University of Arizona |
Department of Mathematics |
Ildar Gabitov |
MATH 485
MATH 485
Mathematical Modeling
Section 001, Spring 2018
ECON 308,
TR, 11:00am–12:15pm
Office Hours:
Tuesday 2–3pm, Wednesday 2–3pm, Thursday 10–10:50am (subject to change) and by appointment.
Homework: Will be assigned
regularly.
Syllabus
Math 485/585 modeling projects:
Past year examples midterm report ,
midterm presentation
- Field: Classical mechanics. Title: Shape of rotating chains.
- Mentor: Loren Champlin ( champlin@math.arizona.edu )
- Team members : Engel, Lily; Granzier-Nakajima, Shawn; Templin, Jasmin Sandoval; and Cutillas, Philippe
- Literature:
1) Darryl Yong, Strings, Chains, and Ropes. Society for Industrial and Applied Mathematics Vol. 48(4), pp. 771 - 781, (2006), https://www.math.hmc.edu/~dyong/papers/strings.pdf;
2) J. A. Hanna, Rotating Strings, J. Phys. A: Math. Theor., 46 235201, (2013) arXiv:1204.4941 [physics.class-ph], https://arxiv.org/pdf/1204.4941.pdf;
3) Y. Verbin, Boundary conditions and modes of the vertically hanging chain, European Journal of Physics, Volume 36(1), (2014), http://iopscience.iop.org/article/10.1088/0143-0807/36/1/015005;
4) C. Y. Wang and C. M. Wang, Exact solutions for vibration of a vertical heavy string with a tip mass, The IES Journal Part A: Civil and Structural Engineering Vol. 3, No. 4, November 2010, 278 - 281, DOI: 10.1080/19373260.2010.521623;
5) Herb Bailey, Motion of a hanging chain after the free end is given an initial velocity, American Journal of Physics 68, 764 (2000); doi.org/10.1119/1.19539;
6) Hung Pham and Quang-Cuong Pham, Robotic manipulation of a rotating chain, arXiv:1604.01507v2 [cs.RO] 5 Sep 2017
- Midterm presentation: Chavez 308, 11:00am - 11:25 am, March 13, 2018
- Midterm report:March 20, 2018
- Final presentation: Chavez 308, 11:00am - 11:18 am, April 26, 2018
- Final report: May 3, 2018
- Poster May 3, 2018
- Field: Sociology.
Title: Mathematical modeling of information confrontations in society
- Mentor: Jonathan Taylor (jtaylor@math.arizona.edu )
- Team members : Cao, Rongrong; Jiang, Steven and You II, Kaitong.
- Literature:
1) Mikhailov, A.P. & Petrov, Alexander & Proncheva, Olga. (2017). Modeling the Effect of Political Polarization on the Outcome of Propaganda Battle. COMPUTATIONAL MATHEMATICS AND INFORMATION TECHNOLOGIES. 1. 65-81. 10.23947/2587-8999-2017-1-1-65-81;
2) M. Nekovee, Y. Moreno, G. Bianconi, M. Marsili. Theory of Rumor Spreading in Complex Social Networks // Physica A. 2007. 374. pp. 457- 470;
3) Yanagizawa-Drott D. Propaganda and Conflict: Evidence from the Rwandan Genocide // The Quarterly Journal of Economics.2014 129(4). 1947-1994. Doi: 10.1093/qje/qju020;
4) Guanghua Chen, Huizhang Shen, Teng Ye, Guangming Chen, and Naphtali Kerr, A Kinetic Model f or the Spread of Rumor in Emergencies, Hindawi Publishing Corporation, Discrete Dynamics in Nature and Society, Volume 2013, Article ID 605854, 8 pages, http://dx.doi.org/10.1155/2013/605854;
5) Mikhailov A. P., Petrov A. P., Proncheva O. G., Marevtseva N. A., Mathematical Modeling of Information Warfare in a Society, Mediterranean Journal of Social Sciences, MCSER Publishing, Rome-Italy, Vol 6 No 5 S2, September 2015, Doi:10.5901/mjss.2015.v6n5s2p27.
- Midterm presentation: Chavez 308, 11:25am - 11:50 am, March 13, 2018
- Midterm report: March 20, 2018
- Final presentation: Chavez 308, 11:20am - 11:38 am, April 26, 2018
- Final report: May 3, 2018
- Poster: May 3, 2018
- Field: Physics. Title: Stability of inverted pendulum with vibrating base.
- Mentor: Ildar Gabitov ( gabitov@math.arizona.edu )
- Team members : Johnston, Jaden; Pascale, Massimo Kuo; Ridley, Evan Jacob; and Driesen, Edward Ramon
- Literature:
1) Landau L. D. & Lifshitz E. M., Mechanics, Second Edition: Volume 1, (Course of Theoretical Physics), (Oxford ; New York : Pergamon Press, 1976), pp 665-70. Oscillations of systems with more than one degree of freedom;
2) Mark Levi 1998 Nonlinearity 11 1365;
3) Shew, Woody, Inverted Equilibrium of a Vertically Driven Pendulum, wooster.edu, College of Wooster. 24 Apr, 1997. Web. 23 Mar, 2013;
4) VanDalen J., Gordon, The driven pendulum at arbitrary drive angles, arvix.org, Department of Physics at University of California and Embry-Riddle Aeronautical University. 2 Feb, 2008. Web. 24 Mar, 2013;
5) Mark Levi, (1988), Stability of the Inverted Pendulum, A Topological Explanation, Siam Review - SIAM REV. 30. 10.1137/1030140.
- Midterm presentation: Chavez 308, 11:50am - 12:15pm, March 13, 2018
- Midterm report: March 20, 2018
- Final presentation: Chavez 308, 11:40am - 11:58 am, April 26, 2018
- Final report: May 3, 2018
- Poster May 3, 2018
- Field: Electrical engineering. Title: Management of power systems with in-line renewable energy sources
- Mentor: Jared McBride ( jaredm@math.arizona.edu> )
- Team members : Shi, Haoliang; Shi, Xiaoyu; Xu, Haozhe and Yu, Ziwei.
- Literature:
1) K. Turitsyn D. Wang and M. Chertkov. \DistFlow ODE: Modeling, analyzing and controlling long distribution feeder." In: Proceedings of the 51st IEEE Conference on Decision and Control (2012). url: http://arxiv.org/abs/1209.5776;
2) M. Chertkov. K. Turitsyn S. Backhouse. \Voltage Collapse and ODE Approach to Power Flows". In: Proceedings of the 51st IEEE Conference on Decision and Control (2011). url: http://ieeexplore.ieee.org.proxylib.skoltech.ru:2048/document/6426054/pdf;
3) Anthony P. \The history of the Smart Grid evolution at Southern California Edison". In: IEEE Xplore (2010). url: http://ieeexplore.ieee.org.proxylib.skoltech.ru: 2048/stamp/stamp.jsp?arnumber=5434757;
4) Enerdata. Electricity production. Global Energy Statistical Yearbook. url: https://yearbook. enerdata.net/world-electricity-production-map-graph-and-data.html;
5) John Stark Henry; Woods. Probability and Random Processes with Applications to Signal Processing. New Jersey: Prentice Hall., 2002. isbn: 0-13-020071-9
.
- Midterm presentation: Chavez 308, 11:00am - 11:25 am, March 15, 2018
- Midterm report: March 20, 2018
- Final presentation Chavez 308, 12:00pm - 12:20 pm, April 26, 2018
- Final report: May 3, 2018
- Poster May 3, 2018
- Field: Mathematics for Text Analysis. Title: Network theory and text analysis.
- Mentor: Jerry Luo (jerryluo@math.arizona.edu )
- Team members : Martins, Taylor Michael; West, Christina; and Hao, Yihe.
- Literature:
1) Padraig Mac Carron and Ralph Kenna, Universal properties of mythological networks, EPL, 99 (2012) 28002, doi: 10.1209/0295-5075/99/28002;
2) M.E.J. Newman, Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002);
3) David Easley and Jon Kleinberg, "Positive and negative relationships," in Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge University Press, 2010;
4) Anand, Ashish, "Complex Network Theory: An Introductory Tutorial," Department of Computer Science and Engineering, Indian Institute of Technology, Guwahati. 12 Sept. 2013. Lecture;
- Midterm presentation: Chavez 308, 11:00am - 11:25 am, March 20, 2018
- Midterm report: March 20, 2018
- Final presentation: Chavez 308, 11:00am - 11:18 am, May 1, 2018
- Final report: May 3, 2018
- Poster May 3, 2018
- Field: Sociology. Title: Modeling Risk in Sociology through Graph Theory and Textual Analysis
- Mentor: William Lippitt (wlippitt@email.arizona.edu )
- Team members : Reeves, Hailey Elizabeth; Brown, Evan Bernard Reiter.
- Literature:
1) Kyunghoon Kim, Mathematical approach for Text Mining, https://www.slideshare.net/koorukuroo/latent-semantic-indexing-37044490;
2) Naoki Saito, Applied Linear Algebra: Text Mining, https://www.math.ucdavis.edu/~saito/courses/167.s12/Lecture22.pdf ;
3) Julia Silge and David Robinson, Text Mining with R, Publisher: O'Reilly Media; 1 edition (July 2, 2017), ISBN - 10: 1491981652 (https://www.tidytextmining.com/topicmodeling.html)
4) Jeffrey L. Solka, Text Data Mining: Theory and Methods, Statistics Surveys Vol. 2 (2008) 94 - 112 ISSN: 1935-7516 DOI: 10.1214/07-SS016
5) ,Padraig Mac Carron and Ralph Kenna, Universal properties of mythological networks, EPL, 99 (2012) 28002, doi: 10.1209/0295-5075/99/28002;
6) M.E.J. Newman, Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002);
7) David Easley and Jon Kleinberg, "Positive and negative relationships," in Networks, Crowds, and Markets: Reasoning about a Highly Connected World, Cambridge University Press, 2010;
8) Anand, Ashish, "Complex Network Theory: An Introductory Tutorial," Department of Computer Science and Engineering, Indian Institute of Technology, Guwahati. 12 Sept. 2013. Lecture;
- Midterm presentation (pdf): Chavez 308, 11:25am - 11:50 am, March 15, 2018
- Midterm report: March 20, 2018
- Final presentation: Chavez 308, 11:20am - 11:38 am, May 1, 2018
- Final report: May 3, 2018
- Poster May 3, 2018
- Field: Machine Learning. Title: Neural Network Recommendation Algorithm.
- Mentor: Joseph Gibney (jgibney@math.arizona.edu )
- Team members : Caputo, Tristan Emile; Lenharth, Paul Thomas; and Ludington, River Joel.
- Literature: 1) Christopher M. Bishop, Neural Networks for Pattern Recognition, Clarendon Press; 1 edition (January 18, 1996), ISBN-10: 0198538642, ISBN-13: 978-0198538646;
2) Ivens Portugal, Alencar Alencar, Donald Cowan (2018). The use of machine learning algorithms in recommender systems: A systematic review. UWSpace.http://hdl.handle.net/10012/12797
- Midterm presentation: Chavez 308, 11:50am - 12:15pm, March 15, 2018
- Midterm report: March 20, 2018
- Final presentation: Chavez 308, 11:40am - 11:58 am, May 1, 2018
- Final report: May 3, 2018
- Poster May 3, 2018
- Field: Biology Title: Multistability in biological systems
- Mentor: J. Ruby Abrams (rabrams12@math.arizona.edu )
- Team members : Smith, Katherine Jane; Nakonechny, Lauren Nicole; Volk, Michael; and Wallace, Rob Wallace .
- Literature: 1) Ertugrul M. Ozbudak , Mukund Thattai1 , Han N. Lim1,, Boris I. Shraiman & Alexander van Oudenaarden , NATURE |VOL 427 | 19 FEBRUARY 2004;2) Ferrell, J. E. Jr & Machleder, E.M. The biochemical basis of an all-or-none cell fate switch in Xenopus
oocytes. Science 280, 895 - 898 (1998); 3) Pomerening, J. R., Sontag, E. D. & Ferrell, J. E. Jr Building a cell cycle oscillator: hysteresis and
bistability in the activation of Cdc2. Nature Cell Biol. 5, 346 - 351 (2003); 4) Sha,W. et al.Hysteresis drives cell-cycle transitions in Xenopus laevis egg extracts. Proc. Natl Acad. Sci.
USA 100, 975 - 980 (2003); 5) Hernday, A., Braaten, B. A. & Low, D. The mechanism by which DNA adenine methylase and PapI activate the pap epigenetic switch. Mol. Cell 12, 947-957 (2003).
- Midterm presentation: Chavez 308, 11:25am - 11:50am, March 20, 2018
- Midterm report: March 20, 2018
- Final presentation: Chavez 308, 12:00pm - 12:20 pm, May 1, 2018
- Final report: May 3, 2018
- Poster May 3, 2018