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Multi-drug resistant (MDR) infections have become a major concern in hospitals worldwide. This study investigates membrane translocation, which is the first step required for drug action on internal bacterial targets. beta-lactams, a major antibiotic class, use porins to pass through the outer membrane barrier of Gram-negative bacteria. Clinical reports have linked the MDR phenotype to altered membrane permeability including porin modification and efflux pump expression. Here influx of beta-lactams through the major Enterobacter aerogenes porin Omp36 is characterized. Conductance measurements through a single Omp36 trimer reconstituted into a planar lipid bilayer allowed us to count the passage of single beta-lactam molecules. Statistical analysis of each transport event yielded the kinetic parameters of antibiotic travel through Omp36 and distinguishable translocation properties of beta-lactams were quantified for ertapenem and cefepime. Expression of Omp36 in an otherwise porin-null bacterial strain is shown to confer increases in the killing rate of these antibiotics and in the corresponding bacterial susceptibility. We propose the idea of a molecular \"passport\" that allows rapid transport of substrates through porins. Deciphering antibiotic translocation provides new insights for the design of novel drugs that may be highly effective at passing through the porin constriction zone. Such data may hold the key for the next generation of antibiotics capable of rapid intracellular accumulation to circumvent the further development MDR infections.

Uncertainty is unavoidable in forming processes due to fluctuating properties in the semi-finished product, the tool system and the environment. For this reason, numerous scientists have addressed this issue by developing control approaches like self-optimizing machine tools or the control of product properties. Machine learning algorithms, in particular reinforcement learning (RL) methods, show promising results for controlling production processes in this way. In this paper, the application of RL is demonstrated on an industrially commonly used process, V-die bending. For this purpose, first a flexible tool system is developed that allows the bending angle to be adjusted continuously between 80 and 110°. The developed tool is initially simulated through an FEM model in order to create a sufficient database for the training of an RL agent for springback compensation. The pre-trained agent is then used to control the springback in the real process. To close the resulting sim-to-real gap, it is then retrained on the experimentally generated data. It is shown that the springback can be significantly reduced compared to the uncontrolled case in both the simulative and the experimental process.

A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation as they usually appear in frictionless markets. In this paper, we show how the models with and without transaction costs can be unified.The bid and ask prices of a risky asset are given by càdlàg processes which are locally bounded from below and may coincide at some points. In a first step, we show that if the bid–ask model satisfies “no unbounded profit with bounded risk” for simple strategies, then there exists a semimartingale lying between the bid and ask price processes.In a second step, under the additional assumption that the zeros of the bid–ask spread are either starting points of an excursion away from zero or inner points from the right, we show that for every bounded predictable strategy specifying the amount of risky assets, the semimartingale can be used to construct the corresponding self-financing risk-free position in a consistent way. Finally, the set of most general strategies is introduced, which also provides a new view on the frictionless case.

This introductory chapter aims to provide an overview of the arbitrage theory in models with proportional transaction costs relevant to this thesis and describes its main results.1.1 Financial market models with transaction costsIn frictionless financial market models, there are no costs associated with trading. All assets can be bought and sold at the same price. Of course, these models are an idealization of the real world as transaction costs are an important feature of financial markets. Typical types of transaction costs are fixed costs and proportional costs. Fixed costs pertain to a constant fee, e.g., a brokerage fee, being charged for each transaction regardless of its size. Thus, fixed costs penalize the frequency of trading. The transaction costs that arise due to a positive bid-ask spread, i.e., the difference between the ask price, which is the lowest price an asset is sold for, and the bid price, which is the highest price offered for an asset, are proportional to the size of each trade. We refer to such costs as proportional transaction costs. In contrast to fixed costs, proportional costs penalize the size of the trades. In general, bid-ask spreads are caused by numerous factors (see, e.g., Harris [39, Chapter 14] and Madhavan [70]). For example, Glosten and Milgrom [33] show that a positive bid-ask spread can arise due to adverse selection, i.e., as liquidity providers may lose money to informed traders, they widen the spread to recover their losses from uninformed traders.In this thesis, we only consider models with proportional transaction costs (for models with fixed costs see, e.g., [3, 9, 48]). In usual models of a stock market with proportional transaction costs and d risky assets (see, e.g., Jouini and Kallal [47]), there are two d-dimensional processes modeling the bid and ask price of each stock, and each transaction involves a bank account (or bond), i.e., a frictionless riskless asset with strictly positive price at any time. In particular, the actions of an investor are limited to buying and selling an asset in exchange for units of the bank account. After passing to relative prices, i.e., expressing all prices as multiples of the bank account, this means that each purchase of a self-financing strategy charges the bank accountwith the ask price, and each sale credits the bank account with the bid price.As identified by Kabanov [50], the existence of a bank account is unrealistic for a currency market which, in contrast to a stock market, allows for the direct exchange of the different assets. Thus, Kabanov [50] introduces a “currency model” with finitely many assets (see, also, Kabanov and Safarian [55, Section 3.1]). In this general framework, which includes the models described above, a bank account need not exist and there is no one-dimensional wealth process. Portfolios are expressed in terms of physical units of the assets. The transaction costs are implicitly modeled by an adapted cone-valued process whose value at time t models the cone of portfolios available at price zero at time t. More specifically, in the discrete-time setup of Kabanov’s model from Schachermayer [85], which we follow in the second chapter of this thesis, the cone of portfolios available at price zero at time t is induced by a random matrix whose entries specify the amount of physical units of an asset needed to purchase one unit of another asset at time t. In this case, a portfolio process is self-financing iff its increment at time t takes values within the cone of portfolios available at price zero at time t for each point in time t.In the case of only two assets, Kabanov’s model is equivalent to the usual model of a stock market, as described above, where all transfers are made via the bank account. In the third chapter of this thesis, we consider such a two-dimensional model in continuous time.

In discrete-time markets with proportional transaction costs, Schachermayer (Math. Financ. 14:19–48, 2004) showed that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov et al. (Finance Stoch. 6:371–382, 2002). The prospective strict no-arbitrage condition is slightly weaker than the robust no-arbitrage condition, and it implies that the set of portfolios attainable from zero initial endowment is closed in probability. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system. In contrast to the fundamental theorem of asset pricing of Schachermayer (Math. Financ. 14:19–48, 2004), the consistent frictionless prices may lie on the boundary of the bid–ask spread. On the technical level, a crucial difference to Schachermayer (Math. Financ. 14:19–48, 2004) and Kabanov et al. (Finance Stoch. 7:403–411, 2003) is that we prove closedness without having at hand that the null-strategies form a linear space.

Wear is one of the key factors that determine the efficiency of multi-stage processes that include blanking operations. Since wear in these processes not only causes unplanned downtime but also directly affects product quality, inline detection of wear and its effect on product quality is of major importance. However, current quality assurance (QA) methods are limited to manual offline inspection by operators at predefined intervals, so that 100% inspection of the product and description of the state of wear is not found in industrial practice. The aim of this work is therefore to develop an optical system that enables in-line acquisition of product images and the associated control of blanking-specific quality features up to stroke rates of 300 strokes per minute (spm). In order to make the system attractive to small- and medium-sized enterprises (SME), the system is designed to minimize integration and investment costs using commercially available components. By combining the system with a methodology for extracting blanking-specific features, so-called key performance parameters (KPPs), the condition of the blanked surface as a relevant quality parameter is derived directly from the workpiece image. To demonstrate the transferability of the methodology to industrial applications, two use cases are investigated. In the first case, the KPPs are used directly to determine the quality of the blanked workpiece and are compared with reference measurements. Here, the KPPs are quantified with a mean absolute error of 18 μm compared to a ground truth. In the second case, the KPPs are used to build a machine learning (ML) model to estimate the wear of the blanking tool. Here, an accuracy of 92% is achieved in classifying the actual wear state.

Closed-loop control of product properties is becoming increasingly important in forming technology research and enables users to counteract unavoidable uncertainties in semi-finished product properties and process environments. Therefore, closed-loop controlled forming processes are considered to have the potential to reduce tolerances on desired product properties, resulting in consistent qualities. The achievement of associated increases in robustness and reliability is linked to enormous requirements, which in particular include the inline recording of the product properties to be controlled and the subsequent adaptation of the process control through the targeted derivation of manipulated variables. The present paper uses the example of an air bending process to show how the bending angle can be controlled camera-based and how springback can be compensated within a stroke by recording force signals and subsequently predicting the loaded bending angle using machine learning algorithms. The results show that the combined application of camera-based control and machine learning assisted springback compensation leads to highly accurate bending angles, whereby the results strongly depend on the machine learning algorithms and associated data transformation processes used.

A standing assumption in the literature on proportional transaction costs is efficient friction. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation, as they usually appear in frictionless markets. In this paper, we show how the models with and without transaction costs can be unified. The bid and the ask price of a risky asset are given by cádlág processes which are locally bounded from below and may coincide at some points. In a first step, we show that if the bid-ask model satisfies \"no unbounded profit with bounded risk\" for simple strategies, then there exists a semimartingale lying between the bid and the ask price process. In a second step, under the additional assumption that the zeros of the bid-ask spread are either starting points of an excursion away from zero or inner points from the right, we show that for every bounded predictable strategy specifying the amount of risky assets, the semimartingale can be used to construct the corresponding self-financing risk-free position in a consistent way. Finally, the set of most general strategies is introduced, which also provides a new view on the frictionless case.

In discrete time markets with proportional transaction costs, Schachermayer (2004) shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system. In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov, Rásonyi, and Stricker (2002). The prospective strict no-arbitrage condition is slightly weaker than robust no-arbitrage, and it implies that the set of portfolios attainable from zero initial endowment is closed in probability. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system. In contrast to the fundamental theorem of asset pricing of Schachermayer (2004), the consistent frictionless prices may lie on the boundary of the bid-ask spread. On the technical level, a crucial difference to Schachermayer (2004) and Kabanov-Rásonyi-Stricker (2003) is that we prove closedness without having at hand that the null-strategies form a linear space.

Multi-drug resistant (MDR) infections have become a major concern in hospitals worldwide. This study investigates membrane translocation, which is the first step required for drug action on internal bacterial targets. [beta]-lactams, a major antibiotic class, use porins to pass through the outer membrane barrier of Gram-negative bacteria. Clinical reports have linked the MDR phenotype to altered membrane permeability including porin modification and efflux pump expression. Here influx of [beta]-lactams through the major Enterobacter aerogenes porin Omp36 is characterized. Conductance measurements through a single Omp36 trimer reconstituted into a planar lipid bilayer allowed us to count the passage of single [beta]-lactam molecules. Statistical analysis of each transport event yielded the kinetic parameters of antibiotic travel through Omp36 and distinguishable translocation properties of [beta]-lactams were quantified for ertapenem and cefepime. Expression of Omp36 in an otherwise porin-null bacterial strain is shown to confer increases in the killing rate of these antibiotics and in the corresponding bacterial susceptibility. We propose the idea of a molecular \"passport\" that allows rapid transport of substrates through porins. Deciphering antibiotic translocation provides new insights for the design of novel drugs that may be highly effective at passing through the porin constriction zone. Such data may hold the key for the next generation of antibiotics capable of rapid intracellular accumulation to circumvent the further development MDR infections.