Nikolaos
Atreas
Nikos Atreas is a mathematician with a Ph.D. in Harmonic Analysis (School of Mathematics, Aristotle University of Thessaloniki) with a thesis entitled “Harmonic and wavelet Analysis with applications in sampling theory”. Since 2013, he has been with the School of Electrical and Computer Engineering of the Aristotle University of Thessaloniki, Greece. He is also teaching in the Hellenic Open University since 2017.
Nikos Atreas published several articles in international referred scientific journals, international conferences, or books and he wrote notes for various courses, such as Linear Algebra, Calculus and Multivariable Calculus, Numerical Analysis, Harmonic Analysis, ODE, PDE, and mathematical foundations of cryptography. He taught a variety of courses such as Linear Algebra, Calculus and Multivariable Calculus, Numerical Analysis, Harmonic Analysis, ODE, PDE, Applied Mathematics and Theory of Computation. He was reviewer for Mathematical Reviews, journals and conference meetings. He participated in many national and international research projects. His current research interests are focused on Applied Harmonic Analysis and Time-Frequency Analysis with applications.
School of Electrical and Computer Engineering
Faculty of Engineering ΑUTH, 2nd floor, Building B (Rural and Surveying Engineering), Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece
2310995953
nikos.atreas
Aristotle University of Thessaloniki
Faculty of Sciences/School of Mathematics
Degree in Mathematics
Aristotle University of Thessaloniki
Faculty of Sciences/School of Mathematics
Ph.D in Mathematics
Undergraduate courses:
- Calculus.
- Multivariable Calculus.
- Numerical Analysis.
- Linear Algebra and Analytic Geometry.
- Complex Analysis.
- Theory of Computation.
- Mathematical Foundations of Cryptography.
- ODE and PDE.
Graduate courses
- Harmonic Analysis.
- Functional Analysis.
- Operator Theory.
- Research Funding Program: ARCHIMEDES III. Investing in knowledge society through the European Social Fund. Archimedes III: Funding of Research Groups in TEI of W. Macedonia, project with the title “Applications of dynamical systems”, (MIS 383583), 2012-2015, co-ordinator: A Bisbas.
- Marie Curie Research Training Networks (RTN), “Conformal structures and dynamics”, 035651-2-CODY, Technological Institution of West Macedonia, 2007-2010, co-ordinator: A Bisbas.
- Ε.P.Ε.Α.Ε.Κ. ΙΙ, Pythagoras ΙΙ – ΕΕΟP, subtask 24, “Mathematics with applications in Bioinformatics”, Department of Informatics, Aristotle University of Thessaloniki, 2005-2007, co-ordinator: C Karanikas.
- G.S.R.T., EPAN, Joint Research program Greece-Bulgaria, “Stydy of biomedical data by the methods of Multiresolution Analysis. Poly-spline wavelet Analysis in Immuno-computations and brain research”, Department of Informatics, Aristotle University of Thessaloniki, 2005-2007, co-ordinator of Greek team: C Karanikas.
- Archimedes II, “Applied Harmonic Analysis and fractals”, Technological Institution of West Macedonia, 2004-2007, co-ordinator: A Bisbas.
- Post-Doc Research program, contract 414: ”Discrete wavelet-type transforms with applications to pattern recognition such as (a) hidden periodicity detection, (b) hidden markovian process detection, (c) bio-data recognition”, Department of Informatics, Aristotle University of Thessaloniki, 2004-2005.
- ΕU Project HPAM-2002-00065 “Nanostructures in Nanoscales”, Department of Informatics, Aristotle University of Thessaloniki, 2002-2004, Co-ordinator: C Karanikas.
- EU Project IST-2000-26016 IMCOMP, “Immunocomputing”, Department of Mathematics, Aristotle University of Thessaloniki, 2001-2003, Co-ordinator: C Karanikas.
- P.EN.E.D. Program number 1914, “Time series analysis and pattern recognition with wavelets”, Department of Mathematics, Aristotle University of Thessaloniki, 1996-1998, Co-ordinator: C Karanikas.
Nikolaos
Atreas
Nikos Atreas is a mathematician with a Ph.D. in Harmonic Analysis (School of Mathematics, Aristotle University of Thessaloniki) with a thesis entitled “Harmonic and wavelet Analysis with applications in sampling theory”. Since 2013, he has been with the School of Electrical and Computer Engineering of the Aristotle University of Thessaloniki, Greece. He is also teaching in the Hellenic Open University since 2017.
Nikos Atreas published several articles in international referred scientific journals, international conferences, or books and he wrote notes for various courses, such as Linear Algebra, Calculus and Multivariable Calculus, Numerical Analysis, Harmonic Analysis, ODE, PDE, and mathematical foundations of cryptography. He taught a variety of courses such as Linear Algebra, Calculus and Multivariable Calculus, Numerical Analysis, Harmonic Analysis, ODE, PDE, Applied Mathematics and Theory of Computation. He was reviewer for Mathematical Reviews, journals and conference meetings. He participated in many national and international research projects. His current research interests are focused on Applied Harmonic Analysis and Time-Frequency Analysis with applications.
Technological Institution of West Macedonia/Department of General Sciences
Scientific collaborator
Aristotle University of Thessaloniki/School of Informatics
Lecturer
Aristotle University of Thessaloniki/School of Mathematical, Physical and Computational SciencesInformatics
Assistant Professor
Aristotle University of Thessaloniki/School of Electrical and Computer Engineering
Associate Professor
Journals
J1. N. Karantzas, N. Atreas, M. Papadakis, T Stavropoulos. On the design of multi-dimensional compactly supported Parseval framelets with directional characteristics. Linear Algebra Appl. 582 (2019), 1–36. https://doi.org/10.1016/j.laa.2019.09.030
J2. Nikolaos Atreas. Characterizations of dual multiwavelet frames of periodic functions, Int. J. Wavelets, Multiresolut. Inf. Process. 14 (3), 1610012 (26 pages), (2016). https://doi.org/10.1142/S0219691316500120
J3. Nikolaos Atreas, Manos Papadakis, Theodoros Stavropoulos. Extension Principles for Dual Multiwavelet frames of L2(Rs) constructed from Multirefinable generators, J. Fourier Anal. Appl., 22 (4), 854-877, (2016). https://doi.org/10.1007/s00041-015-9441-y
J4. Nikolaos Atreas, Antonios Melas, Theodoros Stavropoulos. Affine Dual Frames and Extension Principles, Applied Comput. Harmon. Anal., 36 (1), 51-62, (2014). https://doi.org/10.1016/j.acha.2013.02.003
J5. Nikolaos Atreas and Antonis Bisbas. Generalized Riesz Products produced from orthonormal transforms, Colloq. Math., 126 (2), 141-154, (2012). https://doi.org/10.4064/cm126-2-1
J6. Nikolaos D. Atreas. On a class of non-uniform average sampling expansions and partial reconstruction in subspaces of L2(R), Adv. Comput. Math., 36, 21-38, (2012). https://doi.org/10.1007/s10444-011-9177-4
J7. Nikolaos Atreas, Costas Karanikas. Boolean invertible matrices identified from two permutations and their corresponding Haar-type matrices, Linear Algebra Appl., 435, 95-105, (2011). https://doi.org/10.1016/j.laa.2011.01.005
J8. Nikolaos D. Atreas. Perturbed sampling formulas and local reconstruction in shift-invariant spaces, J. Math. Anal. Appl., 377, 841-852, (2011). https://doi.org/10.1016/j.jmaa.2010.12.011
J9. Nikolaos D. Atreas. Detecting hidden periodicities on symbolic sequences, J. Interdiscip. Math., 12 (5), 639-646, (2009). DOI:10.1080/09720502.2009.10700651
J10. N. D. Atreas and P. Polychronidou. A Class of Sparse Invertible Matrices and Their Use for Non-Linear Prediction of Nearly Periodic Time Series with Fixed Period, Numer. Funct. Anal. Optimiz., 29 (1-2), 66-87, (2008). DOI: 10.1080/01630560701873803
J11. Ν. D. Atreas, C. Karanikas and P. Polychronidou. A Class of Sparse Unimodular Matrices Generating Multiresolution and Sampling Analysis for Data of any Length, SIAM J. Matrix Anal. Appl., 30 (1), 312-323, (2008). https://doi.org/10.1137/050638679
J12. N. D. Atreas and C. Karanikas. Multiscale Haar Unitary Matrices with the Corresponding Riesz Products and a Characterization of Cantor – Type Languages, J. Fourier Anal. Appl., 13 (2), 197-210, (2007). https:doi.org/10.107/s00041-006-6044-7
J13. Nikolaos D. Atreas and C. Karanikas. Discrete Sampling formulas on spaces of pM-periodic sequences with computational applications on edge detection, Numer. Funct. Anal. Optimiz., 26 (3), 285-301, (2005). https://doi.org/10.1081/NFA-200067292
J14. N. Atreas, J. J. Benedetto and C. Karanikas. Local sampling for regular wavelet and Gabor expansions, Sampl. Theory Signal Image Process., 2 (1), 1-25, (2003). DOI: 10.1007/BF03549383
J15. N. Atreas, N. Bagis and C. Karanikas. The information loss error and the jitter error for regular sampling expansions,Sampl. Theory Signal Image Process., 1 (3), 261-276, (2002). DOI: 10.1007/BF03549381
J16. Nikolaos D. Atreas. New bounds for Truncation-type Errors on regular Sampling Expansions, Numer. Funct. Anal. Optimiz., 23 (7&8), 695-704, (2002). https://doi.org/10.1081/NFA-120016265
J17.N. Atreas and C. Karanikas. Truncation Error on Wavelet Sampling Expansions, J. Comput. Anal. Appl., 2 (1), 89-102, (2000). https://doi.org/10.1023/A:1010142431792
J18. N. Atreas and C. Karanikas. Gibbs Phenomenon on Sampling Series based on Shannon’s and Meyer’s wavelet Analysis, J. Fourier Anal. Appl., 5 (6), 575-588, (1999). https://doi.org/10.1007/BF01257192
Conferences
B1. C. Karanikas and N. Atreas. Enumeration and Coding methods for a class of permutations and reversible Logical gates. Facta Universitatis. Series: Electronics and Energetics, 31, 2, 241-255, (2018). DOI Number: 10.2298/FUEE1802241K
B2. N. Atreas, N. Karantzas, M. Papadakis and T. Stavropoulos. Exploring neuronal synapses with directional and symmetric filters with small support. Proceedings of SPIE, Wavelets and Sparsity XVII, V. 10394, id. 1039413, 18 pp., (2017). https://doi.org/10.1117/12.2275213
B3. Nikolaos Atreas and Costas Karanikas. Discrete Transforms produced from two natural numbers and applications. In: EUROCAST 2011, R. Moreno-Diaz et al. (Eds.), LNCS 6928, 304–310, 2012. DOI: 10.1007/978-3-642-27579-1_39
B4. Nikolaos D. Atreas. On a class of multiscale transforms on L2[0,1) and their corresponding sampling theorem. In: Proceedings of the conference SampTA07 N. Atreas and C. Karanikas (Eds), 19-22, 2009.
B5. C. Karanikas and N. D. Atreas. On a Large Class of Non-Linear Coding Methods Based on Boolean Invertible Matrices, Facta Universitatis (Nis), Ser.: Elec. Energ., 21 (3), 365-372, (December 2008). https://doi.org/10.2298/FUEE0803365K
B6. Costas Karanikas, Nikolaos D. Atreas. Discrete type-Riesz Products. In: Proceedings of the workshop Walsh and dyadic Analysis, R. Stankovic (Ed.), 137-143, Nis, 2008.
B7. Nikolaos D. Atreas. A Walsh type Multiresolution Analysis. In: Proceedings of the workshop Walsh and dyadic Analysis, R. Stankovic (Ed.), 177-183, Nis, 2008.
B8. C. Karanikas, N. D. Atreas, A. Bakalakos, P. Polychronidou. Discrete Transforms on Symbolic Sequences for String Matching, Pattern Recognition and Grammar Detection. In NATO Science for Piece and Security. Series D: Information and Communication security, O. Kounchev, R. Willems, V. Shalamanov, T. Tsachev (Eds), 12, 126-138, 2008.
B9. Nikolaos D. Atreas and C. Karanikas. Haar-type Orthonormal systems, data presentation as Riesz Products and a recognition on symbolic sequences, In: Frames and Operator Theory in Analysis and Signal Processing, Contemp. Math., 451, 1-9, (2008).
B10. N. D. Atreas and C. Karanikas. A fast pattern matching algorithm based on prime numbers and hashing approximation. In NATO Science for Piece and Security. Series D: Information and Communication security, O. Kounchev, R. Willems, V. Shalamanov, T. Tsachev (Eds), 12, 118-126, (2008).
B11. Nikolaos D. Atreas, Costas Karanikas and Persefoni Polychronidou. Signal Analysis on Strings for Immune-type pattern recognition, Comp. Funct. Genom., 5 1, 69-74, (2004).
B12. Nikolaos D. Atreas, Costas G. Karanikas and A. O. Tarakanov. Signal Processing by an Immune Type Tree Transform. ICARIS 2003, J.Timmis et al. (Eds), LNCS 2787, 111-119, (2003).
B13. Nikolaos D. Atreas. Wavelet Decomposition and Sampling for p-adic Multiresolution Analysis. In Constructive Theory of Functions, B. Bojanov (Ed.), 198-204, DARBA, Sofia, 2003.
Book Chapters
C1. Νikolaos Αtreas. Finite Shift invariant subspaces of periodic functions: characterizations, approximations and applications. Approximation and Computation in Science and Engineering, 77-90, Springer Optim. Appl. 180, Springer, Cham, 2022. https://link.springer.com/chapter/10.1007/978-3-030-61887-2_1
C2. Νikolaos Αtreas. Sampling and approximation in shift invariant subspaces of L2(R). Harmonic Analysis and Applications, 1-19, Springer Optim. Appl. 168, Springer, Cham, 2021. https://doi.org/10.1007/978-3-030-61887-2_1
C3. Ν. Αtreas and C. Karanikas. Reducing Gibbs ripples for some wavelet sampling series. In: Advances in the Gibbs Phenomenon, Abdul J. Jerri (Ed.), Chapter 11, 335-361, Sampling Publishing, Potsdam, New York, 2011.