1,226 research outputs found
Warped metrics for location-scale models
This paper argues that a class of Riemannian metrics, called warped metrics,
plays a fundamental role in statistical problems involving location-scale
models. The paper reports three new results : i) the Rao-Fisher metric of any
location-scale model is a warped metric, provided that this model satisfies a
natural invariance condition, ii) the analytic expression of the sectional
curvature of this metric, iii) the exact analytic solution of the geodesic
equation of this metric. The paper applies these new results to several
examples of interest, where it shows that warped metrics turn location-scale
models into complete Riemannian manifolds of negative sectional curvature. This
is a very suitable situation for developing algorithms which solve problems of
classification and on-line estimation. Thus, by revealing the connection
between warped metrics and location-scale models, the present paper paves the
way to the introduction of new efficient statistical algorithms.Comment: preprint of a submission to GSI 2017 conferenc
Reconstructing the geometric structure of a Riemannian symmetric space from its Satake diagram
The local geometry of a Riemannian symmetric space is described completely by
the Riemannian metric and the Riemannian curvature tensor of the space. In the
present article I describe how to compute these tensors for any Riemannian
symmetric space from the Satake diagram, in a way that is suited for the use
with computer algebra systems. As an example application, the totally geodesic
submanifolds of the Riemannian symmetric space SU(3)/SO(3) are classified.
The submission also contains an example implementation of the algorithms and
formulas of the paper as a package for Maple 10, the technical documentation
for this implementation, and a worksheet carrying out the computations for the
space SU(3)/SO(3) used in the proof of Proposition 6.1 of the paper.Comment: 23 pages, also contains two Maple worksheets and technical
documentatio
Reconstructing emission from pre-reionization sources with cosmic infrared background fluctuation measurements by the JWST
We present new methodology to use cosmic infrared background (CIB)
fluctuations to probe sources at 10<z<30 from a JWST/NIRCam configuration that
will isolate known galaxies to 28 AB mag at 0.5--5 micron. At present
significant mutually consistent source-subtracted CIB fluctuations have been
identified in the Spitzer and Akari data at 2--5 micron, but we demonstrate
internal inconsistencies at shorter wavelengths in the recent CIBER data. We
evaluate CIB contributions from remaining galaxies and show that the bulk of
the high-z sources will be in the confusion noise of the NIRCam beam, requiring
CIB studies. The accurate measurement of the angular spectrum of the
fluctuations and probing the dependence of its clustering component on the
remaining shot noise power would discriminate between the various currently
proposed models for their origin and probe the flux distribution of its
sources. We show that the contribution to CIB fluctuations from remaining
galaxies is large at visible wavelengths for the current instruments precluding
probing the putative Lyman-break of the CIB fluctuations. We demonstrate that
with the proposed JWST configuration such measurements will enable probing the
Lyman break. We develop a Lyman-break tomography method to use the NIRCam
wavelength coverage to identify or constrain, via the adjacent two-band
subtraction, the history of emissions over 10<z<30 as the Universe comes out of
the 'Dark Ages'. We apply the proposed tomography to the current Spitzer/IRAC
measurements at 3.6 and 4.5 micron, to find that it already leads to
interestingly low upper limit on emissions at z>30.Comment: ApJ, in press. Minor revisions/additions to match the version in
proof
Generalized quantum tomographic maps
Some non-linear generalizations of classical Radon tomography were recently
introduced by M. Asorey et al [Phys. Rev. A 77, 042115 (2008), where the
straight lines of the standard Radon map are replaced by quadratic curves
(ellipses, hyperbolas, circles) or quadratic surfaces (ellipsoids,
hyperboloids, spheres). We consider here the quantum version of this novel
non-linear approach and obtain, by systematic use of the Weyl map, a
tomographic encoding approach to quantum states. Non-linear quantum tomograms
admit a simple formulation within the framework of the star-product
quantization scheme and the reconstruction formulae of the density operators
are explicitly given in a closed form, with an explicit construction of
quantizers and dequantizers. The role of symmetry groups behind the generalized
tomographic maps is analyzed in some detail. We also introduce new
generalizations of the standard singular dequantizers of the symplectic
tomographic schemes, where the Dirac delta-distributions of operator-valued
arguments are replaced by smooth window functions, giving rise to the new
concept of "thick" quantum tomography. Applications for quantum state
measurements of photons and matter waves are discussed.Comment: 8 page
Effective QCD Partition Function in Sectors with Non-Zero Topological Charge and Itzykson-Zuber Type Integral
It was conjectured by Jackson et.al. that the finite volume effective
partition function of QCD with the topological charge coincides with the
Itzyskon-Zuber type integral for rectangular matrices. In the
present article we give a proof of this conjecture, in which the original
Itzykson-Zuber integral is utilized.Comment: 7pages, LaTeX2
Symplectically-invariant soliton equations from non-stretching geometric curve flows
A moving frame formulation of geometric non-stretching flows of curves in the
Riemannian symmetric spaces and is
used to derive two bi-Hamiltonian hierarchies of symplectically-invariant
soliton equations. As main results, multi-component versions of the sine-Gordon
(SG) equation and the modified Korteweg-de Vries (mKdV) equation exhibiting
invariance are obtained along with their bi-Hamiltonian
integrability structure consisting of a shared hierarchy of symmetries and
conservation laws generated by a hereditary recursion operator. The
corresponding geometric curve flows in and
are shown to be described by a non-stretching wave map and a
mKdV analog of a non-stretching Schr\"odinger map.Comment: 39 pages; remarks added on algebraic aspects of the moving frame used
in the constructio
Charge Orbits of Extremal Black Holes in Five Dimensional Supergravity
We derive the U-duality charge orbits, as well as the related moduli spaces,
of "large" and "small" extremal black holes in non-maximal ungauged
Maxwell-Einstein supergravities with symmetric scalar manifolds in d=5
space-time dimensions. The stabilizer groups of the various classes of orbits
are obtained by determining and solving suitable U-invariant sets of
constraints, both in "bare" and "dressed" charges bases, with various methods.
After a general treatment of attractors in real special geometry (also
considering non-symmetric cases), the N=2 "magic" theories, as well as the N=2
Jordan symmetric sequence, are analyzed in detail. Finally, the half-maximal
(N=4) matter-coupled supergravity is also studied in this context.Comment: 1+63 pages, 6 Table
A few remarks on integral representation for zonal spherical functions on the symmetric space
The integral representation on the orthogonal groups for zonal spherical
functions on the symmetric space is used to obtain a
generating function for such functions. For the case N=3 the three-dimensional
integral representation reduces to a one-dimensional one.Comment: Latex file, 10 pages, amssymb.sty require
Quantum Mechanics on SO(3) via Non-commutative Dual Variables
We formulate quantum mechanics on SO(3) using a non-commutative dual space
representation for the quantum states, inspired by recent work in quantum
gravity. The new non-commutative variables have a clear connection to the
corresponding classical variables, and our analysis confirms them as the
natural phase space variables, both mathematically and physically. In
particular, we derive the first order (Hamiltonian) path integral in terms of
the non-commutative variables, as a formulation of the transition amplitudes
alternative to that based on harmonic analysis. We find that the non-trivial
phase space structure gives naturally rise to quantum corrections to the action
for which we find a closed expression. We then study both the semi-classical
approximation of the first order path integral and the example of a free
particle on SO(3). On the basis of these results, we comment on the relevance
of similar structures and methods for more complicated theories with
group-based configuration spaces, such as Loop Quantum Gravity and Spin Foam
models.Comment: 29 pages; matches the published version plus footnote 7, a journal
reference include
Remarks on the naturality of quantization
Hamiltonian quantization of an integral compact symplectic manifold M depends
on a choice of compatible almost complex structure J. For open sets U in the
set of compatible almost complex structures and small enough values of Planck's
constant, the Hilbert spaces of the quantization form a bundle over U with a
natural connection. In this paper we examine the dependence of the Hilbert
spaces on the choice of J, by computing the semi-classical limit of the
curvature of this connection. We also show that parallel transport provides a
link between the action of the group Symp(M) of symplectomorphisms of M and the
Schrodinger equation.Comment: 20 page
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