2009Summer
Synchronization in biological systems
-------------------------------------
Synchronization phenomena are the subject of research in physical, biological, chemical, and social systems [1],[2],[3].
Mathematical description of such system were started by Winfree, Kuramoto and others.
Kuramoto
proposed the model of collective oscillations there each of the
oscillators is considered to have its own intrinsic natural frequency
ωi, and each is coupled to all other oscillators.
Depending on the distribution of natural frequencies, different synchronization scenarios can occur.
If the coupling strength exceeds a certain threshold, the system exhibits a phase transition:
some of the oscillators spontaneously synchronize, while others remain incoherent.
Noise may play a dual role in such systems: it may contribute to resonance (stochastic resonance) or prevent it.
Examining the role of noise in synchronization process is a relatively new area of research.
Noise dominates biochemical systems with a small number of molecules because of the intrinsically
stochastic nature of the reactions involved.
In this project I am planning to develop analytical methods and numerical
simulation for studying the influence of noise (Gaussian and
non-Gaussian) on collective synchronization.
[1] http://scala.uc3m.es/publications_MANS/PDF/finalKura.pdf
[2] http://lpmt090.biomed.uni-erlangen.de/~cmetzner/KomplexeSysteme/026_Synchronisation/kalay07_KuramotoReview.pdf
[3] http://www.ploscompbiol.org/article/info:doi%2F10.1371%2Fjournal.pcbi.1000314
http://sgtnd.narod.ru/publ/rus/index.htm
http://www.unn.ru/pages/issues/aids/2006/16.pdf
http://eqworld.ipmnet.ru/ru/library/theses/mathematics.htm
http://cas.ssu.runnet.ru/book_int/index.htm
http://www.rtindex.ru/s/synhrooscillator.html
http://www.rtindex.ru/s/svyazannye_mayatniki.html
http://sgtnd.narod.ru/science/cml/physys/rus/physys.htm
http://www.nonlin.ru/node/467
http://www.dissers.info/disser_112951.html
http://www.nnspu.ru/Exponenta_Ru/educat/systemat/porshnev/forced_oscs/main.asp.htm
http://ru.wikipedia.org/wiki/%D0%93%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B8%D0%B9_%D0%BE%D1%81%D1%86%D0%B8%D0%BB%D0%BB%D1%8F%D1%82%D0%BE%D1%80
http://www.matheon.de/research/show_project.asp?id=139
http://www.amath.washington.edu/~etsb/
http://www.iop.org/EJ/journal/0951-7715
http://www.math.hu-berlin.de/~yanchuk/pub.html
http://www.masters.donntu.edu.ua/2001/fvti/kuznetsov/diss/lib/neuroosc/2_1_full.htm
http://www.iop.org/EJ/abstract/0295-5075/73/3/328
http://www.math.pitt.edu/~ccc/htdocs/publications.html
http://sciencehouse.wordpress.com/2009/01/17/kinetic-theory-of-coupled-oscillators/
http://tutorials.siam.org/dsweb/cotutorial/index.php?s=5&p=1
http://www.dynamicalsystems.org/tu/tu/
http://chaos.ssu.runnet.ru/nld/khovanov/publications.html Khovanov
Mathematical Models of DNA and Polymer Dynamics
http://www.mat.unimi.it/users/gaeta/mmxdd.html
http://flux.aps.org/meetings/YR01/MAR01/abs/S7730.html
http://thebrain.mcgill.ca/flash/i/i_12/i_12_cl/i_12_cl_con/i_12_cl_con.html
The Division of Graduate Studies and the Office of Summer Session are
pleased to announce the continued availability of a low-cost Summer
Registration program designed specifically for graduate students wishing to
pursue Individual Studies over the summer.
To enroll in this program, you will need to complete both the Petition for
Graduate Individual Studies and the 2009 Summer Session Registration form.
Both forms can be found at the Graduate Studies website. The basic course
fee is $100 for students who do not need a summer ID card. For an
additional $235, you can purchase an ID card which serves as a bus pass and
as an entry pass to the physical education and recreation facilities. These
fees are payable by cash, eCheck, check, Visa, MasterCard, or Discover;
neither fee deferments nor recharges are permitted. You must file the
Registration Form and the completed Petition with the Summer Office and pay
all fees no later than Tuesday, June 30.
Most Graduate Student Researchers, and all doctoral students advanced to
candidacy, will presumably sign up for a 299 (Thesis Research) course with
their dissertation director, while a 297 (Independent Study) course will be
more appropriate for most other students. Summer Registration enrollment
begins April 20 and continues through Tuesday, June 30; be sure to approach
your prospective Individual Studies sponsor early, since some faculty may
not be available during the summer.
Students in need of additional financial support for the summer and who have
qualified for student loans during the current academic year and have
remaining loan eligibility, should submit the completed summer session
registration form to the Summer Session Office and then apply for financial
aid no later than June 27. Eligibility for additional loans is dependent
on annual statutory loan limits and a student's total budget as calculated
by the Financial Aid Office, less other aid and resources that the student
receives.
Please direct any questions that you may have to Jim Moore of the Graduate
Studies staff (extension 2335; jimmoore@ucsc.edu) or Cheryl Becking of the
Summer Session staff (extension 3783, cbecking@ucsc.edu).
Beginning this summer, 2009, the process for hiring TA's for summer classes will change and will mirror the process used in the fall/winter/spring quarters. Each academic department will determine who will serve as a TA for the courses offered in their discipline.
Interested graduate students should fill out the "Summer 2009 TA Application" form (pdf included here) and submit it to the appropriate department no later than Friday, May 22. Please fill out only one application per discipline listing the courses you are qualified to TA and indicate your preference if listing more than one course. The academic departments will determine the assignments and forward those names to the Summer Session Office. Cheryl Becking in the Summer Session Office will contact the graduate student if the course is approved for a TA and will then process the TA appointment letter and handle the hiring. These notifications may occur as late as the week prior to the start of a session as enrollments may not be sufficient until late in the enrollment period. All TA appointments must be approved by an academic department before a graduate student will be hired by Summer Session for a TA position.
NOTE: There are some departments that have used their own application and selection process for the summer for several years. For the following departments, please contact the department manager if you are interested in serving as a TA this summer: Chemistry, Economics, Physics.
For a list of courses that MAY be approved for a TA this summer, please see summer.ucsc.edu/teaching_assistants.html (The application form is available at this link as well). These are projections only and are not guarantees of positions that will be available. Please check this list often as additional courses may be added if enrollments warrant. While the academic department may forward your name for a TA assignment for a class, it is the final decision of the Summer Session office whether a class will be approved for a TA.
Please contact me at pvani@ucsc.edu if you have any questions. We look forward to working with you this summer.
Pat Vani