1,878 research outputs found
Deterministic Constructions of Binary Measurement Matrices from Finite Geometry
Deterministic constructions of measurement matrices in compressed sensing
(CS) are considered in this paper. The constructions are inspired by the recent
discovery of Dimakis, Smarandache and Vontobel which says that parity-check
matrices of good low-density parity-check (LDPC) codes can be used as
{provably} good measurement matrices for compressed sensing under
-minimization. The performance of the proposed binary measurement
matrices is mainly theoretically analyzed with the help of the analyzing
methods and results from (finite geometry) LDPC codes. Particularly, several
lower bounds of the spark (i.e., the smallest number of columns that are
linearly dependent, which totally characterizes the recovery performance of
-minimization) of general binary matrices and finite geometry matrices
are obtained and they improve the previously known results in most cases.
Simulation results show that the proposed matrices perform comparably to,
sometimes even better than, the corresponding Gaussian random matrices.
Moreover, the proposed matrices are sparse, binary, and most of them have
cyclic or quasi-cyclic structure, which will make the hardware realization
convenient and easy.Comment: 12 pages, 11 figure
Differentiable Programming Tensor Networks
Differentiable programming is a fresh programming paradigm which composes
parameterized algorithmic components and trains them using automatic
differentiation (AD). The concept emerges from deep learning but is not only
limited to training neural networks. We present theory and practice of
programming tensor network algorithms in a fully differentiable way. By
formulating the tensor network algorithm as a computation graph, one can
compute higher order derivatives of the program accurately and efficiently
using AD. We present essential techniques to differentiate through the tensor
networks contractions, including stable AD for tensor decomposition and
efficient backpropagation through fixed point iterations. As a demonstration,
we compute the specific heat of the Ising model directly by taking the second
order derivative of the free energy obtained in the tensor renormalization
group calculation. Next, we perform gradient based variational optimization of
infinite projected entangled pair states for quantum antiferromagnetic
Heisenberg model and obtain start-of-the-art variational energy and
magnetization with moderate efforts. Differentiable programming removes
laborious human efforts in deriving and implementing analytical gradients for
tensor network programs, which opens the door to more innovations in tensor
network algorithms and applications.Comment: Typos corrected, discussion and refs added; revised version accepted
for publication in PRX. Source code available at
https://github.com/wangleiphy/tensorgra
Fermionic symmetry-protected topological state in strained graphene
The low-energy physics of graphene is described by relativistic Dirac
fermions with spin and valley degrees of freedom. Mechanical strain can be used
to create a pseudo magnetic field pointing to opposite directions in the two
valleys. We study interacting electrons in graphene exposed to both an external
real magnetic field and a strain-induced pseudo magnetic field. For a certain
ratio between these two fields, it is proposed that a fermionic
symmetry-protected topological state can be realized. The state is
characterized in detail using model wave functions, Chern-Simons field theory,
and numerical calculations. Our paper suggests that graphene with artificial
gauge fields may host a rich set of topological states.Comment: 8 pages, 4 figure
Research on Tomography by Using Seismic Reflection Wave in Laneway
AbstractAs a necessary step and an integral part of works in laneway, the geological prediction is an important means of reducing disaster losses and geological disasters in the works in laneway. This paper mainly discusses tunnel reflection tomography by using seismic reflection wave in laneway. The speed of elastic wave in front of tunnel face and the three-dimensional images can be figured out when the detector check the reflection of elastic wave from the focal points on the tunnel face. The location, size and depth of cave can be ascertained. According to the forecasts of laneway works in the Iron Mine Xishimen, tunnel reflection tomography by using seismic reflection wave can well forecast engineering geology and hydro-geological conditions in front of tunnel face. It will help to supply positive guidance for working plan and construction measures in laneway. Therefore, the construction safety and speed can be ensured, helping to lead to great practical significance and significant economic benefits
Like-sign Di-lepton Signals in Higgsless Models at the LHC
We study the potential LHC discovery of the Z1 KK gauge boson unitarizing
longitudinal W+W- scattering amplitude. In particular, we explore the decay
mode Z1->t tbar along with Z1-> W+W- without specifying the branching
fractions. We propose to exploit the associated production pp-> W Z1, and
select the final state of like-sign dileptons plus multijets and large missing
energy. We conclude that it is possible to observe the Z1 resonance at a 5
sigma level with an integrated luminosity of 100 inverse fb at the LHC upto 650
GeV for a dominant WW channel, and 560 GeV for a dominant ttbar channel.Comment: 13 pages, 7 figure
- …