385,975 research outputs found
-adic exponential sums of polynomials in one variable
The -adic exponential sum of a polynomial in one variable is studied. An
explicit arithmetic polygon in terms of the highest two exponents of the
polynomial is proved to be a lower bound of the Newton polygon of the
-function of the T-adic exponential sum. This bound gives lower bounds for
the Newton polygon of the -function of exponential sums of -power order
Dilaton - fixed scalar correlators and AdS_5 x S^5 - SYM correspondence
We address the question of AdS/CFT correspondence in the case of the 3-point
function . O_4 and O_8 are particular primary states represented
by F^2 + ... and F^4 + ... operators in \N=4 SYM theory and dilaton \phi and
massive `fixed' scalar \nu in D=5 supergravity. While the value of <O_4 O_4
O_8> computed in large N weakly coupled SYM theory is non-vanishing, the D=5
action of type IIB supergravity compactified on S^5 does not contain
\phi\phi\nu coupling and thus the corresponding correlator seems to vanish on
the AdS_5 side. This is in obvious contradiction with arguments suggesting
non-renormalization of 2- and 3-point functions of states from short multiplets
and implying agreement between the supergravity and SYM expressions for them.
We propose a natural resolution of this paradox which emphasizes the
10-dimensional nature of the correspondence. The basic idea is to treat the
constant mode of the dilaton as a part of the full S^5 Kaluza-Klein family of
dilaton modes. This leads to a non-zero result for the correlator
on the supergravity side.Comment: 16 pages, harvmac; references adde
Constructive simulation and topological design of protocols
We give a topological simulation for tensor networks that we call the
two-string model. In this approach we give a new way to design protocols, and
we discover a new multipartite quantum communication protocol. We introduce the
notion of topologically-compressed transformations. Our new protocol can
implement multiple, non-local compressed transformations among multi-parties
using one multipartite resource state.Comment: 16 page
Revisiting the hot matter in the center of gamma-ray bursts and supernova
Hot matter with nucleons can be produced in the inner region of the
neutrino-dominated accretion flow in gamma-ray bursts or during the
proto-neutron star birth in successful supernova. The composition and equation
of state of the matter depend on the dynamic equilibrium under various
neutrino opacities. The strong interaction between nucleons may also play an
important role. We plan to extend the previous studies by incorporating these
two aspects in our model. The modification of the -equilibrium condition
from neutrino optically thin to thick has been modeled by an equilibrium factor
ranging between the neutrino-freely-escaping case and the
neutrino-trapped case. We employ the microscopic Brueckner-Hartree-Fock
approach extended to the finite temperature regime to study the interacting
nucleons. We show that the composition and chemical potentials of the hot
nuclear matter for different densities and temperatures at each stage of
equilibrium. We also compare our realistic equation of states with
those of the free gas model. We find the neutrino opacity and the strong
interaction between nucleons are important for the description and should be
taken into account in model calculations.Comment: accepted Astronomy & Astrophysics (2013
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A Bayesian network approach to explaining time series with changing structure
Many examples exist of multivariate time series where dependencies between variables change over time. If these changing dependencies are not taken into account, any model that is learnt from the data will average over the different dependency structures. Paradigms that try to
explain underlying processes and observed events in multivariate time series must explicitly model these changes in order to allow non-experts to
analyse and understand such data. In this paper we have developed a method for generating explanations in multivariate time series that takes into account changing dependency structure. We make use of a dynamic Bayesian network model with hidden nodes. We introduce a representa-
tion and search technique for learning such models from data and test it on synthetic time series and real-world data from an oil refinery, both of which contain changing underlying structure. We compare our method to an existing EM-based method for learning structure. Results are very promising for our method and we include sample explanations, generated from models learnt from the refinery dataset
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