603 research outputs found
The Fuzzy Kaehler Coset Space with the Darboux Coordinates
The Fedosov deformation quantization of the symplectic manifold is determined
by a 1-form differential r. We identify a class of r for which the
product becomes the Moyal product by taking appropriate Darboux coordinates,
but invariant by canonically transforming the coordinates. This respect of the
product is explained by studying the fuzzy algebrae of the Kaehler
coset space.Comment: LaTeX, 11 pages, no figur
Periods and Prepotential of N=2 SU(2) Supersymmetric Yang-Mills Theory with Massive Hypermultiplets
We derive a simple formula for the periods associated with the low energy
effective action of supersymmetric Yang-Mills theory with massive
hypermultiplets. This is given by evaluating explicitly the integral
associated to the elliptic curve using various identities of hypergeometric
functions. Following this formalism, we can calculate the prepotential with
massive hypermultiplets both in the weak coupling region and in the strong
coupling region. In particular, we show how the Higgs field and its dual field
are expressed as generalized hypergeometric functions when the theory has a
conformal point.Comment: 21 pages, LaTe
Integral Equations of Fields on the Rotating Black Hole
It is known that the radial equation of the massless fields with spin around
Kerr black holes cannot be solved by special functions. Recently, the analytic
solution was obtained by use of the expansion in terms of the special functions
and various astrophysical application have been discussed. It was pointed out
that the coefficients of the expansion by the confluent hypergeometric
functions are identical to those of the expansion by the hypergeometric
functions. We explain the reason of this fact by using the integral equations
of the radial equation. It is shown that the kernel of the equation can be
written by the product of confluent hypergeometric functions. The integral
equaton transforms the expansion in terms of the confluent hypergeometric
functions to that of the hypergeometric functions and vice versa,which explains
the reason why the expansion coefficients are universal.Comment: 14 pages, LaTeX, no figure
Prepotential of Supersymmetric Yang-Mills Theories in the Weak Coupling Region
We show how to obtain the explicite form of the low energy quantum effective
action for supersymmetric Yang-Mills theory in the weak coupling region
from the underlying hyperelliptic Riemann surface. This is achieved by
evaluating the integral representation of the fields explicitly. We calculate
the leading instanton corrections for the group SU(\nc), SO(N) and
and find that the one-instanton contribution of the prepotentials for the these
group coincide with the one obtained recently by using the direct instanton
caluculation.Comment: 13 pages, LaTe
Fuzzy Algebrae of the General Kaehler Coset Space G/H\otimesU(1)^k
We study the fuzzy structure of the general Kaehler coset space
G/S\otimes{U(1)}^k deformed by the Fedosov formalism. It is shown that the
Killing potentials satisfy the fuzzy algebrae working in the Darboux
coordinates.Comment: 8 pages, LaTex, no figur
Prepotentials, Bi-linear Forms on Periods and Enhanced Gauge Symmetries in Type-II Strings
We construct a bi-linear form on the periods of Calabi-Yau spaces. These are
used to obtain the prepotentials around conifold singularities in type-II
strings compactified on Calabi-Yau space. The explicit construction of the
bi-linear forms is achieved for the one-moduli models as well as two moduli
models with K3-fibrations where the enhanced gauge symmetry is known to be
observed at conifold locus. We also show how these bi-linear forms are related
with the existence of flat coordinates. We list the resulting prepotentials in
two moduli models around the conifold locus, which contains alpha' corrections
of 4-D N=2 SUSY SU(2) Yang-Mills theory as the stringy effect.Comment: Latex file(34pp), a reference added, typos correcte
Energy landscape analysis of neuroimaging data
Computational neuroscience models have been used for understanding neural
dynamics in the brain and how they may be altered when physiological or other
conditions change. We review and develop a data-driven approach to neuroimaging
data called the energy landscape analysis. The methods are rooted in
statistical physics theory, in particular the Ising model, also known as the
(pairwise) maximum entropy model and Boltzmann machine. The methods have been
applied to fitting electrophysiological data in neuroscience for a decade, but
their use in neuroimaging data is still in its infancy. We first review the
methods and discuss some algorithms and technical aspects. Then, we apply the
methods to functional magnetic resonance imaging data recorded from healthy
individuals to inspect the relationship between the accuracy of fitting, the
size of the brain system to be analyzed, and the data length.Comment: 22 pages, 4 figures, 1 tabl
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