In this dissertation, we developed a mathematical framework for cohomological field theories (CohFTs) in the language of ``QK-manifolds', which unifies the previous ones in (Baulieu and Singer 1988; Baulieu and Singer 1989; Ouvry, Stora, and Van Baal 1989; Atiyah and Jeffrey 1990; Birmingham et al. 1991; Kalkman 1993; Blau 1993). Within this new framework, we classified the (gauge invariant) solutions to the descent equations in CohFTs (with gauge symmetries). We revisited Witten’s idea of topological twisting and showed that the twisted super-Poincaré algebra gives rise naturally to a ``QK-structure'. We also generalized the Mathai-Quillen construction of the universal Thom class via a variational bicomplex lift of the equivariant cohomology. Our framework enables a uniform treatment of examples like topological quantum mechanics, topological sigma model, and topological Yang-Mills theory.

Learning with neural networks depends on the particular parametrization of the functions represented by the network, that is, the assignment of parameters to functions. It also depends on the identity of the functions, which get assigned typical parameters at initialization, and, later, the parameters that arise during training. The choice of the activation function is a critical aspect of the network design that influences these function properties and requires investigation. This thesis focuses on analyzing the expected behavior of networks with maxout (multi-argument) activation functions. On top of enhancing the practical applicability of maxout networks, these findings add to the theoretical exploration of activation functions beyond the common choices. We believe this work can advance the study of activation functions and complicated neural network architectures. We begin by taking the number of activation regions as a complexity measure and showing that the practical complexity of deep networks with maxout activation functions is often far from the theoretical maximum. This analysis extends the previous results that were valid for deep neural networks with single-argument activation functions such as ReLU. Additionally, we demonstrate that a similar phenomenon occurs when considering the decision boundaries in classification tasks. We also show that the parameter space has a multitude of full-dimensional regions with widely different complexity and obtain nontrivial lower bounds on the expected complexity. Finally, we investigate different parameter initialization procedures and show that they can increase the speed of the gradient descent convergence in training. Further, continuing the investigation of the expected behavior, we study the gradients of a maxout network with respect to inputs and parameters and obtain bounds for the moments depending on the architecture and the parameter distribution. We observe that the distribution of the input-output Jacobian depends on the input, which complicates a stable parameter initialization. Based on the moments of the gradients, we formulate parameter initialization strategies that avoid vanishing and exploding gradients in wide networks. Experiments with deep fully-connected and convolutional networks show that this strategy improves SGD and Adam training of deep maxout networks. In addition, we obtain refined bounds on the expected number of linear regions, results on the expected curve length distortion, and results on the NTK. As the result of the research in this thesis, we develop multiple experiments and helpful components and make the code for them publicly available.

RNAs are biomolecules ubiquitous in all living cells. Usually, they fold into complex molecular structures, which often mediate their biological function. In this work, models of RNA folding have been studied in detail. One can distinguish two fundamentally different approaches to RNA folding. The first one is the thermodynamic approach, which yields information about the distribution of structures in the ensemble in its equilibrium. The second approach, which is required to study the dynamics of folding during the course of time, is the kinetic folding analysis. It is much more computationally expensive, but allows to incorporate changing environmental parameters as well as time-dependent effects into the analysis. Building on these methods, the BarMap framework (Hofacker, Flamm, et al., 2010) allows to chain several pre-computed models and thus simulate folding reactions in a dynamically changing environment, e. g., to model co- transcriptional folding. However, there is no obvious way to identify spurious output, let alone assessing the quality of the simulation results. As a remedy, BarMap-QA, a semi-automatic software pipeline for the analysis of cotranscriptional folding, has been developed. For a given input sequence, it automatically generates the models for every step of the RNA elongation, applies BarMap to link them together, and runs the simulation. Post-processing scripts, visualizations, and an integrated viewer are provided to facilitate the evaluation of the unwieldy BarMap output. Three novel, complementary quality measures are computed on-the-fly, allowing the analyst to evaluate the coverage of the computed models, the exactness of the computed mapping between the individual states of each model, and the fraction of correctly mapped population during the simulation run. In case of deficiencies, the output is automatically re-rendered after parameter adjustment. Statistical evidence is presented that, even when coarse graining the ensemble, kinetic simulations quickly become infeasible for longer RNAs. However, within the individual gradient basins, most high-energy structures only have a marginal probability and could safely be excluded from the analysis. To tell relevant and irrelevant structures apart, a precise knowledge of the distribution of probability mass within a basin is necessary. Both a theoretical result concerning the shape of its density, and possible applications like the prediction of a basin’s partition function are given. To demonstrate the applicability of computational folding simulations to a real-world task of the life sciences, we conducted an in silico design process for a synthetic, transcriptional riboswitch responding to the ligand neomycin. The designed constructs were then transfected into the bacterium Escherichia coli by a collaborative partner and could successfully regulate a fluorescent reporter gene depending on the presence of its ligand. Additionally, it was shown that the sequence context of the riboswitch could have detrimental effects on its functionality, but also that RNA folding simulations are often capable to predict these interactions and provide solutions in the form of decoupling spacer elements. Taken together, this thesis offers the reader deep insights into the world of RNA folding and its models, and how these can be applied to design novel biomolecules.

In this thesis we study three stochastic partial differential equations (SPDE) that arise as stochastic gradient flows via the fluctuation-dissipation principle. For the first equation we establish a finer regularity statement based on a generalized Taylor expansion which is inspired by the theory of rough paths. The second equation is the thin-film equation with thermal noise which is a singular SPDE. In order to circumvent the issue of dealing with possible renormalization, we discretize the gradient flow structure of the deterministic thin-film equation. Choosing a specific discretization of the metric tensor, we resdiscover a well-known discretization of the thin-film equation introduced by Grün and Rumpf that satisfies a discrete entropy estimate. By proving a stochastic entropy estimate in this discrete setting, we obtain positivity of the scheme in the case of no-slip boundary conditions. Moreover, we analyze the associated rate functional and perform numerical experiments which suggest that the scheme converges. The third equation is the massive $\varphi^4_2$-model on the torus which is also a singular SPDE. In the spirit of Bakry and Émery, we obtain a gradient bound on the Markov semigroup. The proof relies on an $L^2$-estimate for the linearization of the equation. Due to the required renormalization, we use a stopping time argument in order to ensure stochastic integrability of the random constant in the estimate. A postprocessing of this estimate yields an even sharper gradient bound. As a corollary, for large enough mass, we establish a local spectral gap inequality which by ergodicity yields a spectral gap inequality for the $\varphi^4_2$- measure.

Salamander limb regeneration is an accurate process which gives rise exclusively to the missing structures, irrespective of the amputation level. This suggests that cells in the stump have an awareness of their spatial location, a property termed positional identity. Little is known about how positional identity is encoded, in salamanders or other biological systems. Through single-cell RNAseq analysis, we identified Tig1/Rarres1 as a potential determinant of proximal identity. Tig1 encodes a conserved cell surface molecule, is regulated by retinoic acid and exhibits a graded expression along the proximo-distal axis of the limb. Its overexpression leads to regeneration defects in the distal elements and elicits proximal displacement of blastema cells, while its neutralisation blocks proximo-distal cell surface interactions. Critically, Tig1 reprogrammes distal cells to a proximal identity, upregulating Prod1 and inhibiting Hoxa13 and distal transcriptional networks. Thus, Tig1 is a central cell surface determinant of proximal identity in the salamander limb.

Site-specific tyrosine-type recombinases are effective tools for genome engineering, with the first engineered variants having demonstrated therapeutic potential. So far, adaptation to new DNA target site selectivity of designerrecombinases has been achieved mostly through iterative cycles of directed molecular evolution. While effective, directed molecular evolution methods are laborious and time consuming. Here we present RecGen (Recombinase Generator), an algorithm for the intelligent generation of designerrecombinases. We gather the sequence information of over one million Crelike recombinase sequences evolved for 89 different target sites with whichwe train Conditional Variational Autoencoders for recombinase generation. Experimental validation demonstrates that the algorithm can predict recombinase sequences with activity on novel target-sites, indicating that RecGen is useful to accelerate the development of future designer-recombinases.

Öffentliche und politische Kommunikation sind heute ohne Soziale Medien nicht mehr vorstellbar. Tatsächlich trägt die effektive Nutzung der Sozialen Medien in einem erheblichen Maß zum Erfolg von Unternehmen, von Organisationen und von politischen Akteuren bei. Die neuen Webtechnologien haben es einerseits für jeden leicht gemacht, eigene Inhalte zu erstellen und zu verbreiten. Andererseits ist damit auch der Einsatz von Algorithmen, Automatisierung und beabsichtigter inhaltlicher Manipulation zur gezielten Entwicklung und Verbreitung irreführender Informationen über entsprechende technische Plattformen ein fester Bestandteil der strategischen Kommunikation von politischen oder auch staatlichen Akteuren geworden, vgl. \cite{woolley_automation_2016}. Der Einsatz der Sozialen Medien für die eigene Kommunikation und für die eigenen Zwecke kann also als strategische Kommunikation bezeichnet werden. Diese Arbeit widmet sich den komplexen sozio-technischen Herausforderungen dieser strategischen Kommunikation. Im Mittelpunkt steht dabei die Analyse und Bewertung von Informationskampagnen als Werkzeug der strategischen Kommunikation. Zur Analyse und Bewertung von Informationskampagnen wird bewusst eine technische Perspektive eingenommen. Die Analyse, im Folgenden auch als Informationsanalyse bezeichnet, betrifft dabei sowohl die Inhalte der Kommunikation als auch den erweiterten Kontext der Verbreitung dieser Inhalte. Zunehmend finden computergestützte Ansätze Verwendung auch bei der Analyse und Bewertung kommunikationsspezifischer Phänomene. Der Einsatz computergestützter Ansätze setzt die formale Modellierung der relevanten Phänomene bzw. Muster voraus. Die Modellierung findet heute zumeist entlang der Wertschöpfungskette des Maschinellen Lernens statt. Entsprechende datengetriebene Methoden sind sowohl bei der Identifikation grundlegender Merkmale und Muster als auch bei der Modellierung komplexer kommunikationsspezifischer Phänomene von zentraler Bedeutung. Dieser Arbeit wird ein Modell zur Wissensgenerierung zugrunde gelegt, das von \cite{sacha_knowledge_2014} vorgeschlagen wurde. Dieses Modell ist in zwei Teile gegliedert. Es umfasst sowohl einen computer-gestützten Anteil, der sich aus Daten, Visualisierung und Analysemodellen zusammensetzt, als auch eine menschliche Komponente, die die kognitiven Prozesse im Zusammenhang mit der Datenanalyse beschreibt. Im Zentrum meiner Beobachtung steht die Frage, in welcher Weise die Modelle des maschinellen Lernens zur Beantwortung von konkreten, realen Fragestellungen beitragen können. Die Entwicklung von Modellen des maschinellen Lernens umfasst üblicherweise eine Abfolge von Schritten. Aus dieser Abfolge ist zunächst nicht ersichtlich, an welchen Ansatzpunkten Domänenwissen zur Entwicklung entsprechender Modelle nützlich oder gar erforderlich ist. Die übliche Abfolge lässt Domänenwissen zunächst überflüssig erscheinen. Sie suggeriert, dass auch ohne tiefgreifende Kenntnisse in einem Bereich exakte Modelle entwickelt werden können, indem Daten erfasst und weitgehend automatisch durch Verfahren des maschinellen Lernens verarbeitet werden. Tatsächlich lassen sich, auch ohne die ursprünglichen Merkmale in den Daten zu kennen, bereits zufriedenstellende Ergebnisse erzielen. Obwohl der Erfolg dieser Vorgehensweise Recht zu geben scheint, werden dabei bewusst oder unbewusst gravierende einschränkende Bedingungen in Kauf genommen. Eine dieser Bedingungen ist beispielsweise die Ineffizienz dieses Ansatzes. In der Praxis erfordert dieser Ansatz nämlich sehr große Mengen an annotierten Datensätzen und ein hohes Maß an Rechenleistung, um Modelle mit zufriedenstellenden Ergebnissen zu erzielen. Der Aufwand eines umfassenden Feature-Engineerings wird hier durch die Menge an Daten aufgelöst. Eine weitere, wenn auch ungleich bedeutsamere einschränkende Bedingung liegt im \glqq Black Box\grqq-Charakters dieses Ansatzes. Ohne die Kenntnis der Bedeutung einzelner Merkmale eines Datensatzes in Bezug auf eine konkrete Fragestellung, sollen anhand der resultierenden Modelle Entscheidungen mit realen Auswirkungen getroffen werden. Unweigerlich führt dies zu einem gewissen Maß an Unsicherheit in Bezug auf die Vertrauenswürdigkeit der vom System vorgeschlagenen Entscheidungen. Diese Arbeit geht den genannten, einschränkenden Bedingungen auf den Grund. Dazu wird die gesamte Wertschöpfungskette des maschinellen Lernens auf Mög\-lichkeiten der Einflussnahme zur Mitigation der Einschränkungen untersucht. An den verschiedenen Schnittstellen möglicher Einflussnahme wird die erforderliche Fachexpertise herausgearbeitet, welche schließlich zur Steigerung nicht nur der Leistungsfähigkeit, sondern auch der Vertrauenswürdigkeit der resultierenden Modelle führt. Der vorgeschlagene Ansatz vertritt damit die Annahme, dass Erkenntnisgewinnung nicht ausschließlich an den Endpunkten, sondern entlang der gesamten Wertschöpfungskette des maschinellen Lernens stattfinden sollte. Dementsprechend sind kognitive Prozesse zur Bewertung und Steuerung der Prozesskette eine zentrale Voraussetzung für den vertrauenswürdigen Einsatz der resultierenden Modelle.

Mechanics is known to play a fundamental role in many cellular and developmental processes. Beyond active forces and material properties, osmotic pressure is believed to control essential cell and tissue characteristics. However, it remains very challenging to perform in situ and in vivo measurements of osmotic pressure. Here we introduce double emulsion droplet sensors that enable local measurements of osmotic pressure intra- and extra-cellularly within 3D multicellular systems, including living tissues. After generating and calibrating the sensors, we measure the osmotic pressure in blastomeres of early zebrafish embryos as well as in the interstitial fluid between the cells of the blastula by monitoring the size of droplets previously inserted in the embryo. Our results show a balance between intracellular and interstitial osmotic pressures, with values of approximately 0.7 MPa, but a large pressure imbalance between the inside and outside of the embryo. The ability to measure osmotic pressure in 3D multicellular systems, including developing embryos and organoids, will help improve our understanding of its role in fundamental biological processes.

Fractionalization is a phenomenon in which strong interactions in a quantum system drive the emergence of excitations with quantum numbers that are absent in the building blocks. Outstanding examples are excitations with charge e/3 in the fractional quantum Hall effect1,2, solitons in one-dimensional conducting polymers3,4 and Majorana states in topological superconductors5. Fractionalization is also predicted to manifest itself in low-dimensional quantum magnets, such as one-dimensional antiferromagnetic S = 1 chains. The fundamental features of this system are gapped excitations in the bulk6 and, remarkably, S = 1/2 edge states at the chain termini7,8,9, leading to a four-fold degenerate ground state that reflects the underlying symmetry-protected topological order10,11. Here, we use on-surface synthesis12 to fabricate one-dimensional spin chains that contain the S = 1 polycyclic aromatic hydrocarbon triangulene as the building block. Using scanning tunnelling microscopy and spectroscopy at 4.5 K, we probe length-dependent magnetic excitations at the atomic scale in both open-ended and cyclic spin chains, and directly observe gapped spin excitations and fractional edge states therein. Exact diagonalization calculations provide conclusive evidence that the spin chains are described by the S = 1 bilinear-biquadratic Hamiltonian in the Haldane symmetry-protected topological phase. Our results open a bottom-up approach to study strongly correlated phases in purely organic materials, with the potential for the realization of measurement-based quantum computation13.

It seems natural that motor responses unfold smoothly and that we are able to easily concatenate different components of movements to achieve goal-directed actions. Theoretical frameworks suggest that different motor features have to be bound to each other to achieve a coherent action. Yet, the nature of the “glue” (i.e., bindings) between elements constituting a motor sequence and enabling a smooth unfolding of motor acts is not well understood. We examined in how far motor feature bindings are affected by reward magnitude or the effects of an unsigned surprise signal. We show that the consistency of action file binding strength is modulated by unsigned surprise, but not by reward magnitude. On a conceptual and theoretical level, the results provide links between frameworks, which have until now not been brought into connection. In particular, theoretical accounts stating that only the unexpectedness (surprisingness) is essential for action control are connected to meta-control accounts of human action control.