1,748 research outputs found
Extremal covariant POVM's
We consider the convex set of positive operator valued measures (POVM) which
are covariant under a finite dimensional unitary projective representation of a
group. We derive a general characterization for the extremal points, and
provide bounds for the ranks of the corresponding POVM densities, also relating
extremality to uniqueness and stability of optimized measurements. Examples of
applications are given.Comment: 15 pages, no figure
The full integration of black hole solutions to symmetric supergravity theories
We prove that all stationary and spherical symmetric black hole solutions to
theories with symmetric target spaces are integrable and we provide an explicit
integration method. This exact integration is based on the description of black
hole solutions as geodesic curves on the moduli space of the theory when
reduced over the time-like direction. These geodesic equations of motion can be
rewritten as a specific Lax pair equation for which mathematicians have
provided the integration algorithms when the initial conditions are described
by a diagonalizable Lax matrix. On the other hand, solutions described by
nilpotent Lax matrices, which originate from extremal regular (small) D = 4
black holes can be obtained as suitable limits of solutions obtained in the
diagonalizable case, as we show on the generating geodesic (i.e. most general
geodesic modulo global symmetries of the D = 3 model) corresponding to regular
(and small) D = 4 black holes. As a byproduct of our analysis we give the
explicit form of the Wick rotation connecting the orbits of BPS and non-BPS
solutions in maximally supersymmetric supergravity and its STU truncation.Comment: 27 pages, typos corrected, references added, 1 figure added,
Discussion on black holes and the generating geodesic significantly extended.
Statement about the relation between the D=3 geodesics from BPS and non-BPS
extreme black holes made explicit by defining the Wick rotation mapping the
corresponding orbit
Polynomials with symmetric zeros
Polynomials whose zeros are symmetric either to the real line or to the unit
circle are very important in mathematics and physics. We can classify them into
three main classes: the self-conjugate polynomials, whose zeros are symmetric
to the real line; the self-inversive polynomials, whose zeros are symmetric to
the unit circle; and the self-reciprocal polynomials, whose zeros are symmetric
by an inversion with respect to the unit circle followed by a reflection in the
real line. Real self-reciprocal polynomials are simultaneously self-conjugate
and self-inversive so that their zeros are symmetric to both the real line and
the unit circle. In this survey, we present a short review of these
polynomials, focusing on the distribution of their zeros.Comment: Keywords: Self-inversive polynomials, self-reciprocal polynomials,
Pisot and Salem polynomials, M\"obius transformations, knot theory, Bethe
equation
Linear feature selection with applications
There are no author-identified significant results in this report
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