10,217 research outputs found
Query-Efficient Locally Decodable Codes of Subexponential Length
We develop the algebraic theory behind the constructions of Yekhanin (2008)
and Efremenko (2009), in an attempt to understand the ``algebraic niceness''
phenomenon in . We show that every integer ,
where , and are prime, possesses the same good algebraic property as
that allows savings in query complexity. We identify 50 numbers of this
form by computer search, which together with 511, are then applied to gain
improvements on query complexity via Itoh and Suzuki's composition method. More
precisely, we construct a -query LDC for every positive
integer and a -query
LDC for every integer , both of length , improving the
queries used by Efremenko (2009) and queries used by Itoh and
Suzuki (2010).
We also obtain new efficient private information retrieval (PIR) schemes from
the new query-efficient LDCs.Comment: to appear in Computational Complexit
Impacts of gravitational-wave standard siren observation of the Einstein Telescope on weighing neutrinos in cosmology
We investigate the impacts of the gravitational-wave (GW) standard siren
observation of the Einstein Telescope (ET) on constraining the total neutrino
mass. We simulate 1000 GW events that would be observed by the ET in its
10-year observation by taking the standard CDM cosmology as a fiducial
model. We combine the simulated GW data with other cosmological observations
including cosmic microwave background (CMB), baryon acoustic oscillations
(BAO), and type Ia supernovae (SN). We consider three mass hierarchy cases for
the neutrino mass, i.e., normal hierarchy (NH), inverted hierarchy (IH), and
degenerate hierarchy (DH). Using Planck+BAO+SN, we obtain eV
for the NH case, eV for the IH case, and
eV for the DH case. After considering the GW data, i.e., using
Planck+BAO+SN+GW, the constraint results become eV for the
NH case, eV for the IH case, and eV for
the DH case. We find that the GW data can help reduce the upper limits of by 13.7%, 7.5%, and 10.3% for the NH, IH, and DH cases, respectively. In
addition, we find that the GW data can also help break the degeneracies between
and other parameters. We show that the GW data of the ET could
greatly improve the constraint accuracies of cosmological parameters.Comment: 8 pages, 4 figure
ShadowNeuS: Neural SDF Reconstruction by Shadow Ray Supervision
By supervising camera rays between a scene and multi-view image planes, NeRF
reconstructs a neural scene representation for the task of novel view
synthesis. On the other hand, shadow rays between the light source and the
scene have yet to be considered. Therefore, we propose a novel shadow ray
supervision scheme that optimizes both the samples along the ray and the ray
location. By supervising shadow rays, we successfully reconstruct a neural SDF
of the scene from single-view pure shadow or RGB images under multiple lighting
conditions. Given single-view binary shadows, we train a neural network to
reconstruct a complete scene not limited by the camera's line of sight. By
further modeling the correlation between the image colors and the shadow rays,
our technique can also be effectively extended to RGB inputs. We compare our
method with previous works on challenging tasks of shape reconstruction from
single-view binary shadow or RGB images and observe significant improvements.
The code and data will be released.Comment: Project page: https://gerwang.github.io/shadowneus
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