It is common to call “virtual world” the set of abstractions given to humans by computers and networks. When the computers and the networks are emulated by programs, i.e. are virtual machines and virtual networks, there is one more layer of virtuality: a kind of virtual squared world. Virtual square (V ) is the project to study how to exploit the possibilities given by multi layered virtuality....

A square involution is a square permutation which is also an involution. In this paper we give the enumeration of square involutions, using purely combinatorial methods, by establishing a bijective correspondence with a class of lattice paths. As a corollary to our result, we enumerate various subclasses of square involutions, including the classes of triangular, decomposable, and fat involutions.

Osmotic homeostasis in the brain involves movement of water through aquaporin-4 (AQP4) membrane channels. Perivascular astrocyte end-feet contain distinctive orthogonal lattices (square arrays) assembled from 4- to 6-nm intramembrane particles (IMPs) corresponding to individual AQP4 tetramers. Two isoforms of AQP4 result from translation initiation at methionine residues M1 and M23, but no func...

The estimation of average-power dissipation of a circuit through exhaustive simulation is impractical due to the large number of primary inputs and their combinations. In this brief, two algorithms based on least square estimation are proposed for determining the average power dissipation in complementary metal–oxide–semiconductor (CMOS) circuits. Least square estimation converges faster by att...

ardy and littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. they believed that the number $mathcal{r}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{r}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1-frac{1}{p-1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is a...

A ring R for which x = 0 for all x e R is called a zerosquare ring. Zero-square rings are easily seen to be locally nilpotent. This leads to two problems: (1) constructing finitely generated zero-square rings with large index of nilpotence, and (2) investigating the structure of finitely generated zerosquare rings with given index of nilpotence. For the first problem we construct a class of zer...

the square map is one of the functions used in cryptography. for instance, the square map is used in rabin encryption scheme, block cipher rc6 and stream cipher rabbit, in different forms. in this paper, we study statistical properties of the output of the square map as a vectorial boolean function. we obtain the joint probability distribution of arbitrary number of the upper and the lower bits...