AG Numerik

Dr. Peter Rashkov

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

Raum: 06 D20
Telefon: +49(0)6421/28-25460
Telefax: +49(0)6421/28-26945
E-Mail: rashkov@mathematik (.uni-marburg.de)
Sprechstunde: n. V.

Forschungs- und Arbeitsgebiete

  • Mathmatische Modelle in der Biologie, Biomathematik
  • Zeit-Frequenz-Analysis

Aktuelles

  • Conference Mathematical Methods and Models in Biosciences (BIOMATH 2014), 22-27.06.2014, Sofia, Bulgarien.
  • SIAM Conference on Nonlinear Waves and Coherent Structures, 11-14.08.2014, Cambridge, England.

Veröffentlichungen und Preprints

  • P. Rashkov. Regular and discontinuous solutions in a singularly perturbed model for hair follicle spacing (eingereicht)
  • P. Rashkov. Remarks on pattern formation in a model for hair follicle spacing (eingereicht)
  • 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 (eingereicht)
  • 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. Time-frequency criteria 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. Proceedings SAMPling Theory and Applications, 2.5. - 6.5.2011, Singapur, 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.
  • P. Rashkov. Time-frequency localized functions and operators in Gabor analysis. PhD Thesis, Jacobs University, Mai 2010.
  • F. Krahmer, G.E. Pfander, P. Rashkov. An open question on the existence of Gabor frames in general linear position. In: Proc. Dagstuhl Seminar 08492 "Structured Decompositions and Efficient Algorithms", 2009.
  • F. Krahmer, G.E. Pfander, P. Rashkov. Applications of the uncertainty principle for finite abelian groups to communications engineering. Bulg. J. Physics, 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. Proceedings in Applied Mathematics and Mechanics, 8 (1): 10825-10826, 2008.

Dissertation

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

Technical Reports


Forschungs- und Lehreaufenthalte

  • International Workshop on Numerical Methods and Emerging Computational Challenges in Mathematical Biology, 12-15.05.2014, Dundee, Schottland.
  • Short-term Visitor, 24.02-01.02.2013, Oxford Centre for Collaborative Applied Mathematics (OCCAM), Mathematisches Institut, Oxford, Großbritannien.
  • Lektor, DAAD Intensive Course "Gabor Frames and Wavelets in Local Analysis", 15-20 September 2011, Universität Novi Sad, Serbien. Ein DAAD Projekt im Rahmen des Stability Pact for South East Europe Center of excellences for applications of mathematics.

Ausgewählte Vorträge

  • 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, Bulgarien.
  • 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, Göteborg, Schweden.
  • 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 (mit 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 (Bulgarien).
  • 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 (Österreich).

Studium

  • 2006 M.Sc. Mathematical Sciences. Jacobs University, Bremen (damals International University Bremen).
  • 2010 Promotion am Fachbereich Mathematical Sciences an der Jacobs University, Bremen, unter der Betreung von Prof. Dr. Götz Pfander.

Lehre und Veranstaltungen


Aktuelles und Interessantes