Workgroup Numerics

Dr. Peter Rashkov

Philipps-Universität Marburg
Fachbereich Mathematik und Informatik
Arbeitsgruppe Numerik/Wavelet-Analysis
Hans-Meerwein-Straße
Lahnberge
35032 Marburg
Germany

Office: 06 D20
Telephone: +49(0)6421/28-25460
Telefax: +49(0)6421/28-26945
E-Mail: rashkov@mathematik(.uni-marburg.de)
Office Hours: by appointment

Research

  • Mathematical Modelling in Biology, Biomathematics
  • Time-frequency and Gabor Analysis

Upcoming Conferences

  • ECMTB 2014, 9th European Conference on Mathematical and Theoretical Biology, 15-19.06.2014, Gothenburg, Sweden.
  • Conference Mathematical Methods and Models in Biosciences (BIOMATH 2014), 22-27.06.2014, Sofia, Bulgaria.
  • SIAM Conference on Nonlinear Waves and Coherent Structures, 11-14.08.2014, Cambridge, England.

Publications and Preprints

  • P. Rashkov. Regular and discontinuous solutions in a singularly perturbed model for hair follicle spacing. (submitted)
  • P. Rashkov. Remarks on pattern formation in a model for hair follicle spacing. (submitted)
  • P. Rashkov, B. A. Schmitt, D. Keilberg, L. Sogaard-Andersen, and S. Dahlke. A model for spatio-temporal dynamics in a regulatory network for cell polarity. (submitted)
  • G.E. Pfander, P. Rashkov. Remarks on multivariate Gaussian Gabor frames. Monatshefte für Mathematik, 172(2): 179-187, 2013 dx.doi.org/10.1007/s00605-013-0556-4.
  • P. Rashkov, B.A. Schmitt, L. Sogaard-Andersen, P. Lenz, S. Dahlke. A model for antagonistic protein dynamics. Int. J. Biomath. Biostat. 2 (1): 75-85, 2013.
  • N. Grip, G.E. Pfander, P. Rashkov. A time-frequency criterion for operator identification. Sampl. Theory Signal Image Process. 12 (1): 1-19, 2013.
  • P. Rashkov, B.A. Schmitt, L. Sogaard-Andersen, P. Lenz, S. Dahlke. A model of oscillatory protein dynamics in bacteria. Bull. Math. Biol. 74: 2183-2203, 2012 dx.doi.org/10.1007/s11538-012-9752-y .
  • N. Grip, G.E. Pfander, P. Rashkov. Density criteria in operator identification. In: Proceedings Sampling Theory and Applications 2011, Singapore, 2011.
  • G.E. Pfander, P. Rashkov, Y. Wang. A geometric construction of tight Gabor frames with multivariate compactly supported smooth windows. J. Four. Analysis and Appl. 18(2): 223-239, 2012.
  • F. Krahmer, G.E. Pfander, P. Rashkov. An open question on the existence of Gabor frames in general linear position. In: Structured Decompositions and Efficient Algorithms, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2009.
  • F. Krahmer, G.E. Pfander, P. Rashkov. Applications of the uncertainty principle for finite abelian groups to communications engineering. Bulg. J. Phys., 36(S2): 54-59, 2009.
  • F. Krahmer, G.E. Pfander, P. Rashkov. Uncertainty in time-frequency representations on finite Abelian groups. Appl. Comp. Harm. Analysis, 25 (2): 209-225, 2008.
  • F. Krahmer, G.E. Pfander, P. Rashkov. Support size restrictions on time-frequency representations of functions on finite abelian groups. PAMM, 8 (1): 10825-10826, 2008.

Thesis

  • P. Rashkov. Time-frequency localized functions and operators in Gabor analysis. Thesis, Jacobs University 2010. PDF

Technical Reports


Research and Teaching Visits

  • International Workshop on Numerical Methods and Emerging Computational Challenges in Mathematical Biology, 12-15.05.2014, Dundee, Scotland.
  • Short-term Visitor, 24.02-01.03.2013, Oxford Centre for Collaborative Applied Mathematics (OCCAM), Mathematical Institute, Oxford, UK.
  • Invited Lecturer, DAAD Intensive Course "Gabor Frames and Wavelets in Local Analysis", 15-20.09.2011, University Novi Sad, Serbia. A DAAD Project in the framework of the Stability Pact for South East Europe Center of Excellences for Applications of Mathematics.

Selected Presentations

  • Self-Organisation in a Reaction-Diffusion System with a Non-Diffusing Component. SIAM Conference on Nonlinear Waves and Coherent Structures, 11-14.08.2014, Cambridge, England.
  • Pattern Formation in a Reaction-Diffusion System with a Singularity. Conference Mathematical Methods and Models in Biosciences (BIOMATH 2014), 22-27.06.2014, Sofia, Bulgaria.
  • A Model for Spatio-Temporal Dynamics in a Regulatory Network for Cell Polarity. ECMTB 2014, 9th European Conference on Mathematical and Theoretical Biology, 15-19.06.2014, Gothenburg, Sweden.
  • Modelling protein oscillations in Myxococcus xanthus. Conference Mathematical Methods and Models in Biosciences (BIOMATH 2013), 16-21.06.2013, Sofia.
  • Modelling cell polarity in Myxococcus xanthus. Conference Mathematical Modeling in Cell Biology, 25-29.03.2013, Lyon.
  • A Model for a Protein Oscillator in Myxococcus xanthus. OCCAM Seminar, OCCAM, Mathematical Institute, Oxford, 27.02.2013.
  • Modellierung und Parameterschätzung zur Fortbewegung einer Bakterienart. Oberseminar AG Numerische Analysis, Marburg, 01.12.2011 (with Alexandra Herzog).
  • A model for protein oscillations in bacteria. SYNMIKRO Seminar, 09.06.2011, Max-Planck-Institut für terrestrische Mikrobiologie, Marburg.
  • Where harmonic analysis and combinatorial geometry meet: design of special Gabor frames. Mathematisches Kolloquium, 12 Juli 2010, Philipps-Universität Marburg.
  • The identification problem for time-frequency localizing operators. Conference "New Trends in Harmonic and Complex Analysis", 29 Juni 2010, Bremen.
  • Identification of time-frequency localizing operators. AAG Oberseminar, 1 Juni 2010, Universität Osnabrück.
  • Applications of the uncertainty principle for finite abelian groups to communications engineering. Humboldt-Kolleg "Modern Trends in Mathematics and Physics", September 2008, Varna (Bulgaria).
  • Uncertainty in time-frequency representations on finite abelian groups with applications to erasure channels and sparsity. Workshop "Young Mathematicians Meet in Bonn", Juli 2008, Bonn.
  • Support size restrictions on time-frequency representations of functions on finite abelian groups. 79th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM), April 2008, Bremen.
  • Uncertainty in time-frequency representations on finite abelian groups. (poster) "Trends in Harmonic Analysis", Juni 2007, Strobl (Austria).

Education

  • 2006 M.Sc. Mathematical Sciences. Jacobs University, Bremen (then International University Bremen).
  • 2010 Ph.D. in Mathematical Sciences. Jacobs University, Bremen. Title of the dissertaion: Time-frequency localized functions and operators in Gabor analysis (Supervisor Prof. Dr. Götz Pfander)

Teaching


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