15,465 research outputs found
Flag varieties and interpretations of Young tableau algorithms
The conjugacy classes of nilpotent matrices can be parametrised
by partitions of , and for a nilpotent in the class
parametrised by , the variety of -stable flags has its
irreducible components parametrised by the standard Young tableaux of shape
. We indicate how several algorithmic constructions defined for Young
tableaux have significance in this context, thus extending Steinberg's result
that the relative position of flags generically chosen in the irreducible
components of parametrised by tableaux and , is the permutation
associated to under the Robinson-Schensted correspondence. Other
constructions for which we give interpretations are Sch\"utzenberger's
involution of the set of Young tableaux, jeu de taquin (leading also to an
interpretation of Littlewood-Richardson coefficients), and the transpose
Robinson-Schensted correspondence (defined using column insertion). In each
case we use a doubly indexed family of partitions, defined in terms of the flag
(or pair of flags) determined by a point chosen in the variety under
consideration. We show that for generic choices, the family satisfies certain
combinatorial relations, whence the family describes the computation of the
algorithmic operation being interpreted, as we described in a previous
publication.Comment: 16 page
Bulk Viscosity of Interacting Hadrons
We show that first approximations to the bulk viscosity are
expressible in terms of factors that depend on the sound speed , the
enthalpy, and the interaction (elastic and inelastic) cross section. The
explicit dependence of on the factor is
demonstrated in the Chapman-Enskog approximation as well as the variational and
relaxation time approaches. The interesting feature of bulk viscosity is that
the dominant contributions at a given temperature arise from particles which
are neither extremely nonrelativistic nor extremely relativistic. Numerical
results for a model binary mixture are reported.Comment: 4 pages, 1 figure, Contribution to Quark Matter 2009, Knoxville,
Tennessee, US
Development of non-equilibrium Green's functions for use with full interaction in complex systems
We present an ongoing development of an existing code for calculating
ground-state, steady-state, and transient properties of many-particle systems.
The development involves the addition of the full four-index two electron
integrals, which allows for the calculation of transport systems, as well as
the extension to multi-level electronic systems, such as atomic and molecular
systems and other applications. The necessary derivations are shown, along with
some preliminary results and a summary of future plans for the code
Learning by a nerual net in a noisy environment - The pseudo-inverse solution revisited
A recurrent neural net is described that learns a set of patterns in the
presence of noise. The learning rule is of Hebbian type, and, if noise would be
absent during the learning process, the resulting final values of the weights
would correspond to the pseudo-inverse solution of the fixed point equation in
question. For a non-vanishing noise parameter, an explicit expression for the
expectation value of the weights is obtained. This result turns out to be
unequal to the pseudo-inverse solution. Furthermore, the stability properties
of the system are discussed.Comment: 16 pages, 3 figure
Probing the basins of attraction of a recurrent neural network
A recurrent neural network is considered that can retrieve a collection of
patterns, as well as slightly perturbed versions of this `pure' set of patterns
via fixed points of its dynamics. By replacing the set of dynamical
constraints, i.e., the fixed point equations, by an extended collection of
fixed-point-like equations, analytical expressions are found for the weights
w_ij(b) of the net, which depend on a certain parameter b. This so-called basin
parameter b is such that for b=0 there are, a priori, no perturbed patterns to
be recognized by the net. It is shown by a numerical study, via probing sets,
that a net constructed to recognize perturbed patterns, i.e., with values of
the connections w_ij(b) with b unequal zero, possesses larger basins of
attraction than a net made with the help of a pure set of patterns, i.e., with
connections w_ij(b=0). The mathematical results obtained can, in principle, be
realized by an actual, biological neural net.Comment: 17 pages, LaTeX, 2 figure
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