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We prove certain L2(ℝn) bilinear estimates for Fourier extension operators associated to spheres and hyperboloids under the action of the k-plane transform. As the estimates are L2-based, they follow from bilinear identities: in particular, these are the analogues of a known identity for paraboloids, and may be seen as higher-dimensional versions of the classical L2(ℝ2)-bilinear identity for Fourier extension operators associated to curves in ℝ2.
This article measures inequality at the provincial level in Spain for different benchmark years between 1860 and 1930. It then empirically assesses the relationship between economic growth and inequality. The results confirm that, although growing incomes did not directly contribute to reducing inequality, at least during the early stages of modern economic growth, other processes associated with economic growth such as the rural exodus to urban and industrial centers, the demographic transition, and the spread of literacy, among others, notably improved the situation of the bottom part of the population.
Products of conjugacy classes is a well-established theme in Group Theory with open conjectures. We summarize known and new results concerning the influence that the product of two conjugacy classes exerts on the structure of a finite group. We add several open questions in order to inspire the reader to solve them and develop new techniques of research.
OBJECTIVES/SPECIFIC AIMS: The objectives of this study are to 1) expand upon the paradigm of HK-D5 accelerated immune cell chemotaxis; 2) characterize the role of FXII in murine models of immune-mediated disease using FXII KO mice and a small molecule inhibitor of FXIIa. METHODS/STUDY POPULATION: To test whether the addition of HK-D5 peptide would accelerate C-C chemokine receptor type 2 (CCR2)-mediated chemotaxis in vitro, a real-time transwell chemotaxis assay was developed utilizing human THP-1 monocyte cell line (Fig 1). For in vivo studies, both pharmacologic FXIIa antagonism and FXll KO mice were used. Genotyping, histopathological review, FXll protein expression, and active partial thromboplastin time (aPTT) measurements were used to phenotypically characterize FXII KO mice compared to C57BL/6 wild type mice (Fig 2). Subsequently, the FXll KO mice were studied in varied models of immune-mediated disease, including LPS-induced sepsis and experimental autoimmune encephalitis (EAE), to see if and how the absence of FXll can mitigate disease severity. The EAE model involved active immunization with myelin oligodendrocyte glycoprotein (MOG) and measurement of established clinical disease severity scores. The LPS sepsis model involved an intraperitoneal injection of LPS followed by 48-hour monitoring of core body temperature using subdermal temperature transponders as a proxy for inflammatory events related to septic shock (Fig 3). RESULTS/ANTICIPATED RESULTS: HK-D5 significantly accelerates CCR2-mediated chemotaxis compared to chemokine alone (p = 0.001) similar to HK-D5’s ability to accelerate CCR7-mediated chemotaxis as previously established. The FXll KO mice were backcrossed to the C57BL/6J background and confirmed by genotyping and complete absence of FXII protein in plasma. Compared to the control, FXII KO mice have a significantly prolonged aPTT without evidence of bleeding abnormalities, which confirms the expected phenotype previously described and recapitulates what is observed in Factor XII deficiency in humans. KO mice showed no significant gross or histopathological differences in secondary lymphoid structures compared to the control. Immunohistochemistry confirmed well-organized lymphoid structures with intact B- and T-cell populations. FXll KO mice are protected in LPS-induced septic shock and EAE models. Regarding the EAE model, FXIIa inhibition significantly reduced disease severity compared to control. In the LPS model, FXll KO mice recover within 24 hours after LPS-challenge measured subjectively and objectively by core body temperature measurement. DISCUSSION/SIGNIFICANCE OF IMPACT: The current study and previous findings suggest a novel immune signaling mechanism by which a peptide fragment of high molecular-weight kininogen (HK-D5) acts as an accelerant of both innate and adaptive immune cell chemotaxis in multiple immune contexts. This has broad implications regarding a mechanism of immune-mediated inflammation in a variety of disease states, which might be amenable to the targeting this pathway for therapeutic intent.