively utilized to forecast short sequences of human motion, the second one remains elusive. In this work we approximate a person's intention via a symbolic representation, for example fine-grained action labels such as walking or sitting down. Forecasting a symbolic representation is much easier than forecasting the full body pose with its complex inter-dependencies. However, knowing the future actions makes forecasting human motion easier. We exploit this connection by first anticipating symbolic labels and then generate human motion, conditioned on the human motion input sequence as well as on the forecast labels. This allows the model to anticipate motion changes many steps ahead and adapt the poses accordingly. We achieve state-of-the-art results on short-term as well as on long-term human motion forecasting.

cs.CV↗

arXiv2019

Bonn Activity Maps: Dataset Description

The key prerequisite for accessing the huge potential of current machine learning techniques is the availability of large databases that capture the complex relations of interest. Previous datasets are focused on either 3D scene representations with semantic information, tracking of multiple persons and recognition of their actions, or activity recognition of a single person in captured 3D environments. We present Bonn Activity Maps, a large-scale dataset for human tracking, activity recognition and anticipation of multiple persons. Our dataset comprises four different scenes that have been recorded by time-synchronized cameras each only capturing the scene partially, the reconstructed 3D models with semantic annotations, motion trajectories for individual people including 3D human poses as well as human activity annotations. We utilize the annotations to generate activity likelihoods on the 3D models called activity maps.

cs.CV↗

arXiv2019

Unsupervised and Generic Short-Term Anticipation of Human Body Motions

Various neural network based methods are capable of anticipating human body motions from data for a short period of time. What these methods lack are the interpretability and explainability of the network and its results. We propose to use Dynamic Mode Decomposition with delays to represent and anticipate human body motions. Exploring the influence of the number of delays on the reconstruction and prediction of various motion classes, we show that the anticipation errors in our results are comparable or even better for very short anticipation times ($<0.4$ sec) to a recurrent neural network based method. We perceive our method as a first step towards the interpretability of the results by representing human body motions as linear combinations of ``factors''. In addition, compared to the neural network based methods large training times are not needed. Actually, our methods do not even regress to any other motions than the one to be anticipated and hence is of a generic nature.

cs.LG↗

arXiv2019

Structural Invertibility and Optimal Sensor Node Placement for Error and Input Reconstruction in Dynamic Systems

Despite recent progress in our understanding of complex dynamic networks, it remains challenging to devisesufficiently accurate models to observe, control or predict the state of real systems in biology, economics or other fields. A largely overlooked fact is that these systems are typically open and receive unknown inputs from their environment. A further fundamental obstacle are structural model errors caused by insufficient or inaccurate knowledge about the quantitative interactions in the real system. Here, we show that unknown inputs to open systems and model errors can be treated under the common framework of invertibility, which is a requirement for reconstructing these disturbances from output measurements. By exploiting the fact that invertibility can be decided from the influence graph of the system, we analyse the relationship between structural network properties and invertibility under different realistic scenarios. We show that sparsely connected scale free networks are the most difficult to invert. We introduce a new sensor node placement algorithm to select a minimum set of measurement positions in the network required for invertibility. This algorithm facilitates optimal experimental design for the reconstruction of inputs or model errors from output measurements. Our results have both fundamental and practical implications for nonlinear systems analysis, modelling and design.

math.DS↗

arXiv2019

Energy Efficient Massive MIMO Array Configurations

The high spectral efficiency of massive MIMO (Multiple Input Multiple Output) is mainly achieved through the exploitation of spatial multiplexing, i.e. by using a high number of MIMO layers that are applied simultaneously to many users. The power consumption of a massive MIMO base station is determined by the hardware driving a high number of antenna ports and elements. This paper focuses on practical deployment situations with varying user load. During hours with low number of users a certain significant part of hardware power consumption would remain with conventional massive MIMO processing, while the full potential of spectral efficiency cannot be exploited due to the low number of users, resulting in low power efficiency and cost. We investigate the impact of different hybrid array architectures on spectral efficiency, average user throughput and power consumption and show how to design a massive MIMO system with significantly improved energy efficiency for a given target scenario, while maintaining a targeted service quality.

eess.SP↗

arXiv2018

Symbolic-Numeric Integration of the Dynamical Cosserat Equations

We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechanical behavior of slender structures, like fibers and rods. This is based on our previous results on the construction of a closed form general solution to the kinematic part of the Cosserat system. Our approach combines methods of numerical exponential integration and symbolic integration of the intermediate system of nonlinear ordinary differential equations describing the dynamics of one of the arbitrary vector-functions in the general solution of the kinematic part in terms of the module of the twist vector-function. We present an experimental comparison with the well-established generalized alpha-method illustrating the computational efficiency of our approach for problems in structural mechanics.

math.AP↗

arXiv2018

On three genetic repressilator topologies

Novel mathematical models of three different repressilator topologies are introduced. As designable transcription factors have been shown to bind to DNA non-cooperatively, we have chosen models containing non-cooperative elements. The extended topologies involve three additional transcription regulatory elements---which can be easily implemented by synthetic biology---forming positive feedback loops. This increases the number of variables to six, and extends the complexity of the equations in the model. To perform our analysis we had to use combinations of modern symbolic algorithms of computer algebra systems Mathematica and Singular. The study shows that all the three models have simple dynamics what can also be called regular behaviour: they have a single asymptotically stable steady state with small amplitude oscillations in the 3D case and no oscillation in one of the 6D cases and damping oscillation in the second 6D case. Using the program QeHopf we were able to exclude the presence of Hopf bifurcation in the 3D system.

math.DS↗

arXiv2018

A Statistical Approach for RF Exposure Compliance Boundary Assessment in Massive MIMO Systems

Massive multiple-input multiple-output (MIMO) is a fundamental enabler to provide high data throughput in next generation cellular networks. By equipping the base stations (BSs) with tens or hundreds of antenna elements, narrow and high gain beams can be used to spatially multiplex several user equipment (UE) devices. While increasing the achievable performance, focusing the transmit power into specific UE directions also poses new issues when performing the radio frequency (RF) exposure assessment. In fact, the spatial distribution of the actual BS transmit power strongly depends on the deployment scenario and on the position of the UEs. Traditional methods for assessing the RF exposure compliance boundaries around BS sites are generally based on maximum transmit power and static beams. In massive MIMO systems, these approaches tend to be very conservative, in particular when time averaging is properly considered. In this work, we propose to leverage the three dimensional spatial channel model standardized by the Third Generation Partnership Project in order to assess reasonably foreseeable compliance boundaries of massive MIMO BSs. The analysis is performed by considering BSs fully loaded and different configurations of active UEs per cell. Numerical results show that the statistical approach developed in this paper allows reducing to nearly half the compliance distance when compared to the traditional method.

cs.NI↗

arXiv2017

A Dual-Source Approach for 3D Human Pose Estimation from a Single Image

In this work we address the challenging problem of 3D human pose estimation from single images. Recent approaches learn deep neural networks to regress 3D pose directly from images. One major challenge for such methods, however, is the collection of training data. Specifically, collecting large amounts of training data containing unconstrained images annotated with accurate 3D poses is infeasible. We therefore propose to use two independent training sources. The first source consists of accurate 3D motion capture data, and the second source consists of unconstrained images with annotated 2D poses. To integrate both sources, we propose a dual-source approach that combines 2D pose estimation with efficient 3D pose retrieval. To this end, we first convert the motion capture data into a normalized 2D pose space, and separately learn a 2D pose estimation model from the image data. During inference, we estimate the 2D pose and efficiently retrieve the nearest 3D poses. We then jointly estimate a mapping from the 3D pose space to the image and reconstruct the 3D pose. We provide a comprehensive evaluation of the proposed method and experimentally demonstrate the effectiveness of our approach, even when the skeleton structures of the two sources differ substantially.

cs.CV↗

arXiv2017

Simulating spiraling bubble movement in the EL approach

Simulating the detailed movement of a rising bubble can be challenging, especially when it comes to bubble path instabilities. Free rising ellipsoidal bubbles not only move in straight lines but can describe sinusoidal, zigzag or spiraling paths. The common Euler Euler (EE) simulation techniques can no longer resolve the actual movement patterns and Direct Numerical Simulations (DNS) tend to be very costly when simulating a larger number of bubbles. A solution based on the Euler Lagrange (EL) approach is presented, where the bubbles show oscillating shape and/or instable paths while computational cost are at a far lower level than in DNS. The model calculates direction, shape and rotation of the bubbles to finally create typical instable path lines. This is embedded in an EL simulation, which can resolve bubble size distribution, mass transfer and chemical reactions. To ensure realistic solution, validation against experimental data of single rising bubbles and bubble swarms are presented. References with 2D and also 3D analysis are taken into account to compare simulative data in terms of typical geometrical parameters and average field values.

physics.flu-dyn↗

arXiv2017

Symbolic Versus Numerical Computation and Visualization of Parameter Regions for Multistationarity of Biological Networks

We investigate models of the mitogenactivated protein kinases (MAPK) network, with the aim of determining where in parameter space there exist multiple positive steady states. We build on recent progress which combines various symbolic computation methods for mixed systems of equalities and inequalities. We demonstrate that those techniques benefit tremendously from a newly implemented graph theoretical symbolic preprocessing method. We compare computation times and quality of results of numerical continuation methods with our symbolic approach before and after the application of our preprocessing.

cs.SC↗

arXiv2017

Flow simulation in a 2D bubble column with the Euler-Lagrange and Euler-Euler method

Bubbly flows, as present in bubble column reactors, can be simulated using a variety of simulation techniques. In order to gain high resolution CFD methods are used to simulate a pseudo 2D bubble column using EL and EE techniques. The forces on bubble dynamics are solved within open access software OpenFOAM with bubble interactions computed via Monte Carlo methods. The estimated bubble size distribution and the predicted hold-up are compared to experimental data and other simulative work using EE approach and show reasonable consensus for both. Benchmarks with state of the art EE simulations shows that the EL approach is advantageous if the bubble number stays at a certain level, as the EL approach scales linearly with the number of bubbles simulated. Therefore, different computational meshes have been used to also account for influence of the resolution quality. The EL approach indicated faster solution for all realistic cases, only deliberate decrease of coalescence rates could push CPU time to the limits. Critical bubble number - when EE becomes advantageous over the EL approach - was estimated to be 40.000 in this particular case.

physics.flu-dyn↗

arXiv2017

A Case Study on the Parametric Occurrence of Multiple Steady States

We consider the problem of determining multiple steady states for positive real values in models of biological networks. Investigating the potential for these in models of the mitogen-activated protein kinases (MAPK) network has consumed considerable effort using special insights into the structure of corresponding models. Here we apply combinations of symbolic computation methods for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition. We determine multistationarity of an 11-dimensional MAPK network when numeric values are known for all but potentially one parameter. More precisely, our considered model has 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment, and furthermore positivity conditions on all variables and parameters.

cs.SC↗

arXiv2016

PANIC - A surface science package for the in situ characterization of a near-Earth asteroid

This paper presents the results of a mission concept study for an autonomous micro-scale surface lander also referred to as PANIC - the Pico Autonomous Near-Earth Asteroid In Situ Characterizer. The lander is based on the shape of a regular tetrahedron with an edge length of 35 cm, has a total mass of approximately 12 kg and utilizes hopping as a locomotion mechanism in microgravity. PANIC houses four scientific instruments in its proposed baseline configuration which enable the in situ characterization of an asteroid. It is carried by an interplanetary probe to its target and released to the surface after rendezvous. Detailed estimates of all critical subsystem parameters were derived to demonstrate the feasibility of this concept. The study illustrates that a small, simple landing element is a viable alternative to complex traditional lander concepts, adding a significant science return to any near-Earth asteroid (NEA) mission while meeting tight mass budget constraints.

astro-ph.IM↗