2,575 research outputs found
Entanglement entropy on a fuzzy sphere with a UV cutoff
We introduce a UV cutoff into free scalar field theory on the noncommutative
(fuzzy) two-sphere. Due to the IR-UV connection, varying the UV cutoff allows
us to control the effective nonlocality scale of the theory. In the resulting
fuzzy geometry, we establish which degrees of freedom lie within a specific
geometric subregion and compute the associated vacuum entanglement entropy.
Entanglement entropy for regions smaller than the effective nonlocality scale
is extensive, while entanglement entropy for regions larger than the effective
nonlocality scale follows the area law. This reproduces features previously
obtained in the strong coupling regime through holography. We also show that
mutual information is unaffected by the UV cutoff.Comment: Significantly revised with improved methodology, 16 pages, 8 figure
Impregnated drill bits strengthened by nanoparticles for mineral exploration drilling
In order to improve the drilling efficiency and service life of impregnated diamond
drill bit, WC and ZrO2 nanoparticles were introduced into traditional drill bit matrix. The matrix formula and fabrication process were optimized to utilize the dispersion strengthening effect of WC and ZrO2 nanoparticles, improving physical and mechanical performance of working layer. Indoor drilling experiment was carried out to compare reinforced drill bits and traditional bit. Results showed that drill bits with 2.5 wt% nano-WC and 1 wt% nano-ZrO2 shows better performance than traditional
bits. WC nanoparticles have better dispersion strengthening effect on diamond drill bit than ZrO2 nanoparticles
Query-Driven Sampling for Collective Entity Resolution
Probabilistic databases play a preeminent role in the processing and
management of uncertain data. Recently, many database research efforts have
integrated probabilistic models into databases to support tasks such as
information extraction and labeling. Many of these efforts are based on batch
oriented inference which inhibits a realtime workflow. One important task is
entity resolution (ER). ER is the process of determining records (mentions) in
a database that correspond to the same real-world entity. Traditional pairwise
ER methods can lead to inconsistencies and low accuracy due to localized
decisions. Leading ER systems solve this problem by collectively resolving all
records using a probabilistic graphical model and Markov chain Monte Carlo
(MCMC) inference. However, for large datasets this is an extremely expensive
process. One key observation is that, such exhaustive ER process incurs a huge
up-front cost, which is wasteful in practice because most users are interested
in only a small subset of entities. In this paper, we advocate pay-as-you-go
entity resolution by developing a number of query-driven collective ER
techniques. We introduce two classes of SQL queries that involve ER operators
--- selection-driven ER and join-driven ER. We implement novel variations of
the MCMC Metropolis Hastings algorithm to generate biased samples and
selectivity-based scheduling algorithms to support the two classes of ER
queries. Finally, we show that query-driven ER algorithms can converge and
return results within minutes over a database populated with the extraction
from a newswire dataset containing 71 million mentions
Cusp Summations and Cusp Relations of Simple Quad Lenses
We review five often used quad lens models, each of which has analytical
solutions and can produce four images at most. Each lens model has two
parameters, including one that describes the intensity of non-dimensional mass
density, and the other one that describes the deviation from the circular lens.
In our recent work, we have found that the cusp and the fold summations are not
equal to 0, when a point source infinitely approaches a cusp or a fold from
inner side of the caustic. Based on the magnification invariant theory, which
states that the sum of signed magnifications of the total images of a given
source is a constant, we calculate the cusp summations for the five lens
models. We find that the cusp summations are always larger than 0 for source on
the major cusps, while can be larger or smaller than 0 for source on the minor
cusps. We also find that if these lenses tend to the circular lens, the major
and minor cusp summations will have infinite values, and with positive and
negative signs respectively. The cusp summations do not change significantly if
the sources are slightly deviated from the cusps. In addition, through the
magnification invariants, we also derive the analytical signed cusp relations
on the axes for three lens models. We find that both on the major and the minor
axes the larger the lenses deviated from the circular lens, the larger the
signed cusp relations. The major cusp relations are usually larger than the
absolute minor cusp relations, but for some lens models with very large
deviation from circular lens, the minor cusp relations can be larger than the
major cusp relations.Comment: 8 pages, 4 figures, accepted for publication in MNRA
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Dynamic Mode Decomposition for Compressive System Identification
Dynamic mode decomposition has emerged as a leading technique to identify
spatiotemporal coherent structures from high-dimensional data, benefiting from
a strong connection to nonlinear dynamical systems via the Koopman operator. In
this work, we integrate and unify two recent innovations that extend DMD to
systems with actuation [Proctor et al., 2016] and systems with heavily
subsampled measurements [Brunton et al., 2015]. When combined, these methods
yield a novel framework for compressive system identification [code is publicly
available at: https://github.com/zhbai/cDMDc]. It is possible to identify a
low-order model from limited input-output data and reconstruct the associated
full-state dynamic modes with compressed sensing, adding interpretability to
the state of the reduced-order model. Moreover, when full-state data is
available, it is possible to dramatically accelerate downstream computations by
first compressing the data. We demonstrate this unified framework on two model
systems, investigating the effects of sensor noise, different types of
measurements (e.g., point sensors, Gaussian random projections, etc.),
compression ratios, and different choices of actuation (e.g., localized,
broadband, etc.). In the first example, we explore this architecture on a test
system with known low-rank dynamics and an artificially inflated state
dimension. The second example consists of a real-world engineering application
given by the fluid flow past a pitching airfoil at low Reynolds number. This
example provides a challenging and realistic test-case for the proposed method,
and results demonstrate that the dominant coherent structures are well
characterized despite actuation and heavily subsampled data
Magnification relations of quad lenses and applications on Einstein crosses
In this work, we mainly study the magnification relations of quad lens models
for cusp, fold and cross configurations. By dividing and ray-tracing in
different image regions, we numerically derive the positions and magnifications
of the four images for a point source lying inside of the astroid caustic.
Then, based on the magnifications, we calculate the signed cusp and fold
relations for the singular isothermal elliptical lenses. The signed fold
relation map has positive and negative regions, and the positive region is
usually larger than the negative region as has been confirmed before. It can
also explain that for many observed fold image pairs, the fluxes of the Fermat
minimum images are apt to be larger than those of the saddle images. We define
a new quantity cross relation which describes the magnification discrepancy
between two minimum images and two saddle images. Distance ratio is also
defined as the ratio of the distance of two saddle images to that of two
minimum images. We calculate the cross relations and distance ratios for nine
observed Einstein crosses. In theory, for most of the quad lens models, the
cross relations decrease as the distance ratios increase. In observation, the
cross relations of the nine samples do not agree with the quad lens models very
well, nevertheless, the cross relations of the nine samples do not give obvious
evidence for anomalous flux ratio as the cusp and fold types do. Then, we
discuss several reasons for the disagreement, and expect good consistencies for
more precise observations and better lens models in the future.Comment: 12 pages, 11 figures, accepted for publication in MNRA
A Coherent Ising Machine Based On Degenerate Optical Parametric Oscillators
A degenerate optical parametric oscillator network is proposed to solve the
NP-hard problem of finding a ground state of the Ising model. The underlying
operating mechanism originates from the bistable output phase of each
oscillator and the inherent preference of the network in selecting oscillation
modes with the minimum photon decay rate. Computational experiments are
performed on all instances reducible to the NP-hard MAX-CUT problems on cubic
graphs of order up to 20. The numerical results reasonably suggest the
effectiveness of the proposed network.Comment: 18 pages, 6 figure
Network of Time-Multiplexed Optical Parametric Oscillators as a Coherent Ising Machine
Finding the ground states of the Ising Hamiltonian [1] maps to various
combinatorial optimization problems in biology, medicine, wireless
communications, artificial intelligence, and social network. So far no
efficient classical and quantum algorithm is known for these problems, and
intensive research is focused on creating physical systems - Ising machines -
capable of finding the absolute or approximate ground states of the Ising
Hamiltonian [2-6]. Here we report a novel Ising machine using a network of
degenerate optical parametric oscillators (OPOs). Spins are represented with
above-threshold binary phases of the OPOs and the Ising couplings are realized
by mutual injections [7]. The network is implemented in a single OPO ring
cavity with multiple trains of femtosecond pulses and configurable mutual
couplings, and operates at room temperature. We programed the smallest
non-deterministic polynomial time (NP)- hard Ising problem on the machine, and
in 1000 runs of the machine no computational error was detected
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