4,319 research outputs found
Dynamics of generalized tachyon field
We investigate the dynamics of generalized tachyon field in FRW spacetime. We
obtain the autonomous dynamical system for the general case. Because the
general autonomous dynamical system cannot be solved analytically, we discuss
two cases in detail: and . We find the critical points and
study their stability. At these critical points, we also consider the stability
of the generalized tachyon field, which is as important as the stability of
critical points. The possible final states of the universe are discussed.Comment: 9 pages, 5 figures, published versio
Attentional Biased Stochastic Gradient for Imbalanced Classification
In this paper, we present a simple yet effective method (ABSGD) for
addressing the data imbalance issue in deep learning. Our method is a simple
modification to momentum SGD where we leverage an attentional mechanism to
assign an individual importance weight to each gradient in the mini-batch.
Unlike many existing heuristic-driven methods for tackling data imbalance, our
method is grounded in {\it theoretically justified distributionally robust
optimization (DRO)}, which is guaranteed to converge to a stationary point of
an information-regularized DRO problem. The individual-level weight of a
sampled data is systematically proportional to the exponential of a scaled loss
value of the data, where the scaling factor is interpreted as the
regularization parameter in the framework of information-regularized DRO.
Compared with existing class-level weighting schemes, our method can capture
the diversity between individual examples within each class. Compared with
existing individual-level weighting methods using meta-learning that require
three backward propagations for computing mini-batch stochastic gradients, our
method is more efficient with only one backward propagation at each iteration
as in standard deep learning methods. To balance between the learning of
feature extraction layers and the learning of the classifier layer, we employ a
two-stage method that uses SGD for pretraining followed by ABSGD for learning a
robust classifier and finetuning lower layers. Our empirical studies on several
benchmark datasets demonstrate the effectiveness of the proposed method.Comment: 29pages, 10 figure
Exit Presentation Fall 2013
Our current International Space Station Probabilistic Risk Assessment (ISS PRA) model assumes all collisions between a visiting vehicle (VV) and the ISS result in worst case loss of the ISS crew and the vehicle (LOCV). Drawing results from the Mir-Progress collision, we know this assumption is inaccurate because that collision did not lead to LOCV. Therefore the PRA team is conducting a study to determine the likelihood of LOCV when a collision occurs between a VV and the ISS. Kinetic energy is calculated and converted to pounds of TNT for the moving VVs when they collide with the ISS. Different scenarios are evaluated to obtain collision related data such as translational kinetic energy and rotational kinetic energy. These calculated data are integrated into the results from the expert elicitation performed on the Mir- Progress collision. As a result of this study, the PRA model will now calculate the probability of a VV collision with ISS, the probability that collision will result in Loss of Soyuz Crew (LOC) or Loss of ISS Crew and Vehicle (LOCV)
Finite-temperature critical behaviors in 2D long-range quantum Heisenberg model
The well-known Mermin-Wagner theorem prohibits the existence of
finite-temperature spontaneous continuous symmetry breaking phase in systems
with short-range interactions at spatial dimension [Phys. Rev. 158,
383; Phys. Rev. Lett. 17, 1133; Journal of Statistical Physics 175, 521-529].
For long-range interaction with monotonic power-law form (), the
theorem further forbids a ferro- or antiferromagnetic order at finite
temperature when [Phys. Rev. Lett. 87, 137203]. However, the
situation for at is beyond the predicting power of the
theorem and the situation is still unclear. Here we address this question by
large-scale quantum Monte Carlo simulations, accompanied with field theoretical
analysis. We find the spontaneous breaking of the symmetry for in ferromagnetic Heisenberg model with interaction at
, and obtain the accurate critical exponents by finite-size analysis for
where the system is above the upper critical dimension with Gaussian
fixed point and for where the system is below the upper critical
dimension with non-Gaussian fixed point. Our results reveal the novel critical
behaviors in 2D long-range Heisenberg models and will intrigue further
experimental studies of quantum materials with long-range interaction beyond
the realm of the Mermin-Wagner theorem
Quantum criticality and entanglement for 2d long-range Heisenberg bilayer
The study of quantum criticality and entanglement in systems with long-range
(LR) interactions is still in its early stages, with many open questions
remaining. In this work, we investigate critical exponents and scaling of
entanglement entropies (EE) in the LR bilayer Heisenberg model using
large-scale quantum Monte Carlo (QMC) simulations and the recently developed
nonequilibrium increment algorithm for measuring EE. By applying modified
(standard) finite-size scaling (FSS) above (below) the upper critical dimension
and field theory analysis, we obtain precise critical exponents in three
regimes: the LR Gaussian regime with a Gaussian fixed point, the short-range
(SR) regime with Wilson-Fisher (WF) exponents, and a LR non-Gaussian regime
where the critical exponents vary continuously from LR Gaussian to SR values.
We compute the R\'enyi EE both along the critical line and in the N\'eel phase
and observe that as the LR interaction is enhanced, the area-law contribution
in EE gradually vanishes both at quantum critical points (QCPs) and in the
N\'eel phase. The log-correction in EE arising from sharp corners at the QCPs
also decays to zero as LR interaction grows, whereas the log-correction for
N\'eel states, caused by the interplay of Goldstone modes and restoration of
the symmetry in a finite system, is enhanced as LR interaction becomes
stronger. We also discuss relevant experimental settings to detect these
nontrivial properties in critical behavior and entanglement information for
quantum many-body systems with LR interactions.Comment: 5pages, 4 figure
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