Online Knapsack Problems with a Resource Buffer

In this paper, we introduce online knapsack problems with a resource buffer. In the problems, we are given a knapsack with capacity 1, a buffer with capacity R >= 1, and items that arrive one by one. Each arriving item has to be taken into the buffer or discarded on its arrival irrevocably. When every item has arrived, we transfer a subset of items in the current buffer into the knapsack. Our goal is to maximize the total value of the items in the knapsack. We consider four variants depending on whether items in the buffer are removable (i.e., we can remove items in the buffer) or non-removable, and proportional (i.e., the value of each item is proportional to its size) or general. For the general&non-removable case, we observe that no constant competitive algorithm exists for any R >= 1. For the proportional&non-removable case, we show that a simple greedy algorithm is optimal for every R >= 1. For the general&removable and the proportional&removable cases, we present optimal algorithms for small R and give asymptotically nearly optimal algorithms for general R

Influence of Molecular Structure on O2-Binding Properties and Blood Circulation of Hemoglobin‒Albumin Clusters.

A hemoglobin wrapped covalently by three human serum albumins, a Hb-HSA3 cluster, is an artificial O2-carrier with the potential to function as a red blood cell substitute. This paper describes the synthesis and O2-binding properties of new hemoglobin‒albumin clusters (i) bearing four HSA units at the periphery (Hb-HSA4, large-size variant) and (ii) containing an intramolecularly crosslinked Hb in the center (XLHb-HSA3, high O2-affinity variant). Dynamic light scattering measurements revealed that the Hb-HSA4 diameter is greater than that of either Hb-HSA3 or XLHb-HSA3. The XLHb-HSA3 showed moderately high O2-affinity compared to the others because of the chemical linkage between the Cys-93(β) residues in Hb. Furthermore, the blood circulation behavior of 125I-labeled clusters was investigated by assay of blood retention and tissue distribution after intravenous administration into anesthetized rats. The XLHb-HSA3 was metabolized faster than Hb-HSA3 and Hb-HSA4. Results suggest that the molecular structure of the protein cluster is a factor that can influence in vivo circulation behavior

Urinary and fecal excretions.

<p>Urinary and fecal excretions of ¹²⁵I radioactivity (% of dose) within 24 h after intravenous administration of ¹²⁵I-labeled Hb-HSA_<i>3</i>, Hb-HSA_<i>4</i>, XLHb-HSA_<i>3</i>, and HSA to rats. Each bar shows the mean ± SD (<i>n</i> = 6). *<i>p</i> < 0.05 vs. Hb-HSA_<i>3</i>, **<i>p</i> < 0.01 vs. Hb-HSA_<i>4</i>.</p

Diameters and IEF patterns of hemoglobin-albumin clusters.

<p>(A) Hydrodynamic diameters of Hb-HSA_<i>3</i>, Hb-HSA_<i>4</i>, and XLHb-HSA_<i>3</i> measured using DLS. (B) IEF patterns of Hb-HSA_<i>3</i>, Hb-HSA_<i>4</i>, and XLHb-HSA_<i>3</i>.</p

Blood circulation parameters of ¹²⁵I-labeled Hb-HSA_<i>3</i>, Hb-HSA_<i>4</i>, XLHb-HSA_<i>3</i>, and HSA after intravenous administration to rats (<i>n</i> = 6).

<p>Blood circulation parameters of ¹²⁵I-labeled Hb-HSA_<i>3</i>, Hb-HSA_<i>4</i>, XLHb-HSA_<i>3</i>, and HSA after intravenous administration to rats (<i>n</i> = 6).</p

Tissue distribution of hemoglobin-albumin clusters.

<p>Tissue (vital organs) distribution of ¹²⁵I radioactivity (% of dose) (A) at 1 h and (B) at 24 h after intravenous administration of ¹²⁵I-labeled Hb-HSA_<i>3</i>, Hb-HSA_<i>4</i>, XLHb-HSA_<i>3</i>, and HSA to rats. Each bar shows the mean ± SD (<i>n</i> = 6). **<i>p</i> < 0.01 vs. HSA.</p

Blood retention of hemoglobin-albumin clusters.

<p>Relative plasma concentrations of ¹²⁵I-labeled Hb-HSA_<i>3</i>, Hb-HSA_<i>4</i>, XLHb-HSA_<i>3</i>, and HSA after intravenous administration to rats. Each data point represents the mean ± SD (<i>n</i> = 6). **<i>p</i> < 0.01 vs. HSA.</p

Schematic illustrations of hemoglobin-albumin clusters.

<p>(A) Molecular structures of Hb-HSA_<i>3</i>, Hb-HSA_<i>4</i>, and XLHb-HSA_<i>3</i>. (B) Structural model of intramolecularly crosslinked Hb, in which sulfhydryl groups of Cys-93(β) residues (distance: 21.6 Å) are connected by BMTEG (molecular length: 18.3 Å, shown in a space-filling representation) [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149526#pone.0149526.ref025" target="_blank">25</a>,<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0149526#pone.0149526.ref026" target="_blank">26</a>].</p