108,130 research outputs found
Complete algebraic vector fields on affine surfaces
Let \AAutH (X) be the subgroup of the group \AutH (X) of holomorphic
automorphisms of a normal affine algebraic surface generated by elements of
flows associated with complete algebraic vector fields. Our main result is a
classification of all normal affine algebraic surfaces quasi-homogeneous
under \AAutH (X) in terms of the dual graphs of the boundaries \bX \setminus
X of their SNC-completions \bX.Comment: 44 page
Fixed points of the EM algorithm and nonnegative rank boundaries
Mixtures of independent distributions for two discrete random variables
can be represented by matrices of nonnegative rank . Likelihood inference
for the model of such joint distributions leads to problems in real algebraic
geometry that are addressed here for the first time. We characterize the set of
fixed points of the Expectation-Maximization algorithm, and we study the
boundary of the space of matrices with nonnegative rank at most . Both of
these sets correspond to algebraic varieties with many irreducible components.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1282 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Can Computer Algebra be Liberated from its Algebraic Yoke ?
So far, the scope of computer algebra has been needlessly restricted to exact
algebraic methods. Its possible extension to approximate analytical methods is
discussed. The entangled roles of functional analysis and symbolic programming,
especially the functional and transformational paradigms, are put forward. In
the future, algebraic algorithms could constitute the core of extended symbolic
manipulation systems including primitives for symbolic approximations.Comment: 8 pages, 2-column presentation, 2 figure
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