Section outline

  • General

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    Algebraic and Discrete Methods in Biology (326.007, SS 2009)

    Time:     Thursday, 13:45-15:15, HS 12.
    Start: March 6, 2009.

    Applications of symbolic (algebraic, logic, discrete) methods to biological problems attracts growing interest. Some of the examples are applications of Groebner bases in the reverse engineering of gene regulatory networks from experimental data; modeling and analysis of signal transduction and metabolic networks in mammalian cells using rewriting logic; modeling biochemical regulatory networks as boolean networks; applications of hybrid automata and cylindrical algebraic decomposition in systems biology; using temporal logics to formalize a set of biological properties such as reachability, checkpoints, stability or oscillations; application of difference equations in population dynamics, constraint solving techniques in molecular biology, etc.

    The course gives an overview of some of the methods from computer algebra and computational logic that can be (potentially) applied to biological problems. In particular, techniques and tools from automated reasoning, polynomial algebra, algorithmic combinatorics, formal methods will be discussed.
    To take part in the course, you have to enrol in the KUSSS system. If you also login in Moodle and register as a course participant, you will receive per email all messages posted in the News forum.

  • Topic 2

    Gröbner Basen in Systembiologie
    Wolfgang Windsteiger

    In dieser Einführung werden wir Anwendungen von Gröbner Basen (GB) in der Systembiologie als Ausgangspunkt für die Beschäftigung mit Gröbner Basen nehmen. Kurz die Theorie der GB, multivariate Polynome, Polynom Reduktion, etc. Anwendungen im speziellen auf das Lösen polynomialer Gleichungssysteme. Wir werden auch die Grundform des GB-Algorithmus behandeln und damit die einfuehrenden Beispiele lösen.

  • Topic 3

    Pattern formation in biological systems
    Lena Kartashova

  • Topic 4

    Anwendungen diskreter Mathematik in der Bioinformatik
    Stephan Dreiseitl

    Wir werden uns mit zwei Anwendungsbereichen diskreter Methoden beschäftigen:
    • Heuristische Lösung eines Problems im Kontext der SNP-Identifizierung, die durch Rückführen auf ein Ergebnis der theoretischen Informatik gelöst werden kann
    • ROC Analyse, mit der die Qualität von Klassifikationsverfahren evaluiert werden kann

  • Topic 5

    Applications of Rewriting Logic in Biology
    Temur Kutsia

    Rewriting logic is a simple computational logic very well suited as a semantic framework within which many different models of computation, systems and languages can be naturally modeled. It is also a flexible logical framework in which many different logical formalisms can be both represented and executed. The Maude system is an implementation of rewriting logic. Pathway Logic is an approach to modeling biological entities and processes based on rewriting logic. It is an example of how formal modeling techniques can be used to develop a new science of symbolic systems biology. This computational science will provide researchers with powerful tools to facilitate the understanding of complex biological systems and accelerate the design of experiments to test hypotheses about their functions in vivo.

    In these lectures we will give a brief introduction to rewriting logic and Maude, and show how pathway logic can be used to model biological processes.

  • Topic 6

    Biological Systems as Concurrent Processes
    Wolfgang Schreiner

    A particular strand of research in systems biology is based on the observation that there are certain similarities between concurrent and mobile software systems and biological systems on the cellular and molecular level. Correspondingly, concepts and techniques developed for the formal specification and verification of concurrent systems have been applied to biological systems, in particular the specification of properties in the language of temporal logic and the verification of such properties by automatic model checking. We will give an overview on recent work in this direction.

    Introduction (4 on 1)
    Part 1: Modeling and Simulating (4 on 1)
    Part 2: Specifying and Verifying (4 on 1)

  • Topic 7

    Exam
    • Thursday, June 25, 13:45-15:15
    No materials are allowed. Do not forget your student id card.