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]

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

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

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

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

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

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

Screening of core genes and prediction of ceRNA regulation mechanism of circRNAs in nasopharyngeal carcinoma by bioinformatics analysis

Background: Nasopharyngeal carcinoma (NPC) represents a highly aggressive malignant tumor. Competing endogenous RNAs (ceRNA) regulation is a common regulatory mechanism in tumors. The ceRNA network links the functions between mRNAs and ncRNAs, thus playing an important regulatory role in diseases. This study screened the potential key genes in NPC and predicted regulatory mechanisms using bioinformatics analysis.Methods: The merged microarray data of three NPC-related mRNA expression microarrays from the Gene Expression Omnibus (GEO) database and the expression data of tumor samples or normal samples from the nasopharynx and tonsil in The Cancer Genome Atlas (TCGA) database were both subjected to differential analysis and Weighted Gene Co-expression Network Analysis (WGCNA). The results from two different databases were intersected with WGCNA results to obtain potential regulatory genes in NPC, followed by Gene Ontology (GO) and Kyoto Encyclopedia of Genes and Genomes (KEGG) functional enrichment analyses. The hub-gene in candidate genes was discerned through Protein-Protein Interaction (PPI) analysis and its upstream regulatory mechanism was predicted by miRwalk and circbank databases.Results: Totally 68 upregulated genes and 96 downregulated genes in NPC were screened through GEO and TCGA. According to WGCNA, the NPC-related modules were screened from GEO and TCGA analysis results, and the genes in the modules were obtained. After the results of differential analysis and WGCNA were intersected, 74 differentially expressed candidate genes associated with NPC were discerned. Finally, fibronectin 1 (FN1) was identified as a hub-gene in NPC. Prediction of upstream regulatory mechanisms of FN1 suggested that FN1 may be regulated by ceRNA mechanisms involving multiple circRNAs, thereby influencing NPC progression through ceRNA regulation.Conclusion: FN1 is identified as a key regulator in NPC development and is likely to be regulated by numerous circRNA-mediated ceRNA mechanisms