VeST: Very Sparse Tucker Factorization of Large-Scale Tensors

Given a large tensor, how can we decompose it to sparse core tensor and factor matrices such that it is easier to interpret the results? How can we do this without reducing the accuracy? Existing approaches either output dense results or give low accuracy. In this paper, we propose VeST, a tensor factorization method for partially observable data to output a very sparse core tensor and factor matrices. VeST performs initial decomposition, determines unimportant entries in the decomposition results, removes the unimportant entries, and carefully updates the remaining entries. To determine unimportant entries, we define and use entry-wise 'responsibility' for the decomposed results. The entries are updated iteratively in a coordinate descent manner in parallel for scalable computation. Extensive experiments show that our method VeST is at least 2.2 times more sparse and at least 2.8 times more accurate compared to competitors. Moreover, VeST is scalable in terms of input order, dimension, and the number of observable entries. Thanks to VeST, we successfully interpret the result of real-world tensor data based on the sparsity pattern of the resulting factor matrices

First-principles study of ferroelectricity induced by p-d hybridization in ferrimagnetic NiFe2O4

We investigate the ferrimagnetism and ferroelectricity of bulk NiFe$_2$O$_4$ with tetragonal $P4_122$ ~symmetry by means of density functional calculations using generalized gradient approximation + Hubbard $U$ approach. Special attention is paid to finding the most energetically favorable configuration on magnetic ordering and further calculating the reliable spontaneous electric polarization. With the fully optimized crystalline structure of the most stable configuration, the spontaneous polarization is obtained to be 23 $\mu$C/cm$^2$ along the z direction, which originates from the hybridization between the 3d states of the Fe$^{3+}$ cation and the 2p states of oxygen induced by Jahn-Teller effect

Influence of halide composition on the structural, electronic, and optical properties of mixed CH3_3NH3_3Pb(I1−x_{1-x}Brx_x)3_3 perovskites calculated using the virtual crystal approximation method

We investigate the structural, electronic and optical properties of mixed bromide-iodide lead perovskite solar cell CH$_3$NH$_3$Pb(I$_{1-x}$Br$_x$)$_3$ by means of the virtual crystal approximation (VCA) within density functional theory (DFT). Optimizing the atomic positions and lattice parameters increasing the bromide content $x$ from 0.0 to 1.0, we fit the calculated lattice parameter and energy band gap to the linear and quadratic function of Br content, respectively, which are in good agreement with the experiment, respecting the Vegard's law. With the calculated exciton binding energy and light absorption coefficient, we make sure that VCA gives consistent results with the experiment, and the mixed halide perovskites are suitable for generating the charge carriers by light absorption and conducting the carriers easily due to their strong photon absorption coefficient, low exciton bindign energy, and high carrier mobility at low Br contents. Furthermore analyzing the bonding lengths between Pb and X (I$_{1-x}$Br$_x$: virtual atom) as well as C and N, we stress that the stability of perovskite solar cell is definitely improved at $x$=0.2

Electronic structure and photo absorption property of pseudo-cubic perovskites CH3_3NH3_3PbX3_3 (X=I, Br) including van der Waals interaction

Using density functional theory with the inclusion of van der Waals (vdW) interaction, we have investigated electronic energy bands, density of states, effective masses of charge carriers, and photo absorption coefficients of pseudo-cubic CH$_3$NH$_3$PbX$_3$ (X=I, Br). Our results confirm the direct bandgap of 1.49 (1.92) eV for X=I (Br) in the pseudo-cubic $Pm$ phase with lattice constant of 6.324 (5.966) \AA, being agreed well with experiment and indicating the necessity of vdW correction. The calculated photo absorption coefficients for X=I (Br) have the onset at red (orange) color and the first peak around violet (ultraviolet) color in overall agreement with the experiment.Comment: 3pages, 3figures, App. Phys. Lett. 201

First-principles study on the electronic and optical properties of inorganic perovskite Rb1-xCsxPbI3 for solar cell applications

Recently, replacing or mixing organic molecules in the hybrid halide perovskites with the inorganic Cs or Rb cations has been reported to increase the material stability with the comparable solar cell performance. In this work, we systematically investigate the electronic and optical properties of all-inorganic alkali iodide perovskites Rb1-xCsxPbI3 using the first-principles virtual crystal approximation calculations. Our calculations show that as increasing the Cs content x, lattice constants, band gaps, exciton binding energies, and effective masses of charge carriers decrease following the quadratic (linear for effective masses) functions, while static dielectric constants increase following the quadratic function, indicating an enhancement of solar cell performance upon the Rb addition to CsPbI3. When including the many-body interaction within the GW approximation and incorporating the spin-orbit coupling (SOC), we obtain more reliable band gap compared with experiment for CsPbI3, highlighting the importance of using GW+SOC approach for the all-inorganic as well as organic-inorganic hybrid halide perovskite materials

Time-Aware Tensor Decomposition for Missing Entry Prediction

Given a time-evolving tensor with missing entries, how can we effectively factorize it for precisely predicting the missing entries? Tensor factorization has been extensively utilized for analyzing various multi-dimensional real-world data. However, existing models for tensor factorization have disregarded the temporal property for tensor factorization while most real-world data are closely related to time. Moreover, they do not address accuracy degradation due to the sparsity of time slices. The essential problems of how to exploit the temporal property for tensor decomposition and consider the sparsity of time slices remain unresolved. In this paper, we propose TATD (Time-Aware Tensor Decomposition), a novel tensor decomposition method for real-world temporal tensors. TATD is designed to exploit temporal dependency and time-varying sparsity of real-world temporal tensors. We propose a new smoothing regularization with Gaussian kernel for modeling time dependency. Moreover, we improve the performance of TATD by considering time-varying sparsity. We design an alternating optimization scheme suitable for temporal tensor factorization with our smoothing regularization. Extensive experiments show that TATD provides the state-of-the-art accuracy for decomposing temporal tensors.Comment: 20 page

Structural and optoelectronic properties of the inorganic perovskites AGeX3 (A = Cs, Rb; X = I, Br, Cl) for solar cell application

We predict the structural, electronic and optic properties of the inorganic Ge-based halide perovskites AGeX3 (A = Cs, Rb; X = I, Br, Cl) by using first-principles method. In particular, absolute electronic energy band levels are calculated using two different surface terminations of each compound, reproducing the experimental band alignment

First-principles study on the chemical decomposition of inorganic perovskites \ce{CsPbI3} and \ce{RbPbI3} at finite temperature and pressure

Inorganic halide perovskite \ce{Cs(Rb)PbI3} has attracted significant research interest in the application of light-absorbing material of perovskite solar cells (PSCs). Although there have been extensive studies on structural and electronic properties of inorganic halide perovskites, the investigation on their thermodynamic stability is lack. Thus, we investigate the effect of substituting Rb for Cs in \ce{CsPbI3} on the chemical decomposition and thermodynamic stability using first-principles thermodynamics. By calculating the formation energies of solid solutions \ce{Cs$_{1-x}$Rb$_x$PbI3} from their ingredients \ce{Cs$_{1-x}$Rb$_x$I} and \ce{PbI2}, we find that the best match between efficiency and stability can be achieved at the Rb content $x\approx$ 0.7. The calculated Helmholtz free energy of solid solutions indicates that \ce{Cs$_{1-x}$Rb$_x$PbI3} has a good thermodynamic stability at room temperature due to a good miscibility of \ce{CsPbI3} and \ce{RbPbI3}. Through lattice-dynamics calculations, we further highlight that \ce{RbPbI3} never stabilize in cubic phase at any temperature and pressure due to the chemical decomposition into its ingredients \ce{RbI} and \ce{PbI2}, while \ce{CsPbI3} can be stabilized in the cubic phase at the temperature range of 0$-$600 K and the pressure range of 0$-$4 GPa. Our work reasonably explains the experimental observations, and paves the way for understanding material stability of the inorganic halide perovskites and designing efficient inorganic halide PSCs

Fast Partial Fourier Transform

Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications. Despite its pervasive use, all known FFT algorithms do not provide a fine-tuning option for the user to specify one's demand, that is, the output size (the number of Fourier coefficients to be computed) is algorithmically determined by the input size. This matters because not every application using FFT requires the whole spectrum of the frequency domain, resulting in an inefficiency due to extra computation. In this paper, we propose a fast Partial Fourier Transform (PFT), a careful modification of the Cooley-Tukey algorithm that enables one to specify an arbitrary consecutive range where the coefficients should be computed. We derive the asymptotic time complexity of PFT with respect to input and output sizes, as well as its numerical accuracy. Experimental results show that our algorithm outperforms the state-of-the-art FFT algorithms, with an order of magnitude of speedup for sufficiently small output sizes without sacrificing accuracy.Comment: 15 pages, 3 figure

First-principles study of ternary graphite compounds cointercalated with alkali atoms (Li, Na, and K) and alkylamines towards alkali ion battery applications

Using density functional theory calculations, we have investigated the structural, energetic, and electronic properties of ternary graphite intercalation compounds (GICs) containing alkali atoms (AM) and normal alkylamine molecules (nC$x$), denoted as AM-nC$x$-GICs (AM=Li, Na, K, $x$=1, 2, 3, 4). The orthorhombic unit cells have been used to build the models for crystalline stage-I AM-nC$x$-GICs. By performing the variable cell relaxations and the analysis of results, we have found that with the increase in the atomic number of alkali atoms the layer separations decreases in contrast to AM-GICs, while the bond lengths of alkali atoms with graphene layer and nitrogen atom of alkylamine decreases. The formation and interlayer binding energies of AM-nC3-GICs have been calculated, indicating the increase in stability from Li to K. The calculated energy barriers for migration of alkali atoms suggest that alkali cation with larger ionic radius diffuses in graphite more smoothly, being similar to AM-GICs. The analysis of density of states, electronic density differences, and atomic populations illustrates a mechanism how the insertion of especially Na among alkali atoms into graphite with first stage can be made easy by cointercalation with alkylamine, more extent of electronic charge transfer is occurred from more electropositive alkali atom to carbon ring of graphene layer, while alkylamine molecules interact strongly with graphene layer through the hybridization of valence electron orbitals.Comment: 22 pages, 9 figure