11,355 research outputs found
Electronic structure of BaFeO3: an abinitio DFT study
First principles calculations were performed to study the ground state
electronic properties of BaFeO3 (BFO) within the density functional theory
(DFT). Adopting generalized gradient approximation (GGA) exchange and
correlation functional and Vosko-Wilk-Nusair correlation energy functional
interpolation, we have systematically conducted the band structure, density of
states and electronic distribution along different crystalline planes.
Calculating results show that band gap in the majority spin band structure and
band gap in the minority spin band structure were found to be 2.7012 eV and
0.6867 eV respectively. Up-spin Fe t2g were fully occupied and down-spin Fe eg
were empty. Moreover, the up-spin Fe eg and down-spin Fe t2g were partially
occupied near the Fermi energy, leading to a finite density of states. The
Fe4+-O-Fe4+ plane superexchange coupling should rearrange the magnetic order to
make the ferromagnetic characteristic being possible, moreover the tetragonal
displacement along the c axis could induce the perovskites materials to acquire
ferroelectric property. These reasons could lead to the fact that the
tetragonal phase BFO could be a potential multiferroics while it was produced
under the very experimental conditions. The charge density along different
crystalline planes were illustrated to show that strong covalent bonding
between O and Fe can be used to investigate the exchange coupling, and this
strong hybridization may further increase the superexchange coupling to enhance
the magnetic ordering.Comment: 6 pages, 12 figure
Electronic structure of barium titanate : an abinitio DFT study
First principle calculations were performed to study the ground state
electronic properties of Barium titanate within the density functional theory
(DFT). In our DFT computations, we used Vosko-Wilk-Nusair correlation energy
functional and generalized gradient approximation (GGA) exchange and
correlation energy functional as suggested by Perdew and Wang (PWGGA). The band
structure, total density of states (DOS) and partial DOS have been
systematically conducted to investigate the electronic configuration of this
prototype ferroelectric perovskits compound. The band gap was 1.92 eV within
our approach, and the quasi-flat band at -17 eV and -10 eV were attributed to
the O 2s and Ba 5p states respectively, which was in good agreement with the
corresponding total DOS and partial DOS. From the DOS investigation, it can be
seen that the Ti eg state intended to interact with the oxygen octahedral
orbitals to form the p-d hybridization. Moreover the strong p-d overlap and
bonding can be observed in the electronic density redistribution along the
different crystalline planes with respect to the corresponding space group, and
the electronic isodense have been shown along the (001), (100), (110) and (111)
crystal planes. From these electronic density maps, the strong bonding between
Ti and O atoms can even be observed in the (111) crystalline plane.Comment: 7 pages, 12 figures. Submitted to Physica
Additive Margin Softmax for Face Verification
In this paper, we propose a conceptually simple and geometrically
interpretable objective function, i.e. additive margin Softmax (AM-Softmax),
for deep face verification. In general, the face verification task can be
viewed as a metric learning problem, so learning large-margin face features
whose intra-class variation is small and inter-class difference is large is of
great importance in order to achieve good performance. Recently, Large-margin
Softmax and Angular Softmax have been proposed to incorporate the angular
margin in a multiplicative manner. In this work, we introduce a novel additive
angular margin for the Softmax loss, which is intuitively appealing and more
interpretable than the existing works. We also emphasize and discuss the
importance of feature normalization in the paper. Most importantly, our
experiments on LFW BLUFR and MegaFace show that our additive margin softmax
loss consistently performs better than the current state-of-the-art methods
using the same network architecture and training dataset. Our code has also
been made available at https://github.com/happynear/AMSoftmaxComment: Published in Signal Processing Letters, Volume: 25 Issue: 7 Pages:
926-93
Semi-groups of stochastic gradient descent and online principal component analysis: properties and diffusion approximations
We study the Markov semigroups for two important algorithms from machine
learning: stochastic gradient descent (SGD) and online principal component
analysis (PCA). We investigate the effects of small jumps on the properties of
the semi-groups. Properties including regularity preserving,
contraction are discussed. These semigroups are the dual of the semigroups for
evolution of probability, while the latter are contracting and
positivity preserving. Using these properties, we show that stochastic
differential equations (SDEs) in (on the sphere
) can be used to approximate SGD (online PCA) weakly. These
SDEs may be used to provide some insights of the behaviors of these algorithms
Projected Wirtinger Gradient Descent for Low-Rank Hankel Matrix Completion in Spectral Compressed Sensing
This paper considers reconstructing a spectrally sparse signal from a small
number of randomly observed time-domain samples. The signal of interest is a
linear combination of complex sinusoids at distinct frequencies. The
frequencies can assume any continuous values in the normalized frequency domain
. After converting the spectrally sparse signal recovery into a low rank
structured matrix completion problem, we propose an efficient feasible point
approach, named projected Wirtinger gradient descent (PWGD) algorithm, to
efficiently solve this structured matrix completion problem. We further
accelerate our proposed algorithm by a scheme inspired by FISTA. We give the
convergence analysis of our proposed algorithms. Extensive numerical
experiments are provided to illustrate the efficiency of our proposed
algorithm. Different from earlier approaches, our algorithm can solve problems
of very large dimensions very efficiently.Comment: 12 page
Fast Rank One Alternating Minimization Algorithm for Phase Retrieval
The phase retrieval problem is a fundamental problem in many fields, which is
appealing for investigation. It is to recover the signal vector
from a set of measurements
, where forms a frame
of . %It is generally a non-convex minimization problem, which is
NP-hard. Existing algorithms usually use a least squares fitting to the
measurements, yielding a quartic polynomial minimization. In this paper, we
employ a new strategy by splitting the variables, and we solve a bi-variate
optimization problem that is quadratic in each of the variables. An alternating
gradient descent algorithm is proposed, and its convergence for any
initialization is provided. Since a larger step size is allowed due to the
smaller Hessian, the alternating gradient descent algorithm converges faster
than the gradient descent algorithm (known as the Wirtinger flow algorithm)
applied to the quartic objective without splitting the variables. Numerical
results illustrate that our proposed algorithm needs less iterations than
Wirtinger flow to achieve the same accuracy.Comment: 18 pages, 5 figure
Topo-electronic transitions in Sb(111) nanofilm: the interplay between quantum confinement and surface effect
When the dimension of a solid structure is reduced, there will be two
emerging effects, quantum confinement and surface effect, which dominate at
nanoscale. Based on first-principles calculations, we demonstrate that due to
an intriguing interplay between these two dominating effects, the topological
and electronic (topo-electronic) properties of Sb (111) nanofilms undergo a
series of transitions as a function of the reducing film thickness:
transforming from a topological semimetal to a topological insulator at 7.8 nm
(22 bilayer), then to a quantum spin hall (QSH) phase at 2.7 nm (8 bilayer),
and finally to a normal (topological trivial) semiconductor at 1.0 nm (3
bilayer). Our theoretical findings for the first time identify the existence of
the QSH in the Sb (111) nanofilms within a narrow range of thickness and
suggest that the Sb (111) nanofilms provide an ideal test bed for experimental
study of topo-electronic phase transitions.Comment: 4 pages, 4 figure
Continuous and discrete one dimensional autonomous fractional ODEs
In this paper, we study 1D autonomous fractional ODEs , where is the unknown function and
is the generalized Caputo derivative introduced by Li and Liu (
arXiv:1612.05103). Based on the existence and uniqueness theorem and regularity
results in previous work, we show the monotonicity of solutions to the
autonomous fractional ODEs and several versions of comparison principles. We
also perform a detailed discussion of the asymptotic behavior for .
In particular, based on an Osgood type blow-up criteria, we find relatively
sharp bounds of the blow-up time in the case . These bounds indicate
that as the memory effect becomes stronger (), if the initial
value is big, the blow-up time tends to zero while if the initial value is
small, the blow-up time tends to infinity. In the case , we show that
the solution decays to zero more slowly compared with the usual derivative.
Lastly, we show several comparison principles and Gr\"onwall inequalities for
discretized equations, and perform some numerical simulations to confirm our
analysis
Iterative resource allocation based on propagation feature of node for identifying the influential nodes
The Identification of the influential nodes in networks is one of the most
promising domains. In this paper, we present an improved iterative resource
allocation (IIRA) method by considering the centrality information of neighbors
and the influence of spreading rate for a target node. Comparing with the
results of the Susceptible Infected Recovered (SIR) model for four real
networks, the IIRA method could identify influential nodes more accurately than
the tradition IRA method. Specially, in the Erdos network, the Kendall's tau
could be enhanced 23\% when the spreading rate is 0.12. In the Protein network,
the Kendall's tau could be enhanced 24\% when the spreading rate is 0.08.Comment: 6 pages, 5 figure
A note on one-dimensional time fractional ODEs
In this note, we prove or re-prove several important results regarding one
dimensional time fractional ODEs following our previous work \cite{fllx17}.
Here we use the definition of Caputo derivative proposed in
\cite{liliu17frac1,liliu2017} based on a convolution group. In particular, we
establish generalized comparison principles consistent with the new definition
of Caputo derivatives. In addition, we establish the full asymptotic behaviors
of the solutions for . Lastly, we provide a simplified
proof for the strict monotonicity and stability in initial values for the time
fractional differential equations with weak assumptions
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