Abstract. We consider a branching random walk initiated by a single particle at location 0 in which particles alternately reproduce according to the law of a Galton-Watson process and disperse according to the law of a driftless random walk on the integers. When the offspring distribution has mean 1 the branching process is critical, and therefore dies out with probability 1. We prove that if the particle jump distribution has mean zero, positive finite variance η 2 , and finite 4 + ε moment, and if the offspring distribution has positive variance σ 2 and finite third moment then the distribution of the rightmost position M reached by a particle of the branching random walk satisfies P{M ≥ x} ∼ 6η 2 /(σ 2 x 2 ) as x → ∞. We also prove a conditional limit theorem for the distribution of the rightmost particle location at time n given that the process survives for n generations.

Cases of CD36 deficiency are not rare in Asian populations, foetal and neonatal alloimmune thrombocytopenia (FNAIT) caused by anti-CD36 isoantibodies appears more frequent than other HPA alloantibodies. However, little is known about the treatment of anti-CD36 mediated FNAIT in this region. A Chinese male foetus, whose mother had a history of multiple intrauterine foetal demise and/or hydrops, was diagnosed with severe FNAIT at 27 weeks of gestational age. Immunological analysis revealed total absence of CD36 on platelets and monocytes from mother, caused by a 329-330delAC mutation of the CD36 gene. Anti-CD36 and anti-HLA class I antibodies were detected in the maternal serum, whereas only anti-CD36 isoantibodies were detectable in the foetal blood sample. Serial intrauterine transfusions with red blood cells (RBC) and platelets from a CD36null donor were performed to improve the severe anaemia and thrombocytopenia. The baby (2250 g; Apgar scores 10) was delivered vaginally at 32 weeks of gestation with normal haemoglobin (186 g/L) but low platelet count (48 × 10/L). After 2 days the platelet count rose to 121 × 10/L. This report suggests that intrauterine transfusions with compatible RBC and CD36null platelets are useful in preventing the deleterious clinical effects of anti-CD36-mediated severe FNAIT.

Portal vein tumor thrombosis (PVTT) in patients with hepatocellular carcinoma (HCC) is known as a major complication associated with poor survival. We clinically defined a type of distinct PVTT (dPVTT) in small HCC patients that is distant to liver parenchyma tumor (PT). The biological features of dPVTT are not clear. We utilized two-dimensional electrophoresis and tandem MS to compare and identify differentially expressed proteins between dPVTT and PT tissues. Of the 65 spots identified as differentially expressed (p < 0.05) between the two cancerous tissues, 19 (corresponding to 19 unique proteins) were identified. Further analysis of five proteins confirmed quantitative differences between the two tumor tissues. Upon comparison with PT tissues of HCC, c-kit was also significantly upregulated in dPVTTs in small HCC patients and the CSQT-2 cell line derived from dPVTT tissues, which validated the differences between the dPVTT and PT tissues. The protein expression profiles and proteins identified in this study demonstrate the presence of dPVTTs with more malignant phenotypes and will be useful in clarifying the mechanisms through which dPVTT develops. Specific treatments targeting dPVTT might be applied to HCC patients with dPVTT.