882 research outputs found
Clifford algebras and new singular Riemannian foliations in spheres
Using representations of Clifford algebras we construct indecomposable
singular Riemannian foliations on round spheres, most of which are
non-homogeneous. This generalizes the construction of non-homogeneous
isoparametric hypersurfaces due to by Ferus, Karcher and Munzner.Comment: 21 pages. Construction of foliations in the Cayley plane added.
Proofs simplified and presentation improved, according to referee's
suggestions. To appear in Geom. Funct. Ana
Aging Relation for Ising Spin Glasses
We derive a rigorous dynamical relation on aging phenomena -- the aging
relation -- for Ising spin glasses using the method of gauge transformation.
The waiting-time dependence of the auto-correlation function in the
zero-field-cooling process is equivalent with that in the field-quenching
process. There is no aging on the Nishimori line; this reveals arguments for
dynamical properties of the Griffiths phase and the mixed phase. The present
method can be applied to other gauge-symmetric models such as the XY gauge
glass.Comment: 9 pages, RevTeX, 2 postscript figure
Non-equilibrium Relations for Spin Glasses with Gauge Symmetry
We study the applications of non-equilibrium relations such as the Jarzynski
equality and fluctuation theorem to spin glasses with gauge symmetry. It is
shown that the exponentiated free-energy difference appearing in the Jarzynski
equality reduces to a simple analytic function written explicitly in terms of
the initial and final temperatures if the temperature satisfies a certain
condition related to gauge symmetry. This result is used to derive a lower
bound on the work done during the non-equilibrium process of temperature
change. We also prove identities relating equilibrium and non-equilibrium
quantities. These identities suggest a method to evaluate equilibrium
quantities from non-equilibrium computations, which may be useful to avoid the
problem of slow relaxation in spin glasses.Comment: 8 pages, 2 figures, submitted to JPS
Laboratory Measurement of the Pure Rotational Transitions of the HCNH+ and its Isotopic Species
The pure rotational transitions of the protonated hydrogen cyanide ion,
HCNH+, and its isotopic species, HCND+ and DCND+, were measured in the 107 -
482 GHz region with a source modulated microwave spectrometer. The ions were
generated in the cell with a magnetically confined dc-glow discharge of HCN
and/or DCN. The rotational constant B0 and the centrifugal distortion constant
D0 for each ion were precisely determined by a least-squares fitting to the
observed spectral lines. The observed rotational transition frequencies by
laboratory spectroscopy and the predicted ones are accurate in about 30 to 40
kHz and are useful as rest frequencies for astronomical searches of HCNH+ and
HCND+.Comment: 14 pages in TeX, 1 figures in JPE
Dynamical Gauge Theory for the XY Gauge Glass Model
Dynamical systems of the gauge glass are investigated by the method of the
gauge transformation.Both stochastic and deterministic dynamics are treated.
Several exact relations are derived among dynamical quantities such as
equilibrium and nonequilibrium auto-correlation functions, relaxation functions
of order parameter and internal energy. They provide physical properties in
terms of dynamics in the SG phase, a possible mixed phase and the Griffiths
phase, the multicritical dynamics and the aging phenomenon. We also have a
plausible argument for the absence of re-entrant transition in two or higher
dimensions.Comment: 3 figure
Random Fixed Point of Three-Dimensional Random-Bond Ising Models
The fixed-point structure of three-dimensional bond-disordered Ising models
is investigated using the numerical domain-wall renormalization-group method.
It is found that, in the +/-J Ising model, there exists a non-trivial fixed
point along the phase boundary between the paramagnetic and ferromagnetic
phases. The fixed-point Hamiltonian of the +/-J model numerically coincides
with that of the unfrustrated random Ising models, strongly suggesting that
both belong to the same universality class. Another fixed point corresponding
to the multicritical point is also found in the +/-J model. Critical properties
associated with the fixed point are qualitatively consistent with theoretical
predictions.Comment: 4 pages, 5 figures, to be published in Journal of the Physical
Society of Japa
Finite Size Scaling Analysis of Exact Ground States for +/-J Spin Glass Models in Two Dimensions
With the help of EXACT ground states obtained by a polynomial algorithm we
compute the domain wall energy at zero-temperature for the bond-random and the
site-random Ising spin glass model in two dimensions. We find that in both
models the stability of the ferromagnetic AND the spin glass order ceases to
exist at a UNIQUE concentration p_c for the ferromagnetic bonds. In the
vicinity of this critical point, the size and concentration dependency of the
first AND second moment of the domain wall energy are, for both models,
described by a COMMON finite size scaling form. Moreover, below this
concentration the stiffness exponent turns out to be slightly negative \theta_S
= -0.056(6) indicating the absence of any intermediate spin glass phase at
non-zero temperature.Comment: 7 pages Latex, 5 postscript-figures include
Transient dynamics for sequence processing neural networks
An exact solution of the transient dynamics for a sequential associative
memory model is discussed through both the path-integral method and the
statistical neurodynamics. Although the path-integral method has the ability to
give an exact solution of the transient dynamics, only stationary properties
have been discussed for the sequential associative memory. We have succeeded in
deriving an exact macroscopic description of the transient dynamics by
analyzing the correlation of crosstalk noise. Surprisingly, the order parameter
equations of this exact solution are completely equivalent to those of the
statistical neurodynamics, which is an approximation theory that assumes
crosstalk noise to obey the Gaussian distribution. In order to examine our
theoretical findings, we numerically obtain cumulants of the crosstalk noise.
We verify that the third- and fourth-order cumulants are equal to zero, and
that the crosstalk noise is normally distributed even in the non-retrieval
case. We show that the results obtained by our theory agree with those obtained
by computer simulations. We have also found that the macroscopic unstable state
completely coincides with the separatrix.Comment: 21 pages, 4 figure
A -Vertex Kernel for Maximum Internal Spanning Tree
We consider the parameterized version of the maximum internal spanning tree
problem, which, given an -vertex graph and a parameter , asks for a
spanning tree with at least internal vertices. Fomin et al. [J. Comput.
System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a
simple application of this rule is sufficient to yield a -vertex kernel.
Here we propose a novel way to use the same reduction rule, resulting in an
improved -vertex kernel. Our algorithm applies first a greedy procedure
consisting of a sequence of local exchange operations, which ends with a
local-optimal spanning tree, and then uses this special tree to find a
reducible structure. As a corollary of our kernel, we obtain a deterministic
algorithm for the problem running in time
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