We introduce a notion of fibred coarse embedding into Hilbert space for metric spaces, which is a generalization of Gromov's notion of coarse embedding into Hilbert space. It turns out that a large class of expander graphs admit such an embedding. We show that the maximal coarse Baum-Connes conjecture holds for metric spaces with bounded geometry which admit a fibred coarse embedding into Hilbert space.
We study an operator norm localization property and its applications to the coarse Novikov conjecture in operator K-theory. In particular, we introduce a sufficient geometric condition (called metric sparsification) for the operator norm localization property. This is used to give many examples of finitely generated groups with infinite asymptotic dimension and the operator norm localization property. We also show that a sequence of expanding graphs does not possess the operator norm localization property.
We show that a finitely generated, residually finite group has the Haagerup property (Gromov's a‐T‐menability) if and only if one (or equivalently, all) of its box spaces admits a fibred coarse embedding into Hilbert space. In contrast, the box spaces of a finitely generated, residually finite hyperbolic group with property (T) do not admit a fibred coarse embedding into Hilbert space, but do admit a fibred coarse embedding into an ℓp‐space for some p>2.
Tumor-associated macrophages (TAMs) are the most abundant population type of tumor-infiltrating immune cells found in the tumor microenvironment (TME), and are evolutionarily associated with microvessel density in tumor tissues. TAMs can be broadly divided into M1-like and M2-like TAMs, which demonstrate antitumor and pro-tumor activity in the TME, respectively. Studies have indicated that: i) The predominate presence of M2-like TAMs in the TME can result in tumor immunosuppression and chemoresistance; ii) the ratio of M1-like to M2-like TAMs in the TME is positively correlated with better long-term prognosis of patients with cancer; iii) epigenetic silencing, preventing the secretion of M1-like TAM-associated molecules, is an important immune evasion mechanism during tumor progression; and iv) the transformation from M2-like to M1-like TAMs following exposure to specific conditions can result in tumor regression. The present study discusses the molecular events underlying the recruitment of macrophages and their polarization into M1-like or M2-like TAMs, and their differential roles in angiogenesis, angiostasis, invasion, metastasis and immune activity in the TME. This insight may inform the improved design of TAM-targeted cancer immunotherapy. Some of these therapeutic strategies show promising effects; however, challenges remain.
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