”In contemporary electronics 80% of a chip may perform digital functions but the 20% of analog functions may take 80% of the development time.” [1]. Aggravating this, the demands on analog design is increasing with rapid technology scaling. Most designs have moved away from analog to digital domains, where possible, however, interacting with the environment will always require analog to digital data conversion. Adding to this problem, the number of sensors used in consumer and industry related products are rapidly increasing. Designers of ADCs are dealing with this problem in several ways, the most important is the migration towards digital designs and time domain techniques. Time to Digital Converters (TDC) are becoming increasingly popular for robust signal processing. Biological neurons make use of spikes, which carry spike timing information and will not be affected by the problems related to technology scaling. Neuromorphic ADCs still remain exotic with few implementations in sub-micron technologies Table 2.7. Even among these few designs, the strengths of biological neurons are rarely exploited. From a previous work [2], LUCOS, a high dynamic range image sensor, the efficiency of spike processing has been validated. The ideas from this work can be generalized to make a highly effective sensor signal conditioning system, which carries the promise to be robust to technology scaling. The goal of this work is to create a novel spiking neural ADC as a novel form of a Multi-Sensor Signal Conditioning and Conversion system, which • Will be able to interface with or be a part of a System on Chip with traditional analog or advanced digital components. • Will have a graceful degradation. • Will be robust to noise and jitter related problems. • Will be able to learn and adapt to static errors and dynamic errors. • Will be capable of self-repair, self-monitoring and self-calibration Sensory systems in humans and other animals analyze the environment using several techniques. These techniques have been evolved and perfected to help the animal sur- vive. Different animals specialize in different sense organs, however, the peripheral neural network architectures remain similar among various animal species with few ex- ceptions. While there are many biological sensing techniques present, most popularly used engineering techniques are based on intensity detection, frequency detection, and edge detection. These techniques are used with traditional analog processing (e.g., colorvi sensors using filters), and with biological techniques (e.g. LUCOS chip [2]). The local- ization capability of animals has never been fully utilized. One of the most important capabilities for animals, vertebrates or invertebrates, is the capability for localization. The object of localization can be predator, prey, sources of water, or food. Since these are basic necessities for survival, they evolve much faster due to the survival of the fittest. In fact, localization capabilities, even if the sensors are different, have convergently evolved to have same processing methods (coincidence detection) in their peripheral neurons (for e.g., forked tongue of a snake, antennae of a cockroach, acoustic localization in fishes and mammals). This convergent evolution increases the validity of the technique. In this work, localization concepts based on acoustic localization and tropotaxis are investigated and employed for creation of novel ADCs. Unlike intensity and frequency detection, which are not linear (for e.g. eyes saturate in bright light, loose color perception in low light), localization is inherently linear. This is mainly because the accurate localization of predator or prey can be the difference between life and death for an animal. Figure 1 visually explains the ADC concept proposed in this work. This has two parts. (1) Sensor to Spike(time) Conversion (SSC), (2) Spike(time) to Digital Conversion(SDC). Both of the structures have been designed with models of biological neurons. The combination of these two structures is called SSDC. To efficiently implement the proposed concept, a comparison of several biological neural models is made and two models are shortlisted. Various synapse structures are also studied. From this study, Leaky Integrate and Fire neuron (LIF) is chosen since it fulfills all the requirements of the proposed structure. The analog neuron and synapse designs from Indiveri et. al. [3], [4] were taken, and simulations were conducted using cadence and the behavioral equivalence with biological counterpart was checked. The LIF neuron had features, that were not required for the proposed approach. A simple LIF neuron stripped of these features and was designed to be as fast as allowed by the technology. The SDC was designed with the neural building blocks and the delays were designed using buffer chains. This SDC converts incoming Time Interval Code (TIC) to sparse place coding using coincidence detection. Coincidence detection is a property of spiking neurons, which is a time domain equivalent of a Gaussian Kernel. The SDC is designed to have an online reconfigurable Gaussian kernel width, weight, threshold, and refractory period. The advantage of sparse place codes, which contain rank order coding wasvii Figure 1: ADC as a localization problem (right), Jeffress model of sound localization visualized (left). The values t 1 and t 2 indicate the time taken from the source to s1 and s2 respectively. described in our work [5]. A time based winner take all circuit with memory was created based on a previous work [6] for reading out of sparse place codes asynchronously. The SSC was also initially designed with the same building blocks. Additionally, a differential synapse was designed for better SSC. The sensor element considered wasviii a Wheatstone full bridge AMR sensor AFF755 from Sensitec GmbH. A reconfigurable version of the synapse was also designed for a more generic sensor interface. The first prototype chip SSDCα was designed with 257 modules of coincidence detectors realizing the SDC and the SSC. Since the spike times are the most important information, the spikes can be treated as digital pulses. This provides the capability for digital communication between analog modules. This creates a lot of freedom for use of digital processing between the discussed analog modules. This advantage is fully exploited in the design of SSDCα. Three SSC modules are multiplexed to the SDC. These SSC modules also provide outputs from the chip simultaneously. A rising edge detecting fixed pulse width generation circuit is used to create pulses that are best suited for efficient performance of the SDC. The delay lines are made reconfigurable to increase robustness and modify the span of the SDC. The readout technique used in the first prototype is a relatively slow but safe shift register. It is used to analyze the characteristics of the core work. This will be replaced by faster alternatives discussed in the work. The area of the chip is 8.5 mm 2 . It has a sampling rate from DC to 150 kHz. It has a resolution from 8-bit to 13-bit. It has 28,200 transistors on the chip. It has been designed in 350 nm CMOS technology from ams. The chip has been manufactured and tested with a sampling rate of 10 kHz and a theoretical resolution of 8 bits. However, due to the limitations of our Time-Interval-Generator, we are able to confirm for only 4 bits of resolution. The key novel contributions of this work are • Neuromorphic implementation of AD conversion as a localization problem based on sound localization and tropotaxis concepts found in nature. • Coincidence detection with sparse place coding to enhance resolution. • Graceful degradation without redundant elements, inherent robustness to noise, which helps in scaling of technologies • Amenable to local adaptation and self-x features. Conceptual goals have all been fulfilled, with the exception of adaptation. The feasibility for local adaptation has been shown with promising results and further investigation is required for future work. This thesis work acts as a baseline, paving the way for R&D in a new direction. The chip design has used 350 nm ams hitkit as a vehicle to prove the functionality of the core concept. The concept can be easily ported to present aggressively-scaled-technologies and future technologies.

Die Akustik liefert einen interessanten Hintergrund, interdisziplinären und fächerverbindenen Unterricht zwischen Mathematik, Physik und Musik durchzuführen. SchülerInnen können hierbei beispielsweise experimentell tätig sein, indem sie Audioaufnahmen selbst erzeugen und sich mit Computersoftware Frequenzspektren erzeugen lassen. Genauso können die Schüler auch Frequenzspektren vorgeben und daraus Klänge erzeugen. Dies kann beispielsweise dazu dienen, den Begriff der Obertöne im Musikunterricht physikalisch oder mathematisch greifbar zu machen oder in der Harmonielehre Frequenzverhältnisse von Intervallen und Dreiklängen näher zu untersuchen. Der Computer ist hier ein sehr nützliches Hilfsmittel, da der mathematische Hintergrund dieser Aufgabe -- das Wechseln zwischen Audioaufnahme und ihrem Frequenzbild -- sich in der Fourier-Analysis findet, die für SchülerInnen äußerst anspruchsvoll ist. Indem man jedoch die Fouriertransformation als numerisches Hilfsmittel einführt, das nicht im Detail verstanden werden muss, lässt sich an anderer Stelle interessante Mathematik betreiben und die Zusammenhänge zwischen Akustik und Musik können spielerisch erfahren werden. Im folgenden Beitrag wird eine Herangehensweise geschildert, wie wir sie bereits bei der Felix-Klein-Modellierungswoche umgesetzt haben: Die SchülerInnen haben den Auftrag erhalten, einen Synthesizer zu entwickeln, mit dem verschiedene Musikinstrumente nachgeahmt werden können. Als Hilfsmittel haben sie eine kurze Einführung in die Eigenschaften der Fouriertransformation erhalten, sowie Audioaufnahmen verschiedener Instrumente.

Der Beitrag beschäftigt sich mit der Frage, ob Schildkröten alleine anhand der Musterung bzw. Struktur ihres Bauch- Rückenpanzers eindeutig identifiziert werden können. Dabei sollen sinnvolle Identifizierungsmerkmale entwickelt werden, die auf der Basis von Fotos ausgewertet werden. Das Besondere an diesem Problem ist, dass es mit Lernenden ganz unterschiedlicher Altersstufen bearbeitet werden kann und dass es eine unheimliche Vielfalt an mathematischen Methoden gibt, die auf dem Weg zu einer Lösung hilfreich sind: Dies reicht von einfachen geometrischen Überlegungen über Analysis (Integration, Kurvendiskussion) bis hin zu mathematischer Bildverarbeitung und Fragen der Robustheit. Genauso breit wie das Spektrum der einsetzbaren mathematischen Werkzeuge ist die Altergruppe, mit der ein derartiges Projekt durchführbar ist: Vom Grundschulalter bis hin zur Masterarbeit ist eine Bearbeitung möglich, und die benötigte Zeitspanne reicht von wenigen Stunden bis hin zu mehreren Monaten. Im Beitrag wird die angesprochene Vielfalt exemplarisch gezeigt, so dass die Leser im Idealfall das Projekt genau an die Bedürfnisse ihrer Lerngruppe anpassen können.

Die Planung von Bushaltestellen in Innenstädten ist ein authentisches Thema, welches sich für den Einsatz in einem realitätsbezogenen Unterricht in unterschiedlichen Klassenstufen eignet. Verschiedene Interessen und Gegebenheiten müssen in einem Modell und in einer Lösungsstrategie vereint werden. Durch eine sehr offen gewählte Fragestellung sind verschiedene Ansätze und Modelle möglich. Somit wird mathematisches Modellieren trainiert und das Durchlaufen eines Modellierungsprozesses in einem interessanten Projekt ermöglicht. Die mathematischen Hintergründe sowie das vielseitige Lösungsspektrum von Schülerinnen und Schülern unterschiedlicher Jahrgangsstufen zu derselben Fragestellung werden im Folgenden vorgestellt.

Typically software engineers implement their software according to the design of the software structure. Relations between classes and interfaces such as method-call relations and inheritance relations are essential parts of a software structure. Accordingly, analyzing several types of relations will benefit the static analysis process of the software structure. The tasks of this analysis include but not limited to: understanding of (legacy) software, checking guidelines, improving product lines, finding structure, or re-engineering of existing software. Graphs with multi-type edges are possible representation for these relations considering them as edges, while nodes represent classes and interfaces of software. Then, this multiple type edges graph can be mapped to visualizations. However, the visualizations should deal with the multiplicity of relations types and scalability, and they should enable the software engineers to recognize visual patterns at the same time. To advance the usage of visualizations for analyzing the static structure of software systems, I tracked difierent development phases of the interactive multi-matrix visualization (IMMV) showing an extended user study at the end. Visual structures were determined and classified systematically using IMMV compared to PNLV in the extended user study as four categories: High degree, Within-package edges, Cross-package edges, No edges. In addition to these structures that were found in these handy tools, other structures that look interesting for software engineers such as cycles and hierarchical structures need additional visualizations to display them and to investigate them. Therefore, an extended approach for graph layout was presented that improves the quality of the decomposition and the drawing of directed graphs according to their topology based on rigorous definitions. The extension involves describing and analyzing the algorithms for decomposition and drawing in detail giving polynomial time complexity and space complexity. Finally, I handled visualizing graphs with multi-type edges using small-multiples, where each tile is dedicated to one edge-type utilizing the topological graph layout to highlight non-trivial cycles, trees, and DAGs for showing and analyzing the static structure of software. Finally, I applied this approach to four software systems to show its usefulness.