Let A 2 SL(2; ZZ) be given and n 2 N I. A induces a map A n on ZZ 2 n by (x; y) 7 ?! (a 11 x + a 12 y, a 21 x + a 22 y) mod n. A n can be thought of as a discrete approximation of the similarly deened map on the unit square. It is known that the A n have a surprisingly small period: there always is an r 3n such that A r n is the identity on ZZ 2 n. One can visualize the properties of the iterat...

Tempol is an amphipathic radical nitroxide (N) that acutely reduces blood pressure (BP) and heart rate (HR) in the spontaneously hypertensive rat (SHR). We investigated the hypothesis that the response to nitroxides is determined by SOD mimetic activity or lipophilicity. Groups (n = 6-10) of anesthetized SHRs received graded intravenous doses of Ns: tempol (T), 4-amino-tempo (AT), 4-oxo-tempo (...

Cryptography is the science and study of protecting data in computer communication systems from unauthorized disclosure modification. An ordinary difference equation (a map) can be used encryption–decryption algorithms. In particular, Arnold’s cat sine-Gordon linear maps cryptographic algorithms for encoding digital images. this article, a two-dimensional mKdV map derived an will algorithm. The...

In this paper we present the applications of image encryption techniques and channel coding techniques, to design scheme effective for secure image transmission over wireless channels, we present three proposed scheme as follow: First scheme apply image encryption by a combination of hybrid chaotic maps using Baker map and our proposed Hénon chaotic map 3 in three different modes of operations,...

We study semi-classical limits of eigenfunctions of a quantized linear hyperbolic automorphism of the torus (“cat map”). For some values of Planck’s constant, the spectrum of the quantized map has large degeneracies. Our first goal in this paper is to show that these degeneracies are coupled to the existence of quantum symmetries. There is a commutative group of unitary operators on the state-s...

In this paper, we propose an effective gray image cryptosystem containing Arnold cat map for pixel permutation and an improved Logistic map for the generation of encryption keys to be used for pixel modification. Firstly, a new chaotic map is designed to show better performance than the standard one in terms of key space range, complexity and uniformity. Generated secret key is not only sensiti...

We study the development of a high dimensional feature map in a retinotopical organised visual cortex. The presented model is an extension of the elastic-net approach employing two basic terms: a stimulus dependent term and a "regularising" constraint term. Interpreting each cortical element as a feature coding vector with selectivity across multiple dimensions, the parallel development of an o...

Cell fusion in genetically identical Neurospora crassa germlings and in hyphae is a highly regulated process involving the activation of a conserved MAP kinase cascade that includes NRC-1, MEK-2 and MAK-2. During chemotrophic growth in germlings, the MAP kinase cascade members localize to conidial anastomosis tube (CAT) tips every ∼8 minutes, perfectly out of phase with another protein that is ...

These notes constitute a substantially extended version of a talk given in the Fields Institute (Toronto) during the semester \Singularities and Geometry", that culminated by Arnoldfest in celebration of V. I. Arnold's 60th anniversary. We give a survey of diierentresults showing how an upper bound for the numberof isolated zeros for functions satisfying ordinary diierential equations, may be o...

We consider the stability of equilibrium positions in the planar circular restricted four-body problem formulated on the basis of Lagrange’s triangular solution of the three-body problem. The stability problem is solved in a strict nonlinear formulation on the basis of Arnold–Moser and Markeev theorems. Peculiar properties of the Hamiltonian normalization are discussed, and the influence of the...