In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing, a 2nd order tensor
has been commonly used to approximate the diffusivity function at each lattice point of the …

A smooth quartic curve in the complex projective plane has 36 inequivalent representations
as a symmetric determinant of linear forms and 63 representations as a sum of three …

If a real polynomial f can be written as a sum of squares of real polynomials, then clearly f is
nonnegative on Rn, and an explicit expression of f as a sum of squares is a certificate of …

Abstract In Diffusion Weighted Magnetic Resonance Image (DW-MRI) processing a 2 nd
order tensor has been commonly used to approximate the diffusivity function at each lattice …

The positive definiteness of a diffusion tensor is important in magnetic resonance imaging
because it reflects the phenomenon of water molecular diffusion in complicated biological …

In 1888, Hilbert described how to find real polynomials in more than one variable which take
only non-negative values but are not a sum of squares of polynomials. His construction was …

Representations of nonnegative polynomials as sums of squares are central to real
algebraic geometry and the subject of active research. The sum-of-squares representations …

The K-length of a form f in K x_ 1, ..., x_ n, K ⊂ C, is the smallest number of d-th powers of
linear forms of which f is a K-linear combination. We present many results, old and new …

Hilbert proved that a non-negative real quartic form f (x, y, z) is the sum of three squares of
quadratic forms. We give a new proof which shows that if the plane curve Q defined by f is …

Enumerative Geometry is concerned with the number of solutions to a structured system of
polynomial equations, when the structure comes from geometry. Enumerative real algebraic …