33,133 research outputs found
Decision Trees, Protocols, and the Fourier Entropy-Influence Conjecture
Given , define the \emph{spectral
distribution} of to be the distribution on subsets of in which the
set is sampled with probability . Then the Fourier
Entropy-Influence (FEI) conjecture of Friedgut and Kalai (1996) states that
there is some absolute constant such that . Here,
denotes the Shannon entropy of 's spectral distribution, and
is the total influence of . This conjecture is one
of the major open problems in the analysis of Boolean functions, and settling
it would have several interesting consequences.
Previous results on the FEI conjecture have been largely through direct
calculation. In this paper we study a natural interpretation of the conjecture,
which states that there exists a communication protocol which, given subset
of distributed as , can communicate the value of using
at most bits in expectation.
Using this interpretation, we are able show the following results:
1. First, if is computable by a read- decision tree, then
.
2. Next, if has and is computable by a
decision tree with expected depth , then .
3. Finally, we give a new proof of the main theorem of O'Donnell and Tan
(ICALP 2013), i.e. that their FEI conjecture composes.
In addition, we show that natural improvements to our decision tree results
would be sufficient to prove the FEI conjecture in its entirety. We believe
that our methods give more illuminating proofs than previous results about the
FEI conjecture
SqueezeSeg: Convolutional Neural Nets with Recurrent CRF for Real-Time Road-Object Segmentation from 3D LiDAR Point Cloud
In this paper, we address semantic segmentation of road-objects from 3D LiDAR
point clouds. In particular, we wish to detect and categorize instances of
interest, such as cars, pedestrians and cyclists. We formulate this problem as
a point- wise classification problem, and propose an end-to-end pipeline called
SqueezeSeg based on convolutional neural networks (CNN): the CNN takes a
transformed LiDAR point cloud as input and directly outputs a point-wise label
map, which is then refined by a conditional random field (CRF) implemented as a
recurrent layer. Instance-level labels are then obtained by conventional
clustering algorithms. Our CNN model is trained on LiDAR point clouds from the
KITTI dataset, and our point-wise segmentation labels are derived from 3D
bounding boxes from KITTI. To obtain extra training data, we built a LiDAR
simulator into Grand Theft Auto V (GTA-V), a popular video game, to synthesize
large amounts of realistic training data. Our experiments show that SqueezeSeg
achieves high accuracy with astonishingly fast and stable runtime (8.7 ms per
frame), highly desirable for autonomous driving applications. Furthermore,
additionally training on synthesized data boosts validation accuracy on
real-world data. Our source code and synthesized data will be open-sourced
Enhancement of Dark Matter Annihilation via Breit-Wigner Resonance
The Breit-Wigner enhancement of the thermally averaged annihilation cross
section is shown to provide a large boost factor when the dark
matter annihilation process nears a narrow resonance. We explicitly demonstrate
the evolution behavior of the Breit-Wigner enhanced as the function
of universe temperature for both the physical and unphysical pole cases. It is
found that both of the cases can lead an enough large boost factor to explain
the recent PAMELA, ATIC and PPB-BETS anomalies. We also calculate the coupling
of annihilation process, which is useful for an appropriate model building to
give the desired dark matter relic density.Comment: 4 pages, 4 figures, references added, accepted for publication in
Physical Review
Direct detection and solar capture of dark matter with momentum and velocity dependent elastic scattering
We explore the momentum and velocity dependent elastic scattering between the
dark matter (DM) particles and the nuclei in detectors and the Sun. In terms of
the non-relativistic effective theory, we phenomenologically discuss ten kinds
of momentum and velocity dependent DM-nucleus interactions and recalculate the
corresponding upper limits on the spin-independent DM-nucleon scattering cross
section from the current direct detection experiments. The DM solar capture
rate is calculated for each interaction. Our numerical results show that the
momentum and velocity dependent cases can give larger solar capture rate than
the usual contact interaction case for almost the whole parameter space. On the
other hand, we deduce the Super-Kamiokande's constraints on the solar capture
rate for eight typical DM annihilation channels. In contrast to the usual
contact interaction, the Super-Kamiokande and IceCube experiments can give more
stringent limits on the DM-nucleon elastic scattering cross section than the
current direct detection experiments for several momentum and velocity
dependent DM-nucleus interactions. In addition, we investigate the mediator
mass's effect on the DM elastic scattering cross section and solar capture
rate.Comment: 18 pages, 4 figures, 2 tables. minor changes and a reference added,
published in Nuclear Physics
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