23,314 research outputs found
A spherical Hopfield model
We introduce a spherical Hopfield-type neural network involving neurons and
patterns that are continuous variables. We study both the thermodynamics and
dynamics of this model. In order to have a retrieval phase a quartic term is
added to the Hamiltonian. The thermodynamics of the model is exactly solvable
and the results are replica symmetric. A Langevin dynamics leads to a closed
set of equations for the order parameters and effective correlation and
response function typical for neural networks. The stationary limit corresponds
to the thermodynamic results. Numerical calculations illustrate our findings.Comment: 9 pages Latex including 3 eps figures, Addition of an author in the
HTML-abstract unintentionally forgotten, no changes to the manuscrip
On the Ricci tensor in type II B string theory
Let be a metric connection with totally skew-symmetric torsion \T
on a Riemannian manifold. Given a spinor field and a dilaton function
, the basic equations in type II B string theory are \bdm \nabla \Psi =
0, \quad \delta(\T) = a \cdot \big(d \Phi \haken \T \big), \quad \T \cdot \Psi
= b \cdot d \Phi \cdot \Psi + \mu \cdot \Psi . \edm We derive some relations
between the length ||\T||^2 of the torsion form, the scalar curvature of
, the dilaton function and the parameters . The main
results deal with the divergence of the Ricci tensor \Ric^{\nabla} of the
connection. In particular, if the supersymmetry is non-trivial and if
the conditions \bdm (d \Phi \haken \T) \haken \T = 0, \quad \delta^{\nabla}(d
\T) \cdot \Psi = 0 \edm hold, then the energy-momentum tensor is
divergence-free. We show that the latter condition is satisfied in many
examples constructed out of special geometries. A special case is . Then
the divergence of the energy-momentum tensor vanishes if and only if one
condition \delta^{\nabla}(d \T) \cdot \Psi = 0 holds. Strong models (d \T =
0) have this property, but there are examples with \delta^{\nabla}(d \T) \neq
0 and \delta^{\nabla}(d \T) \cdot \Psi = 0.Comment: 9 pages, Latex2
Nucleosynthesis and Clump Formation in a Core Collapse Supernova
High-resolution two-dimensional simulations were performed for the first five
minutes of the evolution of a core collapse supernova explosion in a 15 solar
mass blue supergiant progenitor. The computations start shortly after bounce
and include neutrino-matter interactions by using a light-bulb approximation
for the neutrinos, and a treatment of the nucleosynthesis due to explosive
silicon and oxygen burning. We find that newly formed iron-group elements are
distributed throughout the inner half of the helium core by Rayleigh-Taylor
instabilities at the Ni+Si/O and C+O/He interfaces, seeded by convective
overturn during the early stages of the explosion. Fast moving nickel mushrooms
with velocities up to about 4000 km/s are observed. This offers a natural
explanation for the mixing required in light curve and spectral synthesis
studies of Type Ib explosions. A continuation of the calculations to later
times, however, indicates that the iron velocities observed in SN 1987 A cannot
be reproduced because of a strong deceleration of the clumps in the dense shell
left behind by the shock at the He/H interface.Comment: 8 pages, LaTeX, 2 postscript figures, 2 gif figures, shortened and
slightly revised text and references, accepted by ApJ Letter
Color singlet suppression of quark-gluon plasma formation
The rate of quark-gluon plasma droplet nucleation in superheated hadronic
matter is calculated within the MIT bag model. The requirements of color
singletness and (to less extent) fixed momentum suppress the nucleation rate by
many orders of magnitude, making thermal nucleation of quark-gluon plasma
droplets unlikely in ultrarelativistic heavy-ion collisions if the transition
is first order and reasonably described by the bag model.Comment: 9 pages, 3 ps figures. To appear in PhysRevC (April 1996
Solvable glassy system: static versus dynamical transition
A directed polymer is considered on a flat substrate with randomly located
parallel ridges. It prefers to lie inside wide regions between the ridges. When
the transversel width is exponential in the
longitudinal length , there can be a large number of
available wide states. This ``complexity'' causes a phase transition from a
high temperature phase where the polymer lies in the widest lane, to a glassy
low temperature phase where it lies in one of many narrower lanes. Starting
from a uniform initial distribution of independent polymers, equilibration up
to some exponential time scale induces a sharp dynamical transition. When the
temperature is slowly increased with time, this occurs at a tunable
temperature. There is an asymmetry between cooling and heating. The structure
of phase space in the low temperature non-equilibrium glassy phase is of a
one-level tree.Comment: 4 pages revte
Killing spinors in supergravity with 4-fluxes
We study the spinorial Killing equation of supergravity involving a torsion
3-form \T as well as a flux 4-form \F. In dimension seven, we construct
explicit families of compact solutions out of 3-Sasakian geometries, nearly
parallel \G_2-geometries and on the homogeneous Aloff-Wallach space. The
constraint \F \cdot \Psi = 0 defines a non empty subfamily of solutions. We
investigate the constraint \T \cdot \Psi = 0, too, and show that it singles
out a very special choice of numerical parameters in the Killing equation,
which can also be justified geometrically
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