NATIONAL UNIVERSITY OF IRELAND GALWAY
SCHOOL OF MATHEMATICS, STATISTICS AND APPLIED MATHEMATICS
Research
day 2013
Research
Presentations
Computing with
infinite linear groups:
achievements and challenges
Dane
Flannery
School of
Mathematics, Statistics and Applied Mathematics
We survey progress over the past few years in computing with finitely
generated linear groups over an infinite domain. We indicate some
important open questions and suggest avenues for continuing research.
Constellation of
human soluble protein
complexes
Haixuan
Yang
School of Mathematics, Statistics and
Applied Mathematics
Cellular processes often depend on stable physical associations between
proteins. Despite recent progress, knowledge of the composition of
human protein complexes remains limited. To close this gap, we applied
an integrative global proteomic profiling approach, based on
chromatographic separation of cultured human cell extracts into more
than one thousand biochemical fractions that were subsequently analyzed
by quantitative tandem mass spectrometry, to systematically identify a
network of 13,993 high-confidence physical interactions among 3,006
stably associated soluble human proteins. This results in 622 putative
protein complexes, depicted as constellation within a cell -- proteins
as stars and a cell as a universe. Most of these complexes are linked
to core biological processes and encompass both candidate disease genes
and unannotated proteins to inform on mechanism.
How difficult is
Shunting?
Claas
Röver
School of Mathematics, Statistics and
Applied Mathematics
One of the easiest ways to bring structure into a countable set is to
introduce some order. I'll talk about the `pure' mathematics of a fixed
number of shunting tracks that meet at a single point such that
precisely two are connected there at any one time.
Mathematical
modelling of ligaments,
muscles and tendons
Jerry
Murphy
School of Mathematics, Statistics and
Applied Mathematics, NUIG
and Department of Mechanical
Engineering, DCU
Ligaments, muscles and tendons share the same physical characteristics:
they are incompressible, non-linearly elastic, transversely isotropic
materials. There is a well-developed mathematical model for materials
with these characteristics. The difficulties encountered when matching
experimental data with this theory are described.
Adjoints of
finite element models
Patrick
E. Farrell
Imperial College London
The derivatives of PDE models are key ingredients in many important
algorithms of computational mathematics. They find applications in
diverse areas such as sensitivity analysis, PDE-constrained
optimisation, continuation and bifurcation analysis, error estimation,
and generalised stability theory.
These derivatives, computed using the so-called tangent linear and
adjoint models, have made an enormous impact in certain scientific
fields (such as aeronautics, meteorology, and oceanography). However,
their use in other areas has been hampered by the great practical
difficulty of the derivation and implementation of tangent linear and
adjoint models. In his recent book, Naumann (2011) describes the
problem of the robust automated derivation of parallel tangent linear
and adjoint models as ``one of the great open problems in the field of
high-performance scientific computing''.
In this talk, we present an elegant solution to this problem for the
common case where the forward model may be written in variational form,
and discuss some of its applications.