An Accelerated Block Proximal Framework with Adaptive Momentum for Nonconvex and Nonsmooth Optimization

We propose an accelerated block proximal linear framework with adaptive momentum (ABPL$^+$) for nonconvex and nonsmooth optimization. We analyze the potential causes of the extrapolation step failing in some algorithms, and resolve this issue by enhancing the comparison process that evaluates the trade-off between the proximal gradient step and the linear extrapolation step in our algorithm. Furthermore, we extends our algorithm to any scenario involving updating block variables with positive integers, allowing each cycle to randomly shuffle the update order of the variable blocks. Additionally, under mild assumptions, we prove that ABPL$^+$ can monotonically decrease the function value without strictly restricting the extrapolation parameters and step size, demonstrates the viability and effectiveness of updating these blocks in a random order, and we also more obviously and intuitively demonstrate that the derivative set of the sequence generated by our algorithm is a critical point set. Moreover, we demonstrate the global convergence as well as the linear and sublinear convergence rates of our algorithm by utilizing the Kurdyka-Lojasiewicz (K{\L}) condition. To enhance the effectiveness and flexibility of our algorithm, we also expand the study to the imprecise version of our algorithm and construct an adaptive extrapolation parameter strategy, which improving its overall performance. We apply our algorithm to multiple non-negative matrix factorization with the $\ell_0$ norm, nonnegative tensor decomposition with the $\ell_0$ norm, and perform extensive numerical experiments to validate its effectiveness and efficiency

Globally Convergent Accelerated Algorithms for Multilinear Sparse Logistic Regression with ℓ0\ell_0-constraints

Tensor data represents a multidimensional array. Regression methods based on low-rank tensor decomposition leverage structural information to reduce the parameter count. Multilinear logistic regression serves as a powerful tool for the analysis of multidimensional data. To improve its efficacy and interpretability, we present a Multilinear Sparse Logistic Regression model with $\ell_0$-constraints ($\ell_0$-MLSR). In contrast to the $\ell_1$-norm and $\ell_2$-norm, the $\ell_0$-norm constraint is better suited for feature selection. However, due to its nonconvex and nonsmooth properties, solving it is challenging and convergence guarantees are lacking. Additionally, the multilinear operation in $\ell_0$-MLSR also brings non-convexity. To tackle these challenges, we propose an Accelerated Proximal Alternating Linearized Minimization with Adaptive Momentum (APALM$^+$) method to solve the $\ell_0$-MLSR model. We provide a proof that APALM$^+$ can ensure the convergence of the objective function of $\ell_0$-MLSR. We also demonstrate that APALM$^+$ is globally convergent to a first-order critical point as well as establish convergence rate by using the Kurdyka-Lojasiewicz property. Empirical results obtained from synthetic and real-world datasets validate the superior performance of our algorithm in terms of both accuracy and speed compared to other state-of-the-art methods.Comment: arXiv admin note: text overlap with arXiv:2308.1212

Understanding Users’ Continuance Usage for Social Network Services: A Theoretical Model And Empirical Assessment

As a newly emerged e-business model, Social Network Services (SNS) has encouraged new ways of communication and relationship building, also viewed as “the next big thing after Google”. This study draws attention to the substantive differences between adoption and continuance behaviors in the context of SNS, develops the usage continuance model of SNS to investigate continued usage behavior and underlying factors through literature review and theoretical analysis, verified by an empirical test that involved structural equation modeling. This study will advance the theory of IS continuance, provide a comprehensive research model to investigate the post-adoptive behaviors of SNS and help SNS-empowered businesses and organizations to identify critical factors fundamental to long-term viability and the eventual success of their businesses

Unveiling Real Triple Degeneracies in Crystals: Exploring Link and Compound Structures

With their non-Abelian topological charges, real multi-bandgap systems challenge the conventional topological phase classifications. As the minimal sector of multi-bandgap systems, real triple degeneracies (RTPs), which serves as real "Weyl points", lay the foundation for the research on real topological phases. However, experimental observation of RTP and physical systems with global band configuration consisting of multiple RTPs in crystals has not been reported. In this study, we employ Euler number to characterize RTPs, establish their connection with both Abelian and non-Abelian charges, and provide experimental evidence for the existence of RTPs in photonic meta-crystals. By considering RTPs as the basic elements, we further propose the concept of a topological compound, akin to a chemical compound, where we find that certain phases are not topologically allowed. The topological classification of RTPs in crystals demonstrated in our work plays a similar role as the "no-go" theorem in the Weyl system.Comment: 14 pages, 4 figure

Quasar Photometric Redshifts and Candidate Selection: A New Algorithm Based on Optical and Mid-Infrared Photometric Data

We present a new algorithm to estimate quasar photometric redshifts (photo-$z$s), by considering the asymmetries in the relative flux distributions of quasars. The relative flux models are built with multivariate Skew-t distributions in the multi-dimensional space of relative fluxes as a function of redshift and magnitude. For 151,392 quasars in the SDSS, we achieve a photo-$z$ accuracy, defined as the fraction of quasars with the difference between the photo-$z$ $z_p$ and the spectroscopic redshift $z_s$, $|\Delta z| = |z_s-z_p|/(1+z_s)$ within 0.1, of 74%. Combining the WISE W1 and W2 infrared data with the SDSS data, the photo-$z$ accuracy is enhanced to 87%. Using the Pan-STARRS1 or DECaLS photometry with WISE W1 and W2 data, the photo-$z$ accuracies are 79% and 72%, respectively. The prior probabilities as a function of magnitude for quasars, stars and galaxies are calculated respectively based on (1) the quasar luminosity function; (2) the Milky Way synthetic simulation with the Besan\c{c}on model; (3) the Bayesian Galaxy Photometric Redshift estimation. The relative fluxes of stars are obtained with the Padova isochrones, and the relative fluxes of galaxies are modeled through galaxy templates. We test our classification method to select quasars using the DECaLS $g$, $r$, $z$, and WISE W1 and W2 photometry. The quasar selection completeness is higher than 70% for a wide redshift range $0.5<z<4.5$, and a wide magnitude range $18<r<21.5$ mag. Our photo-$z$ regression and classification method has the potential to extend to future surveys. The photo-$z$ code will be publicly available.Comment: 22 pages, 17 figure, accepted by AJ. The code is available at https://doi.org/10.5281/zenodo.101440

Spectroscopy of broad absorption line quasars at 3≲z≲53\lesssim z \lesssim 5 -- I: evidence for quasar winds shaping broad/narrow emission line regions

We present an observational study of 22 broad absorption line quasars (BAL QSOs) at $3\lesssim z \lesssim5$ based on optical/near-IR spectroscopy, aiming to investigate quasar winds and their effects. The near-IR spectroscopy covers the \hb\ and/or \mgii\ broad emission lines (BELs) for these quasars, allowing us to estimate their central black hole (BH) masses in a robust way. We found that our BAL QSOs on average do not have a higher Eddington ratio than that from non-BAL QSOs matched in redshift and/or luminosity. In a subset consisting of seven strong BAL QSOs possessing sub-relativistic BAL outflows, we see the prevalence of large \civ-BEL blueshift ($\sim$3100 km s$^{-1}$) and weak \oiii\ emission (particularly the narrow \oiii$\lambda$5007 component), indicative of nuclear outflows affecting the narrow emission-line (NEL) regions. In another subset consisting of thirteen BAL QSOs having simultaneous observations of \mgii\ and \hb, we found a strong correlation between 3000~\AA\ and 5000~\AA\ monochromatic luminosity, consistent with that from non-BAL QSOs matched in redshift and luminosity; however, there is no correlation between \mgii\ and \hb\ in FWHM, likely due to nuclear outflows influencing the BEL regions. Our spectroscopic investigations offer strong evidence that the presence of nuclear outflows plays an important role in shaping the BEL/NEL regions of these quasars and possibly, regulating the growth of central supermassive black holes (SMBHs). We propose that BEL blueshift and BAL could be different manifestations of the same outflow system viewed at different sightlines and/or phases.Comment: 13 pages, 10 figures. Accepted for publication in Ap