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We study objects whose definition is linked to partial orders. An algebra over the operad of posets is a set whose endomorphisms contain the endomorphisms of posets. Notable examples of such algebras include the zeta values, order polytopes, and shuffle series. The language of operads provides us with tools to better understand the combinatorics of these objects. In these notes we describe a non-trivial example of a suboperad ``The Wixarika posets'', alongside its associated algebras. This example is rich enough to showcase the particularities of the field, without delving into technicalities. An old version of these notes were used to give a minicourse in Govt. College University Lahore in Pakistan 2022, and at the BIRS-CMO workshop ``6th meeting of the Mexican Mathematicians in the World'' 2024., Comment: 10 pages, used to give a minicourse in Govt. College University Lahore in Pakistan 2022, and at the BIRS-CMO workshop "6th meeting of the Mexican Mathematicians in the World'' 2024

Generative AI models are capable of performing a wide range of tasks that traditionally require creativity and human understanding. They learn patterns from existing data during training and can subsequently generate new content such as texts, images, and music that follow these patterns. Due to their versatility and generally high-quality results, they, on the one hand, represent an opportunity for digitalization. On the other hand, the use of generative AI models introduces novel IT security risks that need to be considered for a comprehensive analysis of the threat landscape in relation to IT security. In response to this risk potential, companies or authorities using them should conduct an individual risk analysis before integrating generative AI into their workflows. The same applies to developers and operators, as many risks in the context of generative AI have to be taken into account at the time of development or can only be influenced by the operating company. Based on this, existing security measures can be adjusted, and additional measures can be taken., Comment: 33 pages, 3 figures

Climate neutrality paradigms put electricity systems at the core of a clean energy supply. At the same time, indirect electrification, with a potential uptake of hydrogen or derived fuel economy, plays a crucial role in decarbonising the energy supply and industrial processes. Besides energy markets coordinating the transition, climate and energy policy targets require fundamental changes and expansions in the energy transmission, import, distribution, and storage infrastructures. While existing studies identify relevant demands for hydrogen, critical decisions involve imports versus domestic fuel production and investments in new or repurposing existing pipeline and storage infrastructure. Linking the pan-European energy system planning model SCOPE SD with the multiperiod European gas market model IMAGINE, the case study analysis and its transformation pathway results indicate extensive network development of hydrogen infrastructure, including expansion beyond refurbished methane infrastructure. However, the ranges of future hydrogen storage costs and market uptake restrictions expose and quantify the uncertainty of its role in Europes transformation. The study finds that rapidly planning the construction of hydrogen storage and pipeline infrastructure is crucial to achieving the required capacity by 2050.

These notes loosely follow an introductory course on graph complexes, held at Humboldt-Universit\"at zu Berlin in summer 23. Instead of simply typing up my lecture notes I decided to give here an overview over (parts of) the topic (lecture notes can be found on my homepage). We introduce the associative, commutative and Lie graph complexes, and moduli spaces of metric graphs, then discuss how the commutative and Lie graph complexes can be interpreted as cellular chain complexes associated to certain (pairs of) subspaces of the latter, both for ``even" and ``odd" orientations. We explain why this does not work for the associative complex and how to adjust the space of graphs to deal with this case. Along the way we highlight how algebraic properties on one side translate into geometric statements on the other., Comment: Comments are welcome! 37 pages, 10 figures

Small regulatory RNAs (sRNAs) are short non-coding RNAs in bacteria capable of post-transcriptional regulation. sRNAs have recently gained attention as tools in basic and applied sciences for example to fine-tune genetic circuits or biotechnological processes. Even though sRNAs often have a rather simple and modular structure, the design of functional synthetic sRNAs is not necessarily trivial. This protocol outlines how to use computational predictions and synthetic biology approaches to design, construct and validate synthetic sRNA functionality for their application in bacteria. The computational tool, SEEDling, matches the optimal seed region with the user-selected sRNA scaffold for repression of target mRNAs. The synthetic sRNAs are assembled using Golden Gate cloning and their functionality is subsequently validated. The protocol uses the acrA mRNA as an exemplary proof-of-concept target in Escherichia coli. Since AcrA is part of a multidrug efflux pump, acrA repression can be revealed by assessing oxacillin susceptibility in a phenotypic screen. However, in case target repression does not result in a screenable phenotype, an alternative validation of synthetic sRNA functionality based on a fluorescence reporter is described., Comment: 24 pages, 7 figures

Various mobility applications like advanced driver assistance systems increasingly utilize artificial intelligence (AI) based functionalities. Typically, deep neural networks (DNNs) are used as these provide the best performance on the challenging perception, prediction or planning tasks that occur in real driving environments. However, current regulations like UNECE R 155 or ISO 26262 do not consider AI-related aspects and are only applied to traditional algorithm-based systems. The non-existence of AI-specific standards or norms prevents the practical application and can harm the trust level of users. Hence, it is important to extend existing standardization for security and safety to consider AI-specific challenges and requirements. To take a step towards a suitable regulation we propose 50 technical requirements or best practices that extend existing regulations and address the concrete needs for DNN-based systems. We show the applicability, usefulness and meaningfulness of the proposed requirements by performing an exemplary audit of a DNN-based traffic sign recognition system using three of the proposed requirements., Comment: To appear in Proceedings of the 9th International Conference on Information Systems Security and Privacy

We prove a relative version of the Picard-Lefschetz theorem, describing the variation of relative homology groups $H_d(Y_t \setminus A_t,B_t\setminus A_t)$ in the fibers of a smooth fiber bundle $Y \to T$ of complex manifolds with $A\cup B \subset Y$ transverse. From this we derive the vanishing of certain iterated variations, a system of constraints dubbed "hierarchy". As applications, we rederive the known analytic structure of Aomoto polylogarithms and massive one loop Feynman integrals. Moreover, we introduce the "simple type" to prove hierarchy constraints in degenerate cases where the Picard-Lefschetz formula does not apply, e.g. the massless triangle or the ice cream cone Feynman diagram. We compare our findings with a "classical" hierarchy of iterated variations (from 1960's $S$-matrix theory) and show how our setup not only explains, but also refines the latter. In order to do so, we need to further resolve the geometry of Feynman motives: We boldly blow up what no one has blown up before., Comment: 85 pages, 27 figures

We derive a variant of the loop-tree duality for Feynman integrals in the Schwinger parametric representation. This is achieved by decomposing the integration domain into a disjoint union of cells, one for each spanning tree of the graph under consideration. Each of these cells is the total space of a fiber bundle with contractible fibers over a cube. Loop-tree duality emerges then as the result of first decomposing the integration domain, then integrating along the fibers of each fiber bundle. As a byproduct we obtain a new proof that the moduli space of graphs is homotopy equivalent to its spine. In addition, we outline a potential application to Kontsevich's graph (co-)homology., Comment: 25 pages. Final version

Predicitions made by neural networks can be fraudulently altered by so-called poisoning attacks. A special case are backdoor poisoning attacks. We study suitable detection methods and introduce a new method called Heatmap Clustering. There, we apply a $k$-means clustering algorithm on heatmaps produced by the state-of-the-art explainable AI method Layer-wise relevance propagation. The goal is to separate poisoned from un-poisoned data in the dataset. We compare this method with a similar method, called Activation Clustering, which also uses $k$-means clustering but applies it on the activation of certain hidden layers of the neural network as input. We test the performance of both approaches for standard backdoor poisoning attacks, label-consistent poisoning attacks and label-consistent poisoning attacks with reduced amplitude stickers. We show that Heatmap Clustering consistently performs better than Activation Clustering. However, when considering label-consistent poisoning attacks, the latter method also yields good detection performance.

We provide a method to construct new associators out of Drinfel'd's KZ associator. We obtain two analytic families of associators whose coefficients we can describe explicitly by a generalization of multiple zeta values. The two families contain two different paths that deform the Drinfel'd KZ associator into the trivial associator 1. We show that both paths are injective, that is, all of the associators parametrized by them are different. Our construction is based on the observation that one can recover multiple polylogarithms as generating functions of order polynomials of certain formally constructed posets., Comment: Theorem 4.3 is missing the terms corresponding to the linear pentagon equation

In the last years, AI systems, in particular neural networks, have seen a tremendous increase in performance, and they are now used in a broad range of applications. Unlike classical symbolic AI systems, neural networks are trained using large data sets and their inner structure containing possibly billions of parameters does not lend itself to human interpretation. As a consequence, it is so far not feasible to provide broad guarantees for the correct behaviour of neural networks during operation if they process input data that significantly differ from those seen during training. However, many applications of AI systems are security- or safety-critical, and hence require obtaining statements on the robustness of the systems when facing unexpected events, whether they occur naturally or are induced by an attacker in a targeted way. As a step towards developing robust AI systems for such applications, this paper presents how the robustness of AI systems can be practically examined and which methods and metrics can be used to do so. The robustness testing methodology is described and analysed for the example use case of traffic sign recognition in autonomous driving., Comment: 12 pages, 7 figures. The final publication is available at Springer via https://doi.org/10.1007/978-3-030-79150-6_21