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A critical disadvantage of primal-dual interior-point methods compared to dual interior-point methods for large scale semidefinite programs (SDPs) has been that the primal positive semidefinite matrix variable becomes fully dense in general even when all data matrices are sparse. Based on some fundamental results about positive semidefinite matrix completion, this article proposes a general method of exploiting the aggregate sparsity pattern over all data matrices to overcome this disadvantage. Our method is used in two ways. One is a conversion of a sparse SDP having a large scale positive semidefinite matrix variable into an SDP having multiple but smaller positive semidefinite matrix variables to which we can effectively apply any interior-point method for SDPs employing a standard block-diagonal matrix data structure. The other way is an incorporation of our method into primal-dual interior-point methods which we can apply directly to a given SDP. In Part II of this article, we will investigate an implementation of such a primal-dual interior-point method based on positive definite matrix completion, and report some numerical results.

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The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Several dietary flavonoids exhibit anti-oxidative, anti-inflammatory, and anti-osteoporotic activities relevant to prevention of chronic diseases, including lifestyle-related diseases. Dietary flavonoids (glycoside forms) are enzymatically hydrolyzed and absorbed in the intestine, and are conjugated to their glucuronide/sulfate forms by phase II enzymes in epithelial cells and the liver. The intestinal microbiota plays an important role in the metabolism of flavonoids found in foods. Some specific products of bacterial transformation, such as ring-fission products and reduced metabolites, exhibit enhanced properties. Studies on the metabolism of flavonoids by the intestinal microbiota are crucial for understanding the role of these compounds and their impact on our health. This review focused on the metabolic pathways, bioavailability, and physiological role of flavonoids, especially metabolites of quercetin and isoflavone produced by the intestinal microbiota.

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Soy isoflavonoids have attracted much attention because of their estrogenic activity. To study the intestinal absorption of the isoflavonoids, we investigated the cellular uptake and metabolism of genistein and daidzein and their glucosides, genistin and daidzin, by Caco-2 cell monolayers as a model of the human intestinal epithelium. When Caco-2 monolayers were incubated with genistein or daidzein at 10 micromol/L from the apical (mucosal) side, aglycone was lost from the apical solution for 2.0 h (P < 0.05) and the glucuronide/sulfates appeared at the level of 1-2 micromol/L. In the basolateral (serosal) solution, both intact aglycones and their glucuronide/sulfates increased (P < 0.05) with time and reached approximately 20 and 15% of the initial dose, respectively. The transport of their glucosides, genistin and daidzin, through Caco-2 monolayers was less than one tenth that of the aglycones. The cellular metabolism of genistein was compared with quercetin, kaempferol, luteolin and apigenin. Only genistein aglycone was transported intact to the basolateral solution. Transport was greater (P < 0.05) than that of flavonoid aglycones and was without an appreciable decrease of transepithelial resistance. Radical scavenging activity was not related to the susceptibility to conjugation of flavonoids/isoflavonoids. Affinity to the liposomal membrane was increased in the order of genistin = daidzin < daidzein < genistein << flavonoid aglycones. These results strongly suggest that isoflavone aglycones are taken up into enterocytes more efficiently than their glucosides because of their moderate lipophilicity. Furthermore, they are generally transported to the basolateral side in intact form in contrast to flavonoids, probably due to their unique isoflavonoid structure.