No abstract

Let Mn be the number of steps of the loop-erasure of a simple random walk on Z 3 run until its first exit from a ball of radius n. In the paper, we will show the existence of the growth exponent, i.e., we show that there exists β > 0 such that lim n→∞ log E(Mn) log n = β.

Recent findings have shown the significance of CD163-positive macrophages in tumor progression, yet there have been few studies on the function of CD163 in macrophages. Here, we uncover the role of CD163 in macrophage activation using CD163-deficient mice and human samples. We detected CD163 in 62 undifferentiated pleomorphic sarcoma samples, in which a high percentage of CD163-positive macrophages was associated with decreased overall survival and higher histologic grade. We observed macrophage-induced tumor cell proliferation in cocultures of human monocyte-derived macrophages and leiomyosarcoma (TYLMS-1) and myxofibrosarcoma (NMFH-1) cell lines, which was abrogated by silencing of CD163. Tumor development of sarcoma (MCA205 and LM8) cells in CD163-deficient mice was significantly abrogated in comparison with wild-type (WT) mice. Coculture with WT peritoneal macrophages significantly increased proliferation of MCA205 cells but decreased in the presence of CD163-deficient macrophages. Production of IL6 and CXCL2 in CD163-deficient macrophages was suppressed in comparison with WT macrophages, and overexpression of CD163 in CD163-deficient macrophages induced production of IL6 and CXCL2. Silencing of IL6 but not CXCL2 abrogated macrophage-induced proliferation of MCA205 cells. Taken together, our results show that CD163 is involved in protumoral activation of macrophages and subsequent development and progression of tumors in mice and humans. Macrophage CD163-mediated induction of IL6 promotes tumor development and progression in murine and human malignant tumors. .

We provide a decomposition of the trace of the Brownian motion into a simple path and an independent Brownian soup of loops that intersect the simple path. More precisely, we prove that any subsequential scaling limit of the loop erased random walk is a simple path (a new result in three dimensions), which can be taken as the simple path of the decomposition. In three dimensions, we also prove that the Hausdorff dimension of any such subsequential scaling limit lies in (1, 5 3 ]. We conjecture that our decomposition characterizes uniquely the law of the simple path. If so, our results would give a new strategy to the existence of the scaling limit of the loop erased random walk and its rotational invariance.

Macrophage activation is one of the major immunological events in the pathogenesis of various diseases. Recent studies have disclosed that complicated mechanisms are involved in macrophage activation and polarization, and many published research articles have been based on the M1/M2 polarization concept. It is considered that M1-and M2-like macrophages are associated with T helper (Th)1-type and Th2-type immune responses, respectively, via several immune mediators. In this article, we summarize the correlations between macrophage polarization and metabolic disorders in both humans and mice and discuss the contribution of macrophage polarization to the pathogenic process of metabolic diseases.J Atheroscler Thromb, 2016; 23: 10-17.