Existence of Local Saddle Points for a New Augmented Lagrangian Function

We give a new class of augmented Lagrangian functions for nonlinear programming problem with both equality and inequality constraints. The close relationship between local saddle points of this new augmented Lagrangian and local optimal solutions is discussed. In particular, we show that a local saddle point is a local optimal solution and the converse is also true under rather mild conditions

New Exact Penalty Functions for Nonlinear Constrained Optimization Problems

For two kinds of nonlinear constrained optimization problems, we propose two simple penalty functions, respectively, by augmenting the dimension of the primal problem with a variable that controls the weight of the penalty terms. Both of the penalty functions enjoy improved smoothness. Under mild conditions, it can be proved that our penalty functions are both exact in the sense that local minimizers of the associated penalty problem are precisely the local minimizers of the original constrained problem

Investigation on Percolation Theory and Optimization Method in Low Permeability Reservoir Injection-Production Pattern on the Condition of Fracturing

This passage investigates the productivity formulas in low permeability reservoir with vertical wells combined with fracturing well of the five spot rectangular pattern, seven spot pattern and nine spot pattern as well as the productivity of inverted nine-spot rhombus fractured vertical well mixed pattern. Further, the five-point rectangular patterns and the rectangular fracturing well patterns are optimized. The results reveal that widening well spacing, narrowing row spacing and changing the shape factor well network within a certain range can improve the development effectiveness, while length of the crack and area of well pattern are given, we could determine the length and width of rectangular pattern.Key words: Low permeability; Well pattern; Productivity formula; Optimizatio

Existence and Iteration of Positive Solutions for Multipoint Boundary Value Problems Dependence on the First Order Derivative with One-Dimensional p-Laplacian

Abstract In this paper, we study the existence of monotone positive solutions for the following nonlinear m-point singular boundary value problem with p-Laplacian operator. The main tool is the monotone iterative technique. We obtain not only the existence of positive solutions for the problem, but also establish iterative schemes for approximating solution. Mathematics Subject Classification: 34B1

New Convergence Properties of the Primal Augmented Lagrangian Method

New convergence properties of the proximal augmented Lagrangian method is established for continuous nonconvex optimization problem with both equality and inequality constrains. In particular, the multiplier sequences are not required to be bounded. Different convergence results are discussed dependent on whether the iterative sequence {xk} generated by algorithm is convergent or divergent. Furthermore, under certain convexity assumption, we show that every accumulation point of {xk} is either a degenerate point or a KKT point of the primal problem. Numerical experiments are presented finally

Differential expressed genes in ECV304 Endothelial-like Cells infected with Human Cytomegalovirus

Background: Human cytomegalovirus (HCMV) is a virus which has the potential to alter cellular gene expression through multiple mechanisms.Objective: With the application of DNA microarrays, we could monitor the effects of pathogens on host-cell gene expression programmes in great depth and on a broad scale.Methods: Changes in mRNA expression levels of human endothelial-like ECV304 cells following infection with human cytomegalovirus AD169 strain was analyzed by a microarray system comprising 21073 60-mer oligonucleotide probes which represent 18716 human genes or transcripts.Results: The results from cDNA microarray showed that there were 559 differential expressed genes consisted of 471 upregulated genes and 88 down-regulated genes. Real-time qPCR was performed to validate the expression of 6 selected genes (RPS24, MGC8721, SLC27A3, MST4, TRAF2 and LRRC28), and the results of which were consistent with those from the microarray. Among 237 biology processes, 39 biology processes were found to be related significantly to HCMV-infection. The signal transduction is the most significant biological process with the lowest p value (p=0.005) among all biological process which involved in response to HCMV infection.Conclusion: Several of these gene products might play key roles in virus-induced pathogenesis. These findings may help to elucidate the pathogenic mechanisms of HCMV caused diseases.Keywords: Human cytomegalovirus, microarray, Gene expression profiling; infectomicsAfrican Health Sciences 2013; 13(4): 864 - 87

β-Sitosterol Ameliorates Endometrium Receptivity in PCOS-Like Mice: The Mediation of Gut Microbiota

Background: Polycystic ovary syndrome (PCOS), one of the most common endocrine diseases in women of childbearing age, has been found to be accompanied by changes in the gut microbiota. The Bu Shen Yang Xue formula (BSYXF) is a traditional Chinese medicine widely used for the treatment of PCOS. This study aimed to investigate whether the protective effects of β-sitosterol, the main active ingredient of BSYXF, on PCOS was mediated by regulating gut microbiota.Methods: The presence of β-sitosterol in BSYXF was detected by liquid chromatography-mass spectrometry. The PCOS-like mouse model was induced by dehydroepiandrosterone. The fecal supernatant of β-sitosterol-treated mice was prepared for fecal microbiota transplantation (FMT). Body weight and wet weight of the uterus and ovary of the mice were recorded for organ index calculation. Hematoxylin and eosin stain was used to assess the endometrial morphology and microenvironment changes. Expression of endometrial receptivity markers cyclooxygenase-2 (COX-2), Integrin ανβ3, leukemia inhibitory factor (LIF), and homeobox A10 (HOXA10) in the endometrium were determined by immunohistochemistry and western blot analysis. Enzyme-linked immunosorbent assay was employed to detect the expression of follicle stimulating hormone (FSH), luteinizing hormone (LH), progesterone (P), and testosterone (T) in the serum. The diversity of gut microbiota was examined by 16S rDNA gene sequencing.Results: With the treatment of β-sitosterol and β-sitosterol-FMT, the uterine index of PCOS-like mice increased, the ovarian index decreased, levels of COX-2, LH and T decreased, and levels of Integrin ανβ3, LIF, HOXA10, FSH, and P increased. Under β-sitosterol treatment, the structure of the gut microbiota in PCOS-like mice was also changed.Conclusion: β-sitosterol regulates the endometrial receptivity of PCOS and harmonizes the sex hormone balance, which may be related to the changes in the structure and composition of gut microbiota, thus affecting the pathological process of PCOS

Pushing the Limits of Valiant\u27s Universal Circuits: Simpler, Tighter and More Compact

A universal circuit (UC) is a general-purpose circuit that can simulate arbitrary circuits (up to a certain size $n$). Valiant provides a $k$-way recursive construction of universal circuits (STOC 1976), where $k$ tunes the complexity of the recursion. More concretely, Valiant gives theoretical constructions of 2-way and 4-way UCs of asymptotic (multiplicative) sizes $5n\log n$ and $4.75 n\log n$ respectively, which matches the asymptotic lower bound $\Omega(n\log n)$ up to some constant factor. Motivated by various privacy-preserving cryptographic applications, Kiss et al. (Eurocrypt 2016) validated the practicality of 2-way universal circuits by giving example implementations for private function evaluation. G{ü}nther et al. (Asiacrypt 2017) and Alhassan et al. (J. Cryptology 2020) implemented the 2-way/4-way hybrid UCs with various optimizations in place towards making universal circuits more practical. Zhao et al. (Asiacrypt 2019) optimized Valiant\u27s 4-way UC to asymptotic size $4.5 n\log n$ and proved a lower bound $3.64 n\log n$ for UCs under Valiant framework. As the scale of computation goes beyond 10-million-gate ($n=10^7$) or even billion-gate level ($n=10^9$), the constant factor in circuit size plays an increasingly important role in application performance. In this work, we investigate Valiant\u27s universal circuits and present an improved framework for constructing universal circuits with the following advantages. [*Simplicity*] Parameterization is no longer needed. In contrast to that previous implementations resort to a hybrid construction combining $k=2$ and $k=4$ for a tradeoff between fine granularity and asymptotic size-efficiency, our construction gets the best of both worlds when configured at the lowest complexity (i.e., $k=2$). [*Compactness*] Our universal circuits have asymptotic size $3n\log n$, improving upon the best previously known $4.5n\log n$ by 33\% and beating the $3.64n\log n$ lower bound for UCs constructed under Valiant\u27s framework (Zhao et al., Asiacrypt 2019). [*Tightness*] We show that under our new framework the universal circuit size is lower bounded by $2.95 n\log n$, which almost matches the $3n\log n$ circuit size of our 2-way construction. We implement the 2-way universal circuits and evaluate its performance with other implementations, which confirms our theoretical analysis

High preoperative white blood cell count determines poor prognosis and is associated with an immunosuppressive microenvironment in colorectal cancer

BackgroundThe correlation between high white blood cell (WBC) count and poor prognosis has been identified in various types of cancer; however, the clinical significance and immune context of WBC count in colorectal cancer remains unclear.MethodsBetween February 2009 and November 2014, 7,433 patients at the Shanghai Cancer Center who had undergone elective surgery for colorectal cancer were enrolled in this retrospective cohort study. Patients were divided into two groups: low and high preoperative WBC groups. Propensity score matching was used to address the differences in baseline characteristics. The Kaplan–Meier method and Cox regression analysis were used to identify independent prognostic factors in colorectal cancer patients. Tumor-infiltrating immune cells in the high and low preoperative WBC groups were compared using immunohistochemical staining.ResultsOf the 7,433 patients who underwent colorectal cancer surgery and were available for analysis, 5,750 were included in the low preoperative WBC group, and 1,683 were included in the high preoperative WBC group. After propensity score matching, 1,553 patients were included in each group. Kaplan–Meier survival curves showed that a high preoperative WBC count was associated with a decreased overall survival (P = 0.002) and disease-free survival (P = 0.003), and that preoperative WBC count was an independent risk factor for overall survival (hazard ratio, 1.234; 95% confidence interval, 1.068–1.426; P = 0.004) and disease-free survival (hazard ratio, 1.210; 95% confidence interval, 1.047–1.397, P = 0.01). Compared to the low preoperative WBC group, the high preoperative WBC group exhibited higher expression of regulatory T cells (P = 0.0034), CD68+ macrophages (P = 0.0071), and CD66b+ neutrophils (P = 0.0041); increased expression of programmed cell death protein 1 (P = 0.005) and programmed cell death ligand 1 (P = 0.0019); and lower expression of CD8+ T cells (P = 0.0057) in colorectal cancer patients.ConclusionsOur research indicates that a high preoperative WBC count is a prognostic indicator in colorectal cancer patients and is associated with an immunosuppressive tumor microenvironment, which could aid in future risk stratification

Association between modes of delivery and postpartum dietary patterns: A cross-sectional study in Northwest China

Objective: Puerperae’ dietary patterns (DPs) during the puerperium may be influenced by the mode of delivery, but population studies on this topic are scarce. This study aims to explore the relationship between DPs and different modes of delivery among puerperae. Methods: A cross-sectional study was conducted on 3,345 parturients in Lanzhou, China. The postpartum food intake was measured by a food frequency questionnaire (FFQ). Factor analysis was used to determine the DPs. Multiple linear regression was employed to examine the association between the mode of delivery and DP. Results: In this study, two DPs, i.e., traditional and modern DPs, were identified. Traditional DP was characterized by high energy-adjusted intake of tubers, coarse cereals, rice, whole grains, fishery products, and eggs. Modern DP included a high intake of coffee, non-sugary drinks, wine, tea, and fishery products. Compared with participants with vaginal delivery (reference category), cesarean section had an inverse association with modern DP (β: −0.11, 95% CI: −0.36, −0.09). A significant interaction was found between education level, monthly household income, alcohol drinking, and modes of delivery. The inverse association between cesarean section and modern DP or the intake of coffee was significant among puerperae with higher or lower monthly household income. However, the inverse association between cesarean section and traditional DP was only found among puerperae with higher monthly household income. Moreover, among the participants with high education, cesarean section was positively associated with intake of vegetables. Conclusion: Cesarean puerperae with higher levels of education and those with lower and higher monthly household income had less unhealthy foods intake than those who had vaginal delivery. They need to be accounted for in educational programs and interventions focused on healthy diet recommendations in puerperium.This project was funded by the Chongqing Social Science Planning Project (2017YBSH057) and joint project of the Ministry of Technology and Ministry of Health (2021MSXM215) and Discipline Cultivation Fund of the First Affiliated Hospital of Chongqing Medical University. The funders had no role in the design, analysis, data interpretation and publication of findings