Asymptotics of class numbers

A "simple trace formula" is used to derive an asymptotic result for class numbers of complex cubic orders.Comment: 37 page

Bridging the Reality Gap of Reinforcement Learning based Traffic Signal Control using Domain Randomization and Meta Learning

Reinforcement Learning (RL) has been widely explored in Traffic Signal Control (TSC) applications, however, still no such system has been deployed in practice. A key barrier to progress in this area is the reality gap, the discrepancy that results from differences between simulation models and their real-world equivalents. In this paper, we address this challenge by first presenting a comprehensive analysis of potential simulation parameters that contribute to this reality gap. We then also examine two promising strategies that can bridge this gap: Domain Randomization (DR) and Model-Agnostic Meta-Learning (MAML). Both strategies were trained with a traffic simulation model of an intersection. In addition, the model was embedded in LemgoRL, a framework that integrates realistic, safety-critical requirements into the control system. Subsequently, we evaluated the performance of the two methods on a separate model of the same intersection that was developed with a different traffic simulator. In this way, we mimic the reality gap. Our experimental results show that both DR and MAML outperform a state-of-the-art RL algorithm, therefore highlighting their potential to mitigate the reality gap in RLbased TSC systems.Comment: Paper was accepted by the ITSC 2023 (26th IEEE International Conference on Intelligent Transportation Systems

On Simulating the Propagation and Countermeasures of Hate Speech in Social Networks

Hate speech expresses prejudice and discrimination based on actual or perceived innate characteristics such as gender, race, religion, ethnicity, colour, national origin, disability or sexual orientation. Research has proven that the amount of hateful messages increases inevitably on online social media. Although hate propagators constitute a tiny minority with less than 1% participants they create an unproportionally high amount of hate motivated content. Thus, if not countered properly, hate speech can propagate through the whole society. In this paper we apply agent-based modelling to reproduce how the hate speech phenomenon spreads within social networks. We reuse insights from the research literature to construct and validate a baseline model for the propagation of hate speech. From this, three countermeasures are modelled and simulated to investigate their effectiveness in containing the spread of hatred: Education, deferring hateful content, and cyber activism. Our simulations suggest that: (1) Education consititutes a very successful countermeasure, but it is long term and still cannot eliminate hatred completely; (2) Deferring hateful content has a similar although lower positive effect than education, and it has the advantage of being a short-term countermeasure; (3) In our simulations, extreme cyber activism against hatred shows the poorest performance as a countermeasure, since it seems to increase the likelihood of resulting in highly polarised societies

Bottom-up control of whitefish populations in ultra-oligotrophic Lake Brienz

Abstract.: Lake Brienz, an oligotrophic pre-alpine Swiss lake, went through a mesotrophic period between around 1960 and 1990. The lake is moderately turbid caused by fine suspended solids from glaciers. In 1999, yield of the economically important whitefish collapsed to about 10% of preceding years. Age and growth analysis of the two whitefish types examined - small and large type - revealed an almost complete halt of growth from 1999 until June 2000, paralleled by poor condition. Zooplankton data showed that cladocerans, the preferred food of whitefish, were rare from January 1999 until June 2000. In order to elucidate the trophic relationships between zooplankton and fish, the > was applied. The analysis showed that poor growth and condition of whitefish in 1999 and 2000 were caused by the scarcity of primary food organisms. The relatively small and slender fish could not be caught by legal gillnets, which resulted in poor fishing yield. Evidence is presented that cladoceran biomass governs food consumption by the fish (>), while the effect of fish predation on cladocerans was found to be negligible, most likely also during the period of poor growth. Turbidity did not appear to significantly interfere with the feeding of whitefish. Growth, condition and commercial yield of whitefish partly increased again after 2000, but due to the very low productivity of Lake Brienz, fishing yield will remain low. Food chains in such oligotrophic systems are fragile. It is likely that a future collapse of the cladoceran population and, thus, the whitefish fishery will happen agai

Reinforcement learning control of a biomechanical model of the upper extremity

Among the infinite number of possible movements that can be produced, humans are commonly assumed to choose those that optimize criteria such as minimizing movement time, subject to certain movement constraints like signal-dependent and constant motor noise. While so far these assumptions have only been evaluated for simplified point-mass or planar models, we address the question of whether they can predict reaching movements in a full skeletal model of the human upper extremity. We learn a control policy using a motor babbling approach as implemented in reinforcement learning, using aimed movements of the tip of the right index finger towards randomly placed 3D targets of varying size. We use a state-of-the-art biomechanical model, which includes seven actuated degrees of freedom. To deal with the curse of dimensionality, we use a simplified second-order muscle model, acting at each degree of freedom instead of individual muscles. The results confirm that the assumptions of signal-dependent and constant motor noise, together with the objective of movement time minimization, are sufficient for a state-of-the-art skeletal model of the human upper extremity to reproduce complex phenomena of human movement, in particular Fitts' Law and the 2/3 Power Law. This result supports the notion that control of the complex human biomechanical system can plausibly be determined by a set of simple assumptions and can easily be learned.Comment: 19 pages, 7 figure

Content Rendering for Acoustic Levitation Displays via Optimal Path Following

Recently, volumetric displays based on acoustic levitation have demonstrated the capability to produce mid-air content using the Persistence of Vision (PoV) effect. In these displays, acoustic traps are used to rapidly move a small levitated particle along a prescribed path. This note is based on our recent work OptiTrap (Paneva et al., 2022), the first structured numerical approach for computing trap positions and timings via optimal control to produce feasible and (nearly) time-optimal trajectories that reveal generic levitated graphics. While previously, feasible trap trajectories needed to be tuned manually for each shape and levitator, relying on trial and error, OptiTrap automates this process by allowing for a systematic exploration of the range of contents that a given levitation display can render. This represents a crucial milestone for future content authoring tools for acoustic levitation displays and advances volumetric displays closer toward real-world applications

OptiTrap: Optimal Trap Trajectories for Acoustic Levitation Displays

Acoustic levitation has recently demonstrated the ability to create volumetric content by trapping and quickly moving particles along reference paths to reveal shapes in mid-air. However, the problem of specifying physically feasible trap trajectories to display desired shapes remains unsolved. Even if only the final shape is of interest to the content creator, the trap trajectories need to determine where and when the traps need to be, for the particle to reveal the intended shape. We propose OptiTrap, the first structured numerical approach to compute trap trajectories for acoustic levitation displays. Our approach generates trap trajectories that are physically feasible and nearly time-optimal, and reveal generic mid-air shapes, given only a reference path (i.e., a shape with no time information). We provide a multi-dimensional model of the acoustic forces around a trap to model the trap-particle system dynamics and compute optimal trap trajectories by formulating and solving a non-linear path following problem. We formulate our approach and evaluate it, demonstrating how OptiTrap consistently produces feasible and nearly optimal paths, with increases in size, frequency, and accuracy of the shapes rendered, allowing us to demonstrate larger and more complex shapes than ever shown to date