On the complex constant rank condition and inequalities for differential operators

In this note, we study the complex constant rank condition for differential operators and its implications for coercive differential inequalities. These are inequalities of the form $$\Vert A u \Vert_{L^p} \leq \Vert \mathscr{A} u \Vert_{L^q},$$ for exponents $1\leq p,q <\infty$ and homogeneous constant-coefficient differential operators $A$ and $\mathscr{A}$. The functions $u \colon \Omega \to \mathbb{R}^d$ are defined on open and bounded sets $\Omega \subset \mathbb{R}^N$ satisfying certain regularity assumptions. Depending on the order of $A$ and $\mathscr{A}$, such an inequality might be viewed as a generalisation of either Korn's or Sobolev's inequality, respectively. In both cases, as we are on bounded domains, we assume that the Fourier symbol of $\mathscr{A}$ satisfies an algebraic condition, the complex constant rank property.Comment: 15 page

Driver-aware charging infrastructure design

Public charging infrastructure plays a crucial role in the context of electrifying the private mobility sector in particular for urban regions. Against this background, we develop a new mathematical model for the optimal placement of public charging stations for electric vehicles in cities. While existing approaches strongly aggregate traffic information or are only applicable to small instances, we formulate the problem as a specific combinatorial optimization problem that incorporates individual demand and temporal interactions of drivers, exact positioning of charging stations, as well as various charging speeds, and realistic charging curves. We show that the problem can be naturally cast as an integer program that, together with different reformulation techniques, can be efficiently solved for large instances. More specifically, we show that our approach can compute optimal placements of charging stations for instances based on traffic data for cities with up to $600\,000$ inhabitants and future electrification rates of up to $15\%$

Transport and magnetic properties of La_(1-x)Ca_xMnO_3-films (0.1<x<0.9)

By laser ablation we prepared thin films of the colossal magnetoresistive compound La_(1-x)Ca_xMnO_3 with doping levels 0.1<x<0.9 on MgO substrates. X-ray diffraction revealed epitaxial growth and a systematic decrease of the lattice constants with doping. The variation of the transport and magnetic properties in this doping series was investigated by SQUID magnetization and electrical transport measurements. For the nonmetallic samples resistances up to 10^13 Ohm have been measured with an electrometer setup. While the transport data indicate polaronic transport for the metallic samples above the Curie temperature the low doped ferromagnetic insulating samples show a variable range hopping like transport at low temperature.Comment: 2 pages, 3 EPS figures, LT22 Proceedings to appear in Physica

Contrastive Representation Learning for Whole Brain Cytoarchitectonic Mapping in Histological Human Brain Sections

Cytoarchitectonic maps provide microstructural reference parcellations of the brain, describing its organization in terms of the spatial arrangement of neuronal cell bodies as measured from histological tissue sections. Recent work provided the first automatic segmentations of cytoarchitectonic areas in the visual system using Convolutional Neural Networks. We aim to extend this approach to become applicable to a wider range of brain areas, envisioning a solution for mapping the complete human brain. Inspired by recent success in image classification, we propose a contrastive learning objective for encoding microscopic image patches into robust microstructural features, which are efficient for cytoarchitectonic area classification. We show that a model pre-trained using this learning task outperforms a model trained from scratch, as well as a model pre-trained on a recently proposed auxiliary task. We perform cluster analysis in the feature space to show that the learned representations form anatomically meaningful groups.Comment: Accepted to ISBI 202

BUSSARD -- Better Understanding Social Situations for Autonomous Robot Decision-Making

We report on our effort to create a corpus dataset of different social context situations in an office setting for further disciplinary and interdisciplinary research in computer vision, psychology, and human-robot-interaction. For social robots to be able to behave appropriately, they need to be aware of the social context they act in. Consider, for example, a robot with the task to deliver a personal message to a person. If the person is arguing with an office mate at the time of message delivery, it might be more appropriate to delay playing the message as to respect the recipient's privacy and not to interfere with the current situation. This can only be done if the situation is classified correctly and in a second step if an appropriate behavior is chosen that fits the social situation. Our work aims to enable robots accomplishing the task of classifying social situations by creating a dataset composed of semantically annotated video scenes of office situations from television soap operas. The dataset can then serve as a basis for conducting research in both computer vision and human-robot interaction.Comment: In SCRITA 2023 Workshop Proceedings (arXiv:2311.05401) held in conjunction with 32nd IEEE International Conference on Robot & Human Interactive Communication, 28/08 - 31/08 2023, Busan (Korea

Decision-Theoretic Planning with Linguistic Terms in GOLOG

Abstract In this paper we propose an extension of the action language GOLOG that integrates linguistic terms in non-deterministic argument choices and the reward function for decision-theoretic planning. It is often cumbersome to specify the set of values to pick from in the non-deterministic-choice-of-argument statement. Also, specifying a reward function is not always easy, even for domain experts. Instead of providing a finite domain for values in the non-deterministic-choice-of-argument statement in GOLOG, we now allow for stating the argument domain by simply providing a formula over linguistic terms and fuzzy fluents. In GOLOG&apos;s forwardsearch DT planning algorithm, these formulas are evaluated in order to find the agent&apos;s optimal policy. We illustrate this in the Diner Domain where the agent needs to calculate the optimal serving order