1.1 Addresses, Areas and Regions We iteratively define an area A as a special subspace of a d-dimensional cube as follows: Split the cube with respect to every dimension in the middle, resulting in 2 subcubes numbered in some arbitrary but fixed order (for our implementation and this paper we used Z-ordering) from 1 to 2. An area A1 of level 1 consists of the first i1 closed subcubes. i1 determ...

(1) Let S be an order sorted signature, U0 be a strict non-empty order sorted algebra of S, and A be a subset of U0. Then A is an order sorted generator set of U0 if and only if for every OSSubset O of U0 such that O = OSClA holds OSGenO = U0. Let us consider S, let U0 be a monotone order sorted algebra of S, and let I1 be an order sorted generator set of U0. We say that I1 is osfree if and onl...

Cattle express Major Histocompatibility Complex (MHC) class I1 products encoded by the DR and DQ loci. Each haplotype expresses a single DR product, and one or more DQ products due to duplication of the DQ locus in about half the common cattle haplotypes. In order to define the roles of the individual class I1 products in antigen presentation and T cell responses, we are cloning and transfectin...

Let I1 and I2 be intervals of real numbers. An interval game is played in this way: player 1 secretly selects x ∈ I1 and player 2 secretly and independently selects y ∈ I2. After x and y are revealed, payoffs are given by some predetermined function with domain I1 × I2. The payoff function for a zero sum interval game is a function A : I1 × I2 → R. This is interpreted to mean that the second pl...

Gene regulation networks contain recurring circuit patterns called network motifs. One of the most common network motif is the incoherent type 1 feed-forward loop (I1-FFL), in which an activator controls both gene and repressor of that gene. This motif was shown to act as a pulse generator and response accelerator of gene expression. Here we consider an additional function of this motif: the I1...

It is proved that, for T ε 6 G = G(T ) 6 2 √ T , ∫︁ 2T T (︁ I1(t+G,G)− I1(t, G) )︁2 dt = TG 3 ∑︁ j=0 aj log (︁√ T G )︁ +Oε(T 1+εG1/2 + T 1/2+εG2) with some explicitly computable constants aj (a3 > 0) where, for fixed k ∈ N, Ik(t, G) = 1 √ π ∫︁ ∞ −∞ |ζ( 1 2 + it+ iu)| 2ke−(u/G) 2 du. The generalizations to the mean square of I1(t+U,G)−I1(t, G) over [T, T+H] and the estimation of the mean square ...

The incoherent type-1 feed-forward loop (I1-FFL) is ubiquitous in biological regulatory circuits. Although much is known about the functions of the I1-FFL motif, the energy cost incurred in the network and how it affects the performance of the network have not been investigated. Here, we study a generic I1-FFL enzymatic reaction network modelled after the GEF-GAP-Ras pathway responsible for che...

1. EPR spectra of cobalt-copper bovine superoxide dismutase at liquid nitrogen and liquid helium temperature show that the two metal centers are magnetically coupled. The temperature dependence of the spectra indicates that this coupling arises from an exchange interaction. 2. The EPR spectrum of the Co(I1) of the enzyme can only be seen after reduction of the Cu(II), at very low temperature. I...

The articles [15], [8], [9], [10], [14], [11], [18], [2], [4], [6], [7], [5], [16], [1], [3], [19], [20], [12], [17], and [13] provide the notation and terminology for this paper. For simplicity, we adopt the following rules: a, b are data-locations, i1, i2, i3 are instruction-locations of SCM, s1, s2 are states of SCM, T is an instruction type of SCM, and k is a natural number. We now state a ...

Diglycyl-L-histidine is a peptide molecule designed to mimic the specific Cu(II) transport site of human albumin. The equilibria involved in the Cu(II)-diglycyl-L-histidine system have been investigated by analytical potentiometry in aqueous solution (0.15 M NaCl, 25’). The synthetic peptide molecule bound Cu(I1) exclusively as a 1: I complex in the pH range of 6.50 to 11.00. The results furthe...