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4. A difference-of-convex approach for split feasibility with applications to matrix factorizations and outlier detection

Author

Chen, Chen, Pong, Ting Kei, Tan, Lulin, and Zeng, Liaoyuan

Subjects
Mathematics - Optimization and Control
Abstract

The split feasibility problem is to find an element in the intersection of a closed set $C$ and the linear preimage of another closed set $D$, assuming the projections onto $C$ and $D$ are easy to compute. This class of problems arises naturally in many contemporary applications such as compressed sensing. While the sets $C$ and $D$ are typically assumed to be convex in the literature, in this paper, we allow both sets to be possibly nonconvex. We observe that, in this setting, the split feasibility problem can be formulated as an optimization problem with a difference-of-convex objective so that standard majorization-minimization type algorithms can be applied. Here we focus on the nonmonotone proximal gradient algorithm with majorization studied in [15, Appendix A]. We show that, when this algorithm is applied to a split feasibility problem, the sequence generated clusters at a stationary point of the problem under mild assumptions. We also study local convergence property of the sequence under suitable assumptions on the closed sets involved. Finally, we perform numerical experiments to illustrate the efficiency of our approach on solving split feasibility problems that arise in completely positive matrix factorization, (uniformly) sparse matrix factorization, and outlier detection., Comment: Published in JOGO. In this ArXiv version, 1. We fix an unfortunate error in Lemma 4 and the paragraph after it: the matrices involved should have rank r instead of being full rank; 2. An additional compactness condition is needed for the uniform KL exponent in Proposition 5

Published
2019

6. Hydroxy-γ-sanshool from Zanthoxylum bungeanum (prickly ash) induces apoptosis of human colorectal cancer cell by activating P53 and Caspase 8

Author

Chen Zhaojun, Tan Lulin, Feng Xin, Singab Abdel-nasser, Lei Zunguo, and Liu Xiong

Subjects
hydroxy-γ-sanshool, Zanthoxylum bungeanum, apoptosis, cell arrest, colorectal cancer cells, Nutrition. Foods and food supply, TX341-641
Abstract

Sanshools, long-chain polyunsaturated amides in Zanthoxylum bungeanum (prickly ash), have important bioactivity. The objective was to assess inhibitory effects and molecular mechanisms of sanshools isolated from supercritical fluid (SCF) extract on human colon adenocarcinoma cells (HCT-116) cultured in vitro. Cells were exposed to various concentrations (0, 50, 90, or 130 μM) of sanshools for 24 or 48 h, with assessment of apoptosis and cell cycle arrest as well as regulatory gene and protein expression associated with apoptosis and the cell cycle. Sanshools profoundly inhibited growth of HCT-116 cells, with hydroxy-γ-sanshool (HRS) being the optimal active component (IC50 = 88.01 μM) inhibiting cell proliferation and having no cytotoxic effect to normal cells (IC50 = 481.52 μM) by CCK-8 assay. In HCT-116 cells, HRS inhibited cell growth, induced morphological distortion, and arrested the cell cycle at G1 phase (50.31 ± 4.13% vs. 72.16 ± 8.14% in Control and 130 μM HRS, respectively), and also caused programmed cell death in a dose-dependent manner. The percentage of apoptotic cells were remarkably increased after treated with HRS (6.2, 11.9, 19.8, and 30.7% for 0, 50, 90, and 130 μM, respectively). Moreover, in HCT-116 cells, HRS significantly inhibited mRNA and protein levels of Cyclin D1, CDK4, PCNA, and increased mRNA and protein levels of P21, P53, Fas, and Caspase 8. Furthermore, inhibitors of P53 and Caspase 8 proteins significantly mitigated the HRS-induced cell cycle arrest and apoptosis. In conclusion, our study provides evidence that HRS induced human colorectal cancer cell apoptosis by up-regulating P53 and Caspase 8.

Published
2022
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18. Generalized representer theorems in Banach spaces.

Author

Huang, Liren, Liu, Chunguang, Tan, Lulin, and Ye, Qi

Subjects
BANACH spaces, NONSMOOTH optimization, COST functions
Abstract

In this paper, we generalize the representer theorems in Banach spaces by the theory of nonsmooth analysis. The generalized representer theorems assure that the regularized learning models can be constructed by the nonconvex loss functions, the generalized training data, and the general Banach spaces which are nonreflexive, nonstrictly convex, and nonsmooth. Specially, the sparse representations of the regularized learning in 1-norm reproducing kernel Banach spaces are shown by the generalized representer theorems. [ABSTRACT FROM AUTHOR]

Published
2021
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20. Dietary Grape-Seed Procyanidins Decreased Postweaning Diarrhea by Modulating Intestinal Permeability and Suppressing Oxidative Stress in Rats

Author

Song, Peixia, Zhang, Ruoji, Wang, Xiaoxiao, He, Pingli, Tan, Lulin, and Ma, Xi

Abstract

This study was conducted to evaluate the effects of grape-seed procyanidins in controlling weaning diarrhea using a rat model. Weaned rats were fed either the basal diet or basal diet supplemented with either 250 mg/kg grape-seed procyanidins or 2000 mg/kg ZnO. Treated rats had better performance with a reduced incidence of diarrhea (P< 0.05). Both ZnO and grape-seed procyanidins significantly reduced urinary lactulose to mannitol ratios (P< 0.05) and enhanced the mRNA and protein expression of the intestinal mucosal tight junction proteins Ocln/ZO-1 (P< 0.05). Grape-seed procyanidins increased the activities of SOD, GSH-Px, and GSH while decreasing the level of MDA in the intestinal mucosa (P< 0.05). Furthermore, an in vitro investigation revealed that supplementation with grape-seed procyanidins in IEC-6 intestinal epithelial cells significantly enhanced the expression of Ocln/ZO-1 under H2O2-induced oxidative stress. Collectively, these results indicate that grape-seed procyanidins have the potential to prevent weaning diarrhea by reducing intestinal permeability and improving antioxidant indices.

Published
2024
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21. On merit functions, error bounds, minimizing and stationary sequences for nonsmooth variational inequality problems.

Author

Tan, Lulin., Chinese University of Hong Kong Graduate School. Division of Mathematics., Tan, Lulin., and Chinese University of Hong Kong Graduate School. Division of Mathematics.

Abstract

First, we study the associated regularized gap functions and the D-gap functions and compute their Clarke-Rockafellar directional derivatives and the Clarke generalized gradients. Second, using these tools and extending the works of Fukushima and Pang (who studied the case when F is smooth), we present results on the relationship between minimizing sequences and stationary sequences of the D-gap functions, regardless the existence of solutions of (VIP). Finally, as another application, we show that, under the strongly monotonicity assumption, the regularized gap functions have fractional exponent error bounds, and thereby we provide an algorithm of Armijo type to solve the (VIP)., In this thesis, we investigate a nonsmooth variational inequality problem (VIP) defined by a locally Lipschitz function F which is not necessarily differentiable or monotone on its domain which is a closed convex set in an Euclidean space., Tan Lulin., "December 2005.", Adviser: Kung Fu Ng., Source: Dissertation Abstracts International, Volume: 67-11, Section: B, page: 6444., Thesis (Ph.D.)--Chinese University of Hong Kong, 2005., Includes bibliographical references (p. 79-84) and index., Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web., Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web., s in English and Chinese., School code: 1307., isbn: 9780542967092, Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Published
2005

23. Protective effects of Fagopyrum dibotryson oxidized oil-induced oxidative stress, intestinal barrier impairment, and altered cecal microbiota in broiler chickens

Author

Chen, Zhaojun, Dai, Guotao, Wu, Xian, Li, Lina, Tian, Yujie, and Tan, Lulin

Abstract

The objective of this study was to evaluate protective effects of Fagopyrum dibotryson antioxidant ability, intestinal barrier functions, and cecal microbiota in broiler chickens fed oxidized soybean oil. A total of 640 male Tiejiaoma broilers were randomly assigned to 8 treatments with 8 cages (10 birds per cage), as follows: birds fed basal diets containing fresh soybean oil and 0, 0.5, 1, or 2% F. dibotrys(FSCON, FSFAL, FSFAM, and FSFAH, respectively), and birds fed basal diets containing oxidized oil and 0, 0.5, 1, or 2% F. dibotrys(OSCON, OSFAL, OSFAM, and OSFAH). Oxidized oil significantly decreased transcription of Nrf2 and its downstream genes, including CAT and SOD1 in the jejunal mucosa, increased jejunal mucosa IL-6 mRNA expression, and decreased jejunal mucosa IL-22 mRNA expression and downregulated Claudin-1 and ZO-1; however, all these effects were reversed by F. dibotrys. Either 1 or 2% F. dibotrysalleviated the decreased liver SOD induced by oxidized oil on d 42. The decreased SOD and GPX, and increased MDA induced by oxidized oil were reversed by adding 1 or 2% F. dibotrysin jejunal mucosa. In addition, based on 16S rDNA, 2% F. dibotryspromoted the Firmicutesphylum and Candidatus_Arthromitusgenera, but suppressed the Proteobacteriaphylum and Streptococcus, Enterococcus, and Escherichiagenera. In summary, oxidative stress induced by oxidized oil was ameliorated by F. dibotrysupregulating transcription of Nrf2 and its downstream genes to restore redox balance, reinforcing the intestinal barrier via higher expression of Claudin-1/ZO-1, ameliorating the inflammatory response by regulating expression of IL-6 and IL-22, and facilitating growth of Candidatus_arthromitusin the cecum. Therefore, F. dibotryshas potential as a feed additive for poultry by ameliorating oxidative stress caused by oxidized oil, enhancing barrier function, and improving gut microbiome composition.

Published
2023
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