315,957 research outputs found
Statistical Models with a Line of Defect
The factorization condition for the scattering amplitudes of an integrable
model with a line of defect gives rise to a set of Reflection-Transmission
equations. The solutions of these equations in the case of diagonal -matrix
in the bulk are only those with . The choice corresponds to
the Ising model. We compute the transmission and reflection amplitudes relative
to the interaction of the Majorana fermion with the defect and we discuss their
relevant features.Comment: 14 pages, LATEX file, ISAS/EP/94/30 (Figures added, originally missed
for E-mail transmission problem.
Data Exchange Problem with Helpers
In this paper we construct a deterministic polynomial time algorithm for the
problem where a set of users is interested in gaining access to a common file,
but where each has only partial knowledge of the file. We further assume the
existence of another set of terminals in the system, called helpers, who are
not interested in the common file, but who are willing to help the users. Given
that the collective information of all the terminals is sufficient to allow
recovery of the entire file, the goal is to minimize the (weighted) sum of bits
that these terminals need to exchange over a noiseless public channel in order
achieve this goal. Based on established connections to the multi-terminal
secrecy problem, our algorithm also implies a polynomial-time method for
constructing the largest shared secret key in the presence of an eavesdropper.
We consider the following side-information settings: (i) side-information in
the form of uncoded packets of the file, where the terminals' side-information
consists of subsets of the file; (ii) side-information in the form of linearly
correlated packets, where the terminals have access to linear combinations of
the file packets; and (iii) the general setting where the the terminals'
side-information has an arbitrary (i.i.d.) correlation structure. We provide a
polynomial-time algorithm (in the number of terminals) that finds the optimal
rate allocations for these terminals, and then determines an explicit optimal
transmission scheme for cases (i) and (ii)
Optimal Deterministic Polynomial-Time Data Exchange for Omniscience
We study the problem of constructing a deterministic polynomial time
algorithm that achieves omniscience, in a rate-optimal manner, among a set of
users that are interested in a common file but each has only partial knowledge
about it as side-information. Assuming that the collective information among
all the users is sufficient to allow the reconstruction of the entire file, the
goal is to minimize the (possibly weighted) amount of bits that these users
need to exchange over a noiseless public channel in order for all of them to
learn the entire file. Using established connections to the multi-terminal
secrecy problem, our algorithm also implies a polynomial-time method for
constructing a maximum size secret shared key in the presence of an
eavesdropper. We consider the following types of side-information settings: (i)
side information in the form of uncoded fragments/packets of the file, where
the users' side-information consists of subsets of the file; (ii) side
information in the form of linearly correlated packets, where the users have
access to linear combinations of the file packets; and (iii) the general
setting where the the users' side-information has an arbitrary (i.i.d.)
correlation structure. Building on results from combinatorial optimization, we
provide a polynomial-time algorithm (in the number of users) that, first finds
the optimal rate allocations among these users, then determines an explicit
transmission scheme (i.e., a description of which user should transmit what
information) for cases (i) and (ii)
Electromagnetic waves in a wormhole geometry
We investigate the propagation of electromagnetic waves through a static
wormhole. It is shown that the problem can be reduced to a one-dimensional
Schr\"odinger-like equation with a barrier-type potential. Using numerical
methods, we calculate the transmission coefficient as a function of the energy.
We also discuss the polarization of the outgoing radiation due to this
gravitational scattering.Comment: LaTex file, 5 pages, 2 figures, one reference added, accepted for
publication in PR
Minimum Cost Multicast with Decentralized Sources
In this paper we study the multisource multicast problem where every sink in
a given directed acyclic graph is a client and is interested in a common file.
We consider the case where each node can have partial knowledge about the file
as a side information. Assuming that nodes can communicate over the capacity
constrained links of the graph, the goal is for each client to gain access to
the file, while minimizing some linear cost function of number of bits
transmitted in the network. We consider three types of side-information
settings:(ii) side information in the form of linearly correlated packets; and
(iii) the general setting where the side information at the nodes have an
arbitrary (i.i.d.) correlation structure. In this work we 1) provide a
polynomial time feasibility test, i.e., whether or not all the clients can
recover the file, and 2) we provide a polynomial-time algorithm that finds the
optimal rate allocation among the links of the graph, and then determines an
explicit transmission scheme for cases (i) and (ii)
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