We develop a randomized approximation algorithm for the size of set union problem |A1∪A2∪...∪Am|, which is given list sets A1,...,Am with approximate mi Ai mi∈((1−βL)|Ai|, (1+βR)|Ai|), and biased random generators probability Prob(x=RandomElement(Ai))∈[1−αL|Ai|,1+αR|Ai|] each input element x∈Ai, where i=1,2,...,m αL,αR,βL,βR∈(0,1). The ratio |A1∪A2∪...∪Am| in range [(1−ϵ)(1−αL)(1−βL),(1+ϵ)(1+αR...

It is known that the branching time language ACTL and the linear time language ∀LTL of universally quantified formulae of LTL have incomparable expressive powers, i.e., Sem(ACTL) and Sem(∀LTL) are incomparable sets. Within a standard abstract interpretation framework, ACTL can be viewed as an abstract interpretation LTL∀ of LTL where the universal path quantifier ∀ abstracts each linear tempora...

The accepted model for the interaction of α and β integrins in the transmembrane (TM) domain is based on the pair αIIbβ3. This involves the so-called outer and inner membrane association clasps (OMC and IMC, respectively). In the α chain, the OMC involves a GxxxG-like motif, whereas in the IMC a conserved juxtamembrane GFFKR motif experiences a backbone reversal that partially fills the void ge...

We develop an randomized approximation algorithm for the size of set union problem |A1 ∪ A2 ∪ ... ∪ Am|, which given a list of sets A1, ..., Am with approximate set size mi for Ai with mi ∈ ((1− βL)|Ai|, (1 + βR)|Ai|), and biased random generators with Prob(x = RandomElement(Ai)) ∈ [ 1−αL |Ai| , 1+αR |Ai| ] for each input set Ai and element x ∈ Ai, where i = 1, 2, ..., m. The approximation rati...

Integrins play important roles in regulating a diverse array of cellular functions crucial to the initiation, progression, and metastasis of tumors. Previous studies have shown that a majority of integrins are folded by the endoplasmic reticulum chaperone gp96. Here, we demonstrate that the dimerization of integrin αL and β2 is highly dependent on gp96. The αI domain (AID), a ligand binding dom...

We study the cohomology of the group consisting of all C∞diffeomorphisms of the line, which are C1-flat to the identity at the origin. We construct non-trivial two second real cohomology classes and uncountably many second integral homology classes of this group. 1. Notations and main results We denote by a1 the Lie algebra of all formal vector fields on R with the Krull topology. For k ≥ 0, we...

The aim of this work is to predict relative biological effectiveness (RBE) for protons and clinically relevant heavier ions, by using a simplified semi-empirical process based on rational expectations and published experimental results using different ion species. The model input parameters are: Z (effective nuclear charge) and radiosensitivity parameters αL and βL of the control low linear ene...