1,116 research outputs found
Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras
We introduce a functional realization of the Hamiltonian structure on the
moduli space of P-bundles on the elliptic curve E. Here P is parabolic subgroup
in SL_n. We also introduce a construction of the corresponding quantum
algebras.Comment: 20 pages, Amstex, minor change
Geometrical Description of the Local Integrals of Motion of Maxwell-Bloch Equation
We represent a classical Maxwell-Bloch equation and related to it positive
part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is
given by an infinitesimal action of a nilpotent subalgebra of affine Lie
algebra on a Maxwell-Bloch phase space treated as a homogeneous
space of . A space of local integrals of motion is described using
cohomology methods. We show that hamiltonian flows associated to the
Maxwell-Bloch local integrals of motion (i.e. positive AKNS flows) are
identified with an infinitesimal action of an abelian subalgebra of the
nilpotent subalgebra on a Maxwell- Bloch phase space. Possibilities of
quantization and latticization of Maxwell-Bloch equation are discussed.Comment: 16 pages, no figures, plain TeX, no macro
Free-Field Realization of D-dimensional Cylindrical Gravitational Waves
We find two-dimensional free-field variables for D-dimensional general
relativity on spacetimes with D-2 commuting spacelike Killing vector fields and
non-compact spatial sections for D>4. We show that there is a canonical
transformation which maps the corresponding two-dimensional dilaton gravity
theory into a two-dimensional diffeomorphism invariant theory of the free-field
variables. We also show that the spacetime metric components can be expressed
as asymptotic series in negative powers of the dilaton, with coefficients which
can be determined in terms of the free fields.Comment: 15 pages, Late
Gaudin Model, Bethe Ansatz and Critical Level
We propose a new method of diagonalization of hamiltonians of the Gaudin
model associated to an arbitrary simple Lie algebra, which is based on Wakimoto
modules over affine algebras at the critical level. We construct eigenvectors
of these hamiltonians by restricting certain invariant functionals on tensor
products of Wakimoto modules. In conformal field theory language, the
eigenvectors are given by certain bosonic correlation functions. Analogues of
Bethe ansatz equations naturally appear as Kac-Kazhdan type equations on the
existence of certain singular vectors in Wakimoto modules. We use this
construction to expalain a connection between Gaudin's model and correlation
functions of WZNW models.Comment: 40 pages, postscript-file (references added and corrected
Information methods for predicting risk and outcome of stroke
Stroke is a major cause of disability and mortality in most economically developed countries. It is the second leading cause of death worldwide (after cancer and heart disease) [55.1, 2] and a major cause of disability in adults in developed countries [55.3]. Personalized modeling is an emerging effective computational approach, which has been applied to various disciplines, such as in personalized drug design, ecology, business, and crime prevention; it has recently become more prominent in biomedical applications. Biomedical data on stroke risk factors and prognostic data are available in a large volume, but the data are complex and often difficult to apply to a specific person. Individualizing stroke risk prediction and prognosis will allow patients to focus on risk factors specific to them, thereby reducing their stroke risk and managing stroke outcomes more effectively. This chapter reviews various methods–conventional statistical methods and computational intelligent modeling methods for predicting risk and outcome of stroke
Signature Characters for A_2 and B_2
The signatures of the inner product matrices on a Lie algebra's highest
weight representation are encoded in the representation's signature character.
We show that the signature characters of a finite-dimensional Lie algebra's
highest weight representations obey simple difference equations that have a
unique solution once appropriate boundary conditions are imposed. We use these
results to derive the signature characters of all and highest
weight representations. Our results extend, and explain, signature patterns
analogous to those observed by Friedan, Qiu and Shenker in the Virasoro
algebra's representation theory.Comment: 22 p
Factorizable ribbon quantum groups in logarithmic conformal field theories
We review the properties of quantum groups occurring as Kazhdan--Lusztig dual
to logarithmic conformal field theory models. These quantum groups at even
roots of unity are not quasitriangular but are factorizable and have a ribbon
structure; the modular group representation on their center coincides with the
representation on generalized characters of the chiral algebra in logarithmic
conformal field models.Comment: 27pp., amsart++, xy. v2: references added, some other minor addition
Space-time dynamics from algebra representations
We present a model for introducing dynamics into a space-time geometry. This
space-time structure is constructed from a C*-algebra defined in terms of the
generators of an irreducible unitary representation of a finite-dimensional Lie
algebra G. This algebra is included as a subalgebra in a bigger algebra F, the
generators of which mix the representations of G in a way that relates
different space-times and creates the dynamics. This construction can be
considered eventually as a model for 2-D quantum gravity.Comment: 6 pages, LaTeX, no figures. Old paper submitted for archive reason
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