Endothelial adherens junctions (AJ) promote intercellular adhesion and may contribute to the control of vascular permeability. These structures are formed by a transmembrane and cell-specific adhesive protein, vascular endothelial (VE)-cadherin, which is linked by its cytoplasmic tail to intracellular proteins called catenins (alpha-catenin, beta-catenin, and plakoglobin) and to the actin cytos...

∣ p . Hardy’s inequality thus asserts that the Cesáro matrix operator C = (cj,k), given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ p/(p − 1). (The norm is in fact p/(p − 1).) Hardy’s inequality leads naturally to the study on lp norms of general matrices. For example, we say a matrix A = (aj,k) is a weighted mean matrix if its entries satisfy aj,k = 0, k > j and aj,k ...

The AJ conjecture relates the A-polynomial and the colored Jones polynomial of a knot in the 3-sphere. It has been verified for some classes of knots, including all torus knots, most double twist knots, (−2, 3, 6n ± 1)-pretzel knots, and most cabled knots over torus knots. In this paper we study the AJ conjecture for (r, 2)-cables of a knot, where r is an odd integer. In particular, we show tha...

Apart from IDF, term frequencies are also important and we would like to incorporate them into our scoring function. From now on, we will treat Aj as a random variable that denotes the number of occurrences of term j in a document. So, what should P (Aj = a) and P (Aj = a|Rq = y) be? In other words, how do we model the distributions of these random variables? Here we have two options: continuou...

Suppose A1, . . . , AN are rotation matrices on n-dimensional Euclidean space R, i.e., Aj ∈ SO(n). We want to consider some element of SO(n) that represents an “average” of these elements Aj . There are a number of possible ways to define the notion of an average in this context. One approach has been to write Aj = ej with Zj a real, skew-symmetric n × n matrix (i.e., Zj ∈ skew(n)), and define ...

The expected number of real zeros of an algebraic polynomial ao a1x a2x · · · anx with random coefficient aj , j 0, 1, 2, . . . , n is known. The distribution of the coefficients is often assumed to be identical albeit allowed to have different classes of distributions. For the nonidentical case, there has been much interest where the variance of the jth coefficient is var aj ( n j ) . It is sh...