Substantial progress has been made recently on developing provably accurate and efficient algorithms for low-rank matrix factorization via nonconvex optimization. While conventional wisdom often ...takes a dim view of nonconvex optimization algorithms due to their susceptibility to spurious local minima, simple iterative methods such as gradient descent have been remarkably successful in practice. The theoretical footings, however, had been largely lacking until recently. In this tutorial-style overview, we highlight the important role of statistical models in enabling efficient nonconvex optimization with performance guarantees. We review two contrasting approaches: (1) two-stage algorithms, which consist of a tailored initialization step followed by successive refinement; and (2) global landscape analysis and initialization-free algorithms. Several canonical matrix factorization problems are discussed, including but not limited to matrix sensing, phase retrieval, matrix completion, blind deconvolution, and robust principal component analysis. Special care is taken to illustrate the key technical insights underlying their analyses. This article serves as a testament that the integrated consideration of optimization and statistics leads to fruitful research findings.
Noisy matrix completion aims at estimating a low-rank matrix given only partial and corrupted entries. Despite remarkable progress in designing efficient estimation algorithms, it remains largely ...unclear how to assess the uncertainty of the obtained estimates and how to perform efficient statistical inference on the unknown matrix (e.g., constructing a valid and short confidence interval for an unseen entry). This paper takes a substantial step toward addressing such tasks. We develop a simple procedure to compensate for the bias of the widely used convex and nonconvex estimators. The resulting debiased estimators admit nearly precise nonasymptotic distributional characterizations, which in turn enable optimal construction of confidence intervals/regions for, say, the missing entries and the low-rank factors. Our inferential procedures do not require sample splitting, thus avoiding unnecessary loss of data efficiency. As a byproduct, we obtain a sharp characterization of the estimation accuracy of our debiased estimators in both rate and constant. Our debiased estimators are tractable algorithms that provably achieve full statistical efficiency.
This paper explores the problem of spectral compressed sensing, which aims to recover a spectrally sparse signal from a small random subset of its n time domain samples. The signal of interest is ...assumed to be a superposition of r multidimensional complex sinusoids, while the underlying frequencies can assume any continuous values in the normalized frequency domain. Conventional compressed sensing paradigms suffer from the basis mismatch issue when imposing a discrete dictionary on the Fourier representation. To address this issue, we develop a novel algorithm, called enhanced matrix completion (EMaC), based on structured matrix completion that does not require prior knowledge of the model order. The algorithm starts by arranging the data into a low-rank enhanced form exhibiting multifold Hankel structure, and then attempts recovery via nuclear norm minimization. Under mild incoherence conditions, EMaC allows perfect recovery as soon as the number of samples exceeds the order of r log 4 n, and is stable against bounded noise. Even if a constant portion of samples are corrupted with arbitrary magnitude, EMaC still allows exact recovery, provided that the sample complexity exceeds the order of r 2 log 3 n. Along the way, our results demonstrate the power of convex relaxation in completing a low-rank multifold Hankel or Toeplitz matrix from minimal observed entries. The performance of our algorithm and its applicability to super resolution are further validated by numerical experiments.
Canonical functions of mitochondria include the regulation of cellular survival, orchestration of anabolic and metabolic pathways, as well as reactive oxygen species (ROS) signaling. Recent ...discoveries, nevertheless, have demonstrated that mitochondria are also critical elements to stimulate innate immune signaling cascade that is able to intensify the inflammation upon cytotoxic stimuli beyond microbial infection. Here we review the expanding research field of mitochondria and oxidative stress in innate immune system to highlight the new mechanistic insights and discuss the pathological relevance of mitochondrial dysregulation induced aberrant innate immune responses in a growing list of sterile inflammatory diseases.
Statistical inference and information processing of high-dimensional data often require an efficient and accurate estimation of their second-order statistics. With rapidly changing data, limited ...processing power and storage at the acquisition devices, it is desirable to extract the covariance structure from a single pass over the data and a small number of stored measurements. In this paper, we explore a quadratic (or rank-one) measurement model which imposes minimal memory requirements and low computational complexity during the sampling process, and is shown to be optimal in preserving various low-dimensional covariance structures. Specifically, four popular structural assumptions of covariance matrices, namely, low rank, Toeplitz low rank, sparsity, jointly rank-one and sparse structure, are investigated, while recovery is achieved via convex relaxation paradigms for the respective structure. The proposed quadratic sampling framework has a variety of potential applications, including streaming data processing, high-frequency wireless communication, phase space tomography and phase retrieval in optics, and noncoherent subspace detection. Our method admits universally accurate covariance estimation in the absence of noise, as soon as the number of measurements exceeds the information theoretic limits. We also demonstrate the robustness of this approach against noise and imperfect structural assumptions. Our analysis is established upon a novel notion called the mixed-norm restricted isometry property (RIP-ℓ 2 /ℓ 1 ), as well as the conventional RIP-ℓ 2 /ℓ 2 for near-isotropic and bounded measurements. In addition, our results improve upon the best-known phase retrieval (including both dense and sparse signals) guarantees using PhaseLift with a significantly simpler approach.
•Eco-economy coupling coordination (CCD) index at county level in was evaluated.•Obvious spatial agglomeration of eco-economy CCD index in north China was found.•The driving factors of eco-economy ...CCD index was studied by geodetector.•Terrain has the greatest influence on eco-economic coupling, then is transportation.
Coordinating ecological and socioeconomic development is the only way to achieve regional sustainability. In this paper, the total output value of ecosystem services was selected to evaluate the ecological environment, and socioeconomic indicators were selected to evaluate socioeconomic development. The coupling coordination degree (CCD) between the ecological environment and economy of counties in northern China was evaluated by combining an entropy method and a coupling coordination model. Spatial autocorrelation and a geographical detector model were used to reveal the spatial agglomeration characteristics and factors that influence the coordination degree of the ecological–economic system in northern China. Results showed that, in 2019, most counties were in the ecological–economic transition development stage. Among them, 321 counties had a CCD index between 0.4 and 0.5 (basic coordination stage); 209 counties had a CCD index between 0.5 and 0.6 (primary coordination stage); and 77 counties had a CCD index between 0.6 and 0.8 (moderate coordination stage). The global Moran’s I was 0.349, indicating that there was spatial agglomeration of ecological–economic coupling coordination at a county level. Low-low clusters were mainly found in the central and eastern central part of the study area, and high–high clusters were mainly found in northern Hebei province, Shandong peninsula, and northern Henan province. The factors that influenced the CCD index, ordered from the largest to the smallest, were landscape, terrain, traffic, and climate factors. The interactions between driving factors showed nonlinear and bilinear enhancement. The findings show that the coordination of socioeconomic and ecological development in northern China can be further improved. Relevant policies should emphasize the local ecological advantages, promote the transformation to ecological industrialization, and encourage ecologically and economically balanced development.
Irisin, a recently identified myokine that is released from skeletal muscle following exercise, regulates body weight and influences various metabolic diseases such as obesity and diabetes. In this ...study, human recombinant nonglycosylated P-irisin (expressed in Escherichia coli prokaryote cell system) or glycosylated E-irisin (expressed in Pichia pastoris eukaryote cell system) were compared to examine the role of recombinant irisin against pancreatic cancer (PC) cells lines, MIA PaCa-2 and Panc03.27. MTT 3-(4, 5-dimethylthiazol-2-yl)-2, 5-di phenyltetrazolium bromide and cell colony formation assays revealed that irisin significantly inhibited the growth of MIA PaCa-2 and Panc03.27 in a dose-dependent manner. Irisin also induced G1 arrest in both cell lines. Scratch wound healing and transwell assays revealed that irisin also inhibited the migration of PC cells. Irisin reversed the activity of epithelial-mesenchymal transition (EMT) while increasing E-cadherin expression and reducing vimentin expression. Irisin activated the adenosine monophosphate-activated protein kinase (AMPK) pathway and suppressed the mammalian target of rapamycin (mTOR) signaling. Besides, our results suggest that irisin receptors exist on the surface of human MIA PaCa-2 and Panc03.27 cells. Our results clearly demonstrate that irisin suppressed PC cell growth via the activation of AMPK, thereby downregulating the mTOR pathway and inhibiting EMT of PC cells.
O-GlcNAcylation has been implicated in the tumorigenesis of various tissue origins, but its function in liver tumorigenesis is not clear. Here, we demonstrate that O-GlcNAcylation can enhance the ...expression, stability and function of Yes-associated protein (YAP), the downstream transcriptional regulator of the Hippo pathway and a potent oncogenic factor in liver cancer. O-GlcNAcylation induces transformative phenotypes of liver cancer cells in a YAP-dependent manner. An O-GlcNAc site of YAP was identified at Thr241, and mutating this site decreased the O-GlcNAcylation, stability, and pro-tumorigenic capacities of YAP, while increasing YAP phosphorylation. Importantly, we found via in vitro cell-based and in vivo mouse model experiments that O-GlcNAcylation of YAP was required for high-glucose-induced liver tumorigenesis. Interestingly, a positive feedback between YAP and global cellular O-GlcNAcylation is also uncovered. We conclude that YAP O-GlcNAcylation is a potential therapeutic intervention point for treating liver cancer associated with high blood glucose levels and possibly diabetes.
The traditional luminol–H2O2 electrochemiluminescence (ECL) sensing platform suffers from self‐decomposition of H2O2 at room temperature, hampering its application for quantitative analysis. In this ...work, for the first time we employ iron single‐atom catalysts (Fe‐N‐C SACs) as an advanced co‐reactant accelerator to directly reduce the dissolved oxygen (O2) to reactive oxygen species (ROS). Owing to the unique electronic structure and catalytic activity of Fe‐N‐C SACs, large amounts of ROS are efficiently produced, which then react with the luminol anion radical and significantly amplify the luminol ECL emission. Under the optimum conditions, a Fe‐N‐C SACs–luminol ECL sensor for antioxidant capacity measurement was developed with a good linear range from 0.8 μm to 1.0 mm of Trolox.
Boosting luminescence: The traditional luminol–H2O2 electrochemiluminescence (ECL) sensing platform suffers from self‐decomposition of H2O2 at room temperature, hampering its application for quantitative analysis. Single‐atom iron boosts luminol ECL by in situ generating reactive oxygen species, achieving sensitive detection of antioxidants.
We propose a minimal model of predator–swarm interactions which captures many of the essential dynamics observed in nature. Different outcomes are observed depending on the predator strength. For a ...‘weak’ predator, the swarm is able to escape the predator completely. As the strength is increased, the predator is able to catch up with the swarm as a whole, but the individual prey is able to escape by ‘confusing’ the predator: the prey forms a ring with the predator at the centre. For higher predator strength, complex chasing dynamics are observed which can become chaotic. For even higher strength, the predator is able to successfully capture the prey. Our model is simple enough to be amenable to a full mathematical analysis, which is used to predict the shape of the swarm as well as the resulting predator–prey dynamics as a function of model parameters. We show that, as the predator strength is increased, there is a transition (owing to a Hopf bifurcation) from confusion state to chasing dynamics, and we compute the threshold analytically. Our analysis indicates that the swarming behaviour is not helpful in avoiding the predator, suggesting that there are other reasons why the species may swarm. The complex shape of the swarm in our model during the chasing dynamics is similar to the shape of a flock of sheep avoiding a shepherd.
PDF
