We consider the maximal size of families of k-element subsets of an n element set [n] = {1, 2, . . . , n} that satisfy the properties that every r subsets of the family have non-empty intersection, and no ` subsets contain [n] in their union. We show that for large enough n, the largest such family is the trivial one of all ( n−2 k−1 ) subsets that contain a given element and do not contain ano...

Background: The significance of cTfh cells and their subsets in atherosclerosis is not well understood. We measured the frequency of cTfh subsets in patients with different degrees of stenosis using flow-cytometry. Methods: Participants included high (≥50%; n = 12) and low (<50%; n = 12) stenosis groups, as well as healthy controls (n = 6). Results: The frequency of CCR7loPD-1hiefficient-cTfh w...

The Kneser graph K(n, r) has as vertices all r-subsets of an n-set with two vertices adjacent if the corresponding subsets are disjoint. It is conjectured that, except for K(5, 2), these graphs are Hamiltonian for all n ≥ 2r +1. In this note we describe an inductive construction which relates Hamiltonicity of K(2r + 2s, r) to Hamiltonicity of K(2r′+s, r′). This shows (among other things) that H...

In this article, we study stability estimates when recovering magnetic fields and electric potentials in a simply connected open subset Rn with n≥3, from measurements on subsets of its boundary. This inverse problem is associated Schrödinger operator. Our are quantitative versions the uniqueness results obtained by D. Dos Santos Ferreira, C.E. Kenig, J. Sjöstrand G. Uhlmann [13]. The moduli con...

New families of Fisher information and entropy power inequalities for sums of independent random variables are presented. These inequalities relate the information in the sum of n independent random variables to the information contained in sums over subsets of the random variables, for an arbitrary collection of subsets. As a consequence, a simple proof of the monotonicity of information in ce...

number of k-subsets of an n-set so that the size of the intersection of any two among them is in L. It is proven that for every rational number r 2 1 there is a choice of k and L so that cn'<m(n, k, L) idn', where c, d depend on k and L but not on n. 0 1986 Academic Press. Inc

Given a k-vertex graph H and an integer n, what are the n-vertex graphs with maximum number of induced copies H? This question is closely related to inducibility problem introduced by Pippenger Golumbic in 1975, which asks for possible fraction subsets that induce copy H. Huang, Lee, first author proved random H, almost surely maximizing balanced iterated blow-ups In this article, we consider c...