We prove a version of Kontsevich's formality theorem for two subspaces (branes) of a vector space X. The result implies, in particular, that the Kontsevich deformation quantizations of S(X * ) and ∧(X) associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet's recent paper on Koszul duality in deformation quantization.
Many motor responses to sensory input, like locomotion or eye movements, are much slower than reflexes. Can simpler animals provide fundamental answers about the cellular mechanisms for motor decisions? Can we observe the 'accumulation' of excitation to threshold proposed to underlie decision making elsewhere? We explore how somatosensory touch stimulation leads to the decision to swim in hatchling Xenopus tadpoles. Delays measured to swimming in behaving and immobilised tadpoles are long and variable. Activity in their extensively studied sensory and sensory pathway neurons is too short-lived to explain these response delays. Instead, whole-cell recordings from the hindbrain reticulospinal neurons that drive swimming show that these receive prolonged, variable synaptic excitation lasting for nearly a second following a brief stimulus. They fire and initiate swimming when this excitation reaches threshold. Analysis of the summation of excitation requires us to propose extended firing in currently undefined presynaptic hindbrain neurons. Simple models show that a small excitatory recurrent-network inserted in the sensory pathway can mimic this process. We suggest that such a network may generate slow, variable summation of excitation to threshold. This excitation provides a simple memory of the sensory stimulus. It allows temporal and spatial integration of sensory inputs and explains the long, variable delays to swimming. The process resembles the 'accumulation' of excitation proposed for cortical circuits in mammals. We conclude that fundamental elements of sensory memory and decision making are present in the brainstem at a surprisingly early stage in development.
CD26 (dipeptidyl peptidase IV, DPP IV) is widely expressed by T and natural killer (NK) cells, epithelial and endothelial cells of different tissues, and it is strongly upregulated in activated B-cells; moreover it plays a regulatory role in the neoplastic transformation and progression of various types of tumours. CD26 expression was evaluated by means of flow cytometry in various peripheral B-cell lymphoid tumours: 12 follicular and 12 mantle cell lymphomas, 20 multiple myelomas (MMs), 12 hairy cell leukaemias (HCLs), 112 chronic lymphocytic leukaemias (CLLs), 20 CD5(negative) B-cell chronic lymphoproliferative diseases (CD5(neg) B-CLPDs) and 12 diffuse large cell lymphomas (DLCLs). CD26 expression was absent or barely detectable in follicular and mantle cell lymphomas, high in MMs and HCLs, and variable in CLLs, in CD5(neg) B-CLPDs and in DLCLs. CD26 significantly correlated with CD49d and CD38 expressions (p < 0.0001) in B-CLLs, and there was a significant correlation between CD26 and ZAP-70 expressions or IgVH mutational status (p < 0.0001). After a median follow-up of 36 months, 65 B-CLL patients were treated; taking 10% as the best CD26 cut-off value, Kaplan-Meier curves revealed a significantly shorter time to treatment in the CD26-positive cases (p < 0.0001). Overall, our data indicate that CD26 expression may identify subsets of B-CLL patients with an unfavourable clinical outcome in terms of therapeutic need, thus suggesting its potential role as a marker (together with CD38 and CD49d) in a future routine cytofluorimetric panel to be validated for the prognostic stratification of B-CLLs.
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