The Quantum Monadology

The modern theory of functional programming languages uses monads for encoding computational side-effects and side-contexts, beyond bare-bone program logic. Even though quantum computing is intrinsically side-effectful (as in quantum measurement) and context-dependent (as on mixed ancillary states), little of this monadic paradigm has previously been brought to bear on quantum programming languages. Here we systematically analyze the (co)monads on categories of parameterized module spectra which are induced by Grothendieck's "motivic yoga of operations" -- for the present purpose specialized to HC-modules and further to set-indexed complex vector spaces. Interpreting an indexed vector space as a collection of alternative possible quantum state spaces parameterized by quantum measurement results, as familiar from Proto-Quipper-semantics, we find that these (co)monads provide a comprehensive natural language for functional quantum programming with classical control and with "dynamic lifting" of quantum measurement results back into classical contexts. We close by indicating a domain-specific quantum programming language (QS) expressing these monadic quantum effects in transparent do-notation, embeddable into the recently constructed Linear Homotopy Type Theory (LHoTT) which interprets into parameterized module spectra. Once embedded into LHoTT, this should make for formally verifiable universal quantum programming with linear quantum types, classical control, dynamic lifting, and notably also with topological effects.Comment: 120 pages, various figure

The DS-Pnet modeling formalism for cyber-physical system development

This work presents the DS-Pnet modeling formalism (Dataflow, Signals and Petri nets), designed for the development of cyber-physical systems, combining the characteristics of Petri nets and dataflows to support the modeling of mixed systems containing both reactive parts and data processing operations. Inheriting the features of the parent IOPT Petri net class, including an external interface composed of input and output signals and events, the addition of dataflow operations brings enhanced modeling capabilities to specify mathematical data transformations and graphically express the dependencies between signals. Data-centric systems, that do not require reactive controllers, are designed using pure dataflow models. Component based model composition enables reusing existing components, create libraries of previously tested components and hierarchically decompose complex systems into smaller sub-systems. A precise execution semantics was defined, considering the relationship between dataflow and Petri net nodes, providing an abstraction to define the interface between reactive controllers and input and output signals, including analog sensors and actuators. The new formalism is supported by the IOPT-Flow Web based tool framework, offering tools to design and edit models, simulate model execution on the Web browser, plus model-checking and software/hardware automatic code generation tools to implement controllers running on embedded devices (C,VHDL and JavaScript). A new communication protocol was created to permit the automatic implementation of distributed cyber-physical systems composed of networks of remote components communicating over the Internet. The editor tool connects directly to remote embedded devices running DS-Pnet models and may import remote components into new models, contributing to simplify the creation of distributed cyber-physical applications, where the communication between distributed components is specified just by drawing arcs. Several application examples were designed to validate the proposed formalism and the associated framework, ranging from hardware solutions, industrial applications to distributed software applications

Compression of DNA sequencing data

With the release of the latest generations of sequencing machines, the cost of sequencing a whole human genome has dropped to less than US$1,000. The potential applications in several fields lead to the forecast that the amount of DNA sequencing data will soon surpass the volume of other types of data, such as video data. In this dissertation, we present novel data compression technologies with the aim of enhancing storage, transmission, and processing of DNA sequencing data. The first contribution in this dissertation is a method for the compression of aligned reads, i.e., read-out sequence fragments that have been aligned to a reference sequence. The method improves compression by implicitly assembling local parts of the underlying sequences. Compared to the state of the art, our method achieves the best trade-off between memory usage and compressed size. Our second contribution is a method for the quantization and compression of quality scores, i.e., values that quantify the error probability of each read-out base. Specifically, we propose two Bayesian models that are used to precisely control the quantization. With our method it is possible to compress the data down to 0.15 bit per quality score. Notably, we can recommend a particular parametrization for one of our models which—by removing noise from the data as a side effect—does not lead to any degradation in the distortion metric. This parametrization achieves an average rate of 0.45 bit per quality score. The third contribution is the first implementation of an entropy codec compliant to MPEG-G. We show that, compared to the state of the art, our method achieves the best compression ranks on average, and that adding our method to CRAM would be beneficial both in terms of achievable compression and speed. Finally, we provide an overview of the standardization landscape, and in particular of MPEG-G, in which our contributions have been integrated.Mit der Einführung der neuesten Generationen von Sequenziermaschinen sind die Kosten für die Sequenzierung eines menschlichen Genoms auf weniger als 1.000 US-Dollar gesunken. Es wird prognostiziert, dass die Menge der Sequenzierungsdaten bald diejenige anderer Datentypen, wie z.B. Videodaten, übersteigen wird. Daher werden in dieser Arbeit neue Datenkompressionsverfahren zur Verbesserung der Speicherung, Übertragung und Verarbeitung von Sequenzierungsdaten vorgestellt. Der erste Beitrag in dieser Arbeit ist eine Methode zur Komprimierung von alignierten Reads, d.h. ausgelesenen Sequenzfragmenten, die an eine Referenzsequenz angeglichen wurden. Die Methode verbessert die Komprimierung, indem sie die Reads nutzt, um implizit lokale Teile der zugrunde liegenden Sequenzen zu schätzen. Im Vergleich zum Stand der Technik erzielt die Methode das beste Ergebnis in einer gemeinsamen Betrachtung von Speichernutzung und erzielter Komprimierung. Der zweite Beitrag ist eine Methode zur Quantisierung und Komprimierung von Qualitätswerten, welche die Fehlerwahrscheinlichkeit jeder ausgelesenen Base quantifizieren. Konkret werden zwei Bayes’sche Modelle vorgeschlagen, mit denen die Quantisierung präzise gesteuert werden kann. Mit der vorgeschlagenen Methode können die Daten auf bis zu 0,15 Bit pro Qualitätswert komprimiert werden. Besonders hervorzuheben ist, dass eine bestimmte Parametrisierung für eines der Modelle empfohlen werden kann, die – durch die Entfernung von Rauschen aus den Daten als Nebeneffekt – zu keiner Verschlechterung der Verzerrungsmetrik führt. Mit dieser Parametrisierung wird eine durchschnittliche Rate von 0,45 Bit pro Qualitätswert erreicht. Der dritte Beitrag ist die erste Implementierung eines MPEG-G-konformen Entropie-Codecs. Es wird gezeigt, dass der vorgeschlagene Codec die durchschnittlich besten Kompressionswerte im Vergleich zum Stand der Technik erzielt und dass die Aufnahme des Codecs in CRAM sowohl hinsichtlich der erreichbaren Kompression als auch der Geschwindigkeit von Vorteil wäre. Abschließend wird ein Überblick über Standards zur Komprimierung von Sequenzierungsdaten gegeben. Insbesondere wird hier auf MPEG-G eingangen, da alle Beiträge dieser Arbeit in MPEG-G integriert wurden

Knowledge Representation Concepts for Automated SLA Management

Outsourcing of complex IT infrastructure to IT service providers has increased substantially during the past years. IT service providers must be able to fulfil their service-quality commitments based upon predefined Service Level Agreements (SLAs) with the service customer. They need to manage, execute and maintain thousands of SLAs for different customers and different types of services, which needs new levels of flexibility and automation not available with the current technology. The complexity of contractual logic in SLAs requires new forms of knowledge representation to automatically draw inferences and execute contractual agreements. A logic-based approach provides several advantages including automated rule chaining allowing for compact knowledge representation as well as flexibility to adapt to rapidly changing business requirements. We suggest adequate logical formalisms for representation and enforcement of SLA rules and describe a proof-of-concept implementation. The article describes selected formalisms of the ContractLog KR and their adequacy for automated SLA management and presents results of experiments to demonstrate flexibility and scalability of the approach.Comment: Paschke, A. and Bichler, M.: Knowledge Representation Concepts for Automated SLA Management, Int. Journal of Decision Support Systems (DSS), submitted 19th March 200