The IMA serves as a scientific melting pot, bringing together researchers
from widely different fields or traditionally disjoint
communities within a broad research area. As long-term visitor Govind Menon
expresses it, “The best thing about my stay at the IMA was the
‘organized random conversations’. Since this sounds paradoxical,
let me explain what I mean. I say ‘random’ because I spoke with
visitors who I hadn't met before and whose work I didn't know anything
about. By ‘organized’, I mean that I would never have met these
people if the organizers hadn't invited them.” These
unanticipated interactions are a crucial ingredient in the excitement of the
IMA and, as the following two examples demonstrate, can lead to
important new interdisciplinary collaborations.
Homeostasis in computer security.
The language of computer security is highly biological—systems are
infected by viruses and worms—and computer scientists look to
biological systems for inspiration in combating such attacks. In fact
inspiration flows both ways: biologists can learn about the immune
system by studying some forms of artificial complex systems such as
computer networks. In 1998, biomathematician Lee Segel and computer
scientist Stephanie Forrest brought immunologists, mathematicians, and
computer scientists together at the IMA for a period of concentration
Appropriate Immune Response as a Problem in
Distributed Artificial Intelligence.
Forrest and her group had
already experimented with mimicking immunological mechanisms in
computer intrusion detection programs. But these programs, which
discover invaders by identifying anomalous patterns of activities, are
far from perfect: in a perpetually changing computer environment, false
positives are inevitable. The limited repertoire of responses then
available (most of which were severe and irrevocable), meant that most
intrusion detection systems required a great deal of human oversight
and/or exacted a large cost in system usability.
For Anil Somayaji, a Ph.D. student working with Forrest, inspiration came when
he met Erin O'Neill, a Ph.D. student in immunology from Australian
National University at the IMA. O'Neill explained that the immune
system is primarily homeostatic rather than destructive.
Homeostasis is the physiological process by which
the internal systems of the body are maintained within normal ranges
despite variations in operating conditions. The body achieves
homeostasis, for example, through its reactions to temperature
variations, physical and psychological stresses, and microbial
invaders. For the latter, containment and regulated coexistence is
often the best strategy: drastic countermeasures are rarely called
Basic flow control in pH.
An understanding of the immune system's role in biological
homeostasis led Somayaji to modify the goal for computer security
systems from one of destroying a perceived intruder when it is first
recognized, to one of adapting the system to maintain stability. This
idea blossomed into his Ph.D. project over the next several years. In
his disseration, entitled Operating Systems Stability through
Process Homeostasis, Somayaji developed a Linux kernel extension,
called pH, that maintains system stability by slowing the response to
system calls when abberant behavior is detected.
Somayaji's pioneering concept of process homeostasis is proving its
worth in the computer industry. The ideas behind pH have been
commercialized at Sana Security, founded in 2000 by Steven Hofmeyr,
another participant in the IMA workshop, and a collaborator of
Somayaji's. They have also been incorporated in the software program
Virus Throttle released by Hewlett-Packard Co. in February 2005.
Somayaji, now on the faculty of Carleton University, is currently
researching the application of homeostatic approaches to managing
Breaking down scientific barriers within
Many of the complex physical phenomena in the world around us can be
modeled mathematically by systems of partial differential equations
(PDE). Most PDE systems are far too complex to solve with paper and
pencil, so instead scientists and engineers employ algorithms which
allow them to approximate the solutions on high performance computers.
The development and certification of algorithms which can be used to
provide efficient and accurate solutions to the immense variety of PDE
which arise in applications is a crucial and difficult challenge has
engaged many mathematicians, scientists, and engineers around the world
for the better part of a century. Vast progress has been made—the
speed up obtained in this period through improved algorithms is every
bit as great as that obtained through faster computers—but the need
for fast, robust, and flexible numerical methods promises to challenge
researchers for decades to come.
Because of the number of researchers involved, the variety of methods
employed, and the mature and highly technical nature of the field,
ideas obtained by researchers working on one class of methods of
numerical PDE often take a long time to percolate to other researchers
working on different methods. Important results may not reach the scientists
who need them most. The IMA was designed to break down just such barriers.
Figure of mesh elements
In May 2004 the IMA hosted a workshop entitled
Spatial Discretizations for Partial Differential Equations, designed to
foster communication among diverse groups of researchers developing, applying,
and analyzing numerical methods that mimic fundamental geometry
properties underlying the PDEs. At that meeting Franco Brezzi of Pavia,
one of the world's leading researchers in finite element methods, met
Mikhail Shashkov and Konstantin Lipnikov of Los Alamos National
Laboratory, top scientists in the area of finite difference methods
(and, as such, members of a scientific community nearly disjoint from
Brezzi's). Intense and sometimes heated discussions at the IMA led to a
collaboration which quickly bore fruit. Their joint paper on the
analysis of mimetic finite difference methods on unstructured
curvilinear polyhedral meshes is
in LANL's Mathematical
Modeling and Analysis Research Highlights series, and has been
submitted to SIAM Journal on Numerical Analysis. It is the first paper
on finite difference methods in Brezzi's four decade career.
from paper of Brezzi et al.
The collaboration between Brezzi, Shashkov, and Lipnikov, like others
forged at the IMA 2004 workshop, continues. In response to the success
of the workshop and the enthusiasm of the participants, the Centre of
Mathematics for Applications in Oslo hosted a follow-up workshop on
Discretizations for Partial Differential Equations in September 2005.