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Ahmet Duran

Professor

Department of Mathematical Engineering, Istanbul Technical University, 34469 Maslak, Istanbul

Email: aduran  [no spam]  itu (dot) edu (dot) tr    Phone: +90 (212) 285-3273

Ph.D, Mathematics, University of Pittsburgh

M.S., Computer & Information Sciences, College of Engineering, University of Delaware

M.A., Mathematics, School of Arts & Sciences, University of Pittsburgh

M.S., Mathematics, Middle East Technical University (METU), Turkey

B.S., Mathematics, METU

In the News 

Main Research Interests Applied mathematics, ordinary, partial, and stochastic differential equations, nonlinear differential equations, high performance computing, mathematical finance and economics, quantitative behavioral finance, numerical linear algebra, data analysis, computational finance, optimization, numerical analysis, mathematical modeling, machine learning, networking algorithms and simulation

Appointments

  • Professor, Mathematical Engineering, Istanbul Technical University, 2020 - Present

  • Associate Professor, Mathematics, Istanbul Technical University, 2012 - 2020

  • Assistant Professor, Mathematics, Istanbul Technical University, 2010 - 2012

  • Assistant Professor, Mathematics, University of Michigan at Ann Arbor, 2006 - 2010

  • Graduate Student Researcher, Mathematics, University of Pittsburgh, (May - Aug.) 2005, 2006

  • Teaching Assistant/Fellow, Mathematics, University of Pittsburgh, 2000 - 2001, 2003 - 2006

  • Teaching Assistant, Computer & Information Sciences, University of Delaware, (June - Aug.) 2003

  • Research Assistant, Computer & Information Sciences, University of Delaware, 2001 - 2003

  • Research Assistant, Mathematics, Middle East Technical University, 1995 - 1997

Professional Activities

  • Committee member, SPE & SIAM Conference, Large Scale Computing and Big Data Challenges in Reservoir Simulation Conference and Exhibition, Istanbul, Turkey, September 15-17, 2014

  • Chair, International Conference on Mathematical Finance and Economics, ITU, Istanbul, Turkey, July 6-8, 2011; Editor of Abstracts Book and Proceedings of the International Conference on Mathematical Finance and Economics (ICMFE 2011)

  • Contact person of Turkey for Work Package 7 (WP7) in EU PRACE 1IP project (The Partnership for Advanced Computing in Europe - First Implementation Phase Project), 2013

  • Contact person of Turkey for Work Package 12 (WP12) in EU PRACE 2IP project, 2011-2014

  • Contact person of Turkey for Work Package 7 (WP7) in EU PRACE 3IP project, 2012-2014

  • Committee member, SPE & SIAM Conference on Mathematical Methods in Fluid Dynamics and Simulation of Giant Oil and Gas Reservoirs, Istanbul, Turkey, September 3-5, 2012 

  • Scientific Steering Committee member, SIAM & Gulf International Conference on Applied Mathematics (GICAM 13), Nov. 19-21, 2013

  • Session chair, Big Data Discovery and Impact on Decision Making, SPE & SIAM Conference, Istanbul, Turkey, September 15-17, 2014

  • Minisymposium organizer, Advances in Financial Mathematics, World Congress of Nonlinear Analysts (WCNA), Orlando, FL, July 2008

  • Invited session chair, Finance, SIAM Conference on Computational Science & Engineering, Costa Mesa, CA, Feb. 19-23, 2007

  • Minisymposium organizer, New Horizons in Quantitative Methods for Finance and Economics, SIAM Conference on Financial Mathematics and Engineering, Boston, MA, July 2006

  • Referee for Journal of Computational and Applied Mathematics - Elsevier; Quantitative Finance - Taylor & Francis; Mathematics of Operations Research - Informs; Optimization Methods and Software - Taylor & Francis; Mathematical Modelling and Analysis; Hacettepe Journal of Mathematics and Statistics; Journal of Supercomputing - Springer; Concurrency and Computation: Practice and Experience - Wiley; Expert Systems with Applications - Elsevier; Mobile Ad Hoc Wireless Networks in the Journal of Communications and Networks (JCN); Ad Hoc Networks - Elsevier; IEEE Wireless Communications & Networking Conference (WCNC)

  • Referee for projects - The Scientific and Technological Research Council of Türkiye (TÜBİTAK); US National Science Foundation; US Department of Energy project (2,000,000 USD), EU PRACE

  • Book reviewer

    • Pearson Addison-Wesley, T. Sauer Numerical Analysis 2nd edition

    • MIT Press, Introduction to Quantitative Finance

    • Wiley-Blackwell, Introduction to Financial Economics, Fabozzi Series

Directed Doctoral Theses and Students

  • Burhaneddin Izgi, Ph.D. student, graduated in 2015, currently Associate Professor at ITU

  • Furkan Goktas, Ph.D. student, graduated in 2019, currently Assistant Professor at Karabuk University

  • Mehmet Tuncel, Ph.D. student, graduated in 2023, currently at ITU

  • H. Unsal Ozer, Ph.D. student

Selected International Journal Papers (SCI)

  1. M. Tuncel and A. Duran, Effectiveness of grid and random approaches for a model parameter vector optimization, Journal of Computational Science, Vol. 67, 2023, 101960 DOI: https://doi.org/10.1016/j.jocs.2023.101960

  2. A. Duran and M. Farrukh, Multiple regression analysis for dynamics of patient volumes, Communications in Statistics - Simulation and Computation, 51(6), 2022, pp. 2906-2923, DOI: 10.1080/03610918.2019.1704419, cited by 1 , Taylor & Francis line

  3. A. Duran, Stability analysis of asset flow differential equations, Applied Mathematics Letters, 24(4), 471-477, 2011, doi: 10.1016/j.aml.2010.10.044, download, cited by 7, Elsevier link

  4. A. Duran and G. Caginalp, Parameter optimization for differential equations in asset price forecasting, Optimization Methods & Software, Vol. 23, Issue 4: Mathematical programming in data mining and machine learning, 2008, pp. 551-574, download, cited by 15, Taylor & Francis link

  5. A. Duran and B. İzgi, Application of the Heston stochastic volatility model for Borsa Istanbul using impression matrix norm, Journal of Computational and Applied Mathematics, 281, 2015, pp. 126-134, DOI 10.1016/j.cam.2014.12.020 Elsevier link

  6. A. Duran and G. Caginalp, Overreaction diamonds: Precursors and aftershocks for significant price changes, Quantitative Finance, 7(3), 2007, pp. 321-342, download, cited by 40, Taylor & Francis line

  7. M.J. Bommarito and A. Duran, Spectral analysis of time-dependent market-adjusted return correlation matrix, Physica A, 503, 2018, pp. 273-282 cited by 8, Elsevier link

  8. B. İzgi and A. Duran, 3D extreme value analysis for stock return, interest rate and speed of mean reversion, Journal of Computational and Applied Mathematics, 297, 2016, pp. 51-64, DOI: 10.1016/j.cam.2015.10.009 cited by 11,  Elsevier link

  9. A. Duran, M.S. Celebi, S. Piskin, and M. Tuncel, Scalability of OpenFOAM for Bio-medical Flow Simulations, Journal of Supercomputing, 71(3), 2015, pp. 938-951, DOI 10.1007/s11227-014-1344-1 download, cited by 22, Springer link.

    • This work was financially supported by the PRACE Project funded in part by the EUs 7th Framework Programme under Grant agreement No. RI-312763, (see PRACE white paper WP 162 for an early version, June 9, 2014)

  10. M.S. Celebi, A. Duran, F. Oztoprak, M. Tuncel, and B. Akaydin, On the improvement of a scalable sparse direct solver for unsymmetrical linear equations, Journal of Supercomputing, 73, 2017, pp. 1852-1904, DOI:10.1007/s11227-016-1892-7 cited by 3, Springer link

  11. A. Duran and M.J. Bommarito, A profitable trading and risk management strategy despite transaction costs, Quantitative Finance, 11(6), 2011, pp. 829-848, doi: 10.1080/14697680903449815, cited by 18, key paper

  12. H.U. Ozer and A. Duran, The source of error behavior for the solution of Black-Scholes PDE by finite difference and finite element methods, Int. Journal of Financial Engineering, Vol. 05 No. 03, 2018, pp. 1850028 1-22 https://doi.org/10.1142/S2424786318500287  download World Scientific link

  13. A. Duran, Sensitivity analysis of asset flow differential equations and volatility comparison of two related variables, Numerical Functional Analysis and Optimization, 30(1), 2009, pp. 82-97, download, cited by 9 , Taylor & Francis link

  14. F. Goktas and A. Duran, A new possibilistic mean-variance model based on the principal component analysis: An application on the Turkish holding stocks, Journal of Multiple-Valued Logic and Soft Computing, Vol. 32 Issue 5-6, 2019, pp. 455-476 cited by 1, download

  15. L.S. Kabbani, G. A. Escobar, B. Knipp, C.B. Deatrick, A. Duran, G.R. Upchurch, L.M. Napolitano, APACHE III score on ICU admission predicts hospital mortality after open thoraco-abdominal and open abdominal aortic aneurysm repair, Annals of Vascular Surgery, 24(8), 2010, pp. 1060-1067, doi:10.1016/j.avsg.2010.07.011, cited by 11, Elsevier link

  16. F. Goktas and A. Duran, New robust portfolio selection models based on the principal component analysis: An application on the Turkish holding stocks, Journal of Multiple-Valued Logic and Soft Computing, Vol. 34, 2020, pp. 43-48 cited by 2, download

    Refereed International Proceedings Papers

  17. A. Duran ve M. Tuncel, Evaluation of a new parallel numerical parameter optimization algorithm for a dynamical system, Proceedings of the 2nd International Conference Numerical Computations: Theory and Algorithms (NUMTA2016), Italy, 19-25 June 2016, AIP Conference Proceedings 1776, 090052 (2016), doi: 10.1063/1.4965416 download, cited by

  18. A. Duran, S. Piskin, and M. Tuncel, Evaluating the maturity of OpenFOAM simulations on GPGPU for bio-fluid applications, Proceedings of the Emerging Technology (EMiT) Conference, pp. 11-14, Barcelona Supercomputing Center, Spain, 2-3 June 2016, editors: B.D.Rogers, D.Topping, F.Mantovani, M.K.Bane. ISBN 978-0-9933426-3-9 download, cited by 1

  19. M. Tuncel, A. Duran, M. S. Celebi, B. Akaydin, ve F. O. Topkaya, A comparison of superlu solvers on the intel mic architecture, Proceedings of the 2nd International Conference Numerical Computations: Theory and Algorithms (NUMTA2016), Italy, 19-25 June 2016, AIP Conference Proceedings 1776, 090030 (2016), doi: 10.1063/1.4965394 download, cited by

  20. I. Mazza, A. Duran, Y. Hundur, C. Persi, A. Santoro, and M. Tuncel, Scalability of OpenFOAM for Simulations of a Novel Electromagnetic Stirrer for Steel Casting, Proceedings of the 2016 International Conference on Parallel and Distributed Processing Techniques and Applications (PDPTA'16), World Congress in Computer Science, Computer Engineering & Applied Computing, pp. 111-116, ISBN: 1-60132-444-8, CSREA Press, July 25-28, 2016, Las Vegas, USA download, cited by 1

  21. A. Duran and M. Tuncel, Spectral Effects Of Large Matrices From Oil Reservoir Simulators On Performance Of Scalable Direct Solvers, OnePetro, 172984 SPE Paper - 2014, download , SPE Link

  22. A. Duran and B. İzgi, Solution behavior of Heston model using impression matrix norm, Advances in Applied Mathematics, Springer Proc. in Mathematics & Statistics 87, 215-221, Springer Switzerland, 2014

  23. A. Duran and B. İzgi, Comovement and polarization of interest rate and stock market in Turkey, Borsa İstanbul Finance & Economics Conference (BIFEC) 2013 "Policy Issues and Challenges in the Global Financial System and Economies", BIFEC Book of Abstracts & Proceedings, Volume 1, Issue II, 130-141, Istanbul, March 2014

  24. A. Duran, M.S. Celebi, M. Tuncel and F. Oztoprak, Spectral Analysis of Large Sparse Matrices for Scalable Direct Solvers, Advances in Applied Mathematics, Springer Proceedings in Mathematics & Statistics 87, pp. 153-160, 2014. DOI 10.1007/978-3-319-06923-4__14 (see PRACE-2IP white paper, Scalable Algorithms, WP 82, for an early version, August 20, 2013 download )

  25. A. Duran and G. Caginalp, Data mining for overreaction in financial markets, Proceedings of the IASTED International Conference on Software Engineering and Applications (SEA), Phoenix, AZ, vol. 467, Nov. 14-16, 2005, pp. 28-35, download, cited by 9

  26. A. Duran and C. Shen, Mobile ad hoc p2p file sharing, Proceedings of IEEE Wireless Communications and Networking Conference (WCNC), Atlanta, GA, vol. 1, Mar. 21-25, 2004, pp. 114-119, download , google, cited by 64

  27. A. Duran, B. D. Saunders and Z. Wan, Hybrid algorithms for rank of sparse matrices, Proceedings of the SIAM International Conference on Applied Linear Algebra (SIAM-LA), Williamsburg, VA, July 15-19, 2003, 12 pages, cited by 14

    National Journal Papers

  28. A Duran, M Tuncel, HU Ozer, GPU Programlama ile Yuksek Boyutlu Yogun Matrislerin Kronecker Carpimlarinin Hesaplanmasi, Erciyes Universitesi Fen Bilimleri Enstitusu Fen Bilimleri Dergisi 36 (1), 2020, pp 119-127 download

  29. F. Goktas and A. Duran, Olabilirlik ortalama-varyans modelinin matematiksel analizi, Balikesir Universitesi Fen Bilimleri Enstitusu Dergisi 22 (1), 2020, pp 80-91  download

Theses

  1. Asymptotic Behavior of Solutions of Semilinear Heat Equations with Source, Master's thesis, Middle East Technical University, Ankara, Turkey, Sep. 1998, 101 pages

  2. Overreaction Behavior and Optimization Techniques in Mathematical Finance, PhD thesis, University of Pittsburgh, Pittsburgh, PA, Aug. 1st 2006, 128 pages, cited by 15

Research Projects

  1. Parallel Algorithm (Kernel) Development for Large Scale Sparse Linear Systems in Oil Reservoir Simulation (PASSOR), Project PI, Computational Linear Algebra Project for ARAMCO Overseas, July 1, 2012-2017.

  2. Scalable Parallel Nonlinear Parameter Optimization Algorithm with Parameter Pools, PRACE-2IP WP12 T12.2, Project PI, Sept. 2013 - Aug. 2014  Project closure report:  https://doi.org/10.5281/zenodo.825430

  3. Scalability of OpenFOAM for Bio-medical Flow Simulations, PRACE-3IP WP7 T7.2, Project PI, Sept. 2012 - Aug. 2014 Project closure report: https://doi.org/10.5281/zenodo.822968

  4. HPC-based Design of a Novel Electromagnetic Stirrer for Steel Segment Casting, in EU Horizon 2020 - PRACE 4IP, Project Co-PI, 2015 - 2016 Project closure report: https://doi.org/10.5281/zenodo.825968.

  5. Analysis of SuperLU Solvers on the Intel MIC Architecture, PRACE-1IP WP7 T7.1, Project PI,  2013 Project closure report: https://doi.org/10.5281/zenodo.822644

  6. Several Research Topics in Mathematical Finance and Economics, University of Michigan-Ann Arbor, Assistant Professor, Spring/Summer 2008

  7. ITR/ASC: Collaborative Research, Linbox: A Generic Library for Seminumeric Black Box Linear Algebra,  National Science Foundation (NSF) Grant CCR-0112807, Research Assistant, USA, 2001-2003

  8. Exact Computation in Sparse Linear Algebra, NSF Grant CCR-0098284, Research Assistant, USA, 2001-2003 

  9. Modeling in Mathematical Finance and Economics, research projects for International Foundation for Research in Experimental Economics (IFREE) and LGT Capital Management, Graduate Student Researcher, USA, 2005-2006

  10. Design and implementation of new hybrid algorithm and solver on CPU for large sparse linear systems, PRACE-2IP (The Partnership for Advanced Computing in Europe - Second Implementation Phase Project, persistent pan-European Research Infrastructure for High Performance Computing) WP12 T12.2, 2011 - 2013 Project closure report:  https://doi.org/10.5281/zenodo.810699

  11. Scalable and improved SuperLU on GPU for heterogeneous systems, PRACE-2IP WP12 T12.2, Project Co-PI, 2011 - 2013

  12. Structural Analysis of Large Sparse Matrices for Scalable Direct Solvers, PRACE-2IP WP12 T12.2, Project PI,  2011 - 2013 Project closure report: https://doi.org/10.5281/zenodo.831525

  13. Performance Analysis of BLAS Libraries in SuperLU_DIST for SuperLU_MCDT (Multi Core Distributed) Development, PRACE-2IP WP12 T12.2, Project Co-PI, 2011 - 2013

  14. Default and Asset Correlation, project for Risk Metrics, University of Pittsburgh, Graduate Student, 2003

Peer-Reviewed Research Project White Papers (Proje Resmi Kapanma Yazilari)

  1. I. Mazza, A. Duran, Y. Hundur, C. Persi, A. Santoro, and M. Tuncel, HPC-based Design of a Novel Electromagnetic Stirrer for Steel Segment Casting, in EU Horizon 2020 - PRACE 4IP, white paper, WP214, April 2016, Project closure report: https://doi.org/10.5281/zenodo.825968 download

  2. A. Duran, M.S. Celebi, S. Piskin, and M. Tuncel, Scalability of OpenFOAM for Bio-medical Flow Simulations,  PRACE PN: RI-312763, PRACE-3IP white paper, Application scalability: Computational Fluid Dynamics (CFD) applications, WP 162, June 9, 2014, Project closure report: https://doi.org/10.5281/zenodo.822968

  3. A. Duran and M. Tuncel, Scalable Parallel Nonlinear Parameter Optimization Algorithm with Parameter Pools, PRACE PN: 283493, PRACE-2IP Extension white paper, Scalable Algorithms, WP 185, August 11, 2014, Project closure report:  https://doi.org/10.5281/zenodo.825430 download

  4. A Report on Summary of Novel Programming Techniques Results, D12.5, PRACE (Partnership for Advanced Computing in Europe), PRACE PN:RI-283493, PRACE-2IP Extension, August 31, 2014, Project closure report: https://doi.org/10.5281/zenodo.6572440 download

  5. Exploitation of HPC Tools and Techniques, D7.2.2, PRACE (Partnership for Advanced Computing in Europe), PRACE PN: RI-312763, PRACE-3IP, May 24, 2014, https://doi.org/10.5281/zenodo.6575526 download

  6. A. Duran, M.S. Celebi, B. Akaydin, M. Tuncel and F. Oztoprak, Analysis of SuperLU Solvers on the Intel MIC Architecture, PRACE PN: 261557, PRACE-1IP Extension white paper, Evaluations on Intel MIC, WP 135, December 25, 2013, Project closure report: https://doi.org/10.5281/zenodo.822644 download

  7. A Report on Application Enabiling for Capability Science in the MIC Architecture, D7.1.3, PRACE (Partnership for Advanced Computing in Europe), PRACE PN: RI-261557, PRACE-1IP, December 13, 2013, https://doi.org/10.5281/zenodo.6553059 download

  8. A. Duran, M.S. Celebi, M. Tuncel and F. Oztoprak, Structural Analysis of Large Sparse Matrices for Scalable Direct Solvers, PRACE PN: 283493, PRACE-2IP white paper, Scalable Algorithms, WP 82, August 20, 2013, Project closure report: https://doi.org/10.5281/zenodo.831525 download

  9. M.S. Celebi, A. Duran, M. Tuncel, B. Akaydin and F. Oztoprak, Performance Analysis of BLAS Libraries in SuperLU_DIST for SuperLU_MCDT (Multi Core Distributed) Development, PRACE PN: 283493, PRACE-2IP white paper, Libraries, WP 83, August 20, 2013, Project closure report: https://doi.org/10.5281/zenodo.831527 download

  10. D7.2.1 A Report on the Survey of HPC Tools and Techniques, PRACE (Partnership for Advanced Computing in Europe), PRACE PN: RI-312763, PRACE-3IP , April 29, 2013, Project closure report: https://doi.org/10.5281/zenodo.6575492 download

  11. A. Duran, M.S. Celebi, M. Tuncel and B. Akaydın, Design and implementation of new hybrid algorithm and solver on CPU for large sparse linear systems, PRACE (Partnership for Advanced Computing in Europe), PRACE PN: 283493, PRACE-2IP white paper, Libraries, WP 43, July 13, 2012, Project closure report: https://doi.org/10.5281/zenodo.810699 download

  12. M.S. Celebi, A. Duran, M. Tuncel and B. Akaydın, Scalable and improved SuperLU on GPU for heterogeneous systems, PRACE (Partnership for Advanced Computing in Europe), PRACE PN: 283493, PRACE-2IP white paper, Libraries, WP 44, July 13, 2012, Project closure report: https://doi.org/10.5281/zenodo.815126 download

Software Development

  1. A. Duran and B.D. Saunders, Gen_SuperLU package (version 1.0, August 2002), referenced as GSLU also, a part of LinBox package. GSLU contains a set of subroutines to solve a sparse linear system A*X=B over any field

  2. A. Duran and B.D. Saunders, GenBLAS. Generic Basic Linear Algebra Subroutines in C++, 2002. You can download and use GenBLAS  version 1.0 for academic purpose only, by giving  reference

Other Publications

  1. A. Duran and B.D. Saunders, GenBLAS: Basic linear algebra subroutines in C++ over any fields, poster, East Coast Computer Algebra Day, Association for Computing Machinery (ACM) SIGSAM Bulletin, Communications in Computer Algebra 36(3), pp. 6, New York, NY, 2002

  2. L. Cheng, A. Duran, S.N. Predoiu, and A. Yu, Asset correlation implied by historical default data, working paper, University of Pittsburgh, December 2003, after completion of the project for "Risk Metrics", 22 pages

  3. A. Duran, D. Saunders, and Z. Wan, Rank of sparse {0, 1} matrices, poster, East Coast Computer Algebra Day, Clemson University, Clemson, SC, Apr. 5, 2003

Invited Talks

  1. Courant Institute of Mathematical Sciences, New York University, March 9, 2010

  2. A multi-start approach for parameter optimization of asset flow differential equations, AMS Special Session on Financial Mathematics, Indiana University, Bloomington, IN, April 5-6, 2008

  3. Solution Behavior of Heston Model Using Impression Matrix Norm, Koc University, Department of Mathematics,  November 11, 2014

  4. Stability analysis of asset flow differential equations, Colloquium Talk, Koc University, Department of Mathematics,  May 26, 2011

  5. Computational parameter optimization and differential equations in asset price forecasting, Bogazici University Mathematics Colloquium, Turkey, July 11, 2007

  6. Bilkent University, Faculty of Business Administration, Ankara, September 4, 2009

  7. Sabancı University, Faculty of Management, İstanbul, September 3, 2009

  8. Panelist, Turkish Offshore Hydrocarbon Energy Panel, Turkiye Offshore Energy Conference, ITU, SDKM, June 19-21, 2013

  9. Algorithmic Thinking of Gifted and Talented People, 2. Gifted Education Days, ITU, April 26, 2014

  10. Istanbul Commerce University, Department of Mathematics,  March 12, 2014 

  11. What is quantitative behavioral finance?, ITU Finance Days, December 15-16, 2010

  12. Stability analysis for a high-dimensional dynamical system of stochastic differential equations,  Applied and Interdisciplinary Mathematics Seminar, University of  Michigan, Dept. of Mathematics, April 2, 2010

  13. Financial Engineering Practitioners Seminar, University of  Michigan, February 12, 2010, 1210 Ross School of Business

  14. Mathematical modeling in health economics during economic crisis, Financial/Actuarial Mathematics Seminar, University of  Michigan, Dept. of Mathematics, December 4, 2009

  15. Spectral analysis in mathematical finance, Financial/Actuarial Mathematics Seminar, University of  Michigan, Dept. of Mathematics, March 27, 2008

  16. Computational parameter optimization and differential equations for stock markets, Financial/ Actuarial Mathematics Seminar, University of Michigan, Dept. of Mathematics, September 21, 2006

  17. Overreaction and computational optimization in stock markets, University of Michigan, Dept. of Mathematics, August 28, 2006

Conference Presentations

Awards & Honors

  • Spring/Summer 2008 Research Fellowship award by the Department of Mathematics at the University of Michigan-Ann Arbor

  • B.S. in Mathematics, with rank in class: 2nd among 159 students, Middle East Technical University, 1995

  • SIAM Early Career Award, SIAM Conference on Optimization 2008, Boston, Massachusetts

  • University of Delaware offered teaching assistantship. Exceptional score, 300 out of 300, from Instructional Assessment (UDIA) for Teaching Assistants, 2001

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