In this letter, we propose new digital audio watermarking methods using interval wavelet decomposition. We develop not only non-blind type method, but also blind one. Experimental results demonstrate that the proposed methods give a watermarked audio clip of better quality and are robust against some attacks.

In this letter, we propose a new digital image watermarking method using interval arithmetic. This is a new application of interval arithmetic. Experimental results show that the proposed method gives a watermarked image of better quality and is robust against some attacks.

This paper proposes a simple and efficient method to numerically obtain the mapping degree deg(f, 0, B) of a C1 map f : Rn → Rn at a regular value 0 relative to a bounded open subset B ⊂ Rn. For practical application, this method adopts Aberth's algorithm which does not require computation of derivatives and determinants, and reduces the computational cost with two additional procedures, namely preconditioning using the coordinate transformation and pruning using Krawczyk's method. Numerical examples show that the proposed method gives the mapping degree with 2n+1 operations using interval arithmetic.

This paper provides algorithms in order to solve an interval implicit function of the Poincare map generated by a continuous piece-wise linear (CPWL) vector field, with the use of interval arithmetic. The algorithms are implemented with the use of MATLAB and INTLAB. We present an application to verification of canards in two-dimensional CPWL vector field appearing in nonlinear piecewise linear circuits frequently, and confirm that the algorithms are effective.

Interval arithmetic is able to be applied when we include the ranges of various functions. When we include them applying the interval arithmetic, the serious problem that the widths of the range inclusions increase extremely exists. In range inclusion of polynomials particularly, Horner's method and Alefeld's method are well known as the conventional methods which mitigates this problem. The purpose of this paper is to propose the new methods which are able to mitigate this problem more efficiently than the conventional methods. And in this paper, we show and compare the efficiencies of the new methods by some numerical examples.

Affine arithmetic is a kind of interval arithmetic defined by Stolfi et al. In affine arithmetic, it is difficult to realize the efficient nonlinear binomial operations. The purpose of this letter is to propose a new dividing method which is able to supply more suitable evaluation than the old dividing method. And this letter also shows the efficiency of the new dividing method by numerical examples.

Algorithms are presented for the four elementary arithmetic operations, to perform reliable floating-point arithmetic operations. These arithmetic operations can be achieved by applying residue techniques to the weighted number systems and performed with no accuracy lost in the process of the computing. The arithmetic operations presented can be used as elementary tools (on many existing architectures) to ensure the reliability of numerical computations. Simulation results especially for the solutions of ill-conditioned problems are given with emphasis on the practical usability of the tools.

This paper proposes an approach for approximately realizing nonlinear mappings of interval vectors by interval neural networks. Interval neural networks in this paper are characterized by interval weights and interval biases. This means that the weights and biases are given by intervals instead of real numbers. First, an architecture of interval neural networks is proposed for dealing with interval input vectors. Interval neural networks with the proposed architecture map interval input vectors to interval output vectors by interval arithmetic. Some characteristic features of the nonlinear mappings realized by the interval neural networks are described. Next, a learning algorithm is derived. In the derived learning algorithm, training data are the pairs of interval input vectors and interval target vectors. Last, using a numerical example, the proposed approach is illustrated and compared with other approaches based on the standard back-propagation neural networks with real number weights.