On the convergence analysis of the greedy randomized Kaczmarz method

In this paper, we analyze the greedy randomized Kaczmarz (GRK) method proposed in Bai and Wu (SIAM J. Sci. Comput., 40(1):A592--A606, 2018) for solving linear systems. We develop more precise greedy probability criteria to effectively select the working row from the coefficient matrix. Notably, we prove that the linear convergence of the GRK method is deterministic and demonstrate that using a tighter threshold parameter can lead to a faster convergence rate. Our result revises existing convergence analyses, which are solely based on the expected error by realizing that the iterates of the GRK method are random variables. Consequently, we obtain an improved iteration complexity for the GRK method. Moreover, the Polyak's heavy ball momentum technique is incorporated to improve the performance of the GRK method. We propose a refined convergence analysis, compared with the technique used in Loizou and Richt\'{a}rik (Comput. Optim. Appl., 77(3):653--710, 2020), of momentum variants of randomized iterative methods, which shows that the proposed GRK method with momentum (mGRK) also enjoys a deterministic linear convergence. Numerical experiments show that the mGRK method is more efficient than the GRK method

On adaptive stochastic heavy ball momentum for solving linear systems

The stochastic heavy ball momentum (SHBM) method has gained considerable popularity as a scalable approach for solving large-scale optimization problems. However, one limitation of this method is its reliance on prior knowledge of certain problem parameters, such as singular values of a matrix. In this paper, we propose an adaptive variant of the SHBM method for solving stochastic problems that are reformulated from linear systems using user-defined distributions. Our adaptive SHBM (ASHBM) method utilizes iterative information to update the parameters, addressing an open problem in the literature regarding the adaptive learning of momentum parameters. We prove that our method converges linearly in expectation, with a better convergence rate compared to the basic method. Notably, we demonstrate that the deterministic version of our ASHBM algorithm can be reformulated as a variant of the conjugate gradient (CG) method, inheriting many of its appealing properties, such as finite-time convergence. Consequently, the ASHBM method can be further generalized to develop a brand-new framework of the stochastic CG (SCG) method for solving linear systems. Our theoretical results are supported by numerical experiments

Fast stochastic dual coordinate descent algorithms for linearly constrained convex optimization

The problem of finding a solution to the linear system $Ax = b$ with certain minimization properties arises in numerous scientific and engineering areas. In the era of big data, the stochastic optimization algorithms become increasingly significant due to their scalability for problems of unprecedented size. This paper focuses on the problem of minimizing a strongly convex function subject to linear constraints. We consider the dual formulation of this problem and adopt the stochastic coordinate descent to solve it. The proposed algorithmic framework, called fast stochastic dual coordinate descent, utilizes sampling matrices sampled from user-defined distributions to extract gradient information. Moreover, it employs Polyak's heavy ball momentum acceleration with adaptive parameters learned through iterations, overcoming the limitation of the heavy ball momentum method that it requires prior knowledge of certain parameters, such as the singular values of a matrix. With these extensions, the framework is able to recover many well-known methods in the context, including the randomized sparse Kaczmarz method, the randomized regularized Kaczmarz method, the linearized Bregman iteration, and a variant of the conjugate gradient (CG) method. We prove that, with strongly admissible objective function, the proposed method converges linearly in expectation. Numerical experiments are provided to confirm our results.Comment: arXiv admin note: text overlap with arXiv:2305.0548

Integrated bioinformatics analysis of IFITM1 as a prognostic biomarker and investigation of its immunological role in prostate adenocarcinoma

IntroductionProstate adenocarcinoma (PRAD) is a highly aggressive malignancy with high mortality and poor prognosis, and its potential mechanism remains unclear. Our study aimed to identify novel markers for the prognosis of PRAD using bioinformatics technology.MethodsThe GSE32571 dataset was downloaded from the GEO database, and analyzed via the limma R package to identify differentially expressed genes (DEGs) and differentially expressed immune score-related genes (DEISRGs). The immune-related genes (IRGs) were further obtained by overlapping DEISRGs and DEGs, and the core gene was identified via survival analysis. Furthermore, the expression level, prognostic value, and potential functions of the core gene were evaluated via multiple bioinformatics databases.ResultsA total of 301 IRGs were identified from the GSE32571 dataset, and IFITM1 was a down-regulated gene in several types of cancer, including PRAD. Besides, low expression of IFITM1 was associated with a poor prognosis in PRAD. GSEA indicated that the vital pathways of IFITM1-associated genes were mainly enriched in primary immunodeficiency, Th17 cell differentiation, Th1, and Th2 cell differentiation, natural killer cell-mediated cytotoxicity, myeloid dendritic cell activation, regulation of leukocyte activation, etc. Furthermore, IFITM1 was closely correlated with 22 types of tumor-infiltrating immune cells.DiscussionIFITM1 was a prognostic biomarker for PRAD patients, and it can be acted as a potential immune therapy target in PRAD

Long Non Coding RNA MALAT1 Promotes Tumor Growth and Metastasis by Inducing Epithelial-Mesenchymal Transition in Oral Squamous Cell Carcinoma

The prognosis of advanced oral squamous cell carcinoma (OSCC) patients remains dismal, and a better understanding of the underlying mechanisms is critical for identifying effective targets with therapeutic potential to improve the survival of patients with OSCC. This study aims to clarify the clinical and biological significance of metastasis-associated long non-coding RNA, metastasis-associated lung adenocarcinoma transcript 1 (MALAT1) in OSCC. We found that MALAT1 is overexpressed in OSCC tissues compared to normal oral mucosa by real-time PCR. MALAT1 served as a new prognostic factor in OSCC patients. When knockdown by small interfering RNA (siRNA) in OSCC cell lines TSCCA and Tca8113, MALAT1 was shown to be required for maintaining epithelial-mesenchymal transition (EMT) mediated cell migration and invasion. Western blot and immunofluorescence staining showed that MALAT1 knockdown significantly suppressed N-cadherin and Vimentin expression but induced E-cadherin expression in vitro. Meanwhile, both nucleus and cytoplasm levels of β-catenin and NF-κB were attenuated, while elevated MALAT1 level triggered the expression of β-catenin and NF-κB. More importantly, targeting MALAT1 inhibited TSCCA cell-induced xenograft tumor growth in vivo. Therefore, these findings provide mechanistic insight into the role of MALAT1 in regulating OSCC metastasis, suggesting that MALAT1 is an important prognostic factor and therapeutic target for OSCC

Cloning and expression of a rat brain interleukin-1beta-converting enzyme (ICE)-related protease (IRP) and its possible role in apoptosis of cultured cerebellar granule neurons

Several members of the IL-1beta-converting enzyme (ICE) family of proteases recently have been implicated in the intracellular cascade mediating the apoptotic death of various cell types. It is unclear, however, whether ICE-related proteases are involved in apoptosis of mammalian neurons and, if so, how they are activated. Here we report the cloning of an ICE-related protease (IRP) from rat brain, which displays strong sequence identity to human CPP32. In situ hybridization histochemistry reveals that this IRP mRNA is expressed in neuron-enriched regions of the developing and adult rat brain but is profoundly downregulated in the adult (compared with developing) brain. To investigate whether this IRP is involved in the death of neurons in the developing brain, we studied IRP expression in cultured cerebellar granule neurons. In cultured cerebellar granule neurons, reduction of extracellular K+ reliably induces apoptosis and stimulates overexpression of IRP mRNA. The latter is especially prominent 4 hr after switching from high K+ to low K+ medium. The expression of IRP mRNA was maintained at this level for at least 8 hr and was followed by apoptotic death of these neurons. Induction of IRP mRNA and cell death are blocked completely by adding depolarizing concentrations of K+ </=90 min after switching to low K+ medium (i.e., before the commitment point for apoptosis) and partially blocked by brain-derived neurotrophic factor (BDNF), which also partially rescues granule neurons from low K+-induced apoptosis. In addition, overexpression of IRP cDNA in HeLa cells results in cell death accompanied by strong internucleosomal cleavage of DNA, a typical feature of apoptosis. Finally, we detected cleavage of the putative death substrate poly (ADP-ribose) polymerase (PARP), beginning 8 hr after changing from high K+ to low K+ medium, coinciding with the time course of induced expression of the IRP gene. Our data suggest that transcriptional activation of IRP could be one of the mechanisms involved in the apoptotic death of cerebellar granule neurons

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase&nbsp;1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation&nbsp;disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age&nbsp; 6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score&nbsp; 652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc&nbsp;= 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N&nbsp;= 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in&nbsp;Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in&nbsp;Asia&nbsp;and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701

A Pitman Style Fiber Bragg Grating Displacement Sensor Based on Wedge Cavity Structure

In this paper, a new design of fiber Bragg grating (FBG) displacement sensor is presented based on wedge cavity structure. A new type of pitman FBG displacement sensor with a simple structure, small size and anti-electromagnetic interference is invented. Calibration of the FBG displacement sensor is carried out. The calibrating data shows that the sensitivity is 5.58 pm/mm, adjusted R square is up to 0.99 and the static error is 5.168%. Moreover, the FBG displacement sensor is applied in the hysteresis test of steel frame-reinforced concrete infill wall. The monitoring results from the FBG displacement sensor in this test match well with the resistance strain displacement meter, to prove the FBG displacement sensor with a good accuracy. It is also showed that this new FBG displacement sensor produces smaller influence on the structure, and it is suitable for long-term displacement monitoring of engineering structures

Table_1_Integrated bioinformatics analysis of IFITM1 as a prognostic biomarker and investigation of its immunological role in prostate adenocarcinoma.docx

IntroductionProstate adenocarcinoma (PRAD) is a highly aggressive malignancy with high mortality and poor prognosis, and its potential mechanism remains unclear. Our study aimed to identify novel markers for the prognosis of PRAD using bioinformatics technology.MethodsThe GSE32571 dataset was downloaded from the GEO database, and analyzed via the limma R package to identify differentially expressed genes (DEGs) and differentially expressed immune score-related genes (DEISRGs). The immune-related genes (IRGs) were further obtained by overlapping DEISRGs and DEGs, and the core gene was identified via survival analysis. Furthermore, the expression level, prognostic value, and potential functions of the core gene were evaluated via multiple bioinformatics databases.ResultsA total of 301 IRGs were identified from the GSE32571 dataset, and IFITM1 was a down-regulated gene in several types of cancer, including PRAD. Besides, low expression of IFITM1 was associated with a poor prognosis in PRAD. GSEA indicated that the vital pathways of IFITM1-associated genes were mainly enriched in primary immunodeficiency, Th17 cell differentiation, Th1, and Th2 cell differentiation, natural killer cell-mediated cytotoxicity, myeloid dendritic cell activation, regulation of leukocyte activation, etc. Furthermore, IFITM1 was closely correlated with 22 types of tumor-infiltrating immune cells.DiscussionIFITM1 was a prognostic biomarker for PRAD patients, and it can be acted as a potential immune therapy target in PRAD.</p

Image_3_Integrated bioinformatics analysis of IFITM1 as a prognostic biomarker and investigation of its immunological role in prostate adenocarcinoma.tiff

IntroductionProstate adenocarcinoma (PRAD) is a highly aggressive malignancy with high mortality and poor prognosis, and its potential mechanism remains unclear. Our study aimed to identify novel markers for the prognosis of PRAD using bioinformatics technology.MethodsThe GSE32571 dataset was downloaded from the GEO database, and analyzed via the limma R package to identify differentially expressed genes (DEGs) and differentially expressed immune score-related genes (DEISRGs). The immune-related genes (IRGs) were further obtained by overlapping DEISRGs and DEGs, and the core gene was identified via survival analysis. Furthermore, the expression level, prognostic value, and potential functions of the core gene were evaluated via multiple bioinformatics databases.ResultsA total of 301 IRGs were identified from the GSE32571 dataset, and IFITM1 was a down-regulated gene in several types of cancer, including PRAD. Besides, low expression of IFITM1 was associated with a poor prognosis in PRAD. GSEA indicated that the vital pathways of IFITM1-associated genes were mainly enriched in primary immunodeficiency, Th17 cell differentiation, Th1, and Th2 cell differentiation, natural killer cell-mediated cytotoxicity, myeloid dendritic cell activation, regulation of leukocyte activation, etc. Furthermore, IFITM1 was closely correlated with 22 types of tumor-infiltrating immune cells.DiscussionIFITM1 was a prognostic biomarker for PRAD patients, and it can be acted as a potential immune therapy target in PRAD.</p