4,238 research outputs found
Does Standard Cosmology Express Cosmological Principle Faithfully?
In 1+1 dimensional case, Einstein equation cannot give us any information on
the evolution of the universe because the Einstein tensor of the system is
identically zero. We study such a 1+1 dimensional cosmology and find the metric
of it according to cosmological principle and special relativity, but the
results contradict the usual expression of cosmological principle of standard
cosmology. So we doubt in 1+3 dimensional case, cosmological principle is
expressed faithfully by standard cosmology.Comment: physical interpretation changes, but mathematica formula keep
Dependence in Propositional Logic: Formula-Formula Dependence and Formula Forgetting -- Application to Belief Update and Conservative Extension
Dependence is an important concept for many tasks in artificial intelligence.
A task can be executed more efficiently by discarding something independent
from the task. In this paper, we propose two novel notions of dependence in
propositional logic: formula-formula dependence and formula forgetting. The
first is a relation between formulas capturing whether a formula depends on
another one, while the second is an operation that returns the strongest
consequence independent of a formula. We also apply these two notions in two
well-known issues: belief update and conservative extension. Firstly, we define
a new update operator based on formula-formula dependence. Furthermore, we
reduce conservative extension to formula forgetting.Comment: We find a mistake in this version and we need a period of time to fix
i
Performance Limits of Segmented Compressive Sampling: Correlated Samples versus Bits
This paper gives performance limits of the segmented compressive sampling
(CS) which collects correlated samples. It is shown that the effect of
correlation among samples for the segmented CS can be characterized by a
penalty term in the corresponding bounds on the sampling rate. Moreover, this
penalty term is vanishing as the signal dimension increases. It means that the
performance degradation due to the fixed correlation among samples obtained by
the segmented CS (as compared to the standard CS with equivalent size sampling
matrix) is negligible for a high-dimensional signal. In combination with the
fact that the signal reconstruction quality improves with additional samples
obtained by the segmented CS (as compared to the standard CS with sampling
matrix of the size given by the number of original uncorrelated samples), the
fact that the additional correlated samples also provide new information about
a signal is a strong argument for the segmented CS.Comment: 27 pages, 8 figures, Submitted to IEEE Trans. Signal Processing on
November 201
Asymptotic Properties of Primal-Dual Algorithm for Distributed Stochastic Optimization Over Random Networks
This paper studies a distributed stochastic optimization problem over random
networks with imperfect communications subject to a global constraint, which is
the intersection of local constraint sets assigned to agents. The global cost
function is the sum of local cost functions, each of which is the expectation
of a random cost function. By incorporating the augmented Lagrange technique
with the projection method, a stochastic approximation based distributed
primal-dual algorithm is proposed to solve the problem. Each agent updates its
estimate by using the local observations and the information derived from
neighbors. For the constrained problem, the estimates are first shown to be
bounded almost surely (a.s.), and then are proved to converge to the optimal
solution set a.s. Furthermore, the asymptotic normality and efficiency of the
algorithm are addressed for the unconstrained case. The results demonstrate the
influence of random networks, communication noises, and gradient errors on the
performance of the algorithm. Finally, numerical simulations demonstrate the
theoretic results
Short-term Market Reaction after Trading Halts in Chinese Stock Market
In this paper, we study the dynamics of absolute return, trading volume and
bid-ask spread after the trading halts using high-frequency data from the
Shanghai Stock Exchange. We deal with all three types of trading halts, namely
intraday halts, one-day halts and inter-day halts, of 203 stocks in Shanghai
Stock Exchange from August 2009 to August 2011. We find that absolute return,
trading volume, and in case of bid-ask spread around intraday halts share the
same pattern with a sharp peak and a power law relaxation after that. While for
different types of trading halts, the peaks' height and the relaxation
exponents are different. From the perspective of halt reasons or halt duration,
the relaxation exponents of absolute return after inter-day halts are larger
than that after intraday halts and one-day halts, which implies that inter-day
halts are most effective. From the perspective of price trends, the relaxation
exponents of excess absolute return and excess volume for positive events are
larger than that for negative events in case of intraday halts and one-day
halts, implying that positive events are more effective than negative events
for intraday halts and one-day halts. In contrast, negative events are more
effective than positive events for inter-day halts.Comment: 11 pages, 8 figures, Physica A (2014
Low-Rank Deep Convolutional Neural Network for Multi-Task Learning
In this paper, we propose a novel multi-task learning method based on the
deep convolutional network. The proposed deep network has four convolutional
layers, three max-pooling layers, and two parallel fully connected layers. To
adjust the deep network to multi-task learning problem, we propose to learn a
low-rank deep network so that the relation among different tasks can be
explored. We proposed to minimize the number of independent parameter rows of
one fully connected layer to explore the relations among different tasks, which
is measured by the nuclear norm of the parameter of one fully connected layer,
and seek a low-rank parameter matrix. Meanwhile, we also propose to regularize
another fully connected layer by sparsity penalty, so that the useful features
learned by the lower layers can be selected. The learning problem is solved by
an iterative algorithm based on gradient descent and back-propagation
algorithms. The proposed algorithm is evaluated over benchmark data sets of
multiple face attribute prediction, multi-task natural language processing, and
joint economics index predictions. The evaluation results show the advantage of
the low-rank deep CNN model over multi-task problems
Thermodynamics of the - transition in cerium studied by an LDA + Gutzwiller method
The - transition in cerium has been studied in both zero and
finite temperature by Gutzwiller density functional theory. We find that the
first order transition between and phases persists to the
zero temperature with negative pressure. By further including the entropy
contributed by both electronic quasi-particles and lattice vibration, we obtain
the total free energy at given volume and temperature, from which we obtain the
- transition from the first principle calculation. We also
computed the phase diagram and pressure versus volume isotherms of cerium at
finite temperature and pressure, finding excellent agreement with the
experiments. Our calculation indicate that both the electronic entropy and
lattice vibration entropy plays important role in the -
transition.Comment: 5 pages, 4 figure
Permutation Meets Parallel Compressed Sensing: How to Relax Restricted Isometry Property for 2D Sparse Signals
Traditional compressed sensing considers sampling a 1D signal. For a
multidimensional signal, if reshaped into a vector, the required size of the
sensing matrix becomes dramatically large, which increases the storage and
computational complexity significantly. To solve this problem, we propose to
reshape the multidimensional signal into a 2D signal and sample the 2D signal
using compressed sensing column by column with the same sensing matrix. It is
referred to as parallel compressed sensing, and it has much lower storage and
computational complexity. For a given reconstruction performance of parallel
compressed sensing, if a so-called acceptable permutation is applied to the 2D
signal, we show that the corresponding sensing matrix has a smaller required
order of restricted isometry property condition, and thus, storage and
computation requirements are further lowered. A zigzag-scan-based permutation,
which is shown to be particularly useful for signals satisfying a layer model,
is introduced and investigated. As an application of the parallel compressed
sensing with the zigzag-scan-based permutation, a video compression scheme is
presented. It is shown that the zigzag-scan-based permutation increases the
peak signal-to-noise ratio of reconstructed images and video frames.Comment: 30 pages, 10 figures, 3 tables, submitted to the IEEE Trans. Signal
Processing in November 201
Lateral Migration and Nonuniform Rotation of Biconcave Particle Suspended in Poiseuille Flow
A biconcave particle suspended in a Poiseuille flow is investigated by the
multiple-relaxation-time lattice Boltzmann method with the Galilean-invariant
momentum exchange method. The lateral migration and equilibrium of the particle
are similar to the Segr\'e-Silberberg effect in our numerical simulations.
Surprisingly, two lateral equilibrium positions are observed corresponding to
the releasing positions of the biconcave particle. The upper equilibrium
positions significantly decrease with the growth of the Reynolds number,
whereas the lower ones are almost insensitive to the Reynolds number.
Interestingly, the regular wave accompanied by nonuniform rotation is exhibited
in the lateral movement of the biconcave particle. It can be attributed to that
the biconcave shape in various postures interacts with the parabolic velocity
distribution of the Poiseuille flow. A set of contours illustrate the dynamic
flow field when the biconcave particle has successive postures in a rotating
period.Comment: 13 pages, 5 figure
Vortex lattice and vortex bound states in CsFeAs investigated by scanning tunneling microscopy/spectroscopy
We investigate the vortex lattice and vortex bound states in CsFeAs
single crystals by scanning tunneling microscopy/spectroscopy (STM/STS) under
various magnetic fields. A possible structural transition or crossover of
vortex lattice is observed with the increase of magnetic field, i.e., the
vortex lattice changes from a distorted hexagonal lattice to a distorted
tetragonal one at the magnetic field near 0.5 T. It is found that a mixture of
stripelike hexagonal and square vortex lattices emerges in the crossover
region. The vortex bound state is also observed in the vortex center. The
tunneling spectra crossing a vortex show that the bound-state peak position
holds near zero bias with STM tip moving away from the vortex core center. The
Fermi energy estimated from the vortex bound state energy is very small. Our
investigations provide experimental information to both the vortex lattice and
the vortex bound states in this iron-based superconductor.Comment: 7 pages, 5 figure
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