199,125 research outputs found

    Distinct Volume Subsets

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    Suppose that a and d are positive integers with a ≥ 2. Let h[subscript a,d](n) be the largest integer t such that any set of n points in R[superscript d] contains a subset of t points for which all the nonzero volumes of the ([t over a]) subsets of order a are distinct. Beginning with Erdos in 1957, the function h[subscript 2,d](n) has been closely studied and is known to be at least a power of n. We improve the best known bound for h[subscript 2,d](n) and show that h[subscript a,d](n) is at least a power of n for all a and d.David & Lucile Packard Foundation (Fellowship)Simons Foundation (Fellowship)National Science Foundation (U.S.) (Grant DMS-1069197)Alfred P. Sloan Foundation (Fellowship)NEC Corporation (MIT Award

    Distinct Volume Subsets

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    Suppose that a and d are positive integers with a ≥ 2. Let h_(a,d)(n) be the largest integer t such that any set of n points in ℝ^d contains a subset of t points for which all the nonzero volumes of the [equaton; see abstract in PDF for details] subsets of order a are distinct. Beginning with Erdős in 1957, the function h_(2,d)(n) has been closely studied and is known to be at least a power of n. We improve the best known bound for h_(2,d)(n) and show that h_(a,d)(n) is at least a power of n for all a and d

    Identification of stromal cells in spleen which support myelopoiesis

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    Stromal cells in spleen organize tissue into red pulp, white pulp and marginal zone, and also interact with hematopoietic cells to regulate immune responses. This study has used phenotypic information of a previously described spleen stromal cell line called 5G3, which supports restricted hematopoiesis in vitro, to identify an equivalent stromal cell subset in vivo and to test its capacity to support hematopoiesis. Using stromal cell fractionation, phenotypic analysis, as well as cell growth and hematopoietic support assays, the Sca-1+gp38+Thy1.2+CD29+CD51+ fraction of spleen stroma has been identified as an equivalent stromal subset resembling the 5G3 cell counterpart. While heterogeneity may still exist within that subset, it has been shown to have superior hematopoietic support capacity compared with the 5G3 cell line, and all other spleen stromal cell fractions tested.This work was supported by project grants to HO from the Australian Research Council (#DP130101703) and the National Health and Medical Research Council of Australia (#585443). HL was supported by an Australian National University Postgraduate Scholarship

    Role of distinct natural killer cell subsets in anticancer response

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    Natural killer (NK) cells, the prototypic member of innate lymphoid cells, are important effectors of anticancer immune response. These cells can survey and control tumor initiation due to their capability to recognize and kill malignant cells and to regulate the adaptive immune response via cytokines and chemokines release. However, several studies have shown that tumor-infiltrating NK cells associated with advanced disease can have profound functional defects and display protumor activity. This evidence indicates that NK cell behavior undergoes crucial alterations during cancer progression. Moreover, a further level of complexity is due to the extensive heterogeneity and plasticity of these lymphocytes, implying that different NK cell subsets, endowed with specific phenotypic and functional features, may be involved and play distinct roles in the tumor context. Accordingly, many studies reported the enrichment of selective NK cell subsets within tumor tissue, whereas the underlying mechanisms are not fully elucidated. A malignant microenvironment can significantly impact NK cell activity, by recruiting specific subpopulations and/or influencing their developmental programming or the acquisition of a mature phenotype; in particular, neoplastic, stroma and immune cells, or tumor-derived factors take part in these processes. In this review, we will summarize and discuss the recently acquired knowledge on the possible contribution of distinct NK cell subsets in the control and/or progression of solid and hematological malignancies. Moreover, we will address emerging evidence regarding the role of different components of tumor microenvironment on shaping NK cell response

    A hitchhiker's guide to myeloid cell subsets: practical implementation of a novel mononuclear phagocyte classification system

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    The classification of mononuclear phagocytes as either dendritic cells or macrophages has been mainly based on morphology, the expression of surface markers, and assumed functional specialization. We have recently proposed a novel classification system of mononuclear phagocytes based on their ontogeny. Here, we discuss the practical application of such a classification system through a number of prototypical examples we have encountered while hitchhiking from one subset to another, across species and between steady-state and inflammatory settings. Finally, we discuss the advantages and drawbacks of such a classification system and propose a number of improvements to move from theoretical concepts to concrete guidelines

    The Maximum Number of Subset Divisors of a Given Size

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    If ss is a positive integer and AA is a set of positive integers, we say that BB is an ss-divisor of AA if bBbsaAa\sum_{b\in B} b\mid s\sum_{a\in A} a. We study the maximal number of kk-subsets of an nn-element set that can be ss-divisors. We provide a counterexample to a conjecture of Huynh that for s=1s=1, the answer is (n1k)\binom{n-1}{k} with only finitely many exceptions, but prove that adding a necessary condition makes this true. Moreover, we show that under a similar condition, the answer is (n1k)\binom{n-1}{k} with only finitely many exceptions for each ss.Comment: submitted on July 17, 201
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