Stochastic gradient descent (SGD) holds as a classical method to build large scale machine learning models over big data. A stochastic gradient is typically calculated from a limited number of samples (known as mini-batch), so it potentially incurs a
high variance and causes the estimated parameters bounce around the optimal solution. To improve the stability of stochastic gradient, recent years have witnessed the proposal of several semi-stochastic gradient descent algorithms, which distinguish themselves from standard SGD by incorporating global information into gradient computation. In this paper we contribute a novel stratified semi-stochastic gradient descent (S3GD) algorithm to this nascent research area, accelerating the optimization of a large family of composite convex functions. Though theoretically converging faster, prior semi-stochastic algorithms are found to suffer from high iteration complexity, which makes them even slower than SGD in practice on many datasets. In our proposed S3GD, the semi-stochastic gradient is calculated based on efficient manifold propagation, which can be numerically accomplished by sparse matrix multiplications. This way S3GD is able to generate a highly-accurate estimate of the exact gradient from each mini-batch with largely-reduced computational complexity. Theoretic analysis reveals that the proposed S3GD elegantly balances the geometric algorithmic convergence rate against the space and time complexities during the optimization. The efficacy of S3GD is also experimentally corroborated on several large-scale benchmark datasets.
The problem of three-dimensional (3-D) wind profile prediction is addressed based a trinion wind model, which inherently reckons the coupling of the three perpendicular components of a wind field. The augmented trinion statistics are developed and em
ployed to enhance the prediction performance due to its full exploitation of the second-order statistics. The proposed trinion domain processing can be regarded as a more compact version of the existing quaternion-valued approach, with a lower computational complexity. Simulations based on recorded wind data are provided to demonstrate the effectiveness of the proposed methods.
GRB 131231A was detected by the Large Area Telescope onboard Fermi Space Gamma-ray Telescope. The high energy gamma-ray ($> 100$ MeV) afterglow emission spectrum is $F_ u propto u^{-0.54pm0.15}$ in the first $sim 1300$ s after the trigger and the mo
st energetic photon has an energy $sim 62$ GeV arriving at $tsim 520$ s. With reasonable parameters of the GRB outflow as well as the density of the circum-burst medium, the synchrotron radiation of electrons or protons accelerated at an external forward shock have difficulty accounting for the data. The synchrotron self-Compton radiation of the forward shock-accelerated electrons, instead, can account for both the spectrum and temporal behavior of the GeV afterglow emission. We also show that the prospect for detecting GRB 131231A$-$like GRBs with Cherenkov Telescope Array (CTA) is promising.
The strong long-range Coulomb interaction between massless Dirac fermions in graphene can drive a semimetal-insulator transition. We show that this transition is strongly suppressed when the Coulomb interaction is screened by such effects as disorder
, thermal fluctuation, doping, and finite volume. It is completely suppressed once the screening factor $mu$ is beyond a threshold $mu_{c}$ even for infinitely strong coupling. However, such transition is still possible if there is an additional strong contact four-fermion interaction. The differences between screened and contact interactions are also discussed.
We study chiral phase transition and confinement of matter fields in (2+1)-dimensional U(1) gauge theory of massless Dirac fermions and scalar bosons. The vanishing scalar boson mass, $r=0$, defines a quantum critical point between the Higgs phase an
d the Coulomb phase. We consider only the critical point $r=0$ and the Coulomb phase with $r > 0$. The Dirac fermion acquires a dynamical mass when its flavor is less than certain critical value $N_{f}^{c}$, which depends quantitatively on the flavor $N_{b}$ and the scalar boson mass $r$. When $N_{f} < N_{f}^{c}$, the matter fields carrying internal gauge charge are all confined if $r eq 0$ but are deconfined at the quantum critical point $r = 0$. The system has distinct low-energy elementary excitations at the critical point $r=0$ and in the Coulomb phase with $r eq 0$. We calculate the specific heat and susceptibility of the system at $r=0$ and $r eq 0$, which can help to detect the quantum critical point and to judge whether dynamical fermion mass generation takes place.
Optical-electric technology can measure the tangential position and velocity of spacecraft. To know the feasibility of the use of optical-electric technology, it is necessary to estimate the magnitude of spacecraft first. Since the spacecrafts are no
n-self-illumination objects, the estimation formulas of the optical magnitude of spacecraft is constructed according to the radiation theory and the extra-atmospheric radiant emittance of the Sun in the visible light wave band. Taking Change-1 as an example, the magnitude of it in different situations is calculated.
