Rijndael-like structure is a special case of SPN structure. The linear transformation of Rijndael-like structures consists of linear transformations of two types, the one is byte permutation π and the other is linear transformation θ = (θ1, θ2, θ3, θ4), where each of θi separately operates on each of the four columns of a state. Furthermore, π and θ have some interesting properties. In this pap...

We prove that any C transformation, possibly with a (non-flat) critical or singular region, admits an invariant probability measure absolutely continuous with respect to any expanding measure whose Jacobian satisfies a mild distortion condition. This is an extension to arbitrary dimension of a famous theorem of Keller [37] for maps of the interval with negative Schwarzian derivative. We also sh...

We study a spatial branching model, where the underlying motion is d-dimensional (d ≥ 1) Brownian motion and the branching rate is affected by a random collection of reproduction suppressing sets dubbed mild obstacles. We show that the quenched local growth rate is given by the branching rate in the ‘free’ region. We obtain the asymptotics (in probability) of the quenched global growth rates fo...

The paper extends author’s previous works on a probability/possibility transformation based on a maximum specificity principle to the case of the sum of two identical unimodal symmetric random variables. This transformation requires the knowledge of the dependency relationship between the two added variables. In fact, the comonotone case is closely related to the Zadeh’s extension principle. It...

We present an algorithm for creating a neural network which produces accurate probability estimates as outputs. The network implements a Gibbs probability distribution model of the training database. This model is created by a new transformation relating the joint probabilities of attributes in the database to the weights (Gibbs potentials) of the distributed network model. The theory of this t...

A game-theoretic setting provides a mathematical basis for analysis of strategic interaction among competing agents and provides insights into both classical and quantum decision theory and questions of strategic choice. An outstanding mathematical question is to understand the conditions under which a classical game-theoretic setting can be transformed to a quantum game, and under which condit...

There exist many approaches to discern a functional relationship between two variables. A functional model is useful for two reasons: Firstly, if the function is a relatively simple model in the plane, it provides us with qualitative information about the relationship. Secondly, given a fixed value for one variable, the other one can be calculated as a means for prediction. In this paper an app...