Effective randomness for continuous measures [pdf]
(with Theodore A. Slaman)
Submitted
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, to be published in the STML series of the American Mathematical Society (based on a MASS course taught at Penn State)
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