Strong variational sufficiency of nonsmooth optimization problems on Riemannian manifolds

The Riemannian augmented Lagrangian method (RALM) is proposed to solve the nonsmooth optimization problems on Riemannian manifolds. However, the local convergence rate of this algorithm still remains unknown without imposing any constraint qualifications. In this paper, we introduce the manifold variational sufficient condition and show that its strong version is equivalent to the manifold strong second-order sufficient condition (M-SSOSC) in some cases. More importantly, we formulate a local dual problem based on this condition, consequently establishing the R-linear convergence rate of RALM. Furthermore, the validity of the semismooth Newton method for solving the RALM subproblem is demonstrated under the M-SSOSC

Strong Variational Sufficiency for Nonlinear Semidefinite Programming and its Implications

Strong variational sufficiency is a newly proposed property, which turns out to be of great use in the convergence analysis of multiplier methods. However, what this property implies for non-polyhedral problems remains a puzzle. In this paper, we prove the equivalence between the strong variational sufficiency and the strong second order sufficient condition (SOSC) for nonlinear semidefinite programming (NLSDP), without requiring the uniqueness of multiplier or any other constraint qualifications. Based on this characterization, the local convergence property of the augmented Lagrangian method (ALM) for NLSDP can be established under strong SOSC in the absence of constraint qualifications. Moreover, under the strong SOSC, we can apply the semi-smooth Newton method to solve the ALM subproblems of NLSDP as the positive definiteness of the generalized Hessian of augmented Lagrangian function is satisfied.Comment: 23 page

Link of renal microcirculatory dysfunction to increased coronary microcirculatory resistance in hypertensive patients

Background: This study investigated the correlation between renal microcirculation and coronary microcirculation in hypertensive patients. Methods: Participants consisted of 231 consecutive candidates who were referred to the Second Affiliated Hospital of Wenzhou Medical University from March 2014 to May 2016 for elective coronary angiography due to suspected myocardial ischemia. All participants were evaluated for the index of microvascular resistance (IMR), coronary flow reserve (CFR), and fractional flow reserve (FFR) us¬ing a pressure wire. Blood and urine samples were collected for determination of the levels of urinary microalbuminuria (mALB), b2-microglobulin (b2-MG), serum cystatin C (CysC), and uric acid (UA). All participants were categorized into two groups according to the renal microcirculatory function. Results: Participants in the observation group had a higher IMR (31 ± 5 vs. 22 ± 6; p < 0.01) and a lower FFR (0.84 ± 0.10 vs. 0.87 ± 0.09 U; p < 0.05) during hyperemia than those in the control group. Linear regression tests revealed that mALB, b2-MG, CysC, and UA levels were positively cor¬related with IMR (r = 0.610, 0.553, 0.701, and 0.647, respectively, p < 0.01). The hs-CRP levels were positively correlated with IMR (r = 0.419, p < 0.01). Multiple regression analysis indicated that renal microcirculation was an independent predictor of IMR. Conclusions: Renal microcirculatory dysfunction in hypertensive patients is characterized by higher IMR and lower FFR; in addition, it is closely correlated with an increased coronary microcirculatory resistance

Mechanism of crocin I on ANIT-induced intrahepatic cholestasis by combined metabolomics and transcriptomics

Background: Intrahepatic cholestasis (IC) is a disorder of bile production, secretion, and excretion with various causes. Crocin I (CR) is effective in the treatment of IC, but its underlying mechanisms need to be further explored. We aimed to reveal the therapeutic mechanism of crocin I for IC by combining an integrated strategy of metabolomics and transcriptomics.Methods: The hepatoprotective effect of CR against cholestasis liver injury induced by α-naphthylisothiocyanate (ANIT) was evaluated in rats. The serum biochemical indices, including alanine aminotransferase (ALT), aspartate aminotransferase (AST), total bile acid (TBA), total bilirubin (TBIL), direct bilirubin (DBIL), tumor necrosis factor-α (TNF-α), interleukin 6 (IL-6), and interleukin 1β (IL-1β), as well as the liver oxidative stress indexes and the pathological characteristics of the liver were analyzed. In addition, we also performed a serum metabolomics study using UPLC-Q Exactive HF-X technology to investigate the effect of CR on the serum of rats with ANIT-induced IC and screened potential biomarkers. The enrichment analysis of differential expressed genes (DEGs) was performed by transcriptomics. Finally, the regulatory targets of CR on potential biomarkers were obtained by combined analysis, and the relevant key targets were verified by western blotting.Results: CR improved serum and liver homogenate indexes and alleviated liver histological injury. Compared with ANIT group, the CR group had 76 differential metabolites, and 10 metabolic pathways were enriched. There were 473 DEGs significantly changed after CR treatment, most of which were enriched in the retinol metabolism, calcium signaling pathway, PPAR signaling pathway, circadian rhythm, chemokine signaling pathway, arachidonic acid metabolism, bile secretion, primary bile acid biosynthesis, and other pathways. By constructing the “compound-reaction-enzyme-gene” interaction network, three potential key-target regulation biomarkers were obtained, including 3-hydroxy-3-methylglutaryl-coenzyme A reductase (HMGCR), ATP-binding cassette transporter G5 (ABCG5), and sulfotransferase2A1(SULT2A1), which were further verified by western blotting. Compared with the ANIT group, the CR group significantly increased the expression of ABCG5 and SULT2A1, and the expression of HMGCR significantly decreased.Conclusion: Combined metabolomic and transcriptomic analyses show that CR has a therapeutic effect on IC through regulation of the biosynthesis of bile acids and bilirubin in the bile secretion pathway and regulation of the expression of HMGCR, ABCG5, and SULT2A1

EFFICIENT HESSIAN BASED ALGORITHMS FOR SOLVING SPARSE GROUP LASSO AND MULTIPLE GRAPHICAL LASSO PROBLEMS

Ph.DDOCTOR OF PHILOSOPH

Simple Technique for Transscleral Fixation of a Foldable Posterior Chamber Intraocular Lens Using a Single Suture

Objective: To explore the simplified technique for transscleral fixation of a foldable posterior chamber intraocular lens (IOLs) in patients with aphakia or inadequate posterior capsule support. Methods: A review was conducted of 18 eyes of eighteen patients with the absence of—or inadequate—capsule support, after the simplified technique of using a foldable posterior chamber intraocular lens (PC IOLs) with stable four-point transscleral fixation, as performed by a skilled surgeon. This technique uses only a single suture and a knot to fix a PC IOL firmly without creating a scleral flap. The mean follow-up time was 18 ± 5.8 months (ranging from 12 to 24 months). Results: All patients exhibited improved visual acuity. No IOL tilt or dislocation or iris capture was observed, and all patients exhibited stable and centered IOL after surgery. No complex complications, such as suture shedding and exposure, corneal endothelial decompensation, persistent uveitis, or retinal detachment and endophthalmitis were observed. Conclusion: The simplified technique proposed here is a reliable, economical, and reproducible method of treating patients with aphakia or inadequate posterior capsule support. It provides excellent IOL stability, reduces surgical duration and complexity, and prevents certain complications

Effect of biological amniotic membrane soaked in pirfenidone on scar formation after glaucoma filtration surgery in rabbit eyes

AIM: To investigate the application of biological amniotic membrane soaked in pirfenidone(PFD)and to evaluate its anti-scarring effect and toxic side effects on glaucoma model of rabbit eyes.METHODS: The right eyes of 72 healthy New Zealand white rabbits were randomly divided into 0.5%PFD+ biological amniotic membrane group, biological amniotic membrane group, mitomycin C(MMC)group and blank control group after the glaucoma model was established by anterior chamber injection of compound carbomer solution, and 18 rabbits in each group underwent trabeculectomy, in which the 0.5% PFD+ biological amniotic membrane group was placed with 0.5% PFD solution-soaked biological amniotic membrane under the scleral flap, and the biological amniotic membrane group was placed with normal saline-soaked rehydrated biological amniotic membrane under the scleral flap. In the MMC group, a cotton pad soaked in MMC was placed under the scleral flap for 3 min and immediately rinsed with normal saline, while the blank control group received no implant after the scleral flap was made. The intraocular pressure(IOP), filtration blebs, toxic side effects and complications were evaluated, and the histopathological changes in the filtration area were observed by hematoxylin-eosin(HE), Masson staining and immunohistochemical staining.RESULTS: The mean IOP at 14, 21 and 28 d after trabeculectomy were 0.5%PFD+ biological amniotic membrane group&#x003C;MMC group&#x003C;biological amniotic membrane group&#x003C;blank control group(all P&#x003C;0.05). At 28 d after trabeculectomy, 0.5%PFD+ biological amniotic membrane group had the best effect of anti-inflammatory hyperplasia and inhibition of collagen formation, the highest survival rate of filtration blebs, and the inflammatory reaction was mild.CONCLUSION: Biological amniotic membrane soaked in pirfenidone has more obvious anti-scarring effect on glaucoma model, with less toxic side effects and good safety