Complex Systems: Mathematics, Computation & Science
(Leader: Prof. Greg McColm)
Tuesday, November 26, 2002
| Title |
Crossover From Poisson to Wigner-Dyson Level Statistics in
One-Dimensional Systems With Integrability Breaking |
| Speaker |
Professor David Rabson
Physics Department |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Abstract
Arrange a chain of atoms in a ring, and allow the free electrons on the lattice
to hop from site to neighboring site. If only nearest-neighbor electrons interact,
the system is known to be integrable: there are as many integrals of the motion
as there are solutions. If we then apply an irrelevant perturbation (such as
a magnetic flux through the center of the ring), energy levels will wander independently
as a function of perturbation. Each such level can carry a current; the transport
is termed ballistic. According to the standard view of random-matrix theory,
even an infinitesimal second-neighbor interaction will destroy the integrability;
energy levels will repel as a function of the perturbation, and states will
carry no ballistic current. The transport is called diffusive. The probability
distribution of energy spacings should follow the Wigner-Dyson form.
I will present some numerical evidence that this latter picture is wrong when
the chain is finite and speculate on the possible implications for quantum computing.
Tuesday, November 19, 2002
| Title |
Ozone Production in the Troposphere |
| Speaker |
Professor Noreen Poor
College of Public Health |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Abstract
Formation and destruction of ozone in the lower atmosphere is a cyclical process
driven by sunlight and the availability of nitrogen oxides and volatile organic
compounds. The ambient temperature, degree of atmospheric mixing, and build-up
of pollutants in the atmosphere are factors that contribute to elevated concentrations
of ozone close to the Earth's surface. The complexity of the physical and chemical
processes associated with ozone production make challenging regional control
of ozone to levels below the National Ambient Air Quality Standard.
Tuesday, November 5, 2002
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
The organizers of this seminar invite all interested faculty to join us in
a planning session for the next semester. There are several proposals for a
new format next semester, and we are interested in hearing your ideas.
Tuesday, October 29, 2002
| Title |
Mathematics for a Biological Mystery |
| Speaker |
Professor Richard Stark |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Abstract
How can a totally disorganized system exhibit organized behavior at the global
level? Many mathematicians, the author included, have used irregular networks
of automata to model systems (idealized tissues, insect colonies) which most
clearly present this mystery. A version of calculus (on a domain not related
to the real numbers) has recently yielded some success.
Tuesday, October 15, 2002
| Title |
The Prostate, Mathematics, and Computers |
| Speaker |
Professor Edgar Sanford |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Abstract
Problems in Clinical Medicine will be presented which result from minimal
utilization of fundamental mathematics as well as computer science. The present
status of prostate disease will be used as an example of clinical issues that
could be more rapidly addressed by using mathematical and computer applications.
Frankly, this will be a plea for help from our academic colleagues in disciplines
not obviously related to health care.
Tuesday, October 8, 2002
| Title |
Formal Language Theory Models for DNA Recombinant Processes |
| Speaker |
Professor Natasha Jonoska |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Abstract
We will describe the theoretical model of splicing systems which was originally
developed in thelate 80's by T. Head. This model uses the sequence of DNA
nucleotides to treat molecules as realizations of abstract strings or words. The
detailed definition of the splicing concept comes from considerations of the cut
and paste activity of a ligase and restriction enzymes on double stranded DNA
molecules.
Tuesday, October 1, 2002
| Title |
Birth, death, and the risk of population extinction in
heterogeneous populations |
| Speaker |
Professor Gordon Fox
Department of Biology |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Tuesday, September 24, 2002
| Title |
Community Networks |
| Speaker |
Professor Gary Huxel
Department of Biology |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Abstract
My talk will focus on factors that regulate stability in large networked
systems. Specifically I will examine dynamics and stability of food webs. The
approach can be broadly applied to biological, economical, and social systems.
Furthermore, these highly complex systems represent significant challenges to
computational systems.
Tuesday, September 17, 2002
| Title |
Knots and DNA |
| Speaker |
Professor Masahiko Saito |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Tuesday, September 10, 2002
| Title |
The Mathematics of Threshold Phenomena |
| Speaker |
Professor Greg McColm |
| Time |
1:00-2:00 p.m. |
| Place |
PHY 109 |
Abstract
Many experiments consist of sitting and watching some value N slowly
increase, and waiting for a system to somehow react.
For example, slowly increase the temperature, and see at what temperature a
snowflake melts. Or give a rat increasing amounts of a toxin, and see when it gets
sick.
If T is the time when the system reacts, then T has a
very small variance when the system is highly predictable (snowflake), but lower
variance if the system is less predictable (rat).
There is a well-developed theory of “stopping time random variables”
T for very nice systems. But many systems are quite complicated, and in
this talk we will take a look at how to understand the predictability of such
complicated (and often poorly understood) systems.