For two-dimensional percolation on a domain with the topology of a disc, we introduce a nested-path (NP) operator and thus a continuous family of one-point functions W-k < R . k(l)>, where l... Show moreFor two-dimensional percolation on a domain with the topology of a disc, we introduce a nested-path (NP) operator and thus a continuous family of one-point functions W-k < R . k(l)>, where l is the number of independent (i.e., non-overlapping) nested closed paths surrounding the center, k is a path fugacity, and R projects on configurations having a cluster connecting the center to the boundary. At criticality, we observe a power-law scaling W-k similar to L-XNP with L the linear system size, and we determine the exponent X-NP as a function of k. On the basis of our numerical results, we conjecture an analytical formula, X-NP(k) = 3/4 phi(2) - 5/48 phi(2)/(phi(2) - 2/3) with k = 2 cos(pi phi), which reproduces the exact results for k = 0, 1 and agrees with the high-precision estimate of X-NP for other k values. In addition, we observe that W-2(L) = 1 for site percolation on the triangular lattice with any size L, and we prove this identity for all self-matching lattices. Show less
Nanoparticles (NPs), heavy metals and natural organic matter may co-exist in the water bodies. Currently, knowledge on their interaction effects on the behaviors and fates of NPs and heavy metal... Show moreNanoparticles (NPs), heavy metals and natural organic matter may co-exist in the water bodies. Currently, knowledge on their interaction effects on the behaviors and fates of NPs and heavy metal ions is rather limited, which is critical to comprehensively understand their environmental risk. In this study, the aggregation, solubility and Cd-adsorption of CuO NPs co-existing with humic acid (HA) and Cd2+ upon different solution pH and contact sequences were determined. In the ternary systems of CuO NPs, HA and Cd2+, pH was more important than the contact sequence of the components in affecting the NP aggregation, while the contact sequence was a predominant factor in determining the NP solubility. Pre-equilibration of CuO NPs and HA before addition of Cd2+ resulted in the highest solubility and lowest aggregation of the NPs, relative to other sequences of addition of the components. The adsorption capacity of CuO NPs for Cd-ions increased with an increasing pH value from 5 to 9. HA significantly enhanced the Cd-adsorption capacity of CuO NPs at pH 7 and 9, while at pH 5 a non-significant effect was observed. The results are helpful to better estimate the behaviors and fates of CuO NPs and Cd2+ when they coexisting in natural waters. Show less
GCTB is an osteolytic, locally-aggressive, rarely-metastasizing tumour, characterized by abundance of osteoclastlike giant cells, induced by neoplastic mononuclear cells expressing high-levels of... Show moreGCTB is an osteolytic, locally-aggressive, rarely-metastasizing tumour, characterized by abundance of osteoclastlike giant cells, induced by neoplastic mononuclear cells expressing high-levels of the receptor activator of nuclear factor Kappa-B ligand (RANKL), a mediator of osteoclast activation. Although the mainstay of treatment is complete tumour removal with preservation of bone, therapy with denosumab, an inhibitor of RANKL, has been introduced for selected cases. Objectives: Denosumab-treated GCTB (DT-GCTB) was reported to show a wide spectrum of histological changes such as depletion of osteoclast-like giant cells and intralesional bone deposition, which may lead to diagnostic difficulties. We investigated clinicopathologic and molecular features of DT-GCTB, matched with pre-therapy samples. Participants: 21 cases were included (13 females, 8 males), aged 15 to 64 (median, 30 years). Results: DT-GCTB showed development of sclerotic neocortex and varying degrees of osteosclerosis radiographically. Marked depletion of giant cells, different degree of ossification, fibrosis, and proliferation of mononuclear cells was observed. Staining for H3.3G34W was positive in mononuclear cells in 19 cases (90.5%), while one negative case was positive for H3.3G34V. H3F3A G34W mutation was confirmed in 17 of 19 cases (89.5%), corresponding to nuclear staining with H3.3 G34W antibody. G34L mutation was detected in one G34W negative case, in which H3.3 G34V nuclear positive staining was observed, possibly due to cross-reaction. Conclusions: Post-therapy tumours still exhibit a similar mutation profile, while significantly differing from classic GCTB morphologically. Correlation with history of denosumab administration, awareness of features of DT-GCTB, IHC and molecular studies for histone H3 mutations are important in its assessment. Show less
Tumour-to-tumour metastasis is very unusual and has been defined as a tumour metastasis into another histologically different tumour. It is extremely rare in bone. We report a case of lung squamous... Show moreTumour-to-tumour metastasis is very unusual and has been defined as a tumour metastasis into another histologically different tumour. It is extremely rare in bone. We report a case of lung squamous cell carcinoma metastasized to an enchondroma in the femur of a patient with Ollier disease. A 60-year-old female had a history of a poorly differentiated squamous cell carcinoma of the lung. She underwent a video-assisted thoracoscopic lobectomy, and a follow-up MRI scan showed three lesions in the left distal femur and proximal tibia, which were initially interpreted as metastasis on radiology. Resection of the left proximal tibial lesion was performed, and the pathological findings were consistent with enchondroma with no evidence of metastasis. Subsequent curettage of lesions in the distal left femur revealed metastatic poorly differentiated carcinoma with foci of hyaline cartilage, which was most consistent with metastatic carcinoma in a pre-existing enchondroma. The MRI films were re-reviewed. Characteristic MRI features of enchondroma were found in the lesion in the left proximal tibia and one of the lesions in the left distal femur, while the features of the other lesion in the left distal femur included cortical destruction and extensive oedema in surrounding soft tissue, which were consistent with a malignant tumour. In addition, the enchondroma in the lateral condyle showed blurring and irregular inner margin and adjacent bone oedema, which likely represents a co-existing metastatic tumour and enchondroma. The difference in lineage was confirmed by immunohistochemistry. The final diagnosis was metastatic poorly differentiated carcinoma of the lung into a co-existent enchondroma. The diagnosis can be challenging and could be easily overlooked both radiologically and histologically. Thorough clinical and radiological information is critical for the diagnosis, and despite a very unusual event, awareness of the tumour-to-tumour metastasis phenomenon can avoid an inaccurate diagnosis by the pathologist, therefore preventing inappropriate clinical intervention. Show less
Steiling, K.; Berge, M. van den; Hijazi, K.; Florido, R.; Campbell, J.; Liu, G.; ... ; Lenburg, M.E. 2013
