Publications and Preprints
Publications
Mathematical biology
- V. Suvandjieva, I. Tsacheva, M. Santos, G. Kararigas, P. Rashkov, Modelling the impact of NETosis during the initial stage of Systemic Lupus Erythematosus, to appear in Bull. Math. Biol.
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B.W. Kooi, P. Rashkov, E. Venturino (2023), Multi-strain host-vector dengue modeling: dynamics and control, Chapter 6 in: P. Ghaffari (ed.), Bio-mathematics, Statistics, and Nano-Technologies: Mosquito Control Strategies, Chapman and Hall/CRC.
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P. Rashkov (2022), Modeling repellent-based interventions for control of vector-borne diseases with constraints on extent and duration. Math Biosci Eng 19(4): 4038-4062.
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P. Rashkov (2021), Stability analysis of a model for a vector-borne disease with an asymptomatic class. Proc. 50th Jubilee Spring Conference of the Union of Bulgarian Mathematicians p. 144-149 (PDF)
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P. Rashkov (2021), A model for a vector-borne disease with control based on mosquito repellents: a viability analysis. J Math Analysis Appl 498: 124958.
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P. Rashkov, B.W. Kooi (2021), Complexity of host-vector dynamics in a two-strain dengue model. J Biol Dynam 15: 35-72.
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M. Borisov, G. Dimitriu, P. Rashkov (2019), Modelling the host immune response to mature and immature dengue viruses. Bull Math Biol 81(12): 4951-4976.
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P. Rashkov, E. Venturino, M. Aguiar, N. Stollenwerk, B.W. Kooi (2019),
On the role of vector modelling in a minimalistic epidemic model. Math Biosci Eng 16(5): 4314-4338.
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P. Rashkov (2018), Geometric analysis of a model for cross-feeding in the chemostat. Math Meth Appl Sci 41: 8765-8783.
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P. Rashkov (2018), Competition for resources and space contributes to the emergence of drug resistance in cancer. p. 169-183 In: K. Georgiev et al. (eds.), Advanced Computing in Industrial
Mathematics, Studies in Computational Intelligence 728, Springer.
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P. Rashkov, I.P. Barrett, R.E. Beardmore, C. Bendtsen, I. Gudelj (2016),
Kinase inhibition leads to hormesis in a dual phosphorylation-dephosphorylation cycle.
PLoS Comput Biol 12 (11): e1005216.
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I. Gudelj, M. Kinnersley, P. Rashkov, K. Schmidt, F. Rosenzweig (2016),
Stability of cross-feeding polymorphisms in microbial communities. PLoS Comput Biol 12 (12): e1005269.
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P. Rashkov (2015),
Remarks on pattern formation in a model for hair follicle spacing. Discr Cont Dyn B 20(5): 1555-1572.
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P. Rashkov (2014),
Regular and discontinuous solutions in a singularly perturbed model for hair follicle spacing. Biomath 3: 1411111.
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P. Rashkov, B.A. Schmitt, D. Keilberg, K. Beck, L. Søgaard-Andersen, S. Dahlke (2014),
A model for spatio-temporal dynamics in a regulatory network for cell polarity. Math Biosci 258: 189-200.
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P. Rashkov, B.A. Schmitt, L. Søgaard-Andersen, P. Lenz, S. Dahlke (2013),
A model for antagonistic protein dynamics. Int J Biomath Biostat 2(1): 75-85.
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P. Rashkov, B.A. Schmitt, L. Søgaard-Andersen, P. Lenz, S. Dahlke (2012),
A model of oscillatory protein dynamics in bacteria. Bull Math Biol 74(9): 2183-2203.
Harmonic analysis
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G.E. Pfander, P. Rashkov (2013),
Remarks on multivariate Gaussian Gabor frames. Monatsh Math, 172(2): 179-187.
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N. Grip, G.E. Pfander, P. Rashkov (2013),
A time-frequency criterion for operator identification. Sampl Theory Signal Image Process 12(1): 1-19.
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G.E. Pfander, P. Rashkov, Y. Wang (2012),
A geometric construction of tight Gabor frames with multivariate compactly supported smooth windows.
J Fourier Analysis Appl 18(2): 223-239.
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N. Grip, G.E. Pfander, P. Rashkov (2011), Time frequency analysis of operators and operator identification.
In: International Conference on Sampling Theory and Applications: 02/05/2011-06/05/2011, Singapore, 2011.
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P. Rashkov (2010), Time-frequency localized functions and operators in Gabor analysis. Ph.D. Thesis, Jacobs University, Bremen (Supervisor Prof. Dr. Götz E. Pfander).
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N. Grip, G.E. Pfander, P. Rashkov (2010), Identification of time-frequency localized operators. Technical report No. 22, Jacobs University, Bremen.
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G.E. Pfander, P. Rashkov (2010),
Window design for multivariate Gabor frames on lattices.
Technical Report No. 21, Jacobs University, Bremen.
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F. Krahmer, G.E. Pfander, P. Rashkov (2009),
An open question on the existence of Gabor frames in general linear position.
In: Structured Decompositions and Efficient Algorithms, S. Dahlke et al. (Eds.), Schloss Dagstuhl - Leibniz-Zentrum für Informatik.
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F. Krahmer, G.E. Pfander, P. Rashkov (2009), Applications of the uncertainty principle for finite Abelian groups to communications engineering. Bulg J Phys, 36(S2): 54-59.
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F. Krahmer, G.E. Pfander, P. Rashkov (2008),
Uncertainty in time-frequency representations on finite Abelian groups. Appl Comp Harm Analysis, 25(2): 209-225.
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F. Krahmer, G.E. Pfander, P. Rashkov (2008), Support size restrictions on time-frequency representations of functions on finite Abelian groups. Proc Appl Math Mech, 8(1): 10825-10826.
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F. Krahmer, G.E. Pfander, P. Rashkov (2007),
Support size conditions for time-frequency representations on finite Abelian groups. Technical Report No. 13, School of
Engineering and Science, Jacobs University, Bremen.
Numerical methods
- P. Rashkov (2022), Reduced basis approximation for a spatial Lotka-Volterra model. Mathematics 10(12):1983.
- P. Rashkov (2021), A posteriori error analysis for a reduced-basis
approximation of two parabolic problems for
tumour growth. Научни известия ИМИ-БАН/Scientific Reports of the Institute of Mathematics and Informatics 1/2021, ISSN 1314-541Х (PDF)
Preprints
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F. Acotto, V. Suvandjieva, E. Venturino, P. Rashkov, A model for lions-hyenas interactions
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M. Khalighi, L. Lahti, F. Ndaïrou, P. Rashkov, D.F.M Torres, Fractional modelling of COVID-19 transmission incorporating asymptomatic and super-spreader individuals