On the local convergence of a deformed Newton's method under Argyros-type condition

AbstractFor the iteration which was independently proposed by King [R.F. King, Tangent method for nonlinear equations, Numer. Math. 18 (1972) 298–304] and Werner [W. Werner, Über ein Verfarhren der Ordnung 1+2 zur Nullstellenbestimmung, Numer. Math. 32 (1979) 333–342] for solving a nonlinear operator equation in Banach space, we established a local convergence theorem under the condition which was introduced recently by Argyros [I.K. Argyros, A unifying local-semilocal convergence analysis and application for two-point Newton-like methods in Banach space, J. Math. Anal. Appl. 298 (2004) 374–397]

On the local convergence of inexact Newton-type methods under residual control-type conditions

AbstractA local convergence analysis of inexact Newton-type methods using a new type of residual control was recently presented by C. Li and W. Shen. Here, we introduce the center-Hölder condition on the operator involved, and use it in combination with the Hölder condition to provide a new local convergence analysis with the following advantages: larger radius of convergence, and tighter error bounds on the distances involved. These results are obtained under the same hypotheses and computational cost. Numerical examples further validating the theoretical results are also provided in this study

A simplified proof of the Kantorovich theorem for solving equations using telescopic series

We extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting. Under the same information but using elementary scalar telescopic majorizing series, we provide a simpler proof for the (KT) [2], [7]. Our results provide at least as precise information on the location of the solution. Numerical examples are also provided in this study

Convergence of Halley's method under centered Lipschitz condition on the second Fréchet derivative

We present a semi-local as well as a local convergence analysis of Halley's method for approximating a locally unique solution of a nonlinear equation in a Banach space setting. We assume that the second Fréchet-derivative satisfies a centered Lipschitz condition. Numerical examples are used to show that the new convergence criteria are satisfied but earlier ones are not satisfied

On the semilocal convergence of derivative free methods for solving nonlinear equations

We introduce a Derivative Free Method (DFM) for solving nonlinear equations in a Banach space setting. We provide a semilocal convergence analysis for DFM using recurrence relations. Numerical examples validating our theoretical results are also provided in this study to show that DFM is faster than other derivative free methods [9] using similar information

Fine-grained Domain Adaptive Crowd Counting via Point-derived Segmentation

Due to domain shift, a large performance drop is usually observed when a trained crowd counting model is deployed in the wild. While existing domain-adaptive crowd counting methods achieve promising results, they typically regard each crowd image as a whole and reduce domain discrepancies in a holistic manner, thus limiting further improvement of domain adaptation performance. To this end, we propose to untangle \emph{domain-invariant} crowd and \emph{domain-specific} background from crowd images and design a fine-grained domain adaption method for crowd counting. Specifically, to disentangle crowd from background, we propose to learn crowd segmentation from point-level crowd counting annotations in a weakly-supervised manner. Based on the derived segmentation, we design a crowd-aware domain adaptation mechanism consisting of two crowd-aware adaptation modules, i.e., Crowd Region Transfer (CRT) and Crowd Density Alignment (CDA). The CRT module is designed to guide crowd features transfer across domains beyond background distractions. The CDA module dedicates to regularising target-domain crowd density generation by its own crowd density distribution. Our method outperforms previous approaches consistently in the widely-used adaptation scenarios.Comment: 10 pages, 5 figures, and 9 table

USP7: Novel Drug Target in Cancer Therapy

Ubiquitin specific protease 7 (USP7) is one of the deubiquitinating enzymes (DUB) that erases ubiquitin and protects substrate protein from degradation. Full activity of USP7 requires the C-terminal Ub-like domains fold back onto the catalytic domain, allowing the remodeling of the active site to a catalytically competent state by the C-terminal peptide. Until now, numerous proteins have been identified as substrates of USP7, which play a key role in cell cycle, DNA repair, chromatin remodeling, and epigenetic regulation. Aberrant activation or overexpression of USP7 may promote oncogenesis and viral disease, making it a target for therapeutic intervention. Currently, several synthetic small molecules have been identified as inhibitors of USP7, and applied in the treatment of diverse diseases. Hence, USP7 may be a promising therapeutic target for the treatment of cancer

A multi-subgroup predictive model based on clinical parameters and laboratory biomarkers to predict in-hospital outcomes of plasma exchange-centered artificial liver treatment in patients with hepatitis B virus-related acute-on-chronic liver failure

BackgroundPostoperative risk stratification is challenging in patients with hepatitis B virus-related acute-on-chronic liver failure (HBV-ACLF) who undergo artificial liver treatment. This study characterizes patients’ clinical parameters and laboratory biomarkers with different in-hospital outcomes. The purpose was to establish a multi-subgroup combined predictive model and analyze its predictive capability.MethodsWe enrolled HBV-ACLF patients who received plasma exchange (PE)-centered artificial liver support system (ALSS) therapy from May 6, 2017, to April 6, 2022. There were 110 patients who died (the death group) and 110 propensity score-matched patients who achieved satisfactory outcomes (the survivor group). We compared baseline, before ALSS, after ALSS, and change ratios of laboratory biomarkers. Outcome prediction models were established by generalized estimating equations (GEE). The discrimination was assessed using receiver operating characteristic analyses. Calibration plots compared the mean predicted probability and the mean observed outcome.ResultsWe built a multi-subgroup predictive model (at admission; before ALSS; after ALSS; change ratio) to predict in-hospital outcomes of HBV-ACLF patients who received PE-centered ALSS. There were 110 patients with 363 ALSS sessions who survived and 110 who did not, and 363 ALSS sessions were analyzed. The univariate GEE models revealed that several parameters were independent risk factors. Clinical parameters and laboratory biomarkers were entered into the multivariate GEE model. The discriminative power of the multivariate GEE models was excellent, and calibration showed better agreement between the predicted and observed probabilities than the univariate models.ConclusionsThe multi-subgroup combined predictive model generated accurate prognostic information for patients undergoing HBV-ACLF patients who received PE-centered ALSS

Chemiluminescence determination of surfactant Triton X-100 in environmental water with luminol-hydrogen peroxide system

<p>Abstract</p> <p>Background</p> <p>The rapid, simple determination of surfactants in environmental samples is essential because of the extensive use and its potential as contaminants. We describe a simple, rapid chemiluminescence method for the direct determination of the non-ionic surfactant Triton X-100 (polyethylene glycol tert-octylphenyl ether) in environmental water samples. The optimized experimental conditions were selected, and the mechanism of the Luminol-H₂O₂-Triton X-100 chemiluminesence system was also studied.</p> <p>Results</p> <p>The novel chemiluminescence method for the determination of non-ionic surfactant Triton X-100 was based on the phenomenon that Triton X-100 greatly enhanced the CL signal of the luminol-H₂O₂system. The alkaline medium of luminol and the pH value obviously affected the results. Luminol concentration and hydrogen peroxide concentration also affected the results. The optimal conditions were: Na₂CO₃being the medium, pH value 12.5, luminol concentration 1.0 × 10^-4mol L^-1, H₂O₂concentration 0.4 mol L^-1. The possible mechanism was studied and proposed.</p> <p>Conclusion</p> <p>Under the optimal conditions, the standard curve was drawn up and quotas were evaluated. The linear range was 2 × 10^-4g·mL^-1-4 × 10^-2g·mL^-1(w/v), and the detection limit was 3.97 × 10^-5g·mL^-1Triton X-100 (w/v). The relative standard deviation was less than 4.73% for 2 × 10^-2g·mL^-1(w/v) Triton X-100 (n = 7). This method has been applied to the determination of Triton X-100 in environmental water samples. The desirable recovery ratio was between 96%–102% and the relative standard deviation was 2.5%–3.3%. The luminescence mechanism was also discussed in detail based on the fluorescence spectrum and the kinetic curve, and demonstrated that Triton X-100-luminol-H₂O₂was a rapid reaction.</p