6,595 research outputs found
Stable, Robust and Super Fast Reconstruction of Tensors Using Multi-Way Projections
In the framework of multidimensional Compressed Sensing (CS), we introduce an
analytical reconstruction formula that allows one to recover an th-order
data tensor
from a reduced set of multi-way compressive measurements by exploiting its low
multilinear-rank structure. Moreover, we show that, an interesting property of
multi-way measurements allows us to build the reconstruction based on
compressive linear measurements taken only in two selected modes, independently
of the tensor order . In addition, it is proved that, in the matrix case and
in a particular case with rd-order tensors where the same 2D sensor operator
is applied to all mode-3 slices, the proposed reconstruction
is stable in the sense that the approximation
error is comparable to the one provided by the best low-multilinear-rank
approximation, where is a threshold parameter that controls the
approximation error. Through the analysis of the upper bound of the
approximation error we show that, in the 2D case, an optimal value for the
threshold parameter exists, which is confirmed by our
simulation results. On the other hand, our experiments on 3D datasets show that
very good reconstructions are obtained using , which means that this
parameter does not need to be tuned. Our extensive simulation results
demonstrate the stability and robustness of the method when it is applied to
real-world 2D and 3D signals. A comparison with state-of-the-arts sparsity
based CS methods specialized for multidimensional signals is also included. A
very attractive characteristic of the proposed method is that it provides a
direct computation, i.e. it is non-iterative in contrast to all existing
sparsity based CS algorithms, thus providing super fast computations, even for
large datasets.Comment: Submitted to IEEE Transactions on Signal Processin
Youth opinions matter: retaining human capital in Coos County
As Coos County youth age, their attachment to their communities may deteriorate. This brief presents new data from the Coos Youth Study. This research indicates efforts to keep young people in Coos may benefit from efforts to show students that their views matter to adults in their communities
Prospects for global food security: a critical appraisal of past projections and predictions
During the last half century, a number of individuals and institutions, including the Food and Agriculture Organization of the United Nations (FAO) and IFPRI, have engaged in projections of future food demand, supply, and related variables. In this brief, Alex McCalla and Cesar Revoredo compare projections with real-life outcomes. Projections forecast outcomes on the basis of certain underlying factors. If such forecasted outcomes are undesirable, changes may be made in the underlying factors so that the projections may not, in fact, come to pass. Many projections serve this precise goal. Therefore, the success of projections may not be that they match actual outcomes but that they avoid such outcomes by promoting action to change underlying variables. Unlike predictions, which are successful only if they match actual outcomes, projections that differ from actual outcomes may reflect either poor projection models or changes in underlying variables, possibly caused by the projections themselves.Food consumption., Food security.,
Vacuum stability with spontaneous violation of lepton number
The vacuum of the Standard Model is known to be unstable for the measured
values of the top and Higgs masses. Here we show how vacuum stability can be
achieved naturally if lepton number is violated spontaneously at the TeV scale.
More precise Higgs measurements in the next LHC run should provide a crucial
test of our symmetry breaking scenario. In addition, these schemes typically
lead to enhanced rates for processes involving lepton flavour violation .Comment: 9 pages, 4+2 figures; some references added, some textual
modifications: 2 figures added, appendices added. Results unchanged. Matches
published versio
Geometric Aspects of Holographic Bit Threads
We revisit the recent reformulation of the holographic prescription to
compute entanglement entropy in terms of a convex optimization problem,
introduced by Freedman and Headrick. According to it, the holographic
entanglement entropy associated to a boundary region is given by the maximum
flux of a bounded, divergenceless vector field, through the corresponding
region. Our work leads to two main results: (i) We present a general algorithm
that allows the construction of explicit thread configurations in cases where
the minimal surface is known. We illustrate the method with simple examples:
spheres and strips in vacuum AdS, and strips in a black brane geometry.
Studying more generic bulk metrics, we uncover a sufficient set of conditions
on the geometry and matter fields that must hold to be able to use our
prescription. (ii) Based on the nesting property of holographic entanglement
entropy, we develop a method to construct bit threads that maximize the flux
through a given bulk region. As a byproduct, we are able to construct more
general thread configurations by combining (i) and (ii) in multiple patches. We
apply our methods to study bit threads which simultaneously compute the
entanglement entropy and the entanglement of purification of mixed states and
comment on their interpretation in terms of entanglement distillation. We also
consider the case of disjoint regions for which we can explicitly construct the
so-called multi-commodity flows and show that the monogamy property of mutual
information can be easily illustrated from our constructions.Comment: 48 pages, multiple figures. v3: matches published versio
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