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Action recognition involves capturing temporal information from video clips where the duration varies with videos for the same action. Due to the diverse scale of temporal context, uniform size kernels utilized in convolutional neural networks (CNNs) limit the capability of multiple-scale temporal modeling. In this paper, we propose a novel dilated multi-temporal (DMT) module that provides a solution for modeling multi-temporal information in action recognition. By using dilated convolutions with different dilation rates in different feature map channels, the DMT module captures information at multiple scales without the need for costly multi-branch networks, input-level frame pyramids, or feature map stacking that previous works have usually incurred. Therefore, this approach enables the integration of temporal information from multiple scales. In addition, the DMT module can be integrated into existing 2D CNNs, making it a straightforward and intuitive solution for addressing the challenge of multi-temporal modeling. Our proposed method has demonstrated promising results in performance and has achieved about 2% and 1% accuracy improvement on FineGym99 and SthV1. We conducted an empirical analysis that demonstrates how DMT improves the classification accuracy for action classes with varying durations.

In this paper, we firstly present a block robust structured multifrontal factorization method (in brief, BRSMF) using block diagonalonal structure of three temperature matrices, and then we propose a multi-core parallelization of BRSMF (in brief, MBRSMF) method based on the current mainstream parallel computer multi-core architecture. MBRSMF method parallelizes the nested dissection ordering, symbolic decomposition and numerical decomposition of BRSMF method, which aims to effectively solve three temperature linear systems on the multi-core computer. The multi-core parallelization of symbolic decomposition and numerical decomposition is based on the binary elimination tree. Theoretical analysis proves MBRSMF method has better load balancing capability. Numerical experiments show that the MBRSMF method is effective.

Desmoplasia in the extracellular matrix (ECM) is one of the hallmarks of pancreatic cancer (PC), a virtually incurable disease. Decorin, a classical small leucine-rich proteoglycan found in the ECM, was upregulated in PC tissue samples according to the data of TCGA. However, decorin plays a protective role in the ECM. So it is necessary to study the roles of decorin in the progression of PC. A significantly upregulated expression of decorin was observed in the PC tissue samples compared with the normal tissues. However, there was no considerable difference in the level of expression of decorin during different pathological stages, which was supported by the immunoblot analysis. Western blot showed a higher expression of decorin A in the para-carcinoma tissue than in the cancerous tissue but the expression of decorin B, C, and D was elevated in the cancerous tissue. The results of the MTT and scratch wound healing assays revealed an elevated proliferation ability and migration rate in decorin B-overexpressing cells but were inhibited in the decorin A-overexpressing cells. Overexpression of decorin A significantly elevated the expression of the apoptosis-related genes and Decorin B-overexpression elevated proliferation-related genes. All the results showed that decorin B played important roles in the promoting of PC.

Recently, Tian et al. [Computers and Mathematics with Applications, 75(2018): 2710-2722] came up with the inner-outer iterative method to solve the linear equation Ax=b and studied the corresponding convergence of the method. In this paper, we improve the main results of the inner-outer method and get weaker convergence results. Moreover, the parameters can be adjusted suitably so that the convergence property of the method can be substantially improved.

Recently, Chen and Ma [21] constructed the generalized shift-splitting (GSS) preconditioner, and gave the corresponding theoretical analysis and numerical experiments. In this paper, based on the generalized shift-splitting (GSS) preconditioner, we generalize their algorithms and further study the two-sweep shift-splitting (TSSS) preconditioner for complex symmetric linear systems. Moreover, by similar theoretical analysis, we obtain that the two-sweep shift-splitting iterative method is unconditionally convergent. In finally, one example is provided to confirm the effectiveness.

In this paper, based on global relaxed parallel multisplitting USAOR (GUSAOR) method presented by Zhang et al. (Appl Math Comput 20:121–132, 2008) and similar ideas used by Zhang and Li (Comput Math Appl 67:1954–195, 2014), we further analyze global relaxed parallel multisplitting USAOR (GUSAOR) method and obtain the weaker convergence results compared to Zhang et al.’s when the system matrix is an H-matrix. Moreover, convergence graph and numerical examples clearly show that our new convergence domain is wider.

To investigate the predictive value of neuron-specific enolase (NSE) on intensive care unit (ICU) mortality in patients with septic shock. Seventy-five patients with septic shock hospitalized in the emergency intensive care unit (EICU) of Hebei General Hospital from March 2020 to September 2021 were included, and the patients' baseline characteristics and laboratory findings were collected. NSE levels on the first and fourth days after admission were retrieved. NSE% [(NSEday1 - NSEday4)/NSEday1 × 100%] and δNSE (NSEday1 - NSEday4) were calculated. The outcome indicator was ICU mortality. The patients were divided into the survivors group (n = 57) and the nonsurvivors group (n = 18). Multivariate analysis was performed to assess the relationship between NSE and ICU mortality. The predictive value of NSE was evaluated using receiver operating characteristic (ROC) curve. There were no significant differences in age, gender, systolic blood pressure (SBP), heart rate (HR), acute physiology and chronic health evaluation II score (APACHE II score), source of infection, and comorbidities between the 2 groups (all P .05). Interleukin-6 (IL-6), NSE (day1), and NSE (day4) were significantly higher in patients in the nonsurvivors group (all P .05), and there were no statistical differences in other laboratory tests between the 2 groups (all P .05). APACHE II score, IL-6, lactate (Lac), total bilirubin (TBil), NSE (day1), and NSE (day4) showed a weak positive correlation with ICU mortality in patients with septic shock (all P .05). Multivariate logistic regression analysis demonstrated that APACHE II score (odds ratio [OR] = 1.166, 95% confidence interval [95% confidence interval [CI]] 1.005-1.352, P = .042), IL-6 (OR = 1.001, 95% CI 1.000-1.001, P = .003) and NSE (day4) (OR = 1.099, 95% CI 1.027-1.176, P = .006) were independently associated with the ICU mortality of sepsis shock patients. The area under the curve (AUCs) of APACHE II score, IL-6, NSE (day1), and NSE (day4) for predicting prognosis were 0.650, 0.694, 0.758 and 0.770, respectively (all P .05). NSE(day4) displayed good sensitivity and specificity (Sn = 61.11%, Sp = 91.23%) for predicting ICU mortality with a cutoff value of 25.94 ug/L. High-level NSE (day4) is an independent predictor of ICU mortality in sepsis shock patients, which may become a good alternate option for evaluating sepsis severity. More extensive studies are needed in the future to demonstrate the prognosis value of NSE.

At present, in most damage detection research, the raw structural monitoring data after secondary processing are usually used. To solve the problem, this paper used statistical process control to detect damage based on the raw measurement data. However, these data are measured at a rather high sampling frequency, which often leads to high correlation between them and eventually gives the error of damage detection. To minimize the negative effects, the statistical process control was realized by using the residual error between the original data and the predicted data of the autoregressive model, and the minimization problem is to obtain the appropriate order of the autoregressive model by taking the Aktan Information Criterion (abbreviation of AIC) as the objective function. The benchmark structure designed by International Association for Structural Control and American Society of Civil Engineers was taken as a case to prove the effectiveness of the proposed method.

In 2013, Bai and Zhang (Numer Linear Algebra Appl, 20:425–439 2013) constructed modulus-based synchronous multisplitting iteration methods by an equivalent reformulation of the linear complementarity problem into a system of fixed-point equations and studied the convergence of them. In this paper, we generalize Bai and Zhang’s method and study relaxed modulus-based synchronous multisplitting multi-parameter methods for linear complementarity problems. Furthermore, when the system matrix is an H+-matrix, we give convergence results for our new methods under weaker conditions than those in Bai and Zhang’s. Finally, numerical experiments are presented to illustrate the efficiency of the proposed methods.

Fish sex-determining mechanisms can be classified as genotypic (GSD), temperature (TSD), or genotypic plus temperature effects (GSD+TE). Previous studies have shown that culturing water temperature during thermosensitive periods (TSP) could affect the expression of many genes in the gonad in some fish. However, few studies have focused on gene expression changes in the brain after temperature treatment during TSP in fish species. In this study, three families were developed by crossing XX neomales with XX females and one of them was used for transcriptome analysis. The results showed that a total of 105, 3164 and 4666 DEGs were respectively obtained in FC (female control) vs. FT (high temperature-treated females at TSP), FC vs. MC (male control), and MC vs. FT comparison groups. By profiling analysis, we show that the mRNA expression levels of 16 differentially expressed genes (DEGs) exhibited significant downregulation or upregulation after high temperature treatment and reached a similar level as that in MC. Among the 16 DEGs, LOC100699848 (lysine specific demethylase 6A) and Jarid2 contained JmjC domain, showing the possible important role of JmjC domain in response to temperature treatment in Nile tilapia. Kdm6b (lysine demethylase 6B) and Jarid2 have been shown to play important roles in reptile TSD, showing the relative conservation of underlying regulation mechanisms between TSD in reptile and TSD or GSD+TE in fish species. Finally, the transcriptome profiling was validated by quantitative real-time PCR in nine selected genes. These results provide a direction for investigating the GSD+TE molecular mechanism in fish species.

Recently, Chen and Ma [A generalized shift-splitting preconditioner for saddle point problems, Applied Mathematics Letters, 43 (2015) 49-55] introduced a generalized shift-splitting preconditioner for saddle point problems with symmetric positive definite (1,1)-block. In this paper, I establish a parameterized shift-splitting preconditioner for solving the large sparse augmented systems of linear equations. Furthermore, the preconditioner is based on the parameterized shift-splitting of the saddle point matrix, resulting in an unconditional convergent fixed-point iteration, which has the intersection with the generalized shift-splitting preconditioner. In final, one example is provided to confirm the effectiveness.

This study was designed to explore the sulfation patterns of chondroitin sulfate (CS)/dermatan sulfate (DS), and keratan sulfate (KS) and the expression of carbohydrate sulfotransferases (CHSTs) in 26 pancreatic tumor and normal tissues. CS/DS and KS profiles were simultaneously determined. Pancreatic tumor tissues exhibited increased ΔDi-0S, ΔDi-4S, and ΔDi-6S levels, with absolute ΔDi-4S content being highest, followed by ΔDi-6S. However, as for the contents of KS-6S and KS-6S,6'S, there were no significant regular change. The expression levels of CHST1 and CHST4 were 37 and 15 times higher than those in normal tissues. PCA and OPLS-DA revealed that ΔDi-4S and ΔDi-6S levels could be reliably used to differentiate between healthy and cancerous tissues. The up-regulation of CHST3, CHST12, CHST13, and CHST15 was directly correlated with C-4 and C-6 sulfation. These data provide a foundation for future studies of the role of ΔDi-4S and ΔDi-6S in the progression of pancreatic cancer.

Diabetes mellitus is the most common metabolic disease in the world. The clinical symptoms represent hyperglycemia and low insulin secretion. Type 2 diabetes mellitus (T2DM) accounts for the majority of all diabetic patients (approximately 90%). Our previous study found that tartary buckwheat polysaccharides (TBP) had a good hypoglycemic effect on the T2DM model mice induced by streptozotocin (STZ). However, the underlying mechanism of TBP on hypoglycemic effect is still unclear. In the present study, RNA sequencing (RNA-seq) was applied to study the changes of transcriptome in the liver of mice in the T2DM model group. Compared with model group, 1191 DEGs (differently expressed genes) were screened in the TBP treatment group, in which 313 genes were up-regulated and 878 down-regulated. The KEGG, GO, and KOG analysis of DEGs indicated that many DEGs were associated with glycometabolism. In the T2DM pathway, there are only 5 DEGs including GLUT4, HK3, SOCS3, PYK, and GCK. qRT-PCR further confirm their expressions. All the results indicated that GLUT4, HK3, SOCS3, PYK, and GCK might play important roles in the hypoglycemic mechanism of TBP.

Rationale Iris tectorum Maxim. is a traditional medicinal herb that is commonly used to treat inflammatory conditions. The present study investigated the fragmentation patterns of isoflavone glycosides and their qualitative analysis. In addition, lipopolysaccharide (LPS)-induced RAW264.7 macrophages were used to evaluate the anti-inflammatory properties of I. tectorum Maxim. samples collected at different time points during the year. Methods High-performance liquid chromatography/quadrupole time-of-flight tandem mass spectrometry (HPLC/QTOF-MS/MS) and HPLC with diode-array detection were employed for qualitative and quantitative analysis. The fragmentation patterns of the isoflavones were observed in negative electrospray ionization mode with collision-induced dissociation (CID). Their anti-inflammatory activity was assessed via nitric oxide (NO) production in LPS-treated RAW264.7 macrophages. Results A total of 15 chemical components were observed and tentatively identified using HPLC/QTOF-MS/MS. At low collision energy, the relative abundances of the aglycone radical anions Y0 - , [Y0 - H]-• , [Y0 - CH3 ]-• and [Y0 - H- CH2 ]-• were used for the structural characterization of tectoridin and tectorigenin-4'-O-β-D-glucoside. The radical ions [Y0 - CH3 ]-• and [Y0 - H - 2CH3 ]-• were also employed to differentiate between iristectorin A and iristectorin B based upon their high-energy CID spectra. Levels of 9.02 mg/g of tectoridin and 1.04 mg/g of tectorigenin were found in samples collected in June, which exhibited 69.7% NO inhibitory activity. Conclusions The characteristic fragmentation patterns enabled us to reliably identify isoflavone glycosides. The results of the quantitative determination and NO inhibitory activity offer insight into the optimal I. tectorum Maxim. harvesting time.

In this paper, based on the preconditioners presented by Zhang [A new preconditioner for generalized saddle matrices with highly singular(1,1) blocks. Int J Comput Maths. 2014;91(9):2091-2101], we ...

Context: MOTILIPERM was prepared as a mixture of extracts of three medicinal herbs [roots of Morinda officinalis How (Rubiaceae), outer scales of Allium cepa L. (Liliaceae) and seeds of Cuscuta chinensis Lamark (Convolvulaceae)]. Objective: To investigate the role of reactive oxygen species (ROS)-based endoplasmic reticulum (ER) stress in a rat model of varicocele and the therapeutic efficacy of MOTILIPERM in this model. Materials and methods: Sixty male rats were divided into five experimental groups: a normal control group (CTR + vehicle), a control group administered MOTILIPERM 200 mg/kg (CTR + M 200), a varicocele-induced control group (VC + vehicle) and two varicocele-induced groups administered MOTILIPERM 100 (VC + M 100) or 200 (VC + M 200) mg/kg for 4 weeks. Testis weights were recorded and serums were assayed for hormone concentrations. Tissues were subjected to semen analysis, histopathology, analyses of ER response protein expression levels and oxidative stress were assessed by measuring ROS, reactive nitrogen species (RNS), malondialdehyde (MDA) level and ratios of total glutathione (GSH)/oxidized GSH (GSSG). Results: MOTILIPERM treatment of varicocele-induced groups significantly increased left testis weight, testosterone level, sperm motility, count and spermatogenic cell density. ER-response protein expression levels were dose-dependently decreased in VC + M 200 group compared with VC + vehicle group. MOTILIPERM treatment also decreased MDA and ROS/RNS level but increased GSH/GSSG ratio. Discussion and conclusions: This study suggests that ROS-related ER stress may play a major role in varicocele-induced infertility and MOTILIPERM, a novel compound targeting ROS-based ER stress, may be therapeutically useful in treatment of varicocele, or as a supplement for the treatment of infertility.

To investigate the expression of stearoyl-CoA desaturase-1 (SCD1) in breast cancer cell lines. To analyze the effect of inhibiting SCD1 activity on the proliferation and cell cycle of MCF-7 breast cancer cell and its mechanism.The expression of SCD1 protein were detected by Western blot techniques in breast cancer cell lines and humanskin fibroblasts.Cell viability of MCF-7 cells treated with MF-438 was measured using MTS assay and ICThe expression level of SCD1 in MCF-7 and MDA-MB-231 cells was significantly higher than that in HSF cells (SCD1 plays an important role in the occurrence and development of breast cancer. Inhibition of SCD1 activity can inhibit cell cycle progression and impair cell proliferation by down-regulating the Akt pathway and activating the AMPK pathway. Further research on SCD1 is expected to provide a new target for molecular targeted therapy of breast cancer.

Based on the Adomian decomposition method and Lyapunov stability theory, this paper constructs a fractional-order memristive hyperchaos. Then, the 0–1 test analysis is applied to detect random nature of chaotic sequences exhibited by the fractional-order systems. Comparing with the corresponding integer-order hyperchaotic system, the fractional-order hyperchaos possesses higher complexity. Finally, an image encryption algorithm is proposed based on the fractional-order memristive hyperchaos. Security and performance analysis indicates that the proposed chaos-based image encryption algorithm is highly resistant to statistical attacks.

In most of the present research on damage detection, secondly processed raw monitoring data of structures are usually used. In order to deal with the above problem, damage detection was implemented based on the raw measured data using techniques of statistical process control (abbreviation of SPC) in this paper. However, those data are measured with rather high frequency of sampling, which often produces strong correlations of them and makes errors of damage detection finally. In order to alleviate those negative effects, techniques of SPC were carried out using residuals between raw data and predicted ones of autoregressive (abbreviation of AR) models, and furthermore the minimum problem was given with the objective function of Aktain’s information criterion (abbreviation of AIC) to obtain appropriate orders of AR models. The Benchmark structure, proposed by International Association for Structural Control and American Society of Civil Engineers, was adopted as the case study to prove validity of the method proposed in the paper.

Yu Seob Shin,1,* Li Tao Zhang,1,* Jae Hyung You,1 In Sung Choi,1 Chen Zhao,2 Jong Kwan Park1 1Department of Urology, Chonbuk National University and Research Institute of Clinical Medicine of Chonbuk National University-Biomedical Research Institute and Medical Device Clinical Trial Center of Chonbuk National University, Jeonju, Republic of Korea; 2Department of Urology, Renji Hospital, Shanghai Jiao Tong University School of Medicine, and Shanghai Institute of Andrology, Shanghai, People’s Republic of China *These authors contributed equally tothis work Objective: The objective of this study was to evaluate the safety and efficacy of tamsulosin hydrochloride 0.2mg (TAM) and its combination with solifenacin succinate 5mg (SOL) after transurethral resection of the prostate (TURP).Patients and methods: The patients were randomized into three groups: TURP (group 1), TURP plus TAM (group 2), and TURP plus TAM + SOL (group 3). Patients in group 2 and group 3 received medication for 4weeks. The primary efficacy end points were the mean change in total International Prostate Symptom Score (IPSS) and IPSS subscores. The secondary end points included quality-of-life score, Overactive Bladder Symptom Score, and short-form voiding and storage score of International Continence Society.Results: In total, 37 men (31.8%) in group 1, 37 men (31.8%) in group 2, and 42 men (36.2%) in group 3 completed the study. In total IPSS, no significant improvement was seen from baseline to the end of treatment in groups 2 and 3 compared with group 1. However, in group 2, the decrement in the IPSS storage score was smaller than group 1 (P=0.02), and in group 3, the decrement in the IPSS voiding score was smaller than group 1 (P=0.05). In groups 2 and 3 compared with group 1, improvements in the quality of life score, total score of Overactive Bladder Symptom Score, and short-form voiding score and storage score of International Continence Society were not statistically significant.Conclusion: Treatment with TAM and combination of TAM and SOL did not have significant additional benefits for lower urinary tract symptoms during the early recovery period afterTURP. Keywords: benign prostate hyperplasia, tamsulosin, solifenacin, combination, transurethral resection of the prostate

In this paper, based on the preconditioners presented by Cao [J. Comput. Appl. Math. 2013;238:109–115], we present a block triangular preconditioner for generalized saddle point matrices whose coefficient matrices have singular (1,1) blocks. Moreover, theoretical analysis gives the eigenvalue distribution, forms of the eigenvectors and its minimal polynomial. Finally, numerical examples confirm our analysis when optimal parameters are chosen.

Objectives To investigate the effect of 4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid, a new benzofuroindole derivative, on the intraurethral pressure in a rat model of benign prostatic hyperplasia. Methods Benign prostatic hyperplasia was induced by testosterone and 17β-estradiol, which were administered intramuscularly once a day for 12 weeks. The effects of 4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid and tamsulosin on the intraurethral pressure induced by the electrostimulation of hypogastric nerves after a single intravenous injection of 4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid (10 mg/kg) or tamsulosin (10 μg/kg) were evaluated in a benign prostatic hyperplasia model. The electrostimulation-induced intraurethral pressure was measured just before and after the injection of 4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid. Bodyweight and genitourinary organ weights were recorded, and serums and tissues were subjected to hormone assays and histopathology. In addition, the expression of α1-adrenoceptors in the prostate was measured by western blotting. Results The benign prostatic hyperplasia groups showed increased prostatic index, increased concentrations of testosterone, free testosterone and estradiol in serum, and increased epithelial thickness of the prostate. An injection of 4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid or tamsulosin significantly inhibited the elevation of electrostimulation-induced intraurethral pressure. In addition, 4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid did not cause a significant change in the blood pressure compared with tamsulosin. While the benign prostatic hyperplasia group showed increased the expression of α1-adrenoceptors, the 4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid or tamsulosin injection into a rat model of benign prostatic hyperplasia decreased the expression of α1-adrenoceptors. Conclusions These findings show that 4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid might be beneficial for lowering the intraurethral pressure associated with benign prostatic hyperplasia, and it could represent a therapeutic option for benign prostatic hyperplasia patients.

Many image encryption algorithms have too small key space to prevent exhaust attacks. Based on a novel compound chaotic system, an algorithm with expanded key space is proposed to aim at the problem. Firstly, an adaptive method is provided to design switching controllers during creating a novel compound chaos. Secondly, general Arnold transform is used to realise pixel scrambling technology. Finally, the novel fractional compound chaos is applied in pixel diffusion to improve security of the image encryption algorithm. In numerical simulation, classical colour image, gray image, binary image and non-square image are encrypted sufficiently to identify the encryption algorithm. Both theoretical analysis and experimental results show that the algorithm has larger key space and is suitable for different types of digital images, and encryption image can resist some kinds of external attacks.

An iterative increment is supposed to give the corresponding vector of identification parameters with physical significance in the current iteration. In order to fulfill this requirement, methodologies for limiting iterative increments were presented as the measure to improve the stability of identification results. A constrained optimization problem was given by the transformation of conditions of limiting iterative increments and Levenberg-Marquardt method was proposed. A numerical example suggested that Levenberg-Marquardt method could not only give the solution of the constrained optimization problem but also obtain stable identification results.

Various cutaneous vascular diseases are presented in this chapter: eruptive recurrent pigmented telangiectasia, telangiectasia macularis eruptiva perstans, unilateral nevoid telangiectasia superimposed on the Bier spots, Mondor’s disease, arteriosclerosis obliterans, and eruptive pseudoangiomatosis.

In 2013, Bai and Zhang (Numer Linear Algebra Appl 20:425–439, 2013) constructed modulus-based synchronous multisplitting methods by an equivalent reformulation of the linear complementarity problems into a system of fixed-point equations and studied their convergence. In 2014, Zhang and Li (Comput Math Appl 67:1954–1959, 2014) analyzed and obtained the weaker convergence results for linear complementarity problems. In this paper, based on their ideas, we further study modulus-based synchronous block multisplitting multi-parameter methods for linear complementarity problems. Furthermore, the convergence results of our new method in this paper are wider than those in literature when the system matrix is a block $$H_{+}$$ -matrix. Therefore, new results provide a guarantee for the optimal relaxation parameters.

In this paper, applying the theory of evolution family and Schauder's fixed point theorem, we prove the anti-periodic mild solutions for semilinear nonautonomous evolution equations in Banach space under conditions. Furthermore, an example is given to illustrate our results.

In this paper, based on generalized conjugate residual squared (GCRS2) algorithm in Zhang et al. (2010 Third International Conference on Information and Computing, pp 326–329, 2010) and the ideas in Gu et al. (Appl Math Comput 186:1243–1253, 2007), we present an improved generalized conjugate residual squared (IGCRS2) algorithm, which is designed for distributed parallel environments. The improved algorithm reduces two global synchronization points to one by changing the computation sequence in the GCRS2 algorithm and all inner products per iteration are independent and communication time required for inner product can be overlapped with useful computation. Theoretical analysis and numerical comparison about isoefficiency analysis show that the IGCRS2 method has better parallelism and scalability than the GCRS2 method and the parallel performance can be improved by a factor of about 2.

In this paper, one new parallel version of GPBi-CG method (PGPBi-CG method, in brief) is proposed for solving large sparse linear systems with unsymmetrical coefficient matrices on distributed parallel environments. The method reduces three global synchronization points to one by reconstructing GPBi-CG method and the communication time required for the inner product can be efficiently overlapped with computation time of vector updates. It combines the elements of numerical stability with the characteristics of design of parallel algorithms. The cost is only slightly increased computation time, which can be ignored, compared with the reduction of communication time. Performance and isoefficiency analysis shows that the PGPBi-CG method has better parallelism and scalability than the GPBi-CG method. Numerical experiments show that the scalability can be improved by a factor 3 and the improvement in parallel communication performance approaches 66.7 %.