-. Two-dimensional nine neighbor hood rectangular Cellular Automata rules can be modeled using many different techniques like Rule matrices, State Transition Diagrams, Boolean functions, Algebraic Normal Form etc. In this paper, a new model is introduced using color graphs to model all the 512 linear rules. The graph theoretic properties therefore studied in this paper simplifies the analysis o...

In this paper, we consider a simple discrete-time single-directional network of four neurons. The characteristics equation of the linearized system at the zero solution is a polynomial equation involving very high-order terms. We first derive some sufficient and necessary conditions ensuring that all the characteristic roots have modulus less than 1. Hence, the zero solution of the model is asy...

Compact formulas are derived to represent the Algebraic Normal Form (ANF) of f(x + a mod 2) and f(x × a mod 2) from the ANF of f , where f is a Boolean function on F2 and a is a constant of F2 . We compare the algebraic degree of the composed functions with the algebraic degree of the original function f . As an application, the formula for addition modulo 2 is applied in an algebraic attack on...

In this paper, rational orthogonal basis functions are introduced to realize cascaded-parallel structure of adaptive notch filters (ANF) in the case of identifying and separating multiple sinusoids from wideband signals. The structural orthogonality provides good tradeoff between convergence speed and computational complexity. A simplified mean square output error (MSOE) updating algorithm is d...

An online auxiliary control was designed for Static Var Compensator (SVC) to improve the poorly damped oscillations in multi-machine power system subjected to small and large disturbances. This paper presents auxiliary control based on Adaptive NeuroFuzzy (ANF) control using triangular membership function. Such a model free based control does not require any prior information about the system a...

In this paper, we obtain complete characterization for nested canalyzing functions (NCFs) by obtaining its unique algebraic normal form (polynomial form). We introduce a new concept, LAYER NUMBER for NCF. Based on this, we obtain explicit formulas for the the following important parameters: 1) Number of all the nested canalyzing functions, 2) Number of all the NCFs with given LAYER NUMBER, 3) H...

It has been noted recently that algebraic (annihilator) immunity alone does not provide sufficient resistance against algebraic attacks. In this regard, given a Boolean function f , just checking the minimum degree annihilators of f, 1 + f is not enough and one should check the relationships of the form fg = h, and a function f , even if it has very good algebraic immunity, is not necessarily g...

Algebraic immunity of Boolean functions is a very important concept in recently introduced algebraic attacks of stream cipher. For a n-variable Boolean function f , the algebraic immunity AIn(f) takes values in {0, 1, . . . , d2 e}. For every k in this range, denote Bn,k the set of all n-variable Boolean functions with algebraic immunity k, and we know that Bn,k is always non-empty. According t...

A new elliptic equation rational expansion method is presented by a new general ansätz, which is a direct and unified algebraic method for constructing multiple and more general travelling wave solution for nonlinear partial differential equation and implemented in a computer algebraic system. The proposed method is applied to consider the shallow long wave approximate equation and obtains rich...

d-Monomial tests are statistical randomness tests based on Algebraic Normal Form representation of a Boolean function, and were first introduced by Filiol in 2002. We show that there are strong indications that the Gate Complexity of a Boolean function is related to a bias detectable in a d-Monomial test. We then discuss how to effectively apply d-Monomial tests in chosen-IV attacks against str...