Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing

We study the Parallel Task Scheduling problem $Pm|size_j|C_{\max}$ with a constant number of machines. This problem is known to be strongly NP-complete for each $m \geq 5$, while it is solvable in pseudo-polynomial time for each $m \leq 3$. We give a positive answer to the long-standing open question whether this problem is strongly $NP$-complete for $m=4$. As a second result, we improve the lower bound of $\frac{12}{11}$ for approximating pseudo-polynomial Strip Packing to $\frac{5}{4}$. Since the best known approximation algorithm for this problem has a ratio of $\frac{4}{3} + \varepsilon$, this result narrows the gap between approximation ratio and inapproximability result by a significant step. Both results are proven by a reduction from the strongly $NP$-complete problem 3-Partition

Prominent Plasmacytosis Following Intravenous Immunoglobulin Correlates with Clinical Improvement in Guillain-Barré Syndrome

BACKGROUND: High doses of pooled polyclonal IgG are commonly used to treat numerous autoimmune diseases. Their mode of action nevertheless remains only partially explained. At the same time, until now, no early biological marker has been able to predict their efficacy. METHODOLOGY/PRINCIPAL FINDINGS: In a first pilot retrospective analysis, we reviewed white blood cell counts and blood smears in consecutive patients with autoimmune disease (n = 202) and non-autoimmune disease (n = 104). Autoimmune patients received either intravenous immunoglobulin (IVIg, n = 103), plasma exchange (n = 78) or no specific treatment (n = 21). We then prospectively monitored consecutive autoimmune patients with IVIg injection (n = 67), or without any specific treatment (n = 10) using the same routine laboratory tests, as well as flow cytometry. Both retrospective and prospective analyses identified large plasma-cell mobilization exclusively in IVIg-treated autoimmune patients 7 days after initiation of treatment. The majority of IVIg-mobilized plasma cells were immature HLA-DR(high)/CD138(low)/CXCR4(low) plasma cells expressing intracellular immunoglobulin G which were neither IVIg- nor human IgG-specific. Importantly, we found a strong negative correlation between the absolute number of IVIg-mobilized plasma cells and time to improve neurological function in both retrospective and prospective studies of Guillain-Barré syndrome (GBS), (r = -0.52, p = 0.0031, n = 30, r = -0.47, p = 0.0028, n = 40, respectively). CONCLUSIONS/SIGNIFICANCE: IVIg promotes immature plasma-cell mobilization in patients with GBS, chronic inflammatory demyelinating polyneuropathy, myasthenia gravis and inflammatory myopathy. Prominent day 7 plasma-cell mobilization is a favourable prognostic marker in patients with GBS receiving IVIg treatment