• Effective randomness for continuous measures [pdf]
    (with Theodore A. Slaman)
    To apper in Journal of the American Mathematical Society

  • Information vs dimension – an algorithmic perspective [pdf]
    To appear in SEALS 2017

  • Symbolic Analysis-based Reduced Order Markov Modeling of Time Series Data Signal Processing [pdf]
    (with Devesh K. Jha, Nurali Virani, Abhishek Srivastav, and Asok Ray)
    Signal Processing, 149, 68-81, 2018

  • Irrationality Exponent, Hausdorff Dimension and Effectivization [pdf]
    (with Veronica Becher and Theodore A. Slaman)
    Monatshefte für Mathematik, 185(2), 167-188, 2018

  • Measures and their random reals [pdf]
    (with Theodore A. Slaman)
    Transactions of the American Mathematical Society 367(7), 2015

  • Independence, relative randomness, and PA degrees [pdf]
    (with Adam Day)
    Notre Dame Journal of Formal Logic 55(1), 2014

  • The strength of the Besicovitch-Davies Theorem [pdf]
    (with Bjørn Kjos-Hanssen)
    Computability in Europe 2010
    Lecture Notes in Computer Science 6158, Springer, 2010

  • Randomness beyond Lebesgue measure [pdf]
    Logic Colloquium 06, Nijmegen
    Cambridge University Press, 2009

  • Probability measures and effective randomness [pdf]
    (with Theodore A. Slaman)
    13th International Congress of Logic, Methodology, and Philosophy of Science, Beijing
    College Publications, 2009

  • Effectively closed classes of measures and randomness [pdf]
    Annals of Pure and Applied Logic 156(1), 2008.

  • A lower cone in the wtt degrees of non-integral effective dimension [pdf]
    (with Andre Nies)
    Proceedings of IMS workshop on Computational Prospects of Infinity, Part II
    World Scientific, 2008

  • Schnorr dimension [pdf]
    (with Rodney G. Downey and Wolfgang Merkle)
    Mathematical Structures in Computer Science, 16(5), 2006.
    (an earlier version appeared in: Computability in Europe, LNCS 3526, Springer, 2005)

  • On hierarchies of randomness tests [pdf]
    (with Frank Stephan)
    Proceedings of the 9th Asian Logic Conference, Novosibirsk
    World Scientific Publishing, 2006

  • On selection functions that do not preserve normality [pdf]
    (with Wolfgang Merkle)
    Theory of Computing Systems 39(5), 2006.
    (an earlier version appeared in: Mathematical foundations of computer science 2003, LNCS 2747, Springer, 2003)

  • Kolmogorov-Loveland randomness and stochasticity [pdf]
    (with Woflgang Merkle, Joseph Miller, André Nies, and Frank Stephan)
    Annals of Pure and Applied Logic, 138(1-3), 2005.
    (an earlier version appeared in: STACS 2005 (Stuttgart), LNCS 3404, pp. 422–433, Springer, 2005)

  • Effective Hausdorff dimension [pdf]
    (with Frank Stephan)
    Logic Colloquium ‘01,
    Association for Symbolic Logic, 2005.

  • Almost complete sets [pdf]
    (with Klaus Ambos-Spies, Wolfgang Merkle and Sebastiaan A. Terwijn)
    Theoretical Compter Science 306:177-194, 2003.
    (an earlier version appeared in: STACS 2000 (Lille), LNCS 1770, pp. 419–430, Springer, 2000)

  • Hausdorff dimension in exponential time [pdf]
    (with Klaus Ambos-Spies, Wolfgang Merkle, and Frank Stephan)
    Proc. 16th Conference on Computational Complexity
    IEEE Computer Society, 2001.


  • An introduction to Ramsey Theory
    (with Matt Katz)
    Textbook, #87 in the Student Mathematical Library series of the American Mathematical Society (based on a MASS course taught at Penn State), 2018

  • Lecture notes on Descriptive Set Theory [pdf]

  • Algorithmic randomness [web page]
    (with Rod Downey)
    Scholarpedia, 2(10):2574

  • Computability and Fractal Dimension [pdf]
    Doctoral Dissertation, Universität Heidelberg, 2004

  • Topologische Spiele und resourcenbeschränkte Baire-Kategorie [pdf]
    (Topological games and resource-bounded Baire category)
    Diploma Thesis, Universität Heidelberg, 1997