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]
Draft
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