We consider an online combinatorial prediction problem where each combinatorial concept is represented as a vertex of a polyhedron described by a submodular function (base polyhedron). In general, there are exponentially many vertices in the base polyhedron. We propose polynomial time algorithms with regret bounds. In particular, for cardinalitybased submodular functions, we give O(n 2 )-time algorithms.
In Experiment 1, the effects of calcium maltobionate (MBCa) on calcium and magnesium absorption were examined using male rats. Four diets were designed in which 25%, 50%, and 100% of calcium carbonate (CaCO3, Control) were substituted with MBCa and were designated as MBCa-25, MBCa-50, and MBCa-100, respectively. The cecal concentration of short-chain fatty acids was significantly higher in groups MBCa-50 and MBCa-100; however, pH of cecal contents did not significantly differ among the groups. Retention rates of calcium and magnesium were significantly higher in all MBCa groups as compared to the Control. In Experiment 2, the efficiency of calcium absorption was compared using everted sacs of jejunum and ileum with CaCO3 and MBCa as calcium sources. More calcium from MBCa was absorbed as the concentration of calcium increased in comparison to CaCO3. It was concluded that MBCa is a better calcium source than CaCO3 in terms of both calcium retention and absorption. Abbreviations: ANOVA: analysis of variance; Ca: Calcium; CaCO3: calcium carbonate; ICP-OES: Inductivity coupled plasma optical emission spectrometer; Mg: magnesium; MBCa: calcium maltobionate; OCPC: o-cresolphthalein complexone; SCFAs: short-chain fatty acids; SE: standard error; TRPM6: transient receptor potential melastatin 6.
In experiments 1 and 2, effect of ingestion of maltobionic acid calcium salt (MBCa) on recovery of rats from a latent iron deficiency and from iron deficiency anemia was examined, respectively. After grouping rats into control and iron-deficiency groups, a latent iron deficiency or iron-deficiency anemia was induced in the latter group. And recovery from these states by MBCa containing diets (0%, 3%, and 6% MBCa in diet, classified into MBCa-0, MBCa-3, and MBCa-6 groups) was compared for convalescence period in light of iron sufficient control group. In experiment 1, MBCa ingestion significantly increased the iron concentration in the serum and liver, and promoted recovery from a latent iron deficiency. In experiment 2, hemoglobin and hematocrit levels increased significantly with MBCa intake, and recovery from iron-deficiency anemia was promoted. MBCa effectively promoted the recovery of rats from a subclinical iron deficiency and iron-deficiency anemia. Abbreviations: ANOVA: analysis of variance; DMT1: divalent metal transporter 1; EDTA-2Na: disodium salt of ethylenediaminetetraacetic acid; Fpn: feroportin; Hb: hemoglobin; Ht: hematocrit; ICP-OES: inductivity coupled plasma optical emission spectrometer; MBCa: maltobionic acid calcium salt; nitroso-PSAP: 2-nitroso-5-[N-n-propyl-N-(3-sulfopropyl)amino]phenol; SE: standard error; SI: serum-iron concentration; TSAT: transferrin saturation; TIBC: total iron-binding capacity; UIBC: unsaturated iron-binding capacity.
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