Variational Analysis of Kurdyka-{\L}ojasiewicz Property, Exponent and Modulus

The Kurdyka-{\L}ojasiewicz (K{\L}) property, exponent and modulus have played a very important role in the study of global convergence and rate of convergence for optimal algorithms. In this paper, at a stationary point of a locally lower semicontinuous function, we obtain complete characterizations of the K{\L} property and the K{\L} modulus via the outer limiting subdifferential of an auxilliary function and a newly-introduced subderivative function respectively. In particular, for a class of prox-regular, twice epi-differentiable and subdifferentially continuous functions, we show that the K{\L} property and the K{\L} modulus can be described by its Moreau envelopes and a quadratic growth condition. We apply the obtained results to establish the K{\L} property with exponent $\frac12$ and to provide calculation of the modulus for a smooth function, the pointwise maximum of finitely many smooth functions and regularized functions respectively. These functions often appear in the modelling of structured optimization problems.Comment: 28 page

Projectional Coderivatives and Calculus Rules

This paper is devoted to the study of a newly introduced tool, projectional coderivatives and the corresponding calculus rules in finite dimensions. We show that when the restricted set has some nice properties, more specifically, is a smooth manifold, the projectional coderivative can be refined as a fixed-point expression. We will also improve the generalized Mordukhovich criterion to give a complete characterization of the relative Lipschitz-like property under such a setting. Chain rules and sum rules are obtained to facilitate the application of the tool to a wider range of problems

An Adaptive Incremental Gradient Method With Support for Non-Euclidean Norms

Stochastic variance reduced methods have shown strong performance in solving finite-sum problems. However, these methods usually require the users to manually tune the step-size, which is time-consuming or even infeasible for some large-scale optimization tasks. To overcome the problem, we propose and analyze several novel adaptive variants of the popular SAGA algorithm. Eventually, we design a variant of Barzilai-Borwein step-size which is tailored for the incremental gradient method to ensure memory efficiency and fast convergence. We establish its convergence guarantees under general settings that allow non-Euclidean norms in the definition of smoothness and the composite objectives, which cover a broad range of applications in machine learning. We improve the analysis of SAGA to support non-Euclidean norms, which fills the void of existing work. Numerical experiments on standard datasets demonstrate a competitive performance of the proposed algorithm compared with existing variance-reduced methods and their adaptive variants

Nucleocapsid mutations R203K/G204R increase the infectivity, fitness, and virulence of SARS-CoV-2

Previous work found that the co-occurring mutations R203K/G204R on the SARS-CoV-2 nucleocapsid (N) protein are increasing in frequency among emerging variants of concern or interest. Through a combination of in silico analyses, this study demonstrates that R203K/G204R are adaptive, while large-scale phylogenetic analyses indicate that R203K/G204R associate with the emergence of the high-transmissibility SARS-CoV-2 lineage B.1.1.7. Competition experiments suggest that the 203K/204R variants possess a replication advantage over the preceding R203/G204 variants, possibly related to ribonucleocapsid (RNP) assembly. Moreover, the 203K/204R virus shows increased infectivity in human lung cells and hamsters. Accordingly, we observe a positive association between increased COVID-19 severity and sample frequency of 203K/204R. Our work suggests that the 203K/204R mutations contribute to the increased transmission and virulence of select SARS-CoV-2 variants. In addition to mutations in the spike protein, mutations in the nucleocapsid protein are important for viral spreading during the pandemic

Digoxin protects against intervertebral disc degeneration via TNF/NF-κB and LRP4 signaling

BackgroundIntervertebral disc degeneration (IVDD) is a leading cause of low back pain (LBP). The pathological process of IVDD is associated with inflammatory reactions and extracellular matrix (ECM) disorders. Digoxin is widely used for treating heart failure, and it has been reported to have anti-inflammatory effects.ObjectiveThis study is to investigate the role of digoxin in the pathogenesis of intervertebral disc degeneration as well as the involved molecular mechanism, particularly the potential target protein.MethodsWe exploited a rat needle model to investigate digoxin’s role in intervertebral disc degeneration in vivo. Safranin O staining was used to measure cartilaginous tissue in the intervertebral disc. The morphological changes of intervertebral discs in animal models were determined by Hematoxylin-Eosin (H&E) staining and the pathological score. Primary nucleus pulposus cells (NP cells) from intervertebral discs of patients and murine were used in the present study. Western-Blotting assay, Real-time PCR assay, immunofluorescence staining, and immunochemistry were used to detect the role of digoxin in anti-TNF-α-induced inflammatory effects in vitro. Transfection of siRNA was used to regulate low-density lipoprotein receptor-related protein 4 (LRP4) expression in NP cells to investigate the potential protein target of digoxin.ResultsDigoxin protected against intervertebral disc degeneration in rat needle models. Digoxin was found to exert its disc-protective effects through at least three different pathways by a) suppressing TNF-α-induced inflammation, b) attenuating ECM destruction, c) significantly promoting ECM anabolism. Additionally, LRP4 was found to be the downstream molecule of digoxin in NP cells for anti-inflammation and regulation of ECM metabolism. The knockdown of LRP4 downregulated the protective effect of digoxin in NP cells.ConclusionThese findings suggest that digoxin may be a potential therapeutic agent for intervertebral disc degeneration through anti-catabolism and pro-anabolism. Digoxin might also work as an alternative for other inflammation-related diseases

Feedforward neural network model estimating pollutant removal process within mesophilic upflow anaerobic sludge blanket bioreactor treating industrial starch processing wastewater

In this a, three-layered feedforward-backpropagation artificial neural network (BPANN) model was developed and employed to evaluate COD removal an upflow anaerobic sludge blanket (UASB) reactor treating industrial starch processing wastewater. At the end of UASB operation, microbial community characterization revealed satisfactory composition of microbes whereas morphology depicted rod-shaped archaea. pH, COD, NH, VFA, OLR and biogas yield were selected by principal component analysis and used as input variables. Whilst tangent sigmoid function (tansig) and linear function (purelin) were assigned as activation functions at the hidden-layer and output-layer, respectively, optimum BPANN architecture was achieved with Levenberg-Marquardt algorithm (trainlm) after eleven training algorithms had been tested. Based on performance indicators such the mean squared errors, fractional variance, index of agreement and coefficient of determination (R), the BPANN model demonstrated significant performance with Rreaching 87%. The study revealed that, control and optimization of an anaerobic digestion process with BPANN model was feasible

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead