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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., Comment: Accepted to the 2023 IEEE International Conference on Intelligent Transportation Systems (ITSC 2023)

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., Comment: 11 pages main text and 22 pages supplemental text and proofs This paper appears in: IEEE Transactions on Control of Network Systems, 2021 ( Early Access ). Print ISSN: 2325-5870 Online ISSN: 2325-5870. arXiv admin note: substantial text overlap with arXiv:2006.04694

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.

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.

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.

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.

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 Gr\"obner 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., Comment: We made the presentation clearer and fixed many small flaws and typos. A database with our computations is now available as ancillary file

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.

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.

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., Comment: 28 pages, 6 figures

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., Comment: Accepted at the International Workshop on Smart Antennas (WSA), Bochum (Germany), Mar. 2018