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, $L^{\infty}$ contraction are discussed. These semigroups are the dual of the semigroups for evolution of probability, while the latter are $L^{1}$ contracting and positivity preserving. Using these properties, we show that stochastic differential equations (SDEs) in $\mathbb{R}^d$ (on the sphere $\mathbb{S}^{d-1}$) 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 $R$ distinct frequencies. The frequencies can assume any continuous values in the normalized frequency domain $[0,1)$. 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 $\tilde{x}\in\mathbb{C}^d$ from a set of $N$ measurements $b_n=|f^*_n\tilde{x}|^2,\ n=1,\cdots, N$, where $\{f_n\}_{n=1}^N$ forms a frame of $\mathbb{C}^d$. %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 $D_c^{\gamma}u=f(u), 0< \gamma <1$, where $u: [0,\infty)\mapsto\mathbb{R}$ is the unknown function and $D_c^{\gamma}$ 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 $f(u)=Au^p$. In particular, based on an Osgood type blow-up criteria, we find relatively sharp bounds of the blow-up time in the case $A>0, p>1$. These bounds indicate that as the memory effect becomes stronger ($\gamma\to 0$), 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 $A1$, 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

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 $D_c^{\gamma}u=Au^p$. Lastly, we provide a simplified proof for the strict monotonicity and stability in initial values for the time fractional differential equations with weak assumptions

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