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Kiraly F.J.,University College London | Kiraly F.J.,Mathematisches Forschungsinstitut Oberwolfach | Theran L.,Aalto University | Tomioka R.,Toyota USA
Journal of Machine Learning Research | Year: 2015

We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the treatment of single entries in a closed theoretical and practical framework. More specifically, apart from introducing an algebraic combinatorial theory of low-rank matrix completion, we present probabilityone algorithms to decide whether a particular entry of the matrix can be completed. We also describe methods to complete that entry from a few others, and to estimate the error which is incurred by any method completing that entry. Furthermore, we show how known results on matrix completion and their sampling assumptions can be related to our new perspective and interpreted in terms of a completability phase transition.1 © 2015 Franz J. Kiraly, Louis Theran, and Ryota Tomioka. Source


Ploetzner R.,Freiburg University of Education | Fillisch B.,Freiburg University of Education | Gewald P.-A.,Freiburg University of Education | Ruf T.,Mathematisches Forschungsinstitut Oberwolfach
Interactive Learning Environments | Year: 2015

In two studies, we investigated how learning strategies can support learning from multimedia. In the first study, 112 students learned from a web-based learning environment. On the basis of a strategy, one group of students took typewritten notes. The second group of students wrote a summary. Producing typewritten notes did not benefit learning any more than writing a summary. In the second study, 100 students learned the same subject matter from print. On the basis of a strategy, the first group produced written notes, the second group highlighted, wrote notes, and produced sketches. The third group wrote a summary. The students who highlighted, wrote notes, and produced sketches outperformed the other students. The students who produced written notes only did not learn more successfully than those who wrote a summary. The results suggest that externalizations in general and sketches in particular may play an important role in multimedia learning. © 2015 Taylor & Francis Source


Andres D.,RWTH Aachen | Brickenstein M.,Mathematisches Forschungsinstitut Oberwolfach | Levandovskyy V.,RWTH Aachen | Martin-Morales J.,University of Zaragoza | And 2 more authors.
Mathematics in Computer Science | Year: 2010

We overview numerous algorithms in computational D-module theory together with the theoretical background as well as the implementation in the computer algebra system Singular. We discuss new approaches to the computation of Bernstein operators, of logarithmic annihilator of a polynomial, of annihilators of rational functions as well as complex powers of polynomials. We analyze algorithms for local Bernstein-Sato polynomials and also algorithms, recovering any kind of Bernstein-Sato polynomial from partial knowledge of its roots. We address a novel way to compute the Bernstein-Sato polynomial for an affine variety algorithmically. All the carefully selected nontrivial examples, which we present, have been computed with our implementation. We also address such applications as the computation of a zeta-function for certain integrals and revealing the algebraic dependence between pairwise commuting elements. © 2011 Springer Basel AG. Source


Bulygin S.,Center for Advanced Security Research Darmstadt | Brickenstein M.,Mathematisches Forschungsinstitut Oberwolfach
Mathematics in Computer Science | Year: 2010

This work is devoted to attacking the small scale variants of the Advanced Encryption Standard (AES) via systems that contain only the initial key variables. To this end, we investigate a system of equations that naturally arises in the AES, and then introduce an elimination of all the intermediate variables via normal form reductions. The resulting system in key variables only is solved then. We also consider a possibility to apply our method in the meet-in-the-middle scenario especially with several plaintext/ciphertext pairs. We elaborate on the method further by looking for subsystems which contain fewer variables and are overdetermined, thus facilitating solving the large system. © Birkhäuser Verlag Basel/Switzerland 2010. Source


Grant
Agency: NSF | Branch: Continuing grant | Program: | Phase: | Award Amount: 600.00K | Year: 2011

The Mathematisches Forschungsinstitut Oberwolfach (MFO) in Germany is one of the leading mathematical research centers worldwide. MFO host approximateluy 2,500 internationally renowned guest researchers each year. These scientists come from all over the world, with more than 20% coming from the United States. The scientific programs of the MFO cover all important topics and new developments in mathematics and its applications in science and technology.

This award provides funding to support the participation of additional US-based young researchers, called US Junior Oberwolfach Fellows, in Oberwolfach activities. Participation in the workshops and seminars will give these researchers the opportunity to meet top senior scientists from all over the world and gain experience in the scientific community. The award provides partial support for 100 US Junior Oberwolfach Fellowships per year, in average 2 young scientists per week (graduate students and postdocs with at most 10 years after Ph.D.), starting in April 2011, with a duration of 5 years.

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