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Kiraly F.J.,TU Berlin | Kiraly F.J.,Institute of Mathematics | Kiraly F.J.,Mathematisches Forschungsinstitut Oberwolfach | Ziehe A.,TU Berlin
ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings | Year: 2013

We present an algorithm, AROFAC2, which detects the (CP-)rank of a degree 3 tensor and calculates its factorization into rank-one components. We provide generative conditions for the algorithm to work and demonstrate on both synthetic and real world data that AROFAC2 is a potentially outperforming alternative to the gold standard PARAFAC over which it has the advantages that it can intrinsically detect the true rank, avoids spurious components, and is stable with respect to outliers and non-Gaussian noise. © 2013 IEEE.

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.

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.

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

Kiraly F.J.,University College London | Kiraly F.J.,Mathematisches Forschungsinstitut Oberwolfach | Theran L.,Aalto University | Tomioka R.,Toyota Technological Institute
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.

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.

Agency: NSF | Branch: Continuing grant | Program: | Phase: MATHEMATICAL SCIENCES RES INST | Award Amount: 300.00K | Year: 2016

The Mathematisches Forschungsinstitut Oberwolfach (MFO) is an international mathematical research center that supports the dissemination of new knowledge in mathematics and its applications, the initiation of new research projects, and the interaction of leading junior and senior researchers. Annually nearly 3,000 selected scientific visitors engage in weeklong intensive research programs, which are monitored by an international scientific committee. The broad scope of the program at the MFO includes research topics in pure mathematics as well as a wide range of interdisciplinary topics that reflect mathematical techniques prevalent in all areas of science and technology. This award annually supports the participation in these programs of 100 US-based graduate students, postdoctoral researchers, and junior faculty within ten years of the PhD. Participation in the MFO programs gives these US Junior Oberwolfach Fellows the opportunity at an early stage of their careers to interact with top senior scientists from all over the world in an intense research atmosphere without distractions. In this way the next generation of US mathematicians receives training and access to senior colleagues at the highest level, benefitting the whole field.

The MFO runs its weeklong scientific activities in four central programs that cover all fields of mathematics, including applications in other sciences: the Oberwolfach Workshops, the Mini-Workshops, the Arbeitsgemeinschaften, and the Oberwolfach Seminars. The main scientific program consists of 40 weeklong workshops per year, each with about 50 participants, organized by leading experts selected by a scientific committee. The Mini-Workshop Program offers 12 weeklong mini-workshops with about 15 participants. In all workshops the US Junior Oberwolfach fellows have the opportunity to attend lectures, to work with senior participants, and possibly to present results of their own. In an Arbeitsgemeinschaft (Study Group) junior as well as senior researchers learn about a new active topic outside their current area of research by active presentations of the material. The six Oberwolfach Seminars are graduate schools organized by leading experts in the field and address Ph.D. students and postdocs from all over the world. On average, the project US Junior Oberwolfach Fellows allows the MFO to support two fellows per week from 2016 to 2021, for a total of 500 fellows over a five-year period.

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