Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterization

Many problems encountered in science and engineering can be formulated as estimating a low-rank object (e.g., matrices and tensors) from incomplete, and possibly corrupted, linear measurements. Through the lens of matrix and tensor factorization, one of the most popular approaches is to employ simple iterative algorithms such as gradient descent (GD) to recover the low-rank factors directly, which allow for small memory and computation footprints. However, the convergence rate of GD depends linearly, and sometimes even quadratically, on the condition number of the low-rank object, and therefore, GD slows down painstakingly when the problem is ill-conditioned. This chapter introduces a new algorithmic approach, dubbed scaled gradient descent (ScaledGD), that provably converges linearly at a constant rate independent of the condition number of the low-rank object, while maintaining the low per-iteration cost of gradient descent for a variety of tasks including sensing, robust principal component analysis and completion. In addition, ScaledGD continues to admit fast global convergence to the minimax-optimal solution, again almost independent of the condition number, from a small random initialization when the rank is over-specified in the presence of Gaussian noise. In total, ScaledGD highlights the power of appropriate preconditioning in accelerating nonconvex statistical estimation, where the iteration-varying preconditioners promote desirable invariance properties of the trajectory with respect to the symmetry in low-rank factorization without hurting generalization.Comment: Book chapter for "Explorations in the Mathematics of Data Science - The Inaugural Volume of the Center for Approximation and Mathematical Data Analytics". arXiv admin note: text overlap with arXiv:2104.1452

RTVis: Research Trend Visualization Toolkit

When researchers and practitioners are about to start a new project or have just entered a new research field, choosing a proper research topic is always challenging. To help them have an overall understanding of the research trend in real-time and find out the research topic they are interested in, we develop the Research Trend Visualization toolkit (RTVis) to analyze and visualize the research paper information. RTVis consists of a field theme river, a co-occurrence network, a specialized citation bar chart, and a word frequency race diagram, showing the field change through time respectively, cooperating relationship among authors, paper citation numbers in different venues, and the most common words in the abstract part. Moreover, RTVis is open source and easy to deploy. The demo of our toolkit and code with detailed documentation are both available online.Comment: Work submitted to IEEE VIS 2023 (Poster). 2 pages, 1 figure. For our demo page, visit http://www.rtvis.design

Hierarchical-level rain image generative model based on GAN

Autonomous vehicles are exposed to various weather during operation, which is likely to trigger the performance limitations of the perception system, leading to the safety of the intended functionality (SOTIF) problems. To efficiently generate data for testing the performance of visual perception algorithms under various weather conditions, a hierarchical-level rain image generative model, rain conditional CycleGAN (RCCycleGAN), is constructed. RCCycleGAN is based on the generative adversarial network (GAN) and can generate images of light, medium, and heavy rain. Different rain intensities are introduced as labels in conditional GAN (CGAN). Meanwhile, the model structure is optimized and the training strategy is adjusted to alleviate the problem of mode collapse. In addition, natural rain images of different intensities are collected and processed for model training and validation. Compared with the two baseline models, CycleGAN and DerainCycleGAN, the peak signal-to-noise ratio (PSNR) of RCCycleGAN on the test dataset is improved by 2.58 dB and 0.74 dB, and the structural similarity (SSIM) is improved by 18% and 8%, respectively. The ablation experiments are also carried out to validate the effectiveness of the model tuning

Microbial functional traits are sensitive indicators of mild disturbance by lamb grazing.

Mild disturbances are prevalent in the environment, which may not be easily notable but could have considerable ecological consequences over prolonged periods. To evaluate this, a field study was designed to examine the effects of very light-intensity lamb grazing on grassland soil microbiomes with different soil backgrounds. No significant change (P > 0.05) was observed in any vegetation and soil variables. Nonetheless, hundreds of microbial functional gene families, but not bacterial taxonomy, were significantly (P < 0.05) shifted. The relative abundances of both taxonomic markers and functional genes related to nitrifying bacteria were also changed. The observation highlighted herein, showing a high level of sensitivity with respect to functional traits (functionally categorized taxa or genes) in differentiating mild environmental disturbance, suggests that the key level at which to address microbial responses may not be "species" (by means of rRNA taxonomy), but rather at the functional gene level

Divergent taxonomic and functional responses of microbial communities to field simulation of aeolian soil erosion and deposition.

Aeolian soil erosion and deposition have worldwide impacts on agriculture, air quality and public health. However, ecosystem responses to soil erosion and deposition remain largely unclear in regard to microorganisms, which are the crucial drivers of biogeochemical cycles. Using integrated metagenomics technologies, we analysed microbial communities subjected to simulated soil erosion and deposition in a semiarid grassland of Inner Mongolia, China. As expected, soil total organic carbon and plant coverage were decreased by soil erosion, and soil dissolved organic carbon (DOC) was increased by soil deposition, demonstrating that field simulation was reliable. Soil microbial communities were altered (p < .039) by both soil erosion and deposition, with dramatic increase in Cyanobacteria related to increased stability in soil aggregates. amyA genes encoding α-amylases were specifically increased (p = .01) by soil deposition and positively correlated (p = .02) to DOC, which likely explained changes in DOC. Surprisingly, most of microbial functional genes associated with carbon, nitrogen, phosphorus and potassium cycling were decreased or unaltered by both erosion and deposition, probably arising from acceleration of organic matter mineralization. These divergent responses support the necessity to include microbial components in evaluating ecological consequences. Furthermore, Mantel tests showed strong, significant correlations between soil nutrients and functional structure but not taxonomic structure, demonstrating close relevance of microbial function traits to nutrient cycling

Multidifferential study of identified charged hadron distributions in ZZ-tagged jets in proton-proton collisions at s=\sqrt{s}=13 TeV

Jet fragmentation functions are measured for the first time in proton-proton collisions for charged pions, kaons, and protons within jets recoiling against a $Z$ boson. The charged-hadron distributions are studied longitudinally and transversely to the jet direction for jets with transverse momentum 20 $< p_{\textrm{T}} < 100$ GeV and in the pseudorapidity range $2.5 < \eta < 4$. The data sample was collected with the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 1.64 fb$^{-1}$. Triple differential distributions as a function of the hadron longitudinal momentum fraction, hadron transverse momentum, and jet transverse momentum are also measured for the first time. This helps constrain transverse-momentum-dependent fragmentation functions. Differences in the shapes and magnitudes of the measured distributions for the different hadron species provide insights into the hadronization process for jets predominantly initiated by light quarks.Comment: All figures and tables, along with machine-readable versions and any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-013.html (LHCb public pages

Study of the B−→Λc+Λˉc−K−B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-} decay

The decay $B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-}$ is studied in proton-proton collisions at a center-of-mass energy of $\sqrt{s}=13$ TeV using data corresponding to an integrated luminosity of 5 $\mathrm{fb}^{-1}$ collected by the LHCb experiment. In the $\Lambda_{c}^+ K^{-}$ system, the $\Xi_{c}(2930)^{0}$ state observed at the BaBar and Belle experiments is resolved into two narrower states, $\Xi_{c}(2923)^{0}$ and $\Xi_{c}(2939)^{0}$, whose masses and widths are measured to be $$m(\Xi_{c}(2923)^{0}) = 2924.5 \pm 0.4 \pm 1.1 \,\mathrm{MeV}, \\ m(\Xi_{c}(2939)^{0}) = 2938.5 \pm 0.9 \pm 2.3 \,\mathrm{MeV}, \\ \Gamma(\Xi_{c}(2923)^{0}) = \phantom{000}4.8 \pm 0.9 \pm 1.5 \,\mathrm{MeV},\\ \Gamma(\Xi_{c}(2939)^{0}) = \phantom{00}11.0 \pm 1.9 \pm 7.5 \,\mathrm{MeV},$$ where the first uncertainties are statistical and the second systematic. The results are consistent with a previous LHCb measurement using a prompt $\Lambda_{c}^{+} K^{-}$ sample. Evidence of a new $\Xi_{c}(2880)^{0}$ state is found with a local significance of $3.8\,\sigma$, whose mass and width are measured to be $2881.8 \pm 3.1 \pm 8.5\,\mathrm{MeV}$ and $12.4 \pm 5.3 \pm 5.8 \,\mathrm{MeV}$, respectively. In addition, evidence of a new decay mode $\Xi_{c}(2790)^{0} \to \Lambda_{c}^{+} K^{-}$ is found with a significance of $3.7\,\sigma$. The relative branching fraction of $B^{-} \to \Lambda_{c}^{+} \bar{\Lambda}_{c}^{-} K^{-}$ with respect to the $B^{-} \to D^{+} D^{-} K^{-}$ decay is measured to be $2.36 \pm 0.11 \pm 0.22 \pm 0.25$, where the first uncertainty is statistical, the second systematic and the third originates from the branching fractions of charm hadron decays.Comment: All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2022-028.html (LHCb public pages