3,017 research outputs found
Sampling Large Data on Graphs
We consider the problem of sampling from data defined on the nodes of a
weighted graph, where the edge weights capture the data correlation structure.
As shown recently, using spectral graph theory one can define a cut-off
frequency for the bandlimited graph signals that can be reconstructed from a
given set of samples (i.e., graph nodes). In this work, we show how this
cut-off frequency can be computed exactly. Using this characterization, we
provide efficient algorithms for finding the subset of nodes of a given size
with the largest cut-off frequency and for finding the smallest subset of nodes
with a given cut-off frequency. In addition, we study the performance of random
uniform sampling when compared to the centralized optimal sampling provided by
the proposed algorithms.Comment: To be presented at GlobalSIP 201
Degrees of Freedom of Two-Hop Wireless Networks: "Everyone Gets the Entire Cake"
We show that fully connected two-hop wireless networks with K sources, K
relays and K destinations have K degrees of freedom both in the case of
time-varying channel coefficients and in the case of constant channel
coefficients (in which case the result holds for almost all values of constant
channel coefficients). Our main contribution is a new achievability scheme
which we call Aligned Network Diagonalization. This scheme allows the data
streams transmitted by the sources to undergo a diagonal linear transformation
from the sources to the destinations, thus being received free of interference
by their intended destination. In addition, we extend our scheme to multi-hop
networks with fully connected hops, and multi-hop networks with MIMO nodes, for
which the degrees of freedom are also fully characterized.Comment: Presented at the 2012 Allerton Conference. Submitted to IEEE
Transactions on Information Theor
A Generalized Cut-Set Bound for Deterministic Multi-Flow Networks and its Applications
We present a new outer bound for the sum capacity of general multi-unicast
deterministic networks. Intuitively, this bound can be understood as applying
the cut-set bound to concatenated copies of the original network with a special
restriction on the allowed transmit signal distributions. We first study
applications to finite-field networks, where we obtain a general outer-bound
expression in terms of ranks of the transfer matrices. We then show that, even
though our outer bound is for deterministic networks, a recent result relating
the capacity of AWGN KxKxK networks and the capacity of a deterministic
counterpart allows us to establish an outer bound to the DoF of KxKxK wireless
networks with general connectivity. This bound is tight in the case of the
"adjacent-cell interference" topology, and yields graph-theoretic necessary and
sufficient conditions for K DoF to be achievable in general topologies.Comment: A shorter version of this paper will appear in the Proceedings of
ISIT 201
Risk Perception and Drug Safety Evaluation
The authors present a Risk communication framework based on a survey of empirical research concerning public Risk perceptions. They also apply it to the area of pharmaceutical regulation to suggest more effective regulatory strategies
Alternating Hamiltonian cycles in -edge-colored multigraphs
A path (cycle) in a -edge-colored multigraph is alternating if no two
consecutive edges have the same color. The problem of determining the existence
of alternating Hamiltonian paths and cycles in -edge-colored multigraphs is
an -complete problem and it has been studied by several authors.
In Bang-Jensen and Gutin's book "Digraphs: Theory, Algorithms and
Applications", it is devoted one chapter to survey the last results on this
topic. Most results on the existence of alternating Hamiltonian paths and
cycles concern on complete and bipartite complete multigraphs and a few ones on
multigraphs with high monochromatic degrees or regular monochromatic subgraphs.
In this work, we use a different approach imposing local conditions on the
multigraphs and it is worthwhile to notice that the class of multigraphs we
deal with is much larger than, and includes, complete multigraphs, and we
provide a full characterization of this class.
Given a -edge-colored multigraph , we say that is
--closed (resp. --closed)} if for every
monochromatic (resp. non-monochromatic) -path , there
exists an edge between and . In this work we provide the following
characterization: A --closed multigraph has an alternating
Hamiltonian cycle if and only if it is color-connected and it has an
alternating cycle factor.
Furthermore, we construct an infinite family of --closed
graphs, color-connected, with an alternating cycle factor, and with no
alternating Hamiltonian cycle.Comment: 15 pages, 20 figure
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