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We apply universality limits to asymptotics of spacing of zeros fxkng of orthogonal polynomials, for weights with compact support and for exponential weights. A typical result is lim n!1 xkn xk+1;n ~ Kn (xkn; xkn) = 1 under minimal hypotheses on the weight, with ~ Kn denoting a normalized reproducing kernel. Moreover, for exponential weights, we derive(More)
Previous studies have reported immunoglobulin-positive neurons in Alzheimer's disease (AD) brains, an observation indicative of blood-brain barrier (BBB) breakdown. Recently, we demonstrated the nearly ubiquitous presence of brain-reactive autoantibodies in human sera. The significance of these observations to AD pathology is unknown. Here, we show that(More)
Diabetes mellitus (DM) and hypercholesterolemia (HC) have emerged as major risk factors for Alzheimer's disease, highlighting the importance of vascular health to normal brain functioning. Our previous study showed that DM and HC favor the development of advanced coronary atherosclerosis in a porcine model, and that treatment with darapladib, an inhibitor(More)
Previous studies have reported antibodies bound to cells in postmortem Alzheimer's disease (AD) brains, which are only rarely observed in the brains of healthy, age-matched controls. This implies that brain-reactive autoantibodies exist in the sera of AD individuals and can gain access to the brain interstitium. To investigate this possibility, we(More)
Let, for example, W (x) = exp expk 1 x , x 2 [ 1; 1] where > 0, k 1; and expk = exp (exp (::: exp ())) denotes the kth iterated exponential. Let fAng denote the recurrence coe¢ cients in the recurrence relation xpn (x) = Anpn+1 (x) +An 1pn 1 (x) for the orthonormal polynomials fpng associated with W . We prove that as n!1; 1 2 An = 1 4 (logk n) 1= (1 + o(More)
Early pathological features of Alzheimer's disease (AD) include synaptic loss and dendrite retraction, prior to neuronal loss. How neurons respond to this evolving AD pathology remains elusive. In the present study, we used single- and double-label immunohistochemistry to investigate the relationship between neuronal vimentin expression and local brain(More)
We prove that de Branges spaces of entire functions describe universality limits in the bulk for random matrices, in the unitary case. In particular, under mild conditions on a measure with compact support, we show that each possible universality limit is the reproducing kernel of a de Branges space of entire functions that equals a classical Paley-Wiener(More)