Math 247B Topics in Analysis, Winter 2008

Main Lecture:

MWF 3:00p to 4:30 APM 6218

Instructor: J. William Helton

Main topic is ODE with monotonicity properties
in particular Chemical Networks.
We may do some control later.
A reference for the Chemistry is the book
"Systems Biology" by Bernhard Palsson (of UCSD)
We will use mostly the notation in his book.
A reference for the first day or so of the math is

http://arxiv.org/abs/0711.1552

It also has Chem examples which will give you a little idea
of what some diffeqs look like.

There are two main results in the area I want to focus on and
hopefully extend. They count numbers of equilibria under the hypotheses:

(1) DET JACOBIAN OF THE DYNAMICS HAS ONE SIGN.
A new proof is in the reference above.

OR

(2) THE CLASSICAL DEFICIENCY ZERO THEOREM

See

Chemical Reaction Network Theory for in-silico Biologists

by Jeremy Gunawardena
[Lecture notes. 20 June 2003. PDF.]
obtainable from
Gunawardena web page

Toric dynamical systems G.Craciun, A.Dickenstein, A.Shiu, Sturmfels

A strong paper on deficiency 0
Subnetwork Analysis ...
Conradi ... Stelling

We will meet in several groups on SPECIAL TOPICS:

NONCOMMUTATIVE REAL ALGEBRAIC GEOMETRY: Greene, Klep

DIFFERENTIAL EQS STABILITY and CONTROL:

M. Kinnally - diff eq with delays

presents exposition of "delay type" Lyapunaov eqs.

Global stability analysis of a TCP/AQM protocol...
by
A. Papachristodoulou Conf Dec.and Control Dec 2004

papaPaper

Mike's talk will start with exposition of
The K and the R Lyapunov functions

Related is the work of Peet and Lall IEEE TAC
(one variable case)

Pesic - Bellman eqs with diffusions and free boundary probs
(numerics there of) -first speaker.

"Convergence of approximation schemes for fully nonlinear second order
equations,"
G.Barles, P.E. Souganidis,
Asymptotic Analysis 4 (1991) 271-283.

A short 2 page version is on the net, here is the link:
LINK

Special Pursuits with NETWORKS OF ODE:
Klep, Katsnelson, Kshirsagar
Weds at 5.30 and more.

Everyone is welcome to come to any side meeting
you like. People in the class not listed should
do this or discuss with me something to do.
When time of meeting is unclear send me or group
memebers email.

Misc:
Steady states of futile cycles:
L . Wang and Sontag
On the number of steady states in a multiple futile cycle
Steady states of futile cycles:

Remember
http://arxiv.org/

contains versions of lots of papers which you see.