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Bio-medical symbolic modeling with algebraic patches
http://hdl.handle.net/2307/509
<Title>Bio-medical symbolic modeling with algebraic patches</Title>
<Authors>Portuesi, Simone</Authors>
<Issue Date>2009-01-13</Issue Date>
<Abstract>The mathematical description of geometry is of paramount importance in the modeling
of systems of all kinds. Standard geometric modeling describes curved objects
through parametric functions as the image of compact domains. Alternatively, as in
algebraic geometry, one may describe curved geometry as the zero-set of polynomials.
Geometric modeling of biological systems highlight certain persistent and open
problems more effectively addressed using algebraic geometry.
In this thesis a framework for computer-based geometric representation based on
algebraic geometry is introduced. Several algebraic representation schemes known
as A-splines and A-patches are detailed as a description of geometry, by using a
piecewise continuous gluing of algebraic curves and surfaces. The application of Asplines
and A-patches to biological modeling is discussed in the context of protein
molecular interface modeling. The rationale is to present an algebraic representation
of bio-modeling under an unified point of view. This framework provides a suitable
background for the main contribution of this thesis: the formulation and implementation
of algorithms for Boolean operations (union, intersection, difference, etc.)
on the algebra of curved polyhedra whose boundary is triangulated with A-patches.
Boolean operations on curved geometry are yet an open obstinate research problem
and its exact solution is only definable within the domain of algebraic geometry. The
exact formulation is here used as basis for a geometrically approximate yet topologically
accurate solution, closed in the geometric domain of A-patches. The prototype
implementation has been applied to pairs of molecular models of ligand proteins
in docking configuration. To date, the computational use of algebraic geometry is
still experimental and is far from being a major component of current systems. This
thesis shows an evidence that representation techniques derived from algebraic geometry
have strong potential in bio-medical modeling, still needing much further
research and engineering.</Abstract>Mon, 12 Jan 2009 23:00:00 GMThttp://hdl.handle.net/2307/5092009-01-12T23:00:00Z